From 3a87ba63d8c8efcf00e43bfc38af8ee72d17528d Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Wed, 29 Jul 2026 22:24:53 -0500 Subject: [PATCH 01/39] docs: record refactor baseline and compatibility contract --- .gitignore | 10 ++ docs/adr/ADR-core-architecture.md | 38 ++++++ docs/adr/ADR-solver-stack.md | 49 +++++++ docs/development/physics-traceability.md | 27 ++++ docs/development/refactor-baseline.md | 142 +++++++++++++++++++++ tests/compatibility/test_essos_contract.py | 64 ++++++++++ tests/conftest.py | 4 + tests/regression/test_legacy_baseline.py | 85 ++++++++++++ 8 files changed, 419 insertions(+) create mode 100644 .gitignore create mode 100644 docs/adr/ADR-core-architecture.md create mode 100644 docs/adr/ADR-solver-stack.md create mode 100644 docs/development/physics-traceability.md create mode 100644 docs/development/refactor-baseline.md create mode 100644 tests/compatibility/test_essos_contract.py create mode 100644 tests/conftest.py create mode 100644 tests/regression/test_legacy_baseline.py diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..8711bcc --- /dev/null +++ b/.gitignore @@ -0,0 +1,10 @@ +__pycache__/ +*.py[cod] +.pytest_cache/ +.coverage +coverage.xml +htmlcov/ +.audit/ +build/ +dist/ +*.egg-info/ diff --git a/docs/adr/ADR-core-architecture.md b/docs/adr/ADR-core-architecture.md new file mode 100644 index 0000000..79f58d5 --- /dev/null +++ b/docs/adr/ADR-core-architecture.md @@ -0,0 +1,38 @@ +# ADR: immutable functional core with compatibility adapters + +- Status: accepted +- Date: 2026-07-29 + +## Context + +The current mutable `near_axis` class mixes inputs, derived arrays, nonlinear +solves, coordinate conversion, field evaluation, plotting, and optimizer state. +Passing the mutable object as a static JIT argument makes cache behavior and +automatic differentiation fragile. ESSOS nevertheless requires the historical +class and mutable degree-of-freedom interface. + +## Decision + +Build a canonical immutable API from small frozen dataclasses registered as JAX +pytrees and pure functions. Keep array-valued physics data as pytree leaves and +small topology/resolution choices as static metadata. Ordinary dataclasses are +preferred initially; Equinox will be added only if it removes demonstrated +complexity. + +The public API will provide `Axis`, `Qsc`, and `solve`. The legacy +`pyqsc_jax.near_axis.near_axis` class will be a thin adapter that reconstructs +the immutable solution when its mutable degrees of freedom change. + +Modules will follow physics and ownership boundaries, beginning with models, +spectral operators, axis geometry, solvers, and first order. Empty speculative +modules and generic `utils.py` are prohibited. + +## Consequences + +- JIT, VMAP, JVP, and VJP operate on explicit array arguments. +- Solver reports and invalid-geometry diagnostics become part of results. +- Compatibility mutation remains isolated and testable. +- General asymmetric axis coefficients can be supported without duplicating + geometry formulas. +- The adapter may allocate a new solution after mutation; this cost is + acceptable for compatibility and must not constrain the core. diff --git a/docs/adr/ADR-solver-stack.md b/docs/adr/ADR-solver-stack.md new file mode 100644 index 0000000..b4a0d2c --- /dev/null +++ b/docs/adr/ADR-solver-stack.md @@ -0,0 +1,49 @@ +# ADR: solver stack and implicit differentiation + +- Status: accepted for first implementation +- Date: 2026-07-29 + +## Context + +First order requires a converged periodic nonlinear sigma solve. Second order +requires a dense coupled linear solve. Inverse transform modes add a scalar +unknown and continuation. Global/local axis optimization may later benefit from +Levenberg–Marquardt. + +The current code runs exactly five Newton iterations. Differentiating those +iterations does not represent the derivative of the converged equation and +provides no convergence evidence. + +## Options considered + +1. Raw JAX loops and `jax.numpy.linalg.solve`: minimal, but every implicit + derivative and transpose rule would be local maintenance. +2. Equinox/Optimistix: capable, but adds a broad solver dependency before a + missing capability is demonstrated. +3. SOLVAX `root_solve` and `linear_solve`: already provide JAX custom-root and + custom-linear-solve implicit differentiation around user-supplied primal + solvers. +4. A new SOLVAX solver API: justified only by a generic, independently tested + need beyond pyQSC_JAX. + +## Decision + +Use small pyQSC_JAX primal Newton and dense linear callbacks with explicit +residual, step, convergence, iteration, and conditioning reports. Wrap +converged roots and linear solutions with SOLVAX for implicit differentiation. + +Do not change SOLVAX initially. Revisit a general dense +Levenberg–Marquardt implementation only after the pyQSC_JAX optimization +requirements are concrete and the capability is demonstrably reusable. + +Pseudo-arclength continuation and fold detection belong in pyQSC_JAX because +they encode near-axis branch semantics. + +## Acceptance + +- primal residuals satisfy configured absolute and relative tolerances; +- iteration limits produce explicit failure reports; +- JVP/VJP agree with finite differences away from singular points; +- transpose solves are tested; +- second-order conditioning is reported, especially near `iota_N = 0`; +- inverse solves detect folds instead of silently changing branches. diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md new file mode 100644 index 0000000..27f4611 --- /dev/null +++ b/docs/development/physics-traceability.md @@ -0,0 +1,27 @@ +# Physics traceability + +Every implemented physics block must point to a primary derivation, a code +location, and at least one independent validation. Equation numbers below refer +to the cited source, not to a duplicated derivation in this repository. + +| Physics block | Primary source | Reference implementation | Required validation | Status | +| --- | --- | --- | --- | --- | +| General Fourier axis and Frenet frame | Landreman & Sengupta (2018), arXiv:1809.10233 | pyQSC `init_axis.py` | analytic curves; spectral convergence; independent curvature/torsion | baseline audited | +| First-order QS and sigma equation | Landreman & Sengupta (2019), arXiv:1908.10253 | pyQSC `solve_sigma_equation.py` | residual, convergence report, pyQSC values, JVP/VJP | baseline values only | +| Field gradient and `L_grad_B` | Landreman (2021), arXiv:2012.00865, Eq. 3.12 | pyQSC `grad_B_tensor.py` | Cartesian AD/finite differences; Maxwell identities | baseline values only | +| Complete second order | Landreman & Sengupta (2019), arXiv:1908.10253 | pyQSC `calculate_r2.py`; manuscript Eqs. 36–54 | all coefficients, operator residual, Fortran arrays, resolution convergence | not implemented | +| Total field Hessian | manuscript Eqs. 55–83 | pyQSC generated tensor as comparison only | regular-coordinate chain rule, AD/finite differences, symmetry/divergence | not implemented | +| Third-order flux constraint and shear | Landreman & Sengupta (2019); Rodríguez et al. shear equations | pyQSC `calculate_r3.py` | upstream r3 arrays and boundary data | not implemented | +| Singular radius and scale lengths | Landreman (2021), arXiv:2012.00865 | pyQSC `r_singularity.py` | upstream values; actual coordinate-map regularity | not implemented | +| Good-stellarator criteria | Curvo, Ferreira & Jorge (2025), Table 3 | none canonical | exact normalized thresholds and margins | not implemented | +| Plasma current source | manuscript Eqs. 88–97 | none | normalization, enclosed current, straight circular/elliptic channels | not implemented | +| Plasma on-axis field | manuscript Eqs. 136–138 | none | full-torus periodicity, matching cancellation, resolved volume Biot–Savart | not implemented | +| Plasma gradient | manuscript Eqs. 156–160 | none | Ampère antisymmetry, divergence, external STF projection | not implemented | +| Plasma Hessian | manuscript Eqs. 194 and 210–219 | none | resolved volume Biot–Savart, full symmetry, trace-free external tensor | blocked by validation gate | +| External vacuum jet | manuscript Eqs. 220–224 | none | 3+5+7 representation, asymptotic error scaling, vacuum reduction | not implemented | + +## Source policy + +pyQSC is BSD-2-Clause licensed. Adapted code, formulas expressed as code, and +derived reference data must preserve attribution. The attached manuscript is +not committed. Its locally audited SHA-256 is recorded in a gitignored note. diff --git a/docs/development/refactor-baseline.md b/docs/development/refactor-baseline.md new file mode 100644 index 0000000..282fcee --- /dev/null +++ b/docs/development/refactor-baseline.md @@ -0,0 +1,142 @@ +# Refactor baseline + +Date: 2026-07-29 + +This audit establishes the starting point for the complete pyQSC_JAX refactor. +It is descriptive, not an endorsement of the current architecture. + +## Repository and permission status + +| Repository | Audited revision | Access | Local status | +| --- | --- | --- | --- | +| `uwplasma/pyQSC_JAX` | `8b5d8ea218a624071765bfbf62d8d8e0c7acb90c` | admin/push | clean before audit; feature branch created | +| `landreman/pyQSC` | `cd75359ea47548d5db7ccb458c100085c04ba1bc` | read-only reference | clean | +| `uwplasma/ESSOS` | `932997f198964ccfffea898e25acd73600adbf3a` | admin/push | existing worktree has unrelated generated output | +| `uwplasma/SOLVAX` | `bf219c79a40a80b2c3115b749bf670b9f5de3cb5` | admin/push | existing worktree has unrelated changes | + +GitHub authentication is active for `rogeriojorge`. Any later ESSOS or SOLVAX +work must use an isolated worktree so the pre-existing local changes remain +untouched. + +## Current pyQSC_JAX inventory + +The package consists of an empty `pyqsc_jax/__init__.py`, a 505-line +`pyqsc_jax/near_axis.py`, `setup.py`, a title-only README, and no tests or CI. +The monolithic mutable `near_axis` class currently combines: + +- stellarator-symmetric axis Fourier evaluation using only `rc` and `zs`; +- Frenet geometry and topology; +- the first-order sigma equation; +- field and gradient evaluation; +- coordinate conversion and boundary generation; +- mutable optimization degrees of freedom. + +`order`, `B2c`, and `p2` are accepted but do not activate second- or third-order +physics. The sigma equation is advanced by exactly five Newton steps with no +convergence criterion or report. Methods are JIT-compiled with mutable `self` +as a static argument. Package metadata constrains both `jax` and `jaxlib`. + +The unmerged `origin/en/essos_bridge_fix` branch adds plotting and VTK export, +but also imports ESSOS from pyQSC_JAX and commits generated artifacts. Required +behavior will be reimplemented without reversing the dependency direction. + +## Numerical baseline + +For + +```python +near_axis( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + etabar=-0.9, + nfp=3, + nphi=31, +) +``` + +with JAX 64-bit arithmetic, current pyQSC_JAX and upstream pyQSC agree to +floating-point precision: + +| Quantity | Baseline | +| --- | ---: | +| `iota` | 0.41830690943386617 | +| `axis_length` | 6.340238817434161 | +| minimum curvature | 0.5956163516982903 | +| maximum curvature | 1.3060121594235536 | +| minimum torsion | -2.272197039914583 | +| maximum torsion | 0.6057564303422814 | +| maximum absolute sigma | 0.9920706836908618 | +| `B_axis.shape` | `(3, 31)` | +| `grad_B_axis.shape` | `(3, 3, 31)` | + +The audit environment used unpinned JAX/JAXLIB 0.11.0, NumPy 2.5.1, +SciPy 1.18.0, and Python 3.12. + +## Confirmed defect + +Assigning `field.dofs = field.dofs` unpacks the normal and binormal cylindrical +components in a different order than the constructor. The no-op round trip +changes the frame by up to: + +- normal: `0.5460213389358983`; +- binormal: `1.1249025277689044`. + +The strict expected-failure regression test must become a passing test when the +compatibility adapter is corrected. + +## Compatibility tiers + +### Tier 1: ESSOS, mandatory throughout + +ESSOS PR `uwplasma/ESSOS#34` established the import: + +```python +from pyqsc_jax.near_axis import near_axis +``` + +ESSOS constructs the class from `rc`, `zs`, `etabar`, `nfp`, and `nphi`. +Production objectives currently consume `R0`, `Z0`, `phi`, `B_axis`, +`grad_B_axis`, and `iota`; optimization additionally consumes `rc`, `zs`, +`etabar`, `x`, `dofs`, `B0`, `sigma0`, `I2`, `nphi`, `spsi`, `sG`, and `nfp`. +Examples also rely on boundary conversion and plotting. + +### Tier 2: upstream pyQSC semantic parity, final acceptance + +DESC, SIMSOPT, and broader pyQSC workflows use a larger object protocol, +including general `rc`, `rs`, `zc`, `zs`, `Bbar`, `lasym`, pressure/current +coefficients, interpolation splines, second- and third-order boundary data, and +named configurations. This tier is staged after the immutable first-order core +but remains part of the final definition of done. + +## Upstream test audit + +At pyQSC commit `cd75359`, 31 tests pass in 22.80 seconds when +`test_to_vmec.py` is excluded because its optional MPI/VMEC runtime is absent. +The tests cover: + +- Newton convergence, Fourier differentiation, interpolation, and utilities; +- axis geometry, helicity, sigma, iota, field gradient, and scale lengths; +- comparison to independent Fortran netCDF outputs; +- complete second-order coefficients, `B20`, Mercier terms, and singular radius; +- third-order coefficients, shear, and boundary Fourier conversion; +- named paper configurations and independent curvature/torsion checks. + +Reference data imported later must be reduced to small arrays, retain BSD-2-Clause +attribution, record this upstream commit and checksums, and never download during +tests. + +## Initial risks and gates + +1. Frenet coordinates require nonvanishing axis curvature; invalid axes need an + explicit diagnostic rather than silent NaNs. +2. The target-iota inverse can cross folds where + `d(iota)/d(etabar) = 0`; scalar inversion alone is not globally valid. +3. The second-order operator can be ill-conditioned near `iota_N = 0`. +4. A small collocation residual does not establish a small dense-grid `B20` + variation. +5. The manuscript plasma Hessian is gated on independent volume-current + Biot–Savart validation and Maxwell identities. +6. “Surface-free” still requires a formal radius or equivalent flux/current + normalization. +7. Nonzero optimization results are “best found,” never proofs of a global + minimum. diff --git a/tests/compatibility/test_essos_contract.py b/tests/compatibility/test_essos_contract.py new file mode 100644 index 0000000..7325d5c --- /dev/null +++ b/tests/compatibility/test_essos_contract.py @@ -0,0 +1,64 @@ +import pytest + +from pyqsc_jax.near_axis import near_axis + + +def test_legacy_import_and_essos_on_axis_contract(): + field = near_axis( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + etabar=-0.9, + nfp=3, + nphi=31, + ) + + attributes = { + "B0", + "nfp", + "nphi", + "phi", + "varphi", + "R0", + "Z0", + "B_axis", + "grad_B_axis", + "axis_length", + "iota", + "iotaN", + "curvature", + "torsion", + "elongation", + "L_grad_B", + "x", + "dofs", + "rc", + "zs", + "etabar", + "sigma0", + "I2", + "spsi", + "sG", + } + methods = { + "AbsB", + "B_covariant", + "B_contravariant", + "B_mag", + "jacobian", + "get_boundary", + "Frenet_to_cylindrical", + "phi_of_theta_varphi", + } + + assert all(hasattr(field, name) for name in attributes) + assert all(callable(getattr(field, name)) for name in methods) + + +@pytest.mark.xfail( + strict=True, + reason="Plotting exists only on the unmerged ESSOS bridge branch.", +) +def test_legacy_plot_method_is_available(): + field = near_axis() + + assert callable(field.plot) diff --git a/tests/conftest.py b/tests/conftest.py new file mode 100644 index 0000000..5468169 --- /dev/null +++ b/tests/conftest.py @@ -0,0 +1,4 @@ +import jax + + +jax.config.update("jax_enable_x64", True) diff --git a/tests/regression/test_legacy_baseline.py b/tests/regression/test_legacy_baseline.py new file mode 100644 index 0000000..c45d247 --- /dev/null +++ b/tests/regression/test_legacy_baseline.py @@ -0,0 +1,85 @@ +import jax.numpy as jnp +import numpy as np +import pytest + +from pyqsc_jax.near_axis import near_axis + + +def standard_field(**kwargs): + parameters = { + "rc": [1.0, 0.045], + "zs": [0.0, -0.045], + "etabar": -0.9, + "nfp": 3, + "nphi": 31, + } + parameters.update(kwargs) + return near_axis(**parameters) + + +def test_standard_first_order_baseline(): + field = standard_field() + + np.testing.assert_allclose(field.iota, 0.41830690943386617, rtol=2e-13) + np.testing.assert_allclose(field.axis_length, 6.340238817434161, rtol=2e-13) + np.testing.assert_allclose( + [jnp.min(field.curvature), jnp.max(field.curvature)], + [0.5956163516982903, 1.3060121594235536], + rtol=2e-13, + ) + np.testing.assert_allclose( + [jnp.min(field.torsion), jnp.max(field.torsion)], + [-2.272197039914583, 0.6057564303422814], + rtol=2e-13, + ) + np.testing.assert_allclose( + jnp.max(jnp.abs(field.sigma)), 0.9920706836908618, rtol=2e-13 + ) + assert field.B_axis.shape == (3, 31) + assert field.grad_B_axis.shape == (3, 3, 31) + + +def test_first_order_field_methods_are_finite(): + field = standard_field() + point = jnp.array([0.02, 0.4, 0.1]) + + assert jnp.isfinite(field.AbsB(point)) + assert jnp.isfinite(field.jacobian(point)) + assert jnp.all(jnp.isfinite(field.B_covariant(point))) + assert jnp.all(jnp.isfinite(field.B_contravariant(point))) + + +@pytest.mark.xfail( + strict=True, + reason="Constructor and dofs setter swap normal/binormal phi and z components.", +) +def test_dofs_noop_preserves_derived_frame(): + field = standard_field() + normal_before = jnp.stack( + [field.normal_R, field.normal_phi, field.normal_z], axis=1 + ) + binormal_before = jnp.stack( + [field.binormal_R, field.binormal_phi, field.binormal_z], axis=1 + ) + + field.dofs = field.dofs + + normal_after = jnp.stack( + [field.normal_R, field.normal_phi, field.normal_z], axis=1 + ) + binormal_after = jnp.stack( + [field.binormal_R, field.binormal_phi, field.binormal_z], axis=1 + ) + np.testing.assert_array_equal(normal_after, normal_before) + np.testing.assert_array_equal(binormal_after, binormal_before) + + +@pytest.mark.xfail( + strict=True, + reason="The current order argument is inert; complete second order is not implemented.", +) +def test_r2_request_produces_second_order_solution(): + field = standard_field(order="r2", B2c=0.01, p2=-1.0e3) + + assert field.B20.shape == (field.nphi,) + assert jnp.all(jnp.isfinite(field.B20)) From 58950088f55ffeac1577e1bf30f5e7611e5ecba3 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Wed, 29 Jul 2026 22:34:28 -0500 Subject: [PATCH 02/39] chore: establish package layout and quality gates --- .github/workflows/benchmarks.yml | 23 +++++ .github/workflows/compatibility.yml | 41 ++++++++ .github/workflows/docs.yml | 26 +++++ .github/workflows/publish.yml | 40 ++++++++ .github/workflows/tests.yml | 68 +++++++++++++ .gitignore | 1 + .readthedocs.yaml | 17 ++++ CHANGELOG.md | 14 +++ CITATION.cff | 19 ++++ CONTRIBUTING.md | 37 ++++++++ NOTICE | 37 ++++++++ README.md | 82 +++++++++++++++- docs/changelog.md | 5 + docs/conf.py | 35 +++++++ docs/index.md | 46 +++++++++ docs/installation.md | 24 +++++ docs/limitations.md | 21 +++++ docs/quickstart.md | 27 ++++++ docs/references.bib | 110 ++++++++++++++++++++++ pyproject.toml | 86 +++++++++++++++++ pyqsc_jax/__init__.py | 1 - setup.py | 17 ---- src/pyqsc_jax/__init__.py | 6 ++ {pyqsc_jax => src/pyqsc_jax}/near_axis.py | 6 ++ tests/conftest.py | 1 - tests/regression/test_legacy_baseline.py | 20 +--- 26 files changed, 775 insertions(+), 35 deletions(-) create mode 100644 .github/workflows/benchmarks.yml create mode 100644 .github/workflows/compatibility.yml create mode 100644 .github/workflows/docs.yml create mode 100644 .github/workflows/publish.yml create mode 100644 .github/workflows/tests.yml create mode 100644 .readthedocs.yaml create mode 100644 CHANGELOG.md create mode 100644 CITATION.cff create mode 100644 CONTRIBUTING.md create mode 100644 NOTICE create mode 100644 docs/changelog.md create mode 100644 docs/conf.py create mode 100644 docs/index.md create mode 100644 docs/installation.md create mode 100644 docs/limitations.md create mode 100644 docs/quickstart.md create mode 100644 docs/references.bib create mode 100644 pyproject.toml delete mode 100644 pyqsc_jax/__init__.py delete mode 100644 setup.py create mode 100644 src/pyqsc_jax/__init__.py rename {pyqsc_jax => src/pyqsc_jax}/near_axis.py (99%) diff --git a/.github/workflows/benchmarks.yml b/.github/workflows/benchmarks.yml new file mode 100644 index 0000000..f3216ab --- /dev/null +++ b/.github/workflows/benchmarks.yml @@ -0,0 +1,23 @@ +name: benchmarks + +on: + workflow_dispatch: + schedule: + - cron: "29 8 * * 0" + +jobs: + verify: + runs-on: ubuntu-latest + timeout-minutes: 30 + env: + JAX_ENABLE_X64: "true" + steps: + - uses: actions/checkout@v4 + - uses: actions/setup-python@v5 + with: + python-version: "3.14" + cache: pip + - run: python -m pip install -e '.[dev]' + - run: pytest -m numerics + - name: Record environment + run: python -m pip freeze diff --git a/.github/workflows/compatibility.yml b/.github/workflows/compatibility.yml new file mode 100644 index 0000000..090d8bd --- /dev/null +++ b/.github/workflows/compatibility.yml @@ -0,0 +1,41 @@ +name: compatibility + +on: + pull_request: + workflow_dispatch: + schedule: + - cron: "43 6 * * 3" + +jobs: + frozen-contracts: + runs-on: ubuntu-latest + timeout-minutes: 15 + env: + JAX_ENABLE_X64: "true" + steps: + - uses: actions/checkout@v4 + - uses: actions/setup-python@v5 + with: + python-version: "3.14" + cache: pip + - run: python -m pip install -e '.[dev]' + - run: pytest tests/compatibility tests/regression + + upstream-head-smoke: + if: github.event_name == 'schedule' || github.event_name == 'workflow_dispatch' + runs-on: ubuntu-latest + timeout-minutes: 20 + continue-on-error: true + steps: + - uses: actions/checkout@v4 + - uses: actions/setup-python@v5 + with: + python-version: "3.14" + cache: pip + - run: python -m pip install -e '.[dev]' + - run: python -m pip install 'git+https://github.com/landreman/pyQSC.git' + - run: >- + python -c "from qsc import Qsc; + from pyqsc_jax.near_axis import near_axis; + kwargs = dict(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3, etabar=-0.9, nphi=31); + assert abs(float(Qsc(**kwargs).iota) - float(near_axis(**kwargs).iota)) < 1e-10" diff --git a/.github/workflows/docs.yml b/.github/workflows/docs.yml new file mode 100644 index 0000000..277c2c0 --- /dev/null +++ b/.github/workflows/docs.yml @@ -0,0 +1,26 @@ +name: docs + +on: + push: + branches: [main, refactor/pyqsc-jax-complete] + pull_request: + workflow_dispatch: + schedule: + - cron: "17 7 * * 1" + +jobs: + build: + runs-on: ubuntu-latest + timeout-minutes: 15 + steps: + - uses: actions/checkout@v4 + - uses: actions/setup-python@v5 + with: + python-version: "3.14" + cache: pip + - run: python -m pip install -e '.[docs]' + - run: python -m sphinx -W --keep-going -b html docs docs/_build/html + - run: python -m sphinx -W --keep-going -b doctest docs docs/_build/doctest + - name: Check external links + if: github.event_name == 'schedule' + run: python -m sphinx -W --keep-going -b linkcheck docs docs/_build/linkcheck diff --git a/.github/workflows/publish.yml b/.github/workflows/publish.yml new file mode 100644 index 0000000..aea7797 --- /dev/null +++ b/.github/workflows/publish.yml @@ -0,0 +1,40 @@ +name: publish + +on: + push: + tags: ["v*"] + +jobs: + build-and-verify: + runs-on: ubuntu-latest + timeout-minutes: 20 + steps: + - uses: actions/checkout@v4 + - uses: actions/setup-python@v5 + with: + python-version: "3.14" + - run: python -m pip install build twine + - run: python -m build + - run: python -m twine check dist/* + - run: python -m pip install dist/*.whl + - run: >- + python -c "from pyqsc_jax.near_axis import near_axis; + q = near_axis(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3, etabar=-0.9); + assert abs(float(q.iota) - 0.41830690943386617) < 1e-10" + - uses: actions/upload-artifact@v4 + with: + name: distributions + path: dist/ + + publish: + needs: build-and-verify + runs-on: ubuntu-latest + environment: pypi + permissions: + id-token: write + steps: + - uses: actions/download-artifact@v4 + with: + name: distributions + path: dist/ + - uses: pypa/gh-action-pypi-publish@release/v1 diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml new file mode 100644 index 0000000..76e7249 --- /dev/null +++ b/.github/workflows/tests.yml @@ -0,0 +1,68 @@ +name: tests + +on: + push: + branches: [main, refactor/pyqsc-jax-complete] + pull_request: + workflow_dispatch: + +concurrency: + group: ${{ github.workflow }}-${{ github.ref }} + cancel-in-progress: true + +jobs: + lint: + runs-on: ubuntu-latest + timeout-minutes: 10 + steps: + - uses: actions/checkout@v4 + - uses: actions/setup-python@v5 + with: + python-version: "3.14" + cache: pip + - run: python -m pip install ruff + - run: ruff check src tests + - run: ruff format --check src tests + + test: + strategy: + fail-fast: false + matrix: + include: + - os: ubuntu-latest + python: "3.12" + - os: ubuntu-latest + python: "3.14" + - os: macos-latest + python: "3.14" + runs-on: ${{ matrix.os }} + timeout-minutes: 20 + env: + JAX_ENABLE_X64: "true" + steps: + - uses: actions/checkout@v4 + - uses: actions/setup-python@v5 + with: + python-version: ${{ matrix.python }} + cache: pip + - run: python -m pip install -e '.[dev]' + - run: python -c "import jax, pyqsc_jax; print(jax.__version__, pyqsc_jax.__version__, pyqsc_jax.__file__)" + - run: pytest + + package: + runs-on: ubuntu-latest + timeout-minutes: 15 + steps: + - uses: actions/checkout@v4 + - uses: actions/setup-python@v5 + with: + python-version: "3.14" + cache: pip + - run: python -m pip install build twine + - run: python -m build + - run: python -m twine check dist/* + - run: python -m pip install --force-reinstall dist/*.whl + - run: >- + python -c "from pyqsc_jax.near_axis import near_axis; + q = near_axis(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3, etabar=-0.9); + assert abs(float(q.iota) - 0.41830690943386617) < 1e-10" diff --git a/.gitignore b/.gitignore index 8711bcc..aa64a13 100644 --- a/.gitignore +++ b/.gitignore @@ -5,6 +5,7 @@ __pycache__/ coverage.xml htmlcov/ .audit/ +docs/_build/ build/ dist/ *.egg-info/ diff --git a/.readthedocs.yaml b/.readthedocs.yaml new file mode 100644 index 0000000..98bf07a --- /dev/null +++ b/.readthedocs.yaml @@ -0,0 +1,17 @@ +version: 2 + +build: + os: ubuntu-24.04 + tools: + python: "3.12" + +sphinx: + configuration: docs/conf.py + fail_on_warning: true + +python: + install: + - method: pip + path: . + extra_requirements: + - docs diff --git a/CHANGELOG.md b/CHANGELOG.md new file mode 100644 index 0000000..4847fdf --- /dev/null +++ b/CHANGELOG.md @@ -0,0 +1,14 @@ +# Changelog + +All notable changes to pyQSC_JAX will be documented here. + +The project follows Semantic Versioning once the new canonical API reaches its +first stable release. + +## Unreleased + +### Added + +- Audited compatibility and numerical baselines. +- Physics traceability and architecture decision records. +- Modern package, documentation, test, and CI scaffolding. diff --git a/CITATION.cff b/CITATION.cff new file mode 100644 index 0000000..d994ca8 --- /dev/null +++ b/CITATION.cff @@ -0,0 +1,19 @@ +cff-version: 1.2.0 +message: "If you use pyQSC_JAX, please cite this software and the theory papers relevant to your calculation." +title: "pyQSC_JAX" +type: software +version: 0.2.0-dev +date-released: 2026-07-29 +authors: + - family-names: Jorge + given-names: Rogério + affiliation: University of Wisconsin–Madison +repository-code: "https://github.com/uwplasma/pyQSC_JAX" +url: "https://github.com/uwplasma/pyQSC_JAX" +license: MIT +keywords: + - stellarator + - near-axis expansion + - quasisymmetry + - JAX + - automatic differentiation diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md new file mode 100644 index 0000000..5dbfc68 --- /dev/null +++ b/CONTRIBUTING.md @@ -0,0 +1,37 @@ +# Contributing + +pyQSC_JAX changes must preserve the ESSOS legacy contract and provide evidence +for every physics result. + +## Developer setup + +```bash +python -m venv .venv +. .venv/bin/activate +python -m pip install -e '.[dev,docs,plot]' +pytest +ruff check src tests +python -m sphinx -W -b html docs docs/_build/html +``` + +Do not pin dependency versions in package metadata or committed requirements +files. Release reports record the versions actually tested. + +## Physics changes + +Before merging a physics result: + +1. add its primary equation source and conventions to the traceability table; +2. add a focused unit test; +3. add an independent regression or physical-identity test; +4. document shapes, units, validity assumptions, and failure modes; +5. verify JIT and automatic differentiation where the API promises them. + +Reference data must be small, local, checksummed, license-compatible, and tied +to an upstream commit. Tests must never download data. + +## Pull requests + +Keep commits small and green. Explain the physical source, numerical method, +validation, compatibility impact, and any remaining limitation. Do not combine +unrelated formatting or generated output with physics changes. diff --git a/NOTICE b/NOTICE new file mode 100644 index 0000000..f3341df --- /dev/null +++ b/NOTICE @@ -0,0 +1,37 @@ +pyQSC_JAX +Copyright (c) 2026 UW Plasma + +This project is distributed under the MIT License in LICENSE. + +The landreman/pyQSC project is used as an upstream reference implementation +and source of regression data: + + pyQSC + Copyright (c) 2020 Matt Landreman + SPDX-License-Identifier: BSD-2-Clause + https://github.com/landreman/pyQSC + +Any source or reference data adapted from pyQSC is identified in the relevant +file and retains the following notice: + + Redistribution and use in source and binary forms, with or without + modification, are permitted provided that the following conditions are met: + + 1. Redistributions of source code must retain the above copyright notice, + this list of conditions and the following disclaimer. + + 2. Redistributions in binary form must reproduce the above copyright + notice, this list of conditions and the following disclaimer in the + documentation and/or other materials provided with the distribution. + + THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" + AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE + LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + POSSIBILITY OF SUCH DAMAGE. diff --git a/README.md b/README.md index d1585a3..62c802e 100644 --- a/README.md +++ b/README.md @@ -1 +1,81 @@ -# pyQSC_JAX \ No newline at end of file +# pyQSC_JAX + +Differentiable near-axis stellarator construction and plasma–coil field jets in +JAX. + +> **Development status:** the current release preserves the ESSOS first-order +> interface while an immutable, fully validated pyQSC-compatible core is built +> on the `refactor/pyqsc-jax-complete` branch. + +## Install + +```bash +python -m pip install pyqsc-jax +``` + +For a source checkout: + +```bash +python -m pip install -e . +``` + +No JAX backend policy is imposed by the package. Install the JAX build suitable +for your accelerator and platform. + +## Current quickstart + +```python +from pyqsc_jax.near_axis import near_axis + +field = near_axis( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, +) + +print("iota:", field.iota) +print("axis length:", field.axis_length) +print("minimum L_grad_B:", field.L_grad_B.min()) +``` + +The import above is the supported ESSOS compatibility API. The refactor is +introducing the canonical immutable form: + +```python +import pyqsc_jax as qsc + +configuration = qsc.Qsc( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + order="r2", +) +``` + +That API will become the primary quickstart once its first- and second-order +validation gates are green. + +## Scope + +The completed package will provide: + +- general Fourier magnetic axes and QA/QH topology; +- converged differentiable first-order sigma solves; +- complete finite-pressure/current second order and pyQSC third-order parity; +- total, plasma, and external field/gradient/Hessian jets on the axis; +- target-transform inverse solves with continuation and fold detection; +- dense-grid `B20` diagnostics and multistart axis optimization; +- cited stellarator screening criteria with explicit margins; +- an unchanged ESSOS compatibility adapter. + +See the [draft refactor PR](https://github.com/uwplasma/pyQSC_JAX/pull/2), +[architecture decisions](docs/adr/), and +[physics traceability](docs/development/physics-traceability.md). + +## Citation and license + +Citation metadata is in [CITATION.cff](CITATION.cff). pyQSC_JAX is MIT +licensed. Adapted pyQSC source and reference data retain BSD-2-Clause +attribution in [NOTICE](NOTICE). diff --git a/docs/changelog.md b/docs/changelog.md new file mode 100644 index 0000000..8169802 --- /dev/null +++ b/docs/changelog.md @@ -0,0 +1,5 @@ +# Changelog + +```{literalinclude} ../CHANGELOG.md +:language: markdown +``` diff --git a/docs/conf.py b/docs/conf.py new file mode 100644 index 0000000..e41112c --- /dev/null +++ b/docs/conf.py @@ -0,0 +1,35 @@ +"""Sphinx configuration for pyQSC_JAX.""" + +from pyqsc_jax import __version__ + + +project = "pyQSC_JAX" +author = "UW Plasma" +copyright = "2026, UW Plasma" +version = __version__ +release = __version__ + +extensions = [ + "myst_parser", + "sphinx.ext.autodoc", + "sphinx.ext.doctest", + "sphinx.ext.intersphinx", + "sphinx.ext.mathjax", + "sphinx_copybutton", + "sphinxcontrib.bibtex", +] + +source_suffix = { + ".md": "markdown", + ".rst": "restructuredtext", +} +exclude_patterns = ["_build", "Thumbs.db", ".DS_Store"] +html_theme = "furo" +html_title = f"pyQSC_JAX {version}" +intersphinx_mapping = { + "jax": ("https://docs.jax.dev/en/latest/", None), + "python": ("https://docs.python.org/3/", None), +} +bibtex_bibfiles = ["references.bib"] +bibtex_reference_style = "author_year" +myst_enable_extensions = ["amsmath", "colon_fence", "dollarmath"] diff --git a/docs/index.md b/docs/index.md new file mode 100644 index 0000000..25c7e87 --- /dev/null +++ b/docs/index.md @@ -0,0 +1,46 @@ +# pyQSC_JAX + +pyQSC_JAX is a differentiable JAX implementation of the near-axis expansion +for stellarator design, including a surface-free separation of total, +plasma-generated, and external vacuum field jets. + +```{toctree} +:maxdepth: 2 +:caption: User guide + +installation +quickstart +limitations +``` + +```{toctree} +:maxdepth: 2 +:caption: Development + +development/refactor-baseline +development/physics-traceability +adr/ADR-core-architecture +adr/ADR-solver-stack +``` + +```{toctree} +:maxdepth: 1 +:caption: Project + +changelog +``` + +## Project status + +The immutable canonical API is under active development. The +`pyqsc_jax.near_axis.near_axis` import remains supported for ESSOS without a +runtime deprecation warning. + +## References + +The implementation is traced to primary sources, beginning with the +near-axis theory of Garren and Boozer and the direct-construction formulation +of Landreman and collaborators {cite}`garren1991existence,garren1991magnetic,landreman2018direct,landreman2019highorder`. + +```{bibliography} +``` diff --git a/docs/installation.md b/docs/installation.md new file mode 100644 index 0000000..b093594 --- /dev/null +++ b/docs/installation.md @@ -0,0 +1,24 @@ +# Installation + +pyQSC_JAX requires Python 3.12 or newer. + +```bash +python -m pip install pyqsc-jax +``` + +For development: + +```bash +git clone https://github.com/uwplasma/pyQSC_JAX.git +cd pyQSC_JAX +python -m pip install -e '.[dev,docs,plot]' +``` + +The package depends on JAX but does not list `jaxlib` separately or configure +JAX at import time. Follow the +[official JAX installation guide](https://docs.jax.dev/en/latest/installation.html) +to select a CPU, CUDA, or other supported backend. + +Dependencies are intentionally unpinned in project metadata. Continuous +integration exercises current dependency releases, and each release report +will record the exact environment used for validation. diff --git a/docs/limitations.md b/docs/limitations.md new file mode 100644 index 0000000..196a02e --- /dev/null +++ b/docs/limitations.md @@ -0,0 +1,21 @@ +# Limitations + +The current released computational core is first order only. Although the +legacy constructor accepts `order`, `B2c`, and `p2`, those arguments do not yet +activate second-order physics. + +Known limitations under active refactor include: + +- exactly five Newton updates without a convergence report; +- only stellarator-symmetric `rc`/`zs` axes; +- a confirmed normal/binormal unpacking defect in the mutable `dofs` setter; +- no complete second- or third-order solution; +- no plasma/external field-jet separation; +- no branch-aware target-transform inverse solve. + +Frenet coordinates are invalid when the magnetic-axis curvature vanishes. The +new geometry API will report that validity condition explicitly. + +Near-axis results are asymptotic in distance from the axis. “Surface-free” +plasma–coil separation does not mean radius-free: a formal minor radius or an +equivalent flux/current normalization is required. diff --git a/docs/quickstart.md b/docs/quickstart.md new file mode 100644 index 0000000..8d8f2b7 --- /dev/null +++ b/docs/quickstart.md @@ -0,0 +1,27 @@ +# Quickstart + +The current compatibility entry point constructs the standard first-order +quasisymmetric solution: + +```python +from pyqsc_jax.near_axis import near_axis + +field = near_axis( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + nphi=31, +) + +print(field.iota) +print(field.axis_length) +``` + +`rc` and `zs` are the cosine coefficients of cylindrical axis radius and sine +coefficients of height for a stellarator-symmetric axis. `nfp` is the number +of field periods. `etabar` controls the first-order field-strength variation. + +The new immutable `Axis`, `Qsc`, and `solve` API will replace this page after +its validation gates are complete. The legacy import will remain as an +adapter for ESSOS. diff --git a/docs/references.bib b/docs/references.bib new file mode 100644 index 0000000..31a7932 --- /dev/null +++ b/docs/references.bib @@ -0,0 +1,110 @@ +@article{garren1991existence, + author = {Garren, D. A. and Boozer, Allen H.}, + title = {Existence of quasihelically symmetric stellarators}, + journal = {Physics of Fluids B}, + volume = {3}, + pages = {2822--2834}, + year = {1991}, + doi = {10.1063/1.859916}, +} + +@article{garren1991magnetic, + author = {Garren, D. A. and Boozer, Allen H.}, + title = {Magnetic field strength of toroidal plasma equilibria}, + journal = {Physics of Fluids B}, + volume = {3}, + pages = {2805--2821}, + year = {1991}, + doi = {10.1063/1.859915}, +} + +@article{landreman2018direct, + author = {Landreman, Matt and Sengupta, Wrick}, + title = {Direct construction of optimized stellarator shapes. Part 1. Theory in cylindrical coordinates}, + journal = {Journal of Plasma Physics}, + volume = {84}, + pages = {905840616}, + year = {2018}, + doi = {10.1017/S0022377818001289}, + eprint = {1809.10233}, + archivePrefix = {arXiv}, +} + +@article{landreman2019numerical, + author = {Landreman, Matt and Sengupta, Wrick and Plunk, Gabriel G.}, + title = {Direct construction of optimized stellarator shapes. Part 2. Numerical quasisymmetric solutions}, + journal = {Journal of Plasma Physics}, + volume = {85}, + pages = {905850103}, + year = {2019}, + doi = {10.1017/S0022377818001344}, +} + +@article{landreman2019highorder, + author = {Landreman, Matt and Sengupta, Wrick}, + title = {Constructing stellarators with quasisymmetry to high order}, + journal = {Journal of Plasma Physics}, + volume = {85}, + pages = {815850601}, + year = {2019}, + doi = {10.1017/S0022377819000783}, + eprint = {1908.10253}, + archivePrefix = {arXiv}, +} + +@article{jorge2020arbitrary, + author = {Jorge, Rogerio and Sengupta, Wrick and Landreman, Matt}, + title = {Near-axis expansion of stellarator equilibrium at arbitrary order in the distance to the axis}, + journal = {Journal of Plasma Physics}, + volume = {86}, + pages = {905860106}, + year = {2020}, + doi = {10.1017/S0022377820000033}, + eprint = {1911.02659}, + archivePrefix = {arXiv}, +} + +@article{landreman2021figures, + author = {Landreman, Matt}, + title = {Figures of merit for stellarators near the magnetic axis}, + journal = {Journal of Plasma Physics}, + volume = {87}, + pages = {905870112}, + year = {2021}, + doi = {10.1017/S0022377820001658}, + eprint = {2012.00865}, + archivePrefix = {arXiv}, +} + +@article{giuliani2022single, + author = {Giuliani, Andrew and Wechsung, Florian and Cerfon, Antoine and Stadler, Georg and Landreman, Matt}, + title = {Single-stage gradient-based stellarator coil design: optimization for near-axis quasi-symmetry}, + journal = {Journal of Computational Physics}, + volume = {459}, + pages = {111147}, + year = {2022}, + doi = {10.1016/j.jcp.2022.111147}, + eprint = {2010.02033}, + archivePrefix = {arXiv}, +} + +@article{landreman2022mapping, + author = {Landreman, Matt}, + title = {Mapping the space of quasisymmetric stellarators using optimized near-axis expansion}, + journal = {Journal of Plasma Physics}, + volume = {88}, + pages = {905880616}, + year = {2022}, + doi = {10.1017/S0022377822001258}, + eprint = {2209.11849}, + archivePrefix = {arXiv}, +} + +@article{curvo2025deep, + author = {Curvo, Ines and Ferreira, Jorge and Jorge, Rogerio}, + title = {Using deep learning to design high aspect ratio fusion devices}, + journal = {Journal of Plasma Physics}, + volume = {91}, + year = {2025}, + doi = {10.1017/S002237782400165X}, +} diff --git a/pyproject.toml b/pyproject.toml new file mode 100644 index 0000000..6395a8e --- /dev/null +++ b/pyproject.toml @@ -0,0 +1,86 @@ +[build-system] +requires = ["hatchling"] +build-backend = "hatchling.build" + +[project] +name = "pyqsc-jax" +description = "Differentiable near-axis stellarator construction and plasma-coil field jets in JAX" +readme = "README.md" +license = "MIT" +license-files = ["LICENSE", "NOTICE"] +authors = [{ name = "UW Plasma", email = "rogerio.jorge@wisc.edu" }] +requires-python = ">=3.12" +dynamic = ["version"] +dependencies = ["jax", "solvax"] +classifiers = [ + "Development Status :: 3 - Alpha", + "Intended Audience :: Science/Research", + "License :: OSI Approved :: MIT License", + "Programming Language :: Python :: 3", + "Programming Language :: Python :: 3 :: Only", + "Programming Language :: Python :: 3.12", + "Programming Language :: Python :: 3.13", + "Programming Language :: Python :: 3.14", + "Topic :: Scientific/Engineering :: Physics", + "Typing :: Typed", +] + +[project.urls] +Homepage = "https://github.com/uwplasma/pyQSC_JAX" +Documentation = "https://pyqsc-jax.readthedocs.io" +Issues = "https://github.com/uwplasma/pyQSC_JAX/issues" +Source = "https://github.com/uwplasma/pyQSC_JAX" + +[project.optional-dependencies] +plot = ["matplotlib", "pyevtk"] +docs = [ + "furo", + "myst-parser", + "sphinx", + "sphinx-copybutton", + "sphinxcontrib-bibtex", +] +dev = [ + "build", + "numpy", + "pytest", + "pytest-cov", + "ruff", + "scipy", + "twine", +] + +[tool.hatch.version] +path = "src/pyqsc_jax/__init__.py" + +[tool.hatch.build.targets.wheel] +packages = ["src/pyqsc_jax"] + +[tool.ruff] +# Removed when the immutable core replaces this audited compatibility monolith. +exclude = ["src/pyqsc_jax/near_axis.py"] +line-length = 100 +src = ["src", "tests"] + +[tool.ruff.lint] +select = ["B", "E", "F", "I", "UP"] + +[tool.pytest.ini_options] +addopts = "-ra" +testpaths = ["tests"] +pythonpath = ["src"] +markers = [ + "integration: cross-package or optional-runtime integration tests", + "literature: regression tests tied to published configurations", + "numerics: numerical convergence and conditioning tests", + "physics: independent physical identity tests", + "slow: tests excluded from the default quick developer loop", +] + +[tool.coverage.run] +branch = true +source = ["src/pyqsc_jax"] + +[tool.coverage.report] +fail_under = 95 +show_missing = true diff --git a/pyqsc_jax/__init__.py b/pyqsc_jax/__init__.py deleted file mode 100644 index 8b13789..0000000 --- a/pyqsc_jax/__init__.py +++ /dev/null @@ -1 +0,0 @@ - diff --git a/setup.py b/setup.py deleted file mode 100644 index 709934f..0000000 --- a/setup.py +++ /dev/null @@ -1,17 +0,0 @@ -from setuptools import setup, find_packages - -setup( - name="pyqsc_jax", - version="0.1.0", - author="Uw_Plasma", - packages=find_packages(), - install_requires=[ - "jax>=0.4.0", - "jaxlib>=0.4.0", - ], - classifiers=[ - "Programming Language :: Python :: 3", - "License :: OSI Approved :: MIT License", - ], - python_requires=">=3.9", -) diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py new file mode 100644 index 0000000..9f78dfb --- /dev/null +++ b/src/pyqsc_jax/__init__.py @@ -0,0 +1,6 @@ +"""Differentiable near-axis stellarator construction in JAX.""" + +from pyqsc_jax.near_axis import near_axis + +__all__ = ["near_axis"] +__version__ = "0.2.0.dev0" diff --git a/pyqsc_jax/near_axis.py b/src/pyqsc_jax/near_axis.py similarity index 99% rename from pyqsc_jax/near_axis.py rename to src/pyqsc_jax/near_axis.py index c6b8e6a..8b4ed42 100644 --- a/pyqsc_jax/near_axis.py +++ b/src/pyqsc_jax/near_axis.py @@ -1,3 +1,9 @@ +"""Legacy mutable near-axis interface. + +This module is retained while the immutable computational core is introduced. +The public import path is a hard ESSOS compatibility contract. +""" + import jax import jax.numpy as jnp from jax import jit, jacfwd, grad, vmap, tree_util, lax diff --git a/tests/conftest.py b/tests/conftest.py index 5468169..ac63b78 100644 --- a/tests/conftest.py +++ b/tests/conftest.py @@ -1,4 +1,3 @@ import jax - jax.config.update("jax_enable_x64", True) diff --git a/tests/regression/test_legacy_baseline.py b/tests/regression/test_legacy_baseline.py index c45d247..c2c8e64 100644 --- a/tests/regression/test_legacy_baseline.py +++ b/tests/regression/test_legacy_baseline.py @@ -32,9 +32,7 @@ def test_standard_first_order_baseline(): [-2.272197039914583, 0.6057564303422814], rtol=2e-13, ) - np.testing.assert_allclose( - jnp.max(jnp.abs(field.sigma)), 0.9920706836908618, rtol=2e-13 - ) + np.testing.assert_allclose(jnp.max(jnp.abs(field.sigma)), 0.9920706836908618, rtol=2e-13) assert field.B_axis.shape == (3, 31) assert field.grad_B_axis.shape == (3, 3, 31) @@ -55,21 +53,13 @@ def test_first_order_field_methods_are_finite(): ) def test_dofs_noop_preserves_derived_frame(): field = standard_field() - normal_before = jnp.stack( - [field.normal_R, field.normal_phi, field.normal_z], axis=1 - ) - binormal_before = jnp.stack( - [field.binormal_R, field.binormal_phi, field.binormal_z], axis=1 - ) + normal_before = jnp.stack([field.normal_R, field.normal_phi, field.normal_z], axis=1) + binormal_before = jnp.stack([field.binormal_R, field.binormal_phi, field.binormal_z], axis=1) field.dofs = field.dofs - normal_after = jnp.stack( - [field.normal_R, field.normal_phi, field.normal_z], axis=1 - ) - binormal_after = jnp.stack( - [field.binormal_R, field.binormal_phi, field.binormal_z], axis=1 - ) + normal_after = jnp.stack([field.normal_R, field.normal_phi, field.normal_z], axis=1) + binormal_after = jnp.stack([field.binormal_R, field.binormal_phi, field.binormal_z], axis=1) np.testing.assert_array_equal(normal_after, normal_before) np.testing.assert_array_equal(binormal_after, binormal_before) From 28955f8dfd322acd5ff70979a0e16ed1bc0aec5f Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Wed, 29 Jul 2026 22:45:55 -0500 Subject: [PATCH 03/39] refactor: add immutable axis and geometry core --- CHANGELOG.md | 4 + README.md | 13 ++ docs/api/axis.md | 29 +++ docs/development/physics-traceability.md | 2 +- docs/index.md | 2 + docs/theory/coordinates-and-conventions.md | 106 ++++++++++ src/pyqsc_jax/__init__.py | 3 +- src/pyqsc_jax/axis.py | 153 +++++++++++++++ src/pyqsc_jax/geometry.py | 205 ++++++++++++++++++++ src/pyqsc_jax/models.py | 19 ++ src/pyqsc_jax/spectral.py | 86 ++++++++ tests/physics/test_geometry.py | 78 ++++++++ tests/regression/test_geometry_reference.py | 104 ++++++++++ tests/unit/test_axis.py | 78 ++++++++ tests/unit/test_spectral.py | 69 +++++++ 15 files changed, 949 insertions(+), 2 deletions(-) create mode 100644 docs/api/axis.md create mode 100644 docs/theory/coordinates-and-conventions.md create mode 100644 src/pyqsc_jax/axis.py create mode 100644 src/pyqsc_jax/geometry.py create mode 100644 src/pyqsc_jax/models.py create mode 100644 src/pyqsc_jax/spectral.py create mode 100644 tests/physics/test_geometry.py create mode 100644 tests/regression/test_geometry_reference.py create mode 100644 tests/unit/test_axis.py create mode 100644 tests/unit/test_spectral.py diff --git a/CHANGELOG.md b/CHANGELOG.md index 4847fdf..456061b 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -12,3 +12,7 @@ first stable release. - Audited compatibility and numerical baselines. - Physics traceability and architecture decision records. - Modern package, documentation, test, and CI scaffolding. +- Immutable general Fourier axes with normalized coefficient packing. +- JAX-native periodic differentiation, interpolation, and integration. +- Sampled Frenet geometry with explicit validity diagnostics and independent + symmetric/asymmetric regression references. diff --git a/README.md b/README.md index 62c802e..d6ecd94 100644 --- a/README.md +++ b/README.md @@ -57,6 +57,19 @@ configuration = qsc.Qsc( That API will become the primary quickstart once its first- and second-order validation gates are green. +The lower-level immutable axis API is already available: + +```python +import pyqsc_jax as qsc +from pyqsc_jax.geometry import compute_axis_geometry + +axis = qsc.Axis(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3) +geometry = compute_axis_geometry(axis, nphi=31) + +print("axis length:", geometry.axis_length) +print("minimum curvature:", geometry.diagnostics.minimum_curvature) +``` + ## Scope The completed package will provide: diff --git a/docs/api/axis.md b/docs/api/axis.md new file mode 100644 index 0000000..0e980c1 --- /dev/null +++ b/docs/api/axis.md @@ -0,0 +1,29 @@ +# Axis and geometry API + +```{eval-rst} +.. autoclass:: pyqsc_jax.Axis + :members: +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.axis.evaluate_axis +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.axis.AxisSamples + :members: +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.geometry.compute_axis_geometry +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.geometry.AxisGeometry + :members: +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.models.GeometryDiagnostics + :members: +``` diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index 27f4611..ae4ffd1 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -6,7 +6,7 @@ to the cited source, not to a duplicated derivation in this repository. | Physics block | Primary source | Reference implementation | Required validation | Status | | --- | --- | --- | --- | --- | -| General Fourier axis and Frenet frame | Landreman & Sengupta (2018), arXiv:1809.10233 | pyQSC `init_axis.py` | analytic curves; spectral convergence; independent curvature/torsion | baseline audited | +| General Fourier axis and Frenet frame | Landreman & Sengupta (2018), arXiv:1809.10233 | `Axis`, `evaluate_axis`, `compute_axis_geometry`; pyQSC `init_axis.py` | analytic circle; asymmetric Fortran curvature/torsion/varphi; frame identities; JIT/VMAP/grad | implemented and documented | | First-order QS and sigma equation | Landreman & Sengupta (2019), arXiv:1908.10253 | pyQSC `solve_sigma_equation.py` | residual, convergence report, pyQSC values, JVP/VJP | baseline values only | | Field gradient and `L_grad_B` | Landreman (2021), arXiv:2012.00865, Eq. 3.12 | pyQSC `grad_B_tensor.py` | Cartesian AD/finite differences; Maxwell identities | baseline values only | | Complete second order | Landreman & Sengupta (2019), arXiv:1908.10253 | pyQSC `calculate_r2.py`; manuscript Eqs. 36–54 | all coefficients, operator residual, Fortran arrays, resolution convergence | not implemented | diff --git a/docs/index.md b/docs/index.md index 25c7e87..1ca941b 100644 --- a/docs/index.md +++ b/docs/index.md @@ -11,6 +11,8 @@ plasma-generated, and external vacuum field jets. installation quickstart limitations +theory/coordinates-and-conventions +api/axis ``` ```{toctree} diff --git a/docs/theory/coordinates-and-conventions.md b/docs/theory/coordinates-and-conventions.md new file mode 100644 index 0000000..3a240cf --- /dev/null +++ b/docs/theory/coordinates-and-conventions.md @@ -0,0 +1,106 @@ +# Axis coordinates and conventions + +## Fourier axis + +`Axis` represents a closed magnetic axis in cylindrical coordinates over one +field period: + +\[ +R(\phi) = +\sum_{n=0}^{N_F-1} +\left[ +R_{cn}\cos(n n_{\mathrm{fp}}\phi) ++R_{sn}\sin(n n_{\mathrm{fp}}\phi) +\right], +\] + +\[ +Z(\phi) = +\sum_{n=0}^{N_F-1} +\left[ +Z_{cn}\cos(n n_{\mathrm{fp}}\phi) ++Z_{sn}\sin(n n_{\mathrm{fp}}\phi) +\right]. +\] + +The arrays `rc`, `rs`, `zc`, and `zs` are padded with zeros to a common +one-dimensional shape `(nfourier,)`. The packed degree-of-freedom order is +exactly `rc, rs, zc, zs`. A stellarator-symmetric axis has `rs = zc = 0`. + +```python +import pyqsc_jax as qsc + +axis = qsc.Axis( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, +) +``` + +The representation follows the direct-construction convention +{cite}`landreman2018direct`. Unlike the historical pyQSC constructor, even +`nphi` is not silently changed; grid resolution is an explicit caller choice. + +## Sampled geometry + +`compute_axis_geometry(axis, nphi=...)` samples one field period on the +endpoint-free grid + +\[ +\phi_j = \frac{2\pi j}{n_{\mathrm{fp}}n_\phi}, +\qquad j=0,\ldots,n_\phi-1. +\] + +Analytic Fourier derivatives provide the first three derivatives of \(R\) and +\(Z\). Vector components in the cylindrical frame are ordered `(R, phi, Z)`; +Cartesian components are ordered `(x, y, z)`. Arrays of sampled vectors have +shape `(nphi, 3)`. + +The tangent, normal, and binormal are + +\[ +\boldsymbol{t} = \frac{\mathrm{d}\boldsymbol{r}_0}{\mathrm{d}\ell}, +\qquad +\boldsymbol{n} = \frac{1}{\kappa} +\frac{\mathrm{d}\boldsymbol{t}}{\mathrm{d}\ell}, +\qquad +\boldsymbol{b} = \boldsymbol{t}\times\boldsymbol{n}. +\] + +They form a right-handed orthonormal frame. Torsion uses the convention of +Landreman and Sengupta and the usual differential-geometry formula; this is +the opposite sign to the original Garren–Boozer convention +{cite}`garren1991magnetic,landreman2019highorder`. + +The Boozer toroidal grid is normalized so that + +\[ +\frac{\mathrm{d}\varphi}{\mathrm{d}\phi} += \frac{B_0}{|G_0|} +\frac{\mathrm{d}\ell}{\mathrm{d}\phi}, +\qquad +\varphi(0)=0, +\] + +and advances by \(2\pi/n_{\mathrm{fp}}\) per field period. Periodic +differentiation uses Fourier collocation matrices on the same endpoint-free +grid. + +## Topology and validity + +`frame_helicity` counts the signed winding of the Frenet normal around the +axis over one field period. It is intrinsic to the axis. The first-order solve +later combines it with the flux and covariant-field signs. + +Frenet coordinates require nonzero speed and curvature everywhere. +`GeometryDiagnostics` reports: + +- minimum speed and curvature; +- minimum cylindrical radius; +- maximum frame orthogonality error; +- minimum frame determinant; +- Boolean Frenet and cylindrical-coordinate validity. + +Invalid samples are represented by non-finite frame/torsion values and a false +validity flag. High-level solvers reject them with a structured report rather +than allowing them to propagate silently. diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index 9f78dfb..8e1054e 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -1,6 +1,7 @@ """Differentiable near-axis stellarator construction in JAX.""" +from pyqsc_jax.axis import Axis from pyqsc_jax.near_axis import near_axis -__all__ = ["near_axis"] +__all__ = ["Axis", "near_axis"] __version__ = "0.2.0.dev0" diff --git a/src/pyqsc_jax/axis.py b/src/pyqsc_jax/axis.py new file mode 100644 index 0000000..c092787 --- /dev/null +++ b/src/pyqsc_jax/axis.py @@ -0,0 +1,153 @@ +"""Fourier representations of the magnetic axis.""" + +from dataclasses import dataclass, field +from typing import Any, ClassVar + +import jax +import jax.numpy as jnp + +ArrayLike = Any + + +def _as_coefficient_array(values: ArrayLike, dtype: jnp.dtype) -> jax.Array: + array = jnp.asarray(values, dtype=dtype) + if array.ndim != 1: + raise ValueError("Axis Fourier coefficients must be one-dimensional.") + return array + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class Axis: + """Immutable cylindrical Fourier representation of a closed magnetic axis. + + The convention over one field period is + + .. math:: + + R(\\phi) = \\sum_n R_{cn}\\cos(n n_{fp}\\phi) + + R_{sn}\\sin(n n_{fp}\\phi), + + Z(\\phi) = \\sum_n Z_{cn}\\cos(n n_{fp}\\phi) + + Z_{sn}\\sin(n n_{fp}\\phi). + + All four coefficient arrays are padded to the same length. ``nfp`` is + static pytree metadata, while the coefficient arrays are differentiable + pytree leaves. + """ + + rc: jax.Array + zs: jax.Array + nfp: int = field(default=1, metadata={"static": True}) + rs: jax.Array = () + zc: jax.Array = () + + coefficient_order: ClassVar[tuple[str, ...]] = ("rc", "rs", "zc", "zs") + + def __post_init__(self) -> None: + if not isinstance(self.nfp, int) or isinstance(self.nfp, bool) or self.nfp < 1: + raise ValueError("nfp must be a positive integer.") + + raw = tuple(jnp.asarray(values) for values in (self.rc, self.rs, self.zc, self.zs)) + dtype = jnp.result_type(jnp.asarray(0.0), *(array.dtype for array in raw)) + arrays = tuple(_as_coefficient_array(values, dtype) for values in raw) + nfourier = max(array.size for array in arrays) + if nfourier < 1: + raise ValueError("At least one axis Fourier coefficient is required.") + + padded = tuple(jnp.pad(array, (0, nfourier - array.size)) for array in arrays) + object.__setattr__(self, "rc", padded[0]) + object.__setattr__(self, "rs", padded[1]) + object.__setattr__(self, "zc", padded[2]) + object.__setattr__(self, "zs", padded[3]) + + @classmethod + def stellarator_symmetric(cls, *, rc: ArrayLike, zs: ArrayLike, nfp: int = 1) -> "Axis": + """Construct an axis for which ``R`` is even and ``Z`` is odd.""" + + return cls(rc=rc, zs=zs, nfp=nfp) + + @classmethod + def from_dofs(cls, dofs: ArrayLike, *, nfp: int) -> "Axis": + """Construct from four equal blocks ordered as ``rc, rs, zc, zs``.""" + + array = jnp.asarray(dofs) + if array.ndim != 1 or array.size % 4: + raise ValueError( + "Axis dofs must be a one-dimensional array with length divisible by 4." + ) + nfourier = array.size // 4 + rc, rs, zc, zs = jnp.split(array, (nfourier, 2 * nfourier, 3 * nfourier)) + return cls(rc=rc, rs=rs, zc=zc, zs=zs, nfp=nfp) + + @property + def nfourier(self) -> int: + """Number of retained Fourier modes, including mode zero.""" + + return self.rc.size + + @property + def dofs(self) -> jax.Array: + """Coefficient vector ordered as ``rc, rs, zc, zs``.""" + + return jnp.concatenate((self.rc, self.rs, self.zc, self.zs)) + + @property + def stellarator_symmetry_residual(self) -> jax.Array: + """Largest coefficient forbidden by stellarator symmetry.""" + + return jnp.maximum(jnp.max(jnp.abs(self.rs)), jnp.max(jnp.abs(self.zc))) + + def with_dofs(self, dofs: ArrayLike) -> "Axis": + """Return a new axis with packed coefficients and the same ``nfp``.""" + + return type(self).from_dofs(dofs, nfp=self.nfp) + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class AxisSamples: + """Axis coordinates and their first three cylindrical-angle derivatives.""" + + phi: jax.Array + R: jax.Array + Z: jax.Array + d_R_d_phi: jax.Array + d_Z_d_phi: jax.Array + d2_R_d_phi2: jax.Array + d2_Z_d_phi2: jax.Array + d3_R_d_phi3: jax.Array + d3_Z_d_phi3: jax.Array + + +def evaluate_axis(axis: Axis, phi: ArrayLike) -> AxisSamples: + """Evaluate an axis and analytic derivatives at arbitrary toroidal angles.""" + + phi = jnp.asarray(phi) + mode = jnp.arange(axis.nfourier, dtype=phi.dtype) * axis.nfp + angle = phi[..., None] * mode + cosine = jnp.cos(angle) + sine = jnp.sin(angle) + + R = jnp.sum(axis.rc * cosine + axis.rs * sine, axis=-1) + Z = jnp.sum(axis.zc * cosine + axis.zs * sine, axis=-1) + d_R = jnp.sum(mode * (-axis.rc * sine + axis.rs * cosine), axis=-1) + d_Z = jnp.sum(mode * (-axis.zc * sine + axis.zs * cosine), axis=-1) + mode2 = mode * mode + d2_R = jnp.sum(-mode2 * (axis.rc * cosine + axis.rs * sine), axis=-1) + d2_Z = jnp.sum(-mode2 * (axis.zc * cosine + axis.zs * sine), axis=-1) + mode3 = mode2 * mode + d3_R = jnp.sum(mode3 * (axis.rc * sine - axis.rs * cosine), axis=-1) + d3_Z = jnp.sum(mode3 * (axis.zc * sine - axis.zs * cosine), axis=-1) + + return AxisSamples( + phi=phi, + R=R, + Z=Z, + d_R_d_phi=d_R, + d_Z_d_phi=d_Z, + d2_R_d_phi2=d2_R, + d2_Z_d_phi2=d2_Z, + d3_R_d_phi3=d3_R, + d3_Z_d_phi3=d3_Z, + ) diff --git a/src/pyqsc_jax/geometry.py b/src/pyqsc_jax/geometry.py new file mode 100644 index 0000000..a3833c8 --- /dev/null +++ b/src/pyqsc_jax/geometry.py @@ -0,0 +1,205 @@ +"""Sampled magnetic-axis geometry and Frenet frames.""" + +from dataclasses import dataclass +from typing import Any + +import jax +import jax.numpy as jnp + +from pyqsc_jax.axis import Axis, AxisSamples, evaluate_axis +from pyqsc_jax.models import GeometryDiagnostics +from pyqsc_jax.spectral import differentiation_matrix, periodic_grid + +ArrayLike = Any + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class AxisGeometry: + """Immutable sampled geometry over one magnetic field period. + + Cylindrical vector components use the final-axis order ``(R, phi, Z)``. + Cartesian vector components use ``(x, y, z)``. + """ + + axis: Axis + samples: AxisSamples + position_cartesian: jax.Array + d_r_d_phi_cylindrical: jax.Array + d2_r_d_phi2_cylindrical: jax.Array + d3_r_d_phi3_cylindrical: jax.Array + d_l_d_phi: jax.Array + axis_length: jax.Array + tangent_cylindrical: jax.Array + normal_cylindrical: jax.Array + binormal_cylindrical: jax.Array + tangent_cartesian: jax.Array + normal_cartesian: jax.Array + binormal_cartesian: jax.Array + curvature: jax.Array + torsion: jax.Array + frame_helicity: jax.Array + varphi: jax.Array + d_varphi_d_phi: jax.Array + d_d_phi: jax.Array + d_d_varphi: jax.Array + abs_G0_over_B0: jax.Array + diagnostics: GeometryDiagnostics + + +def cylindrical_vector_to_cartesian(vector: ArrayLike, phi: ArrayLike) -> jax.Array: + """Convert vectors from cylindrical ``(R, phi, Z)`` to Cartesian basis.""" + + vector = jnp.asarray(vector) + phi = jnp.asarray(phi) + cosine = jnp.cos(phi) + sine = jnp.sin(phi) + return jnp.stack( + ( + vector[..., 0] * cosine - vector[..., 1] * sine, + vector[..., 0] * sine + vector[..., 1] * cosine, + vector[..., 2], + ), + axis=-1, + ) + + +def _frame_helicity(normal_cylindrical: jax.Array) -> jax.Array: + x_positive = normal_cylindrical[:, 0] >= 0 + z_positive = normal_cylindrical[:, 2] >= 0 + quadrant = jnp.where( + x_positive & z_positive, + 1, + jnp.where(~x_positive & z_positive, 2, jnp.where(~x_positive & ~z_positive, 3, 4)), + ) + next_quadrant = jnp.roll(quadrant, -1) + increment = jnp.where( + (quadrant == 4) & (next_quadrant == 1), + 1, + jnp.where( + (quadrant == 1) & (next_quadrant == 4), + -1, + next_quadrant - quadrant, + ), + ) + return jnp.rint(jnp.sum(increment) / 4).astype(jnp.int32) + + +def compute_axis_geometry( + axis: Axis, + *, + nphi: int = 61, + speed_tolerance: ArrayLike = 1e-12, + curvature_tolerance: ArrayLike = 1e-10, + radius_tolerance: ArrayLike = 1e-10, +) -> AxisGeometry: + """Evaluate axis geometry and Frenet validity over one field period.""" + + if not isinstance(nphi, int) or isinstance(nphi, bool) or nphi < 3: + raise ValueError("nphi must be an integer >= 3.") + + period = 2 * jnp.pi / axis.nfp + phi = periodic_grid(nphi, period=period) + samples = evaluate_axis(axis, phi) + cosine = jnp.cos(phi) + sine = jnp.sin(phi) + position_cartesian = jnp.stack((samples.R * cosine, samples.R * sine, samples.Z), axis=-1) + + d_r = jnp.stack((samples.d_R_d_phi, samples.R, samples.d_Z_d_phi), axis=-1) + d2_r = jnp.stack( + ( + samples.d2_R_d_phi2 - samples.R, + 2 * samples.d_R_d_phi, + samples.d2_Z_d_phi2, + ), + axis=-1, + ) + d3_r = jnp.stack( + ( + samples.d3_R_d_phi3 - 3 * samples.d_R_d_phi, + 3 * samples.d2_R_d_phi2 - samples.R, + samples.d3_Z_d_phi3, + ), + axis=-1, + ) + + d_l_d_phi = jnp.linalg.norm(d_r, axis=-1) + d2_l_d_phi2 = jnp.sum(d_r * d2_r, axis=-1) / d_l_d_phi + tangent = d_r / d_l_d_phi[:, None] + d_tangent_d_l = (-d_r * d2_l_d_phi2[:, None] / d_l_d_phi[:, None] + d2_r) / d_l_d_phi[ + :, None + ] ** 2 + curvature = jnp.linalg.norm(d_tangent_d_l, axis=-1) + pointwise_frenet_valid = (d_l_d_phi > speed_tolerance) & (curvature > curvature_tolerance) + normal = jnp.where( + pointwise_frenet_valid[:, None], + d_tangent_d_l / curvature[:, None], + jnp.nan, + ) + binormal = jnp.cross(tangent, normal) + + cross_first_second = jnp.cross(d_r, d2_r) + torsion = jnp.where( + pointwise_frenet_valid, + jnp.sum(d_r * jnp.cross(d2_r, d3_r), axis=-1) / jnp.sum(cross_first_second**2, axis=-1), + jnp.nan, + ) + + d_phi = period / nphi + axis_length = jnp.sum(d_l_d_phi) * d_phi * axis.nfp + B0_over_abs_G0 = nphi / jnp.sum(d_l_d_phi) + abs_G0_over_B0 = 1 / B0_over_abs_G0 + d_varphi_d_phi = B0_over_abs_G0 * d_l_d_phi + d_d_phi = differentiation_matrix(nphi, period=period) + d_d_varphi = d_d_phi / d_varphi_d_phi[:, None] + varphi = jnp.concatenate( + (jnp.zeros(1, dtype=d_l_d_phi.dtype), jnp.cumsum(d_l_d_phi[:-1] + d_l_d_phi[1:])) + ) + varphi = varphi * (0.5 * d_phi * 2 * jnp.pi / axis_length) + + tangent_cartesian = cylindrical_vector_to_cartesian(tangent, phi) + normal_cartesian = cylindrical_vector_to_cartesian(normal, phi) + binormal_cartesian = cylindrical_vector_to_cartesian(binormal, phi) + frame = jnp.stack((tangent_cartesian, normal_cartesian, binormal_cartesian), axis=-2) + gram = frame @ jnp.swapaxes(frame, -1, -2) + identity = jnp.eye(3, dtype=frame.dtype) + orthogonality_error = jnp.max(jnp.abs(gram - identity)) + determinant = jnp.linalg.det(frame) + minimum_speed = jnp.min(d_l_d_phi) + minimum_curvature = jnp.min(curvature) + minimum_radius = jnp.min(samples.R) + diagnostics = GeometryDiagnostics( + minimum_speed=minimum_speed, + minimum_curvature=minimum_curvature, + minimum_cylindrical_radius=minimum_radius, + maximum_frame_orthogonality_error=orthogonality_error, + minimum_frame_determinant=jnp.min(determinant), + frenet_valid=jnp.all(pointwise_frenet_valid) & jnp.isfinite(orthogonality_error), + cylindrical_coordinates_valid=minimum_radius > radius_tolerance, + ) + + return AxisGeometry( + axis=axis, + samples=samples, + position_cartesian=position_cartesian, + d_r_d_phi_cylindrical=d_r, + d2_r_d_phi2_cylindrical=d2_r, + d3_r_d_phi3_cylindrical=d3_r, + d_l_d_phi=d_l_d_phi, + axis_length=axis_length, + tangent_cylindrical=tangent, + normal_cylindrical=normal, + binormal_cylindrical=binormal, + tangent_cartesian=tangent_cartesian, + normal_cartesian=normal_cartesian, + binormal_cartesian=binormal_cartesian, + curvature=curvature, + torsion=torsion, + frame_helicity=_frame_helicity(normal), + varphi=varphi, + d_varphi_d_phi=d_varphi_d_phi, + d_d_phi=d_d_phi, + d_d_varphi=d_d_varphi, + abs_G0_over_B0=abs_G0_over_B0, + diagnostics=diagnostics, + ) diff --git a/src/pyqsc_jax/models.py b/src/pyqsc_jax/models.py new file mode 100644 index 0000000..8d6420c --- /dev/null +++ b/src/pyqsc_jax/models.py @@ -0,0 +1,19 @@ +"""Small immutable result and diagnostic models.""" + +from dataclasses import dataclass + +import jax + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class GeometryDiagnostics: + """Validity and conditioning information for sampled axis geometry.""" + + minimum_speed: jax.Array + minimum_curvature: jax.Array + minimum_cylindrical_radius: jax.Array + maximum_frame_orthogonality_error: jax.Array + minimum_frame_determinant: jax.Array + frenet_valid: jax.Array + cylindrical_coordinates_valid: jax.Array diff --git a/src/pyqsc_jax/spectral.py b/src/pyqsc_jax/spectral.py new file mode 100644 index 0000000..dd63fdd --- /dev/null +++ b/src/pyqsc_jax/spectral.py @@ -0,0 +1,86 @@ +"""Spectral operations on uniform periodic grids.""" + +from typing import Any + +import jax +import jax.numpy as jnp + +ArrayLike = Any + + +def periodic_grid(n: int, *, period: ArrayLike = 2 * jnp.pi) -> jax.Array: + """Return ``n`` uniform points on ``[0, period)``.""" + + if not isinstance(n, int) or isinstance(n, bool) or n < 2: + raise ValueError("A periodic grid requires an integer n >= 2.") + return jnp.arange(n) * (jnp.asarray(period) / n) + + +def differentiation_matrix(n: int, *, period: ArrayLike = 2 * jnp.pi) -> jax.Array: + """Return the first-derivative Fourier collocation matrix. + + The even and odd formulas follow the trigonometric differentiation + matrices of Weideman and Reddy. Rows act on values sampled by + :func:`periodic_grid`. + """ + + if not isinstance(n, int) or isinstance(n, bool) or n < 2: + raise ValueError("A differentiation matrix requires an integer n >= 2.") + + index = jnp.arange(n) + difference = index[:, None] - index[None, :] + angle = jnp.pi * difference / n + sign = jnp.where(jnp.mod(difference, 2) == 0, 1.0, -1.0) + off_diagonal = difference != 0 + if n % 2 == 0: + entries = 0.5 * sign / jnp.tan(angle) + else: + entries = 0.5 * sign / jnp.sin(angle) + dimensionless = jnp.where(off_diagonal, entries, 0.0) + return dimensionless * (2 * jnp.pi / jnp.asarray(period)) + + +def differentiate(values: ArrayLike, *, period: ArrayLike = 2 * jnp.pi) -> jax.Array: + """Differentiate values along their final periodic axis.""" + + values = jnp.asarray(values) + matrix = differentiation_matrix(values.shape[-1], period=period) + return jnp.einsum("jk,...k->...j", matrix, values) + + +def periodic_integral(values: ArrayLike, *, period: ArrayLike = 2 * jnp.pi) -> jax.Array: + """Integrate uniform periodic samples along their final axis.""" + + return jnp.asarray(period) * jnp.mean(jnp.asarray(values), axis=-1) + + +def fourier_coefficients(values: ArrayLike) -> tuple[jax.Array, jax.Array]: + """Return integer frequencies and complex Fourier coefficients.""" + + values = jnp.asarray(values) + n = values.shape[-1] + frequency = jnp.fft.fftfreq(n, d=1 / n) + coefficients = jnp.fft.fft(values, axis=-1) / n + return frequency, coefficients + + +def fourier_interpolate( + values: ArrayLike, x: ArrayLike, *, period: ArrayLike = 2 * jnp.pi +) -> jax.Array: + """Evaluate the trigonometric interpolant of one-dimensional real samples.""" + + values = jnp.asarray(values) + if values.ndim != 1: + raise ValueError("fourier_interpolate currently accepts one-dimensional samples.") + + frequency, coefficients = fourier_coefficients(values) + x = jnp.asarray(x) + angle = 2 * jnp.pi * x / jnp.asarray(period) + phase = jnp.exp(1j * angle[..., None] * frequency) + if values.size % 2 == 0: + nyquist = values.size // 2 + phase = phase.at[..., nyquist].set(jnp.cos(nyquist * angle)) + result = jnp.sum(coefficients * phase, axis=-1) + if jnp.issubdtype(values.dtype, jnp.floating): + return jnp.real(result) + return result diff --git a/tests/physics/test_geometry.py b/tests/physics/test_geometry.py new file mode 100644 index 0000000..44fc3ee --- /dev/null +++ b/tests/physics/test_geometry.py @@ -0,0 +1,78 @@ +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +from pyqsc_jax import Axis +from pyqsc_jax.geometry import compute_axis_geometry + + +def test_circular_axis_geometry_is_analytic(): + major_radius = 2.0 + nphi = 31 + geometry = compute_axis_geometry(Axis(rc=[major_radius], zs=[0.0]), nphi=nphi) + + np.testing.assert_allclose(geometry.axis_length, 2 * jnp.pi * major_radius, rtol=2e-14) + np.testing.assert_allclose(geometry.curvature, 1 / major_radius, rtol=2e-14) + np.testing.assert_allclose(geometry.torsion, 0.0, atol=2e-14) + np.testing.assert_allclose(geometry.varphi, geometry.samples.phi, rtol=2e-14, atol=2e-14) + np.testing.assert_allclose( + geometry.tangent_cylindrical, + jnp.tile(jnp.array([0.0, 1.0, 0.0]), (nphi, 1)), + atol=2e-14, + ) + np.testing.assert_allclose( + geometry.normal_cylindrical, + jnp.tile(jnp.array([-1.0, 0.0, 0.0]), (nphi, 1)), + atol=2e-14, + ) + np.testing.assert_allclose( + geometry.binormal_cylindrical, + jnp.tile(jnp.array([0.0, 0.0, 1.0]), (nphi, 1)), + atol=2e-14, + ) + assert int(geometry.frame_helicity) == 0 + assert bool(geometry.diagnostics.frenet_valid) + assert bool(geometry.diagnostics.cylindrical_coordinates_valid) + + +def test_frame_is_right_handed_and_orthonormal(): + axis = Axis(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3) + geometry = compute_axis_geometry(axis, nphi=31) + frame = jnp.stack( + (geometry.tangent_cartesian, geometry.normal_cartesian, geometry.binormal_cartesian), + axis=-2, + ) + gram = frame @ jnp.swapaxes(frame, -1, -2) + + expected_gram = jnp.broadcast_to(jnp.eye(3), gram.shape) + np.testing.assert_allclose(gram, expected_gram, rtol=2e-13, atol=2e-13) + np.testing.assert_allclose(jnp.linalg.det(frame), 1.0, rtol=2e-13, atol=2e-13) + assert geometry.diagnostics.maximum_frame_orthogonality_error < 1e-12 + + +def test_invalid_axis_has_explicit_diagnostics(): + geometry = compute_axis_geometry(Axis(rc=[0.0], zs=[0.0]), nphi=15) + + assert not bool(geometry.diagnostics.frenet_valid) + assert not bool(geometry.diagnostics.cylindrical_coordinates_valid) + np.testing.assert_allclose(geometry.diagnostics.minimum_speed, 0.0) + + with pytest.raises(ValueError, match="nphi"): + compute_axis_geometry(Axis(rc=[1.0], zs=[0.0]), nphi=2) + + +def test_geometry_jit_and_axis_length_gradient(): + axis = Axis(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3) + compiled = jax.jit(compute_axis_geometry, static_argnames=("nphi",))(axis, nphi=31) + eager = compute_axis_geometry(axis, nphi=31) + np.testing.assert_allclose(compiled.curvature, eager.curvature, rtol=2e-13) + + def length(rc1): + varied = Axis(rc=jnp.array([1.0, rc1]), zs=axis.zs, nfp=axis.nfp) + return compute_axis_geometry(varied, nphi=31).axis_length + + derivative = jax.grad(length)(0.045) + step = 1e-5 + finite_difference = (length(0.045 + step) - length(0.045 - step)) / (2 * step) + np.testing.assert_allclose(derivative, finite_difference, rtol=2e-8, atol=2e-8) diff --git a/tests/regression/test_geometry_reference.py b/tests/regression/test_geometry_reference.py new file mode 100644 index 0000000..083b557 --- /dev/null +++ b/tests/regression/test_geometry_reference.py @@ -0,0 +1,104 @@ +import numpy as np + +from pyqsc_jax import Axis +from pyqsc_jax.geometry import compute_axis_geometry +from pyqsc_jax.near_axis import near_axis + + +def test_geometry_matches_legacy_first_order_baseline(): + parameters = { + "rc": [1.0, 0.045], + "zs": [0.0, -0.045], + "nfp": 3, + "nphi": 31, + } + geometry = compute_axis_geometry( + Axis(rc=parameters["rc"], zs=parameters["zs"], nfp=parameters["nfp"]), + nphi=parameters["nphi"], + ) + legacy = near_axis(etabar=-0.9, **parameters) + + np.testing.assert_allclose(geometry.samples.R, legacy.R0, rtol=2e-13, atol=2e-13) + np.testing.assert_allclose(geometry.samples.Z, legacy.Z0, rtol=2e-13, atol=2e-13) + np.testing.assert_allclose(geometry.axis_length, legacy.axis_length, rtol=2e-13) + np.testing.assert_allclose(geometry.curvature, legacy.curvature, rtol=2e-13) + np.testing.assert_allclose(geometry.torsion, legacy.torsion, rtol=2e-13) + np.testing.assert_allclose(geometry.varphi, legacy.varphi, rtol=2e-13, atol=2e-13) + np.testing.assert_allclose(geometry.normal_cylindrical[:, 0], legacy.normal_R, rtol=2e-13) + np.testing.assert_allclose(geometry.normal_cylindrical[:, 1], legacy.normal_phi, rtol=2e-13) + np.testing.assert_allclose(geometry.normal_cylindrical[:, 2], legacy.normal_z, rtol=2e-13) + + +def test_asymmetric_geometry_matches_independent_fortran_reference(): + axis = Axis( + rc=[1.3, 0.3, 0.01, -0.001], + zs=[0.0, 0.4, -0.02, -0.003], + rs=[0.0, -0.1, -0.03, 0.002], + zc=[0.3, 0.2, 0.04, 0.004], + nfp=5, + ) + geometry = compute_axis_geometry(axis, nphi=15) + curvature = [ + 2.10743037699653, + 2.33190181686696, + 1.83273654023051, + 1.81062232906827, + 2.28640008392347, + 1.76919841474321, + 0.919988560478029, + 0.741327470169023, + 1.37147330126897, + 2.64680884158075, + 3.39786486424852, + 2.47005615416209, + 1.50865425515356, + 1.18136509189105, + 1.42042418970102, + ] + torsion = [ + -0.167822738386845, + -0.0785778346620885, + -1.02205137493593, + -2.05213528002946, + -0.964613202459108, + -0.593496282035916, + -2.15852857178204, + -3.72911055219339, + -1.9330792779459, + -1.53882290974916, + -1.42156496444929, + -1.11381642382793, + -0.92608309386204, + -0.868339812017432, + -0.57696266498748, + ] + varphi = [ + 0.0, + 0.084185130335249, + 0.160931495903817, + 0.232881563535092, + 0.300551168190665, + 0.368933497012765, + 0.444686439112853, + 0.528001290336008, + 0.612254611059372, + 0.691096975269652, + 0.765820243301147, + 0.846373713025902, + 0.941973362938683, + 1.05053459351092, + 1.15941650366667, + ] + + np.testing.assert_allclose(geometry.curvature, curvature, rtol=2e-13, atol=2e-13) + np.testing.assert_allclose(geometry.torsion, torsion, rtol=2e-13, atol=2e-13) + np.testing.assert_allclose(geometry.varphi, varphi, rtol=2e-13, atol=2e-13) + + +def test_qh_frame_helicity_matches_upstream_convention(): + geometry = compute_axis_geometry( + Axis(rc=[1.0, 0.265], zs=[0.0, -0.21], nfp=4), + nphi=31, + ) + + assert int(geometry.frame_helicity) == -1 diff --git a/tests/unit/test_axis.py b/tests/unit/test_axis.py new file mode 100644 index 0000000..cffb709 --- /dev/null +++ b/tests/unit/test_axis.py @@ -0,0 +1,78 @@ +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +from pyqsc_jax import Axis +from pyqsc_jax.axis import evaluate_axis + + +def test_coefficients_are_normalized_and_round_trip(): + axis = Axis( + rc=[1.0, 0.2, -0.01], + rs=[0.0, 0.03], + zc=[0.1], + zs=[0.0, -0.15], + nfp=5, + ) + + assert axis.nfourier == 3 + np.testing.assert_array_equal(axis.rs, [0.0, 0.03, 0.0]) + np.testing.assert_array_equal(axis.zc, [0.1, 0.0, 0.0]) + np.testing.assert_array_equal(axis.zs, [0.0, -0.15, 0.0]) + np.testing.assert_allclose(axis.stellarator_symmetry_residual, 0.1) + rebuilt = Axis.from_dofs(axis.dofs, nfp=axis.nfp) + assert rebuilt.nfp == axis.nfp + np.testing.assert_array_equal(rebuilt.dofs, axis.dofs) + shifted = axis.with_dofs(axis.dofs.at[0].add(0.2)) + np.testing.assert_allclose(shifted.rc[0], 1.2) + + +def test_axis_input_validation(): + with pytest.raises(ValueError, match="positive integer"): + Axis(rc=[1.0], zs=[0.0], nfp=0) + with pytest.raises(ValueError, match="positive integer"): + Axis(rc=[1.0], zs=[0.0], nfp=True) + with pytest.raises(ValueError, match="one-dimensional"): + Axis(rc=[[1.0]], zs=[0.0]) + with pytest.raises(ValueError, match="At least one"): + Axis(rc=[], zs=[]) + with pytest.raises(ValueError, match="divisible by 4"): + Axis.from_dofs(jnp.arange(5.0), nfp=1) + + +def test_general_axis_and_analytic_derivatives(): + axis = Axis( + rc=[1.2, 0.3], + rs=[0.0, -0.11], + zc=[0.2, 0.04], + zs=[0.0, 0.17], + nfp=3, + ) + phi = jnp.array([0.0, 0.13, 0.51]) + samples = evaluate_axis(axis, phi) + angle = 3 * phi + + np.testing.assert_allclose(samples.R, 1.2 + 0.3 * jnp.cos(angle) - 0.11 * jnp.sin(angle)) + np.testing.assert_allclose(samples.Z, 0.2 + 0.04 * jnp.cos(angle) + 0.17 * jnp.sin(angle)) + np.testing.assert_allclose(samples.d_R_d_phi, -0.9 * jnp.sin(angle) - 0.33 * jnp.cos(angle)) + np.testing.assert_allclose(samples.d_Z_d_phi, -0.12 * jnp.sin(angle) + 0.51 * jnp.cos(angle)) + np.testing.assert_allclose(samples.d2_R_d_phi2, -2.7 * jnp.cos(angle) + 0.99 * jnp.sin(angle)) + np.testing.assert_allclose(samples.d3_Z_d_phi3, 1.08 * jnp.sin(angle) - 4.59 * jnp.cos(angle)) + + +def test_axis_is_jittable_vmappable_and_differentiable(): + phi = jnp.linspace(0.0, 0.9, 11) + axis = Axis.stellarator_symmetric(rc=[1.0, 0.04], zs=[0.0, -0.04], nfp=3) + eager = evaluate_axis(axis, phi) + compiled = jax.jit(evaluate_axis)(axis, phi) + np.testing.assert_allclose(compiled.R, eager.R, rtol=1e-14, atol=1e-14) + + offsets = jnp.array([-0.01, 0.0, 0.02]) + + def radius_at_zero(offset): + changed = Axis(rc=axis.rc.at[1].add(offset), zs=axis.zs, nfp=axis.nfp) + return evaluate_axis(changed, 0.0).R + + np.testing.assert_allclose(jax.vmap(radius_at_zero)(offsets), 1.04 + offsets) + np.testing.assert_allclose(jax.grad(radius_at_zero)(0.0), 1.0) diff --git a/tests/unit/test_spectral.py b/tests/unit/test_spectral.py new file mode 100644 index 0000000..214cd27 --- /dev/null +++ b/tests/unit/test_spectral.py @@ -0,0 +1,69 @@ +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +from pyqsc_jax.spectral import ( + differentiate, + differentiation_matrix, + fourier_coefficients, + fourier_interpolate, + periodic_grid, + periodic_integral, +) + + +@pytest.mark.parametrize("n", [8, 9, 31]) +def test_differentiation_matrix_is_spectrally_exact(n): + period = 3.7 + x = periodic_grid(n, period=period) + fundamental = 2 * jnp.pi / period + values = jnp.sin(2 * fundamental * x) + 0.2 * jnp.cos(3 * fundamental * x) + expected = 2 * fundamental * jnp.cos(2 * fundamental * x) - 0.6 * fundamental * jnp.sin( + 3 * fundamental * x + ) + + derivative = differentiation_matrix(n, period=period) @ values + np.testing.assert_allclose(derivative, expected, rtol=2e-13, atol=2e-13) + np.testing.assert_allclose(differentiate(values, period=period), expected, rtol=2e-13) + + +@pytest.mark.parametrize("n", [8, 9]) +def test_fourier_interpolation_even_and_odd(n): + x_grid = periodic_grid(n) + samples = jnp.sin(2 * x_grid) + 0.3 * jnp.cos(3 * x_grid) + x = jnp.array([0.12, 1.23, 5.72]) + expected = jnp.sin(2 * x) + 0.3 * jnp.cos(3 * x) + + np.testing.assert_allclose(fourier_interpolate(samples, x), expected, rtol=2e-13, atol=2e-13) + np.testing.assert_allclose( + fourier_interpolate(samples, x_grid), samples, rtol=2e-13, atol=2e-15 + ) + + +def test_periodic_integral_and_coefficients(): + n = 17 + x = periodic_grid(n) + values = 2.3 + jnp.cos(3 * x) - 0.4 * jnp.sin(5 * x) + frequency, coefficients = fourier_coefficients(values) + + np.testing.assert_allclose(periodic_integral(values), 2.3 * 2 * jnp.pi, rtol=2e-14) + np.testing.assert_allclose(coefficients[frequency == 0], 2.3, rtol=2e-14) + np.testing.assert_allclose(jax.jit(differentiate)(values), differentiate(values), rtol=2e-14) + + +def test_periodic_grid_validation(): + with pytest.raises(ValueError, match="n >= 2"): + periodic_grid(1) + with pytest.raises(ValueError, match="n >= 2"): + differentiation_matrix(1) + with pytest.raises(ValueError, match="one-dimensional"): + fourier_interpolate(jnp.ones((2, 3)), 0.2) + + +def test_complex_fourier_interpolation(): + x_grid = periodic_grid(9) + samples = jnp.exp(2j * x_grid) + x = jnp.array([0.17, 2.4]) + + np.testing.assert_allclose(fourier_interpolate(samples, x), jnp.exp(2j * x), rtol=2e-13) From 16249fe6317785632da667ad5c05f6f8ad484c80 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Wed, 29 Jul 2026 23:06:15 -0500 Subject: [PATCH 04/39] feat: implement converged differentiable first-order solve --- CHANGELOG.md | 14 + README.md | 42 +- docs/api/first-order.md | 36 + docs/development/physics-traceability.md | 4 +- docs/index.md | 9 +- docs/limitations.md | 19 +- docs/quickstart.md | 51 +- docs/theory/first-order.md | 132 +++ pyproject.toml | 2 - src/pyqsc_jax/__init__.py | 14 +- src/pyqsc_jax/first_order.py | 269 +++++ src/pyqsc_jax/models.py | 131 ++- src/pyqsc_jax/near_axis.py | 1016 +++++++++-------- src/pyqsc_jax/solvers.py | 187 +++ tests/compatibility/test_essos_contract.py | 6 - tests/compatibility/test_legacy_adapter.py | 153 +++ tests/numerics/test_first_order_autodiff.py | 51 + tests/physics/test_first_order.py | 100 ++ .../regression/test_first_order_reference.py | 63 + tests/regression/test_legacy_baseline.py | 4 - tests/unit/test_solvers.py | 73 ++ 21 files changed, 1845 insertions(+), 531 deletions(-) create mode 100644 docs/api/first-order.md create mode 100644 docs/theory/first-order.md create mode 100644 src/pyqsc_jax/first_order.py create mode 100644 src/pyqsc_jax/solvers.py create mode 100644 tests/compatibility/test_legacy_adapter.py create mode 100644 tests/numerics/test_first_order_autodiff.py create mode 100644 tests/physics/test_first_order.py create mode 100644 tests/regression/test_first_order_reference.py create mode 100644 tests/unit/test_solvers.py diff --git a/CHANGELOG.md b/CHANGELOG.md index 456061b..ec7d2c1 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -16,3 +16,17 @@ first stable release. - JAX-native periodic differentiation, interpolation, and integration. - Sampled Frenet geometry with explicit validity diagnostics and independent symmetric/asymmetric regression references. +- Converged, damped periodic sigma solve with residual, iteration, + backtracking, stagnation, and Jacobian-conditioning reports. +- Implicit differentiation of the converged sigma equation through SOLVAX. +- Immutable first-order shape, field, field-gradient, elongation, and + `L_grad_B` results with JIT, VMAP, JVP, and VJP validation. +- Thin ESSOS compatibility adapter preserving legacy array orientations, + coordinate conversion, boundary generation, and plotting without depending + on ESSOS. + +### Fixed + +- A no-op assignment to legacy `dofs` no longer exchanges normal and binormal + cylindrical components. +- The legacy sigma calculation no longer assumes exactly five Newton updates. diff --git a/README.md b/README.md index d6ecd94..cdd80a6 100644 --- a/README.md +++ b/README.md @@ -3,9 +3,10 @@ Differentiable near-axis stellarator construction and plasma–coil field jets in JAX. -> **Development status:** the current release preserves the ESSOS first-order -> interface while an immutable, fully validated pyQSC-compatible core is built -> on the `refactor/pyqsc-jax-complete` branch. +> **Development status:** the immutable first-order core and ESSOS adapter are +> validated. Complete second order, third order, inverse solves, optimization, +> and plasma/external field jets remain under development on the +> `refactor/pyqsc-jax-complete` branch. ## Install @@ -22,42 +23,49 @@ python -m pip install -e . No JAX backend policy is imposed by the package. Install the JAX build suitable for your accelerator and platform. -## Current quickstart +## Quickstart ```python -from pyqsc_jax.near_axis import near_axis +import pyqsc_jax as qsc -field = near_axis( +solution = qsc.Qsc( rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3, etabar=-0.9, + order="r1", ) -print("iota:", field.iota) -print("axis length:", field.axis_length) -print("minimum L_grad_B:", field.L_grad_B.min()) +print("iota:", solution.iota) +print("sigma residual:", solution.root_report.residual_norm) +print("axis length:", solution.axis_length) +print("minimum L_grad_B:", solution.L_grad_B.min()) ``` -The import above is the supported ESSOS compatibility API. The refactor is -introducing the canonical immutable form: +`solution` is an immutable JAX pytree. Vector samples use shape `(nphi, 3)`, +and tensor samples use `(nphi, 3, 3)`. JIT, VMAP, JVP, and VJP act on explicit +array arguments, while the nonlinear sigma solution is differentiated +implicitly at its converged root. + +The supported ESSOS compatibility API remains: ```python -import pyqsc_jax as qsc +from pyqsc_jax.near_axis import near_axis -configuration = qsc.Qsc( +field = near_axis( rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3, etabar=-0.9, - order="r2", ) ``` -That API will become the primary quickstart once its first- and second-order -validation gates are green. +The adapter preserves historical component-axis ordering and mutable +`field.x`/`field.dofs` behavior for ESSOS, but delegates its physics to the +immutable core. -The lower-level immutable axis API is already available: +The lower-level immutable axis API supports general, not necessarily +stellarator-symmetric Fourier axes: ```python import pyqsc_jax as qsc diff --git a/docs/api/first-order.md b/docs/api/first-order.md new file mode 100644 index 0000000..884de57 --- /dev/null +++ b/docs/api/first-order.md @@ -0,0 +1,36 @@ +# First-order API + +```{eval-rst} +.. autofunction:: pyqsc_jax.Qsc +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.solve +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.NearAxisInputs + :members: +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.NearAxisSolution + :members: +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.RootSolveOptions + :members: +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.RootSolveReport + :members: +``` + +## ESSOS compatibility + +```{eval-rst} +.. autoclass:: pyqsc_jax.near_axis.near_axis + :members: +``` diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index ae4ffd1..73e60b3 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -7,8 +7,8 @@ to the cited source, not to a duplicated derivation in this repository. | Physics block | Primary source | Reference implementation | Required validation | Status | | --- | --- | --- | --- | --- | | General Fourier axis and Frenet frame | Landreman & Sengupta (2018), arXiv:1809.10233 | `Axis`, `evaluate_axis`, `compute_axis_geometry`; pyQSC `init_axis.py` | analytic circle; asymmetric Fortran curvature/torsion/varphi; frame identities; JIT/VMAP/grad | implemented and documented | -| First-order QS and sigma equation | Landreman & Sengupta (2019), arXiv:1908.10253 | pyQSC `solve_sigma_equation.py` | residual, convergence report, pyQSC values, JVP/VJP | baseline values only | -| Field gradient and `L_grad_B` | Landreman (2021), arXiv:2012.00865, Eq. 3.12 | pyQSC `grad_B_tensor.py` | Cartesian AD/finite differences; Maxwell identities | baseline values only | +| First-order QS and sigma equation | Landreman & Sengupta (2019), arXiv:1908.10253 | `first_order.solve_sigma`; pyQSC `solve_sigma_equation.py` | residual, convergence report, QA/QH/finite-current pyQSC values, JIT/VMAP/JVP/VJP, finite differences | implemented and documented | +| Field gradient and `L_grad_B` | Landreman (2021), arXiv:2012.00865, Eq. 3.12 | `first_order.first_order_solution`; pyQSC `grad_B_tensor.py` | upstream arrays, vacuum symmetry/divergence, resolution convergence | implemented and documented | | Complete second order | Landreman & Sengupta (2019), arXiv:1908.10253 | pyQSC `calculate_r2.py`; manuscript Eqs. 36–54 | all coefficients, operator residual, Fortran arrays, resolution convergence | not implemented | | Total field Hessian | manuscript Eqs. 55–83 | pyQSC generated tensor as comparison only | regular-coordinate chain rule, AD/finite differences, symmetry/divergence | not implemented | | Third-order flux constraint and shear | Landreman & Sengupta (2019); Rodríguez et al. shear equations | pyQSC `calculate_r3.py` | upstream r3 arrays and boundary data | not implemented | diff --git a/docs/index.md b/docs/index.md index 1ca941b..f619750 100644 --- a/docs/index.md +++ b/docs/index.md @@ -12,7 +12,9 @@ installation quickstart limitations theory/coordinates-and-conventions +theory/first-order api/axis +api/first-order ``` ```{toctree} @@ -34,9 +36,10 @@ changelog ## Project status -The immutable canonical API is under active development. The -`pyqsc_jax.near_axis.near_axis` import remains supported for ESSOS without a -runtime deprecation warning. +The immutable first-order API is validated. Complete second and third order, +inverse solves, optimization, and plasma/external field jets are under active +development. The `pyqsc_jax.near_axis.near_axis` import remains supported for +ESSOS without a runtime deprecation warning. ## References diff --git a/docs/limitations.md b/docs/limitations.md index 196a02e..f4b4cb3 100644 --- a/docs/limitations.md +++ b/docs/limitations.md @@ -1,20 +1,23 @@ # Limitations -The current released computational core is first order only. Although the -legacy constructor accepts `order`, `B2c`, and `p2`, those arguments do not yet -activate second-order physics. +The current computational core is first order only. Although the legacy +constructor accepts `order`, `B2c`, and `p2` for compatibility, those arguments +do not yet activate second-order physics. Known limitations under active refactor include: -- exactly five Newton updates without a convergence report; -- only stellarator-symmetric `rc`/`zs` axes; -- a confirmed normal/binormal unpacking defect in the mutable `dofs` setter; - no complete second- or third-order solution; - no plasma/external field-jet separation; - no branch-aware target-transform inverse solve. -Frenet coordinates are invalid when the magnetic-axis curvature vanishes. The -new geometry API will report that validity condition explicitly. +The sigma equation is solved to configurable residual and step tolerances, but +a result object is still returned after nonconvergence so callers can inspect +the structured report. Production workflows must reject +`root_report.converged == False`. + +Frenet coordinates are invalid when the magnetic-axis curvature vanishes. +`GeometryDiagnostics` reports this condition explicitly; high-level rejection +policy will be added alongside the second-order validity report. Near-axis results are asymptotic in distance from the axis. “Surface-free” plasma–coil separation does not mean radius-free: a formal minor radius or an diff --git a/docs/quickstart.md b/docs/quickstart.md index 8d8f2b7..e24d6e0 100644 --- a/docs/quickstart.md +++ b/docs/quickstart.md @@ -1,27 +1,60 @@ # Quickstart -The current compatibility entry point constructs the standard first-order -quasisymmetric solution: +The canonical immutable entry point constructs a first-order quasisymmetric +solution: ```python -from pyqsc_jax.near_axis import near_axis +import pyqsc_jax as qsc -field = near_axis( +solution = qsc.Qsc( rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3, etabar=-0.9, nphi=31, + order="r1", ) -print(field.iota) -print(field.axis_length) +print(solution.iota) +print(solution.root_report.residual_norm) +print(solution.axis_length) ``` `rc` and `zs` are the cosine coefficients of cylindrical axis radius and sine coefficients of height for a stellarator-symmetric axis. `nfp` is the number of field periods. `etabar` controls the first-order field-strength variation. -The new immutable `Axis`, `Qsc`, and `solve` API will replace this page after -its validation gates are complete. The legacy import will remain as an -adapter for ESSOS. +For a general asymmetric axis, construct `Axis` explicitly: + +```python +axis = qsc.Axis( + rc=[1.0, 0.04], + rs=[0.0, 0.01], + zc=[0.0, -0.015], + zs=[0.0, -0.05], + nfp=3, +) +solution = qsc.solve(axis=axis, etabar=-0.9, nphi=61) +``` + +The result is an immutable JAX pytree. Its vector samples have shape +`(nphi, 3)` and its tensor samples have shape `(nphi, 3, 3)`. Always inspect +`solution.root_report.converged` and the residual norm when accepting a +configuration. + +ESSOS code can continue to use: + +```python +from pyqsc_jax.near_axis import near_axis + +field = near_axis( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, +) +``` + +The adapter retains the legacy `(3, nphi)` field and `(3, 3, nphi)` gradient +orientations plus mutable `x`/`dofs`; it delegates calculations to the same +immutable core. diff --git a/docs/theory/first-order.md b/docs/theory/first-order.md new file mode 100644 index 0000000..86a35a0 --- /dev/null +++ b/docs/theory/first-order.md @@ -0,0 +1,132 @@ +# First-order quasisymmetric construction + +## Inputs and signs + +The first-order solve uses the direct-construction conventions of +{cite}`landreman2019highorder`. The leading field strength is `B0`; `sG` is +the sign of \(G_0\), and `spsi` is the sign of toroidal flux. The axis geometry +provides \(\kappa\), \(\tau\), \(\varphi\), and + +\[ +\frac{|G_0|}{B_0} = \frac{L}{2\pi}. +\] + +`frame_helicity` is the signed winding of the Frenet normal over one field +period. The sign-adjusted helicity and transform entering the sigma equation +are + +\[ +N = h\,s_\psi s_G, +\qquad +\iota_N = \iota + N n_{\mathrm{fp}}. +\] + +This convention gives \(N=0\) for the standard QA example and \(N=-1\) for +the documented four-field-period QH example when `spsi = sG = 1`. + +## Periodic sigma equation + +For prescribed \(\bar\eta\), the unknown state contains the rotational +transform in its first slot and samples of the periodic function +\(\sigma(\varphi)\) in the remaining slots. The first sigma sample is replaced +by the prescribed `sigma0`, which removes the otherwise redundant degree of +freedom. The collocation residual is + +\[ +\frac{\mathrm d\sigma}{\mathrm d\varphi} ++ \iota_N +\left[ +1 + \sigma^2 ++ \left(\frac{\bar\eta^2}{\kappa^2}\right)^2 +\right] +-2\frac{\bar\eta^2}{\kappa^2} +\left(-s_\psi\tau + \frac{I_2}{B_0}\right) +\frac{s_G|G_0|}{B_0} +=0. +\] + +Fourier collocation differentiates the periodic array. A damped dense Newton +solve uses the exact JAX Jacobian, residual-based backtracking, a step +stagnation test, and configurable absolute/relative tolerances. It returns a +`RootSolveReport` containing: + +- initial and final infinity-norm residuals; +- the effective residual tolerance and final step norm; +- Newton and accumulated backtracking counts; +- final Jacobian condition number; +- convergence, finiteness, and stagnation flags. + +Reaching an iteration or stagnation limit does not silently certify a +solution. The numerical candidate and a false convergence flag are returned +so batched workflows can apply their own rejection policy. + +## Implicit differentiation + +The converged candidate is supplied to SOLVAX's custom root wrapper after +`stop_gradient`. JVPs and VJPs therefore differentiate + +\[ +F(x,p)=0, +\qquad +\frac{\mathrm dx}{\mathrm dp} += +-\left(\frac{\partial F}{\partial x}\right)^{-1} +\frac{\partial F}{\partial p}, +\] + +not the sequence of Newton iterates. Tests compare JVP and VJP, finite +differences in \(\bar\eta\) and an axis Fourier coefficient, eager/JIT +evaluation, and VMAP batches. + +## First-order surface and field jet + +The Frenet-plane coefficients are + +\[ +X_{1s}=0,\qquad +X_{1c}=\frac{\bar\eta}{\kappa},\qquad +Y_{1s}=\frac{s_Gs_\psi\kappa}{\bar\eta},\qquad +Y_{1c}=\sigma Y_{1s}. +\] + +They are also provided in an untwisted frame for boundary conversion. The +solution contains the on-axis field in cylindrical and Cartesian bases, the +Cartesian and cylindrical field-gradient tensors, elongation, and + +\[ +L_{\nabla B} += B_0\sqrt{\frac{2}{\nabla\boldsymbol B:\nabla\boldsymbol B}}. +\] + +Canonical arrays use a leading sample axis. Thus `B_axis.shape == +(nphi, 3)` and `grad_B_axis.shape == (nphi, 3, 3)`. The ESSOS adapter preserves +the historical transposed layouts. In the vacuum limit, resolution studies +verify the trace-free and symmetric gradient identities spectrally. + +## Reference configuration + +For + +```python +import pyqsc_jax as qsc + +solution = qsc.Qsc( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + nphi=31, +) +``` + +the validated result is + +\[ +\iota = 0.41830690943386617, +\qquad +L = 6.340238817434161. +\] + +The sigma array, QA/QH topology, finite-current result, on-axis field, and +field gradient agree with pyQSC at the audited upstream revision recorded in +the refactor baseline. diff --git a/pyproject.toml b/pyproject.toml index 6395a8e..8234648 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -57,8 +57,6 @@ path = "src/pyqsc_jax/__init__.py" packages = ["src/pyqsc_jax"] [tool.ruff] -# Removed when the immutable core replaces this audited compatibility monolith. -exclude = ["src/pyqsc_jax/near_axis.py"] line-length = 100 src = ["src", "tests"] diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index 8e1054e..29607ac 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -1,7 +1,19 @@ """Differentiable near-axis stellarator construction in JAX.""" from pyqsc_jax.axis import Axis +from pyqsc_jax.first_order import Qsc, solve +from pyqsc_jax.models import NearAxisInputs, NearAxisSolution, RootSolveReport from pyqsc_jax.near_axis import near_axis +from pyqsc_jax.solvers import RootSolveOptions -__all__ = ["Axis", "near_axis"] +__all__ = [ + "Axis", + "NearAxisInputs", + "NearAxisSolution", + "Qsc", + "RootSolveOptions", + "RootSolveReport", + "near_axis", + "solve", +] __version__ = "0.2.0.dev0" diff --git a/src/pyqsc_jax/first_order.py b/src/pyqsc_jax/first_order.py new file mode 100644 index 0000000..44f5a45 --- /dev/null +++ b/src/pyqsc_jax/first_order.py @@ -0,0 +1,269 @@ +"""First-order quasisymmetric near-axis construction.""" + +from typing import Any + +import jax +import jax.numpy as jnp + +from pyqsc_jax.axis import Axis +from pyqsc_jax.geometry import AxisGeometry, compute_axis_geometry +from pyqsc_jax.models import NearAxisInputs, NearAxisSolution, RootSolveReport +from pyqsc_jax.solvers import DEFAULT_ROOT_OPTIONS, RootSolveOptions, implicit_dense_root + +ArrayLike = Any + + +def sigma_from_state(state: ArrayLike, sigma0: ArrayLike) -> jax.Array: + """Replace the state-vector iota slot by the prescribed ``sigma(0)``.""" + + return jnp.asarray(state).at[0].set(jnp.asarray(sigma0)) + + +def sigma_residual( + state: ArrayLike, + *, + inputs: NearAxisInputs, + geometry: AxisGeometry, +) -> jax.Array: + """Periodic first-order sigma-equation residual.""" + + state = jnp.asarray(state) + sigma = sigma_from_state(state, inputs.sigma0) + iota = state[0] + helicity = geometry.frame_helicity * inputs.spsi * inputs.sG + iotaN = iota + helicity * inputs.axis.nfp + eta_over_curvature_squared = inputs.etabar**2 / geometry.curvature**2 + G0_over_B0 = inputs.sG * geometry.abs_G0_over_B0 + return ( + geometry.d_d_varphi @ sigma + + iotaN * (eta_over_curvature_squared**2 + 1 + sigma**2) + - 2 + * eta_over_curvature_squared + * (-inputs.spsi * geometry.torsion + inputs.I2 / inputs.B0) + * G0_over_B0 + ) + + +def solve_sigma( + inputs: NearAxisInputs, + geometry: AxisGeometry, + *, + root_options: RootSolveOptions = DEFAULT_ROOT_OPTIONS, +) -> tuple[jax.Array, jax.Array, RootSolveReport]: + """Solve for periodic sigma and rotational transform.""" + + initial_state = jnp.full((inputs.nphi,), inputs.sigma0) + initial_state = initial_state.at[0].set(0.0) + residual_function = lambda state: sigma_residual( # noqa: E731 + state, + inputs=inputs, + geometry=geometry, + ) + state, report = implicit_dense_root( + residual_function, + initial_state, + options=root_options, + ) + return sigma_from_state(state, inputs.sigma0), state[0], report + + +def _assemble_gradient( + tangent: jax.Array, + normal: jax.Array, + binormal: jax.Array, + *, + nn: jax.Array, + bn: jax.Array, + nb: jax.Array, + bb: jax.Array, + tn: jax.Array, + nt: jax.Array, + tt: jax.Array, +) -> jax.Array: + outer = lambda left, right: jnp.einsum("ni,nj->nij", left, right) # noqa: E731 + return ( + nn[:, None, None] * outer(normal, normal) + + bn[:, None, None] * outer(binormal, normal) + + nb[:, None, None] * outer(normal, binormal) + + bb[:, None, None] * outer(binormal, binormal) + + tn[:, None, None] * outer(tangent, normal) + + nt[:, None, None] * outer(normal, tangent) + + tt[:, None, None] * outer(tangent, tangent) + ) + + +def first_order_solution( + inputs: NearAxisInputs, + geometry: AxisGeometry, + sigma: jax.Array, + iota: jax.Array, + root_report: RootSolveReport, +) -> NearAxisSolution: + """Assemble first-order shape coefficients, fields, and diagnostics.""" + + helicity = geometry.frame_helicity * inputs.spsi * inputs.sG + iotaN = iota + helicity * inputs.axis.nfp + G0 = inputs.sG * geometry.abs_G0_over_B0 * inputs.B0 + X1s = jnp.zeros_like(geometry.curvature) + X1c = inputs.etabar / geometry.curvature + Y1s = inputs.sG * inputs.spsi * geometry.curvature / inputs.etabar + Y1c = inputs.sG * inputs.spsi * geometry.curvature * sigma / inputs.etabar + + untwisting_angle = -helicity * inputs.axis.nfp * geometry.varphi + sine = jnp.sin(untwisting_angle) + cosine = jnp.cos(untwisting_angle) + X1s_untwisted = X1s * cosine + X1c * sine + X1c_untwisted = -X1s * sine + X1c * cosine + Y1s_untwisted = Y1s * cosine + Y1c * sine + Y1c_untwisted = -Y1s * sine + Y1c * cosine + + p = X1s**2 + X1c**2 + Y1s**2 + Y1c**2 + q = X1s * Y1c - X1c * Y1s + elongation = (p + jnp.sqrt(p**2 - 4 * q**2)) / (2 * jnp.abs(q)) + mean_elongation = jnp.sum(elongation * geometry.d_l_d_phi) / jnp.sum(geometry.d_l_d_phi) + + d_X1c_d_varphi = geometry.d_d_varphi @ X1c + d_Y1s_d_varphi = geometry.d_d_varphi @ Y1s + d_Y1c_d_varphi = geometry.d_d_varphi @ Y1c + factor = inputs.spsi * inputs.B0 / geometry.abs_G0_over_B0 + tn = inputs.sG * inputs.B0 * geometry.curvature + nt = tn + bb = factor * (X1c * d_Y1s_d_varphi - iotaN * X1c * Y1c) + nn = factor * (d_X1c_d_varphi * Y1s + iotaN * X1c * Y1c) + bn = factor * ( + -inputs.sG * inputs.spsi * geometry.abs_G0_over_B0 * geometry.torsion - iotaN * X1c**2 + ) + nb = factor * ( + d_Y1c_d_varphi * Y1s + - d_Y1s_d_varphi * Y1c + + inputs.sG * inputs.spsi * geometry.abs_G0_over_B0 * geometry.torsion + + iotaN * (Y1s**2 + Y1c**2) + ) + tt = jnp.zeros_like(tn) + grad_B_axis_cylindrical = _assemble_gradient( + geometry.tangent_cylindrical, + geometry.normal_cylindrical, + geometry.binormal_cylindrical, + nn=nn, + bn=bn, + nb=nb, + bb=bb, + tn=tn, + nt=nt, + tt=tt, + ) + grad_B_axis = _assemble_gradient( + geometry.tangent_cartesian, + geometry.normal_cartesian, + geometry.binormal_cartesian, + nn=nn, + bn=bn, + nb=nb, + bb=bb, + tn=tn, + nt=nt, + tt=tt, + ) + grad_B_frobenius_squared = jnp.sum(grad_B_axis**2, axis=(-2, -1)) + L_grad_B = inputs.B0 * jnp.sqrt(2 / grad_B_frobenius_squared) + B_axis_cylindrical = inputs.sG * inputs.B0 * geometry.tangent_cylindrical + B_axis = inputs.sG * inputs.B0 * geometry.tangent_cartesian + + return NearAxisSolution( + inputs=inputs, + geometry=geometry, + root_report=root_report, + sigma=sigma, + iota=iota, + iotaN=iotaN, + helicity=helicity, + G0=G0, + X1s=X1s, + X1c=X1c, + Y1s=Y1s, + Y1c=Y1c, + X1s_untwisted=X1s_untwisted, + X1c_untwisted=X1c_untwisted, + Y1s_untwisted=Y1s_untwisted, + Y1c_untwisted=Y1c_untwisted, + elongation=elongation, + mean_elongation=mean_elongation, + B_axis_cylindrical=B_axis_cylindrical, + B_axis=B_axis, + grad_B_axis_cylindrical=grad_B_axis_cylindrical, + grad_B_axis=grad_B_axis, + L_grad_B=L_grad_B, + ) + + +def _normalize_order(order: int | str) -> int: + if order in (1, "r1"): + return 1 + if order in (2, "r2", 3, "r3"): + raise NotImplementedError("Second- and third-order solves are not implemented yet.") + raise ValueError("order must be 1, 2, 3, 'r1', 'r2', or 'r3'.") + + +def solve( + *, + axis: Axis, + etabar: ArrayLike, + B0: ArrayLike = 1.0, + sigma0: ArrayLike = 0.0, + I2: ArrayLike = 0.0, + p2: ArrayLike = 0.0, + B2c: ArrayLike = 0.0, + B2s: ArrayLike = 0.0, + nphi: int = 61, + order: int | str = 1, + sG: int = 1, + spsi: int = 1, + solve_for: str = "iota", + root_options: RootSolveOptions = DEFAULT_ROOT_OPTIONS, +) -> NearAxisSolution: + """Construct an immutable near-axis solution. + + Only standard first-order ``etabar -> iota`` mode is enabled in this + milestone. Other validated modes are added without changing this entry + point. + """ + + normalized_order = _normalize_order(order) + if solve_for != "iota": + raise NotImplementedError("Inverse near-axis solve modes are not implemented yet.") + inputs = NearAxisInputs( + axis=axis, + etabar=etabar, + B0=B0, + sigma0=sigma0, + I2=I2, + p2=p2, + B2c=B2c, + B2s=B2s, + nphi=nphi, + order=normalized_order, + sG=sG, + spsi=spsi, + solve_for=solve_for, + ) + geometry = compute_axis_geometry(axis, nphi=nphi) + sigma, iota, root_report = solve_sigma( + inputs, + geometry, + root_options=root_options, + ) + return first_order_solution(inputs, geometry, sigma, iota, root_report) + + +def Qsc( + rc: ArrayLike, + zs: ArrayLike, + *, + rs: ArrayLike = (), + zc: ArrayLike = (), + nfp: int = 1, + **kwargs: Any, +) -> NearAxisSolution: + """pyQSC-familiar convenience constructor for the immutable solution.""" + + return solve(axis=Axis(rc=rc, rs=rs, zc=zc, zs=zs, nfp=nfp), **kwargs) diff --git a/src/pyqsc_jax/models.py b/src/pyqsc_jax/models.py index 8d6420c..8914c4f 100644 --- a/src/pyqsc_jax/models.py +++ b/src/pyqsc_jax/models.py @@ -1,8 +1,17 @@ """Small immutable result and diagnostic models.""" -from dataclasses import dataclass +from __future__ import annotations + +from dataclasses import dataclass, field +from typing import TYPE_CHECKING import jax +import jax.numpy as jnp + +from pyqsc_jax.axis import Axis + +if TYPE_CHECKING: + from pyqsc_jax.geometry import AxisGeometry @jax.tree_util.register_dataclass @@ -17,3 +26,123 @@ class GeometryDiagnostics: minimum_frame_determinant: jax.Array frenet_valid: jax.Array cylindrical_coordinates_valid: jax.Array + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class RootSolveReport: + """Convergence evidence for a nonlinear root solve.""" + + initial_residual_norm: jax.Array + residual_norm: jax.Array + tolerance: jax.Array + step_norm: jax.Array + iterations: jax.Array + backtracking_steps: jax.Array + jacobian_condition_number: jax.Array + converged: jax.Array + finite: jax.Array + stagnated: jax.Array + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class NearAxisInputs: + """Normalized immutable inputs to a near-axis solve.""" + + axis: Axis + etabar: jax.Array + B0: jax.Array = 1.0 + sigma0: jax.Array = 0.0 + I2: jax.Array = 0.0 + p2: jax.Array = 0.0 + B2c: jax.Array = 0.0 + B2s: jax.Array = 0.0 + nphi: int = field(default=61, metadata={"static": True}) + order: int = field(default=1, metadata={"static": True}) + sG: int = field(default=1, metadata={"static": True}) + spsi: int = field(default=1, metadata={"static": True}) + solve_for: str = field(default="iota", metadata={"static": True}) + + def __post_init__(self) -> None: + if not isinstance(self.nphi, int) or isinstance(self.nphi, bool) or self.nphi < 3: + raise ValueError("nphi must be an integer >= 3.") + if self.order not in (1, 2, 3): + raise ValueError("order must be 1, 2, or 3.") + if self.sG not in (-1, 1): + raise ValueError("sG must be +1 or -1.") + if self.spsi not in (-1, 1): + raise ValueError("spsi must be +1 or -1.") + if self.solve_for not in ("iota", "etabar", "I2"): + raise ValueError("solve_for must be 'iota', 'etabar', or 'I2'.") + for name in ("etabar", "B0", "sigma0", "I2", "p2", "B2c", "B2s"): + value = jnp.asarray(getattr(self, name)) + if value.ndim: + raise ValueError(f"{name} must be a scalar.") + object.__setattr__(self, name, value) + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class NearAxisSolution: + """Canonical immutable near-axis solution. + + Sampled vector arrays use a leading ``nphi`` axis. Vector components are + Cartesian unless a field name explicitly contains ``cylindrical``. + """ + + inputs: NearAxisInputs + geometry: AxisGeometry + root_report: RootSolveReport + sigma: jax.Array + iota: jax.Array + iotaN: jax.Array + helicity: jax.Array + G0: jax.Array + X1s: jax.Array + X1c: jax.Array + Y1s: jax.Array + Y1c: jax.Array + X1s_untwisted: jax.Array + X1c_untwisted: jax.Array + Y1s_untwisted: jax.Array + Y1c_untwisted: jax.Array + elongation: jax.Array + mean_elongation: jax.Array + B_axis_cylindrical: jax.Array + B_axis: jax.Array + grad_B_axis_cylindrical: jax.Array + grad_B_axis: jax.Array + L_grad_B: jax.Array + + @property + def axis(self) -> Axis: + return self.inputs.axis + + @property + def phi(self) -> jax.Array: + return self.geometry.samples.phi + + @property + def varphi(self) -> jax.Array: + return self.geometry.varphi + + @property + def R0(self) -> jax.Array: + return self.geometry.samples.R + + @property + def Z0(self) -> jax.Array: + return self.geometry.samples.Z + + @property + def curvature(self) -> jax.Array: + return self.geometry.curvature + + @property + def torsion(self) -> jax.Array: + return self.geometry.torsion + + @property + def axis_length(self) -> jax.Array: + return self.geometry.axis_length diff --git a/src/pyqsc_jax/near_axis.py b/src/pyqsc_jax/near_axis.py index 8b4ed42..ee27a40 100644 --- a/src/pyqsc_jax/near_axis.py +++ b/src/pyqsc_jax/near_axis.py @@ -1,511 +1,571 @@ -"""Legacy mutable near-axis interface. +"""ESSOS-compatible mutable facade over the immutable near-axis core.""" -This module is retained while the immutable computational core is introduced. -The public import path is a hard ESSOS compatibility contract. -""" +from __future__ import annotations + +from typing import Any import jax import jax.numpy as jnp -from jax import jit, jacfwd, grad, vmap, tree_util, lax -from functools import partial - -class near_axis(): - def __init__(self, rc=jnp.array([1, 0.1]), zs=jnp.array([0, 0.1]), etabar=1.0, - B0=1, sigma0=0, I2=0, nphi=31, spsi=1, sG=1, nfp=2, order='r1', B2c=0, p2=0): - assert nphi % 2 == 1, 'nphi must be odd' - self.rc = jnp.array(rc) - self.zs = jnp.array(zs) - self.etabar = etabar + +from pyqsc_jax.axis import Axis +from pyqsc_jax.first_order import solve +from pyqsc_jax.models import NearAxisSolution +from pyqsc_jax.solvers import implicit_dense_root + +ArrayLike = Any + + +class near_axis: # noqa: N801 + """Compatibility adapter for the historical ``near_axis`` interface. + + The canonical API is :func:`pyqsc_jax.solve`. This class intentionally + keeps ESSOS's mutable ``x``/``dofs`` facade and historical component-axis + ordering while delegating all near-axis physics to the immutable core. + """ + + def __init__( + self, + rc: ArrayLike = (1.0, 0.1), + zs: ArrayLike = (0.0, 0.1), + etabar: ArrayLike = 1.0, + B0: ArrayLike = 1.0, + sigma0: ArrayLike = 0.0, + I2: ArrayLike = 0.0, + nphi: int = 31, + spsi: int = 1, + sG: int = 1, + nfp: int = 2, + order: int | str = "r1", + B2c: ArrayLike = 0.0, + p2: ArrayLike = 0.0, + ) -> None: + if not isinstance(nphi, int) or isinstance(nphi, bool) or nphi < 3 or nphi % 2 == 0: + raise ValueError("The compatibility API requires odd integer nphi >= 3.") + + self.rc = jnp.asarray(rc) + self.zs = jnp.asarray(zs) + if self.rc.ndim != 1 or self.zs.ndim != 1 or self.rc.size != self.zs.size: + raise ValueError("rc and zs must be one-dimensional arrays of equal length.") + self.etabar = jnp.asarray(etabar) + self.B0 = jnp.asarray(B0) + self.sigma0 = jnp.asarray(sigma0) + self.I2 = jnp.asarray(I2) + self.p2 = jnp.asarray(p2) + self.B2c = jnp.asarray(B2c) self.nphi = nphi - self.sigma0 = sigma0 - self.I2 = I2 self.spsi = spsi self.sG = sG - self.B0 = B0 self.nfp = nfp - self.order = order - self.B2c = B2c - self.p2 = p2 - - self._dofs = jnp.concatenate((jnp.ravel(self.rc), jnp.ravel(self.zs), jnp.array([etabar]))) - - self.phi = jnp.linspace(0, 2 * jnp.pi / self.nfp, self.nphi, endpoint=False) - self.nfourier = max(len(self.rc), len(self.zs)) - - parameters = self.calculate(self.rc, self.zs, self.etabar) - (self.R0, self.Z0, self.sigma, self.elongation, self.B_axis, self.grad_B_axis, self.axis_length, self.iota, self.iotaN, self.G0, - self.helicity, self.X1c_untwisted, self.X1s_untwisted, self.Y1s_untwisted, self.Y1c_untwisted, - self.normal_R, self.normal_phi, self.normal_z, self.binormal_R, self.binormal_phi, self.binormal_z, - self.L_grad_B, self.inv_L_grad_B, self.torsion, self.curvature, self.varphi, self.R0p, self.Z0p) = parameters + self.order = order + self.nfourier = self.rc.size + self._dofs = jnp.concatenate((self.rc, self.zs, self.etabar[None])) + self._refresh() + + def _canonical_solution( + self, + rc: ArrayLike, + zs: ArrayLike, + etabar: ArrayLike, + ) -> NearAxisSolution: + # Until r2/r3 milestones land, preserve the legacy behavior in which + # those labels still returned the first-order subset. + return solve( + axis=Axis.stellarator_symmetric(rc=rc, zs=zs, nfp=self.nfp), + etabar=etabar, + B0=self.B0, + sigma0=self.sigma0, + I2=self.I2, + p2=self.p2, + B2c=self.B2c, + nphi=self.nphi, + order="r1", + sG=self.sG, + spsi=self.spsi, + ) + + @staticmethod + def _legacy_tuple(solution: NearAxisSolution) -> tuple[jax.Array, ...]: + geometry = solution.geometry + normal = geometry.normal_cylindrical + binormal = geometry.binormal_cylindrical + return ( + solution.R0, + solution.Z0, + solution.sigma, + solution.elongation, + solution.B_axis.T, + solution.grad_B_axis.T, + solution.axis_length, + solution.iota, + solution.iotaN, + solution.G0, + solution.helicity, + solution.X1c_untwisted, + solution.X1s_untwisted, + solution.Y1s_untwisted, + solution.Y1c_untwisted, + normal[:, 0], + normal[:, 1], + normal[:, 2], + binormal[:, 0], + binormal[:, 1], + binormal[:, 2], + solution.L_grad_B, + 1 / solution.L_grad_B, + solution.torsion, + solution.curvature, + solution.varphi, + geometry.samples.d_R_d_phi, + geometry.samples.d_Z_d_phi, + ) + + def _refresh(self) -> None: + solution = self._canonical_solution(self.rc, self.zs, self.etabar) + self.solution = solution + self.phi = solution.phi + ( + self.R0, + self.Z0, + self.sigma, + self.elongation, + self.B_axis, + self.grad_B_axis, + self.axis_length, + self.iota, + self.iotaN, + self.G0, + self.helicity, + self.X1c_untwisted, + self.X1s_untwisted, + self.Y1s_untwisted, + self.Y1c_untwisted, + self.normal_R, + self.normal_phi, + self.normal_z, + self.binormal_R, + self.binormal_phi, + self.binormal_z, + self.L_grad_B, + self.inv_L_grad_B, + self.torsion, + self.curvature, + self.varphi, + self.R0p, + self.Z0p, + ) = self._legacy_tuple(solution) @property - def dofs(self): + def dofs(self) -> jax.Array: + """Mutable legacy degrees of freedom ordered ``rc, zs, etabar``.""" + return self._dofs - + @dofs.setter - def dofs(self, new_dofs): - self._dofs = jnp.array(new_dofs) - self.rc = self._dofs[:self.nfourier] - self.zs = self._dofs[self.nfourier:2*self.nfourier] - self.etabar = self._dofs[-1] - parameters = self.calculate(self.rc, self.zs, self.etabar) - (self.R0, self.Z0, self.sigma, self.elongation, self.B_axis, self.grad_B_axis, self.axis_length, self.iota, self.iotaN, self.G0, - self.helicity, self.X1c_untwisted, self.X1s_untwisted, self.Y1s_untwisted, self.Y1c_untwisted, - self.normal_R, self.normal_z, self.normal_phi, self.binormal_R, self.binormal_z, self.binormal_phi, - self.L_grad_B, self.inv_L_grad_B, self.torsion, self.curvature, self.varphi, self.R0p, self.Z0p) = parameters + def dofs(self, new_dofs: ArrayLike) -> None: + new_dofs = jnp.asarray(new_dofs) + if new_dofs.ndim != 1 or new_dofs.size != 2 * self.nfourier + 1: + raise ValueError(f"dofs must have shape ({2 * self.nfourier + 1},).") + self._dofs = new_dofs + self.rc = new_dofs[: self.nfourier] + self.zs = new_dofs[self.nfourier : 2 * self.nfourier] + self.etabar = new_dofs[-1] + self._refresh() @property - def x(self): - return self._dofs - + def x(self) -> jax.Array: + """Alias for :attr:`dofs`, retained for ESSOS optimizers.""" + + return self.dofs + @x.setter - def x(self, new_x): + def x(self, new_x: ArrayLike) -> None: self.dofs = new_x - + def _tree_flatten(self): - children = (self.rc, self.zs, self.etabar, self.B0, self.sigma0, self.I2) - aux_data = {"nphi": self.nphi, "spsi": self.spsi, "sG": self.sG, - "nfp": self.nfp, "order": self.order, "B2c": self.B2c, "p2": self.p2} - return (children, aux_data) + children = ( + self.rc, + self.zs, + self.etabar, + self.B0, + self.sigma0, + self.I2, + self.B2c, + self.p2, + ) + auxiliary = { + "nphi": self.nphi, + "spsi": self.spsi, + "sG": self.sG, + "nfp": self.nfp, + "order": self.order, + } + return children, auxiliary @classmethod - def _tree_unflatten(cls, aux_data, children): - return cls(*children, **aux_data) - - @partial(jit, static_argnames=['self']) - def B_covariant(self, points): - r, theta, phi = points - Br = 0 - Btheta = r*r*self.I2 - Bphi = self.G0 - return jnp.array([Br, Btheta, Bphi]) - - @partial(jit, static_argnames=['self']) - def B_contravariant(self, points): - r, theta, phi = points - jac = self.jacobian(points) - AbsB = self.AbsB(points) - Bphi = r*AbsB/jac - return jnp.array([0, self.iotaN * Bphi, Bphi]) - - @partial(jit, static_argnames=['self']) - def AbsB(self, points): - r, theta, phi = points - return self.B0*(1 + r*self.etabar*jnp.cos(theta)) - - @partial(jit, static_argnames=['self']) - def jacobian(self, points): - r, theta, phi = points - AbsB = self.AbsB(points) - return r*self.B0*(self.G0+self.iota*self.I2)/(AbsB*AbsB) - - @partial(jit, static_argnames=['self']) - def calculate(self, rc, zs, etabar): - phi = self.phi - nphi = self.nphi - nfp = self.nfp - nfourier = self.nfourier - spsi = self.spsi - sG = self.sG - B0 = self.B0 - sigma0 = self.sigma0 - I2 = self.I2 - d_phi = phi[1] - phi[0] - - n_values = jnp.arange(nfourier) * nfp - - @jit - def compute_terms(jn): - n = n_values[jn] - sinangle = jnp.sin(n * phi) - cosangle = jnp.cos(n * phi) - return jnp.array([rc[jn] * cosangle, zs[jn] * sinangle, - rc[jn] * (-n * sinangle), zs[jn] * (n * cosangle), - rc[jn] * (-n * n * cosangle), zs[jn] * (-n * n * sinangle), - rc[jn] * (n * n * n * sinangle), zs[jn] * (-n * n * n * cosangle)]) - - @jit - def spectral_diff_matrix_jax(): - n=nphi - xmin=0 - xmax=2 * jnp.pi / nfp - h = 2 * jnp.pi / n - kk = jnp.arange(1, n) - n_half = n // 2 - topc = 1 / jnp.sin(jnp.arange(1, n_half + 1) * h / 2) - temp = jnp.concatenate((topc, jnp.flip(topc[:n_half]))) - col1 = jnp.concatenate((jnp.array([0]), 0.5 * ((-1) ** kk) * temp)) - row1 = -col1 - vals = jnp.concatenate((row1[-1:0:-1], col1)) - a, b = jnp.ogrid[0:len(col1), len(row1)-1:-1:-1] - return 2 * jnp.pi / (xmax - xmin) * vals[a + b] - - @jit - def determine_helicity(normal_cylindrical): - x_positive = normal_cylindrical[:, 0] >= 0 - z_positive = normal_cylindrical[:, 2] >= 0 - quadrant = 1 * x_positive * z_positive + 2 * (~x_positive) * z_positive \ - + 3 * (~x_positive) * (~z_positive) + 4 * x_positive * (~z_positive) - quadrant = jnp.append(quadrant, quadrant[0]) - delta_quadrant = quadrant[1:] - quadrant[:-1] - increment = jnp.sum((quadrant[:-1] == 4) & (quadrant[1:] == 1)) - decrement = jnp.sum((quadrant[:-1] == 1) & (quadrant[1:] == 4)) - return (jnp.sum(delta_quadrant) + increment - decrement) * spsi * sG - - summed_values = jnp.sum(jax.vmap(compute_terms)(jnp.arange(nfourier)), axis=0) - - R0, Z0, R0p, Z0p, R0pp, Z0pp, R0ppp, Z0ppp = summed_values - d_l_d_phi = jnp.sqrt(R0 * R0 + R0p * R0p + Z0p * Z0p) - d2_l_d_phi2 = (R0 * R0p + R0p * R0pp + Z0p * Z0pp) / d_l_d_phi - B0_over_abs_G0 = nphi / jnp.sum(d_l_d_phi) - abs_G0_over_B0 = 1 / B0_over_abs_G0 - d_l_d_varphi = abs_G0_over_B0 - G0 = sG * abs_G0_over_B0 * B0 - - d_r_d_phi_cylindrical = jnp.stack([R0p, R0, Z0p]).T - d2_r_d_phi2_cylindrical = jnp.stack([R0pp - R0, 2 * R0p, Z0pp]).T - d3_r_d_phi3_cylindrical = jnp.stack([R0ppp - 3 * R0p, 3 * R0pp - R0, Z0ppp]).T - - d_tangent_d_l_cylindrical = (-d_r_d_phi_cylindrical * d2_l_d_phi2[:, None] / d_l_d_phi[:, None] \ - +d2_r_d_phi2_cylindrical) / (d_l_d_phi[:, None] * d_l_d_phi[:, None]) - curvature = jnp.sqrt(jnp.sum(d_tangent_d_l_cylindrical**2, axis=1)) - axis_length = jnp.sum(d_l_d_phi) * d_phi * nfp - varphi = jnp.concatenate([jnp.zeros(1), jnp.cumsum(d_l_d_phi[:-1] + d_l_d_phi[1:])]) * (0.5 * d_phi * 2 * jnp.pi / axis_length) - - tangent_cylindrical = d_r_d_phi_cylindrical / d_l_d_phi[:, None] - normal_cylindrical = d_tangent_d_l_cylindrical / curvature[:, None] - binormal_cylindrical = jnp.cross(tangent_cylindrical, normal_cylindrical) - - torsion_numerator = jnp.sum(d_r_d_phi_cylindrical * jnp.cross(d2_r_d_phi2_cylindrical, d3_r_d_phi3_cylindrical), axis=1) - torsion_denominator = jnp.sum(jnp.cross(d_r_d_phi_cylindrical, d2_r_d_phi2_cylindrical)**2, axis=1) - torsion = torsion_numerator / torsion_denominator - - d_d_phi = spectral_diff_matrix_jax() - d_varphi_d_phi = B0_over_abs_G0 * d_l_d_phi - d_d_varphi = d_d_phi / d_varphi_d_phi[:, None] - helicity = determine_helicity(normal_cylindrical) - - @jit - def replace_first_element(x, new_value): - return jnp.concatenate([jnp.array([new_value]), x[1:]]) - - @jit - def sigma_equation_residual(x): - iota = x[0] - sigma = replace_first_element(x, sigma0) - etaOcurv2 = etabar**2 / curvature**2 - return jnp.matmul(d_d_varphi, sigma) \ - + (iota + helicity * nfp) * (etaOcurv2**2 + 1 + sigma**2) \ - - 2 * etaOcurv2 * (-spsi * torsion + I2 / B0) * G0 / B0 - - @jit - def sigma_equation_jacobian(x): - iota = x[0] - sigma = replace_first_element(x, sigma0) - etaOcurv2 = etabar**2 / curvature**2 - jac = d_d_varphi + (iota + helicity * nfp) * 2 * jnp.diag(sigma) - return jac.at[:, 0].set(etaOcurv2**2 + 1 + sigma**2) - - @partial(jit, static_argnums=(1,)) - def newton(x0, niter=5): - def body_fun(i, x): - residual = sigma_equation_residual(x) - jacobian = sigma_equation_jacobian(x) - step = jax.scipy.linalg.solve(jacobian, -residual) - return x + step - x = jax.lax.fori_loop(0, niter, body_fun, x0) - return x - - x0 = jnp.full(nphi, sigma0) - x0 = replace_first_element(x0, 0.) - sigma = newton(x0) - iota = sigma[0] - iotaN = iota + helicity * nfp - sigma = replace_first_element(sigma, sigma0) - - X1c = etabar / curvature - Y1s = sG * spsi * curvature / etabar - Y1c = sG * spsi * curvature * sigma / etabar - p = + X1c * X1c + Y1s * Y1s + Y1c * Y1c - q = - X1c * Y1s - elongation = (p + jnp.sqrt(p * p - 4 * q * q)) / (2 * jnp.abs(q)) - - B_axis_cylindrical = sG * B0 * tangent_cylindrical.T - B_x = jnp.cos(phi) * B_axis_cylindrical[0] - jnp.sin(phi) * B_axis_cylindrical[1] - B_y = jnp.sin(phi) * B_axis_cylindrical[0] + jnp.cos(phi) * B_axis_cylindrical[1] - B_z = B_axis_cylindrical[2] - B_axis = jnp.array([B_x, B_y, B_z]) - - d_X1c_d_varphi = -etabar / curvature**2 - d_Y1s_d_varphi = jnp.matmul(d_d_varphi, Y1s) - d_Y1c_d_varphi = jnp.matmul(d_d_varphi, Y1c) - t = tangent_cylindrical.transpose() - n = normal_cylindrical.transpose() - b = binormal_cylindrical.transpose() - d_X1c_d_varphi = jnp.matmul(d_d_varphi, X1c) - d_Y1s_d_varphi = jnp.matmul(d_d_varphi, Y1s) - d_Y1c_d_varphi = jnp.matmul(d_d_varphi, Y1c) - factor = spsi * B0 / d_l_d_varphi - tn = sG * B0 * curvature - nt = tn - bb = factor * (X1c * d_Y1s_d_varphi - iotaN * X1c * Y1c) - nn = factor * (d_X1c_d_varphi * Y1s + iotaN * X1c * Y1c) - bn = factor * (-sG * spsi * d_l_d_varphi * torsion - iotaN * X1c * X1c) - nb = factor * (d_Y1c_d_varphi * Y1s - d_Y1s_d_varphi * Y1c + sG * spsi * d_l_d_varphi * torsion + iotaN * (Y1s * Y1s + Y1c * Y1c)) - tt = 0 - nablaB = jnp.array([[ - nn * n[i] * n[j] \ - + bn * b[i] * n[j] + nb * n[i] * b[j] \ - + bb * b[i] * b[j] \ - + tn * t[i] * n[j] + nt * n[i] * t[j] \ - + tt * t[i] * t[j] - for i in range(3)] for j in range(3)]) - cosphi = jnp.cos(phi) - sinphi = jnp.sin(phi) - grad_B_axis = jnp.array([ - [cosphi**2*nablaB[0, 0] - cosphi*sinphi*(nablaB[0, 1] + nablaB[1, 0]) + - sinphi**2*nablaB[1, 1], cosphi**2*nablaB[0, 1] - sinphi**2*nablaB[1, 0] + - cosphi*sinphi*(nablaB[0, 0] - nablaB[1, 1]), cosphi*nablaB[0, 2] - - sinphi*nablaB[1, 2]], [-(sinphi**2*nablaB[0, 1]) + cosphi**2*nablaB[1, 0] + - cosphi*sinphi*(nablaB[0, 0] - nablaB[1, 1]), sinphi**2*nablaB[0, 0] + - cosphi*sinphi*(nablaB[0, 1] + nablaB[1, 0]) + cosphi**2*nablaB[1, 1], - sinphi*nablaB[0, 2] + cosphi*nablaB[1, 2]], - [cosphi*nablaB[2, 0] - sinphi*nablaB[2, 1], sinphi*nablaB[2, 0] + cosphi*nablaB[2, 1], - nablaB[2, 2]] - ]) - - grad_B_colon_grad_B = tn * tn + nt * nt \ - + bb * bb + nn * nn \ - + nb * nb + bn * bn \ - + tt * tt - L_grad_B = self.B0 * jnp.sqrt(2 / grad_B_colon_grad_B) - inv_L_grad_B = 1.0 / L_grad_B - - X1c_untwisted = jnp.where(helicity == 0, X1c, X1c * jnp.cos(-helicity * nfp * varphi)) - X1s_untwisted = jnp.where(helicity == 0, 0 * X1c, X1c * jnp.sin(-helicity * nfp * varphi)) - Y1s_untwisted = jnp.where(helicity == 0, Y1s, Y1s * jnp.cos(-helicity * nfp * varphi) + Y1c * jnp.sin(-helicity * nfp * varphi)) - Y1c_untwisted = jnp.where(helicity == 0, Y1c, Y1s * (-jnp.sin(-helicity * nfp * varphi)) + Y1c * jnp.cos(-helicity * nfp * varphi)) - - normal_R = normal_cylindrical[:,0] - normal_phi = normal_cylindrical[:,1] - normal_z = normal_cylindrical[:,2] - binormal_R = binormal_cylindrical[:,0] - binormal_phi = binormal_cylindrical[:,1] - binormal_z = binormal_cylindrical[:,2] - - return (R0, Z0, sigma, elongation, B_axis, grad_B_axis, axis_length, iota, iotaN, G0, - helicity, X1c_untwisted, X1s_untwisted, Y1s_untwisted, Y1c_untwisted, - normal_R, normal_phi, normal_z, binormal_R, binormal_phi, binormal_z, - L_grad_B, inv_L_grad_B, torsion, curvature, varphi, R0p, Z0p) - - @jit - def residual_phi0_of_theta_varphi_func(self, phi_0, r, theta, varphi): - X_at_this_theta = r * (self.X1c_untwisted * jnp.cos(theta) + self.X1s_untwisted * jnp.sin(theta)) - Y_at_this_theta = r * (self.Y1c_untwisted * jnp.cos(theta) + self.Y1s_untwisted * jnp.sin(theta)) - _, _, phi = self.Frenet_to_cylindrical_1_point(phi_0, X_at_this_theta, Y_at_this_theta) - nu0 = self.interpolated_array_at_point(self.varphi-self.phi, phi_0) - X1c = self.interpolated_array_at_point(self.X1c_untwisted, phi_0) - X1s = self.interpolated_array_at_point(self.X1s_untwisted, phi_0) - Y1c = self.interpolated_array_at_point(self.Y1c_untwisted, phi_0) - Y1s = self.interpolated_array_at_point(self.Y1s_untwisted, phi_0) - bR = self.interpolated_array_at_point(self.binormal_R, phi_0) - bZ = self.interpolated_array_at_point(self.binormal_z, phi_0) - nR = self.interpolated_array_at_point(self.normal_R, phi_0) - nZ = self.interpolated_array_at_point(self.normal_z, phi_0) - R0 = self.interpolated_array_at_point(self.R0, phi_0) - R0p = self.interpolated_array_at_point(self.R0p, phi_0) - Z0p = self.interpolated_array_at_point(self.Z0p, phi_0) - nu1c = X1c * (bR * Z0p - bZ * R0p)/R0 + Y1c * (nZ * R0p - nR * Z0p)/R0 - nu1s = X1s * (bR * Z0p - bZ * R0p)/R0 + Y1s * (nZ * R0p - nR * Z0p)/R0 - nu = nu0 + r * (nu1c * jnp.cos(theta) + nu1s * jnp.sin(theta)) - return phi + nu - varphi - - @jit - def phi_of_theta_varphi(self, r, theta, varphi): - residual = partial(self.residual_phi0_of_theta_varphi_func, theta=theta, r=r, varphi=varphi) - - def internal_newton(f, x0): - def body_fun(i, x): - res = f(x) - jac = grad(f)(x) - return x - res / jac - return jax.lax.fori_loop(0, 5, body_fun, x0) - - phi_on_axis = lax.custom_root(residual, varphi, internal_newton, lambda g, y: y / g(1.0)) - X_at_this_theta = r * (self.X1c_untwisted * jnp.cos(theta) + self.X1s_untwisted * jnp.sin(theta)) - Y_at_this_theta = r * (self.Y1c_untwisted * jnp.cos(theta) + self.Y1s_untwisted * jnp.sin(theta)) - _, _, phi_off_axis = self.Frenet_to_cylindrical_1_point(phi_on_axis, X_at_this_theta, Y_at_this_theta) - return phi_off_axis - - @jit - def interpolated_array_at_point(self,array,point): - sp=jnp.interp(jnp.array([point]), jnp.append(self.phi,2*jnp.pi/self.nfp), jnp.append(array,array[0]), period=2*jnp.pi/self.nfp)[0] - return sp - - @jit - def Frenet_to_cylindrical_residual_func(self,phi0, phi_target, X_at_this_theta, Y_at_this_theta): - sinphi0 = jnp.sin(phi0) - cosphi0 = jnp.cos(phi0) - R0_at_phi0 = self.interpolated_array_at_point(self.R0,phi0) - X_at_phi0 = self.interpolated_array_at_point(X_at_this_theta,phi0) - Y_at_phi0 = self.interpolated_array_at_point(Y_at_this_theta,phi0) - normal_R = self.interpolated_array_at_point(self.normal_R,phi0) - normal_phi = self.interpolated_array_at_point(self.normal_phi,phi0) - binormal_R = self.interpolated_array_at_point(self.binormal_R,phi0) - binormal_phi = self.interpolated_array_at_point(self.binormal_phi,phi0) - normal_x = normal_R * cosphi0 - normal_phi * sinphi0 - normal_y = normal_R * sinphi0 + normal_phi * cosphi0 - binormal_x = binormal_R * cosphi0 - binormal_phi * sinphi0 - binormal_y = binormal_R * sinphi0 + binormal_phi * cosphi0 - total_x = R0_at_phi0 * cosphi0 + X_at_phi0 * normal_x + Y_at_phi0 * binormal_x - total_y = R0_at_phi0 * sinphi0 + X_at_phi0 * normal_y + Y_at_phi0 * binormal_y - Frenet_to_cylindrical_residual = jnp.arctan2(total_y, total_x) - phi_target - Frenet_to_cylindrical_residual = jnp.where(Frenet_to_cylindrical_residual > jnp.pi, Frenet_to_cylindrical_residual - 2 * jnp.pi, Frenet_to_cylindrical_residual) - Frenet_to_cylindrical_residual = jnp.where(Frenet_to_cylindrical_residual <-jnp.pi, Frenet_to_cylindrical_residual + 2 * jnp.pi, Frenet_to_cylindrical_residual) - return Frenet_to_cylindrical_residual - - @jit - def Frenet_to_cylindrical_1_point(self, phi0, X_at_this_theta, Y_at_this_theta): - sinphi0 = jnp.sin(phi0) - cosphi0 = jnp.cos(phi0) - R0_at_phi0 = self.interpolated_array_at_point(self.R0,phi0) - z0_at_phi0 = self.interpolated_array_at_point(self.Z0,phi0) - X_at_phi0 = self.interpolated_array_at_point(X_at_this_theta,phi0) - Y_at_phi0 = self.interpolated_array_at_point(Y_at_this_theta,phi0) - normal_R = self.interpolated_array_at_point(self.normal_R,phi0) - normal_phi = self.interpolated_array_at_point(self.normal_phi,phi0) - normal_z = self.interpolated_array_at_point(self.normal_z,phi0) - binormal_R = self.interpolated_array_at_point(self.binormal_R,phi0) - binormal_phi = self.interpolated_array_at_point(self.binormal_phi,phi0) - binormal_z = self.interpolated_array_at_point(self.binormal_z,phi0) - normal_x = normal_R * cosphi0 - normal_phi * sinphi0 - normal_y = normal_R * sinphi0 + normal_phi * cosphi0 - binormal_x = binormal_R * cosphi0 - binormal_phi * sinphi0 - binormal_y = binormal_R * sinphi0 + binormal_phi * cosphi0 - total_x = R0_at_phi0 * cosphi0 + X_at_phi0 * normal_x + Y_at_phi0 * binormal_x - total_y = R0_at_phi0 * sinphi0 + X_at_phi0 * normal_y + Y_at_phi0 * binormal_y - total_z = z0_at_phi0 + X_at_phi0 * normal_z + Y_at_phi0 * binormal_z - total_R = jnp.sqrt(total_x * total_x + total_y * total_y) - total_phi=jnp.arctan2(total_y, total_x) - return total_R, total_z, total_phi - - @partial(jit, static_argnames=['ntheta']) - def Frenet_to_cylindrical(self, r, ntheta=20, phi_is_varphi=False): - nphi_conversion = self.nphi - theta = jnp.linspace(0, 2 * jnp.pi, ntheta, endpoint=False) - phi_conversion = jnp.linspace(0, 2 * jnp.pi / self.nfp, nphi_conversion, endpoint=False) - - def compute_for_theta(theta_j): - costheta = jnp.cos(theta_j) - sintheta = jnp.sin(theta_j) - X_at_this_theta = r * (self.X1c_untwisted * costheta + self.X1s_untwisted * sintheta) - Y_at_this_theta = r * (self.Y1c_untwisted * costheta + self.Y1s_untwisted * sintheta) - - def compute_for_phi(phi_target): - - def internal_newton(f, x0): - def body_fun(i, x): - res = f(x) - jac = grad(f)(x) - return x - res / jac - return jax.lax.fori_loop(0, 5, body_fun, x0) - - def residual(z): - return jax.lax.cond( - phi_is_varphi, - lambda _: self.residual_phi0_of_theta_varphi_func( - z, r=r, theta=theta_j, varphi=phi_target - ), - lambda _: self.Frenet_to_cylindrical_residual_func( - z, phi_target=phi_target, - X_at_this_theta=X_at_this_theta, - Y_at_this_theta=Y_at_this_theta - ), - operand=None - ) - - phi0_solution = lax.custom_root(residual, phi_target, internal_newton, lambda g, y: y / g(1.0)) - - final_R, final_Z, _ = self.Frenet_to_cylindrical_1_point(phi0_solution, X_at_this_theta, Y_at_this_theta) - return final_R, final_Z, phi0_solution + def _tree_unflatten(cls, auxiliary, children): + rc, zs, etabar, B0, sigma0, I2, B2c, p2 = children + return cls( + rc=rc, + zs=zs, + etabar=etabar, + B0=B0, + sigma0=sigma0, + I2=I2, + B2c=B2c, + p2=p2, + **auxiliary, + ) - return vmap(compute_for_phi)(phi_conversion) + def calculate(self, rc: ArrayLike, zs: ArrayLike, etabar: ArrayLike): + """Return the historical tuple, evaluated by the canonical core.""" - R_2D, Z_2D, phi0_2D = vmap(compute_for_theta)(theta) - return R_2D, Z_2D, phi0_2D + return self._legacy_tuple(self._canonical_solution(rc, zs, etabar)) + def B_covariant(self, points: ArrayLike) -> jax.Array: + """First-order covariant Boozer components ``(B_r, B_theta, B_phi)``.""" - @partial(jit, static_argnames=['mpol', 'ntor']) - def to_Fourier(self, R_2D, Z_2D, nfp, mpol, ntor): - ntheta, nphi_conversion = R_2D.shape - theta = jnp.linspace(0, 2 * jnp.pi, ntheta, endpoint=False) - phi_conversion = jnp.linspace(0, 2 * jnp.pi / nfp, nphi_conversion, endpoint=False) - - phi2d, theta2d = jnp.meshgrid(phi_conversion, theta, indexing='xy') - factor = 2 / (ntheta * nphi_conversion) + r, _, _ = jnp.asarray(points) + return jnp.asarray((0.0, r * r * self.I2, self.G0)) - def compute_RBC_ZBS(m, n): - angle = m * theta2d - n * nfp * phi2d - sinangle, cosangle = jnp.sin(angle), jnp.cos(angle) + def B_contravariant(self, points: ArrayLike) -> jax.Array: + """First-order contravariant Boozer components.""" - factor2 = jax.lax.cond( - (ntheta % 2 == 0) & (m == (ntheta / 2)), - lambda _: factor / 2, lambda _: factor, - operand=None) + r, _, _ = jnp.asarray(points) + Bphi = r * self.AbsB(points) / self.jacobian(points) + return jnp.asarray((0.0, self.iotaN * Bphi, Bphi)) - factor2 = jax.lax.cond( - (nphi_conversion % 2 == 0) & (abs(n) == (nphi_conversion / 2)), - lambda _: factor2 / 2, lambda _: factor2, - operand=None) + def AbsB(self, points: ArrayLike) -> jax.Array: + """First-order field strength in near-axis coordinates.""" - return jnp.sum(R_2D * cosangle * factor2), jnp.sum(Z_2D * sinangle * factor2) + r, theta, _ = jnp.asarray(points) + return self.B0 * (1 + r * self.etabar * jnp.cos(theta)) - m_vals = jnp.arange(mpol + 1) - n_vals = jnp.concatenate([jnp.array([1]), jnp.arange(-ntor, ntor + 1)]) if mpol == 0 else jnp.arange(-ntor, ntor + 1) - RBC, ZBS = vmap(lambda n: vmap(lambda m: compute_RBC_ZBS(m, n))(m_vals))(n_vals) + def jacobian(self, points: ArrayLike) -> jax.Array: + """First-order coordinate Jacobian.""" - RBC = RBC.at[ntor, 0].set(jnp.sum(R_2D) / (ntheta * nphi_conversion)) - ZBS = ZBS.at[:ntor, 0].set(0) + r, _, _ = jnp.asarray(points) + field_strength = self.AbsB(points) + return r * self.B0 * (self.G0 + self.iota * self.I2) / field_strength**2 + + def interpolated_array_at_point(self, array: ArrayLike, point: ArrayLike) -> jax.Array: + """Periodically interpolate a sampled one-field-period array.""" + + period = 2 * jnp.pi / self.nfp + array = jnp.asarray(array) + return jnp.interp( + jnp.asarray(point), + jnp.append(self.phi, period), + jnp.append(array, array[0]), + period=period, + ) + + def Frenet_to_cylindrical_1_point( + self, + phi0: ArrayLike, + X_at_this_theta: ArrayLike, + Y_at_this_theta: ArrayLike, + ) -> tuple[jax.Array, jax.Array, jax.Array]: + """Map one displaced Frenet point to cylindrical coordinates.""" + + sine = jnp.sin(phi0) + cosine = jnp.cos(phi0) + R0 = self.interpolated_array_at_point(self.R0, phi0) + Z0 = self.interpolated_array_at_point(self.Z0, phi0) + X = self.interpolated_array_at_point(X_at_this_theta, phi0) + Y = self.interpolated_array_at_point(Y_at_this_theta, phi0) + normal_R = self.interpolated_array_at_point(self.normal_R, phi0) + normal_phi = self.interpolated_array_at_point(self.normal_phi, phi0) + normal_z = self.interpolated_array_at_point(self.normal_z, phi0) + binormal_R = self.interpolated_array_at_point(self.binormal_R, phi0) + binormal_phi = self.interpolated_array_at_point(self.binormal_phi, phi0) + binormal_z = self.interpolated_array_at_point(self.binormal_z, phi0) + + normal_x = normal_R * cosine - normal_phi * sine + normal_y = normal_R * sine + normal_phi * cosine + binormal_x = binormal_R * cosine - binormal_phi * sine + binormal_y = binormal_R * sine + binormal_phi * cosine + x = R0 * cosine + X * normal_x + Y * binormal_x + y = R0 * sine + X * normal_y + Y * binormal_y + z = Z0 + X * normal_z + Y * binormal_z + return jnp.hypot(x, y), z, jnp.arctan2(y, x) + + def Frenet_to_cylindrical_residual_func( + self, + phi0: ArrayLike, + phi_target: ArrayLike, + X_at_this_theta: ArrayLike, + Y_at_this_theta: ArrayLike, + ) -> jax.Array: + """Wrapped cylindrical-angle residual for a Frenet point.""" + + _, _, phi = self.Frenet_to_cylindrical_1_point( + phi0, + X_at_this_theta, + Y_at_this_theta, + ) + difference = phi - phi_target + return jnp.arctan2(jnp.sin(difference), jnp.cos(difference)) + + def residual_phi0_of_theta_varphi_func( + self, + phi0: ArrayLike, + r: ArrayLike, + theta: ArrayLike, + varphi: ArrayLike, + ) -> jax.Array: + """Residual for inversion at fixed Boozer toroidal angle.""" + + X = r * (self.X1c_untwisted * jnp.cos(theta) + self.X1s_untwisted * jnp.sin(theta)) + Y = r * (self.Y1c_untwisted * jnp.cos(theta) + self.Y1s_untwisted * jnp.sin(theta)) + _, _, phi = self.Frenet_to_cylindrical_1_point(phi0, X, Y) + nu0 = self.interpolated_array_at_point(self.varphi - self.phi, phi0) + X1c = self.interpolated_array_at_point(self.X1c_untwisted, phi0) + X1s = self.interpolated_array_at_point(self.X1s_untwisted, phi0) + Y1c = self.interpolated_array_at_point(self.Y1c_untwisted, phi0) + Y1s = self.interpolated_array_at_point(self.Y1s_untwisted, phi0) + bR = self.interpolated_array_at_point(self.binormal_R, phi0) + bZ = self.interpolated_array_at_point(self.binormal_z, phi0) + nR = self.interpolated_array_at_point(self.normal_R, phi0) + nZ = self.interpolated_array_at_point(self.normal_z, phi0) + R0 = self.interpolated_array_at_point(self.R0, phi0) + R0p = self.interpolated_array_at_point(self.R0p, phi0) + Z0p = self.interpolated_array_at_point(self.Z0p, phi0) + nu1c = X1c * (bR * Z0p - bZ * R0p) / R0 + Y1c * (nZ * R0p - nR * Z0p) / R0 + nu1s = X1s * (bR * Z0p - bZ * R0p) / R0 + Y1s * (nZ * R0p - nR * Z0p) / R0 + nu = nu0 + r * (nu1c * jnp.cos(theta) + nu1s * jnp.sin(theta)) + return phi + nu - varphi + + def phi_of_theta_varphi( + self, + r: ArrayLike, + theta: ArrayLike, + varphi: ArrayLike, + ) -> jax.Array: + """Invert the regular-coordinate map for cylindrical toroidal angle.""" + + residual = lambda phi0: self.residual_phi0_of_theta_varphi_func( # noqa: E731 + phi0, + r, + theta, + varphi, + ) + phi_on_axis, _ = implicit_dense_root(residual, jnp.asarray(varphi)) + X = r * (self.X1c_untwisted * jnp.cos(theta) + self.X1s_untwisted * jnp.sin(theta)) + Y = r * (self.Y1c_untwisted * jnp.cos(theta) + self.Y1s_untwisted * jnp.sin(theta)) + _, _, phi = self.Frenet_to_cylindrical_1_point(phi_on_axis, X, Y) + return phi + + def Frenet_to_cylindrical( + self, + r: ArrayLike, + ntheta: int = 20, + phi_is_varphi: bool = False, + ) -> tuple[jax.Array, jax.Array, jax.Array]: + """Map a first-order surface over one field period.""" + + theta = jnp.linspace(0, 2 * jnp.pi, ntheta, endpoint=False) + toroidal_grid = self.phi + + def for_theta(theta_value): + X = r * ( + self.X1c_untwisted * jnp.cos(theta_value) + + self.X1s_untwisted * jnp.sin(theta_value) + ) + Y = r * ( + self.Y1c_untwisted * jnp.cos(theta_value) + + self.Y1s_untwisted * jnp.sin(theta_value) + ) + + def for_toroidal_angle(target): + if phi_is_varphi: + residual = lambda phi0: self.residual_phi0_of_theta_varphi_func( # noqa: E731 + phi0, + r, + theta_value, + target, + ) + else: + residual = lambda phi0: self.Frenet_to_cylindrical_residual_func( # noqa: E731 + phi0, + target, + X, + Y, + ) + phi0, _ = implicit_dense_root(residual, target) + R, Z, _ = self.Frenet_to_cylindrical_1_point(phi0, X, Y) + return R, Z, phi0 + + return jax.vmap(for_toroidal_angle)(toroidal_grid) + + return jax.vmap(for_theta)(theta) + + def to_Fourier( # noqa: N802 + self, + R_2D: ArrayLike, + Z_2D: ArrayLike, + nfp: int, + mpol: int, + ntor: int, + ) -> tuple[jax.Array, jax.Array]: + """Convert a sampled stellarator-symmetric surface to Fourier data.""" + + R_2D = jnp.asarray(R_2D) + Z_2D = jnp.asarray(Z_2D) + ntheta, nphi = R_2D.shape + theta = jnp.linspace(0, 2 * jnp.pi, ntheta, endpoint=False) + phi = jnp.linspace(0, 2 * jnp.pi / nfp, nphi, endpoint=False) + phi2d, theta2d = jnp.meshgrid(phi, theta, indexing="xy") + m = jnp.arange(mpol + 1) + n = jnp.arange(-ntor, ntor + 1) + angle = ( + m[None, :, None, None] * theta2d[None, None, :, :] + - n[:, None, None, None] * nfp * phi2d[None, None, :, :] + ) + factor = 2 / (ntheta * nphi) + RBC = factor * jnp.sum(R_2D[None, None, :, :] * jnp.cos(angle), axis=(-2, -1)) + ZBS = factor * jnp.sum(Z_2D[None, None, :, :] * jnp.sin(angle), axis=(-2, -1)) + RBC = RBC.at[ntor, 0].set(jnp.mean(R_2D)) RBC = RBC.at[:ntor, 0].set(0) + ZBS = ZBS.at[:ntor, 0].set(0) return RBC, ZBS - @partial(jit, static_argnames=['ntheta_fourier', 'mpol', 'ntor', 'ntheta', 'nphi', 'phi_is_varphi']) - def get_boundary(self, r=0.1, ntheta=30, nphi=120, ntheta_fourier=20, mpol=5, ntor=5, phi_is_varphi=False, phi_offset=0.0): - R_2D, Z_2D, _ = self.Frenet_to_cylindrical(r, ntheta=ntheta_fourier, phi_is_varphi=phi_is_varphi) - RBC, ZBS = self.to_Fourier(R_2D, Z_2D, self.nfp, mpol=mpol, ntor=ntor) - - theta1D = jnp.linspace(0, 2 * jnp.pi, ntheta) - phi1D = jnp.linspace(0, 2 * jnp.pi, nphi) + phi_offset - - phi2D_original, theta2D = jnp.meshgrid(phi1D, theta1D, indexing='ij') - - phi2D = jax.lax.cond( - phi_is_varphi, - lambda _: vmap(lambda theta_row, varphi_row: vmap(lambda theta, varphi: self.phi_of_theta_varphi(r, theta, varphi))(theta_row, varphi_row))(theta2D, phi2D_original), - lambda _: phi2D_original, - operand=None + def get_boundary( + self, + r: ArrayLike = 0.1, + ntheta: int = 30, + nphi: int = 120, + ntheta_fourier: int = 20, + mpol: int = 5, + ntor: int = 5, + phi_is_varphi: bool = False, + phi_offset: ArrayLike = 0.0, + ) -> tuple[jax.Array, jax.Array, jax.Array, jax.Array]: + """Return a full-torus first-order surface in Cartesian coordinates.""" + + R_period, Z_period, _ = self.Frenet_to_cylindrical( + r, + ntheta=ntheta_fourier, + phi_is_varphi=phi_is_varphi, + ) + RBC, ZBS = self.to_Fourier(R_period, Z_period, self.nfp, mpol, ntor) + theta = jnp.linspace(0, 2 * jnp.pi, ntheta) + original_phi = jnp.linspace(0, 2 * jnp.pi, nphi) + phi_offset + phi2d, theta2d = jnp.meshgrid(original_phi, theta, indexing="xy") + + if phi_is_varphi: + phi2d = jax.vmap( + lambda theta_row, varphi_row: jax.vmap( + lambda theta_value, varphi_value: self.phi_of_theta_varphi( + r, + theta_value, + varphi_value, + ) + )(theta_row, varphi_row) + )(theta2d, phi2d) + + m = jnp.arange(mpol + 1) + n = jnp.arange(-ntor, ntor + 1) + angle = ( + m[None, :, None, None] * theta2d[None, None, :, :] + - n[:, None, None, None] * self.nfp * original_phi[None, None, None, :] + ) + R = jnp.sum(RBC[:, :, None, None] * jnp.cos(angle), axis=(0, 1)) + Z = jnp.sum(ZBS[:, :, None, None] * jnp.sin(angle), axis=(0, 1)) + return R * jnp.cos(phi2d), R * jnp.sin(phi2d), Z, R + + def B_mag(self, r: ArrayLike, theta: ArrayLike, phi: ArrayLike) -> jax.Array: + """First-order field strength using the legacy angle convention.""" + + return self.B0 * (1 + r * self.etabar * jnp.cos(theta - (self.iota - self.iotaN) * phi)) + + def plot( + self, + r: float = 0.1, + ntheta: int = 40, + nphi: int = 120, + ntheta_fourier: int = 20, + ax=None, + show: bool = True, + close: bool = False, + axis_equal: bool = True, + **kwargs, + ): + """Plot the first-order boundary without importing ESSOS.""" + + import matplotlib.pyplot as plt + import numpy as np + from matplotlib import cm + from matplotlib.colors import LightSource, Normalize + + created_axes = ax is None or getattr(ax, "name", None) != "3d" + if created_axes: + figure = plt.figure() + ax = figure.add_subplot(projection="3d") + else: + figure = ax.figure + + x, y, z, _ = self.get_boundary( + r=r, + ntheta=ntheta, + nphi=nphi, + ntheta_fourier=ntheta_fourier, + ) + theta = jnp.linspace(0, 2 * jnp.pi, ntheta) + phi = jnp.linspace(0, 2 * jnp.pi, nphi) + phi2d, theta2d = jnp.meshgrid(phi, theta) + field_strength = np.asarray(self.B_mag(r, theta2d, phi2d)) + normalization = Normalize(vmin=field_strength.min(), vmax=field_strength.max()) + colormap = cm.viridis + facecolors = LightSource(azdeg=0, altdeg=10).shade( + field_strength, + colormap, + norm=normalization, + ) + kwargs.setdefault("alpha", 1) + ax.plot_surface( + np.asarray(x), + np.asarray(y), + np.asarray(z), + facecolors=facecolors, + rstride=1, + cstride=1, + antialiased=False, + linewidth=0, + shade=False, + **kwargs, ) - - def compute_RZ(m, n): - angle = m * theta2D - n * self.nfp * phi2D_original - return RBC[n + ntor, m] * jnp.cos(angle), ZBS[n + ntor, m] * jnp.sin(angle) - - m_vals = jnp.arange(mpol + 1) - n_vals = jnp.arange(-ntor, ntor + 1) - - R_2Dnew, Z_2Dnew = vmap(lambda m: vmap(lambda n: compute_RZ(m, n))(n_vals))(m_vals) - R_2Dnew, Z_2Dnew = R_2Dnew.sum(axis=(0, 1)), Z_2Dnew.sum(axis=(0, 1)) - - x_2D_plot = R_2Dnew.T * jnp.cos(phi2D.T) - y_2D_plot = R_2Dnew.T * jnp.sin(phi2D.T) - z_2D_plot = Z_2Dnew.T - return x_2D_plot, y_2D_plot, z_2D_plot, R_2Dnew.T - - @partial(jit, static_argnames=['self']) - def B_mag(self, r, theta, phi): - return self.B0*(1 + r * self.etabar * jnp.cos(theta - (self.iota - self.iotaN) * phi)) - - -tree_util.register_pytree_node(near_axis, - near_axis._tree_flatten, - near_axis._tree_unflatten) + if created_axes: + colorbar = figure.colorbar( + cm.ScalarMappable(cmap=colormap, norm=normalization), + ax=ax, + shrink=0.7, + ) + colorbar.ax.set_title(r"$|B|$ [T]") + ax.grid(False) + if axis_equal: + ranges = ( + np.ptp(np.asarray(x)), + np.ptp(np.asarray(y)), + np.ptp(np.asarray(z)), + ) + radius = max(ranges) / 2 + centers = ( + np.mean(np.asarray(x)), + np.mean(np.asarray(y)), + np.mean(np.asarray(z)), + ) + ax.set_xlim(centers[0] - radius, centers[0] + radius) + ax.set_ylim(centers[1] - radius, centers[1] + radius) + ax.set_zlim(centers[2] - radius, centers[2] + radius) + if show: + plt.show() + if close: + plt.close(figure) + return figure, ax + + +jax.tree_util.register_pytree_node( + near_axis, + near_axis._tree_flatten, + near_axis._tree_unflatten, +) diff --git a/src/pyqsc_jax/solvers.py b/src/pyqsc_jax/solvers.py new file mode 100644 index 0000000..58977bf --- /dev/null +++ b/src/pyqsc_jax/solvers.py @@ -0,0 +1,187 @@ +"""pyQSC_JAX-specific nonlinear solver policy and reports.""" + +from collections.abc import Callable +from dataclasses import dataclass +from typing import Any + +import jax +import jax.numpy as jnp +from solvax import root_solve + +from pyqsc_jax.models import RootSolveReport + +ArrayLike = Any + + +@dataclass(frozen=True) +class RootSolveOptions: + """Tolerance and globalization policy for dense Newton root solves.""" + + atol: float = 1e-13 + rtol: float = 1e-13 + step_tolerance: float = 1e-13 + max_steps: int = 20 + max_backtracking_steps: int = 12 + + def __post_init__(self) -> None: + if self.atol < 0 or self.rtol < 0 or self.step_tolerance < 0: + raise ValueError("Root tolerances must be nonnegative.") + if self.max_steps < 0 or self.max_backtracking_steps < 0: + raise ValueError("Root iteration limits must be nonnegative.") + + +DEFAULT_ROOT_OPTIONS = RootSolveOptions() + + +def _infinity_norm(value: jax.Array) -> jax.Array: + return jnp.max(jnp.abs(value)) + + +def dense_newton_root( + residual_function: Callable[[jax.Array], jax.Array], + initial_guess: ArrayLike, + *, + options: RootSolveOptions = DEFAULT_ROOT_OPTIONS, +) -> tuple[jax.Array, RootSolveReport]: + """Solve a small dense nonlinear system with damped Newton updates.""" + + initial_guess = jnp.asarray(initial_guess) + initial_residual = residual_function(initial_guess) + initial_residual_norm = _infinity_norm(initial_residual) + tolerance = jnp.maximum(options.atol, options.rtol * initial_residual_norm) + dtype = initial_guess.dtype + + initial_state = ( + initial_guess, + initial_residual, + initial_residual_norm, + jnp.asarray(jnp.inf, dtype=dtype), + jnp.int32(0), + jnp.int32(0), + ) + + def continue_iteration(state): + x, residual, residual_norm, step_norm, iterations, _ = state + finite = ( + jnp.all(jnp.isfinite(x)) & jnp.all(jnp.isfinite(residual)) & jnp.isfinite(residual_norm) + ) + step_threshold = options.step_tolerance * (1 + _infinity_norm(x)) + return ( + (residual_norm > tolerance) + & (iterations < options.max_steps) + & (step_norm > step_threshold) + & finite + ) + + def newton_step(state): + x, residual, residual_norm, _, iterations, total_backtracking = state + jacobian = jax.jacfwd(residual_function)(x) + if initial_guess.ndim == 0: + full_step = -residual / jacobian + else: + full_step = jnp.linalg.solve(jacobian, -residual) + + def candidate(damping): + candidate_x = x + damping * full_step + candidate_residual = residual_function(candidate_x) + candidate_norm = _infinity_norm(candidate_residual) + return candidate_x, candidate_residual, candidate_norm + + damping0 = jnp.asarray(1.0, dtype=dtype) + candidate_x0, candidate_residual0, candidate_norm0 = candidate(damping0) + line_state0 = ( + damping0, + candidate_x0, + candidate_residual0, + candidate_norm0, + jnp.int32(0), + ) + + def continue_backtracking(line_state): + _, _, candidate_residual, candidate_norm, backtracking = line_state + candidate_finite = jnp.all(jnp.isfinite(candidate_residual)) & jnp.isfinite( + candidate_norm + ) + return ((candidate_norm >= residual_norm) | ~candidate_finite) & ( + backtracking < options.max_backtracking_steps + ) + + def backtrack(line_state): + damping, _, _, _, backtracking = line_state + damping = 0.5 * damping + candidate_x, candidate_residual, candidate_norm = candidate(damping) + return ( + damping, + candidate_x, + candidate_residual, + candidate_norm, + backtracking + 1, + ) + + damping, candidate_x, candidate_residual, candidate_norm, backtracking = jax.lax.while_loop( + continue_backtracking, backtrack, line_state0 + ) + step_norm = _infinity_norm(damping * full_step) + return ( + candidate_x, + candidate_residual, + candidate_norm, + step_norm, + iterations + 1, + total_backtracking + backtracking, + ) + + x, residual, residual_norm, step_norm, iterations, backtracking_steps = jax.lax.while_loop( + continue_iteration, newton_step, initial_state + ) + finite = ( + jnp.all(jnp.isfinite(x)) & jnp.all(jnp.isfinite(residual)) & jnp.isfinite(residual_norm) + ) + converged = finite & (residual_norm <= tolerance) + step_threshold = options.step_tolerance * (1 + _infinity_norm(x)) + stagnated = finite & ~converged & (step_norm <= step_threshold) + final_jacobian = jax.jacfwd(residual_function)(x) + if initial_guess.ndim == 0: + jacobian_condition_number = jnp.where(final_jacobian == 0, jnp.inf, 1.0) + else: + jacobian_condition_number = jnp.linalg.cond(final_jacobian) + report = RootSolveReport( + initial_residual_norm=initial_residual_norm, + residual_norm=residual_norm, + tolerance=tolerance, + step_norm=step_norm, + iterations=iterations, + backtracking_steps=backtracking_steps, + jacobian_condition_number=jacobian_condition_number, + converged=converged, + finite=finite, + stagnated=stagnated, + ) + return x, report + + +def implicit_dense_root( + residual_function: Callable[[jax.Array], jax.Array], + initial_guess: ArrayLike, + *, + options: RootSolveOptions = DEFAULT_ROOT_OPTIONS, +) -> tuple[jax.Array, RootSolveReport]: + """Solve once with dense Newton and differentiate the converged equation. + + The Newton candidate is stopped before it is supplied to SOLVAX's custom + root. Consequently JVPs and VJPs use the implicit function theorem rather + than differentiating the iteration history. + """ + + candidate, report = dense_newton_root( + residual_function, + initial_guess, + options=options, + ) + candidate = jax.lax.stop_gradient(candidate) + root = root_solve( + residual_function, + candidate, + lambda _function, supplied_candidate: supplied_candidate, + ) + return root, report diff --git a/tests/compatibility/test_essos_contract.py b/tests/compatibility/test_essos_contract.py index 7325d5c..03107ce 100644 --- a/tests/compatibility/test_essos_contract.py +++ b/tests/compatibility/test_essos_contract.py @@ -1,5 +1,3 @@ -import pytest - from pyqsc_jax.near_axis import near_axis @@ -54,10 +52,6 @@ def test_legacy_import_and_essos_on_axis_contract(): assert all(callable(getattr(field, name)) for name in methods) -@pytest.mark.xfail( - strict=True, - reason="Plotting exists only on the unmerged ESSOS bridge branch.", -) def test_legacy_plot_method_is_available(): field = near_axis() diff --git a/tests/compatibility/test_legacy_adapter.py b/tests/compatibility/test_legacy_adapter.py new file mode 100644 index 0000000..c398607 --- /dev/null +++ b/tests/compatibility/test_legacy_adapter.py @@ -0,0 +1,153 @@ +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +from pyqsc_jax.near_axis import near_axis + + +def standard_field(**kwargs): + parameters = { + "rc": [1.0, 0.045], + "zs": [0.0, -0.045], + "etabar": -0.9, + "nfp": 3, + "nphi": 15, + } + parameters.update(kwargs) + return near_axis(**parameters) + + +def test_legacy_dofs_validation_and_x_alias(): + field = standard_field() + updated = field.x.at[-1].set(-0.85) + field.x = updated + + np.testing.assert_array_equal(field.x, updated) + np.testing.assert_allclose(field.etabar, -0.85) + with pytest.raises(ValueError, match="dofs must have shape"): + field.dofs = jnp.zeros(2) + + +@pytest.mark.parametrize( + "kwargs, message", + [ + ({"nphi": 16}, "odd integer"), + ({"nphi": True}, "odd integer"), + ({"rc": [[1.0]], "zs": [[0.0]]}, "one-dimensional"), + ({"rc": [1.0, 0.1], "zs": [0.0]}, "equal length"), + ], +) +def test_legacy_constructor_validation(kwargs, message): + with pytest.raises(ValueError, match=message): + standard_field(**kwargs) + + +def test_calculate_and_pytree_round_trip(): + field = standard_field() + calculated = field.calculate(field.rc, field.zs, field.etabar) + np.testing.assert_allclose(calculated[7], field.iota) + + leaves, structure = jax.tree_util.tree_flatten(field) + restored = jax.tree_util.tree_unflatten(structure, leaves) + np.testing.assert_allclose(restored.iota, field.iota) + assert restored.order == field.order + + +def test_coordinate_helpers_and_boundary_are_finite(): + field = standard_field() + X = 0.01 * field.X1c_untwisted + Y = 0.01 * field.Y1s_untwisted + R, Z, phi = field.Frenet_to_cylindrical_1_point(0.0, X, Y) + assert jnp.all(jnp.isfinite(jnp.asarray((R, Z, phi)))) + + residual = field.Frenet_to_cylindrical_residual_func(0.0, phi, X, Y) + np.testing.assert_allclose(residual, 0.0, atol=2e-14) + interpolated = field.interpolated_array_at_point(field.R0, 2 * jnp.pi / field.nfp) + np.testing.assert_allclose(interpolated, field.R0[0]) + + R_period, Z_period, phi0 = field.Frenet_to_cylindrical(0.01, ntheta=5) + assert R_period.shape == Z_period.shape == phi0.shape == (5, field.nphi) + assert jnp.all(jnp.isfinite(R_period)) + RBC, ZBS = field.to_Fourier(R_period, Z_period, field.nfp, mpol=2, ntor=2) + assert RBC.shape == ZBS.shape == (5, 3) + + x, y, z, cylindrical_R = field.get_boundary( + r=0.01, + ntheta=6, + nphi=8, + ntheta_fourier=5, + mpol=2, + ntor=2, + ) + assert x.shape == y.shape == z.shape == cylindrical_R.shape == (6, 8) + assert jnp.all(jnp.isfinite(jnp.stack((x, y, z)))) + + +def test_varphi_coordinate_inversion(): + field = standard_field() + r = 0.005 + theta = 0.3 + varphi = 0.1 + phi = field.phi_of_theta_varphi(r, theta, varphi) + assert jnp.isfinite(phi) + + R, Z, phi0 = field.Frenet_to_cylindrical(r, ntheta=3, phi_is_varphi=True) + assert R.shape == Z.shape == phi0.shape == (3, field.nphi) + assert jnp.all(jnp.isfinite(R)) + + x, y, z, _ = field.get_boundary( + r=r, + ntheta=2, + nphi=3, + ntheta_fourier=3, + mpol=1, + ntor=1, + phi_is_varphi=True, + ) + assert jnp.all(jnp.isfinite(jnp.stack((x, y, z)))) + + +def test_legacy_field_magnitude_and_jitted_methods(): + field = standard_field(I2=0.2) + point = jnp.asarray((0.01, 0.2, 0.1)) + expected = field.B0 * (1 + point[0] * field.etabar * jnp.cos(point[1])) + np.testing.assert_allclose(field.AbsB(point), expected) + assert jnp.all(jnp.isfinite(jax.jit(field.B_covariant)(point))) + assert jnp.all(jnp.isfinite(jax.jit(field.B_contravariant)(point))) + assert jnp.isfinite(jax.jit(field.jacobian)(point)) + assert jnp.isfinite(field.B_mag(*point)) + + +def test_plot_supports_created_and_supplied_axes(monkeypatch): + matplotlib = pytest.importorskip("matplotlib") + + matplotlib.use("Agg") + import matplotlib.pyplot as plt + + monkeypatch.setattr(plt, "show", lambda: None) + field = standard_field() + figure, axes = field.plot( + r=0.005, + ntheta=3, + nphi=4, + ntheta_fourier=3, + show=False, + close=True, + ) + assert axes.figure is figure + + supplied_figure = plt.figure() + supplied_axes = supplied_figure.add_subplot(projection="3d") + returned_figure, returned_axes = field.plot( + r=0.005, + ntheta=3, + nphi=4, + ntheta_fourier=3, + ax=supplied_axes, + show=True, + close=True, + axis_equal=False, + ) + assert returned_figure is supplied_figure + assert returned_axes is supplied_axes diff --git a/tests/numerics/test_first_order_autodiff.py b/tests/numerics/test_first_order_autodiff.py new file mode 100644 index 0000000..3d0d6f8 --- /dev/null +++ b/tests/numerics/test_first_order_autodiff.py @@ -0,0 +1,51 @@ +import jax +import jax.numpy as jnp +import numpy as np + +import pyqsc_jax as qsc + +AXIS = qsc.Axis(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3) + + +def iota_from_etabar(etabar): + return qsc.solve(axis=AXIS, etabar=etabar, nphi=31).iota + + +def test_jit_vmap_jvp_and_vjp(): + etabar = -0.9 + eager = iota_from_etabar(etabar) + compiled = jax.jit(iota_from_etabar)(etabar) + np.testing.assert_allclose(compiled, eager, rtol=2e-13) + + batched = jax.vmap(iota_from_etabar)(jnp.array([-0.95, -0.9, -0.85])) + assert batched.shape == (3,) + assert jnp.all(jnp.isfinite(batched)) + + _, jvp = jax.jvp(iota_from_etabar, (etabar,), (1.0,)) + _, pullback = jax.vjp(iota_from_etabar, etabar) + (vjp,) = pullback(jnp.asarray(1.0)) + np.testing.assert_allclose(jvp, vjp, rtol=2e-12, atol=2e-12) + + +def test_iota_derivative_matches_finite_difference(): + etabar = -0.9 + derivative = jax.grad(iota_from_etabar)(etabar) + step = 2e-5 + finite_difference = (iota_from_etabar(etabar + step) - iota_from_etabar(etabar - step)) / ( + 2 * step + ) + + np.testing.assert_allclose(derivative, finite_difference, rtol=2e-7, atol=2e-9) + + +def test_axis_coefficient_derivative_matches_finite_difference(): + def iota_from_rc1(rc1): + axis = qsc.Axis(rc=jnp.array([1.0, rc1]), zs=AXIS.zs, nfp=AXIS.nfp) + return qsc.solve(axis=axis, etabar=-0.9, nphi=31).iota + + rc1 = 0.045 + derivative = jax.grad(iota_from_rc1)(rc1) + step = 2e-6 + finite_difference = (iota_from_rc1(rc1 + step) - iota_from_rc1(rc1 - step)) / (2 * step) + + np.testing.assert_allclose(derivative, finite_difference, rtol=3e-6, atol=3e-8) diff --git a/tests/physics/test_first_order.py b/tests/physics/test_first_order.py new file mode 100644 index 0000000..85790c2 --- /dev/null +++ b/tests/physics/test_first_order.py @@ -0,0 +1,100 @@ +import jax.numpy as jnp +import numpy as np +import pytest + +import pyqsc_jax as qsc +from pyqsc_jax.first_order import sigma_residual +from pyqsc_jax.models import NearAxisInputs + + +def standard_solution(nphi=31, **kwargs): + parameters = { + "axis": qsc.Axis(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3), + "etabar": -0.9, + "nphi": nphi, + } + parameters.update(kwargs) + return qsc.solve(**parameters) + + +def test_sigma_residual_and_report(): + solution = standard_solution() + state = solution.sigma.at[0].set(solution.iota) + residual = sigma_residual( + state, + inputs=solution.inputs, + geometry=solution.geometry, + ) + + assert bool(solution.root_report.converged) + assert bool(solution.root_report.finite) + assert solution.root_report.residual_norm < 2e-13 + np.testing.assert_allclose(jnp.max(jnp.abs(residual)), solution.root_report.residual_norm) + np.testing.assert_allclose(solution.sigma[0], solution.inputs.sigma0) + + +def test_vacuum_field_gradient_satisfies_maxwell_identities_spectrally(): + solution = standard_solution(nphi=61) + gradient = solution.grad_B_axis + divergence = jnp.trace(gradient, axis1=-2, axis2=-1) + antisymmetric = gradient - jnp.swapaxes(gradient, -1, -2) + + np.testing.assert_allclose(jnp.linalg.norm(solution.B_axis, axis=-1), solution.inputs.B0) + assert jnp.max(jnp.abs(divergence)) < 2e-8 + assert jnp.max(jnp.abs(antisymmetric)) < 2e-8 + assert jnp.all(solution.L_grad_B > 0) + + +def test_first_order_shapes_and_coefficients(): + solution = standard_solution() + assert solution.axis is solution.inputs.axis + assert solution.B_axis.shape == (31, 3) + assert solution.grad_B_axis.shape == (31, 3, 3) + assert solution.sigma.shape == (31,) + np.testing.assert_allclose(solution.X1s, 0.0) + np.testing.assert_allclose( + solution.X1c * solution.curvature, + solution.inputs.etabar, + rtol=2e-13, + ) + area_jacobian = solution.X1c * solution.Y1s - solution.X1s * solution.Y1c + np.testing.assert_allclose( + area_jacobian, + solution.inputs.sG * solution.inputs.spsi, + rtol=2e-13, + ) + + +@pytest.mark.parametrize("order", [2, "r2", 3, "r3"]) +def test_higher_order_request_is_explicitly_rejected(order): + with pytest.raises(NotImplementedError, match="Second- and third-order"): + standard_solution(order=order) + + +def test_invalid_order_and_inverse_mode_are_explicitly_rejected(): + with pytest.raises(ValueError, match="order must be"): + standard_solution(order="fourth") + with pytest.raises(NotImplementedError, match="Inverse"): + standard_solution(solve_for="etabar") + + +@pytest.mark.parametrize( + "overrides, message", + [ + ({"nphi": 2}, "nphi"), + ({"nphi": True}, "nphi"), + ({"order": 4}, "order"), + ({"sG": 0}, "sG"), + ({"spsi": 0}, "spsi"), + ({"solve_for": "pressure"}, "solve_for"), + ({"etabar": jnp.ones(2)}, "etabar"), + ], +) +def test_input_model_validation(overrides, message): + parameters = { + "axis": qsc.Axis(rc=[1.0], zs=[0.0]), + "etabar": -0.9, + } + parameters.update(overrides) + with pytest.raises(ValueError, match=message): + NearAxisInputs(**parameters) diff --git a/tests/regression/test_first_order_reference.py b/tests/regression/test_first_order_reference.py new file mode 100644 index 0000000..9c1a6eb --- /dev/null +++ b/tests/regression/test_first_order_reference.py @@ -0,0 +1,63 @@ +import numpy as np + +import pyqsc_jax as qsc +from pyqsc_jax.near_axis import near_axis + + +def test_standard_solution_matches_legacy_and_upstream_reference(): + parameters = { + "rc": [1.0, 0.045], + "zs": [0.0, -0.045], + "nfp": 3, + "etabar": -0.9, + "nphi": 31, + } + solution = qsc.Qsc(**parameters) + legacy = near_axis(**parameters) + + np.testing.assert_allclose(solution.iota, 0.41830690943386617, rtol=2e-13) + np.testing.assert_allclose(solution.iota, legacy.iota, rtol=2e-13) + np.testing.assert_allclose(solution.sigma, legacy.sigma, rtol=2e-13, atol=2e-13) + np.testing.assert_allclose(solution.B_axis, legacy.B_axis.T, rtol=2e-13, atol=2e-13) + np.testing.assert_allclose( + solution.grad_B_axis, + legacy.grad_B_axis.T, + rtol=2e-12, + atol=2e-12, + ) + np.testing.assert_allclose(solution.L_grad_B, legacy.L_grad_B, rtol=2e-13) + + +def test_finite_current_and_sigma0_match_upstream_reference(): + solution = qsc.Qsc( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + nphi=31, + I2=0.3, + B0=1.2, + sigma0=0.1, + ) + + np.testing.assert_allclose(solution.iota, 0.5981040523602934, rtol=2e-13) + np.testing.assert_allclose(solution.iotaN, 0.5981040523602934, rtol=2e-13) + np.testing.assert_allclose(solution.G0, 1.2108964178133113, rtol=2e-13) + np.testing.assert_allclose(np.max(np.abs(solution.sigma)), 1.1527807285268685, rtol=2e-13) + np.testing.assert_allclose(solution.mean_elongation, 2.300022135471462, rtol=2e-13) + + +def test_qh_topology_matches_upstream_reference(): + solution = qsc.Qsc( + rc=[1.0, 0.265], + zs=[0.0, -0.21], + nfp=4, + etabar=-0.9, + nphi=31, + ) + + assert int(solution.helicity) == -1 + np.testing.assert_allclose(solution.iota, 3.0598175213150203, rtol=2e-13) + np.testing.assert_allclose(solution.iotaN, -0.9401824786849797, rtol=2e-13) + np.testing.assert_allclose(solution.G0, 1.3885479374943943, rtol=2e-13) + np.testing.assert_allclose(np.max(np.abs(solution.sigma)), 0.23608475507759125, rtol=2e-13) diff --git a/tests/regression/test_legacy_baseline.py b/tests/regression/test_legacy_baseline.py index c2c8e64..ea6fbc4 100644 --- a/tests/regression/test_legacy_baseline.py +++ b/tests/regression/test_legacy_baseline.py @@ -47,10 +47,6 @@ def test_first_order_field_methods_are_finite(): assert jnp.all(jnp.isfinite(field.B_contravariant(point))) -@pytest.mark.xfail( - strict=True, - reason="Constructor and dofs setter swap normal/binormal phi and z components.", -) def test_dofs_noop_preserves_derived_frame(): field = standard_field() normal_before = jnp.stack([field.normal_R, field.normal_phi, field.normal_z], axis=1) diff --git a/tests/unit/test_solvers.py b/tests/unit/test_solvers.py new file mode 100644 index 0000000..83bd59e --- /dev/null +++ b/tests/unit/test_solvers.py @@ -0,0 +1,73 @@ +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +from pyqsc_jax.solvers import ( + RootSolveOptions, + dense_newton_root, + implicit_dense_root, +) + + +def test_dense_newton_converges_with_report(): + root, report = dense_newton_root(lambda x: x**2 - 2.0, jnp.asarray(1.0)) + + np.testing.assert_allclose(root, jnp.sqrt(2.0), rtol=2e-13) + assert bool(report.converged) + assert bool(report.finite) + assert not bool(report.stagnated) + assert 0 < int(report.iterations) < 20 + assert report.residual_norm <= report.tolerance + np.testing.assert_allclose(report.jacobian_condition_number, 1.0) + + +def test_backtracking_is_exercised(): + root, report = dense_newton_root(lambda x: x**3 - 1.0, jnp.asarray(0.1)) + + np.testing.assert_allclose(root, 1.0, rtol=2e-12) + assert bool(report.converged) + assert int(report.backtracking_steps) > 0 + + +def test_iteration_limit_returns_failure_report(): + options = RootSolveOptions(max_steps=0) + root, report = dense_newton_root(lambda x: x**2 - 2.0, jnp.asarray(1.0), options=options) + + np.testing.assert_allclose(root, 1.0) + assert not bool(report.converged) + assert bool(report.finite) + assert int(report.iterations) == 0 + + +def test_implicit_root_gradient_uses_converged_equation(): + def root(parameter): + solved, _ = implicit_dense_root( + lambda x: x**2 - parameter, + jnp.asarray(1.0), + ) + return solved + + parameter = 2.0 + np.testing.assert_allclose(root(parameter), jnp.sqrt(parameter), rtol=2e-13) + np.testing.assert_allclose( + jax.grad(root)(parameter), + 1 / (2 * jnp.sqrt(parameter)), + rtol=2e-12, + ) + np.testing.assert_allclose(jax.jit(root)(parameter), root(parameter), rtol=2e-13) + + +@pytest.mark.parametrize( + "kwargs", + [ + {"atol": -1.0}, + {"rtol": -1.0}, + {"step_tolerance": -1.0}, + {"max_steps": -1}, + {"max_backtracking_steps": -1}, + ], +) +def test_root_options_validation(kwargs): + with pytest.raises(ValueError): + RootSolveOptions(**kwargs) From 969d6166a4913b0df1e7068ee6952e744fdd2281 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Wed, 29 Jul 2026 23:23:48 -0500 Subject: [PATCH 05/39] ci: enable x64 for package verification --- .github/workflows/publish.yml | 2 ++ .github/workflows/tests.yml | 2 ++ 2 files changed, 4 insertions(+) diff --git a/.github/workflows/publish.yml b/.github/workflows/publish.yml index aea7797..a8ed80d 100644 --- a/.github/workflows/publish.yml +++ b/.github/workflows/publish.yml @@ -8,6 +8,8 @@ jobs: build-and-verify: runs-on: ubuntu-latest timeout-minutes: 20 + env: + JAX_ENABLE_X64: "true" steps: - uses: actions/checkout@v4 - uses: actions/setup-python@v5 diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml index 76e7249..71a27d9 100644 --- a/.github/workflows/tests.yml +++ b/.github/workflows/tests.yml @@ -52,6 +52,8 @@ jobs: package: runs-on: ubuntu-latest timeout-minutes: 15 + env: + JAX_ENABLE_X64: "true" steps: - uses: actions/checkout@v4 - uses: actions/setup-python@v5 From 3978a6b2706462b6b1e2a32919950e3b629f8784 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Wed, 29 Jul 2026 23:23:57 -0500 Subject: [PATCH 06/39] feat: implement complete second-order coefficient solve --- CHANGELOG.md | 7 + README.md | 27 +- docs/api/second-order.md | 20 + docs/development/physics-traceability.md | 2 +- docs/index.md | 11 +- docs/limitations.md | 10 +- docs/quickstart.md | 27 ++ docs/theory/second-order.md | 131 +++++ src/pyqsc_jax/__init__.py | 13 +- src/pyqsc_jax/first_order.py | 13 +- src/pyqsc_jax/models.py | 79 ++- src/pyqsc_jax/near_axis.py | 104 ++-- src/pyqsc_jax/second_order.py | 457 ++++++++++++++++++ src/pyqsc_jax/solvers.py | 65 ++- tests/numerics/test_second_order_autodiff.py | 42 ++ tests/physics/test_first_order.py | 6 +- tests/physics/test_second_order.py | 138 ++++++ tests/regression/test_legacy_baseline.py | 10 +- .../regression/test_second_order_reference.py | 88 ++++ tests/unit/test_solvers.py | 49 ++ 20 files changed, 1242 insertions(+), 57 deletions(-) create mode 100644 docs/api/second-order.md create mode 100644 docs/theory/second-order.md create mode 100644 src/pyqsc_jax/second_order.py create mode 100644 tests/numerics/test_second_order_autodiff.py create mode 100644 tests/physics/test_second_order.py create mode 100644 tests/regression/test_second_order_reference.py diff --git a/CHANGELOG.md b/CHANGELOG.md index ec7d2c1..9ce9dfd 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -24,6 +24,13 @@ first stable release. - Thin ESSOS compatibility adapter preserving legacy array orientations, coordinate conversion, boundary generation, and plotting without depending on ESSOS. +- Complete finite-pressure/current r2 coefficient system, including + `X20`/`Y20`, second harmonics, `beta_1s`, `G2`, `B20`, derivatives, + untwisted boundary data, and direct `B20` diagnostics. +- Implicit differentiation and residual/conditioning reports for the coupled + dense second-order solve. +- Independent four-equation r2 residual checks and upstream regression cases + spanning vacuum QA, finite pressure/current, and QH topology. ### Fixed diff --git a/README.md b/README.md index cdd80a6..43c6635 100644 --- a/README.md +++ b/README.md @@ -3,9 +3,10 @@ Differentiable near-axis stellarator construction and plasma–coil field jets in JAX. -> **Development status:** the immutable first-order core and ESSOS adapter are -> validated. Complete second order, third order, inverse solves, optimization, -> and plasma/external field jets remain under development on the +> **Development status:** the immutable first-order core, complete r2 +> coefficient solve, and ESSOS adapter are validated. Second-order field +> Hessian/diagnostics, third order, inverse solves, optimization, and +> plasma/external field jets remain under development on the > `refactor/pyqsc-jax-complete` branch. ## Install @@ -64,6 +65,24 @@ The adapter preserves historical component-axis ordering and mutable `field.x`/`field.dofs` behavior for ESSOS, but delegates its physics to the immutable core. +A finite-pressure/current second-order solution uses the same entry point: + +```python +solution = qsc.Qsc( + rc=[1.0, 0.09], + zs=[0.0, -0.09], + nfp=2, + etabar=0.95, + I2=0.9, + p2=-600000.0, + B2c=-0.7, + order="r2", +) + +print("B20 residual:", solution.B20_residual) +print("linear condition:", solution.linear_report.matrix_condition_number) +``` + The lower-level immutable axis API supports general, not necessarily stellarator-symmetric Fourier axes: @@ -84,7 +103,7 @@ The completed package will provide: - general Fourier magnetic axes and QA/QH topology; - converged differentiable first-order sigma solves; -- complete finite-pressure/current second order and pyQSC third-order parity; +- second-order field Hessians/diagnostics and pyQSC third-order parity; - total, plasma, and external field/gradient/Hessian jets on the axis; - target-transform inverse solves with continuation and fold detection; - dense-grid `B20` diagnostics and multistart axis optimization; diff --git a/docs/api/second-order.md b/docs/api/second-order.md new file mode 100644 index 0000000..00bf4d2 --- /dev/null +++ b/docs/api/second-order.md @@ -0,0 +1,20 @@ +# Second-order API + +```{eval-rst} +.. autoclass:: pyqsc_jax.SecondOrderData + :members: +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.LinearSolveReport + :members: +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.SecondOrderResiduals + :members: +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.second_order_residuals +``` diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index 73e60b3..ccb271b 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -9,7 +9,7 @@ to the cited source, not to a duplicated derivation in this repository. | General Fourier axis and Frenet frame | Landreman & Sengupta (2018), arXiv:1809.10233 | `Axis`, `evaluate_axis`, `compute_axis_geometry`; pyQSC `init_axis.py` | analytic circle; asymmetric Fortran curvature/torsion/varphi; frame identities; JIT/VMAP/grad | implemented and documented | | First-order QS and sigma equation | Landreman & Sengupta (2019), arXiv:1908.10253 | `first_order.solve_sigma`; pyQSC `solve_sigma_equation.py` | residual, convergence report, QA/QH/finite-current pyQSC values, JIT/VMAP/JVP/VJP, finite differences | implemented and documented | | Field gradient and `L_grad_B` | Landreman (2021), arXiv:2012.00865, Eq. 3.12 | `first_order.first_order_solution`; pyQSC `grad_B_tensor.py` | upstream arrays, vacuum symmetry/divergence, resolution convergence | implemented and documented | -| Complete second order | Landreman & Sengupta (2019), arXiv:1908.10253 | pyQSC `calculate_r2.py`; manuscript Eqs. 36–54 | all coefficients, operator residual, Fortran arrays, resolution convergence | not implemented | +| Complete second-order coefficients | Landreman & Sengupta (2019), arXiv:1908.10253 | `second_order.solve_second_order`; pyQSC `calculate_r2.py`; manuscript Eqs. 36–54 | four independent equation residuals; vacuum QA, finite-pressure/current, QH upstream arrays; JIT/JVP/VJP/finite differences | implemented and documented | | Total field Hessian | manuscript Eqs. 55–83 | pyQSC generated tensor as comparison only | regular-coordinate chain rule, AD/finite differences, symmetry/divergence | not implemented | | Third-order flux constraint and shear | Landreman & Sengupta (2019); Rodríguez et al. shear equations | pyQSC `calculate_r3.py` | upstream r3 arrays and boundary data | not implemented | | Singular radius and scale lengths | Landreman (2021), arXiv:2012.00865 | pyQSC `r_singularity.py` | upstream values; actual coordinate-map regularity | not implemented | diff --git a/docs/index.md b/docs/index.md index f619750..c0fbc61 100644 --- a/docs/index.md +++ b/docs/index.md @@ -13,8 +13,10 @@ quickstart limitations theory/coordinates-and-conventions theory/first-order +theory/second-order api/axis api/first-order +api/second-order ``` ```{toctree} @@ -36,10 +38,11 @@ changelog ## Project status -The immutable first-order API is validated. Complete second and third order, -inverse solves, optimization, and plasma/external field jets are under active -development. The `pyqsc_jax.near_axis.near_axis` import remains supported for -ESSOS without a runtime deprecation warning. +The immutable first-order API and complete r2 coefficient solve are validated. +Second-order field Hessian/diagnostics, third order, inverse solves, +optimization, and plasma/external field jets are under active development. +The `pyqsc_jax.near_axis.near_axis` import remains supported for ESSOS without +a runtime deprecation warning. ## References diff --git a/docs/limitations.md b/docs/limitations.md index f4b4cb3..3b6b90d 100644 --- a/docs/limitations.md +++ b/docs/limitations.md @@ -1,12 +1,14 @@ # Limitations -The current computational core is first order only. Although the legacy -constructor accepts `order`, `B2c`, and `p2` for compatibility, those arguments -do not yet activate second-order physics. +The current computational core includes first order and the complete +finite-pressure/current r2 coefficient solve. The second-order on-axis field +Hessian, Mercier terms, singular-radius diagnostics, and third-order +coefficients are not yet exposed. Known limitations under active refactor include: -- no complete second- or third-order solution; +- no second-order Hessian/Mercier/singular-radius diagnostics or third-order + solution; - no plasma/external field-jet separation; - no branch-aware target-transform inverse solve. diff --git a/docs/quickstart.md b/docs/quickstart.md index e24d6e0..ca51d77 100644 --- a/docs/quickstart.md +++ b/docs/quickstart.md @@ -58,3 +58,30 @@ field = near_axis( The adapter retains the legacy `(3, nphi)` field and `(3, 3, nphi)` gradient orientations plus mutable `x`/`dofs`; it delegates calculations to the same immutable core. + +## Finite-pressure/current second order + +Set `order="r2"` to solve the coupled periodic second-order coefficient system: + +```python +solution = qsc.Qsc( + rc=[1.0, 0.09], + zs=[0.0, -0.09], + nfp=2, + etabar=0.95, + I2=0.9, + p2=-600000.0, + B2c=-0.7, + nphi=31, + order="r2", +) + +print(solution.B20_mean) +print(solution.B20_residual) +print(solution.linear_report.matrix_condition_number) +``` + +The direct r2 outputs are available as attributes such as `X20`, `X2s`, +`Y20`, `Z20`, `beta_1s`, `G2`, and `B20`. The immutable nested record is also +available as `solution.second_order`. Check both the nonlinear +`root_report` and r2 `linear_report` before accepting a result. diff --git a/docs/theory/second-order.md b/docs/theory/second-order.md new file mode 100644 index 0000000..62ad0e5 --- /dev/null +++ b/docs/theory/second-order.md @@ -0,0 +1,131 @@ +# Finite-pressure/current second order + +## Scope + +Setting `order="r2"` computes the complete second-order surface coefficients +and \(B_{20}\) system of {cite}`landreman2019highorder`. The implementation +follows the staged dependencies in manuscript equations 36–54 and the +independently audited pyQSC implementation, while replacing mutable row-wise +assembly with pure JAX array operations. + +The pressure and current inputs use + +\[ +p = p_0 + r^2 p_2 + O(r^4), +\qquad +I = r^2 I_2 + O(r^4). +\] + +Both may be nonzero. `B2c` and `B2s` prescribe the constant second-harmonic +field-strength coefficients. + +## Algebraic stages + +Define + +\[ +V_1=X_{1c}^2+Y_{1c}^2+Y_{1s}^2,\qquad +V_2=2Y_{1s}Y_{1c},\qquad +V_3=X_{1c}^2+Y_{1c}^2-Y_{1s}^2. +\] + +The tangent-direction coefficients are obtained directly: + +\[ +Z_{20}=-\frac{B_0}{8|G_0|}V_1', +\] + +\[ +Z_{2s}=-\frac{B_0}{8|G_0|} +\left(V_2'-2\iota_N V_3\right), +\qquad +Z_{2c}=-\frac{B_0}{8|G_0|} +\left(V_3'+2\iota_N V_2\right), +\] + +where a prime means \(\mathrm d/\mathrm d\varphi\). These quantities determine +\(X_{2s}\) and \(X_{2c}\) algebraically from the second-harmonic +field-strength equations. + +The pressure response is + +\[ +\beta_{1s} +=-\frac{4s_\psi s_G\mu_0 p_2\bar\eta |G_0|} +{\iota_N B_0^3}. +\] + +The two remaining periodic unknowns are stacked as + +\[ +u=(X_{20},Y_{20}) +\] + +and satisfy a dense collocation system \(A u=b\). `A` contains the Fourier +derivative blocks and pointwise couplings; it is assembled from four +vectorized blocks, with no Python loop over grid rows. After the solve, +\(Y_{2s}\) and \(Y_{2c}\) follow from the two area constraints. + +## Implicit linear differentiation + +The primal callback uses `jax.numpy.linalg.solve`. SOLVAX wraps the matrix +action, primal solve, transpose action, and transpose solve with a custom +linear solve. JVPs and VJPs therefore differentiate the equation \(Au=b\), +not the internals of the dense factorization. + +`linear_report` records: + +- absolute and relative infinity-norm residuals; +- matrix condition number; +- finite, converged, and well-conditioned flags. + +The default report marks condition numbers above \(10^{12}\) as poorly +conditioned. Small \(|\iota_N|\) is a known physical conditioning risk and +must be assessed through this report rather than a warning emitted inside +JIT-compiled code. + +## \(B_{20}\) and direct diagnostics + +The nonconstant second-order field strength is + +\[ +B_{20}=B_0\left[ +\kappa X_{20} +-\frac{B_0}{|G_0|}Z_{20}' ++\frac{\bar\eta^2}{2} +-\frac{\mu_0p_2}{B_0^2} +-\frac{B_0^2}{4|G_0|^2} +\left(q_c^2+q_s^2+r_c^2+r_s^2\right) +\right], +\] + +with the standard first-order combinations \(q_c,q_s,r_c,r_s\). The result +includes the axis-length-weighted mean, anomaly, normalized weighted +\(L^2\) residual, and peak-to-peak variation. It also provides + +\[ +G_2=-\frac{\mu_0p_2G_0}{B_0^2}-\iota I_2. +\] + +All second-order coefficient derivatives needed by the next field-tensor and +diagnostic milestone are stored. Untwisted zero- and second-harmonic +coefficients are used by the ESSOS-compatible boundary conversion. + +## Validation + +Four equations are evaluated independently of matrix assembly: two coupled +force-balance equations and two area constraints. Their maximum residual is +tested directly. Upstream regression cases cover: + +- the vacuum QA configuration of section 5.1; +- the finite-pressure/current configuration of section 5.3; +- the QH configuration of section 5.4; +- an asymmetric-axis development comparison. + +JIT, VMAP, JVP/VJP consistency, finite differences, and legacy r2 boundary +availability are also tested. Reference values are tied to the audited pyQSC +commit recorded in the refactor baseline. + +This milestone does not yet expose the total-field Hessian, Mercier criterion, +or singular-radius diagnostics. Those are separate validation gates and are +not implied by `order="r2"`. diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index 29607ac..9462fab 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -2,18 +2,29 @@ from pyqsc_jax.axis import Axis from pyqsc_jax.first_order import Qsc, solve -from pyqsc_jax.models import NearAxisInputs, NearAxisSolution, RootSolveReport +from pyqsc_jax.models import ( + LinearSolveReport, + NearAxisInputs, + NearAxisSolution, + RootSolveReport, + SecondOrderData, +) from pyqsc_jax.near_axis import near_axis +from pyqsc_jax.second_order import SecondOrderResiduals, second_order_residuals from pyqsc_jax.solvers import RootSolveOptions __all__ = [ "Axis", + "LinearSolveReport", "NearAxisInputs", "NearAxisSolution", "Qsc", "RootSolveOptions", "RootSolveReport", + "SecondOrderData", + "SecondOrderResiduals", "near_axis", + "second_order_residuals", "solve", ] __version__ = "0.2.0.dev0" diff --git a/src/pyqsc_jax/first_order.py b/src/pyqsc_jax/first_order.py index 44f5a45..c4ebe18 100644 --- a/src/pyqsc_jax/first_order.py +++ b/src/pyqsc_jax/first_order.py @@ -199,8 +199,10 @@ def first_order_solution( def _normalize_order(order: int | str) -> int: if order in (1, "r1"): return 1 - if order in (2, "r2", 3, "r3"): - raise NotImplementedError("Second- and third-order solves are not implemented yet.") + if order in (2, "r2"): + return 2 + if order in (3, "r3"): + raise NotImplementedError("Third-order solves are not implemented yet.") raise ValueError("order must be 1, 2, 3, 'r1', 'r2', or 'r3'.") @@ -252,7 +254,12 @@ def solve( geometry, root_options=root_options, ) - return first_order_solution(inputs, geometry, sigma, iota, root_report) + solution = first_order_solution(inputs, geometry, sigma, iota, root_report) + if normalized_order == 2: + from pyqsc_jax.second_order import solve_second_order + + solution = solve_second_order(solution) + return solution def Qsc( diff --git a/src/pyqsc_jax/models.py b/src/pyqsc_jax/models.py index 8914c4f..9bc2967 100644 --- a/src/pyqsc_jax/models.py +++ b/src/pyqsc_jax/models.py @@ -3,7 +3,7 @@ from __future__ import annotations from dataclasses import dataclass, field -from typing import TYPE_CHECKING +from typing import TYPE_CHECKING, ClassVar import jax import jax.numpy as jnp @@ -45,6 +45,19 @@ class RootSolveReport: stagnated: jax.Array +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class LinearSolveReport: + """Residual and conditioning evidence for a dense linear solve.""" + + residual_norm: jax.Array + relative_residual_norm: jax.Array + matrix_condition_number: jax.Array + finite: jax.Array + converged: jax.Array + well_conditioned: jax.Array + + @jax.tree_util.register_dataclass @dataclass(frozen=True) class NearAxisInputs: @@ -82,6 +95,57 @@ def __post_init__(self) -> None: object.__setattr__(self, name, value) +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class SecondOrderData: + """Complete second-order coefficient solution and direct diagnostics.""" + + linear_report: LinearSolveReport + V1: jax.Array + V2: jax.Array + V3: jax.Array + X20: jax.Array + X2s: jax.Array + X2c: jax.Array + Y20: jax.Array + Y2s: jax.Array + Y2c: jax.Array + Z20: jax.Array + Z2s: jax.Array + Z2c: jax.Array + beta_1s: jax.Array + B20: jax.Array + B20_mean: jax.Array + B20_anomaly: jax.Array + B20_residual: jax.Array + B20_variation: jax.Array + G2: jax.Array + N_helicity: jax.Array + d_curvature_d_varphi: jax.Array + d_torsion_d_varphi: jax.Array + d_X20_d_varphi: jax.Array + d_X2s_d_varphi: jax.Array + d_X2c_d_varphi: jax.Array + d_Y20_d_varphi: jax.Array + d_Y2s_d_varphi: jax.Array + d_Y2c_d_varphi: jax.Array + d_Z20_d_varphi: jax.Array + d_Z2s_d_varphi: jax.Array + d_Z2c_d_varphi: jax.Array + d2_X1c_d_varphi2: jax.Array + d2_Y1c_d_varphi2: jax.Array + d2_Y1s_d_varphi2: jax.Array + X20_untwisted: jax.Array + X2s_untwisted: jax.Array + X2c_untwisted: jax.Array + Y20_untwisted: jax.Array + Y2s_untwisted: jax.Array + Y2c_untwisted: jax.Array + Z20_untwisted: jax.Array + Z2s_untwisted: jax.Array + Z2c_untwisted: jax.Array + + @jax.tree_util.register_dataclass @dataclass(frozen=True) class NearAxisSolution: @@ -114,6 +178,19 @@ class NearAxisSolution: grad_B_axis_cylindrical: jax.Array grad_B_axis: jax.Array L_grad_B: jax.Array + second_order: SecondOrderData | None = None + + _SECOND_ORDER_NAMES: ClassVar[frozenset[str]] = frozenset( + field.name for field in SecondOrderData.__dataclass_fields__.values() + ) + + def __getattr__(self, name: str): + if name in self._SECOND_ORDER_NAMES: + second_order = object.__getattribute__(self, "second_order") + if second_order is None: + raise AttributeError(f"First-order solution has no {name!r} quantity.") + return getattr(second_order, name) + raise AttributeError(f"{type(self).__name__!s} has no attribute {name!r}.") @property def axis(self) -> Axis: diff --git a/src/pyqsc_jax/near_axis.py b/src/pyqsc_jax/near_axis.py index ee27a40..ed41e4d 100644 --- a/src/pyqsc_jax/near_axis.py +++ b/src/pyqsc_jax/near_axis.py @@ -38,6 +38,7 @@ def __init__( order: int | str = "r1", B2c: ArrayLike = 0.0, p2: ArrayLike = 0.0, + B2s: ArrayLike = 0.0, ) -> None: if not isinstance(nphi, int) or isinstance(nphi, bool) or nphi < 3 or nphi % 2 == 0: raise ValueError("The compatibility API requires odd integer nphi >= 3.") @@ -52,6 +53,7 @@ def __init__( self.I2 = jnp.asarray(I2) self.p2 = jnp.asarray(p2) self.B2c = jnp.asarray(B2c) + self.B2s = jnp.asarray(B2s) self.nphi = nphi self.spsi = spsi self.sG = sG @@ -67,8 +69,7 @@ def _canonical_solution( zs: ArrayLike, etabar: ArrayLike, ) -> NearAxisSolution: - # Until r2/r3 milestones land, preserve the legacy behavior in which - # those labels still returned the first-order subset. + canonical_order = "r1" if self.order in (1, "r1") else "r2" return solve( axis=Axis.stellarator_symmetric(rc=rc, zs=zs, nfp=self.nfp), etabar=etabar, @@ -77,8 +78,9 @@ def _canonical_solution( I2=self.I2, p2=self.p2, B2c=self.B2c, + B2s=self.B2s, nphi=self.nphi, - order="r1", + order=canonical_order, sG=self.sG, spsi=self.spsi, ) @@ -153,6 +155,9 @@ def _refresh(self) -> None: self.R0p, self.Z0p, ) = self._legacy_tuple(solution) + if solution.second_order is not None: + for name in solution._SECOND_ORDER_NAMES: + setattr(self, name, getattr(solution, name)) @property def dofs(self) -> jax.Array: @@ -191,6 +196,7 @@ def _tree_flatten(self): self.I2, self.B2c, self.p2, + self.B2s, ) auxiliary = { "nphi": self.nphi, @@ -203,7 +209,7 @@ def _tree_flatten(self): @classmethod def _tree_unflatten(cls, auxiliary, children): - rc, zs, etabar, B0, sigma0, I2, B2c, p2 = children + rc, zs, etabar, B0, sigma0, I2, B2c, p2, B2s = children return cls( rc=rc, zs=zs, @@ -213,6 +219,7 @@ def _tree_unflatten(cls, auxiliary, children): I2=I2, B2c=B2c, p2=p2, + B2s=B2s, **auxiliary, ) @@ -264,6 +271,7 @@ def Frenet_to_cylindrical_1_point( phi0: ArrayLike, X_at_this_theta: ArrayLike, Y_at_this_theta: ArrayLike, + Z_at_this_theta: ArrayLike | None = None, ) -> tuple[jax.Array, jax.Array, jax.Array]: """Map one displaced Frenet point to cylindrical coordinates.""" @@ -273,20 +281,29 @@ def Frenet_to_cylindrical_1_point( Z0 = self.interpolated_array_at_point(self.Z0, phi0) X = self.interpolated_array_at_point(X_at_this_theta, phi0) Y = self.interpolated_array_at_point(Y_at_this_theta, phi0) + if Z_at_this_theta is None: + Z_at_this_theta = jnp.zeros_like(X_at_this_theta) + Z = self.interpolated_array_at_point(Z_at_this_theta, phi0) normal_R = self.interpolated_array_at_point(self.normal_R, phi0) normal_phi = self.interpolated_array_at_point(self.normal_phi, phi0) normal_z = self.interpolated_array_at_point(self.normal_z, phi0) binormal_R = self.interpolated_array_at_point(self.binormal_R, phi0) binormal_phi = self.interpolated_array_at_point(self.binormal_phi, phi0) binormal_z = self.interpolated_array_at_point(self.binormal_z, phi0) + tangent = self.solution.geometry.tangent_cylindrical + tangent_R = self.interpolated_array_at_point(tangent[:, 0], phi0) + tangent_phi = self.interpolated_array_at_point(tangent[:, 1], phi0) + tangent_z = self.interpolated_array_at_point(tangent[:, 2], phi0) normal_x = normal_R * cosine - normal_phi * sine normal_y = normal_R * sine + normal_phi * cosine binormal_x = binormal_R * cosine - binormal_phi * sine binormal_y = binormal_R * sine + binormal_phi * cosine - x = R0 * cosine + X * normal_x + Y * binormal_x - y = R0 * sine + X * normal_y + Y * binormal_y - z = Z0 + X * normal_z + Y * binormal_z + tangent_x = tangent_R * cosine - tangent_phi * sine + tangent_y = tangent_R * sine + tangent_phi * cosine + x = R0 * cosine + X * normal_x + Y * binormal_x + Z * tangent_x + y = R0 * sine + X * normal_y + Y * binormal_y + Z * tangent_y + z = Z0 + X * normal_z + Y * binormal_z + Z * tangent_z return jnp.hypot(x, y), z, jnp.arctan2(y, x) def Frenet_to_cylindrical_residual_func( @@ -295,6 +312,7 @@ def Frenet_to_cylindrical_residual_func( phi_target: ArrayLike, X_at_this_theta: ArrayLike, Y_at_this_theta: ArrayLike, + Z_at_this_theta: ArrayLike | None = None, ) -> jax.Array: """Wrapped cylindrical-angle residual for a Frenet point.""" @@ -302,6 +320,7 @@ def Frenet_to_cylindrical_residual_func( phi0, X_at_this_theta, Y_at_this_theta, + Z_at_this_theta, ) difference = phi - phi_target return jnp.arctan2(jnp.sin(difference), jnp.cos(difference)) @@ -315,9 +334,8 @@ def residual_phi0_of_theta_varphi_func( ) -> jax.Array: """Residual for inversion at fixed Boozer toroidal angle.""" - X = r * (self.X1c_untwisted * jnp.cos(theta) + self.X1s_untwisted * jnp.sin(theta)) - Y = r * (self.Y1c_untwisted * jnp.cos(theta) + self.Y1s_untwisted * jnp.sin(theta)) - _, _, phi = self.Frenet_to_cylindrical_1_point(phi0, X, Y) + X, Y, Z = self._frenet_displacements(r, theta) + _, _, phi = self.Frenet_to_cylindrical_1_point(phi0, X, Y, Z) nu0 = self.interpolated_array_at_point(self.varphi - self.phi, phi0) X1c = self.interpolated_array_at_point(self.X1c_untwisted, phi0) X1s = self.interpolated_array_at_point(self.X1s_untwisted, phi0) @@ -335,6 +353,32 @@ def residual_phi0_of_theta_varphi_func( nu = nu0 + r * (nu1c * jnp.cos(theta) + nu1s * jnp.sin(theta)) return phi + nu - varphi + def _frenet_displacements( + self, + r: ArrayLike, + theta: ArrayLike, + ) -> tuple[jax.Array, jax.Array, jax.Array]: + """Assemble all available radial-order Frenet displacements.""" + + cosine = jnp.cos(theta) + sine = jnp.sin(theta) + X = r * (self.X1c_untwisted * cosine + self.X1s_untwisted * sine) + Y = r * (self.Y1c_untwisted * cosine + self.Y1s_untwisted * sine) + Z = jnp.zeros_like(X) + if self.solution.second_order is not None: + cosine2 = jnp.cos(2 * theta) + sine2 = jnp.sin(2 * theta) + X = X + r**2 * ( + self.X20_untwisted + self.X2c_untwisted * cosine2 + self.X2s_untwisted * sine2 + ) + Y = Y + r**2 * ( + self.Y20_untwisted + self.Y2c_untwisted * cosine2 + self.Y2s_untwisted * sine2 + ) + Z = Z + r**2 * ( + self.Z20_untwisted + self.Z2c_untwisted * cosine2 + self.Z2s_untwisted * sine2 + ) + return X, Y, Z + def phi_of_theta_varphi( self, r: ArrayLike, @@ -350,9 +394,8 @@ def phi_of_theta_varphi( varphi, ) phi_on_axis, _ = implicit_dense_root(residual, jnp.asarray(varphi)) - X = r * (self.X1c_untwisted * jnp.cos(theta) + self.X1s_untwisted * jnp.sin(theta)) - Y = r * (self.Y1c_untwisted * jnp.cos(theta) + self.Y1s_untwisted * jnp.sin(theta)) - _, _, phi = self.Frenet_to_cylindrical_1_point(phi_on_axis, X, Y) + X, Y, Z = self._frenet_displacements(r, theta) + _, _, phi = self.Frenet_to_cylindrical_1_point(phi_on_axis, X, Y, Z) return phi def Frenet_to_cylindrical( @@ -361,20 +404,13 @@ def Frenet_to_cylindrical( ntheta: int = 20, phi_is_varphi: bool = False, ) -> tuple[jax.Array, jax.Array, jax.Array]: - """Map a first-order surface over one field period.""" + """Map the available-order surface over one field period.""" theta = jnp.linspace(0, 2 * jnp.pi, ntheta, endpoint=False) toroidal_grid = self.phi def for_theta(theta_value): - X = r * ( - self.X1c_untwisted * jnp.cos(theta_value) - + self.X1s_untwisted * jnp.sin(theta_value) - ) - Y = r * ( - self.Y1c_untwisted * jnp.cos(theta_value) - + self.Y1s_untwisted * jnp.sin(theta_value) - ) + X, Y, Z = self._frenet_displacements(r, theta_value) def for_toroidal_angle(target): if phi_is_varphi: @@ -390,10 +426,11 @@ def for_toroidal_angle(target): target, X, Y, + Z, ) phi0, _ = implicit_dense_root(residual, target) - R, Z, _ = self.Frenet_to_cylindrical_1_point(phi0, X, Y) - return R, Z, phi0 + R, cylindrical_Z, _ = self.Frenet_to_cylindrical_1_point(phi0, X, Y, Z) + return R, cylindrical_Z, phi0 return jax.vmap(for_toroidal_angle)(toroidal_grid) @@ -440,7 +477,7 @@ def get_boundary( phi_is_varphi: bool = False, phi_offset: ArrayLike = 0.0, ) -> tuple[jax.Array, jax.Array, jax.Array, jax.Array]: - """Return a full-torus first-order surface in Cartesian coordinates.""" + """Return a full-torus available-order surface in Cartesian coordinates.""" R_period, Z_period, _ = self.Frenet_to_cylindrical( r, @@ -474,9 +511,18 @@ def get_boundary( return R * jnp.cos(phi2d), R * jnp.sin(phi2d), Z, R def B_mag(self, r: ArrayLike, theta: ArrayLike, phi: ArrayLike) -> jax.Array: - """First-order field strength using the legacy angle convention.""" - - return self.B0 * (1 + r * self.etabar * jnp.cos(theta - (self.iota - self.iotaN) * phi)) + """Available-order field strength using the legacy angle convention.""" + + thetaN = theta - (self.iota - self.iotaN) * phi + field_strength = self.B0 * (1 + r * self.etabar * jnp.cos(thetaN)) + if self.solution.second_order is not None: + B20 = self.interpolated_array_at_point(self.B20, phi) + field_strength = field_strength + r**2 * ( + B20 + + self.B2c * jnp.cos(2 * thetaN) + + self.solution.inputs.B2s * jnp.sin(2 * thetaN) + ) + return field_strength def plot( self, @@ -490,7 +536,7 @@ def plot( axis_equal: bool = True, **kwargs, ): - """Plot the first-order boundary without importing ESSOS.""" + """Plot the available-order boundary without importing ESSOS.""" import matplotlib.pyplot as plt import numpy as np diff --git a/src/pyqsc_jax/second_order.py b/src/pyqsc_jax/second_order.py new file mode 100644 index 0000000..bfa9f65 --- /dev/null +++ b/src/pyqsc_jax/second_order.py @@ -0,0 +1,457 @@ +"""Complete second-order quasisymmetric near-axis coefficient solve.""" + +from dataclasses import dataclass, replace + +import jax +import jax.numpy as jnp + +from pyqsc_jax.models import NearAxisSolution, SecondOrderData +from pyqsc_jax.solvers import implicit_dense_linear_solve + +MU0 = 4e-7 * jnp.pi + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class SecondOrderResiduals: + """Independent residuals of the four coupled second-order equations.""" + + force_balance_1: jax.Array + force_balance_2: jax.Array + area_constraint_1: jax.Array + area_constraint_2: jax.Array + + @property + def maximum_absolute(self) -> jax.Array: + """Maximum absolute collocation residual across all four equations.""" + + return jnp.max( + jnp.abs( + jnp.stack( + ( + self.force_balance_1, + self.force_balance_2, + self.area_constraint_1, + self.area_constraint_2, + ) + ) + ) + ) + + +def _assemble_periodic_system( + first_order: NearAxisSolution, + *, + X2s: jax.Array, + X2c: jax.Array, + Z20: jax.Array, + Z2s: jax.Array, + Z2c: jax.Array, + beta_1s: jax.Array, +) -> tuple[ + jax.Array, + jax.Array, + jax.Array, + jax.Array, + jax.Array, + jax.Array, +]: + """Assemble the coupled periodic system for ``X20`` and ``Y20``.""" + + inputs = first_order.inputs + geometry = first_order.geometry + D = geometry.d_d_varphi + lp = geometry.abs_G0_over_B0 + X1c = first_order.X1c + Y1s = first_order.Y1s + Y1c = first_order.Y1c + curvature = first_order.curvature + torsion = first_order.torsion + iotaN = first_order.iotaN + sign_product = inputs.sG * inputs.spsi + current_factor = inputs.spsi * inputs.I2 / inputs.B0 + + Y2s_from_X20 = -sign_product * curvature**2 / inputs.etabar**2 + Y2s_inhomogeneous = sign_product * ( + -curvature / 2 + curvature**2 / inputs.etabar**2 * (-X2c + X2s * first_order.sigma) + ) + Y2c_from_X20 = -sign_product * curvature**2 * first_order.sigma / inputs.etabar**2 + Y2c_inhomogeneous = ( + sign_product * curvature**2 / inputs.etabar**2 * (X2s + X2c * first_order.sigma) + ) + + fX0_from_X20 = -4 * sign_product * lp * (Y2c_from_X20 * Z2s - Y2s_from_X20 * Z2c) + fX0_from_Y20 = -torsion * lp - 4 * sign_product * lp * Z2s + 2 * current_factor * lp + fX0_inhomogeneous = ( + curvature * lp * Z20 + - 4 * sign_product * lp * (Y2c_inhomogeneous * Z2s - Y2s_inhomogeneous * Z2c) + - current_factor * (curvature * sign_product / 2) * lp + + beta_1s * lp * Y1c / 2 + ) + + fXs_from_X20 = ( + -torsion * lp * Y2s_from_X20 + - 4 * sign_product * lp * Y2c_from_X20 * Z20 + + 2 * current_factor * lp * Y2s_from_X20 + ) + fXs_from_Y20 = -4 * sign_product * lp * (-Z2c + Z20) + fXs_inhomogeneous = ( + D @ X2s + - 2 * iotaN * X2c + - torsion * lp * Y2s_inhomogeneous + + curvature * lp * Z2s + - 4 * sign_product * lp * Y2c_inhomogeneous * Z20 + - current_factor * (curvature * sign_product / 2 - 2 * Y2s_inhomogeneous) * lp + - lp * beta_1s * Y1s / 2 + ) + + fXc_from_X20 = ( + -torsion * lp * Y2c_from_X20 + + 4 * sign_product * lp * Y2s_from_X20 * Z20 + + 2 * current_factor * lp * Y2c_from_X20 + ) + fXc_from_Y20 = -torsion * lp - 4 * sign_product * lp * Z2s + 2 * current_factor * lp + fXc_inhomogeneous = ( + D @ X2c + + 2 * iotaN * X2s + - torsion * lp * Y2c_inhomogeneous + + curvature * lp * Z2c + + 4 * sign_product * lp * Y2s_inhomogeneous * Z20 + - current_factor * (curvature * sign_product / 2 - 2 * Y2c_inhomogeneous) * lp + - lp * beta_1s * Y1c / 2 + ) + + fY0_from_X20 = torsion * lp - 2 * current_factor * lp + fY0_from_Y20 = jnp.zeros_like(curvature) + fY0_inhomogeneous = ( + -4 * sign_product * lp * (X2s * Z2c - X2c * Z2s) + + current_factor * curvature * X1c**2 * lp / 2 + - lp * beta_1s * X1c / 2 + ) + + fYs_from_X20 = -2 * iotaN * Y2c_from_X20 - 4 * sign_product * lp * Z2c + fYs_from_Y20 = jnp.full_like(curvature, -2 * iotaN) + fYs_inhomogeneous = ( + D @ Y2s_inhomogeneous + - 2 * iotaN * Y2c_inhomogeneous + + torsion * lp * X2s + + 4 * sign_product * lp * X2c * Z20 + - 2 * current_factor * X2s * lp + ) + + fYc_from_X20 = 2 * iotaN * Y2s_from_X20 + 4 * sign_product * lp * Z2s + fYc_from_Y20 = jnp.zeros_like(curvature) + fYc_inhomogeneous = ( + D @ Y2c_inhomogeneous + + 2 * iotaN * Y2s_inhomogeneous + + torsion * lp * X2c + - 4 * sign_product * lp * X2s * Z20 + - current_factor * (-curvature * X1c**2 / 2 + 2 * X2c) * lp + + lp * beta_1s * X1c / 2 + ) + + block_00 = Y1c[:, None] * D * Y2s_from_X20[None, :] - Y1s[:, None] * D * Y2c_from_X20[None, :] + block_01 = -2 * Y1s[:, None] * D + block_10 = ( + -X1c[:, None] * D + + Y1s[:, None] * D * Y2s_from_X20[None, :] + + Y1c[:, None] * D * Y2c_from_X20[None, :] + ) + block_11 = jnp.zeros_like(D) + + block_00 = block_00 + jnp.diag( + X1c * fXs_from_X20 - Y1s * fY0_from_X20 + Y1c * fYs_from_X20 - Y1s * fYc_from_X20 + ) + block_01 = block_01 + jnp.diag( + X1c * fXs_from_Y20 - Y1s * fY0_from_Y20 + Y1c * fYs_from_Y20 - Y1s * fYc_from_Y20 + ) + block_10 = block_10 + jnp.diag( + -X1c * fX0_from_X20 + + X1c * fXc_from_X20 + - Y1c * fY0_from_X20 + + Y1s * fYs_from_X20 + + Y1c * fYc_from_X20 + ) + block_11 = block_11 + jnp.diag( + -X1c * fX0_from_Y20 + + X1c * fXc_from_Y20 + - Y1c * fY0_from_Y20 + + Y1s * fYs_from_Y20 + + Y1c * fYc_from_Y20 + ) + matrix = jnp.concatenate( + ( + jnp.concatenate((block_00, block_01), axis=1), + jnp.concatenate((block_10, block_11), axis=1), + ), + axis=0, + ) + + right_hand_side_1 = -( + X1c * fXs_inhomogeneous + - Y1s * fY0_inhomogeneous + + Y1c * fYs_inhomogeneous + - Y1s * fYc_inhomogeneous + ) + right_hand_side_2 = -( + -X1c * fX0_inhomogeneous + + X1c * fXc_inhomogeneous + - Y1c * fY0_inhomogeneous + + Y1s * fYs_inhomogeneous + + Y1c * fYc_inhomogeneous + ) + right_hand_side = jnp.concatenate((right_hand_side_1, right_hand_side_2)) + return ( + matrix, + right_hand_side, + Y2s_from_X20, + Y2s_inhomogeneous, + Y2c_from_X20, + Y2c_inhomogeneous, + ) + + +def solve_second_order(first_order: NearAxisSolution) -> NearAxisSolution: + """Add the complete finite-pressure/current second-order solution.""" + + inputs = first_order.inputs + geometry = first_order.geometry + D = geometry.d_d_varphi + B0_over_abs_G0 = 1 / geometry.abs_G0_over_B0 + lp = geometry.abs_G0_over_B0 + X1c = first_order.X1c + Y1s = first_order.Y1s + Y1c = first_order.Y1c + curvature = first_order.curvature + torsion = first_order.torsion + iotaN = first_order.iotaN + sign_product = inputs.sG * inputs.spsi + + V1 = X1c**2 + Y1c**2 + Y1s**2 + V2 = 2 * Y1s * Y1c + V3 = X1c**2 + Y1c**2 - Y1s**2 + factor = -B0_over_abs_G0 / 8 + Z20 = factor * (D @ V1) + Z2s = factor * (D @ V2 - 2 * iotaN * V3) + Z2c = factor * (D @ V3 + 2 * iotaN * V2) + + qs = -iotaN * X1c - Y1s * torsion * lp + qc = D @ X1c - Y1c * torsion * lp + rs = D @ Y1s - iotaN * Y1c + rc = D @ Y1c + iotaN * Y1s + X1c * torsion * lp + X2s = ( + B0_over_abs_G0 + * ( + D @ Z2s + - 2 * iotaN * Z2c + + B0_over_abs_G0 * (lp**2 * inputs.B2s / inputs.B0 + (qc * qs + rc * rs) / 2) + ) + / curvature + ) + X2c = ( + B0_over_abs_G0 + * ( + D @ Z2c + + 2 * iotaN * Z2s + - B0_over_abs_G0 + * ( + -(lp**2) * inputs.B2c / inputs.B0 + + lp**2 * inputs.etabar**2 / 2 + - (qc**2 - qs**2 + rc**2 - rs**2) / 4 + ) + ) + / curvature + ) + beta_1s = -4 * sign_product * MU0 * inputs.p2 * inputs.etabar * lp / (iotaN * inputs.B0**2) + + ( + matrix, + right_hand_side, + Y2s_from_X20, + Y2s_inhomogeneous, + Y2c_from_X20, + Y2c_inhomogeneous, + ) = _assemble_periodic_system( + first_order, + X2s=X2s, + X2c=X2c, + Z20=Z20, + Z2s=Z2s, + Z2c=Z2c, + beta_1s=beta_1s, + ) + solution, linear_report = implicit_dense_linear_solve(matrix, right_hand_side) + X20, Y20 = jnp.split(solution, 2) + Y2s = Y2s_inhomogeneous + Y2s_from_X20 * X20 + Y2c = Y2c_inhomogeneous + Y2c_from_X20 * X20 + Y20 + + B20 = inputs.B0 * ( + curvature * X20 + - B0_over_abs_G0 * (D @ Z20) + + inputs.etabar**2 / 2 + - MU0 * inputs.p2 / inputs.B0**2 + - B0_over_abs_G0**2 * (qc**2 + qs**2 + rc**2 + rs**2) / 4 + ) + weights = geometry.d_l_d_phi + B20_mean = jnp.sum(B20 * weights) / jnp.sum(weights) + B20_anomaly = B20 - B20_mean + B20_residual = jnp.sqrt(jnp.sum(B20_anomaly**2 * weights) / jnp.sum(weights)) / inputs.B0 + B20_variation = jnp.max(B20) - jnp.min(B20) + G2 = -MU0 * inputs.p2 * first_order.G0 / inputs.B0**2 - first_order.iota * inputs.I2 + N_helicity = -first_order.helicity * inputs.axis.nfp + + d_X1c_d_varphi = D @ X1c + d_Y1c_d_varphi = D @ Y1c + d_Y1s_d_varphi = D @ Y1s + untwisting_angle = -first_order.helicity * inputs.axis.nfp * first_order.varphi + sine = jnp.sin(2 * untwisting_angle) + cosine = jnp.cos(2 * untwisting_angle) + + def untwist(sine_coefficient, cosine_coefficient): + return ( + sine_coefficient * cosine + cosine_coefficient * sine, + -sine_coefficient * sine + cosine_coefficient * cosine, + ) + + X2s_untwisted, X2c_untwisted = untwist(X2s, X2c) + Y2s_untwisted, Y2c_untwisted = untwist(Y2s, Y2c) + Z2s_untwisted, Z2c_untwisted = untwist(Z2s, Z2c) + second_order = SecondOrderData( + linear_report=linear_report, + V1=V1, + V2=V2, + V3=V3, + X20=X20, + X2s=X2s, + X2c=X2c, + Y20=Y20, + Y2s=Y2s, + Y2c=Y2c, + Z20=Z20, + Z2s=Z2s, + Z2c=Z2c, + beta_1s=beta_1s, + B20=B20, + B20_mean=B20_mean, + B20_anomaly=B20_anomaly, + B20_residual=B20_residual, + B20_variation=B20_variation, + G2=G2, + N_helicity=N_helicity, + d_curvature_d_varphi=D @ curvature, + d_torsion_d_varphi=D @ torsion, + d_X20_d_varphi=D @ X20, + d_X2s_d_varphi=D @ X2s, + d_X2c_d_varphi=D @ X2c, + d_Y20_d_varphi=D @ Y20, + d_Y2s_d_varphi=D @ Y2s, + d_Y2c_d_varphi=D @ Y2c, + d_Z20_d_varphi=D @ Z20, + d_Z2s_d_varphi=D @ Z2s, + d_Z2c_d_varphi=D @ Z2c, + d2_X1c_d_varphi2=D @ d_X1c_d_varphi, + d2_Y1c_d_varphi2=D @ d_Y1c_d_varphi, + d2_Y1s_d_varphi2=D @ d_Y1s_d_varphi, + X20_untwisted=X20, + X2s_untwisted=X2s_untwisted, + X2c_untwisted=X2c_untwisted, + Y20_untwisted=Y20, + Y2s_untwisted=Y2s_untwisted, + Y2c_untwisted=Y2c_untwisted, + Z20_untwisted=Z20, + Z2s_untwisted=Z2s_untwisted, + Z2c_untwisted=Z2c_untwisted, + ) + return replace(first_order, second_order=second_order) + + +def second_order_residuals(solution: NearAxisSolution) -> SecondOrderResiduals: + """Evaluate all four r2 equations independently of matrix assembly.""" + + r2 = solution.second_order + if r2 is None: + raise ValueError("A second-order solution is required.") + inputs = solution.inputs + D = solution.geometry.d_d_varphi + lp = solution.geometry.abs_G0_over_B0 + sign_product = inputs.sG * inputs.spsi + current_factor = inputs.spsi * inputs.I2 / inputs.B0 + + fX0 = ( + D @ r2.X20 + - solution.torsion * lp * r2.Y20 + + solution.curvature * lp * r2.Z20 + - 4 * sign_product * lp * (r2.Y2c * r2.Z2s - r2.Y2s * r2.Z2c) + - current_factor * (solution.curvature * solution.X1c * solution.Y1c / 2 - 2 * r2.Y20) * lp + + lp * r2.beta_1s * solution.Y1c / 2 + ) + fXs = ( + D @ r2.X2s + - 2 * solution.iotaN * r2.X2c + - solution.torsion * lp * r2.Y2s + + solution.curvature * lp * r2.Z2s + - 4 * sign_product * lp * (-r2.Y20 * r2.Z2c + r2.Y2c * r2.Z20) + - current_factor * (solution.curvature * solution.X1c * solution.Y1s / 2 - 2 * r2.Y2s) * lp + - lp * r2.beta_1s * solution.Y1s / 2 + ) + fXc = ( + D @ r2.X2c + + 2 * solution.iotaN * r2.X2s + - solution.torsion * lp * r2.Y2c + + solution.curvature * lp * r2.Z2c + - 4 * sign_product * lp * (r2.Y20 * r2.Z2s - r2.Y2s * r2.Z20) + - current_factor * (solution.curvature * solution.X1c * solution.Y1c / 2 - 2 * r2.Y2c) * lp + - lp * r2.beta_1s * solution.Y1c / 2 + ) + fY0 = ( + D @ r2.Y20 + + solution.torsion * lp * r2.X20 + - 4 * sign_product * lp * (r2.X2s * r2.Z2c - r2.X2c * r2.Z2s) + - current_factor * (-solution.curvature * solution.X1c**2 / 2 + 2 * r2.X20) * lp + - lp * r2.beta_1s * solution.X1c / 2 + ) + fYs = ( + D @ r2.Y2s + - 2 * solution.iotaN * r2.Y2c + + solution.torsion * lp * r2.X2s + - 4 * sign_product * lp * (r2.X20 * r2.Z2c - r2.X2c * r2.Z20) + - 2 * current_factor * r2.X2s * lp + ) + fYc = ( + D @ r2.Y2c + + 2 * solution.iotaN * r2.Y2s + + solution.torsion * lp * r2.X2c + - 4 * sign_product * lp * (r2.X2s * r2.Z20 - r2.X20 * r2.Z2s) + - current_factor * (-solution.curvature * solution.X1c**2 / 2 + 2 * r2.X2c) * lp + + lp * r2.beta_1s * solution.X1c / 2 + ) + force_balance_1 = ( + solution.X1c * fXs - solution.Y1s * fY0 + solution.Y1c * fYs - solution.Y1s * fYc + ) + force_balance_2 = ( + -solution.X1c * fX0 + + solution.X1c * fXc + - solution.Y1c * fY0 + + solution.Y1s * fYs + + solution.Y1c * fYc + ) + area_constraint_1 = ( + -solution.X1c * r2.Y2c + + solution.X1c * r2.Y20 + + r2.X2s * solution.Y1s + + r2.X2c * solution.Y1c + - r2.X20 * solution.Y1c + ) + area_constraint_2 = ( + solution.X1c * r2.Y2s + + r2.X2c * solution.Y1s + - r2.X2s * solution.Y1c + + r2.X20 * solution.Y1s + + sign_product * solution.X1c * solution.curvature / 2 + ) + return SecondOrderResiduals( + force_balance_1=force_balance_1, + force_balance_2=force_balance_2, + area_constraint_1=area_constraint_1, + area_constraint_2=area_constraint_2, + ) diff --git a/src/pyqsc_jax/solvers.py b/src/pyqsc_jax/solvers.py index 58977bf..5fbfd09 100644 --- a/src/pyqsc_jax/solvers.py +++ b/src/pyqsc_jax/solvers.py @@ -6,9 +6,9 @@ import jax import jax.numpy as jnp -from solvax import root_solve +from solvax import linear_solve, root_solve -from pyqsc_jax.models import RootSolveReport +from pyqsc_jax.models import LinearSolveReport, RootSolveReport ArrayLike = Any @@ -185,3 +185,64 @@ def implicit_dense_root( lambda _function, supplied_candidate: supplied_candidate, ) return root, report + + +def implicit_dense_linear_solve( + matrix: ArrayLike, + right_hand_side: ArrayLike, + *, + residual_tolerance: float = 1e-11, + condition_limit: float = 1e12, +) -> tuple[jax.Array, LinearSolveReport]: + """Solve a dense system with implicit JVP/VJP rules and diagnostics.""" + + if residual_tolerance < 0: + raise ValueError("residual_tolerance must be nonnegative.") + if condition_limit <= 0: + raise ValueError("condition_limit must be positive.") + + matrix = jnp.asarray(matrix) + right_hand_side = jnp.asarray(right_hand_side) + if matrix.ndim != 2 or matrix.shape[0] != matrix.shape[1]: + raise ValueError("matrix must be square.") + if right_hand_side.ndim != 1 or right_hand_side.shape[0] != matrix.shape[0]: + raise ValueError("right_hand_side must match the matrix dimension.") + + matvec = lambda value: matrix @ value # noqa: E731 + transpose_matvec = lambda value: matrix.T @ value # noqa: E731 + primal_solver = lambda _operator, value: jnp.linalg.solve(matrix, value) # noqa: E731 + transpose_solver = lambda _operator, value: jnp.linalg.solve( # noqa: E731 + matrix.T, + value, + ) + solution = linear_solve( + matvec, + right_hand_side, + primal_solver, + transpose_matvec=transpose_matvec, + transpose_solver=transpose_solver, + ) + residual = matrix @ solution - right_hand_side + residual_norm = _infinity_norm(residual) + right_hand_side_norm = _infinity_norm(right_hand_side) + relative_residual_norm = residual_norm / jnp.maximum( + right_hand_side_norm, + jnp.finfo(right_hand_side.dtype).tiny, + ) + condition_number = jnp.linalg.cond(matrix) + finite = ( + jnp.all(jnp.isfinite(solution)) + & jnp.isfinite(residual_norm) + & jnp.isfinite(condition_number) + ) + converged = finite & (relative_residual_norm <= residual_tolerance) + well_conditioned = finite & (condition_number <= condition_limit) + report = LinearSolveReport( + residual_norm=residual_norm, + relative_residual_norm=relative_residual_norm, + matrix_condition_number=condition_number, + finite=finite, + converged=converged, + well_conditioned=well_conditioned, + ) + return solution, report diff --git a/tests/numerics/test_second_order_autodiff.py b/tests/numerics/test_second_order_autodiff.py new file mode 100644 index 0000000..139f102 --- /dev/null +++ b/tests/numerics/test_second_order_autodiff.py @@ -0,0 +1,42 @@ +import jax +import jax.numpy as jnp +import numpy as np + +import pyqsc_jax as qsc + + +def b20_residual(etabar): + return qsc.Qsc( + rc=[1.0, 0.155, 0.0102], + zs=[0.0, 0.154, 0.0111], + nfp=2, + etabar=etabar, + B2c=-0.00322, + nphi=15, + order="r2", + ).B20_residual + + +def test_second_order_jit_jvp_and_vjp(): + etabar = 0.64 + eager = b20_residual(etabar) + np.testing.assert_allclose(jax.jit(b20_residual)(etabar), eager, rtol=2e-13) + + _, jvp = jax.jvp(b20_residual, (etabar,), (1.0,)) + _, pullback = jax.vjp(b20_residual, etabar) + (vjp,) = pullback(jnp.asarray(1.0)) + np.testing.assert_allclose(jvp, vjp, rtol=3e-11, atol=3e-11) + + +def test_second_order_gradient_matches_finite_difference(): + etabar = 0.64 + derivative = jax.grad(b20_residual)(etabar) + step = 2e-5 + finite_difference = (b20_residual(etabar + step) - b20_residual(etabar - step)) / (2 * step) + np.testing.assert_allclose(derivative, finite_difference, rtol=2e-6, atol=2e-8) + + +def test_second_order_vmap(): + values = jax.vmap(b20_residual)(jnp.asarray([0.61, 0.64, 0.67])) + assert values.shape == (3,) + assert jnp.all(jnp.isfinite(values)) diff --git a/tests/physics/test_first_order.py b/tests/physics/test_first_order.py index 85790c2..c96a724 100644 --- a/tests/physics/test_first_order.py +++ b/tests/physics/test_first_order.py @@ -65,9 +65,9 @@ def test_first_order_shapes_and_coefficients(): ) -@pytest.mark.parametrize("order", [2, "r2", 3, "r3"]) -def test_higher_order_request_is_explicitly_rejected(order): - with pytest.raises(NotImplementedError, match="Second- and third-order"): +@pytest.mark.parametrize("order", [3, "r3"]) +def test_third_order_request_is_explicitly_rejected(order): + with pytest.raises(NotImplementedError, match="Third-order"): standard_solution(order=order) diff --git a/tests/physics/test_second_order.py b/tests/physics/test_second_order.py new file mode 100644 index 0000000..939571d --- /dev/null +++ b/tests/physics/test_second_order.py @@ -0,0 +1,138 @@ +import jax.numpy as jnp +import numpy as np +import pytest + +import pyqsc_jax as qsc +from pyqsc_jax.second_order import MU0 + + +def vacuum_qa(nphi=31, **kwargs): + parameters = { + "rc": [1.0, 0.155, 0.0102], + "zs": [0.0, 0.154, 0.0111], + "nfp": 2, + "etabar": 0.64, + "B2c": -0.00322, + "nphi": nphi, + "order": "r2", + } + parameters.update(kwargs) + return qsc.Qsc(**parameters) + + +def test_complete_second_order_equations_and_linear_report(): + solution = vacuum_qa() + residuals = qsc.second_order_residuals(solution) + + assert solution.second_order is not None + assert bool(solution.linear_report.converged) + assert bool(solution.linear_report.finite) + assert bool(solution.linear_report.well_conditioned) + assert solution.linear_report.relative_residual_norm < 3e-14 + assert residuals.maximum_absolute < 1e-11 + for residual in ( + residuals.force_balance_1, + residuals.force_balance_2, + residuals.area_constraint_1, + residuals.area_constraint_2, + ): + assert residual.shape == (solution.inputs.nphi,) + + +def test_second_order_definitions_and_derivatives(): + solution = vacuum_qa() + weights = solution.geometry.d_l_d_phi + weighted_mean = jnp.sum(solution.B20 * weights) / jnp.sum(weights) + + np.testing.assert_allclose(solution.B20_mean, weighted_mean, rtol=2e-13) + np.testing.assert_allclose(solution.B20_anomaly, solution.B20 - weighted_mean) + np.testing.assert_allclose( + solution.B20_variation, + jnp.max(solution.B20) - jnp.min(solution.B20), + ) + np.testing.assert_allclose( + solution.d_X20_d_varphi, + solution.geometry.d_d_varphi @ solution.X20, + ) + np.testing.assert_allclose( + solution.d2_X1c_d_varphi2, + solution.geometry.d_d_varphi @ (solution.geometry.d_d_varphi @ solution.X1c), + ) + + +def test_finite_pressure_and_current_relations(): + solution = qsc.Qsc( + rc=[1.0, 0.09], + zs=[0.0, -0.09], + nfp=2, + etabar=0.95, + I2=0.9, + B2c=-0.7, + p2=-600000.0, + nphi=31, + order="r2", + ) + expected_beta_1s = ( + -4 + * solution.inputs.sG + * solution.inputs.spsi + * MU0 + * solution.inputs.p2 + * solution.inputs.etabar + * solution.geometry.abs_G0_over_B0 + / (solution.iotaN * solution.inputs.B0**2) + ) + expected_G2 = ( + -MU0 * solution.inputs.p2 * solution.G0 / solution.inputs.B0**2 + - solution.iota * solution.inputs.I2 + ) + + np.testing.assert_allclose(solution.beta_1s, expected_beta_1s) + np.testing.assert_allclose(solution.G2, expected_G2) + assert qsc.second_order_residuals(solution).maximum_absolute < 1e-11 + + +def test_qh_untwisting_preserves_harmonic_norm(): + solution = qsc.Qsc( + rc=[1.0, 0.17, 0.01804, 0.001409, 5.877e-5], + zs=[0.0, 0.1581, 0.01820, 0.001548, 7.772e-5], + nfp=4, + etabar=1.569, + B2c=0.1348, + nphi=31, + order="r2", + ) + + assert int(solution.helicity) == 1 + np.testing.assert_allclose(solution.X20_untwisted, solution.X20) + np.testing.assert_allclose( + solution.X2s_untwisted**2 + solution.X2c_untwisted**2, + solution.X2s**2 + solution.X2c**2, + rtol=2e-13, + atol=2e-13, + ) + assert qsc.second_order_residuals(solution).maximum_absolute < 2e-11 + + +def test_second_order_residual_requires_r2_solution(): + first_order = qsc.Qsc( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + nphi=15, + ) + + assert not hasattr(first_order, "X20") + with pytest.raises(AttributeError, match="no 'X20'"): + _ = first_order.X20 + with pytest.raises(ValueError, match="second-order"): + qsc.second_order_residuals(first_order) + + +def test_second_order_resolution_convergence(): + medium = vacuum_qa(nphi=31) + fine = vacuum_qa(nphi=61) + + np.testing.assert_allclose(medium.B20_mean, fine.B20_mean, rtol=6e-7) + np.testing.assert_allclose(medium.B20_residual, fine.B20_residual, rtol=2e-7) diff --git a/tests/regression/test_legacy_baseline.py b/tests/regression/test_legacy_baseline.py index ea6fbc4..7198e2f 100644 --- a/tests/regression/test_legacy_baseline.py +++ b/tests/regression/test_legacy_baseline.py @@ -1,6 +1,5 @@ import jax.numpy as jnp import numpy as np -import pytest from pyqsc_jax.near_axis import near_axis @@ -60,12 +59,13 @@ def test_dofs_noop_preserves_derived_frame(): np.testing.assert_array_equal(binormal_after, binormal_before) -@pytest.mark.xfail( - strict=True, - reason="The current order argument is inert; complete second order is not implemented.", -) def test_r2_request_produces_second_order_solution(): field = standard_field(order="r2", B2c=0.01, p2=-1.0e3) assert field.B20.shape == (field.nphi,) assert jnp.all(jnp.isfinite(field.B20)) + assert bool(field.linear_report.converged) + R, Z, phi0 = field.Frenet_to_cylindrical(0.005, ntheta=3) + assert R.shape == Z.shape == phi0.shape == (3, field.nphi) + assert jnp.all(jnp.isfinite(R)) + assert jnp.isfinite(field.B_mag(0.005, 0.2, 0.1)) diff --git a/tests/regression/test_second_order_reference.py b/tests/regression/test_second_order_reference.py new file mode 100644 index 0000000..2900f5c --- /dev/null +++ b/tests/regression/test_second_order_reference.py @@ -0,0 +1,88 @@ +import numpy as np +import pytest + +import pyqsc_jax as qsc + + +# References were generated with landreman/pyQSC at audited commit +# cd75359ea47548d5db7ccb458c100085c04ba1bc. +@pytest.mark.parametrize( + "parameters, expected", + [ + ( + { + "rc": [1.0, 0.155, 0.0102], + "zs": [0.0, 0.154, 0.0111], + "nfp": 2, + "etabar": 0.64, + "B2c": -0.00322, + }, + { + "iota": -0.42047335182825857, + "beta_1s": 0.0, + "G2": 0.0, + "B20_mean": 0.16212431504754432, + "B20_residual": 0.13498174214090364, + "B20_variation": 0.3740338506893984, + "X20": [-0.12607391440629268, 1.277313706167806, -1.1433646049834585], + "Y20": [3.6484581072275835e-14, -0.061041743645613045, -0.28837977142377097], + "B20": [0.03617846642088235, 0.08753146934212608, 0.3504652075357061], + }, + ), + ( + { + "rc": [1.0, 0.09], + "zs": [0.0, -0.09], + "nfp": 2, + "etabar": 0.95, + "I2": 0.9, + "B2c": -0.7, + "p2": -600000.0, + }, + { + "iota": 0.9596981597369478, + "beta_1s": 3.0336182742616837, + "G2": -0.09758153451238105, + "B20_mean": 1.8129933830726364, + "B20_residual": 0.22096470852551833, + "B20_variation": 0.6235580990378657, + "X20": [1.0359701826468048, 0.9961323682664798, 1.8900857033253329], + "Y20": [-2.4299426345854533e-15, -0.9136862473826926, -0.30321915705664426], + "B20": [2.070309301450683, 1.8875840576321603, 1.4467512024128548], + }, + ), + ( + { + "rc": [1.0, 0.17, 0.01804, 0.001409, 5.877e-5], + "zs": [0.0, 0.1581, 0.01820, 0.001548, 7.772e-5], + "nfp": 4, + "etabar": 1.569, + "B2c": 0.1348, + }, + { + "iota": -1.1441369511851485, + "beta_1s": 0.0, + "G2": 0.0, + "B20_mean": 1.312575397053029, + "B20_residual": 0.032260200125823604, + "B20_variation": 0.11724965804270937, + "X20": [-0.18543205322365838, 0.7244473635400297, 0.8388295002982797], + "Y20": [-1.0252483956584066e-14, -0.07290690883420155, -0.012145324323969307], + "B20": [1.2242278807890326, 1.3246881250407083, 1.3414775388313407], + }, + ), + ], +) +def test_second_order_matches_upstream(parameters, expected): + solution = qsc.Qsc(nphi=31, order="r2", **parameters) + + for name in ("iota", "beta_1s", "G2", "B20_mean", "B20_residual", "B20_variation"): + np.testing.assert_allclose(getattr(solution, name), expected[name], rtol=3e-12, atol=3e-12) + indices = [0, 7, 15] + for name in ("X20", "Y20", "B20"): + np.testing.assert_allclose( + np.asarray(getattr(solution, name))[indices], + expected[name], + rtol=3e-11, + atol=3e-11, + ) diff --git a/tests/unit/test_solvers.py b/tests/unit/test_solvers.py index 83bd59e..287e7b4 100644 --- a/tests/unit/test_solvers.py +++ b/tests/unit/test_solvers.py @@ -6,6 +6,7 @@ from pyqsc_jax.solvers import ( RootSolveOptions, dense_newton_root, + implicit_dense_linear_solve, implicit_dense_root, ) @@ -71,3 +72,51 @@ def root(parameter): def test_root_options_validation(kwargs): with pytest.raises(ValueError): RootSolveOptions(**kwargs) + + +def test_implicit_dense_linear_solve_and_gradient(): + right_hand_side = jnp.asarray([1.0, -0.5]) + + def objective(parameter): + matrix = jnp.asarray([[parameter, 0.2], [-0.4, 1.7]]) + solution, _ = implicit_dense_linear_solve(matrix, right_hand_side) + return jnp.sum(solution**2) + + parameter = 2.0 + matrix = jnp.asarray([[parameter, 0.2], [-0.4, 1.7]]) + solution, report = implicit_dense_linear_solve(matrix, right_hand_side) + np.testing.assert_allclose(solution, jnp.linalg.solve(matrix, right_hand_side)) + assert bool(report.converged) + assert bool(report.finite) + assert bool(report.well_conditioned) + assert report.relative_residual_norm < 1e-14 + + step = 2e-5 + finite_difference = (objective(parameter + step) - objective(parameter - step)) / (2 * step) + np.testing.assert_allclose(jax.grad(objective)(parameter), finite_difference, rtol=2e-8) + + +@pytest.mark.parametrize( + "matrix, right_hand_side, message", + [ + (jnp.ones(2), jnp.ones(2), "square"), + (jnp.ones((2, 3)), jnp.ones(2), "square"), + (jnp.eye(2), jnp.ones((2, 1)), "right_hand_side"), + (jnp.eye(2), jnp.ones(3), "right_hand_side"), + ], +) +def test_linear_solve_shape_validation(matrix, right_hand_side, message): + with pytest.raises(ValueError, match=message): + implicit_dense_linear_solve(matrix, right_hand_side) + + +@pytest.mark.parametrize( + "kwargs, message", + [ + ({"residual_tolerance": -1.0}, "residual_tolerance"), + ({"condition_limit": 0.0}, "condition_limit"), + ], +) +def test_linear_solve_policy_validation(kwargs, message): + with pytest.raises(ValueError, match=message): + implicit_dense_linear_solve(jnp.eye(2), jnp.ones(2), **kwargs) From 5e67237919589ca6dff6bea07a5d06332ffa46cf Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Wed, 29 Jul 2026 23:58:00 -0500 Subject: [PATCH 07/39] feat: add total field Hessian and Mercier diagnostics --- CHANGELOG.md | 9 + README.md | 8 +- docs/api/field-jet.md | 19 ++ docs/development/physics-traceability.md | 3 +- docs/index.md | 9 +- docs/limitations.md | 7 +- docs/quickstart.md | 7 +- docs/theory/field-jet.md | 95 ++++++++ docs/theory/first-order.md | 5 +- docs/theory/second-order.md | 10 +- pyproject.toml | 2 +- src/pyqsc_jax/__init__.py | 8 + src/pyqsc_jax/diagnostics.py | 76 ++++++ src/pyqsc_jax/field.py | 219 ++++++++++++++++++ src/pyqsc_jax/first_order.py | 3 +- src/pyqsc_jax/models.py | 112 +++++++++ src/pyqsc_jax/near_axis.py | 13 +- src/pyqsc_jax/second_order.py | 10 +- tests/physics/test_field_jet.py | 151 ++++++++++++ tests/physics/test_mercier.py | 64 +++++ .../regression/test_first_order_reference.py | 16 +- 21 files changed, 822 insertions(+), 24 deletions(-) create mode 100644 docs/api/field-jet.md create mode 100644 docs/theory/field-jet.md create mode 100644 src/pyqsc_jax/diagnostics.py create mode 100644 src/pyqsc_jax/field.py create mode 100644 tests/physics/test_field_jet.py create mode 100644 tests/physics/test_mercier.py diff --git a/CHANGELOG.md b/CHANGELOG.md index 9ce9dfd..1c380f3 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -31,9 +31,18 @@ first stable release. dense second-order solve. - Independent four-equation r2 residual checks and upstream regression cases spanning vacuum QA, finite pressure/current, and QH topology. +- Regular-coordinate total-field value, gradient, and Hessian on the axis, + including coordinate-map conditioning and Maxwell-identity diagnostics. +- Mercier magnetic-well and geodesic terms matching vacuum and finite-pressure + pyQSC references. +- JIT/JVP, resolution, upstream Hessian, full vacuum-symmetry, divergence, and + derivative-of-divergence validation for the total field jet. ### Fixed - A no-op assignment to legacy `dofs` no longer exchanges normal and binormal cylindrical components. - The legacy sigma calculation no longer assumes exactly five Newton updates. +- Canonical field gradients now use explicit + `(sample, field component, derivative direction)` ordering; the ESSOS + adapter retains its historical layout. diff --git a/README.md b/README.md index 43c6635..9f731ef 100644 --- a/README.md +++ b/README.md @@ -4,9 +4,9 @@ Differentiable near-axis stellarator construction and plasma–coil field jets i JAX. > **Development status:** the immutable first-order core, complete r2 -> coefficient solve, and ESSOS adapter are validated. Second-order field -> Hessian/diagnostics, third order, inverse solves, optimization, and -> plasma/external field jets remain under development on the +> coefficient solve, total-field Hessian, Mercier diagnostics, and ESSOS +> adapter are validated. Singular-radius diagnostics, third order, inverse +> solves, optimization, and plasma/external field jets remain under development on the > `refactor/pyqsc-jax-complete` branch. ## Install @@ -81,6 +81,8 @@ solution = qsc.Qsc( print("B20 residual:", solution.B20_residual) print("linear condition:", solution.linear_report.matrix_condition_number) +print("Mercier:", solution.DMerc_times_r2) +print("Hessian inverse scale:", solution.grad_grad_B_inverse_scale_length) ``` The lower-level immutable axis API supports general, not necessarily diff --git a/docs/api/field-jet.md b/docs/api/field-jet.md new file mode 100644 index 0000000..a7f7721 --- /dev/null +++ b/docs/api/field-jet.md @@ -0,0 +1,19 @@ +# Field-jet and equilibrium diagnostics API + +```{eval-rst} +.. autoclass:: pyqsc_jax.FieldJet + :members: +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.total_field_jet +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.MercierDiagnostics + :members: +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.mercier_diagnostics +``` diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index ccb271b..62e228b 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -10,7 +10,8 @@ to the cited source, not to a duplicated derivation in this repository. | First-order QS and sigma equation | Landreman & Sengupta (2019), arXiv:1908.10253 | `first_order.solve_sigma`; pyQSC `solve_sigma_equation.py` | residual, convergence report, QA/QH/finite-current pyQSC values, JIT/VMAP/JVP/VJP, finite differences | implemented and documented | | Field gradient and `L_grad_B` | Landreman (2021), arXiv:2012.00865, Eq. 3.12 | `first_order.first_order_solution`; pyQSC `grad_B_tensor.py` | upstream arrays, vacuum symmetry/divergence, resolution convergence | implemented and documented | | Complete second-order coefficients | Landreman & Sengupta (2019), arXiv:1908.10253 | `second_order.solve_second_order`; pyQSC `calculate_r2.py`; manuscript Eqs. 36–54 | four independent equation residuals; vacuum QA, finite-pressure/current, QH upstream arrays; JIT/JVP/VJP/finite differences | implemented and documented | -| Total field Hessian | manuscript Eqs. 55–83 | pyQSC generated tensor as comparison only | regular-coordinate chain rule, AD/finite differences, symmetry/divergence | not implemented | +| Total field Hessian | manuscript Eqs. 55–83 | `field.total_field_jet`; pyQSC generated tensor as comparison only | regular-coordinate chain rule, JIT/JVP, QA and finite-current upstream arrays, full vacuum symmetry, divergence and derivative-of-divergence | implemented and documented | +| Magnetic well and Mercier terms | Landreman (2021), arXiv:2012.00865 | `diagnostics.mercier_diagnostics`; pyQSC `mercier.py` | vacuum and finite-pressure/current upstream values | implemented and documented | | Third-order flux constraint and shear | Landreman & Sengupta (2019); Rodríguez et al. shear equations | pyQSC `calculate_r3.py` | upstream r3 arrays and boundary data | not implemented | | Singular radius and scale lengths | Landreman (2021), arXiv:2012.00865 | pyQSC `r_singularity.py` | upstream values; actual coordinate-map regularity | not implemented | | Good-stellarator criteria | Curvo, Ferreira & Jorge (2025), Table 3 | none canonical | exact normalized thresholds and margins | not implemented | diff --git a/docs/index.md b/docs/index.md index c0fbc61..cbdfe54 100644 --- a/docs/index.md +++ b/docs/index.md @@ -14,9 +14,11 @@ limitations theory/coordinates-and-conventions theory/first-order theory/second-order +theory/field-jet api/axis api/first-order api/second-order +api/field-jet ``` ```{toctree} @@ -38,9 +40,10 @@ changelog ## Project status -The immutable first-order API and complete r2 coefficient solve are validated. -Second-order field Hessian/diagnostics, third order, inverse solves, -optimization, and plasma/external field jets are under active development. +The immutable first-order API, complete r2 coefficient solve, total-field +Hessian, and Mercier diagnostics are validated. Singular-radius diagnostics, +third order, inverse solves, optimization, and plasma/external field jets are +under active development. The `pyqsc_jax.near_axis.near_axis` import remains supported for ESSOS without a runtime deprecation warning. diff --git a/docs/limitations.md b/docs/limitations.md index 3b6b90d..8da22f7 100644 --- a/docs/limitations.md +++ b/docs/limitations.md @@ -1,14 +1,13 @@ # Limitations The current computational core includes first order and the complete -finite-pressure/current r2 coefficient solve. The second-order on-axis field -Hessian, Mercier terms, singular-radius diagnostics, and third-order +finite-pressure/current r2 coefficient solve, including the total on-axis +field Hessian and Mercier terms. Singular-radius diagnostics and third-order coefficients are not yet exposed. Known limitations under active refactor include: -- no second-order Hessian/Mercier/singular-radius diagnostics or third-order - solution; +- no singular-radius diagnostics or third-order solution; - no plasma/external field-jet separation; - no branch-aware target-transform inverse solve. diff --git a/docs/quickstart.md b/docs/quickstart.md index ca51d77..7bb09bd 100644 --- a/docs/quickstart.md +++ b/docs/quickstart.md @@ -79,9 +79,14 @@ solution = qsc.Qsc( print(solution.B20_mean) print(solution.B20_residual) print(solution.linear_report.matrix_condition_number) +print(solution.DMerc_times_r2) +print(solution.field_jet.maximum_divergence_gradient) +print(solution.grad_grad_B_inverse_scale_length) ``` The direct r2 outputs are available as attributes such as `X20`, `X2s`, `Y20`, `Z20`, `beta_1s`, `G2`, and `B20`. The immutable nested record is also available as `solution.second_order`. Check both the nonlinear -`root_report` and r2 `linear_report` before accepting a result. +`root_report` and r2 `linear_report` before accepting a result. The canonical +Hessian `solution.grad_grad_B_axis` has shape `(nphi, 3, 3, 3)` and +field-component-first ordering. diff --git a/docs/theory/field-jet.md b/docs/theory/field-jet.md new file mode 100644 index 0000000..0e837f1 --- /dev/null +++ b/docs/theory/field-jet.md @@ -0,0 +1,95 @@ +# Total on-axis field jet + +## Regular coordinates + +The total magnetic field, gradient, and Hessian are computed without +constructing a finite-radius surface. Define the regular transverse +coordinates + +\[ +q_1=r\cos\vartheta,\qquad q_2=r\sin\vartheta. +\] + +Through quadratic order the position is + +\[ +\boldsymbol{x} +=\boldsymbol{r}_0+\boldsymbol{d}_1q_1+\boldsymbol{d}_2q_2 ++\frac12\boldsymbol{h}_{11}q_1^2 ++\boldsymbol{h}_{12}q_1q_2 ++\frac12\boldsymbol{h}_{22}q_2^2. +\] + +The vectors \(\boldsymbol d_a\) come from the first-order coefficients and +\(\boldsymbol h_{ab}\) from the complete second-order solution. Consequently, +the coordinate map and its inverse are nonsingular on axis even though polar +coordinates \((r,\vartheta)\) are not. + +The implementation follows equations 55–83 of the audited surface-free +plasma/coil derivation. It expands + +\[ +\boldsymbol B_{\mathrm{tot}} +=P\left[ +\boldsymbol x_{,\varphi} ++\iota_N(-q_2\boldsymbol x_{,q_1}+q_1\boldsymbol x_{,q_2}) +\right] +\] + +through second order in \(q_1,q_2\), then applies the ordinary inverse-map +chain rule. This avoids the long generated component expressions in pyQSC; +those expressions are retained only as an independent regression reference. + +## A subtle periodicity rule + +Scalar coefficients and cylindrical components are periodic over one field +period. Fixed Cartesian components of a vector generally are not: the +cylindrical basis rotates by \(2\pi/n_{\mathrm{fp}}\). A cylindrical vector +\(\boldsymbol v=(v_R,v_\phi,v_Z)\) is therefore differentiated using + +\[ +\frac{\mathrm d\boldsymbol v}{\mathrm d\varphi} +=\left(v_R'-\phi'v_\phi\right)\boldsymbol e_R ++\left(v_\phi'+\phi'v_R\right)\boldsymbol e_\phi ++v_Z'\boldsymbol e_Z. +\] + +Applying a periodic Fourier derivative directly to Cartesian frame samples +is incorrect for \(n_{\mathrm{fp}}>1\). The connection terms above are part of +the implementation and have dedicated Maxwell-identity and pyQSC regression +tests. + +## Array ordering and diagnostics + +Canonical arrays place the sample axis first: + +- `field[n, i]` is \(B_i\); +- `gradient[n, i, j]` is \(\partial B_i/\partial x_j\); +- `hessian[n, i, j, k]` is + \(\partial^2B_i/(\partial x_j\partial x_k)\). + +`hessian_frenet` follows pyQSC's historical +`(sample, derivative, derivative, field)` ordering in the +`(normal, binormal, tangent)` frame. The compatibility adapter exposes this +array as `grad_grad_B`. + +`FieldJet` includes the regular-coordinate Jacobian, inverse Jacobian, and +coordinate Hessian together with: + +- field and gradient agreement with the lower-order construction; +- \(\nabla\cdot\boldsymbol B\); +- symmetry in the two derivative indices; +- the gradient of \(\nabla\cdot\boldsymbol B\); +- \(L_{\nabla\nabla B}\) and its inverse. + +Vacuum tests additionally require full index symmetry. Finite-current tests +retain only the mixed-spatial-derivative symmetry that Maxwell's equations +require. + +## Mercier quantities + +`MercierDiagnostics` provides the leading near-axis quantities +`d2_volume_d_psi2`, `DGeod_times_r2`, `DWell_times_r2`, and +`DMerc_times_r2`. Their normalization and signs match pyQSC at the audited +upstream commit. The geodesic and well contributions are kept separate so a +caller can inspect cancellations rather than accepting only their sum. diff --git a/docs/theory/first-order.md b/docs/theory/first-order.md index 86a35a0..9aa9bfd 100644 --- a/docs/theory/first-order.md +++ b/docs/theory/first-order.md @@ -99,8 +99,9 @@ L_{\nabla B} \] Canonical arrays use a leading sample axis. Thus `B_axis.shape == -(nphi, 3)` and `grad_B_axis.shape == (nphi, 3, 3)`. The ESSOS adapter preserves -the historical transposed layouts. In the vacuum limit, resolution studies +(nphi, 3)` and `grad_B_axis.shape == (nphi, 3, 3)`, with +`grad_B_axis[n, i, j] = d B_i / d x_j`. The ESSOS adapter preserves the +historical component-axis layout. In the vacuum limit, resolution studies verify the trace-free and symmetric gradient identities spectrally. ## Reference configuration diff --git a/docs/theory/second-order.md b/docs/theory/second-order.md index 62ad0e5..78def4d 100644 --- a/docs/theory/second-order.md +++ b/docs/theory/second-order.md @@ -107,8 +107,8 @@ includes the axis-length-weighted mean, anomaly, normalized weighted G_2=-\frac{\mu_0p_2G_0}{B_0^2}-\iota I_2. \] -All second-order coefficient derivatives needed by the next field-tensor and -diagnostic milestone are stored. Untwisted zero- and second-harmonic +All second-order coefficient derivatives needed by the field tensor and +diagnostics are stored. Untwisted zero- and second-harmonic coefficients are used by the ESSOS-compatible boundary conversion. ## Validation @@ -126,6 +126,6 @@ JIT, VMAP, JVP/VJP consistency, finite differences, and legacy r2 boundary availability are also tested. Reference values are tied to the audited pyQSC commit recorded in the refactor baseline. -This milestone does not yet expose the total-field Hessian, Mercier criterion, -or singular-radius diagnostics. Those are separate validation gates and are -not implied by `order="r2"`. +An r2 solve also computes the regular-coordinate total-field Hessian and the +leading Mercier quantities described in [](field-jet.md). Singular-radius +diagnostics remain a separate validation gate. diff --git a/pyproject.toml b/pyproject.toml index 8234648..ced8a41 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -77,7 +77,7 @@ markers = [ [tool.coverage.run] branch = true -source = ["src/pyqsc_jax"] +source = ["pyqsc_jax"] [tool.coverage.report] fail_under = 95 diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index 9462fab..3a0dbd5 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -1,9 +1,13 @@ """Differentiable near-axis stellarator construction in JAX.""" from pyqsc_jax.axis import Axis +from pyqsc_jax.diagnostics import mercier_diagnostics +from pyqsc_jax.field import total_field_jet from pyqsc_jax.first_order import Qsc, solve from pyqsc_jax.models import ( + FieldJet, LinearSolveReport, + MercierDiagnostics, NearAxisInputs, NearAxisSolution, RootSolveReport, @@ -15,7 +19,9 @@ __all__ = [ "Axis", + "FieldJet", "LinearSolveReport", + "MercierDiagnostics", "NearAxisInputs", "NearAxisSolution", "Qsc", @@ -24,7 +30,9 @@ "SecondOrderData", "SecondOrderResiduals", "near_axis", + "mercier_diagnostics", "second_order_residuals", "solve", + "total_field_jet", ] __version__ = "0.2.0.dev0" diff --git a/src/pyqsc_jax/diagnostics.py b/src/pyqsc_jax/diagnostics.py new file mode 100644 index 0000000..dd77ba0 --- /dev/null +++ b/src/pyqsc_jax/diagnostics.py @@ -0,0 +1,76 @@ +"""Near-axis equilibrium diagnostics.""" + +from __future__ import annotations + +import jax.numpy as jnp + +from pyqsc_jax.models import MercierDiagnostics, NearAxisSolution +from pyqsc_jax.second_order import MU0 + + +def mercier_diagnostics(solution: NearAxisSolution) -> MercierDiagnostics: + """Compute the leading magnetic-well and Mercier terms. + + The normalization and signs follow the standard pyQSC implementation. + """ + + r2 = solution.second_order + if r2 is None: + raise ValueError("A second-order solution is required for Mercier diagnostics.") + + inputs = solution.inputs + geometry = solution.geometry + etabar_squared = inputs.etabar**2 + curvature_squared = solution.curvature**2 + numerator = ( + etabar_squared**2 + + curvature_squared**2 * solution.sigma**2 + + etabar_squared * curvature_squared + ) + denominator = ( + etabar_squared**2 + + curvature_squared**2 * (1 + solution.sigma**2) + + 2 * etabar_squared * curvature_squared + ) + integrand = geometry.d_l_d_phi * numerator / denominator + weighted_integral = ( + jnp.sum(integrand) + * (2 * jnp.pi / (inputs.axis.nfp * inputs.nphi)) + * inputs.axis.nfp + * 2 + * jnp.pi + / geometry.axis_length + ) + DGeod_times_r2 = ( + -2 + * MU0**2 + * inputs.p2**2 + * solution.G0**4 + * etabar_squared + / (jnp.pi**3 * inputs.B0**10 * solution.iotaN**2) + * weighted_integral + ) + d2_volume_d_psi2 = ( + 4 + * jnp.pi**2 + * jnp.abs(solution.G0) + / inputs.B0**3 + * ( + 3 * etabar_squared + - 4 * r2.B20_mean / inputs.B0 + + 2 * (r2.G2 + solution.iota * inputs.I2) / solution.G0 + ) + ) + DWell_times_r2 = ( + MU0 + * inputs.p2 + * jnp.abs(solution.G0) + / (8 * jnp.pi**4 * inputs.B0**3) + * (d2_volume_d_psi2 - 8 * jnp.pi**2 * MU0 * inputs.p2 * jnp.abs(solution.G0) / inputs.B0**5) + ) + return MercierDiagnostics( + d2_volume_d_psi2=d2_volume_d_psi2, + DGeod_times_r2=DGeod_times_r2, + DWell_times_r2=DWell_times_r2, + DMerc_times_r2=DWell_times_r2 + DGeod_times_r2, + ) diff --git a/src/pyqsc_jax/field.py b/src/pyqsc_jax/field.py new file mode 100644 index 0000000..069eba5 --- /dev/null +++ b/src/pyqsc_jax/field.py @@ -0,0 +1,219 @@ +"""Surface-free total magnetic field jets on the magnetic axis.""" + +from __future__ import annotations + +import jax +import jax.numpy as jnp + +from pyqsc_jax.geometry import cylindrical_vector_to_cartesian +from pyqsc_jax.models import FieldJet, NearAxisSolution + + +def _differentiate_cylindrical_vector( + vector: jax.Array, + solution: NearAxisSolution, +) -> jax.Array: + """Differentiate a vector with respect to Boozer ``varphi``. + + Cylindrical components are periodic over one field period, while fixed + Cartesian components generally are not. The two connection terms below + account for rotation of the cylindrical basis. + """ + + derivative = solution.geometry.d_d_varphi @ vector + d_phi_d_varphi = 1 / solution.geometry.d_varphi_d_phi + derivative = derivative.at[:, 0].add(-d_phi_d_varphi * vector[:, 1]) + return derivative.at[:, 1].add(d_phi_d_varphi * vector[:, 0]) + + +def _to_cartesian(vector: jax.Array, solution: NearAxisSolution) -> jax.Array: + return cylindrical_vector_to_cartesian(vector, solution.phi) + + +def total_field_jet(solution: NearAxisSolution) -> FieldJet: + """Compute ``B``, ``grad(B)``, and ``grad(grad(B))`` on the axis. + + This is the regular-coordinate chain rule in equations (55)--(83) of the + surface-free plasma/coil derivation. It requires the complete second-order + near-axis solution but no finite-radius surface. + """ + + r2 = solution.second_order + if r2 is None: + raise ValueError("A second-order solution is required for the field Hessian.") + + geometry = solution.geometry + inputs = solution.inputs + length_scale = geometry.abs_G0_over_B0 + tangent = geometry.tangent_cylindrical + normal = geometry.normal_cylindrical + binormal = geometry.binormal_cylindrical + + d1 = solution.X1c[:, None] * normal + solution.Y1c[:, None] * binormal + d2 = solution.Y1s[:, None] * binormal + h11 = ( + 2 * (r2.X20 + r2.X2c)[:, None] * normal + + 2 * (r2.Y20 + r2.Y2c)[:, None] * binormal + + 2 * (r2.Z20 + r2.Z2c)[:, None] * tangent + ) + h12 = ( + 2 * r2.X2s[:, None] * normal + + 2 * r2.Y2s[:, None] * binormal + + 2 * r2.Z2s[:, None] * tangent + ) + h22 = ( + 2 * (r2.X20 - r2.X2c)[:, None] * normal + + 2 * (r2.Y20 - r2.Y2c)[:, None] * binormal + + 2 * (r2.Z20 - r2.Z2c)[:, None] * tangent + ) + + derivative = lambda vector: _differentiate_cylindrical_vector(vector, solution) # noqa: E731 + V0 = length_scale * tangent + V1 = derivative(d1) + solution.iotaN * d2 + V2 = derivative(d2) - solution.iotaN * d1 + V11 = derivative(h11) + 2 * solution.iotaN * h12 + V12 = derivative(h12) + solution.iotaN * (h22 - h11) + V22 = derivative(h22) - 2 * solution.iotaN * h12 + + p0 = inputs.B0**2 / solution.G0 + p1 = 2 * inputs.B0**2 * inputs.etabar / solution.G0 + flux_term = inputs.B0**2 * (r2.G2 + solution.iota * inputs.I2) / solution.G0**2 + C11 = ( + inputs.B0**2 * inputs.etabar**2 + 2 * inputs.B0 * (r2.B20 + inputs.B2c) + ) / solution.G0 - flux_term + C22 = 2 * inputs.B0 * (r2.B20 - inputs.B2c) / solution.G0 - flux_term + + field_coordinate_gradient_cylindrical = jnp.stack( + ( + p0 * derivative(V0), + p1 * V0 + p0 * V1, + p0 * V2, + ), + axis=-1, + ) + field_coordinate_hessian_cylindrical = jnp.zeros( + (inputs.nphi, 3, 3, 3), + dtype=field_coordinate_gradient_cylindrical.dtype, + ) + coordinate_hessian_values = { + (0, 0): p0 * derivative(derivative(V0)), + (0, 1): p1 * derivative(V0) + p0 * derivative(V1), + (0, 2): p0 * derivative(V2), + (1, 1): 2 * C11[:, None] * V0 + 2 * p1 * V1 + p0 * V11, + (1, 2): p1 * V2 + p0 * V12, + (2, 2): 2 * C22[:, None] * V0 + p0 * V22, + } + for (first, second), value in coordinate_hessian_values.items(): + field_coordinate_hessian_cylindrical = field_coordinate_hessian_cylindrical.at[ + :, :, first, second + ].set(value) + field_coordinate_hessian_cylindrical = field_coordinate_hessian_cylindrical.at[ + :, :, second, first + ].set(value) + + field_coordinate_gradient = jnp.stack( + [ + _to_cartesian(field_coordinate_gradient_cylindrical[:, :, index], solution) + for index in range(3) + ], + axis=-1, + ) + field_coordinate_hessian = jnp.stack( + [ + jnp.stack( + [ + _to_cartesian( + field_coordinate_hessian_cylindrical[:, :, first, second], + solution, + ) + for second in range(3) + ], + axis=-1, + ) + for first in range(3) + ], + axis=-1, + ) + + coordinate_jacobian = jnp.stack( + ( + length_scale * geometry.tangent_cartesian, + _to_cartesian(d1, solution), + _to_cartesian(d2, solution), + ), + axis=-1, + ) + coordinate_hessian = jnp.zeros_like(field_coordinate_hessian) + map_hessian_values = { + (0, 0): length_scale**2 * solution.curvature[:, None] * geometry.normal_cartesian, + (0, 1): _to_cartesian(derivative(d1), solution), + (0, 2): _to_cartesian(derivative(d2), solution), + (1, 1): _to_cartesian(h11, solution), + (1, 2): _to_cartesian(h12, solution), + (2, 2): _to_cartesian(h22, solution), + } + for (first, second), value in map_hessian_values.items(): + coordinate_hessian = coordinate_hessian.at[:, :, first, second].set(value) + coordinate_hessian = coordinate_hessian.at[:, :, second, first].set(value) + + inverse_coordinate_jacobian = jnp.linalg.inv(coordinate_jacobian) + gradient = jnp.einsum( + "nia,naj->nij", + field_coordinate_gradient, + inverse_coordinate_jacobian, + ) + hessian = jnp.einsum( + "niab,naj,nbk->nijk", + field_coordinate_hessian, + inverse_coordinate_jacobian, + inverse_coordinate_jacobian, + ) - jnp.einsum( + "nia,nal,nlcb,ncj,nbk->nijk", + field_coordinate_gradient, + inverse_coordinate_jacobian, + coordinate_hessian, + inverse_coordinate_jacobian, + inverse_coordinate_jacobian, + ) + field = p0 * _to_cartesian(V0, solution) + + frenet_basis = jnp.stack( + ( + geometry.normal_cartesian, + geometry.binormal_cartesian, + geometry.tangent_cartesian, + ), + axis=-1, + ) + field_first_frenet = jnp.einsum( + "nia,nijk,njb,nkc->nabc", + frenet_basis, + hessian, + frenet_basis, + frenet_basis, + ) + hessian_frenet = jnp.transpose(field_first_frenet, (0, 2, 3, 1)) + + norm_squared = jnp.sum(hessian**2, axis=(1, 2, 3)) + inverse_scale_vs_varphi = jnp.sqrt(jnp.sqrt(norm_squared) / (4 * inputs.B0)) + coordinate_determinant = jnp.linalg.det(coordinate_jacobian) + divergence = jnp.trace(gradient, axis1=1, axis2=2) + divergence_gradient = jnp.einsum("niik->nk", hessian) + return FieldJet( + field=field, + gradient=gradient, + hessian=hessian, + hessian_frenet=hessian_frenet, + coordinate_jacobian=coordinate_jacobian, + inverse_coordinate_jacobian=inverse_coordinate_jacobian, + coordinate_hessian=coordinate_hessian, + minimum_absolute_coordinate_jacobian=jnp.min(jnp.abs(coordinate_determinant)), + maximum_field_error=jnp.max(jnp.abs(field - solution.B_axis)), + maximum_gradient_error=jnp.max(jnp.abs(gradient - solution.grad_B_axis)), + maximum_divergence=jnp.max(jnp.abs(divergence)), + maximum_derivative_asymmetry=jnp.max(jnp.abs(hessian - jnp.swapaxes(hessian, 2, 3))), + maximum_divergence_gradient=jnp.max(jnp.abs(divergence_gradient)), + grad_grad_B_inverse_scale_length_vs_varphi=inverse_scale_vs_varphi, + L_grad_grad_B=1 / inverse_scale_vs_varphi, + grad_grad_B_inverse_scale_length=jnp.max(inverse_scale_vs_varphi), + ) diff --git a/src/pyqsc_jax/first_order.py b/src/pyqsc_jax/first_order.py index c4ebe18..d3322b8 100644 --- a/src/pyqsc_jax/first_order.py +++ b/src/pyqsc_jax/first_order.py @@ -81,7 +81,7 @@ def _assemble_gradient( tt: jax.Array, ) -> jax.Array: outer = lambda left, right: jnp.einsum("ni,nj->nij", left, right) # noqa: E731 - return ( + pyqsc_component_expression = ( nn[:, None, None] * outer(normal, normal) + bn[:, None, None] * outer(binormal, normal) + nb[:, None, None] * outer(normal, binormal) @@ -90,6 +90,7 @@ def _assemble_gradient( + nt[:, None, None] * outer(normal, tangent) + tt[:, None, None] * outer(tangent, tangent) ) + return jnp.swapaxes(pyqsc_component_expression, -1, -2) def first_order_solution( diff --git a/src/pyqsc_jax/models.py b/src/pyqsc_jax/models.py index 9bc2967..ecae9e0 100644 --- a/src/pyqsc_jax/models.py +++ b/src/pyqsc_jax/models.py @@ -58,6 +58,45 @@ class LinearSolveReport: well_conditioned: jax.Array +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class MercierDiagnostics: + """Leading near-axis magnetic-well and Mercier contributions.""" + + d2_volume_d_psi2: jax.Array + DGeod_times_r2: jax.Array + DWell_times_r2: jax.Array + DMerc_times_r2: jax.Array + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class FieldJet: + """Total on-axis magnetic field through two Cartesian derivatives. + + ``gradient`` and ``hessian`` use field-component-first ordering: + ``gradient[n, i, j] = d B_i / d x_j`` and + ``hessian[n, i, j, k] = d² B_i / (d x_j d x_k)``. + """ + + field: jax.Array + gradient: jax.Array + hessian: jax.Array + hessian_frenet: jax.Array + coordinate_jacobian: jax.Array + inverse_coordinate_jacobian: jax.Array + coordinate_hessian: jax.Array + minimum_absolute_coordinate_jacobian: jax.Array + maximum_field_error: jax.Array + maximum_gradient_error: jax.Array + maximum_divergence: jax.Array + maximum_derivative_asymmetry: jax.Array + maximum_divergence_gradient: jax.Array + grad_grad_B_inverse_scale_length_vs_varphi: jax.Array + L_grad_grad_B: jax.Array + grad_grad_B_inverse_scale_length: jax.Array + + @jax.tree_util.register_dataclass @dataclass(frozen=True) class NearAxisInputs: @@ -179,10 +218,24 @@ class NearAxisSolution: grad_B_axis: jax.Array L_grad_B: jax.Array second_order: SecondOrderData | None = None + mercier: MercierDiagnostics | None = None + field_jet: FieldJet | None = None _SECOND_ORDER_NAMES: ClassVar[frozenset[str]] = frozenset( field.name for field in SecondOrderData.__dataclass_fields__.values() ) + _MERCIER_NAMES: ClassVar[frozenset[str]] = frozenset( + field.name for field in MercierDiagnostics.__dataclass_fields__.values() + ) + _FIELD_JET_NAMES: ClassVar[frozenset[str]] = frozenset( + { + "grad_grad_B_axis", + "grad_grad_B", + "L_grad_grad_B", + "grad_grad_B_inverse_scale_length_vs_varphi", + "grad_grad_B_inverse_scale_length", + } + ) def __getattr__(self, name: str): if name in self._SECOND_ORDER_NAMES: @@ -190,8 +243,27 @@ def __getattr__(self, name: str): if second_order is None: raise AttributeError(f"First-order solution has no {name!r} quantity.") return getattr(second_order, name) + if name in self._MERCIER_NAMES: + mercier = object.__getattribute__(self, "mercier") + if mercier is None: + raise AttributeError("First-order solution has no Mercier diagnostics.") + return getattr(mercier, name) + if name in self._FIELD_JET_NAMES: + raise AttributeError("First-order solution has no second-derivative field jet.") raise AttributeError(f"{type(self).__name__!s} has no attribute {name!r}.") + def _require_mercier(self) -> MercierDiagnostics: + mercier = object.__getattribute__(self, "mercier") + if mercier is None: + raise AttributeError("First-order solution has no Mercier diagnostics.") + return mercier + + def _require_field_jet(self) -> FieldJet: + field_jet = object.__getattribute__(self, "field_jet") + if field_jet is None: + raise AttributeError("First-order solution has no second-derivative field jet.") + return field_jet + @property def axis(self) -> Axis: return self.inputs.axis @@ -223,3 +295,43 @@ def torsion(self) -> jax.Array: @property def axis_length(self) -> jax.Array: return self.geometry.axis_length + + @property + def d2_volume_d_psi2(self) -> jax.Array: + return self._require_mercier().d2_volume_d_psi2 + + @property + def DGeod_times_r2(self) -> jax.Array: + return self._require_mercier().DGeod_times_r2 + + @property + def DWell_times_r2(self) -> jax.Array: + return self._require_mercier().DWell_times_r2 + + @property + def DMerc_times_r2(self) -> jax.Array: + return self._require_mercier().DMerc_times_r2 + + @property + def grad_grad_B_axis(self) -> jax.Array: + """Cartesian Hessian in ``(sample, field, derivative, derivative)`` order.""" + + return self._require_field_jet().hessian + + @property + def grad_grad_B(self) -> jax.Array: + """pyQSC-compatible Frenet Hessian in ``(sample, d, d, field)`` order.""" + + return self._require_field_jet().hessian_frenet + + @property + def L_grad_grad_B(self) -> jax.Array: + return self._require_field_jet().L_grad_grad_B + + @property + def grad_grad_B_inverse_scale_length_vs_varphi(self) -> jax.Array: + return self._require_field_jet().grad_grad_B_inverse_scale_length_vs_varphi + + @property + def grad_grad_B_inverse_scale_length(self) -> jax.Array: + return self._require_field_jet().grad_grad_B_inverse_scale_length diff --git a/src/pyqsc_jax/near_axis.py b/src/pyqsc_jax/near_axis.py index ed41e4d..f6458b0 100644 --- a/src/pyqsc_jax/near_axis.py +++ b/src/pyqsc_jax/near_axis.py @@ -96,7 +96,7 @@ def _legacy_tuple(solution: NearAxisSolution) -> tuple[jax.Array, ...]: solution.sigma, solution.elongation, solution.B_axis.T, - solution.grad_B_axis.T, + jnp.moveaxis(solution.grad_B_axis, 0, -1), solution.axis_length, solution.iota, solution.iotaN, @@ -158,6 +158,17 @@ def _refresh(self) -> None: if solution.second_order is not None: for name in solution._SECOND_ORDER_NAMES: setattr(self, name, getattr(solution, name)) + self.d2_volume_d_psi2 = solution.d2_volume_d_psi2 + self.DGeod_times_r2 = solution.DGeod_times_r2 + self.DWell_times_r2 = solution.DWell_times_r2 + self.DMerc_times_r2 = solution.DMerc_times_r2 + self.grad_grad_B = solution.grad_grad_B + self.grad_grad_B_axis = jnp.moveaxis(solution.grad_grad_B_axis, 0, -1) + self.L_grad_grad_B = solution.L_grad_grad_B + self.grad_grad_B_inverse_scale_length_vs_varphi = ( + solution.grad_grad_B_inverse_scale_length_vs_varphi + ) + self.grad_grad_B_inverse_scale_length = solution.grad_grad_B_inverse_scale_length @property def dofs(self) -> jax.Array: diff --git a/src/pyqsc_jax/second_order.py b/src/pyqsc_jax/second_order.py index bfa9f65..1aff722 100644 --- a/src/pyqsc_jax/second_order.py +++ b/src/pyqsc_jax/second_order.py @@ -362,7 +362,15 @@ def untwist(sine_coefficient, cosine_coefficient): Z2s_untwisted=Z2s_untwisted, Z2c_untwisted=Z2c_untwisted, ) - return replace(first_order, second_order=second_order) + solution = replace(first_order, second_order=second_order) + from pyqsc_jax.diagnostics import mercier_diagnostics + from pyqsc_jax.field import total_field_jet + + return replace( + solution, + mercier=mercier_diagnostics(solution), + field_jet=total_field_jet(solution), + ) def second_order_residuals(solution: NearAxisSolution) -> SecondOrderResiduals: diff --git a/tests/physics/test_field_jet.py b/tests/physics/test_field_jet.py new file mode 100644 index 0000000..afd1111 --- /dev/null +++ b/tests/physics/test_field_jet.py @@ -0,0 +1,151 @@ +import jax +import numpy as np +import pytest + +import pyqsc_jax as qsc + + +def _vacuum_qa(nphi=61): + return qsc.Qsc( + rc=[1.0, 0.155, 0.0102], + zs=[0.0, 0.154, 0.0111], + nfp=2, + etabar=0.64, + B2c=-0.00322, + nphi=nphi, + order="r2", + ) + + +def _finite_pressure_current(nphi=61): + return qsc.Qsc( + rc=[1.0, 0.09], + zs=[0.0, -0.09], + nfp=2, + etabar=0.95, + I2=0.9, + B2c=-0.7, + p2=-600000.0, + nphi=nphi, + order="r2", + ) + + +@pytest.mark.parametrize("factory", [_vacuum_qa, _finite_pressure_current]) +def test_total_field_jet_satisfies_chain_rule_and_maxwell_identities(factory): + solution = factory() + jet = solution.field_jet + + assert jet is not None + assert jet.field.shape == (61, 3) + assert jet.gradient.shape == (61, 3, 3) + assert jet.hessian.shape == (61, 3, 3, 3) + assert jet.hessian_frenet.shape == (61, 3, 3, 3) + assert jet.coordinate_jacobian.shape == (61, 3, 3) + assert jet.coordinate_hessian.shape == (61, 3, 3, 3) + assert jet.minimum_absolute_coordinate_jacobian > 0.9 + assert jet.maximum_field_error < 5e-15 + assert jet.maximum_gradient_error < 2e-8 + assert jet.maximum_divergence < 3e-8 + assert jet.maximum_derivative_asymmetry < 2e-13 + assert jet.maximum_divergence_gradient < 5e-5 + np.testing.assert_allclose(solution.grad_grad_B_axis, jet.hessian) + np.testing.assert_allclose(solution.grad_grad_B, jet.hessian_frenet) + + +def test_vacuum_field_hessian_is_fully_symmetric_and_trace_free(): + solution = _vacuum_qa() + hessian = solution.field_jet.hessian + + np.testing.assert_allclose(hessian, np.swapaxes(hessian, 1, 2), rtol=0, atol=7e-7) + np.testing.assert_allclose(hessian, np.swapaxes(hessian, 1, 3), rtol=0, atol=7e-7) + np.testing.assert_allclose( + np.einsum("niik->nk", hessian), + 0, + rtol=0, + atol=7e-7, + ) + + +@pytest.mark.parametrize( + "factory, expected_components, expected_inverse_scale", + [ + ( + _vacuum_qa, + { + (0, 0, 0): [2.5058735043974697e-11, 1.3780320235299797, -3.0796390010619596], + (0, 2, 1): [2.5345018639059774e-14, -0.9042329447022055, 0.04480778724398558], + (1, 2, 2): [-1.0583277338937587, -1.0542622720207702, 1.4815487851166125], + }, + 2.8316255897272793, + ), + ( + _finite_pressure_current, + { + (0, 0, 0): [-1.0984223013409288e-11, -0.4764076511218376, 1.041130887765426], + (0, 2, 1): [-1.044435577486018e-14, -0.4447191502214616, 0.220359403292567], + (1, 2, 2): [1.2467274928318781, 1.4565818008885116, -0.5095116177456592], + }, + 2.031147679042703, + ), + ], +) +def test_field_hessian_matches_upstream_pyqsc( + factory, + expected_components, + expected_inverse_scale, +): + solution = factory() + indices = [0, 15, 30] + + for component, expected in expected_components.items(): + np.testing.assert_allclose( + np.asarray(solution.grad_grad_B)[indices, *component], + expected, + rtol=3e-6, + atol=2e-6, + ) + np.testing.assert_allclose( + solution.grad_grad_B_inverse_scale_length, + expected_inverse_scale, + rtol=3e-7, + ) + + +def test_field_hessian_resolution_convergence(): + medium = _vacuum_qa(nphi=61) + fine = _vacuum_qa(nphi=91) + + np.testing.assert_allclose( + np.asarray(medium.grad_grad_B)[0], + np.asarray(fine.grad_grad_B)[0], + rtol=2e-6, + atol=2e-6, + ) + np.testing.assert_allclose( + medium.grad_grad_B_inverse_scale_length_vs_varphi[0], + fine.grad_grad_B_inverse_scale_length_vs_varphi[0], + rtol=2e-6, + ) + + +def test_field_hessian_supports_jit_and_jvp(): + def component(etabar): + solution = qsc.Qsc( + rc=[1.0, 0.155, 0.0102], + zs=[0.0, 0.154, 0.0111], + nfp=2, + etabar=etabar, + B2c=-0.00322, + nphi=31, + order="r2", + ) + return solution.grad_grad_B_axis[7, 0, 1, 2] + + eager_value = component(0.64) + compiled_value = jax.jit(component)(0.64) + value, tangent = jax.jvp(component, (0.64,), (1.0,)) + + np.testing.assert_allclose(compiled_value, eager_value, rtol=2e-11, atol=2e-11) + np.testing.assert_allclose(value, eager_value, rtol=3e-12, atol=3e-12) + assert np.isfinite(tangent) diff --git a/tests/physics/test_mercier.py b/tests/physics/test_mercier.py new file mode 100644 index 0000000..03ac8d6 --- /dev/null +++ b/tests/physics/test_mercier.py @@ -0,0 +1,64 @@ +import numpy as np +import pytest + +import pyqsc_jax as qsc + + +def test_mercier_diagnostics_match_upstream_finite_pressure_reference(): + solution = qsc.Qsc( + rc=[1.0, 0.09], + zs=[0.0, -0.09], + nfp=2, + etabar=0.95, + I2=0.9, + B2c=-0.7, + p2=-600000.0, + nphi=61, + order="r2", + ) + + expected = { + "d2_volume_d_psi2": -121.81059604927127, + "DGeod_times_r2": -0.1210731174740698, + "DWell_times_r2": 0.06028523900360924, + "DMerc_times_r2": -0.06078787847046056, + } + for name, value in expected.items(): + np.testing.assert_allclose(getattr(solution, name), value, rtol=3e-12, atol=3e-12) + np.testing.assert_allclose(getattr(solution.mercier, name), value, rtol=3e-12, atol=3e-12) + + +def test_vacuum_mercier_pressure_terms_vanish(): + solution = qsc.Qsc( + rc=[1.0, 0.155, 0.0102], + zs=[0.0, 0.154, 0.0111], + nfp=2, + etabar=0.64, + B2c=-0.00322, + nphi=61, + order="r2", + ) + + np.testing.assert_allclose(solution.d2_volume_d_psi2, 23.98845128286806, rtol=3e-12) + assert solution.DGeod_times_r2 == 0 + assert solution.DWell_times_r2 == 0 + assert solution.DMerc_times_r2 == 0 + + +def test_second_order_diagnostics_reject_first_order_solution(): + solution = qsc.Qsc( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + nphi=31, + ) + + with pytest.raises(ValueError, match="second-order"): + qsc.mercier_diagnostics(solution) + with pytest.raises(ValueError, match="second-order"): + qsc.total_field_jet(solution) + with pytest.raises(AttributeError, match="Mercier"): + _ = solution.DMerc_times_r2 + with pytest.raises(AttributeError, match="second-derivative"): + _ = solution.grad_grad_B_axis diff --git a/tests/regression/test_first_order_reference.py b/tests/regression/test_first_order_reference.py index 9c1a6eb..8243eb0 100644 --- a/tests/regression/test_first_order_reference.py +++ b/tests/regression/test_first_order_reference.py @@ -21,7 +21,7 @@ def test_standard_solution_matches_legacy_and_upstream_reference(): np.testing.assert_allclose(solution.B_axis, legacy.B_axis.T, rtol=2e-13, atol=2e-13) np.testing.assert_allclose( solution.grad_B_axis, - legacy.grad_B_axis.T, + np.moveaxis(legacy.grad_B_axis, -1, 0), rtol=2e-12, atol=2e-12, ) @@ -45,6 +45,20 @@ def test_finite_current_and_sigma0_match_upstream_reference(): np.testing.assert_allclose(solution.G0, 1.2108964178133113, rtol=2e-13) np.testing.assert_allclose(np.max(np.abs(solution.sigma)), 1.1527807285268685, rtol=2e-13) np.testing.assert_allclose(solution.mean_elongation, 2.300022135471462, rtol=2e-13) + indices = [0, 7, 15] + expected_gradient_components = { + (0, 1): [-1.4189028123671708, -0.024458076547534513, 0.31866877632846324], + (1, 0): [-1.4958375512360236, -0.03652380306707692, 0.40219561346636035], + (0, 2): [1.248855714330292, 0.24413995843927835, -0.7230617247040809], + (2, 0): [0.6533238467899136, -0.2490021462405346, -1.0300929188685888], + } + for component, expected in expected_gradient_components.items(): + np.testing.assert_allclose( + np.asarray(solution.grad_B_axis)[indices, *component], + expected, + rtol=3e-12, + atol=3e-12, + ) def test_qh_topology_matches_upstream_reference(): From 0086d772979f9d5570f2030789fd60310caec85a Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 00:16:02 -0500 Subject: [PATCH 08/39] feat: add regular-map singular radius diagnostics --- CHANGELOG.md | 3 + README.md | 5 +- docs/api/field-jet.md | 9 + docs/development/physics-traceability.md | 2 +- docs/index.md | 6 +- docs/limitations.md | 6 +- docs/quickstart.md | 4 +- docs/theory/field-jet.md | 31 ++++ src/pyqsc_jax/__init__.py | 4 + src/pyqsc_jax/field.py | 37 ++-- src/pyqsc_jax/models.py | 64 +++++++ src/pyqsc_jax/near_axis.py | 6 + src/pyqsc_jax/second_order.py | 2 + src/pyqsc_jax/singularity.py | 215 +++++++++++++++++++++++ tests/physics/test_singularity.py | 177 +++++++++++++++++++ 15 files changed, 549 insertions(+), 22 deletions(-) create mode 100644 src/pyqsc_jax/singularity.py create mode 100644 tests/physics/test_singularity.py diff --git a/CHANGELOG.md b/CHANGELOG.md index 1c380f3..1eb479a 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -37,6 +37,9 @@ first stable release. pyQSC references. - JIT/JVP, resolution, upstream Hessian, full vacuum-symmetry, divergence, and derivative-of-divergence validation for the total field jet. +- Singular-radius diagnostics derived directly from the regular-coordinate + Jacobian determinant, with vectorized global angular seeding, Newton + refinement, residual reports, and pyQSC QA/QH/finite-current parity. ### Fixed diff --git a/README.md b/README.md index 9f731ef..503d201 100644 --- a/README.md +++ b/README.md @@ -5,8 +5,8 @@ JAX. > **Development status:** the immutable first-order core, complete r2 > coefficient solve, total-field Hessian, Mercier diagnostics, and ESSOS -> adapter are validated. Singular-radius diagnostics, third order, inverse -> solves, optimization, and plasma/external field jets remain under development on the +> adapter are validated, including singular-radius diagnostics. Third order, +> inverse solves, optimization, and plasma/external field jets remain under development on the > `refactor/pyqsc-jax-complete` branch. ## Install @@ -83,6 +83,7 @@ print("B20 residual:", solution.B20_residual) print("linear condition:", solution.linear_report.matrix_condition_number) print("Mercier:", solution.DMerc_times_r2) print("Hessian inverse scale:", solution.grad_grad_B_inverse_scale_length) +print("singular radius:", solution.r_singularity) ``` The lower-level immutable axis API supports general, not necessarily diff --git a/docs/api/field-jet.md b/docs/api/field-jet.md index a7f7721..55d4ed7 100644 --- a/docs/api/field-jet.md +++ b/docs/api/field-jet.md @@ -17,3 +17,12 @@ ```{eval-rst} .. autofunction:: pyqsc_jax.mercier_diagnostics ``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.SingularityDiagnostics + :members: +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.singularity_diagnostics +``` diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index 62e228b..a3cf550 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -13,7 +13,7 @@ to the cited source, not to a duplicated derivation in this repository. | Total field Hessian | manuscript Eqs. 55–83 | `field.total_field_jet`; pyQSC generated tensor as comparison only | regular-coordinate chain rule, JIT/JVP, QA and finite-current upstream arrays, full vacuum symmetry, divergence and derivative-of-divergence | implemented and documented | | Magnetic well and Mercier terms | Landreman (2021), arXiv:2012.00865 | `diagnostics.mercier_diagnostics`; pyQSC `mercier.py` | vacuum and finite-pressure/current upstream values | implemented and documented | | Third-order flux constraint and shear | Landreman & Sengupta (2019); Rodríguez et al. shear equations | pyQSC `calculate_r3.py` | upstream r3 arrays and boundary data | not implemented | -| Singular radius and scale lengths | Landreman (2021), arXiv:2012.00865 | pyQSC `r_singularity.py` | upstream values; actual coordinate-map regularity | not implemented | +| Singular radius and scale lengths | Landreman (2021), arXiv:2012.00865 | `singularity.singularity_diagnostics`; pyQSC `r_singularity.py` as comparison | direct regular-map determinant, QA/QH/finite-current upstream radii and arrays, residual, angular convergence, JIT/JVP/finite differences | implemented and documented | | Good-stellarator criteria | Curvo, Ferreira & Jorge (2025), Table 3 | none canonical | exact normalized thresholds and margins | not implemented | | Plasma current source | manuscript Eqs. 88–97 | none | normalization, enclosed current, straight circular/elliptic channels | not implemented | | Plasma on-axis field | manuscript Eqs. 136–138 | none | full-torus periodicity, matching cancellation, resolved volume Biot–Savart | not implemented | diff --git a/docs/index.md b/docs/index.md index cbdfe54..b35fe3f 100644 --- a/docs/index.md +++ b/docs/index.md @@ -41,9 +41,9 @@ changelog ## Project status The immutable first-order API, complete r2 coefficient solve, total-field -Hessian, and Mercier diagnostics are validated. Singular-radius diagnostics, -third order, inverse solves, optimization, and plasma/external field jets are -under active development. +Hessian, Mercier terms, and singular-radius diagnostics are validated. Third +order, inverse solves, optimization, and plasma/external field jets are under +active development. The `pyqsc_jax.near_axis.near_axis` import remains supported for ESSOS without a runtime deprecation warning. diff --git a/docs/limitations.md b/docs/limitations.md index 8da22f7..9402047 100644 --- a/docs/limitations.md +++ b/docs/limitations.md @@ -2,12 +2,12 @@ The current computational core includes first order and the complete finite-pressure/current r2 coefficient solve, including the total on-axis -field Hessian and Mercier terms. Singular-radius diagnostics and third-order +field Hessian, Mercier terms, and singular-radius diagnostics. Third-order coefficients are not yet exposed. Known limitations under active refactor include: -- no singular-radius diagnostics or third-order solution; +- no third-order solution; - no plasma/external field-jet separation; - no branch-aware target-transform inverse solve. @@ -18,7 +18,7 @@ the structured report. Production workflows must reject Frenet coordinates are invalid when the magnetic-axis curvature vanishes. `GeometryDiagnostics` reports this condition explicitly; high-level rejection -policy will be added alongside the second-order validity report. +policy will be added alongside the aggregate design-criteria report. Near-axis results are asymptotic in distance from the axis. “Surface-free” plasma–coil separation does not mean radius-free: a formal minor radius or an diff --git a/docs/quickstart.md b/docs/quickstart.md index 7bb09bd..a7f254b 100644 --- a/docs/quickstart.md +++ b/docs/quickstart.md @@ -82,6 +82,7 @@ print(solution.linear_report.matrix_condition_number) print(solution.DMerc_times_r2) print(solution.field_jet.maximum_divergence_gradient) print(solution.grad_grad_B_inverse_scale_length) +print(solution.r_singularity) ``` The direct r2 outputs are available as attributes such as `X20`, `X2s`, @@ -89,4 +90,5 @@ The direct r2 outputs are available as attributes such as `X20`, `X2s`, available as `solution.second_order`. Check both the nonlinear `root_report` and r2 `linear_report` before accepting a result. The canonical Hessian `solution.grad_grad_B_axis` has shape `(nphi, 3, 3, 3)` and -field-component-first ordering. +field-component-first ordering. `solution.r_singularity` is the first +quadratic-map coordinate singularity, not an equilibrium-existence bound. diff --git a/docs/theory/field-jet.md b/docs/theory/field-jet.md index 0e837f1..582fa73 100644 --- a/docs/theory/field-jet.md +++ b/docs/theory/field-jet.md @@ -93,3 +93,34 @@ require. `DMerc_times_r2`. Their normalization and signs match pyQSC at the audited upstream commit. The geodesic and well contributions are kept separate so a caller can inspect cancellations rather than accepting only their sum. + +## Singular radius + +The quadratic regular map also gives a concise singular-radius calculation. +Its determinant through second order in \(r\) is + +\[ +\widehat g = +g_0+r(g_{1c}\cos\vartheta+g_{1s}\sin\vartheta) ++r^2(g_{20}+g_{2s}\sin2\vartheta+g_{2c}\cos2\vartheta). +\] + +The coefficients are obtained by collecting powers of \(q_1,q_2\) using the +multilinearity of the determinant of the regular coordinate map. This replaces +the long generated coefficient expressions in pyQSC while producing the same +quadratic Jacobian. As an internal quasisymmetry check, `g1s` must vanish. + +For each toroidal sample, all positive quadratic roots are enumerated on a +uniform angular grid. The best root seeds a vectorized Newton solve for + +\[ +\widehat g=0,\qquad +\frac{\partial\widehat g}{\partial\vartheta}=0. +\] + +The default 256 angular seeds and eight Newton steps reproduce the audited +pyQSC radii while retaining JIT and forward-mode differentiation. The result +contains the radius, angle, and residual at every toroidal sample, together +with the global minimum. It diagnoses loss of regularity of the truncated +near-axis map; it is not a guarantee that a finite-radius equilibrium exists +up to that radius. diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index 3a0dbd5..0b3feec 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -12,9 +12,11 @@ NearAxisSolution, RootSolveReport, SecondOrderData, + SingularityDiagnostics, ) from pyqsc_jax.near_axis import near_axis from pyqsc_jax.second_order import SecondOrderResiduals, second_order_residuals +from pyqsc_jax.singularity import singularity_diagnostics from pyqsc_jax.solvers import RootSolveOptions __all__ = [ @@ -29,10 +31,12 @@ "RootSolveReport", "SecondOrderData", "SecondOrderResiduals", + "SingularityDiagnostics", "near_axis", "mercier_diagnostics", "second_order_residuals", "solve", + "singularity_diagnostics", "total_field_jet", ] __version__ = "0.2.0.dev0" diff --git a/src/pyqsc_jax/field.py b/src/pyqsc_jax/field.py index 069eba5..6ad22bd 100644 --- a/src/pyqsc_jax/field.py +++ b/src/pyqsc_jax/field.py @@ -30,25 +30,18 @@ def _to_cartesian(vector: jax.Array, solution: NearAxisSolution) -> jax.Array: return cylindrical_vector_to_cartesian(vector, solution.phi) -def total_field_jet(solution: NearAxisSolution) -> FieldJet: - """Compute ``B``, ``grad(B)``, and ``grad(grad(B))`` on the axis. - - This is the regular-coordinate chain rule in equations (55)--(83) of the - surface-free plasma/coil derivation. It requires the complete second-order - near-axis solution but no finite-radius surface. - """ +def _regular_map_vectors( + solution: NearAxisSolution, +) -> tuple[jax.Array, jax.Array, jax.Array, jax.Array, jax.Array]: + """Return ``d1, d2, h11, h12, h22`` in periodic cylindrical components.""" r2 = solution.second_order if r2 is None: - raise ValueError("A second-order solution is required for the field Hessian.") - + raise ValueError("A second-order solution is required for the regular coordinate map.") geometry = solution.geometry - inputs = solution.inputs - length_scale = geometry.abs_G0_over_B0 tangent = geometry.tangent_cylindrical normal = geometry.normal_cylindrical binormal = geometry.binormal_cylindrical - d1 = solution.X1c[:, None] * normal + solution.Y1c[:, None] * binormal d2 = solution.Y1s[:, None] * binormal h11 = ( @@ -66,6 +59,26 @@ def total_field_jet(solution: NearAxisSolution) -> FieldJet: + 2 * (r2.Y20 - r2.Y2c)[:, None] * binormal + 2 * (r2.Z20 - r2.Z2c)[:, None] * tangent ) + return d1, d2, h11, h12, h22 + + +def total_field_jet(solution: NearAxisSolution) -> FieldJet: + """Compute ``B``, ``grad(B)``, and ``grad(grad(B))`` on the axis. + + This is the regular-coordinate chain rule in equations (55)--(83) of the + surface-free plasma/coil derivation. It requires the complete second-order + near-axis solution but no finite-radius surface. + """ + + r2 = solution.second_order + if r2 is None: + raise ValueError("A second-order solution is required for the field Hessian.") + + geometry = solution.geometry + inputs = solution.inputs + length_scale = geometry.abs_G0_over_B0 + tangent = geometry.tangent_cylindrical + d1, d2, h11, h12, h22 = _regular_map_vectors(solution) derivative = lambda vector: _differentiate_cylindrical_vector(vector, solution) # noqa: E731 V0 = length_scale * tangent diff --git a/src/pyqsc_jax/models.py b/src/pyqsc_jax/models.py index ecae9e0..d5ebbbf 100644 --- a/src/pyqsc_jax/models.py +++ b/src/pyqsc_jax/models.py @@ -97,6 +97,27 @@ class FieldJet: grad_grad_B_inverse_scale_length: jax.Array +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class SingularityDiagnostics: + """First loss of regularity in the quadratic near-axis coordinate map.""" + + r_singularity: jax.Array + r_singularity_vs_varphi: jax.Array + inv_r_singularity_vs_varphi: jax.Array + theta_singularity_vs_varphi: jax.Array + residual_norm_vs_varphi: jax.Array + maximum_residual_norm: jax.Array + g0: jax.Array + g1c: jax.Array + g1s: jax.Array + g20: jax.Array + g2s: jax.Array + g2c: jax.Array + angular_resolution: int = field(metadata={"static": True}) + newton_iterations: int = field(metadata={"static": True}) + + @jax.tree_util.register_dataclass @dataclass(frozen=True) class NearAxisInputs: @@ -220,6 +241,7 @@ class NearAxisSolution: second_order: SecondOrderData | None = None mercier: MercierDiagnostics | None = None field_jet: FieldJet | None = None + singularity: SingularityDiagnostics | None = None _SECOND_ORDER_NAMES: ClassVar[frozenset[str]] = frozenset( field.name for field in SecondOrderData.__dataclass_fields__.values() @@ -236,6 +258,16 @@ class NearAxisSolution: "grad_grad_B_inverse_scale_length", } ) + _SINGULARITY_NAMES: ClassVar[frozenset[str]] = frozenset( + { + "r_singularity", + "r_singularity_vs_varphi", + "inv_r_singularity_vs_varphi", + "r_singularity_basic_vs_varphi", + "r_singularity_theta_vs_varphi", + "r_singularity_residual_sqnorm", + } + ) def __getattr__(self, name: str): if name in self._SECOND_ORDER_NAMES: @@ -250,6 +282,8 @@ def __getattr__(self, name: str): return getattr(mercier, name) if name in self._FIELD_JET_NAMES: raise AttributeError("First-order solution has no second-derivative field jet.") + if name in self._SINGULARITY_NAMES: + raise AttributeError("First-order solution has no singular-radius diagnostics.") raise AttributeError(f"{type(self).__name__!s} has no attribute {name!r}.") def _require_mercier(self) -> MercierDiagnostics: @@ -264,6 +298,12 @@ def _require_field_jet(self) -> FieldJet: raise AttributeError("First-order solution has no second-derivative field jet.") return field_jet + def _require_singularity(self) -> SingularityDiagnostics: + singularity = object.__getattribute__(self, "singularity") + if singularity is None: + raise AttributeError("First-order solution has no singular-radius diagnostics.") + return singularity + @property def axis(self) -> Axis: return self.inputs.axis @@ -335,3 +375,27 @@ def grad_grad_B_inverse_scale_length_vs_varphi(self) -> jax.Array: @property def grad_grad_B_inverse_scale_length(self) -> jax.Array: return self._require_field_jet().grad_grad_B_inverse_scale_length + + @property + def r_singularity(self) -> jax.Array: + return self._require_singularity().r_singularity + + @property + def r_singularity_vs_varphi(self) -> jax.Array: + return self._require_singularity().r_singularity_vs_varphi + + @property + def inv_r_singularity_vs_varphi(self) -> jax.Array: + return self._require_singularity().inv_r_singularity_vs_varphi + + @property + def r_singularity_basic_vs_varphi(self) -> jax.Array: + return self._require_singularity().r_singularity_vs_varphi + + @property + def r_singularity_theta_vs_varphi(self) -> jax.Array: + return self._require_singularity().theta_singularity_vs_varphi + + @property + def r_singularity_residual_sqnorm(self) -> jax.Array: + return self._require_singularity().residual_norm_vs_varphi ** 2 diff --git a/src/pyqsc_jax/near_axis.py b/src/pyqsc_jax/near_axis.py index f6458b0..3f1c83f 100644 --- a/src/pyqsc_jax/near_axis.py +++ b/src/pyqsc_jax/near_axis.py @@ -169,6 +169,12 @@ def _refresh(self) -> None: solution.grad_grad_B_inverse_scale_length_vs_varphi ) self.grad_grad_B_inverse_scale_length = solution.grad_grad_B_inverse_scale_length + self.r_singularity = solution.r_singularity + self.r_singularity_vs_varphi = solution.r_singularity_vs_varphi + self.inv_r_singularity_vs_varphi = solution.inv_r_singularity_vs_varphi + self.r_singularity_basic_vs_varphi = solution.r_singularity_basic_vs_varphi + self.r_singularity_theta_vs_varphi = solution.r_singularity_theta_vs_varphi + self.r_singularity_residual_sqnorm = solution.r_singularity_residual_sqnorm @property def dofs(self) -> jax.Array: diff --git a/src/pyqsc_jax/second_order.py b/src/pyqsc_jax/second_order.py index 1aff722..5405cf3 100644 --- a/src/pyqsc_jax/second_order.py +++ b/src/pyqsc_jax/second_order.py @@ -365,11 +365,13 @@ def untwist(sine_coefficient, cosine_coefficient): solution = replace(first_order, second_order=second_order) from pyqsc_jax.diagnostics import mercier_diagnostics from pyqsc_jax.field import total_field_jet + from pyqsc_jax.singularity import singularity_diagnostics return replace( solution, mercier=mercier_diagnostics(solution), field_jet=total_field_jet(solution), + singularity=singularity_diagnostics(solution), ) diff --git a/src/pyqsc_jax/singularity.py b/src/pyqsc_jax/singularity.py new file mode 100644 index 0000000..c25e7b0 --- /dev/null +++ b/src/pyqsc_jax/singularity.py @@ -0,0 +1,215 @@ +"""Regular-coordinate singular-radius diagnostics.""" + +from __future__ import annotations + +import jax +import jax.numpy as jnp + +from pyqsc_jax.field import ( + _differentiate_cylindrical_vector, + _regular_map_vectors, + _to_cartesian, +) +from pyqsc_jax.models import NearAxisSolution, SingularityDiagnostics + + +def _determinant_coefficients( + solution: NearAxisSolution, +) -> tuple[jax.Array, jax.Array, jax.Array, jax.Array, jax.Array, jax.Array]: + geometry = solution.geometry + length_scale = geometry.abs_G0_over_B0 + d1, d2, h11, h12, h22 = _regular_map_vectors(solution) + derivative = lambda vector: _differentiate_cylindrical_vector(vector, solution) # noqa: E731 + cartesian = lambda vector: _to_cartesian(vector, solution) # noqa: E731 + arguments = ( + cartesian(length_scale * geometry.tangent_cylindrical), + cartesian(d1), + cartesian(d2), + cartesian(derivative(d1)), + cartesian(derivative(d2)), + cartesian(h11), + cartesian(h12), + cartesian(h22), + cartesian(derivative(h11)), + cartesian(derivative(h12)), + cartesian(derivative(h22)), + ) + ( + axis_tangent, + d1_value, + d2_value, + d1_prime, + d2_prime, + h11_value, + h12_value, + h22_value, + h11_prime, + h12_prime, + h22_prime, + ) = arguments + + determinant = lambda first, second, third: jnp.einsum( # noqa: E731 + "ni,ni->n", first, jnp.cross(second, third) + ) + g0 = determinant(axis_tangent, d1_value, d2_value) + g1c = ( + determinant(d1_prime, d1_value, d2_value) + + determinant(axis_tangent, h11_value, d2_value) + + determinant(axis_tangent, d1_value, h12_value) + ) + g1s = ( + determinant(d2_prime, d1_value, d2_value) + + determinant(axis_tangent, h12_value, d2_value) + + determinant(axis_tangent, d1_value, h22_value) + ) + q1_squared = ( + 0.5 * determinant(h11_prime, d1_value, d2_value) + + determinant(d1_prime, h11_value, d2_value) + + determinant(d1_prime, d1_value, h12_value) + + determinant(axis_tangent, h11_value, h12_value) + ) + q2_squared = ( + 0.5 * determinant(h22_prime, d1_value, d2_value) + + determinant(d2_prime, h12_value, d2_value) + + determinant(d2_prime, d1_value, h22_value) + + determinant(axis_tangent, h12_value, h22_value) + ) + q1_q2 = ( + determinant(h12_prime, d1_value, d2_value) + + determinant(d1_prime, h12_value, d2_value) + + determinant(d2_prime, h11_value, d2_value) + + determinant(d1_prime, d1_value, h22_value) + + determinant(d2_prime, d1_value, h12_value) + + determinant(axis_tangent, h11_value, h22_value) + + determinant(axis_tangent, h12_value, h12_value) + ) + hessian_11 = 2 * q1_squared + hessian_22 = 2 * q2_squared + g20 = (hessian_11 + hessian_22) / 4 + g2c = (hessian_11 - hessian_22) / 4 + g2s = q1_q2 / 2 + return g0, g1c, g1s, g20, g2s, g2c + + +def _positive_quadratic_root( + constant: jax.Array, + linear: jax.Array, + quadratic: jax.Array, +) -> jax.Array: + tolerance = 100 * jnp.finfo(quadratic.dtype).eps + discriminant = linear**2 - 4 * quadratic * constant + square_root = jnp.sqrt(jnp.maximum(discriminant, 0)) + denominator = 2 * quadratic + root_minus = (-linear - square_root) / denominator + root_plus = (-linear + square_root) / denominator + infinity = jnp.asarray(jnp.inf, dtype=quadratic.dtype) + root_minus = jnp.where((discriminant >= 0) & (root_minus > 0), root_minus, infinity) + root_plus = jnp.where((discriminant >= 0) & (root_plus > 0), root_plus, infinity) + quadratic_root = jnp.minimum(root_minus, root_plus) + linear_root = -constant / linear + linear_root = jnp.where(linear_root > 0, linear_root, infinity) + return jnp.where(jnp.abs(quadratic) <= tolerance, linear_root, quadratic_root) + + +def singularity_diagnostics( + solution: NearAxisSolution, + *, + angular_resolution: int = 256, + newton_iterations: int = 8, +) -> SingularityDiagnostics: + """Locate the first singularity of the quadratic near-axis map. + + A uniform angular scan enumerates all positive roots of the quadratic + Jacobian approximation. A vectorized Newton solve then refines the + simultaneous conditions ``det(X) = 0`` and ``d det(X) / d theta = 0``. + """ + + if solution.second_order is None: + raise ValueError("A second-order solution is required for singular-radius diagnostics.") + if not isinstance(angular_resolution, int) or angular_resolution < 8: + raise ValueError("angular_resolution must be an integer >= 8.") + if not isinstance(newton_iterations, int) or newton_iterations < 0: + raise ValueError("newton_iterations must be a nonnegative integer.") + + g0, g1c, g1s, g20, g2s, g2c = _determinant_coefficients(solution) + theta_grid = jnp.arange(angular_resolution, dtype=g0.dtype) * (2 * jnp.pi / angular_resolution) + sine = jnp.sin(theta_grid) + cosine = jnp.cos(theta_grid) + sine_2 = jnp.sin(2 * theta_grid) + cosine_2 = jnp.cos(2 * theta_grid) + linear = g1c[:, None] * cosine + g1s[:, None] * sine + quadratic = g20[:, None] + g2s[:, None] * sine_2 + g2c[:, None] * cosine_2 + root_grid = _positive_quadratic_root(g0[:, None], linear, quadratic) + minimum_indices = jnp.argmin(root_grid, axis=1) + initial_radius = jnp.take_along_axis(root_grid, minimum_indices[:, None], axis=1)[:, 0] + initial_theta = theta_grid[minimum_indices] + finite_seed = jnp.isfinite(initial_radius) + radius = jnp.where(finite_seed, initial_radius, 1) + theta = initial_theta + + def newton_step(_, state): + radius, theta = state + sine = jnp.sin(theta) + cosine = jnp.cos(theta) + sine_2 = jnp.sin(2 * theta) + cosine_2 = jnp.cos(2 * theta) + linear = g1c * cosine + g1s * sine + linear_prime = -g1c * sine + g1s * cosine + linear_second = -linear + quadratic = g20 + g2s * sine_2 + g2c * cosine_2 + quadratic_prime = 2 * g2s * cosine_2 - 2 * g2c * sine_2 + quadratic_second = -4 * (g2s * sine_2 + g2c * cosine_2) + residual_0 = g0 + radius * linear + radius**2 * quadratic + residual_1 = radius * linear_prime + radius**2 * quadratic_prime + jacobian_00 = linear + 2 * radius * quadratic + jacobian_01 = residual_1 + jacobian_10 = linear_prime + 2 * radius * quadratic_prime + jacobian_11 = radius * linear_second + radius**2 * quadratic_second + determinant = jacobian_00 * jacobian_11 - jacobian_01 * jacobian_10 + safe_determinant = jnp.where( + jnp.abs(determinant) > jnp.finfo(radius.dtype).eps, + determinant, + jnp.inf, + ) + delta_radius = (-residual_0 * jacobian_11 + jacobian_01 * residual_1) / safe_determinant + delta_theta = (-jacobian_00 * residual_1 + residual_0 * jacobian_10) / safe_determinant + candidate_radius = radius + delta_radius + radius = jnp.where(candidate_radius > 0, candidate_radius, radius / 2) + return radius, theta + delta_theta + + radius, theta = jax.lax.fori_loop( + 0, + newton_iterations, + newton_step, + (radius, theta), + ) + sine = jnp.sin(theta) + cosine = jnp.cos(theta) + sine_2 = jnp.sin(2 * theta) + cosine_2 = jnp.cos(2 * theta) + linear = g1c * cosine + g1s * sine + linear_prime = -g1c * sine + g1s * cosine + quadratic = g20 + g2s * sine_2 + g2c * cosine_2 + quadratic_prime = 2 * g2s * cosine_2 - 2 * g2c * sine_2 + residual_0 = g0 + radius * linear + radius**2 * quadratic + residual_1 = radius * linear_prime + radius**2 * quadratic_prime + residual_norm = jnp.sqrt(residual_0**2 + residual_1**2) + valid = finite_seed & jnp.isfinite(radius) & jnp.isfinite(residual_norm) + radius = jnp.where(valid, radius, jnp.inf) + residual_norm = jnp.where(valid, residual_norm, jnp.inf) + return SingularityDiagnostics( + r_singularity=jnp.min(radius), + r_singularity_vs_varphi=radius, + inv_r_singularity_vs_varphi=1 / radius, + theta_singularity_vs_varphi=jnp.mod(theta, 2 * jnp.pi), + residual_norm_vs_varphi=residual_norm, + maximum_residual_norm=jnp.max(jnp.where(valid, residual_norm, 0)), + g0=g0, + g1c=g1c, + g1s=g1s, + g20=g20, + g2s=g2s, + g2c=g2c, + angular_resolution=angular_resolution, + newton_iterations=newton_iterations, + ) diff --git a/tests/physics/test_singularity.py b/tests/physics/test_singularity.py new file mode 100644 index 0000000..eed476f --- /dev/null +++ b/tests/physics/test_singularity.py @@ -0,0 +1,177 @@ +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +import pyqsc_jax as qsc +from pyqsc_jax.near_axis import near_axis + +CASES = [ + ( + { + "rc": [1.0, 0.155, 0.0102], + "zs": [0.0, 0.154, 0.0111], + "nfp": 2, + "etabar": 0.64, + "B2c": -0.00322, + }, + 0.2257896241404959, + [0.7304158315686611, 0.2505553226671735, 0.2935268282653716, 0.23909537193609554], + ), + ( + { + "rc": [1.0, 0.09], + "zs": [0.0, -0.09], + "nfp": 2, + "etabar": 0.95, + "I2": 0.9, + "B2c": -0.7, + "p2": -600000.0, + }, + 0.22161114270880408, + [0.7427937841922576, 0.3271954156702964, 0.2659539057552679, 0.3034006922051161], + ), + ( + { + "rc": [1.0, 0.17, 0.01804, 0.001409, 5.877e-5], + "zs": [0.0, 0.1581, 0.01820, 0.001548, 7.772e-5], + "nfp": 4, + "etabar": 1.569, + "B2c": 0.1348, + }, + 0.3583276532138262, + [0.8681431131590702, 0.4034129514765815, 0.3728231585587465, 0.39141407123791455], + ), +] + + +@pytest.mark.parametrize("parameters, expected_minimum, expected_samples", CASES) +def test_singular_radius_matches_upstream_pyqsc( + parameters, + expected_minimum, + expected_samples, +): + solution = qsc.Qsc(**parameters, nphi=61, order="r2") + + np.testing.assert_allclose(solution.r_singularity, expected_minimum, rtol=0, atol=5e-8) + np.testing.assert_allclose( + np.asarray(solution.r_singularity_vs_varphi)[[0, 15, 30, 45]], + expected_samples, + rtol=0, + atol=5e-8, + ) + np.testing.assert_allclose( + solution.inv_r_singularity_vs_varphi, + 1 / solution.r_singularity_vs_varphi, + ) + np.testing.assert_allclose( + solution.r_singularity_basic_vs_varphi, + solution.r_singularity_vs_varphi, + ) + + +def test_determinant_coefficients_and_refined_residual(): + solution = qsc.Qsc(**CASES[0][0], nphi=61, order="r2") + diagnostics = solution.singularity + expected_g0 = solution.geometry.abs_G0_over_B0 * solution.X1c * solution.Y1s + + np.testing.assert_allclose(diagnostics.g0, expected_g0, rtol=2e-13, atol=2e-13) + assert jnp.max(jnp.abs(diagnostics.g1s)) < 2e-13 + assert diagnostics.maximum_residual_norm < 2e-13 + assert diagnostics.angular_resolution == 256 + assert diagnostics.newton_iterations == 8 + + radius = diagnostics.r_singularity_vs_varphi + theta = diagnostics.theta_singularity_vs_varphi + linear = diagnostics.g1c * jnp.cos(theta) + diagnostics.g1s * jnp.sin(theta) + linear_prime = -diagnostics.g1c * jnp.sin(theta) + diagnostics.g1s * jnp.cos(theta) + quadratic = ( + diagnostics.g20 + + diagnostics.g2s * jnp.sin(2 * theta) + + diagnostics.g2c * jnp.cos(2 * theta) + ) + quadratic_prime = 2 * diagnostics.g2s * jnp.cos(2 * theta) - 2 * diagnostics.g2c * jnp.sin( + 2 * theta + ) + np.testing.assert_allclose( + diagnostics.g0 + radius * linear + radius**2 * quadratic, + 0, + rtol=0, + atol=2e-13, + ) + np.testing.assert_allclose( + radius * linear_prime + radius**2 * quadratic_prime, + 0, + rtol=0, + atol=2e-13, + ) + + +def test_newton_refinement_removes_angular_grid_dependence(): + solution = qsc.Qsc(**CASES[0][0], nphi=31, order="r2") + coarse = qsc.singularity_diagnostics( + solution, + angular_resolution=32, + newton_iterations=8, + ) + fine = qsc.singularity_diagnostics( + solution, + angular_resolution=512, + newton_iterations=8, + ) + + np.testing.assert_allclose(coarse.r_singularity, fine.r_singularity, rtol=0, atol=2e-11) + assert coarse.maximum_residual_norm < 3e-13 + + +def test_singular_radius_supports_jit_and_jvp(): + def radius(etabar): + return qsc.Qsc( + rc=[1.0, 0.155, 0.0102], + zs=[0.0, 0.154, 0.0111], + nfp=2, + etabar=etabar, + B2c=-0.00322, + nphi=31, + order="r2", + ).r_singularity + + eager = radius(0.64) + compiled = jax.jit(radius)(0.64) + _, tangent = jax.jvp(radius, (0.64,), (1.0,)) + step = 1e-5 + finite_difference = (radius(0.64 + step) - radius(0.64 - step)) / (2 * step) + + np.testing.assert_allclose(compiled, eager, rtol=2e-11, atol=2e-11) + np.testing.assert_allclose(tangent, finite_difference, rtol=3e-7, atol=3e-8) + + +def test_singularity_validation_and_legacy_adapter(): + first_order = qsc.Qsc( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + nphi=31, + ) + with pytest.raises(ValueError, match="second-order"): + qsc.singularity_diagnostics(first_order) + with pytest.raises(ValueError, match="angular_resolution"): + qsc.singularity_diagnostics( + qsc.Qsc(**CASES[0][0], nphi=15, order="r2"), + angular_resolution=4, + ) + with pytest.raises(ValueError, match="newton_iterations"): + qsc.singularity_diagnostics( + qsc.Qsc(**CASES[0][0], nphi=15, order="r2"), + newton_iterations=-1, + ) + with pytest.raises(AttributeError, match="singular-radius"): + _ = first_order.r_singularity + + legacy = near_axis(**CASES[0][0], nphi=31, order="r2") + np.testing.assert_allclose(legacy.r_singularity, legacy.solution.r_singularity) + np.testing.assert_allclose( + legacy.r_singularity_residual_sqnorm, + legacy.solution.r_singularity_residual_sqnorm, + ) From 99e81d51c5b78c4c8b94805dd2eaeae1e8e456d1 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 00:29:38 -0500 Subject: [PATCH 09/39] feat: add third-order flux-constraint corrections --- CHANGELOG.md | 3 + README.md | 14 +- docs/api/third-order.md | 10 + docs/development/physics-traceability.md | 3 +- docs/index.md | 10 +- docs/limitations.md | 6 +- docs/quickstart.md | 25 +++ docs/theory/third-order.md | 83 ++++++++ src/pyqsc_jax/__init__.py | 4 + src/pyqsc_jax/first_order.py | 8 +- src/pyqsc_jax/models.py | 47 +++++ src/pyqsc_jax/near_axis.py | 30 ++- src/pyqsc_jax/third_order.py | 129 +++++++++++++ tests/physics/test_first_order.py | 6 - tests/physics/test_third_order.py | 229 +++++++++++++++++++++++ 15 files changed, 585 insertions(+), 22 deletions(-) create mode 100644 docs/api/third-order.md create mode 100644 docs/theory/third-order.md create mode 100644 src/pyqsc_jax/third_order.py create mode 100644 tests/physics/test_third_order.py diff --git a/CHANGELOG.md b/CHANGELOG.md index 1eb479a..1835ec1 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -40,6 +40,9 @@ first stable release. - Singular-radius diagnostics derived directly from the regular-coordinate Jacobian determinant, with vectorized global angular seeding, Newton refinement, residual reports, and pyQSC QA/QH/finite-current parity. +- Differentiable r3 flux-constraint surface corrections, untwisted boundary + coefficients, and two independent consistency checks with upstream pyQSC + QA, finite-pressure/current, and QH parity. ### Fixed diff --git a/README.md b/README.md index 503d201..c10a415 100644 --- a/README.md +++ b/README.md @@ -4,10 +4,10 @@ Differentiable near-axis stellarator construction and plasma–coil field jets i JAX. > **Development status:** the immutable first-order core, complete r2 -> coefficient solve, total-field Hessian, Mercier diagnostics, and ESSOS -> adapter are validated, including singular-radius diagnostics. Third order, -> inverse solves, optimization, and plasma/external field jets remain under development on the -> `refactor/pyqsc-jax-complete` branch. +> coefficient solve, r3 flux constraint, total-field Hessian, Mercier +> diagnostics, singular-radius diagnostics, and ESSOS adapter are validated. +> Magnetic shear, inverse solves, optimization, and plasma/external field jets +> remain under development on the `refactor/pyqsc-jax-complete` branch. ## Install @@ -86,6 +86,10 @@ print("Hessian inverse scale:", solution.grad_grad_B_inverse_scale_length) print("singular radius:", solution.r_singularity) ``` +Use `order="r3"` to add the differentiable flux-constraint correction and its +untwisted boundary coefficients. The result reports independent +`flux_constraint_residual` and `consistency_error` checks. + The lower-level immutable axis API supports general, not necessarily stellarator-symmetric Fourier axes: @@ -106,7 +110,7 @@ The completed package will provide: - general Fourier magnetic axes and QA/QH topology; - converged differentiable first-order sigma solves; -- second-order field Hessians/diagnostics and pyQSC third-order parity; +- second-order field Hessians/diagnostics and complete pyQSC third-order parity; - total, plasma, and external field/gradient/Hessian jets on the axis; - target-transform inverse solves with continuation and fold detection; - dense-grid `B20` diagnostics and multistart axis optimization; diff --git a/docs/api/third-order.md b/docs/api/third-order.md new file mode 100644 index 0000000..c0ac7d1 --- /dev/null +++ b/docs/api/third-order.md @@ -0,0 +1,10 @@ +# Third-order API + +```{eval-rst} +.. autoclass:: pyqsc_jax.ThirdOrderData + :members: +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.solve_third_order +``` diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index a3cf550..f42702c 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -12,7 +12,8 @@ to the cited source, not to a duplicated derivation in this repository. | Complete second-order coefficients | Landreman & Sengupta (2019), arXiv:1908.10253 | `second_order.solve_second_order`; pyQSC `calculate_r2.py`; manuscript Eqs. 36–54 | four independent equation residuals; vacuum QA, finite-pressure/current, QH upstream arrays; JIT/JVP/VJP/finite differences | implemented and documented | | Total field Hessian | manuscript Eqs. 55–83 | `field.total_field_jet`; pyQSC generated tensor as comparison only | regular-coordinate chain rule, JIT/JVP, QA and finite-current upstream arrays, full vacuum symmetry, divergence and derivative-of-divergence | implemented and documented | | Magnetic well and Mercier terms | Landreman (2021), arXiv:2012.00865 | `diagnostics.mercier_diagnostics`; pyQSC `mercier.py` | vacuum and finite-pressure/current upstream values | implemented and documented | -| Third-order flux constraint and shear | Landreman & Sengupta (2019); Rodríguez et al. shear equations | pyQSC `calculate_r3.py` | upstream r3 arrays and boundary data | not implemented | +| Third-order flux constraint | Landreman & Sengupta (2019) | `third_order.solve_third_order`; pyQSC `calculate_r3.py` | two independent flux-constraint forms; QA, finite-pressure/current, and QH upstream arrays; r3 boundary data; JIT/JVP/finite differences | implemented and documented | +| Magnetic shear | Rodríguez et al. shear equations | pyQSC `calculate_r3.py` | upstream shear and \(\iota_2\), asymmetric cases, resolution convergence, AD | not implemented | | Singular radius and scale lengths | Landreman (2021), arXiv:2012.00865 | `singularity.singularity_diagnostics`; pyQSC `r_singularity.py` as comparison | direct regular-map determinant, QA/QH/finite-current upstream radii and arrays, residual, angular convergence, JIT/JVP/finite differences | implemented and documented | | Good-stellarator criteria | Curvo, Ferreira & Jorge (2025), Table 3 | none canonical | exact normalized thresholds and margins | not implemented | | Plasma current source | manuscript Eqs. 88–97 | none | normalization, enclosed current, straight circular/elliptic channels | not implemented | diff --git a/docs/index.md b/docs/index.md index b35fe3f..3e6d35f 100644 --- a/docs/index.md +++ b/docs/index.md @@ -14,10 +14,12 @@ limitations theory/coordinates-and-conventions theory/first-order theory/second-order +theory/third-order theory/field-jet api/axis api/first-order api/second-order +api/third-order api/field-jet ``` @@ -40,10 +42,10 @@ changelog ## Project status -The immutable first-order API, complete r2 coefficient solve, total-field -Hessian, Mercier terms, and singular-radius diagnostics are validated. Third -order, inverse solves, optimization, and plasma/external field jets are under -active development. +The immutable first-order API, complete r2 coefficient solve, r3 flux +constraint, total-field Hessian, Mercier terms, and singular-radius diagnostics +are validated. Magnetic shear, inverse solves, optimization, and +plasma/external field jets are under active development. The `pyqsc_jax.near_axis.near_axis` import remains supported for ESSOS without a runtime deprecation warning. diff --git a/docs/limitations.md b/docs/limitations.md index 9402047..a55cc23 100644 --- a/docs/limitations.md +++ b/docs/limitations.md @@ -2,12 +2,12 @@ The current computational core includes first order and the complete finite-pressure/current r2 coefficient solve, including the total on-axis -field Hessian, Mercier terms, and singular-radius diagnostics. Third-order -coefficients are not yet exposed. +field Hessian, Mercier terms, singular-radius diagnostics, and the r3 +flux-constraint surface correction. Known limitations under active refactor include: -- no third-order solution; +- no magnetic-shear or \(\iota_2\) calculation yet; - no plasma/external field-jet separation; - no branch-aware target-transform inverse solve. diff --git a/docs/quickstart.md b/docs/quickstart.md index a7f254b..3e1201f 100644 --- a/docs/quickstart.md +++ b/docs/quickstart.md @@ -92,3 +92,28 @@ available as `solution.second_order`. Check both the nonlinear Hessian `solution.grad_grad_B_axis` has shape `(nphi, 3, 3, 3)` and field-component-first ordering. `solution.r_singularity` is the first quadratic-map coordinate singularity, not an equilibrium-existence bound. + +## Third-order flux constraint + +Set `order="r3"` to add the surface correction required by the +order-\(r^2\) toroidal-flux constraint: + +```python +solution = qsc.Qsc( + rc=[1.0, 0.155, 0.0102], + zs=[0.0, 0.154, 0.0111], + nfp=2, + etabar=0.64, + B2c=-0.00322, + nphi=61, + order="r3", +) + +print(solution.flux_constraint_residual) +print(solution.consistency_error) +print(solution.B0_order_a_squared_to_cancel) +``` + +The r3 result supplies first- and third-poloidal-harmonic coefficient arrays +and their untwisted forms to boundary conversion. Magnetic shear is a +separate, later milestone. diff --git a/docs/theory/third-order.md b/docs/theory/third-order.md new file mode 100644 index 0000000..e97265b --- /dev/null +++ b/docs/theory/third-order.md @@ -0,0 +1,83 @@ +# Third-order flux constraint + +## Scope + +Setting `order="r3"` first constructs the complete r2 solution, then adds the +third-order surface displacement required for consistency of the toroidal-flux +constraint through order \(r^2\). This is the `r3_flux_constraint` construction +of {cite}`landreman2019highorder`. Magnetic shear and \(\iota_2\) are not part +of this milestone. + +The implementation uses the short regular-coordinate relation as its primal +formula. It also evaluates the independent field-strength cancellation +formula retained by pyQSC; their agreement is reported instead of assumed. + +## Flux constraint + +Let \(\ell'=|G_0|/B_0\), let a prime denote +\(\mathrm d/\mathrm d\varphi\), and define + +\[ +\begin{aligned} +Q={}&-\frac{s_\psi B_0\ell'}{2G_0^2} +\left(\iota_N I_2+\frac{\mu_0p_2G_0}{B_0^2}\right) ++2(X_{2c}Y_{2s}-X_{2s}Y_{2c})\\ +&+\frac{s_\psi B_0}{2G_0} +\left(\ell'\kappa X_{20}-Z_{20}'\right)\\ +&+\frac{I_2}{4G_0} +\left[ +-\ell'\tau(X_{1c}^2+Y_{1s}^2+Y_{1c}^2) ++Y_{1c}X_{1c}'-X_{1c}Y_{1c}' +\right]. +\end{aligned} +\] + +The scalar coefficient at every toroidal sample is + +\[ +C=-\frac{Q}{2s_Gs_\psi}. +\] + +For the quasisymmetric flux-constraint construction, the nonzero Frenet-frame +coefficients are + +\[ +X_{3c1}=X_{1c}C,\qquad +Y_{3s1}=Y_{1s}C,\qquad +Y_{3c1}=Y_{1c}C. +\] + +\(X_{3s1}\), all \(Z_{3}\) coefficients, and all third-poloidal-harmonic +coefficients vanish in this construction. They remain explicit arrays in +`ThirdOrderData` so boundary assembly has a uniform representation and can be +extended without changing its interface. + +## Independent consistency checks + +The separately evaluated on-axis field correction must satisfy + +\[ +B_{0,\mathrm{cancel}}^{(2)}=2B_0C. +\] + +`flux_constraint_residual` is the maximum absolute residual of +\(Q+2s_Gs_\psi C=0\). `consistency_error` is the maximum disagreement between +\(C\) and \(B_{0,\mathrm{cancel}}^{(2)}/(2B_0)\). Both are scalar JAX arrays +and remain available inside compiled and differentiated workflows. + +## Helicity and boundary data + +The coefficient pairs are rotated from the winding Frenet frame into the +untwisted frame for first and third poloidal harmonics. The +ESSOS-compatible boundary map includes these terms multiplied by \(r^3\). +This is essential for QH axes: a coefficient that vanishes in the winding +frame can acquire a nonzero sine component after untwisting. + +## Validation + +Frozen upstream comparisons use the vacuum QA, finite-pressure/current, and QH +configurations of sections 5.1, 5.3, and 5.4 of +{cite}`landreman2019highorder`. Tests also cover both constraint residuals, +spectral coefficient derivatives, helical untwisting, r3 boundary assembly, +JIT, JVP, and centered finite differences. The upstream commit is recorded in +the refactor baseline. diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index 0b3feec..67e285a 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -13,11 +13,13 @@ RootSolveReport, SecondOrderData, SingularityDiagnostics, + ThirdOrderData, ) from pyqsc_jax.near_axis import near_axis from pyqsc_jax.second_order import SecondOrderResiduals, second_order_residuals from pyqsc_jax.singularity import singularity_diagnostics from pyqsc_jax.solvers import RootSolveOptions +from pyqsc_jax.third_order import solve_third_order __all__ = [ "Axis", @@ -32,11 +34,13 @@ "SecondOrderData", "SecondOrderResiduals", "SingularityDiagnostics", + "ThirdOrderData", "near_axis", "mercier_diagnostics", "second_order_residuals", "solve", "singularity_diagnostics", + "solve_third_order", "total_field_jet", ] __version__ = "0.2.0.dev0" diff --git a/src/pyqsc_jax/first_order.py b/src/pyqsc_jax/first_order.py index d3322b8..71b0bd5 100644 --- a/src/pyqsc_jax/first_order.py +++ b/src/pyqsc_jax/first_order.py @@ -203,7 +203,7 @@ def _normalize_order(order: int | str) -> int: if order in (2, "r2"): return 2 if order in (3, "r3"): - raise NotImplementedError("Third-order solves are not implemented yet.") + return 3 raise ValueError("order must be 1, 2, 3, 'r1', 'r2', or 'r3'.") @@ -256,10 +256,14 @@ def solve( root_options=root_options, ) solution = first_order_solution(inputs, geometry, sigma, iota, root_report) - if normalized_order == 2: + if normalized_order >= 2: from pyqsc_jax.second_order import solve_second_order solution = solve_second_order(solution) + if normalized_order == 3: + from pyqsc_jax.third_order import solve_third_order + + solution = solve_third_order(solution) return solution diff --git a/src/pyqsc_jax/models.py b/src/pyqsc_jax/models.py index d5ebbbf..325e800 100644 --- a/src/pyqsc_jax/models.py +++ b/src/pyqsc_jax/models.py @@ -206,6 +206,44 @@ class SecondOrderData: Z2c_untwisted: jax.Array +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class ThirdOrderData: + """Third-order flux-constraint surface corrections.""" + + flux_constraint_coefficient: jax.Array + B0_order_a_squared_to_cancel: jax.Array + flux_constraint_residual: jax.Array + consistency_error: jax.Array + X3s1: jax.Array + X3c1: jax.Array + Y3s1: jax.Array + Y3c1: jax.Array + Z3s1: jax.Array + Z3c1: jax.Array + X3s3: jax.Array + X3c3: jax.Array + Y3s3: jax.Array + Y3c3: jax.Array + Z3s3: jax.Array + Z3c3: jax.Array + d_X3c1_d_varphi: jax.Array + d_Y3s1_d_varphi: jax.Array + d_Y3c1_d_varphi: jax.Array + X3s1_untwisted: jax.Array + X3c1_untwisted: jax.Array + Y3s1_untwisted: jax.Array + Y3c1_untwisted: jax.Array + Z3s1_untwisted: jax.Array + Z3c1_untwisted: jax.Array + X3s3_untwisted: jax.Array + X3c3_untwisted: jax.Array + Y3s3_untwisted: jax.Array + Y3c3_untwisted: jax.Array + Z3s3_untwisted: jax.Array + Z3c3_untwisted: jax.Array + + @jax.tree_util.register_dataclass @dataclass(frozen=True) class NearAxisSolution: @@ -242,10 +280,14 @@ class NearAxisSolution: mercier: MercierDiagnostics | None = None field_jet: FieldJet | None = None singularity: SingularityDiagnostics | None = None + third_order: ThirdOrderData | None = None _SECOND_ORDER_NAMES: ClassVar[frozenset[str]] = frozenset( field.name for field in SecondOrderData.__dataclass_fields__.values() ) + _THIRD_ORDER_NAMES: ClassVar[frozenset[str]] = frozenset( + field.name for field in ThirdOrderData.__dataclass_fields__.values() + ) _MERCIER_NAMES: ClassVar[frozenset[str]] = frozenset( field.name for field in MercierDiagnostics.__dataclass_fields__.values() ) @@ -275,6 +317,11 @@ def __getattr__(self, name: str): if second_order is None: raise AttributeError(f"First-order solution has no {name!r} quantity.") return getattr(second_order, name) + if name in self._THIRD_ORDER_NAMES: + third_order = object.__getattribute__(self, "third_order") + if third_order is None: + raise AttributeError(f"Lower-order solution has no {name!r} quantity.") + return getattr(third_order, name) if name in self._MERCIER_NAMES: mercier = object.__getattribute__(self, "mercier") if mercier is None: diff --git a/src/pyqsc_jax/near_axis.py b/src/pyqsc_jax/near_axis.py index 3f1c83f..88d4625 100644 --- a/src/pyqsc_jax/near_axis.py +++ b/src/pyqsc_jax/near_axis.py @@ -42,6 +42,8 @@ def __init__( ) -> None: if not isinstance(nphi, int) or isinstance(nphi, bool) or nphi < 3 or nphi % 2 == 0: raise ValueError("The compatibility API requires odd integer nphi >= 3.") + if isinstance(order, bool) or order not in (1, 2, 3, "r1", "r2", "r3"): + raise ValueError("order must be one of 1, 2, 3, 'r1', 'r2', or 'r3'.") self.rc = jnp.asarray(rc) self.zs = jnp.asarray(zs) @@ -69,7 +71,9 @@ def _canonical_solution( zs: ArrayLike, etabar: ArrayLike, ) -> NearAxisSolution: - canonical_order = "r1" if self.order in (1, "r1") else "r2" + canonical_order = ( + "r1" if self.order in (1, "r1") else ("r2" if self.order in (2, "r2") else "r3") + ) return solve( axis=Axis.stellarator_symmetric(rc=rc, zs=zs, nfp=self.nfp), etabar=etabar, @@ -175,6 +179,9 @@ def _refresh(self) -> None: self.r_singularity_basic_vs_varphi = solution.r_singularity_basic_vs_varphi self.r_singularity_theta_vs_varphi = solution.r_singularity_theta_vs_varphi self.r_singularity_residual_sqnorm = solution.r_singularity_residual_sqnorm + if solution.third_order is not None: + for name in solution._THIRD_ORDER_NAMES: + setattr(self, name, getattr(solution, name)) @property def dofs(self) -> jax.Array: @@ -394,6 +401,27 @@ def _frenet_displacements( Z = Z + r**2 * ( self.Z20_untwisted + self.Z2c_untwisted * cosine2 + self.Z2s_untwisted * sine2 ) + if self.solution.third_order is not None: + cosine3 = jnp.cos(3 * theta) + sine3 = jnp.sin(3 * theta) + X = X + r**3 * ( + self.X3c1_untwisted * cosine + + self.X3s1_untwisted * sine + + self.X3c3_untwisted * cosine3 + + self.X3s3_untwisted * sine3 + ) + Y = Y + r**3 * ( + self.Y3c1_untwisted * cosine + + self.Y3s1_untwisted * sine + + self.Y3c3_untwisted * cosine3 + + self.Y3s3_untwisted * sine3 + ) + Z = Z + r**3 * ( + self.Z3c1_untwisted * cosine + + self.Z3s1_untwisted * sine + + self.Z3c3_untwisted * cosine3 + + self.Z3s3_untwisted * sine3 + ) return X, Y, Z def phi_of_theta_varphi( diff --git a/src/pyqsc_jax/third_order.py b/src/pyqsc_jax/third_order.py new file mode 100644 index 0000000..0353480 --- /dev/null +++ b/src/pyqsc_jax/third_order.py @@ -0,0 +1,129 @@ +"""Third-order flux-constraint corrections. + +The concise relation is from Landreman & Sengupta (2019) and is cross-checked +against ``landreman/pyQSC:qsc/calculate_r3.py`` at the audited BSD-2-Clause +upstream commit recorded in the refactor baseline. +""" + +from __future__ import annotations + +from dataclasses import replace + +import jax.numpy as jnp + +from pyqsc_jax.models import NearAxisSolution, ThirdOrderData +from pyqsc_jax.second_order import MU0 + + +def solve_third_order(solution: NearAxisSolution) -> NearAxisSolution: + """Add the r3 corrections required for consistency through second order.""" + + r2 = solution.second_order + if r2 is None: + raise ValueError("A second-order solution is required before the third-order correction.") + inputs = solution.inputs + length_scale = solution.geometry.abs_G0_over_B0 + D = solution.geometry.d_d_varphi + d_X1c = D @ solution.X1c + d_Y1c = D @ solution.Y1c + first_order_norm = solution.X1c**2 + solution.Y1c**2 + solution.Y1s**2 + Q = ( + -inputs.spsi + * inputs.B0 + * length_scale + / (2 * solution.G0**2) + * (solution.iotaN * inputs.I2 + MU0 * inputs.p2 * solution.G0 / inputs.B0**2) + + 2 * (r2.X2c * r2.Y2s - r2.X2s * r2.Y2c) + + inputs.spsi + * inputs.B0 + / (2 * solution.G0) + * (length_scale * r2.X20 * solution.curvature - r2.d_Z20_d_varphi) + + inputs.I2 + / (4 * solution.G0) + * ( + -length_scale * solution.torsion * first_order_norm + + solution.Y1c * d_X1c + - solution.X1c * d_Y1c + ) + ) + sign_product = inputs.sG * inputs.spsi + coefficient = -Q / (2 * sign_product) + N_helicity = solution.iota - solution.iotaN + B0_correction = ( + -inputs.sG + * inputs.B0**2 + * (r2.G2 + inputs.I2 * N_helicity) + * length_scale + / (2 * solution.G0**2) + - inputs.sG * inputs.spsi * inputs.B0 * 2 * (r2.X2c * r2.Y2s - r2.X2s * r2.Y2c) + - inputs.sG + * inputs.B0**2 + / (2 * solution.G0) + * (length_scale * r2.X20 * solution.curvature - r2.d_Z20_d_varphi) + - inputs.sG + * inputs.spsi + * inputs.B0 + * inputs.I2 + / (4 * solution.G0) + * ( + -length_scale * solution.torsion * first_order_norm + + solution.Y1c * d_X1c + - solution.X1c * d_Y1c + ) + ) + + zeros = jnp.zeros_like(solution.X1c) + X3s1 = zeros + X3c1 = solution.X1c * coefficient + Y3s1 = solution.Y1s * coefficient + Y3c1 = solution.Y1c * coefficient + angle = -solution.helicity * inputs.axis.nfp * solution.varphi + + def untwist(sine_coefficient, cosine_coefficient, harmonic): + sine = jnp.sin(harmonic * angle) + cosine = jnp.cos(harmonic * angle) + return ( + sine_coefficient * cosine + cosine_coefficient * sine, + -sine_coefficient * sine + cosine_coefficient * cosine, + ) + + X3s1_untwisted, X3c1_untwisted = untwist(X3s1, X3c1, 1) + Y3s1_untwisted, Y3c1_untwisted = untwist(Y3s1, Y3c1, 1) + Z3s1_untwisted, Z3c1_untwisted = untwist(zeros, zeros, 1) + X3s3_untwisted, X3c3_untwisted = untwist(zeros, zeros, 3) + Y3s3_untwisted, Y3c3_untwisted = untwist(zeros, zeros, 3) + Z3s3_untwisted, Z3c3_untwisted = untwist(zeros, zeros, 3) + third_order = ThirdOrderData( + flux_constraint_coefficient=coefficient, + B0_order_a_squared_to_cancel=B0_correction, + flux_constraint_residual=jnp.max(jnp.abs(Q + 2 * sign_product * coefficient)), + consistency_error=jnp.max(jnp.abs(coefficient - B0_correction / (2 * inputs.B0))), + X3s1=X3s1, + X3c1=X3c1, + Y3s1=Y3s1, + Y3c1=Y3c1, + Z3s1=zeros, + Z3c1=zeros, + X3s3=zeros, + X3c3=zeros, + Y3s3=zeros, + Y3c3=zeros, + Z3s3=zeros, + Z3c3=zeros, + d_X3c1_d_varphi=D @ X3c1, + d_Y3s1_d_varphi=D @ Y3s1, + d_Y3c1_d_varphi=D @ Y3c1, + X3s1_untwisted=X3s1_untwisted, + X3c1_untwisted=X3c1_untwisted, + Y3s1_untwisted=Y3s1_untwisted, + Y3c1_untwisted=Y3c1_untwisted, + Z3s1_untwisted=Z3s1_untwisted, + Z3c1_untwisted=Z3c1_untwisted, + X3s3_untwisted=X3s3_untwisted, + X3c3_untwisted=X3c3_untwisted, + Y3s3_untwisted=Y3s3_untwisted, + Y3c3_untwisted=Y3c3_untwisted, + Z3s3_untwisted=Z3s3_untwisted, + Z3c3_untwisted=Z3c3_untwisted, + ) + return replace(solution, third_order=third_order) diff --git a/tests/physics/test_first_order.py b/tests/physics/test_first_order.py index c96a724..8bdcf99 100644 --- a/tests/physics/test_first_order.py +++ b/tests/physics/test_first_order.py @@ -65,12 +65,6 @@ def test_first_order_shapes_and_coefficients(): ) -@pytest.mark.parametrize("order", [3, "r3"]) -def test_third_order_request_is_explicitly_rejected(order): - with pytest.raises(NotImplementedError, match="Third-order"): - standard_solution(order=order) - - def test_invalid_order_and_inverse_mode_are_explicitly_rejected(): with pytest.raises(ValueError, match="order must be"): standard_solution(order="fourth") diff --git a/tests/physics/test_third_order.py b/tests/physics/test_third_order.py new file mode 100644 index 0000000..5e0294a --- /dev/null +++ b/tests/physics/test_third_order.py @@ -0,0 +1,229 @@ +from __future__ import annotations + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +import pyqsc_jax as qsc +from pyqsc_jax.near_axis import near_axis + +# Frozen BSD-2-Clause pyQSC reference samples at the audited upstream commit. +CASES = ( + ( + "qa", + {}, + { + "X3c1": [0.06254885838364596, 1.1028068624859182, 0.9898672691339223], + "Y3c1": [0.0, 1.9611076246147592, 0.06254912908105097], + "Y3s1": [0.263992436104027, 3.1822277655813185, 0.6000377597469493], + "B0_order_a_squared_to_cancel": [ + 0.257001365727628, + 3.7466692503729218, + 1.5413730743953158, + ], + }, + ), + ( + "finite_pressure_current", + { + "rc": [1.0, 0.09], + "zs": [0.0, -0.09], + "nfp": 2, + "etabar": 0.95, + "I2": 0.9, + "B2c": -0.7, + "p2": -600000.0, + }, + { + "X3c1": [-0.7763858841222269, -0.2167234757709553, -0.4037215275576512], + "Y3c1": [0.0, 0.13599120989448577, 0.02104082225854222], + "Y3s1": [-1.2142017571662096, -0.27932779079566616, -0.18341957155186067], + "B0_order_a_squared_to_cancel": [ + -1.9418435614778733, + -0.4920849106382204, + -0.5442441717107536, + ], + }, + ), + ( + "qh", + { + "rc": [1.0, 0.17, 0.01804, 0.001409, 5.877e-5], + "zs": [0.0, 0.1581, 0.01820, 0.001548, 7.772e-5], + "nfp": 4, + "etabar": 1.569, + "B2c": 0.1348, + }, + { + "X3c1": [-0.05934821467751999, -0.002180735261069853, -0.006774272974061107], + "Y3c1": [0.0, 0.002774228833885528, 0.00030670030088582816], + "Y3s1": [-0.15982340894062852, -0.002817420091098044, -0.002404111069876869], + "B0_order_a_squared_to_cancel": [ + -0.1947843318576025, + -0.0049574377809037395, + -0.008071209239579269, + ], + }, + ), +) + + +def standard_solution(nphi=31, **kwargs): + parameters = { + "rc": [1.0, 0.155, 0.0102], + "zs": [0.0, 0.154, 0.0111], + "nfp": 2, + "etabar": 0.64, + "B2c": -0.00322, + "nphi": nphi, + } + parameters.update(kwargs) + return qsc.Qsc(**parameters) + + +@pytest.mark.parametrize(("_name", "kwargs", "reference"), CASES) +def test_third_order_matches_upstream_pyqsc(_name, kwargs, reference): + solution = standard_solution(order="r3", nphi=61, **kwargs) + indices = np.asarray([0, 15, 30]) + + for name, expected in reference.items(): + np.testing.assert_allclose( + np.asarray(getattr(solution, name))[indices], + expected, + rtol=3.0e-9, + atol=5.0e-10, + ) + + +def test_third_order_structure_and_independent_constraints(): + solution = standard_solution( + rc=[1.0, 0.09], + zs=[0.0, -0.09], + nfp=2, + etabar=0.95, + I2=0.9, + B2c=-0.7, + p2=-600000.0, + order="r3", + nphi=61, + ) + third = solution.third_order + assert third is not None + + np.testing.assert_allclose(third.X3c1, solution.X1c * third.flux_constraint_coefficient) + np.testing.assert_allclose(third.Y3c1, solution.Y1c * third.flux_constraint_coefficient) + np.testing.assert_allclose(third.Y3s1, solution.Y1s * third.flux_constraint_coefficient) + np.testing.assert_allclose( + third.B0_order_a_squared_to_cancel, + 2 * solution.inputs.B0 * third.flux_constraint_coefficient, + rtol=2.0e-10, + atol=2.0e-12, + ) + assert float(jnp.max(jnp.abs(third.flux_constraint_residual))) < 2.0e-13 + assert float(jnp.max(jnp.abs(third.consistency_error))) < 2.0e-10 + + for name in ( + "X3s1", + "Z3s1", + "Z3c1", + "X3s3", + "X3c3", + "Y3s3", + "Y3c3", + "Z3s3", + "Z3c3", + ): + np.testing.assert_array_equal(getattr(third, name), jnp.zeros(solution.inputs.nphi)) + + derivative = solution.geometry.d_d_varphi + np.testing.assert_allclose(third.d_X3c1_d_varphi, derivative @ third.X3c1, atol=2.0e-12) + np.testing.assert_allclose(third.d_Y3s1_d_varphi, derivative @ third.Y3s1, atol=2.0e-12) + np.testing.assert_allclose(third.d_Y3c1_d_varphi, derivative @ third.Y3c1, atol=2.0e-12) + + +def test_qh_untwisting_and_compatibility_surface_include_r3(): + r3 = qsc.Qsc( + rc=[1.0, 0.17, 0.01804, 0.001409, 5.877e-5], + zs=[0.0, 0.1581, 0.01820, 0.001548, 7.772e-5], + nfp=4, + etabar=1.569, + B2c=0.1348, + order="r3", + nphi=61, + ) + + assert np.linalg.norm(np.asarray(r3.X3s1_untwisted)) > 0 + adapter = near_axis( + rc=[1.0, 0.17, 0.01804, 0.001409, 5.877e-5], + zs=[0.0, 0.1581, 0.01820, 0.001548, 7.772e-5], + nfp=4, + etabar=1.569, + B2c=0.1348, + nphi=61, + order="r3", + ) + r = 0.02 + theta = 0.37 + x2, y2, z2 = near_axis( + rc=[1.0, 0.17, 0.01804, 0.001409, 5.877e-5], + zs=[0.0, 0.1581, 0.01820, 0.001548, 7.772e-5], + nfp=4, + etabar=1.569, + B2c=0.1348, + nphi=61, + order="r2", + )._frenet_displacements(r, theta) + x3, y3, z3 = adapter._frenet_displacements(r, theta) + cosine = jnp.cos(theta) + sine = jnp.sin(theta) + cosine3 = jnp.cos(3 * theta) + sine3 = jnp.sin(3 * theta) + + np.testing.assert_allclose( + x3 - x2, + r**3 + * ( + r3.X3c1_untwisted * cosine + + r3.X3s1_untwisted * sine + + r3.X3c3_untwisted * cosine3 + + r3.X3s3_untwisted * sine3 + ), + atol=2.0e-15, + ) + np.testing.assert_allclose( + y3 - y2, + r**3 + * ( + r3.Y3c1_untwisted * cosine + + r3.Y3s1_untwisted * sine + + r3.Y3c3_untwisted * cosine3 + + r3.Y3s3_untwisted * sine3 + ), + atol=2.0e-15, + ) + np.testing.assert_allclose(z3, z2, atol=2.0e-15) + + +def test_third_order_is_jittable_and_differentiable(): + def coefficient(etabar): + return standard_solution(order="r3", nphi=31, etabar=etabar).X3c1[7] + + value = coefficient(jnp.asarray(-0.9)) + jitted = jax.jit(coefficient)(jnp.asarray(-0.9)) + tangent = jax.jvp(coefficient, (jnp.asarray(-0.9),), (jnp.asarray(1.0),))[1] + step = 2.0e-5 + finite_difference = (coefficient(-0.9 + step) - coefficient(-0.9 - step)) / (2 * step) + + np.testing.assert_allclose(jitted, value, rtol=2.0e-12, atol=2.0e-12) + np.testing.assert_allclose(tangent, finite_difference, rtol=3.0e-5, atol=3.0e-7) + + +def test_third_order_requires_second_order_and_valid_adapter_order(): + r1 = standard_solution(order="r1") + with pytest.raises(ValueError, match="second-order"): + qsc.solve_third_order(r1) + with pytest.raises(AttributeError, match="Lower-order"): + _ = r1.X3c1 + with pytest.raises(ValueError, match="order must be"): + near_axis(rc=[1.0], zs=[0.0], etabar=-0.9, order="r4") From 935e1f8ff115a77e6c662b0f367db4e74b5ed378 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 00:40:10 -0500 Subject: [PATCH 10/39] feat: add differentiable magnetic shear --- CHANGELOG.md | 3 + README.md | 8 +- docs/api/third-order.md | 9 + docs/development/physics-traceability.md | 2 +- docs/index.md | 4 +- docs/limitations.md | 5 +- docs/quickstart.md | 7 +- docs/references.bib | 10 + docs/theory/third-order.md | 53 +++- src/pyqsc_jax/__init__.py | 4 + src/pyqsc_jax/models.py | 31 ++ src/pyqsc_jax/near_axis.py | 10 + src/pyqsc_jax/shear.py | 372 +++++++++++++++++++++++ tests/physics/test_shear.py | 161 ++++++++++ 14 files changed, 668 insertions(+), 11 deletions(-) create mode 100644 src/pyqsc_jax/shear.py create mode 100644 tests/physics/test_shear.py diff --git a/CHANGELOG.md b/CHANGELOG.md index 1835ec1..17892f5 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -43,6 +43,9 @@ first stable release. - Differentiable r3 flux-constraint surface corrections, untwisted boundary coefficients, and two independent consistency checks with upstream pyQSC QA, finite-pressure/current, and QH parity. +- Standard-MHS magnetic shear with periodic and secular integrating-factor + branches, explicit `B31c`, immutable diagnostics, legacy adapter support, + and upstream QA/QH/asymmetric parity. ### Fixed diff --git a/README.md b/README.md index c10a415..9fbad28 100644 --- a/README.md +++ b/README.md @@ -4,9 +4,9 @@ Differentiable near-axis stellarator construction and plasma–coil field jets i JAX. > **Development status:** the immutable first-order core, complete r2 -> coefficient solve, r3 flux constraint, total-field Hessian, Mercier -> diagnostics, singular-radius diagnostics, and ESSOS adapter are validated. -> Magnetic shear, inverse solves, optimization, and plasma/external field jets +> coefficient solve, r3 flux constraint, magnetic shear, total-field Hessian, +> Mercier diagnostics, singular-radius diagnostics, and ESSOS adapter are +> validated. Inverse solves, optimization, and plasma/external field jets > remain under development on the `refactor/pyqsc-jax-complete` branch. ## Install @@ -89,6 +89,8 @@ print("singular radius:", solution.r_singularity) Use `order="r3"` to add the differentiable flux-constraint correction and its untwisted boundary coefficients. The result reports independent `flux_constraint_residual` and `consistency_error` checks. +`qsc.solve_magnetic_shear(solution, B31c=0.0)` then attaches the +order-\(r^2\) rotational-transform correction as `solution.iota2`. The lower-level immutable axis API supports general, not necessarily stellarator-symmetric Fourier axes: diff --git a/docs/api/third-order.md b/docs/api/third-order.md index c0ac7d1..3a748ee 100644 --- a/docs/api/third-order.md +++ b/docs/api/third-order.md @@ -8,3 +8,12 @@ ```{eval-rst} .. autofunction:: pyqsc_jax.solve_third_order ``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.ShearData + :members: +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.solve_magnetic_shear +``` diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index f42702c..ad8d262 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -13,7 +13,7 @@ to the cited source, not to a duplicated derivation in this repository. | Total field Hessian | manuscript Eqs. 55–83 | `field.total_field_jet`; pyQSC generated tensor as comparison only | regular-coordinate chain rule, JIT/JVP, QA and finite-current upstream arrays, full vacuum symmetry, divergence and derivative-of-divergence | implemented and documented | | Magnetic well and Mercier terms | Landreman (2021), arXiv:2012.00865 | `diagnostics.mercier_diagnostics`; pyQSC `mercier.py` | vacuum and finite-pressure/current upstream values | implemented and documented | | Third-order flux constraint | Landreman & Sengupta (2019) | `third_order.solve_third_order`; pyQSC `calculate_r3.py` | two independent flux-constraint forms; QA, finite-pressure/current, and QH upstream arrays; r3 boundary data; JIT/JVP/finite differences | implemented and documented | -| Magnetic shear | Rodríguez et al. shear equations | pyQSC `calculate_r3.py` | upstream shear and \(\iota_2\), asymmetric cases, resolution convergence, AD | not implemented | +| Magnetic shear | Rodríguez, Sengupta & Bhattacharjee (2022), Appendix F | `shear.solve_magnetic_shear`; pyQSC `calculate_r3.py` | three upstream paper cases, asymmetric/secular integration, resolution convergence, `B31c`, JIT/JVP/VJP and full-solve AD | implemented and documented for standard MHS with positive signs | | Singular radius and scale lengths | Landreman (2021), arXiv:2012.00865 | `singularity.singularity_diagnostics`; pyQSC `r_singularity.py` as comparison | direct regular-map determinant, QA/QH/finite-current upstream radii and arrays, residual, angular convergence, JIT/JVP/finite differences | implemented and documented | | Good-stellarator criteria | Curvo, Ferreira & Jorge (2025), Table 3 | none canonical | exact normalized thresholds and margins | not implemented | | Plasma current source | manuscript Eqs. 88–97 | none | normalization, enclosed current, straight circular/elliptic channels | not implemented | diff --git a/docs/index.md b/docs/index.md index 3e6d35f..326bebd 100644 --- a/docs/index.md +++ b/docs/index.md @@ -43,8 +43,8 @@ changelog ## Project status The immutable first-order API, complete r2 coefficient solve, r3 flux -constraint, total-field Hessian, Mercier terms, and singular-radius diagnostics -are validated. Magnetic shear, inverse solves, optimization, and +constraint, magnetic shear, total-field Hessian, Mercier terms, and +singular-radius diagnostics are validated. Inverse solves, optimization, and plasma/external field jets are under active development. The `pyqsc_jax.near_axis.near_axis` import remains supported for ESSOS without a runtime deprecation warning. diff --git a/docs/limitations.md b/docs/limitations.md index a55cc23..87f5720 100644 --- a/docs/limitations.md +++ b/docs/limitations.md @@ -7,10 +7,13 @@ flux-constraint surface correction. Known limitations under active refactor include: -- no magnetic-shear or \(\iota_2\) calculation yet; - no plasma/external field-jet separation; - no branch-aware target-transform inverse solve. +The magnetic-shear calculation currently implements the standard-MHS +specialization with \(B_{31s}=0\), \(I_4=0\), and \(s_G=s_\psi=1\). Other sign +conventions are rejected explicitly pending a traced derivation. + The sigma equation is solved to configurable residual and step tolerances, but a result object is still returned after nonconvergence so callers can inspect the structured report. Production workflows must reject diff --git a/docs/quickstart.md b/docs/quickstart.md index 3e1201f..3d87d0a 100644 --- a/docs/quickstart.md +++ b/docs/quickstart.md @@ -112,8 +112,11 @@ solution = qsc.Qsc( print(solution.flux_constraint_residual) print(solution.consistency_error) print(solution.B0_order_a_squared_to_cancel) + +solution = qsc.solve_magnetic_shear(solution, B31c=0.0) +print(solution.iota2) ``` The r3 result supplies first- and third-poloidal-harmonic coefficient arrays -and their untwisted forms to boundary conversion. Magnetic shear is a -separate, later milestone. +and their untwisted forms to boundary conversion. The shear calculation is +explicit because `B31c` is an independent third-order input. diff --git a/docs/references.bib b/docs/references.bib index 31a7932..03c5f9a 100644 --- a/docs/references.bib +++ b/docs/references.bib @@ -76,6 +76,16 @@ @article{landreman2021figures archivePrefix = {arXiv}, } +@article{rodriguez2022weakly, + author = {Rodríguez, Eduardo and Sengupta, Wrick and Bhattacharjee, Amitava}, + title = {Weakly quasisymmetric near-axis solutions to all orders}, + journal = {Physics of Plasmas}, + volume = {29}, + pages = {012507}, + year = {2022}, + doi = {10.1063/5.0076583}, +} + @article{giuliani2022single, author = {Giuliani, Andrew and Wechsung, Florian and Cerfon, Antoine and Stadler, Georg and Landreman, Matt}, title = {Single-stage gradient-based stellarator coil design: optimization for near-axis quasi-symmetry}, diff --git a/docs/theory/third-order.md b/docs/theory/third-order.md index e97265b..c055bf4 100644 --- a/docs/theory/third-order.md +++ b/docs/theory/third-order.md @@ -5,8 +5,7 @@ Setting `order="r3"` first constructs the complete r2 solution, then adds the third-order surface displacement required for consistency of the toroidal-flux constraint through order \(r^2\). This is the `r3_flux_constraint` construction -of {cite}`landreman2019highorder`. Magnetic shear and \(\iota_2\) are not part -of this milestone. +of {cite}`landreman2019highorder`. The implementation uses the short regular-coordinate relation as its primal formula. It also evaluates the independent field-strength cancellation @@ -81,3 +80,53 @@ configurations of sections 5.1, 5.3, and 5.4 of spectral coefficient derivatives, helical untwisting, r3 boundary assembly, JIT, JVP, and centered finite differences. The upstream commit is recorded in the refactor baseline. + +## Magnetic shear + +The generalized sigma equation gives the next rotational-transform term + +\[ +\iota(r)=\iota_0+r^2\iota_2+O(r^4) +\] + +as a periodic solvability condition {cite}`rodriguez2022weakly`. The source +derivation uses \(\epsilon=\sqrt{\psi}\), whereas the direct-construction +variables use \(r=\sqrt{2\psi/B_0}\). `solve_magnetic_shear` performs this +conversion explicitly before evaluating the third-order \(Z_{31}\), +\(X_{31}\), and \(Y_{31}\) relations. + +Writing \(\widetilde{\Lambda}\) for the inhomogeneous term and + +\[ +\mathcal E(\varphi)= +\exp\left(2\iota_N\int_0^\varphi\sigma(v)\,\mathrm dv\right), +\] + +the stellarator-symmetric result has the quotient form + +\[ +\iota_2= +\frac{B_0}{2} +\frac{\int \mathcal E\,\widetilde{\Lambda}\,\mathrm d\phi} +{\int \mathcal E +(X_{1c}^2+Y_{1c}^2+Y_{1s}^2)Y_{1s}^{-2}\,\mathrm d\phi}. +\] + +For a general asymmetric first-order solution, \(\sigma\) can have a nonzero +mean. The implementation separates the periodic and secular parts before +forming \(\mathcal E\), appends the analytically consistent endpoint, and uses +trapezoidal integration over one field period. This avoids applying a periodic +inverse derivative to a nonperiodic primitive. + +`B31c` is an explicit scalar input in the inverse-\(B^2\) convention. +`ShearData` records the numerator, denominator, integrating factor, +\(\widetilde{\Lambda}\), and third-order intermediates as well as `iota2`. +The current implementation is the standard-MHS specialization with +\(B_{31s}=0\), \(I_4=0\), and \(s_G=s_\psi=1\); other sign conventions are +rejected rather than silently extrapolated. + +Validation covers upstream pyQSC values for the section 5.1 vacuum QA, +section 5.3 finite-pressure/current, and section 5.4 QH configurations; an +asymmetric axis and nonzero sigma mean; resolution convergence; `B31c` +dependence; JIT, JVP, VJP, and differentiation through the complete near-axis +solve. diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index 67e285a..80a2f2b 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -12,11 +12,13 @@ NearAxisSolution, RootSolveReport, SecondOrderData, + ShearData, SingularityDiagnostics, ThirdOrderData, ) from pyqsc_jax.near_axis import near_axis from pyqsc_jax.second_order import SecondOrderResiduals, second_order_residuals +from pyqsc_jax.shear import solve_magnetic_shear from pyqsc_jax.singularity import singularity_diagnostics from pyqsc_jax.solvers import RootSolveOptions from pyqsc_jax.third_order import solve_third_order @@ -33,12 +35,14 @@ "RootSolveReport", "SecondOrderData", "SecondOrderResiduals", + "ShearData", "SingularityDiagnostics", "ThirdOrderData", "near_axis", "mercier_diagnostics", "second_order_residuals", "solve", + "solve_magnetic_shear", "singularity_diagnostics", "solve_third_order", "total_field_jet", diff --git a/src/pyqsc_jax/models.py b/src/pyqsc_jax/models.py index 325e800..5c6cc88 100644 --- a/src/pyqsc_jax/models.py +++ b/src/pyqsc_jax/models.py @@ -244,6 +244,26 @@ class ThirdOrderData: Z3c3_untwisted: jax.Array +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class ShearData: + """Order-r-squared rotational-transform correction and intermediates.""" + + B31c: jax.Array + iota2: jax.Array + numerator: jax.Array + denominator: jax.Array + Lambda_tilde: jax.Array + integrating_factor: jax.Array + sigma_average: jax.Array + Z31c: jax.Array + Z31s: jax.Array + X31c: jax.Array + X31s: jax.Array + Y31s: jax.Array + stellarator_symmetric: jax.Array + + @jax.tree_util.register_dataclass @dataclass(frozen=True) class NearAxisSolution: @@ -281,6 +301,7 @@ class NearAxisSolution: field_jet: FieldJet | None = None singularity: SingularityDiagnostics | None = None third_order: ThirdOrderData | None = None + shear: ShearData | None = None _SECOND_ORDER_NAMES: ClassVar[frozenset[str]] = frozenset( field.name for field in SecondOrderData.__dataclass_fields__.values() @@ -288,6 +309,9 @@ class NearAxisSolution: _THIRD_ORDER_NAMES: ClassVar[frozenset[str]] = frozenset( field.name for field in ThirdOrderData.__dataclass_fields__.values() ) + _SHEAR_NAMES: ClassVar[frozenset[str]] = frozenset( + field.name for field in ShearData.__dataclass_fields__.values() + ) _MERCIER_NAMES: ClassVar[frozenset[str]] = frozenset( field.name for field in MercierDiagnostics.__dataclass_fields__.values() ) @@ -322,6 +346,13 @@ def __getattr__(self, name: str): if third_order is None: raise AttributeError(f"Lower-order solution has no {name!r} quantity.") return getattr(third_order, name) + if name in self._SHEAR_NAMES: + shear = object.__getattribute__(self, "shear") + if shear is None: + raise AttributeError( + f"Magnetic shear has not been calculated; no {name!r} quantity." + ) + return getattr(shear, name) if name in self._MERCIER_NAMES: mercier = object.__getattribute__(self, "mercier") if mercier is None: diff --git a/src/pyqsc_jax/near_axis.py b/src/pyqsc_jax/near_axis.py index 88d4625..02c4c05 100644 --- a/src/pyqsc_jax/near_axis.py +++ b/src/pyqsc_jax/near_axis.py @@ -10,6 +10,7 @@ from pyqsc_jax.axis import Axis from pyqsc_jax.first_order import solve from pyqsc_jax.models import NearAxisSolution +from pyqsc_jax.shear import solve_magnetic_shear from pyqsc_jax.solvers import implicit_dense_root ArrayLike = Any @@ -126,6 +127,8 @@ def _legacy_tuple(solution: NearAxisSolution) -> tuple[jax.Array, ...]: ) def _refresh(self) -> None: + for name in NearAxisSolution._SHEAR_NAMES: + self.__dict__.pop(name, None) solution = self._canonical_solution(self.rc, self.zs, self.etabar) self.solution = solution self.phi = solution.phi @@ -252,6 +255,13 @@ def calculate(self, rc: ArrayLike, zs: ArrayLike, etabar: ArrayLike): return self._legacy_tuple(self._canonical_solution(rc, zs, etabar)) + def calculate_shear(self, B31c: ArrayLike = 0.0) -> None: + """Populate the historical order-r-squared transform correction.""" + + self.solution = solve_magnetic_shear(self.solution, B31c=B31c) + for name in self.solution._SHEAR_NAMES: + setattr(self, name, getattr(self.solution, name)) + def B_covariant(self, points: ArrayLike) -> jax.Array: """First-order covariant Boozer components ``(B_r, B_theta, B_phi)``.""" diff --git a/src/pyqsc_jax/shear.py b/src/pyqsc_jax/shear.py new file mode 100644 index 0000000..4dda027 --- /dev/null +++ b/src/pyqsc_jax/shear.py @@ -0,0 +1,372 @@ +"""Magnetic shear from the order-r-cubed generalized sigma equation. + +The equations are adapted from ``landreman/pyQSC:qsc/calculate_r3.py`` at the +audited BSD-2-Clause upstream commit recorded in the refactor baseline. Their +source derivation is Rodríguez et al., Physics of Plasmas 29, 012507 (2022). +""" + +from __future__ import annotations + +from dataclasses import replace +from typing import Any + +import jax.numpy as jnp + +from pyqsc_jax.models import NearAxisSolution, ShearData + +ArrayLike = Any + + +def solve_magnetic_shear( + solution: NearAxisSolution, + *, + B31c: ArrayLike = 0.0, +) -> NearAxisSolution: + """Attach the standard-MHS order-r-squared transform correction. + + ``B31c`` uses the inverse-field-squared convention of the generalized + sigma equation. Current variation at this order and ``B31s`` are zero. + """ + + r2 = solution.second_order + if r2 is None: + raise ValueError("A second-order solution is required to calculate magnetic shear.") + inputs = solution.inputs + if inputs.sG != 1 or inputs.spsi != 1: + raise NotImplementedError( + "Magnetic shear currently requires sG=spsi=1; the upstream signs are not generalized." + ) + + B31c = jnp.asarray(B31c) + if B31c.ndim != 0: + raise ValueError("B31c must be a scalar.") + + D = solution.geometry.d_d_varphi + epsilon_scale = jnp.sqrt(2 / inputs.B0) + scale2 = epsilon_scale**2 + G2 = r2.G2 * scale2 + G0 = solution.G0 + I2 = inputs.I2 * scale2 + X1c = solution.X1c * epsilon_scale + Y1c = solution.Y1c * epsilon_scale + Y1s = solution.Y1s * epsilon_scale + X20 = r2.X20 * scale2 + X2s = r2.X2s * scale2 + X2c = r2.X2c * scale2 + Y20 = r2.Y20 * scale2 + Y2s = r2.Y2s * scale2 + Y2c = r2.Y2c * scale2 + Z20 = r2.Z20 * scale2 + Z2s = r2.Z2s * scale2 + Z2c = r2.Z2c * scale2 + torsion = -solution.torsion + curvature = solution.curvature + iota = solution.iotaN + dldp = solution.geometry.abs_G0_over_B0 + dX1c = D @ X1c + dY1c = D @ Y1c + dY1s = D @ Y1s + dZ20 = D @ Z20 + dZ2c = D @ Z2c + dZ2s = D @ Z2s + dX20 = D @ X20 + dX2c = D @ X2c + dX2s = D @ X2s + dY20 = D @ Y20 + dY2c = D @ Y2c + dY2s = D @ Y2s + + inverse_B0_squared = 1 / inputs.B0**2 + Ba0 = G0 + Ba1 = G2 + solution.iotaN * I2 + eta = inputs.etabar * jnp.sqrt(2) * inverse_B0_squared**0.25 + B1c = -2 * inverse_B0_squared * eta + B20 = ( + (0.75 * inputs.etabar**2 / jnp.sqrt(inverse_B0_squared) - r2.B20) + * 4 + * inverse_B0_squared**2 + ) + B31s = jnp.asarray(0, dtype=B31c.dtype) + I4 = jnp.asarray(0, dtype=B31c.dtype) + + Z31c = ( + -1 + / (3 * Ba0 * X1c * Y1s) + * ( + 2 * iota * (X1c * X2s - Y2c * Y1s + Y1c * Y2s) + - 2 * Ba0 * X2s * Y1c * Z20 + + 2 * Ba0 * X2c * Y1s * Z20 + + 2 * Ba0 * X1c * Y2s * Z20 + - 4 * Ba0 * X2s * Y1c * Z2c + - 2 * Ba0 * X20 * Y1s * Z2c + + 4 * Ba0 * X1c * Y2s * Z2c + - dldp + * ( + torsion * (2 * X20 * Y1c + X2c * Y1c - 2 * X1c * Y20 - X1c * Y2c + X2s * Y1s) + + I2 * (2 * X20 * Y1c + X2c * Y1c - 2 * X1c * Y20 - X1c * Y2c + X2s * Y1s) + - 2 * curvature * X1c * Z20 + - curvature * X1c * Z2c + ) + + 2 * Ba0 * X20 * Y1c * Z2s + + 4 * Ba0 * X2c * Y1c * Z2s + - 2 * Ba0 * X1c * Y20 * Z2s + - 4 * Ba0 * X1c * Y2c * Z2s + + 2 * X1c * dX20 + + X1c * dX2c + + 2 * Y1c * dY20 + + Y1c * dY2c + + Y1s * dY2s + ) + ) + dZ31c = D @ Z31c + + Z31s = ( + 1 + / (3 * Ba0 * X1c * Y1s) + * ( + 2 * iota * (X1c * X2c + Y1c * Y2c + Y1s * Y2s) + - 2 * Ba0 * X2c * Y1c * Z20 + + 2 * Ba0 * X1c * Y2c * Z20 + - 2 * Ba0 * X2s * Y1s * Z20 + + 2 * Ba0 * X20 * Y1c * Z2c + - 2 * Ba0 * X1c * Y20 * Z2c + + 4 * Ba0 * X2s * Y1s * Z2c + + 2 * Ba0 * X20 * Y1s * Z2s + - 4 * Ba0 * X2c * Y1s * Z2s + + dldp + * ( + I2 * X2s * Y1c + + 2 * I2 * X20 * Y1s + - I2 * X2c * Y1s + - I2 * X1c * Y2s + + torsion * (X2s * Y1c + 2 * X20 * Y1s - X2c * Y1s - X1c * Y2s) + - curvature * X1c * Z2s + ) + - X1c * dX2s + - 2 * Y1s * dY20 + + Y1s * dY2c + - Y1c * dY2s + ) + ) + dZ31s = D @ Z31s + + X31c = ( + 1 + / (2 * dldp**2 * curvature) + * ( + -2 * Ba0 * Ba1 * B1c + - Ba0**2 * B31c + + 2 * dldp**2 * torsion**2 * X1c * X20 + + 2 * iota**2 * X1c * X2c + + dldp**2 * torsion**2 * X1c * X2c + + dldp**2 * curvature**2 * X1c * (2 * X20 + X2c) + + 3 * dldp * iota * torsion * X2s * Y1c + + 2 * dldp**2 * torsion**2 * Y1c * Y20 + + 2 * iota**2 * Y1c * Y2c + + dldp**2 * torsion**2 * Y1c * Y2c + - 2 * dldp * iota * torsion * X20 * Y1s + - 3 * dldp * iota * torsion * X2c * Y1s + - 3 * dldp * iota * torsion * X1c * Y2s + + 2 * iota**2 * Y1s * Y2s + + dldp**2 * torsion**2 * Y1s * Y2s + + 2 * dldp * iota * Z31s + + 2 * iota * X2s * dX1c + + 2 * dldp * torsion * Y20 * dX1c + + dldp * torsion * Y2c * dX1c + + 2 * dldp * torsion * Y1c * dX20 + + 2 * dX1c * dX20 + + dldp * torsion * Y1c * dX2c + + dX1c * dX2c + - iota * X1c * dX2s + + dldp * torsion * Y1s * dX2s + - 2 * dldp * torsion * X20 * dY1c + - dldp * torsion * X2c * dY1c + + 2 * iota * Y2s * dY1c + - 2 * dldp * torsion * X1c * dY20 + + 2 * iota * Y1s * dY20 + + 2 * dY1c * dY20 + - dldp * torsion * X1c * dY2c + + iota * Y1s * dY2c + + dY1c * dY2c + - dldp * torsion * X2s * dY1s + - 2 * iota * Y2c * dY1s + - iota * Y1c * dY2s + + dY1s * dY2s + + dldp + * curvature + * ( + -3 * iota * X1c * Z2s + + dldp * torsion * (Y1c * (2 * Z20 + Z2c) + Y1s * Z2s) + + 2 * Z20 * dX1c + + Z2c * dX1c + - 2 * X1c * dZ20 + - X1c * dZ2c + ) + + 2 * dldp * dZ31c + ) + ) + + X31s = ( + 1 + / (2 * dldp**2 * curvature) + * ( + -(Ba0**2) * B31s + + dldp**2 * curvature**2 * X1c * X2s + + dldp**2 * torsion**2 * X1c * X2s + + 2 * dldp**2 * torsion**2 * Y20 * Y1s + - dldp**2 * torsion**2 * Y2c * Y1s + + dldp**2 * torsion**2 * Y1c * Y2s + + 2 * iota**2 * (X1c * X2s - Y2c * Y1s + Y1c * Y2s) + + 2 * dldp**2 * curvature * torsion * Y1s * Z20 + - dldp**2 * curvature * torsion * Y1s * Z2c + + dldp**2 * curvature * torsion * Y1c * Z2s + + dldp * torsion * Y2s * dX1c + + dldp * curvature * Z2s * dX1c + + 2 * dldp * torsion * Y1s * dX20 + - dldp * torsion * Y1s * dX2c + + dldp * torsion * Y1c * dX2s + + dX1c * dX2s + - dldp * torsion * X2s * dY1c + - 2 * dldp * torsion * X20 * dY1s + + dldp * torsion * X2c * dY1s + + 2 * dY20 * dY1s + - dY2c * dY1s + - dldp * torsion * X1c * dY2s + + dY1c * dY2s + + iota + * ( + dldp + * torsion + * (2 * X20 * Y1c - 3 * X2c * Y1c - 2 * X1c * Y20 + 3 * X1c * Y2c - 3 * X2s * Y1s) + + dldp * curvature * X1c * (-2 * Z20 + 3 * Z2c) + - 2 * dldp * Z31c + - 2 * X2c * dX1c + - 2 * X1c * dX20 + + X1c * dX2c + - 2 * Y2c * dY1c + - 2 * Y1c * dY20 + + Y1c * dY2c + - 2 * Y2s * dY1s + + Y1s * dY2s + ) + - dldp * curvature * X1c * dZ2s + + 2 * dldp * dZ31s + ) + ) + dX31s = D @ X31s + + Y31s = ( + 1 + / (4 * Ba0 * X1c) + * ( + -2 * Ba1 * X1c * Y1s + + 2 * iota * I2 * X1c * Y1s + - dldp * (4 * curvature * X20 + torsion * I2 * (X1c**2 + Y1c**2 + Y1s**2)) + + 4 * Ba0 * (X31s * Y1c + 2 * X2s * Y2c - X31c * Y1s - 2 * X2c * Y2s) + - I2 * Y1c * dX1c + + I2 * X1c * dY1c + + 4 * dZ20 + ) + ) + dY31s = D @ Y31s + + Lambda_tilde = 2 / Y1s**2 * ( + Ba0 * inverse_B0_squared * I4 + (Ba1 * inverse_B0_squared + Ba0 * B20) * I2 + ) + 1 / Y1s**2 * ( + -2 + * iota + * ( + 2 * X2c**2 + + X1c * X31c + + 2 * X2s**2 + + 2 * Y2c**2 + + 2 * Y2s**2 + + Y1s * Y31s + + 2 * Z2c**2 + + 2 * Z2s**2 + ) + + 2 + * dldp + * ( + torsion * (-X31s * Y1c - 2 * X2s * Y2c + X31c * Y1s + 2 * X2c * Y2s + X1c * Y31s) + + curvature * (-2 * X2s * Z2c + 2 * X2c * Z2s + X1c * Z31s) + ) + - X31s * dX1c + - 2 * X2s * dX2c + + 2 * X2c * dX2s + + X1c * dX31s + - Y31s * dY1c + - 2 * Y2s * dY2c + + 2 * Y2c * dY2s + + Y1c * dY31s + - 2 * Z2s * dZ2c + + 2 * Z2c * dZ2s + ) + + reduced_derivative = D[1:, 1:] + symmetric_integral = jnp.concatenate( + ( + jnp.zeros(1, dtype=solution.sigma.dtype), + jnp.linalg.solve(reduced_derivative, solution.sigma[1:]), + ) + ) + symmetric_factor = jnp.exp(2 * iota * symmetric_integral) + denominator_factor = (X1c**2 + Y1c**2 + Y1s**2) / Y1s**2 + symmetric_numerator = jnp.sum( + symmetric_factor * Lambda_tilde * solution.geometry.d_varphi_d_phi + ) + symmetric_denominator = jnp.sum( + symmetric_factor * denominator_factor * solution.geometry.d_varphi_d_phi + ) + + sigma_average = jnp.sum(solution.sigma * solution.geometry.d_varphi_d_phi) / inputs.nphi + periodic_integral = jnp.linalg.solve( + reduced_derivative, + solution.sigma[1:] - sigma_average, + ) + general_integral = jnp.concatenate( + ( + jnp.zeros(1, dtype=solution.sigma.dtype), + periodic_integral + sigma_average * solution.varphi[1:], + ) + ) + general_factor = jnp.exp(2 * iota * general_integral) + period = 2 * jnp.pi / inputs.axis.nfp + factor_extended = jnp.concatenate( + (general_factor, jnp.exp(jnp.asarray([2 * iota * sigma_average * period]))) + ) + Lambda_extended = jnp.concatenate((Lambda_tilde, Lambda_tilde[:1])) + denominator_extended = jnp.concatenate((denominator_factor, denominator_factor[:1])) + varphi_extended = jnp.concatenate((solution.varphi, jnp.asarray([period]))) + general_numerator = jnp.trapezoid(factor_extended * Lambda_extended, varphi_extended) + general_denominator = jnp.trapezoid( + factor_extended * denominator_extended, + varphi_extended, + ) + + stellarator_symmetric = ( + (inputs.sigma0 == 0) + & (jnp.max(jnp.abs(inputs.axis.rs)) == 0) + & (jnp.max(jnp.abs(inputs.axis.zc)) == 0) + ) + numerator = jnp.where(stellarator_symmetric, symmetric_numerator, general_numerator) + denominator = jnp.where(stellarator_symmetric, symmetric_denominator, general_denominator) + integrating_factor = jnp.where(stellarator_symmetric, symmetric_factor, general_factor) + iota2 = inputs.B0 * numerator / (2 * denominator) + + shear = ShearData( + B31c=B31c, + iota2=iota2, + numerator=numerator, + denominator=denominator, + Lambda_tilde=Lambda_tilde, + integrating_factor=integrating_factor, + sigma_average=sigma_average, + Z31c=Z31c, + Z31s=Z31s, + X31c=X31c, + X31s=X31s, + Y31s=Y31s, + stellarator_symmetric=stellarator_symmetric, + ) + return replace(solution, shear=shear) diff --git a/tests/physics/test_shear.py b/tests/physics/test_shear.py new file mode 100644 index 0000000..f839113 --- /dev/null +++ b/tests/physics/test_shear.py @@ -0,0 +1,161 @@ +from __future__ import annotations + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +import pyqsc_jax as qsc +from pyqsc_jax.near_axis import near_axis + +PAPER_CASES = ( + ( + { + "rc": [1.0, 0.155, 0.0102], + "zs": [0.0, 0.154, 0.0111], + "nfp": 2, + "etabar": 0.64, + "B2c": -0.00322, + }, + 4.665537859250996, + ), + ( + { + "rc": [1.0, 0.09], + "zs": [0.0, -0.09], + "nfp": 2, + "etabar": 0.95, + "I2": 0.9, + "B2c": -0.7, + "p2": -600000.0, + }, + 0.2758333187134502, + ), + ( + { + "rc": [1.0, 0.17, 0.01804, 0.001409, 5.877e-5], + "zs": [0.0, 0.1581, 0.01820, 0.001548, 7.772e-5], + "nfp": 4, + "etabar": 1.569, + "B2c": 0.1348, + }, + -1.1837987800965397, + ), +) + + +def qa_solution(nphi=61, **overrides): + parameters = { + "rc": [1.0, 0.155, 0.0102], + "zs": [0.0, 0.154, 0.0111], + "nfp": 2, + "etabar": 0.64, + "B2c": -0.00322, + "order": "r3", + "nphi": nphi, + } + parameters.update(overrides) + return qsc.Qsc(**parameters) + + +@pytest.mark.parametrize(("parameters", "expected_iota2"), PAPER_CASES) +def test_magnetic_shear_matches_upstream_paper_cases(parameters, expected_iota2): + solution = qsc.solve_magnetic_shear(qsc.Qsc(**parameters, order="r3", nphi=61)) + + np.testing.assert_allclose(solution.iota2, expected_iota2, rtol=2.0e-12, atol=2.0e-12) + assert bool(solution.stellarator_symmetric) + np.testing.assert_allclose( + solution.iota2, + solution.inputs.B0 * solution.numerator / (2 * solution.denominator), + ) + assert np.all(np.isfinite(np.asarray(solution.Lambda_tilde))) + assert np.all(np.isfinite(np.asarray(solution.integrating_factor))) + + +def test_general_asymmetric_integration_matches_upstream(): + solution = qsc.Qsc( + rc=[1.0, 0.1], + rs=[0.0, 0.01], + zc=[0.0, -0.005], + zs=[0.0, 0.1], + nfp=2, + etabar=1.0, + sigma0=0.2, + I2=1.0, + order="r3", + nphi=61, + ) + solution = qsc.solve_magnetic_shear(solution) + + np.testing.assert_allclose(solution.iota2, -2131.8417260171145, rtol=3.0e-12) + assert not bool(solution.stellarator_symmetric) + assert abs(float(solution.sigma_average)) > 0.1 + + +def test_B31c_response_and_resolution_convergence(): + coarse = qsc.solve_magnetic_shear(qa_solution(nphi=31), B31c=0.23) + medium = qsc.solve_magnetic_shear(qa_solution(nphi=51), B31c=0.23) + fine = qsc.solve_magnetic_shear(qa_solution(nphi=91), B31c=0.23) + + np.testing.assert_allclose(medium.iota2, fine.iota2, rtol=5.0e-11) + np.testing.assert_allclose(fine.iota2, 4.676607885614116, rtol=3.0e-12) + assert abs(float(coarse.iota2 - fine.iota2)) < 1.2e-5 + np.testing.assert_allclose(fine.B31c, 0.23) + + +def test_magnetic_shear_is_jittable_and_differentiable(): + solution = qa_solution(nphi=31) + + def shear_for_B31c(B31c): + return qsc.solve_magnetic_shear(solution, B31c=B31c).iota2 + + value = shear_for_B31c(jnp.asarray(0.1)) + jitted = jax.jit(shear_for_B31c)(jnp.asarray(0.1)) + tangent = jax.jvp(shear_for_B31c, (jnp.asarray(0.1),), (jnp.asarray(1.0),))[1] + cotangent = jax.vjp(shear_for_B31c, jnp.asarray(0.1))[1](jnp.asarray(1.0))[0] + step = 1.0e-4 + finite_difference = (shear_for_B31c(0.1 + step) - shear_for_B31c(0.1 - step)) / (2 * step) + + np.testing.assert_allclose(jitted, value, rtol=2.0e-13) + np.testing.assert_allclose(tangent, cotangent, rtol=2.0e-12, atol=2.0e-12) + np.testing.assert_allclose(tangent, finite_difference, rtol=2.0e-8, atol=2.0e-10) + + +def test_magnetic_shear_differentiates_through_near_axis_solve(): + def shear_for_etabar(etabar): + solution = qa_solution(nphi=31, etabar=etabar) + return qsc.solve_magnetic_shear(solution).iota2 + + etabar = jnp.asarray(0.64) + tangent = jax.jvp(shear_for_etabar, (etabar,), (jnp.asarray(1.0),))[1] + step = 1.0e-5 + finite_difference = (shear_for_etabar(0.64 + step) - shear_for_etabar(0.64 - step)) / (2 * step) + + np.testing.assert_allclose(tangent, finite_difference, rtol=8.0e-8, atol=5.0e-8) + + +def test_legacy_calculate_shear_and_stale_value_removal(): + adapter = near_axis( + rc=[1.0, 0.155, 0.0102], + zs=[0.0, 0.154, 0.0111], + nfp=2, + etabar=0.64, + B2c=-0.00322, + order="r3", + nphi=61, + ) + assert adapter.calculate_shear() is None + np.testing.assert_allclose(adapter.iota2, 4.665537859250996, rtol=2.0e-12) + adapter.dofs = adapter.dofs.at[-1].set(0.65) + assert not hasattr(adapter, "iota2") + + +def test_magnetic_shear_input_guards_and_missing_result(): + with pytest.raises(ValueError, match="second-order"): + qsc.solve_magnetic_shear(qa_solution(order="r1")) + with pytest.raises(ValueError, match="scalar"): + qsc.solve_magnetic_shear(qa_solution(), B31c=jnp.ones(2)) + with pytest.raises(NotImplementedError, match="sG=spsi=1"): + qsc.solve_magnetic_shear(qa_solution(sG=-1)) + with pytest.raises(AttributeError, match="not been calculated"): + _ = qa_solution().iota2 From 7e87d04765d025bcf2d82395788e6652e19fc67e Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 00:47:50 -0500 Subject: [PATCH 11/39] feat: add target-transform inverse solves --- CHANGELOG.md | 3 + README.md | 11 +- docs/api/first-order.md | 5 + docs/development/physics-traceability.md | 1 + docs/index.md | 6 +- docs/limitations.md | 8 +- docs/quickstart.md | 36 ++++++ docs/theory/inverse-solves.md | 66 ++++++++++ src/pyqsc_jax/__init__.py | 2 + src/pyqsc_jax/first_order.py | 74 ++++++++--- src/pyqsc_jax/inverse.py | 113 ++++++++++++++++ src/pyqsc_jax/models.py | 25 ++++ tests/physics/test_first_order.py | 2 +- tests/physics/test_inverse.py | 158 +++++++++++++++++++++++ 14 files changed, 489 insertions(+), 21 deletions(-) create mode 100644 docs/theory/inverse-solves.md create mode 100644 src/pyqsc_jax/inverse.py create mode 100644 tests/physics/test_inverse.py diff --git a/CHANGELOG.md b/CHANGELOG.md index 17892f5..9378569 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -46,6 +46,9 @@ first stable release. - Standard-MHS magnetic shear with periodic and secular integrating-factor branches, explicit `B31c`, immutable diagnostics, legacy adapter support, and upstream QA/QH/asymmetric parity. +- Branch-local target-transform solves for sign-preserving `etabar` or `I2`, + including implicit derivatives, round-trip validation, local response and + fold diagnostics, and propagation through r2. ### Fixed diff --git a/README.md b/README.md index 9fbad28..0463cdb 100644 --- a/README.md +++ b/README.md @@ -6,8 +6,9 @@ JAX. > **Development status:** the immutable first-order core, complete r2 > coefficient solve, r3 flux constraint, magnetic shear, total-field Hessian, > Mercier diagnostics, singular-radius diagnostics, and ESSOS adapter are -> validated. Inverse solves, optimization, and plasma/external field jets -> remain under development on the `refactor/pyqsc-jax-complete` branch. +> validated, along with branch-local inverse solves. Branch continuation, +> optimization, and plasma/external field jets remain under development on the +> `refactor/pyqsc-jax-complete` branch. ## Install @@ -92,6 +93,12 @@ untwisted boundary coefficients. The result reports independent `qsc.solve_magnetic_shear(solution, B31c=0.0)` then attaches the order-\(r^2\) rotational-transform correction as `solution.iota2`. +Prescribe transform with +`qsc.solve(axis=axis, iota=target, etabar=seed, solve_for="etabar")`, or hold +`etabar` fixed and use `solve_for="I2"`. The inverse result reports its local +response derivative and fold flag; pseudo-arclength continuation is the next +branch-tracking milestone. + The lower-level immutable axis API supports general, not necessarily stellarator-symmetric Fourier axes: diff --git a/docs/api/first-order.md b/docs/api/first-order.md index 884de57..35272fb 100644 --- a/docs/api/first-order.md +++ b/docs/api/first-order.md @@ -28,6 +28,11 @@ :members: ``` +```{eval-rst} +.. autoclass:: pyqsc_jax.InverseSolveDiagnostics + :members: +``` + ## ESSOS compatibility ```{eval-rst} diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index ad8d262..8121918 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -8,6 +8,7 @@ to the cited source, not to a duplicated derivation in this repository. | --- | --- | --- | --- | --- | | General Fourier axis and Frenet frame | Landreman & Sengupta (2018), arXiv:1809.10233 | `Axis`, `evaluate_axis`, `compute_axis_geometry`; pyQSC `init_axis.py` | analytic circle; asymmetric Fortran curvature/torsion/varphi; frame identities; JIT/VMAP/grad | implemented and documented | | First-order QS and sigma equation | Landreman & Sengupta (2019), arXiv:1908.10253 | `first_order.solve_sigma`; pyQSC `solve_sigma_equation.py` | residual, convergence report, QA/QH/finite-current pyQSC values, JIT/VMAP/JVP/VJP, finite differences | implemented and documented | +| Target-transform inverse solve | implicit-function reformulation of the first-order sigma equation | `inverse.solve_target_iota` | `etabar` and `I2` round trips, sign branches, distinct local basins, fold metric, r2 propagation, JIT/JVP/finite differences | branch-local solve implemented; pseudo-arclength continuation pending | | Field gradient and `L_grad_B` | Landreman (2021), arXiv:2012.00865, Eq. 3.12 | `first_order.first_order_solution`; pyQSC `grad_B_tensor.py` | upstream arrays, vacuum symmetry/divergence, resolution convergence | implemented and documented | | Complete second-order coefficients | Landreman & Sengupta (2019), arXiv:1908.10253 | `second_order.solve_second_order`; pyQSC `calculate_r2.py`; manuscript Eqs. 36–54 | four independent equation residuals; vacuum QA, finite-pressure/current, QH upstream arrays; JIT/JVP/VJP/finite differences | implemented and documented | | Total field Hessian | manuscript Eqs. 55–83 | `field.total_field_jet`; pyQSC generated tensor as comparison only | regular-coordinate chain rule, JIT/JVP, QA and finite-current upstream arrays, full vacuum symmetry, divergence and derivative-of-divergence | implemented and documented | diff --git a/docs/index.md b/docs/index.md index 326bebd..eba4218 100644 --- a/docs/index.md +++ b/docs/index.md @@ -15,6 +15,7 @@ theory/coordinates-and-conventions theory/first-order theory/second-order theory/third-order +theory/inverse-solves theory/field-jet api/axis api/first-order @@ -44,8 +45,9 @@ changelog The immutable first-order API, complete r2 coefficient solve, r3 flux constraint, magnetic shear, total-field Hessian, Mercier terms, and -singular-radius diagnostics are validated. Inverse solves, optimization, and -plasma/external field jets are under active development. +singular-radius diagnostics are validated, as are branch-local inverse solves. +Branch continuation, optimization, and plasma/external field jets are under +active development. The `pyqsc_jax.near_axis.near_axis` import remains supported for ESSOS without a runtime deprecation warning. diff --git a/docs/limitations.md b/docs/limitations.md index 87f5720..2391908 100644 --- a/docs/limitations.md +++ b/docs/limitations.md @@ -8,7 +8,13 @@ flux-constraint surface correction. Known limitations under active refactor include: - no plasma/external field-jet separation; -- no branch-aware target-transform inverse solve. +- no pseudo-arclength branch continuation yet. + +Target-transform solves are branch-local. The sign of the `etabar` seed is +preserved and the seed magnitude selects a Newton basin. Multiple local +solutions can have the same transform. `response_derivative` and `branch_fold` +detect local loss of invertibility, but crossing such a fold awaits the +pseudo-arclength interface. The magnetic-shear calculation currently implements the standard-MHS specialization with \(B_{31s}=0\), \(I_4=0\), and \(s_G=s_\psi=1\). Other sign diff --git a/docs/quickstart.md b/docs/quickstart.md index 3d87d0a..67aef3d 100644 --- a/docs/quickstart.md +++ b/docs/quickstart.md @@ -42,6 +42,42 @@ The result is an immutable JAX pytree. Its vector samples have shape `solution.root_report.converged` and the residual norm when accepting a configuration. +## Targeting rotational transform + +At fixed target `iota`, solve for `etabar` on a selected sign branch: + +```python +inverse = qsc.solve( + axis=axis, + iota=0.42, + etabar=-1.0, + solve_for="etabar", + nphi=61, +) + +print(inverse.inputs.etabar) +print(inverse.response_derivative) +print(inverse.branch_fold) +``` + +The sign of the `etabar` seed is preserved. Omitting it selects the documented +default negative branch with a seed of `-1.0`. The seed also chooses a local +basin: distinct magnitudes can yield the same transform. Always check +`root_report.converged`; `branch_fold` reports a locally vanishing +\(\partial\iota/\partial\bar\eta\). + +To solve for current instead: + +```python +inverse_current = qsc.solve( + axis=axis, + iota=0.42, + etabar=-0.9, + I2=0.0, + solve_for="I2", +) +``` + ESSOS code can continue to use: ```python diff --git a/docs/theory/inverse-solves.md b/docs/theory/inverse-solves.md new file mode 100644 index 0000000..d8664fc --- /dev/null +++ b/docs/theory/inverse-solves.md @@ -0,0 +1,66 @@ +# Target-transform inverse solves + +## Coupled formulation + +The forward first-order problem prescribes \(\bar\eta\) and solves the +periodic sigma equation for \(\sigma(\varphi)\) and \(\iota\). The inverse +problem instead fixes \(\iota_\star\) and promotes either \(\bar\eta\) or +\(I_2\) to the scalar unknown. The collocation state still has `nphi` +unknowns: one scalar parameter and `nphi - 1` sigma samples, with +\(\sigma(0)=\sigma_0\) imposed by substitution. + +For `solve_for="etabar"`, the scalar state is \(u\) and + +\[ +\bar\eta=s_\eta\exp(u), +\qquad s_\eta\in\{-1,1\}. +\] + +This prevents a Newton step from crossing the singular +\(\bar\eta=0\) surface and changing the orientation branch. The sign comes +from the seed. If no seed is supplied, `-1.0` selects the default negative +branch. A zero seed selects the positive branch from the smallest +representable positive magnitude. + +For `solve_for="I2"`, the scalar state is \(I_2\) directly. In both cases the +same converged dense Newton policy and SOLVAX implicit-root rule used by the +forward sigma solve apply to the coupled inverse system. + +## Local folds + +After convergence, the forward sigma residual is differentiated with respect +to its ordinary state \(y=(\iota,\sigma_1,\ldots)\) and the solved parameter +\(p\). The response is obtained from + +\[ +\frac{\partial F}{\partial y}\frac{\mathrm dy}{\mathrm dp} +=-\frac{\partial F}{\partial p}. +\] + +`response_derivative` is \(\mathrm d\iota/\mathrm dp\). Its reciprocal is the +implicit derivative of the branch-local inverse away from a fold. +`branch_fold` is true when this response is nonfinite or its magnitude is no +larger than `fold_tolerance`. + +A fold does not imply that the full solution branch is singular. It means the +projection \(p(\iota)\) is locally multivalued. The direct tests contain two +different negative-\(\bar\eta\) solutions with the same transform and +opposite response slopes. Therefore a nonconverged target solve must not be +interpreted as proof that no branch exists. + +## Validation and acceptance + +Tests cover: + +- negative and positive \(\bar\eta\) sign branches; +- forward/inverse round trips for \(\bar\eta\) and finite \(I_2\); +- two distinct local \(\bar\eta\) basins at one target transform; +- r2 coefficient propagation; +- JIT and implicit JVPs against the reciprocal forward response and centered + finite differences; +- invalid and non-scalar inputs. + +Every caller must reject a result unless `root_report.converged` and +`root_report.finite` are true. Crossing a detected fold requires the +pseudo-arclength continuation interface rather than repeated fixed-transform +solves. diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index 80a2f2b..23dcc8f 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -6,6 +6,7 @@ from pyqsc_jax.first_order import Qsc, solve from pyqsc_jax.models import ( FieldJet, + InverseSolveDiagnostics, LinearSolveReport, MercierDiagnostics, NearAxisInputs, @@ -26,6 +27,7 @@ __all__ = [ "Axis", "FieldJet", + "InverseSolveDiagnostics", "LinearSolveReport", "MercierDiagnostics", "NearAxisInputs", diff --git a/src/pyqsc_jax/first_order.py b/src/pyqsc_jax/first_order.py index 71b0bd5..5443bf9 100644 --- a/src/pyqsc_jax/first_order.py +++ b/src/pyqsc_jax/first_order.py @@ -1,5 +1,6 @@ """First-order quasisymmetric near-axis construction.""" +from dataclasses import replace from typing import Any import jax @@ -30,6 +31,25 @@ def sigma_residual( state = jnp.asarray(state) sigma = sigma_from_state(state, inputs.sigma0) iota = state[0] + return sigma_equation( + sigma, + iota, + inputs=inputs, + geometry=geometry, + ) + + +def sigma_equation( + sigma: ArrayLike, + iota: ArrayLike, + *, + inputs: NearAxisInputs, + geometry: AxisGeometry, +) -> jax.Array: + """Periodic sigma equation for explicit sigma, iota, and inputs.""" + + sigma = jnp.asarray(sigma) + iota = jnp.asarray(iota) helicity = geometry.frame_helicity * inputs.spsi * inputs.sG iotaN = iota + helicity * inputs.axis.nfp eta_over_curvature_squared = inputs.etabar**2 / geometry.curvature**2 @@ -210,7 +230,8 @@ def _normalize_order(order: int | str) -> int: def solve( *, axis: Axis, - etabar: ArrayLike, + etabar: ArrayLike | None = None, + iota: ArrayLike | None = None, B0: ArrayLike = 1.0, sigma0: ArrayLike = 0.0, I2: ArrayLike = 0.0, @@ -223,17 +244,27 @@ def solve( spsi: int = 1, solve_for: str = "iota", root_options: RootSolveOptions = DEFAULT_ROOT_OPTIONS, + fold_tolerance: float = 1e-8, ) -> NearAxisSolution: - """Construct an immutable near-axis solution. - - Only standard first-order ``etabar -> iota`` mode is enabled in this - milestone. Other validated modes are added without changing this entry - point. - """ + """Construct an immutable forward or target-transform solution.""" normalized_order = _normalize_order(order) - if solve_for != "iota": - raise NotImplementedError("Inverse near-axis solve modes are not implemented yet.") + if solve_for not in ("iota", "etabar", "I2"): + raise ValueError("solve_for must be 'iota', 'etabar', or 'I2'.") + if fold_tolerance < 0: + raise ValueError("fold_tolerance must be nonnegative.") + if solve_for == "iota": + if etabar is None: + raise ValueError("etabar is required when solve_for='iota'.") + if iota is not None: + raise ValueError("iota is prescribed only when solve_for is 'etabar' or 'I2'.") + else: + if iota is None: + raise ValueError(f"iota is required when solve_for={solve_for!r}.") + if solve_for == "I2" and etabar is None: + raise ValueError("etabar is required when solve_for='I2'.") + if etabar is None: + etabar = -1.0 inputs = NearAxisInputs( axis=axis, etabar=etabar, @@ -250,12 +281,25 @@ def solve( solve_for=solve_for, ) geometry = compute_axis_geometry(axis, nphi=nphi) - sigma, iota, root_report = solve_sigma( - inputs, - geometry, - root_options=root_options, - ) - solution = first_order_solution(inputs, geometry, sigma, iota, root_report) + if solve_for == "iota": + sigma, solved_iota, root_report = solve_sigma( + inputs, + geometry, + root_options=root_options, + ) + inverse = None + else: + from pyqsc_jax.inverse import solve_target_iota + + inputs, sigma, solved_iota, root_report, inverse = solve_target_iota( + inputs, + geometry, + target_iota=iota, + root_options=root_options, + fold_tolerance=fold_tolerance, + ) + solution = first_order_solution(inputs, geometry, sigma, solved_iota, root_report) + solution = replace(solution, inverse=inverse) if normalized_order >= 2: from pyqsc_jax.second_order import solve_second_order diff --git a/src/pyqsc_jax/inverse.py b/src/pyqsc_jax/inverse.py new file mode 100644 index 0000000..e706364 --- /dev/null +++ b/src/pyqsc_jax/inverse.py @@ -0,0 +1,113 @@ +"""Branch-local inverse solves for a prescribed rotational transform.""" + +from __future__ import annotations + +from dataclasses import replace +from typing import Any + +import jax +import jax.numpy as jnp + +from pyqsc_jax.first_order import sigma_equation, sigma_residual +from pyqsc_jax.geometry import AxisGeometry +from pyqsc_jax.models import InverseSolveDiagnostics, NearAxisInputs, RootSolveReport +from pyqsc_jax.solvers import DEFAULT_ROOT_OPTIONS, RootSolveOptions, implicit_dense_root + +ArrayLike = Any + + +def solve_target_iota( + inputs: NearAxisInputs, + geometry: AxisGeometry, + *, + target_iota: ArrayLike, + root_options: RootSolveOptions = DEFAULT_ROOT_OPTIONS, + fold_tolerance: float = 1e-8, +) -> tuple[ + NearAxisInputs, + jax.Array, + jax.Array, + RootSolveReport, + InverseSolveDiagnostics, +]: + """Solve the sigma equation at fixed iota for etabar or I2.""" + + target_iota = jnp.asarray(target_iota) + if target_iota.ndim != 0: + raise ValueError("iota must be a scalar.") + if inputs.solve_for not in ("etabar", "I2"): + raise ValueError("Target-iota mode requires solve_for='etabar' or solve_for='I2'.") + + initial_state = jnp.full((inputs.nphi,), inputs.sigma0) + if inputs.solve_for == "etabar": + parameter_sign = jnp.where(inputs.etabar < 0, -1.0, 1.0) + safe_magnitude = jnp.maximum(jnp.abs(inputs.etabar), jnp.finfo(inputs.etabar.dtype).tiny) + initial_state = initial_state.at[0].set(jnp.log(safe_magnitude)) + + def parameter_from_state(state): + return parameter_sign * jnp.exp(state[0]) + + def inputs_from_parameter(parameter): + return replace(inputs, etabar=parameter) + + else: + parameter_sign = jnp.sign(inputs.I2) + initial_state = initial_state.at[0].set(inputs.I2) + + def parameter_from_state(state): + return state[0] + + def inputs_from_parameter(parameter): + return replace(inputs, I2=parameter) + + def residual(state): + parameter = parameter_from_state(state) + local_inputs = inputs_from_parameter(parameter) + sigma = state.at[0].set(inputs.sigma0) + return sigma_equation( + sigma, + target_iota, + inputs=local_inputs, + geometry=geometry, + ) + + state, report = implicit_dense_root( + residual, + initial_state, + options=root_options, + ) + solved_parameter = parameter_from_state(state) + solved_inputs = inputs_from_parameter(solved_parameter) + sigma = state.at[0].set(inputs.sigma0) + + forward_state = state.at[0].set(target_iota) + forward_jacobian = jax.jacfwd( + lambda candidate: sigma_residual( + candidate, + inputs=solved_inputs, + geometry=geometry, + ) + )(forward_state) + parameter_derivative = jax.jacfwd( + lambda parameter: sigma_residual( + forward_state, + inputs=inputs_from_parameter(parameter), + geometry=geometry, + ) + )(solved_parameter) + forward_response = jnp.linalg.solve(forward_jacobian, -parameter_derivative) + response_derivative = forward_response[0] + absolute_response = jnp.abs(response_derivative) + branch_fold = ~jnp.isfinite(response_derivative) | (absolute_response <= fold_tolerance) + diagnostics = InverseSolveDiagnostics( + target_iota=target_iota, + achieved_iota=target_iota, + solved_value=solved_parameter, + response_derivative=response_derivative, + absolute_response_derivative=absolute_response, + fold_tolerance=jnp.asarray(fold_tolerance), + branch_fold=branch_fold, + parameter_sign=jnp.sign(solved_parameter), + parameter=inputs.solve_for, + ) + return solved_inputs, sigma, target_iota, report, diagnostics diff --git a/src/pyqsc_jax/models.py b/src/pyqsc_jax/models.py index 5c6cc88..e255869 100644 --- a/src/pyqsc_jax/models.py +++ b/src/pyqsc_jax/models.py @@ -45,6 +45,22 @@ class RootSolveReport: stagnated: jax.Array +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class InverseSolveDiagnostics: + """Local branch and fold diagnostics for a target-transform solve.""" + + target_iota: jax.Array + achieved_iota: jax.Array + solved_value: jax.Array + response_derivative: jax.Array + absolute_response_derivative: jax.Array + fold_tolerance: jax.Array + branch_fold: jax.Array + parameter_sign: jax.Array + parameter: str = field(metadata={"static": True}) + + @jax.tree_util.register_dataclass @dataclass(frozen=True) class LinearSolveReport: @@ -302,6 +318,7 @@ class NearAxisSolution: singularity: SingularityDiagnostics | None = None third_order: ThirdOrderData | None = None shear: ShearData | None = None + inverse: InverseSolveDiagnostics | None = None _SECOND_ORDER_NAMES: ClassVar[frozenset[str]] = frozenset( field.name for field in SecondOrderData.__dataclass_fields__.values() @@ -312,6 +329,9 @@ class NearAxisSolution: _SHEAR_NAMES: ClassVar[frozenset[str]] = frozenset( field.name for field in ShearData.__dataclass_fields__.values() ) + _INVERSE_NAMES: ClassVar[frozenset[str]] = frozenset( + field.name for field in InverseSolveDiagnostics.__dataclass_fields__.values() + ) _MERCIER_NAMES: ClassVar[frozenset[str]] = frozenset( field.name for field in MercierDiagnostics.__dataclass_fields__.values() ) @@ -353,6 +373,11 @@ def __getattr__(self, name: str): f"Magnetic shear has not been calculated; no {name!r} quantity." ) return getattr(shear, name) + if name in self._INVERSE_NAMES: + inverse = object.__getattribute__(self, "inverse") + if inverse is None: + raise AttributeError(f"Forward solution has no inverse diagnostic {name!r}.") + return getattr(inverse, name) if name in self._MERCIER_NAMES: mercier = object.__getattribute__(self, "mercier") if mercier is None: diff --git a/tests/physics/test_first_order.py b/tests/physics/test_first_order.py index 8bdcf99..c723e16 100644 --- a/tests/physics/test_first_order.py +++ b/tests/physics/test_first_order.py @@ -68,7 +68,7 @@ def test_first_order_shapes_and_coefficients(): def test_invalid_order_and_inverse_mode_are_explicitly_rejected(): with pytest.raises(ValueError, match="order must be"): standard_solution(order="fourth") - with pytest.raises(NotImplementedError, match="Inverse"): + with pytest.raises(ValueError, match="iota is required"): standard_solution(solve_for="etabar") diff --git a/tests/physics/test_inverse.py b/tests/physics/test_inverse.py new file mode 100644 index 0000000..5ae5a14 --- /dev/null +++ b/tests/physics/test_inverse.py @@ -0,0 +1,158 @@ +from __future__ import annotations + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +import pyqsc_jax as qsc + +AXIS = qsc.Axis(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3) + + +def test_target_iota_etabar_round_trip_and_sign_branches(): + forward = qsc.solve(axis=AXIS, etabar=-0.9, nphi=31) + negative = qsc.solve( + axis=AXIS, + etabar=-1.0, + iota=forward.iota, + solve_for="etabar", + nphi=31, + ) + positive = qsc.solve( + axis=AXIS, + etabar=1.0, + iota=forward.iota, + solve_for="etabar", + nphi=31, + ) + + np.testing.assert_allclose(negative.inputs.etabar, -0.9, rtol=2.0e-12) + np.testing.assert_allclose(positive.inputs.etabar, 0.9, rtol=2.0e-12) + np.testing.assert_allclose(negative.iota, forward.iota) + np.testing.assert_allclose(negative.sigma, forward.sigma, atol=2.0e-12) + assert bool(negative.root_report.converged) + assert negative.root_report.residual_norm < 2.0e-13 + assert negative.inverse is not None + assert negative.parameter == "etabar" + assert int(negative.parameter_sign) == -1 + assert not bool(negative.branch_fold) + + +def test_target_iota_exposes_distinct_local_etabar_branches(): + target = qsc.solve(axis=AXIS, etabar=-0.9, nphi=31).iota + outer = qsc.solve( + axis=AXIS, + etabar=-1.0, + iota=target, + solve_for="etabar", + nphi=31, + ) + inner = qsc.solve( + axis=AXIS, + etabar=-0.8, + iota=target, + solve_for="etabar", + nphi=31, + ) + inner_forward = qsc.solve(axis=AXIS, etabar=inner.inputs.etabar, nphi=31) + + assert abs(float(outer.inputs.etabar - inner.inputs.etabar)) > 0.1 + np.testing.assert_allclose(inner.iota, target) + np.testing.assert_allclose(inner_forward.iota, target, atol=2.0e-13) + assert np.sign(float(outer.response_derivative)) != np.sign(float(inner.response_derivative)) + + +@pytest.mark.parametrize("actual_I2", [-0.5, 0.2, 1.0]) +def test_target_iota_I2_round_trip(actual_I2): + forward = qsc.solve(axis=AXIS, etabar=-0.9, I2=actual_I2, nphi=31) + inverse = qsc.solve( + axis=AXIS, + etabar=-0.9, + I2=0.0, + iota=forward.iota, + solve_for="I2", + nphi=31, + ) + + np.testing.assert_allclose(inverse.inputs.I2, actual_I2, rtol=2.0e-12, atol=2.0e-12) + np.testing.assert_allclose(inverse.iota, forward.iota) + assert inverse.parameter == "I2" + assert bool(inverse.root_report.converged) + + +def test_inverse_mode_propagates_to_second_order(): + forward = qsc.solve(axis=AXIS, etabar=-0.9, I2=0.2, nphi=31, order="r2") + inverse = qsc.solve( + axis=AXIS, + etabar=-1.0, + I2=0.2, + iota=forward.iota, + solve_for="etabar", + nphi=31, + order="r2", + ) + + np.testing.assert_allclose(inverse.inputs.etabar, -0.9, rtol=2.0e-12) + np.testing.assert_allclose(inverse.B20, forward.B20, rtol=3.0e-11, atol=3.0e-11) + assert bool(inverse.linear_report.converged) + + +def test_inverse_solve_is_jittable_and_implicitly_differentiable(): + def etabar_for_iota(target_iota): + return qsc.solve( + axis=AXIS, + etabar=-1.0, + iota=target_iota, + solve_for="etabar", + nphi=31, + ).inputs.etabar + + target = qsc.solve(axis=AXIS, etabar=-0.9, nphi=31).iota + solution = qsc.solve( + axis=AXIS, + etabar=-1.0, + iota=target, + solve_for="etabar", + nphi=31, + ) + value = etabar_for_iota(target) + jitted = jax.jit(etabar_for_iota)(target) + tangent = jax.jvp(etabar_for_iota, (target,), (jnp.asarray(1.0),))[1] + step = 1.0e-5 + finite_difference = (etabar_for_iota(target + step) - etabar_for_iota(target - step)) / ( + 2 * step + ) + + np.testing.assert_allclose(jitted, value, rtol=2.0e-12) + np.testing.assert_allclose(tangent, 1 / solution.response_derivative, rtol=2.0e-11) + np.testing.assert_allclose(tangent, finite_difference, rtol=2.0e-6) + + +def test_inverse_input_guards_and_forward_diagnostic_absence(): + forward = qsc.solve(axis=AXIS, etabar=-0.9, nphi=31) + with pytest.raises(AttributeError, match="Forward solution"): + _ = forward.target_iota + with pytest.raises(ValueError, match="etabar is required"): + qsc.solve(axis=AXIS) + with pytest.raises(ValueError, match="prescribed only"): + qsc.solve(axis=AXIS, etabar=-0.9, iota=0.4) + with pytest.raises(ValueError, match="iota is required"): + qsc.solve(axis=AXIS, etabar=-0.9, solve_for="I2") + with pytest.raises(ValueError, match="etabar is required"): + qsc.solve(axis=AXIS, iota=0.4, solve_for="I2") + with pytest.raises(ValueError, match="scalar"): + qsc.solve( + axis=AXIS, + etabar=-1.0, + iota=jnp.ones(2), + solve_for="etabar", + ) + with pytest.raises(ValueError, match="fold_tolerance"): + qsc.solve( + axis=AXIS, + etabar=-1.0, + iota=0.4, + solve_for="etabar", + fold_tolerance=-1.0, + ) From abcbd0a4e486f36c243d36b8a7b1c8af010af677 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 00:54:28 -0500 Subject: [PATCH 12/39] feat: add pseudo-arclength branch continuation --- CHANGELOG.md | 3 + README.md | 10 +- docs/api/continuation.md | 10 + docs/development/physics-traceability.md | 2 +- docs/index.md | 5 +- docs/limitations.md | 8 +- docs/quickstart.md | 20 ++ docs/theory/inverse-solves.md | 32 +++- src/pyqsc_jax/__init__.py | 3 + src/pyqsc_jax/continuation.py | 229 +++++++++++++++++++++++ src/pyqsc_jax/inverse.py | 55 ++++-- tests/physics/test_continuation.py | 112 +++++++++++ 12 files changed, 458 insertions(+), 31 deletions(-) create mode 100644 docs/api/continuation.md create mode 100644 src/pyqsc_jax/continuation.py create mode 100644 tests/physics/test_continuation.py diff --git a/CHANGELOG.md b/CHANGELOG.md index 9378569..ad26de1 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -49,6 +49,9 @@ first stable release. - Branch-local target-transform solves for sign-preserving `etabar` or `I2`, including implicit derivatives, round-trip validation, local response and fold diagnostics, and propagation through r2. +- Full-state fixed-sign pseudo-arclength continuation for `etabar`, including + fold-crossing detection, corrected solution records, and explicit partial + completion statuses. ### Fixed diff --git a/README.md b/README.md index 0463cdb..5ae5792 100644 --- a/README.md +++ b/README.md @@ -6,9 +6,9 @@ JAX. > **Development status:** the immutable first-order core, complete r2 > coefficient solve, r3 flux constraint, magnetic shear, total-field Hessian, > Mercier diagnostics, singular-radius diagnostics, and ESSOS adapter are -> validated, along with branch-local inverse solves. Branch continuation, -> optimization, and plasma/external field jets remain under development on the -> `refactor/pyqsc-jax-complete` branch. +> validated, along with branch-local inverse solves and pseudo-arclength +> continuation. Optimization and plasma/external field jets remain under +> development on the `refactor/pyqsc-jax-complete` branch. ## Install @@ -96,8 +96,8 @@ order-\(r^2\) rotational-transform correction as `solution.iota2`. Prescribe transform with `qsc.solve(axis=axis, iota=target, etabar=seed, solve_for="etabar")`, or hold `etabar` fixed and use `solve_for="I2"`. The inverse result reports its local -response derivative and fold flag; pseudo-arclength continuation is the next -branch-tracking milestone. +response derivative and fold flag. `qsc.continue_etabar_branch(...)` traces +the full sigma collocation state across such a fold. The lower-level immutable axis API supports general, not necessarily stellarator-symmetric Fourier axes: diff --git a/docs/api/continuation.md b/docs/api/continuation.md new file mode 100644 index 0000000..a9de35f --- /dev/null +++ b/docs/api/continuation.md @@ -0,0 +1,10 @@ +# Continuation API + +```{eval-rst} +.. autofunction:: pyqsc_jax.continue_etabar_branch +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.ContinuationResult + :members: +``` diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index 8121918..8b0f923 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -8,7 +8,7 @@ to the cited source, not to a duplicated derivation in this repository. | --- | --- | --- | --- | --- | | General Fourier axis and Frenet frame | Landreman & Sengupta (2018), arXiv:1809.10233 | `Axis`, `evaluate_axis`, `compute_axis_geometry`; pyQSC `init_axis.py` | analytic circle; asymmetric Fortran curvature/torsion/varphi; frame identities; JIT/VMAP/grad | implemented and documented | | First-order QS and sigma equation | Landreman & Sengupta (2019), arXiv:1908.10253 | `first_order.solve_sigma`; pyQSC `solve_sigma_equation.py` | residual, convergence report, QA/QH/finite-current pyQSC values, JIT/VMAP/JVP/VJP, finite differences | implemented and documented | -| Target-transform inverse solve | implicit-function reformulation of the first-order sigma equation | `inverse.solve_target_iota` | `etabar` and `I2` round trips, sign branches, distinct local basins, fold metric, r2 propagation, JIT/JVP/finite differences | branch-local solve implemented; pseudo-arclength continuation pending | +| Target-transform inverse solve and continuation | implicit-function reformulation of the first-order sigma equation | `inverse.solve_target_iota`; `continuation.continue_etabar_branch` | `etabar` and `I2` round trips, sign branches, distinct local basins, fold crossing, independent forward correction, r2 propagation, JIT/JVP/finite differences | branch-local inverse and fixed-step `etabar` pseudo-arclength implemented | | Field gradient and `L_grad_B` | Landreman (2021), arXiv:2012.00865, Eq. 3.12 | `first_order.first_order_solution`; pyQSC `grad_B_tensor.py` | upstream arrays, vacuum symmetry/divergence, resolution convergence | implemented and documented | | Complete second-order coefficients | Landreman & Sengupta (2019), arXiv:1908.10253 | `second_order.solve_second_order`; pyQSC `calculate_r2.py`; manuscript Eqs. 36–54 | four independent equation residuals; vacuum QA, finite-pressure/current, QH upstream arrays; JIT/JVP/VJP/finite differences | implemented and documented | | Total field Hessian | manuscript Eqs. 55–83 | `field.total_field_jet`; pyQSC generated tensor as comparison only | regular-coordinate chain rule, JIT/JVP, QA and finite-current upstream arrays, full vacuum symmetry, divergence and derivative-of-divergence | implemented and documented | diff --git a/docs/index.md b/docs/index.md index eba4218..5f79926 100644 --- a/docs/index.md +++ b/docs/index.md @@ -19,6 +19,7 @@ theory/inverse-solves theory/field-jet api/axis api/first-order +api/continuation api/second-order api/third-order api/field-jet @@ -46,8 +47,8 @@ changelog The immutable first-order API, complete r2 coefficient solve, r3 flux constraint, magnetic shear, total-field Hessian, Mercier terms, and singular-radius diagnostics are validated, as are branch-local inverse solves. -Branch continuation, optimization, and plasma/external field jets are under -active development. +Pseudo-arclength branch continuation is also validated. Optimization and +plasma/external field jets are under active development. The `pyqsc_jax.near_axis.near_axis` import remains supported for ESSOS without a runtime deprecation warning. diff --git a/docs/limitations.md b/docs/limitations.md index 2391908..0536b1c 100644 --- a/docs/limitations.md +++ b/docs/limitations.md @@ -8,13 +8,15 @@ flux-constraint surface correction. Known limitations under active refactor include: - no plasma/external field-jet separation; -- no pseudo-arclength branch continuation yet. +- pseudo-arclength continuation currently traces `etabar` branches only and + uses a fixed arclength step. Target-transform solves are branch-local. The sign of the `etabar` seed is preserved and the seed magnitude selects a Newton basin. Multiple local solutions can have the same transform. `response_derivative` and `branch_fold` -detect local loss of invertibility, but crossing such a fold awaits the -pseudo-arclength interface. +detect local loss of invertibility. `continue_etabar_branch` crosses these +folds using the full sigma collocation state and an augmented arclength +condition. The magnetic-shear calculation currently implements the standard-MHS specialization with \(B_{31s}=0\), \(I_4=0\), and \(s_G=s_\psi=1\). Other sign diff --git a/docs/quickstart.md b/docs/quickstart.md index 67aef3d..69149d2 100644 --- a/docs/quickstart.md +++ b/docs/quickstart.md @@ -78,6 +78,26 @@ inverse_current = qsc.solve( ) ``` +Trace a branch through a fold with two nearby forward seeds: + +```python +branch = qsc.continue_etabar_branch( + axis=axis, + etabar_start=-1.0, + etabar_next=-0.98, + num_points=20, + nphi=61, +) + +print(branch.status) +print(branch.etabar) +print(branch.iota) +print(branch.fold_detected) +``` + +Each corrected point has its own `root_report`. `branch.complete` is true only +when every requested point converged. + ESSOS code can continue to use: ```python diff --git a/docs/theory/inverse-solves.md b/docs/theory/inverse-solves.md index d8664fc..b1e7064 100644 --- a/docs/theory/inverse-solves.md +++ b/docs/theory/inverse-solves.md @@ -48,6 +48,31 @@ different negative-\(\bar\eta\) solutions with the same transform and opposite response slopes. Therefore a nonconverged target solve must not be interpreted as proof that no branch exists. +## Pseudo-arclength continuation + +`continue_etabar_branch` begins from two converged forward points. A secant in +physical \((\bar\eta,\iota)\) coordinates supplies the oriented tangent and +predictor. The corrector solves the complete sigma collocation system together +with + +\[ +\boldsymbol t\mathbin{\cdot} +\left[ +(\bar\eta,\iota)-(\bar\eta,\iota)_{\mathrm{predict}} +\right]=0. +\] + +The nonlinear state contains the log-magnitude of \(\bar\eta\), \(\iota\), and +all free sigma samples. Thus the corrector can pass through +\(\mathrm d\iota/\mathrm d\bar\eta=0\) without changing the selected +\(\bar\eta\) sign. A response-slope sign change marks a fold even when no +discrete point lands exactly at zero slope. + +`ContinuationResult` retains every corrected immutable solution, the branch +tangents, response derivatives, and fold flags. It stops with +`status="solver_failure"` after a failed corrector or +`status="branch_zero_crossing"` before leaving the fixed-sign branch. + ## Validation and acceptance Tests cover: @@ -55,12 +80,13 @@ Tests cover: - negative and positive \(\bar\eta\) sign branches; - forward/inverse round trips for \(\bar\eta\) and finite \(I_2\); - two distinct local \(\bar\eta\) basins at one target transform; +- full-state pseudo-arclength traversal across their intervening fold; +- independent forward-solve checks of corrected continuation points; - r2 coefficient propagation; - JIT and implicit JVPs against the reciprocal forward response and centered finite differences; - invalid and non-scalar inputs. Every caller must reject a result unless `root_report.converged` and -`root_report.finite` are true. Crossing a detected fold requires the -pseudo-arclength continuation interface rather than repeated fixed-transform -solves. +`root_report.finite` are true. Crossing a detected fold requires +pseudo-arclength continuation rather than repeated fixed-transform solves. diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index 23dcc8f..a20cdd6 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -1,6 +1,7 @@ """Differentiable near-axis stellarator construction in JAX.""" from pyqsc_jax.axis import Axis +from pyqsc_jax.continuation import ContinuationResult, continue_etabar_branch from pyqsc_jax.diagnostics import mercier_diagnostics from pyqsc_jax.field import total_field_jet from pyqsc_jax.first_order import Qsc, solve @@ -26,6 +27,7 @@ __all__ = [ "Axis", + "ContinuationResult", "FieldJet", "InverseSolveDiagnostics", "LinearSolveReport", @@ -41,6 +43,7 @@ "SingularityDiagnostics", "ThirdOrderData", "near_axis", + "continue_etabar_branch", "mercier_diagnostics", "second_order_residuals", "solve", diff --git a/src/pyqsc_jax/continuation.py b/src/pyqsc_jax/continuation.py new file mode 100644 index 0000000..90c5d60 --- /dev/null +++ b/src/pyqsc_jax/continuation.py @@ -0,0 +1,229 @@ +"""Pseudo-arclength continuation of first-order near-axis branches.""" + +from __future__ import annotations + +from dataclasses import dataclass, replace +from typing import Any + +import jax +import jax.numpy as jnp + +from pyqsc_jax.axis import Axis +from pyqsc_jax.first_order import first_order_solution, sigma_equation, solve +from pyqsc_jax.inverse import parameter_response_derivative +from pyqsc_jax.models import NearAxisSolution +from pyqsc_jax.solvers import DEFAULT_ROOT_OPTIONS, RootSolveOptions, implicit_dense_root + +ArrayLike = Any + + +@dataclass(frozen=True) +class ContinuationResult: + """A variable-length sequence of corrected pseudo-arclength points.""" + + solutions: tuple[NearAxisSolution, ...] + tangents: jax.Array + response_derivative: jax.Array + fold_detected: jax.Array + requested_points: int + status: str + + @property + def etabar(self) -> jax.Array: + """Etabar values along the corrected branch.""" + + return jnp.stack(tuple(solution.inputs.etabar for solution in self.solutions)) + + @property + def iota(self) -> jax.Array: + """Rotational-transform values along the corrected branch.""" + + return jnp.stack(tuple(solution.iota for solution in self.solutions)) + + @property + def sigma(self) -> jax.Array: + """Periodic sigma samples along the corrected branch.""" + + return jnp.stack(tuple(solution.sigma for solution in self.solutions)) + + @property + def complete(self) -> bool: + """Whether all requested points converged.""" + + return self.status == "complete" and len(self.solutions) == self.requested_points + + +def continue_etabar_branch( + *, + axis: Axis, + etabar_start: ArrayLike, + etabar_next: ArrayLike, + num_points: int = 25, + step_size: float | None = None, + B0: ArrayLike = 1.0, + sigma0: ArrayLike = 0.0, + I2: ArrayLike = 0.0, + nphi: int = 61, + sG: int = 1, + spsi: int = 1, + root_options: RootSolveOptions = DEFAULT_ROOT_OPTIONS, + fold_tolerance: float = 1e-4, +) -> ContinuationResult: + """Trace a fixed-sign etabar branch through folds in iota(etabar).""" + + if not isinstance(num_points, int) or isinstance(num_points, bool) or num_points < 2: + raise ValueError("num_points must be an integer >= 2.") + if step_size is not None and step_size <= 0: + raise ValueError("step_size must be positive.") + if fold_tolerance < 0: + raise ValueError("fold_tolerance must be nonnegative.") + + etabar_start = jnp.asarray(etabar_start) + etabar_next = jnp.asarray(etabar_next) + if etabar_start.ndim != 0 or etabar_next.ndim != 0: + raise ValueError("etabar_start and etabar_next must be scalars.") + sign = jnp.where(etabar_start < 0, -1.0, 1.0) + if bool(etabar_start == 0) or bool(etabar_next == 0): + raise ValueError("Continuation seeds must have nonzero etabar.") + if bool(jnp.sign(etabar_start) != jnp.sign(etabar_next)): + raise ValueError("Continuation seeds must have the same etabar sign.") + + common = { + "axis": axis, + "B0": B0, + "sigma0": sigma0, + "I2": I2, + "nphi": nphi, + "order": "r1", + "sG": sG, + "spsi": spsi, + } + first = solve(etabar=etabar_start, **common) + second = solve(etabar=etabar_next, **common) + if not bool(first.root_report.converged) or not bool(second.root_report.converged): + raise ValueError("Both initial continuation points must converge.") + + solutions = [first, second] + pair0 = jnp.asarray((first.inputs.etabar, first.iota)) + pair1 = jnp.asarray((second.inputs.etabar, second.iota)) + secant = pair1 - pair0 + secant_norm = jnp.linalg.norm(secant) + if not bool(jnp.isfinite(secant_norm)) or bool(secant_norm == 0): + raise ValueError("Initial continuation points must be finite and distinct.") + tangent = secant / secant_norm + arclength_step = float(secant_norm) if step_size is None else step_size + tangents = [tangent, tangent] + responses = [ + parameter_response_derivative( + first.inputs, + first.geometry, + first.sigma, + first.iota, + parameter="etabar", + ), + parameter_response_derivative( + second.inputs, + second.geometry, + second.sigma, + second.iota, + parameter="etabar", + ), + ] + fold_flags = [ + jnp.abs(responses[0]) <= fold_tolerance, + (jnp.abs(responses[1]) <= fold_tolerance) | (responses[0] * responses[1] < 0), + ] + status = "complete" + + for _ in range(2, num_points): + previous = solutions[-1] + before_previous = solutions[-2] + previous_pair = jnp.asarray((previous.inputs.etabar, previous.iota)) + predicted_pair = previous_pair + arclength_step * tangent + predicted_etabar = predicted_pair[0] + if bool(sign * predicted_etabar <= 0): + status = "branch_zero_crossing" + break + + sigma_scale = arclength_step / jnp.linalg.norm( + previous_pair - jnp.asarray((before_previous.inputs.etabar, before_previous.iota)) + ) + predicted_sigma = previous.sigma + sigma_scale * (previous.sigma - before_previous.sigma) + initial_state = jnp.concatenate( + ( + jnp.log(jnp.abs(predicted_etabar))[None], + predicted_pair[1:], + predicted_sigma[1:], + ) + ) + base_inputs = previous.inputs + + def residual( + state, + base_inputs=base_inputs, + geometry=previous.geometry, + predicted_pair=predicted_pair, + tangent=tangent, + ): + etabar = sign * jnp.exp(state[0]) + iota = state[1] + sigma = jnp.concatenate((base_inputs.sigma0[None], state[2:])) + local_inputs = replace(base_inputs, etabar=etabar) + sigma_part = sigma_equation( + sigma, + iota, + inputs=local_inputs, + geometry=geometry, + ) + arclength_part = jnp.dot( + jnp.asarray((etabar, iota)) - predicted_pair, + tangent, + ) + return jnp.concatenate((sigma_part, arclength_part[None])) + + state, report = implicit_dense_root( + residual, + initial_state, + options=root_options, + ) + corrected_etabar = sign * jnp.exp(state[0]) + corrected_iota = state[1] + corrected_sigma = jnp.concatenate((base_inputs.sigma0[None], state[2:])) + corrected_inputs = replace(base_inputs, etabar=corrected_etabar) + corrected = first_order_solution( + corrected_inputs, + previous.geometry, + corrected_sigma, + corrected_iota, + report, + ) + if not bool(report.converged): + status = "solver_failure" + break + + corrected_pair = jnp.asarray((corrected_etabar, corrected_iota)) + new_tangent = corrected_pair - previous_pair + new_tangent = new_tangent / jnp.linalg.norm(new_tangent) + new_tangent = jnp.where(jnp.dot(new_tangent, tangent) < 0, -new_tangent, new_tangent) + response = parameter_response_derivative( + corrected.inputs, + corrected.geometry, + corrected.sigma, + corrected.iota, + parameter="etabar", + ) + fold = (jnp.abs(response) <= fold_tolerance) | (responses[-1] * response < 0) + solutions.append(corrected) + tangents.append(new_tangent) + responses.append(response) + fold_flags.append(fold) + tangent = new_tangent + + return ContinuationResult( + solutions=tuple(solutions), + tangents=jnp.stack(tuple(tangents)), + response_derivative=jnp.stack(tuple(responses)), + fold_detected=jnp.stack(tuple(fold_flags)), + requested_points=num_points, + status=status, + ) diff --git a/src/pyqsc_jax/inverse.py b/src/pyqsc_jax/inverse.py index e706364..e9c60b1 100644 --- a/src/pyqsc_jax/inverse.py +++ b/src/pyqsc_jax/inverse.py @@ -16,6 +16,37 @@ ArrayLike = Any +def parameter_response_derivative( + inputs: NearAxisInputs, + geometry: AxisGeometry, + sigma: jax.Array, + iota: jax.Array, + *, + parameter: str, +) -> jax.Array: + """Return the local forward derivative d(iota)/d(parameter).""" + + if parameter not in ("etabar", "I2"): + raise ValueError("parameter must be 'etabar' or 'I2'.") + parameter_value = getattr(inputs, parameter) + forward_state = jnp.asarray(sigma).at[0].set(iota) + forward_jacobian = jax.jacfwd( + lambda candidate: sigma_residual( + candidate, + inputs=inputs, + geometry=geometry, + ) + )(forward_state) + parameter_derivative = jax.jacfwd( + lambda value: sigma_residual( + forward_state, + inputs=replace(inputs, **{parameter: value}), + geometry=geometry, + ) + )(parameter_value) + return jnp.linalg.solve(forward_jacobian, -parameter_derivative)[0] + + def solve_target_iota( inputs: NearAxisInputs, geometry: AxisGeometry, @@ -80,23 +111,13 @@ def residual(state): solved_inputs = inputs_from_parameter(solved_parameter) sigma = state.at[0].set(inputs.sigma0) - forward_state = state.at[0].set(target_iota) - forward_jacobian = jax.jacfwd( - lambda candidate: sigma_residual( - candidate, - inputs=solved_inputs, - geometry=geometry, - ) - )(forward_state) - parameter_derivative = jax.jacfwd( - lambda parameter: sigma_residual( - forward_state, - inputs=inputs_from_parameter(parameter), - geometry=geometry, - ) - )(solved_parameter) - forward_response = jnp.linalg.solve(forward_jacobian, -parameter_derivative) - response_derivative = forward_response[0] + response_derivative = parameter_response_derivative( + solved_inputs, + geometry, + sigma, + target_iota, + parameter=inputs.solve_for, + ) absolute_response = jnp.abs(response_derivative) branch_fold = ~jnp.isfinite(response_derivative) | (absolute_response <= fold_tolerance) diagnostics = InverseSolveDiagnostics( diff --git a/tests/physics/test_continuation.py b/tests/physics/test_continuation.py new file mode 100644 index 0000000..0e6f138 --- /dev/null +++ b/tests/physics/test_continuation.py @@ -0,0 +1,112 @@ +from __future__ import annotations + +import numpy as np +import pytest + +import pyqsc_jax as qsc + +AXIS = qsc.Axis(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3) + + +def test_pseudo_arclength_crosses_etabar_iota_fold(): + branch = qsc.continue_etabar_branch( + axis=AXIS, + etabar_start=-1.0, + etabar_next=-0.98, + num_points=15, + nphi=31, + ) + + assert branch.complete + assert branch.status == "complete" + assert len(branch.solutions) == 15 + assert branch.etabar.shape == (15,) + assert branch.iota.shape == (15,) + assert branch.sigma.shape == (15, 31) + assert branch.tangents.shape == (15, 2) + assert int(np.count_nonzero(np.asarray(branch.fold_detected))) == 1 + fold_index = int(np.flatnonzero(np.asarray(branch.fold_detected))[0]) + assert fold_index == 9 + assert float(branch.response_derivative[fold_index - 1]) > 0 + assert float(branch.response_derivative[fold_index]) < 0 + assert float(branch.iota[fold_index]) > float(branch.iota[fold_index - 2]) + assert float(branch.iota[fold_index]) > float(branch.iota[fold_index + 2]) + assert np.all(np.diff(np.asarray(branch.etabar)) > 0) + + for solution in branch.solutions: + assert bool(solution.root_report.converged) + assert solution.root_report.residual_norm < 1.0e-12 + + +def test_corrected_points_match_independent_forward_solves(): + branch = qsc.continue_etabar_branch( + axis=AXIS, + etabar_start=-0.9, + etabar_next=-0.88, + num_points=6, + step_size=0.018, + nphi=31, + ) + + for index in (2, 4, 5): + direct = qsc.solve(axis=AXIS, etabar=branch.etabar[index], nphi=31) + np.testing.assert_allclose(branch.iota[index], direct.iota, atol=2.0e-13) + np.testing.assert_allclose(branch.sigma[index], direct.sigma, atol=3.0e-12) + + norms = np.linalg.norm(np.diff(np.stack((branch.etabar, branch.iota), axis=1), axis=0), axis=1) + np.testing.assert_allclose(norms[1:], 0.018, rtol=8.0e-4) + + +def test_positive_branch_and_two_point_result(): + branch = qsc.continue_etabar_branch( + axis=AXIS, + etabar_start=0.9, + etabar_next=0.88, + num_points=2, + nphi=31, + ) + + assert branch.complete + assert np.all(np.asarray(branch.etabar) > 0) + np.testing.assert_allclose(branch.iota[0], 0.41830690943386584, rtol=2.0e-13) + + +def test_continuation_reports_fixed_sign_boundary(): + branch = qsc.continue_etabar_branch( + axis=AXIS, + etabar_start=-0.1, + etabar_next=-0.05, + num_points=5, + step_size=0.2, + nphi=31, + ) + + assert branch.status == "branch_zero_crossing" + assert not branch.complete + assert len(branch.solutions) == 2 + + +@pytest.mark.parametrize( + ("overrides", "message"), + [ + ({"num_points": 1}, "num_points"), + ({"num_points": True}, "num_points"), + ({"step_size": 0.0}, "step_size"), + ({"fold_tolerance": -1.0}, "fold_tolerance"), + ({"etabar_start": [-1.0]}, "scalars"), + ({"etabar_start": 0.0}, "nonzero"), + ({"etabar_next": 0.9}, "same etabar sign"), + ({"etabar_next": -1.0}, "distinct"), + ], +) +def test_continuation_input_guards(overrides, message): + parameters = { + "axis": AXIS, + "etabar_start": -1.0, + "etabar_next": -0.98, + "num_points": 3, + "nphi": 15, + } + parameters.update(overrides) + with pytest.raises(ValueError, match=message): + qsc.continue_etabar_branch(**parameters) From 516917378a7eb62761c78442a91f177c17bd7f86 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 01:02:34 -0500 Subject: [PATCH 13/39] feat: add dense B20 diagnostics and optimal B2c --- CHANGELOG.md | 3 + README.md | 5 + docs/api/optimization.md | 32 +++ docs/development/physics-traceability.md | 1 + docs/index.md | 2 + docs/limitations.md | 2 + docs/quickstart.md | 24 ++ docs/theory/b20-optimization.md | 82 +++++++ src/pyqsc_jax/__init__.py | 16 ++ src/pyqsc_jax/optimize.py | 270 +++++++++++++++++++++++ src/pyqsc_jax/second_order.py | 8 +- tests/physics/test_b20_optimization.py | 144 ++++++++++++ 12 files changed, 588 insertions(+), 1 deletion(-) create mode 100644 docs/api/optimization.md create mode 100644 docs/theory/b20-optimization.md create mode 100644 src/pyqsc_jax/optimize.py create mode 100644 tests/physics/test_b20_optimization.py diff --git a/CHANGELOG.md b/CHANGELOG.md index ad26de1..9e0b069 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -52,6 +52,9 @@ first stable release. - Full-state fixed-sign pseudo-arclength continuation for `etabar`, including fold-crossing detection, corrected solution records, and explicit partial completion statuses. +- Dense nonconstant-`B20` diagnostics, exact affine elimination of `B2c`, + degenerate-response handling, and independent doubled/quadrupled-grid + verification. ### Fixed diff --git a/README.md b/README.md index 5ae5792..dbe1934 100644 --- a/README.md +++ b/README.md @@ -99,6 +99,11 @@ Prescribe transform with response derivative and fold flag. `qsc.continue_etabar_branch(...)` traces the full sigma collocation state across such a fold. +`qsc.optimize_B2c(solution)` eliminates the affine \(B_{2c}\) subproblem +exactly and returns dense weighted, smooth-maximum, grid-maximum, Fourier, and +tail diagnostics. `qsc.verify_B20_resolution(...)` independently rebuilds the +candidate on doubled and quadrupled grids. + The lower-level immutable axis API supports general, not necessarily stellarator-symmetric Fourier axes: diff --git a/docs/api/optimization.md b/docs/api/optimization.md new file mode 100644 index 0000000..6851ae5 --- /dev/null +++ b/docs/api/optimization.md @@ -0,0 +1,32 @@ +# Optimization API + +```{eval-rst} +.. autofunction:: pyqsc_jax.b20_diagnostics +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.optimal_B2c_value +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.optimize_B2c +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.verify_B20_resolution +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.B20Diagnostics + :members: +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.B2cOptimizationResult + :members: +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.B20ResolutionVerification + :members: +``` diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index 8b0f923..171e873 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -9,6 +9,7 @@ to the cited source, not to a duplicated derivation in this repository. | General Fourier axis and Frenet frame | Landreman & Sengupta (2018), arXiv:1809.10233 | `Axis`, `evaluate_axis`, `compute_axis_geometry`; pyQSC `init_axis.py` | analytic circle; asymmetric Fortran curvature/torsion/varphi; frame identities; JIT/VMAP/grad | implemented and documented | | First-order QS and sigma equation | Landreman & Sengupta (2019), arXiv:1908.10253 | `first_order.solve_sigma`; pyQSC `solve_sigma_equation.py` | residual, convergence report, QA/QH/finite-current pyQSC values, JIT/VMAP/JVP/VJP, finite differences | implemented and documented | | Target-transform inverse solve and continuation | implicit-function reformulation of the first-order sigma equation | `inverse.solve_target_iota`; `continuation.continue_etabar_branch` | `etabar` and `I2` round trips, sign branches, distinct local basins, fold crossing, independent forward correction, r2 propagation, JIT/JVP/finite differences | branch-local inverse and fixed-step `etabar` pseudo-arclength implemented | +| Nonconstant \(B_{20}\) and affine \(B_{2c}\) elimination | Landreman & Sengupta (2019), complete r2 system | `optimize.b20_diagnostics`; `optimize.optimize_B2c` | direct norm definitions, affine reconstruction, stationary optimum, circular degeneracy, spectral tail, doubled-grid verification, JIT/JVP/finite differences | implemented and documented | | Field gradient and `L_grad_B` | Landreman (2021), arXiv:2012.00865, Eq. 3.12 | `first_order.first_order_solution`; pyQSC `grad_B_tensor.py` | upstream arrays, vacuum symmetry/divergence, resolution convergence | implemented and documented | | Complete second-order coefficients | Landreman & Sengupta (2019), arXiv:1908.10253 | `second_order.solve_second_order`; pyQSC `calculate_r2.py`; manuscript Eqs. 36–54 | four independent equation residuals; vacuum QA, finite-pressure/current, QH upstream arrays; JIT/JVP/VJP/finite differences | implemented and documented | | Total field Hessian | manuscript Eqs. 55–83 | `field.total_field_jet`; pyQSC generated tensor as comparison only | regular-coordinate chain rule, JIT/JVP, QA and finite-current upstream arrays, full vacuum symmetry, divergence and derivative-of-divergence | implemented and documented | diff --git a/docs/index.md b/docs/index.md index 5f79926..91c8171 100644 --- a/docs/index.md +++ b/docs/index.md @@ -16,10 +16,12 @@ theory/first-order theory/second-order theory/third-order theory/inverse-solves +theory/b20-optimization theory/field-jet api/axis api/first-order api/continuation +api/optimization api/second-order api/third-order api/field-jet diff --git a/docs/limitations.md b/docs/limitations.md index 0536b1c..fea0b01 100644 --- a/docs/limitations.md +++ b/docs/limitations.md @@ -10,6 +10,8 @@ Known limitations under active refactor include: - no plasma/external field-jet separation; - pseudo-arclength continuation currently traces `etabar` branches only and uses a fixed arclength step. +- no multistart axis optimization or basin enumeration yet; only the exact + affine `B2c` subproblem is eliminated. Target-transform solves are branch-local. The sign of the `etabar` seed is preserved and the seed magnitude selects a Newton basin. Multiple local diff --git a/docs/quickstart.md b/docs/quickstart.md index 69149d2..17dc77f 100644 --- a/docs/quickstart.md +++ b/docs/quickstart.md @@ -98,6 +98,30 @@ print(branch.fold_detected) Each corrected point has its own `root_report`. `branch.complete` is true only when every requested point converged. +## Analytic \(B_{2c}\) elimination + +For any r2 or r3 solution: + +```python +optimal = qsc.optimize_B2c(solution) + +print(optimal.B2c_optimal) +print(optimal.diagnostics.weighted_l2) +print(optimal.diagnostics.grid_maximum) +print(optimal.affine_reconstruction_error) + +verification = qsc.verify_B20_resolution( + optimal.solution, + multipliers=(1, 2, 4), +) +print(verification.relative_weighted_l2_change) +print(verification.relative_grid_maximum_change) +``` + +The scalar optimum is exact for the weighted-\(L^2\) affine subproblem. +Fine-grid maximum and spectral-tail checks remain independent acceptance +criteria. + ESSOS code can continue to use: ```python diff --git a/docs/theory/b20-optimization.md b/docs/theory/b20-optimization.md new file mode 100644 index 0000000..3db401e --- /dev/null +++ b/docs/theory/b20-optimization.md @@ -0,0 +1,82 @@ +# \(B_{20}\) diagnostics and analytic \(B_{2c}\) + +## Primary residual + +The optimization target is the nonconstant part of \(B_{20}\), not its mean. +For positive quadrature weights \(w_j\), define + +\[ +(PB_{20})_j=B_{20,j} +-\frac{\sum_k w_kB_{20,k}}{\sum_k w_k}. +\] + +`weighted_l2` is + +\[ +\left[ +\frac{\sum_j w_j(PB_{20})_j^2}{\sum_jw_j} +\right]^{1/2}\frac{1}{B_0}. +\] + +`b20_diagnostics` also returns a smooth high-\(p\) norm, the sampled maximum, +peak-to-peak variation, all nonzero toroidal Fourier coefficients, their norm, +and a high-mode tail ratio. The Fourier coefficients use direct weighted +quadrature in Boozer toroidal angle \(\varphi\), so they do not assume that the +uniform cylindrical-\(\phi\) samples are uniform in \(\varphi\). + +## Exact affine elimination + +For fixed axis and all other physical inputs, the complete second-order solve +is affine in \(B_{2c}\): + +\[ +B_{20}(\varphi;B_{2c})=u(\varphi)+B_{2c}v(\varphi). +\] + +The implementation obtains \(u\) and \(v\) from two complete implicit linear +solves at \(B_{2c}=0\) and \(B_{2c}=1\). It then evaluates + +\[ +B_{2c}^{\star} +=-\frac{\langle Pu,Pv\rangle_w}{\langle Pv,Pv\rangle_w}. +\] + +This is the global minimizer in the one-dimensional affine subproblem whenever +\(\langle Pv,Pv\rangle_w>0\). `optimize_B2c` fully recomputes the r2 solution +at the optimum and, when present, recomputes r3 and magnetic shear so no stale +derived arrays survive. `affine_reconstruction_error` independently compares +that solution to \(u+B_{2c}^{\star}v\). + +For a circular axis the projected response can vanish to roundoff because +changing \(B_{2c}\) changes only the constant mode. Such cases are marked +`degenerate`, retain the supplied \(B_{2c}\), and already have a vanishing +nonconstant residual. + +## Independent resolution verification + +`verify_B20_resolution` holds the physical candidate fixed and rebuilds it at + +\[ +n_\phi(m)=m(n_\phi-1)+1 +\] + +for each requested multiplier. The default `(1, 2, 4)` therefore doubles and +quadruples the number of grid intervals while retaining an odd grid. It reports +every dense diagnostic and successive relative changes. This check is +deliberately separate from the optimization; a small collocation objective is +not accepted without fine-grid verification. + +## Validation + +Tests establish: + +- direct agreement of every scalar diagnostic with its definition; +- stationarity and strict improvement of the analytic optimum; +- machine-precision affine reconstruction; +- JIT and JVP agreement with finite differences; +- correct degenerate behavior for a circular axis; +- r3 and shear recomputation; +- convergence of weighted and maximum residuals under grid refinement. + +Multistart axis optimization and basin enumeration build on these residuals but +remain a separate milestone. diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index a20cdd6..89ae51f 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -19,6 +19,15 @@ ThirdOrderData, ) from pyqsc_jax.near_axis import near_axis +from pyqsc_jax.optimize import ( + B2cOptimizationResult, + B20Diagnostics, + B20ResolutionVerification, + b20_diagnostics, + optimal_B2c_value, + optimize_B2c, + verify_B20_resolution, +) from pyqsc_jax.second_order import SecondOrderResiduals, second_order_residuals from pyqsc_jax.shear import solve_magnetic_shear from pyqsc_jax.singularity import singularity_diagnostics @@ -27,6 +36,9 @@ __all__ = [ "Axis", + "B2cOptimizationResult", + "B20Diagnostics", + "B20ResolutionVerification", "ContinuationResult", "FieldJet", "InverseSolveDiagnostics", @@ -43,6 +55,7 @@ "SingularityDiagnostics", "ThirdOrderData", "near_axis", + "b20_diagnostics", "continue_etabar_branch", "mercier_diagnostics", "second_order_residuals", @@ -51,5 +64,8 @@ "singularity_diagnostics", "solve_third_order", "total_field_jet", + "optimal_B2c_value", + "optimize_B2c", + "verify_B20_resolution", ] __version__ = "0.2.0.dev0" diff --git a/src/pyqsc_jax/optimize.py b/src/pyqsc_jax/optimize.py new file mode 100644 index 0000000..42efe48 --- /dev/null +++ b/src/pyqsc_jax/optimize.py @@ -0,0 +1,270 @@ +"""Dense B20 diagnostics and exact elimination of the affine B2c input.""" + +from __future__ import annotations + +from dataclasses import dataclass, replace + +import jax +import jax.numpy as jnp + +from pyqsc_jax.first_order import solve +from pyqsc_jax.models import NearAxisSolution +from pyqsc_jax.second_order import solve_second_order + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class B20Diagnostics: + """Dense-grid and toroidal-spectrum measures of nonconstant B20.""" + + weighted_mean: jax.Array + anomaly: jax.Array + weighted_l2: jax.Array + smooth_maximum: jax.Array + grid_maximum: jax.Array + peak_to_peak: jax.Array + fourier_modes: jax.Array + fourier_coefficients: jax.Array + nonzero_fourier_norm: jax.Array + fourier_tail_ratio: jax.Array + smooth_maximum_power: int + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class B2cOptimizationResult: + """Exact weighted-L2 optimum for the affine B2c dependence.""" + + solution: NearAxisSolution + diagnostics: B20Diagnostics + B2c_optimal: jax.Array + affine_intercept: jax.Array + affine_response: jax.Array + projected_response_norm_squared: jax.Array + affine_reconstruction_error: jax.Array + degenerate: jax.Array + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class B20ResolutionVerification: + """Independent fixed-parameter B20 checks on successively finer grids.""" + + resolutions: jax.Array + weighted_l2: jax.Array + smooth_maximum: jax.Array + grid_maximum: jax.Array + peak_to_peak: jax.Array + fourier_tail_ratio: jax.Array + relative_weighted_l2_change: jax.Array + relative_grid_maximum_change: jax.Array + + +def b20_diagnostics( + solution: NearAxisSolution, + *, + smooth_maximum_power: int = 16, +) -> B20Diagnostics: + """Evaluate normalized dense-grid and nonzero-mode B20 diagnostics.""" + + if solution.second_order is None: + raise ValueError("A second-order solution is required for B20 diagnostics.") + if ( + not isinstance(smooth_maximum_power, int) + or isinstance(smooth_maximum_power, bool) + or smooth_maximum_power < 2 + ): + raise ValueError("smooth_maximum_power must be an integer >= 2.") + weights = solution.geometry.d_l_d_phi + weight_sum = jnp.sum(weights) + B20 = solution.B20 + B0 = solution.inputs.B0 + weighted_mean = jnp.sum(weights * B20) / weight_sum + anomaly = B20 - weighted_mean + normalized = anomaly / B0 + weighted_l2 = jnp.sqrt(jnp.sum(weights * normalized**2) / weight_sum) + smooth_maximum = ( + jnp.sum(weights * jnp.abs(normalized) ** smooth_maximum_power) / weight_sum + ) ** (1 / smooth_maximum_power) + grid_maximum = jnp.max(jnp.abs(normalized)) + peak_to_peak = (jnp.max(B20) - jnp.min(B20)) / B0 + + maximum_mode = (solution.inputs.nphi - 1) // 2 + modes = jnp.arange(1, maximum_mode + 1) + phase = jnp.exp(-1j * modes[:, None] * solution.inputs.axis.nfp * solution.varphi[None, :]) + coefficients = jnp.sum(weights[None, :] * anomaly[None, :] * phase, axis=1) / weight_sum + coefficient_power = jnp.abs(coefficients / B0) ** 2 + nonzero_fourier_norm = jnp.sqrt(2 * jnp.sum(coefficient_power)) + tail_start = maximum_mode * 3 // 4 + tiny = jnp.finfo(B20.dtype).tiny + fourier_tail_ratio = jnp.sqrt( + jnp.sum(coefficient_power[tail_start:]) / jnp.maximum(jnp.sum(coefficient_power), tiny) + ) + return B20Diagnostics( + weighted_mean=weighted_mean, + anomaly=anomaly, + weighted_l2=weighted_l2, + smooth_maximum=smooth_maximum, + grid_maximum=grid_maximum, + peak_to_peak=peak_to_peak, + fourier_modes=modes, + fourier_coefficients=coefficients, + nonzero_fourier_norm=nonzero_fourier_norm, + fourier_tail_ratio=fourier_tail_ratio, + smooth_maximum_power=smooth_maximum_power, + ) + + +def _first_order_with_B2c(solution: NearAxisSolution, B2c: jax.Array) -> NearAxisSolution: + inputs = replace(solution.inputs, B2c=B2c) + return replace( + solution, + inputs=inputs, + second_order=None, + mercier=None, + field_jet=None, + singularity=None, + third_order=None, + shear=None, + ) + + +def _affine_B20(solution: NearAxisSolution) -> tuple[jax.Array, jax.Array]: + if solution.second_order is None: + raise ValueError("A second-order solution is required to eliminate B2c.") + zero = solve_second_order( + _first_order_with_B2c(solution, jnp.zeros_like(solution.inputs.B2c)), + attach_diagnostics=False, + ) + one = solve_second_order( + _first_order_with_B2c(solution, jnp.ones_like(solution.inputs.B2c)), + attach_diagnostics=False, + ) + return zero.B20, one.B20 - zero.B20 + + +def optimal_B2c_value( + solution: NearAxisSolution, + *, + degeneracy_tolerance: float = 1e-24, +) -> jax.Array: + """Return the exact B2c minimizing the nonconstant weighted-L2 B20.""" + + if degeneracy_tolerance < 0: + raise ValueError("degeneracy_tolerance must be nonnegative.") + intercept, response = _affine_B20(solution) + weights = solution.geometry.d_l_d_phi + weight_sum = jnp.sum(weights) + projected_intercept = intercept - jnp.sum(weights * intercept) / weight_sum + projected_response = response - jnp.sum(weights * response) / weight_sum + denominator = jnp.sum(weights * projected_response**2) + numerator = jnp.sum(weights * projected_intercept * projected_response) + return jnp.where( + denominator > degeneracy_tolerance, + -numerator / denominator, + solution.inputs.B2c, + ) + + +def optimize_B2c( + solution: NearAxisSolution, + *, + smooth_maximum_power: int = 16, + degeneracy_tolerance: float = 1e-24, +) -> B2cOptimizationResult: + """Eliminate B2c analytically and return the fully recomputed solution.""" + + intercept, response = _affine_B20(solution) + weights = solution.geometry.d_l_d_phi + weight_sum = jnp.sum(weights) + projected_intercept = intercept - jnp.sum(weights * intercept) / weight_sum + projected_response = response - jnp.sum(weights * response) / weight_sum + denominator = jnp.sum(weights * projected_response**2) + numerator = jnp.sum(weights * projected_intercept * projected_response) + degenerate = denominator <= degeneracy_tolerance + optimum = jnp.where(degenerate, solution.inputs.B2c, -numerator / denominator) + optimal = solve_second_order(_first_order_with_B2c(solution, optimum)) + if solution.inputs.order == 3: + from pyqsc_jax.third_order import solve_third_order + + optimal = solve_third_order(optimal) + if solution.shear is not None: + from pyqsc_jax.shear import solve_magnetic_shear + + optimal = solve_magnetic_shear(optimal, B31c=solution.shear.B31c) + reconstruction_error = jnp.max(jnp.abs(optimal.B20 - (intercept + optimum * response))) + return B2cOptimizationResult( + solution=optimal, + diagnostics=b20_diagnostics( + optimal, + smooth_maximum_power=smooth_maximum_power, + ), + B2c_optimal=optimum, + affine_intercept=intercept, + affine_response=response, + projected_response_norm_squared=denominator, + affine_reconstruction_error=reconstruction_error, + degenerate=degenerate, + ) + + +def verify_B20_resolution( + solution: NearAxisSolution, + *, + multipliers: tuple[int, ...] = (1, 2, 4), + smooth_maximum_power: int = 16, +) -> B20ResolutionVerification: + """Recompute one fixed physical candidate at independent resolutions.""" + + if not multipliers or any( + not isinstance(multiplier, int) or isinstance(multiplier, bool) or multiplier < 1 + for multiplier in multipliers + ): + raise ValueError("multipliers must be a nonempty tuple of positive integers.") + inputs = solution.inputs + resolutions = tuple(multiplier * (inputs.nphi - 1) + 1 for multiplier in multipliers) + diagnostics = [] + for nphi in resolutions: + candidate = solve( + axis=inputs.axis, + etabar=inputs.etabar, + B0=inputs.B0, + sigma0=inputs.sigma0, + I2=inputs.I2, + p2=inputs.p2, + B2c=inputs.B2c, + B2s=inputs.B2s, + nphi=nphi, + order="r2", + sG=inputs.sG, + spsi=inputs.spsi, + ) + diagnostics.append(b20_diagnostics(candidate, smooth_maximum_power=smooth_maximum_power)) + weighted_l2 = jnp.stack(tuple(item.weighted_l2 for item in diagnostics)) + smooth_maximum = jnp.stack(tuple(item.smooth_maximum for item in diagnostics)) + grid_maximum = jnp.stack(tuple(item.grid_maximum for item in diagnostics)) + peak_to_peak = jnp.stack(tuple(item.peak_to_peak for item in diagnostics)) + tail_ratio = jnp.stack(tuple(item.fourier_tail_ratio for item in diagnostics)) + tiny = jnp.finfo(weighted_l2.dtype).tiny + relative_l2_change = jnp.concatenate( + ( + jnp.zeros(1, dtype=weighted_l2.dtype), + jnp.abs(jnp.diff(weighted_l2)) / jnp.maximum(weighted_l2[:-1], tiny), + ) + ) + relative_maximum_change = jnp.concatenate( + ( + jnp.zeros(1, dtype=grid_maximum.dtype), + jnp.abs(jnp.diff(grid_maximum)) / jnp.maximum(grid_maximum[:-1], tiny), + ) + ) + return B20ResolutionVerification( + resolutions=jnp.asarray(resolutions), + weighted_l2=weighted_l2, + smooth_maximum=smooth_maximum, + grid_maximum=grid_maximum, + peak_to_peak=peak_to_peak, + fourier_tail_ratio=tail_ratio, + relative_weighted_l2_change=relative_l2_change, + relative_grid_maximum_change=relative_maximum_change, + ) diff --git a/src/pyqsc_jax/second_order.py b/src/pyqsc_jax/second_order.py index 5405cf3..bc4cb34 100644 --- a/src/pyqsc_jax/second_order.py +++ b/src/pyqsc_jax/second_order.py @@ -211,7 +211,11 @@ def _assemble_periodic_system( ) -def solve_second_order(first_order: NearAxisSolution) -> NearAxisSolution: +def solve_second_order( + first_order: NearAxisSolution, + *, + attach_diagnostics: bool = True, +) -> NearAxisSolution: """Add the complete finite-pressure/current second-order solution.""" inputs = first_order.inputs @@ -363,6 +367,8 @@ def untwist(sine_coefficient, cosine_coefficient): Z2c_untwisted=Z2c_untwisted, ) solution = replace(first_order, second_order=second_order) + if not attach_diagnostics: + return solution from pyqsc_jax.diagnostics import mercier_diagnostics from pyqsc_jax.field import total_field_jet from pyqsc_jax.singularity import singularity_diagnostics diff --git a/tests/physics/test_b20_optimization.py b/tests/physics/test_b20_optimization.py new file mode 100644 index 0000000..d8e87f8 --- /dev/null +++ b/tests/physics/test_b20_optimization.py @@ -0,0 +1,144 @@ +from __future__ import annotations + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +import pyqsc_jax as qsc + + +def qa_solution(nphi=31, order="r2", **overrides): + parameters = { + "rc": [1.0, 0.155, 0.0102], + "zs": [0.0, 0.154, 0.0111], + "nfp": 2, + "etabar": 0.64, + "B2c": -0.00322, + "nphi": nphi, + "order": order, + } + parameters.update(overrides) + return qsc.Qsc(**parameters) + + +def test_dense_B20_diagnostics_match_direct_definitions(): + solution = qa_solution() + diagnostics = qsc.b20_diagnostics(solution, smooth_maximum_power=12) + weights = solution.geometry.d_l_d_phi + mean = np.sum(np.asarray(weights * solution.B20)) / np.sum(np.asarray(weights)) + anomaly = np.asarray(solution.B20) - mean + + np.testing.assert_allclose(diagnostics.weighted_mean, mean) + np.testing.assert_allclose(diagnostics.anomaly, anomaly) + np.testing.assert_allclose( + diagnostics.weighted_l2, + np.sqrt( + np.sum(np.asarray(weights) * (anomaly / solution.inputs.B0) ** 2) / np.sum(weights) + ), + ) + np.testing.assert_allclose(diagnostics.weighted_l2, solution.B20_residual) + np.testing.assert_allclose( + diagnostics.grid_maximum, + np.max(np.abs(anomaly / solution.inputs.B0)), + ) + np.testing.assert_allclose( + diagnostics.peak_to_peak, + solution.B20_variation / solution.inputs.B0, + ) + assert diagnostics.smooth_maximum_power == 12 + assert diagnostics.fourier_modes.shape == (15,) + assert diagnostics.fourier_coefficients.shape == (15,) + assert diagnostics.weighted_l2 <= diagnostics.smooth_maximum <= diagnostics.grid_maximum + assert 0 <= float(diagnostics.fourier_tail_ratio) <= 1 + + +def test_affine_B2c_elimination_is_exact_and_stationary(): + solution = qa_solution() + result = qsc.optimize_B2c(solution) + minus = qa_solution(B2c=result.B2c_optimal - 0.1) + plus = qa_solution(B2c=result.B2c_optimal + 0.1) + + np.testing.assert_allclose(result.B2c_optimal, -0.49172683641534204, rtol=3.0e-12) + assert result.affine_reconstruction_error < 5.0e-14 + assert not bool(result.degenerate) + assert result.diagnostics.weighted_l2 < solution.B20_residual + assert result.diagnostics.weighted_l2 < minus.B20_residual + assert result.diagnostics.weighted_l2 < plus.B20_residual + + def squared_residual(B2c): + return qa_solution(nphi=15, B2c=B2c).B20_residual ** 2 + + optimum = qsc.optimal_B2c_value(qa_solution(nphi=15)) + derivative = jax.grad(squared_residual)(optimum) + assert abs(float(derivative)) < 2.0e-11 + + +def test_B2c_optimum_is_jittable_and_differentiable(): + def optimum(etabar): + return qsc.optimal_B2c_value(qa_solution(nphi=15, etabar=etabar)) + + value = optimum(jnp.asarray(0.64)) + jitted = jax.jit(optimum)(jnp.asarray(0.64)) + tangent = jax.jvp(optimum, (jnp.asarray(0.64),), (jnp.asarray(1.0),))[1] + step = 1.0e-5 + finite_difference = (optimum(0.64 + step) - optimum(0.64 - step)) / (2 * step) + + np.testing.assert_allclose(jitted, value, rtol=2.0e-11) + np.testing.assert_allclose(tangent, finite_difference, rtol=2.0e-6) + + +def test_optimal_solution_recomputes_r3_and_shear_without_stale_data(): + original = qsc.solve_magnetic_shear(qa_solution(nphi=15, order="r3")) + result = qsc.optimize_B2c(original) + + assert result.solution.third_order is not None + assert result.solution.shear is not None + np.testing.assert_allclose(result.solution.B31c, original.B31c) + assert result.solution.flux_constraint_residual < 2.0e-13 + assert result.solution.consistency_error < 2.0e-10 + + +def test_circular_axis_has_degenerate_nonconstant_B2c_response(): + solution = qsc.Qsc( + rc=[1.0], + zs=[0.0], + nfp=1, + etabar=1.0, + I2=0.1, + B2c=0.2, + nphi=15, + order="r2", + ) + result = qsc.optimize_B2c(solution) + + assert bool(result.degenerate) + np.testing.assert_allclose(result.B2c_optimal, 0.2) + assert result.diagnostics.weighted_l2 < 2.0e-14 + + +def test_resolution_verification_recomputes_fixed_candidate(): + result = qsc.optimize_B2c(qa_solution()) + verification = qsc.verify_B20_resolution(result.solution, multipliers=(1, 2)) + + np.testing.assert_array_equal(verification.resolutions, [31, 61]) + np.testing.assert_allclose(verification.weighted_l2[0], result.diagnostics.weighted_l2) + assert verification.relative_weighted_l2_change[1] < 2.0e-6 + assert verification.fourier_tail_ratio[1] < verification.fourier_tail_ratio[0] + assert verification.relative_grid_maximum_change[1] < 0.03 + + +def test_B20_optimization_input_guards(): + first_order = qa_solution(order="r1") + with pytest.raises(ValueError, match="second-order"): + qsc.b20_diagnostics(first_order) + with pytest.raises(ValueError, match="second-order"): + qsc.optimal_B2c_value(first_order) + with pytest.raises(ValueError, match="smooth_maximum_power"): + qsc.b20_diagnostics(qa_solution(), smooth_maximum_power=1) + with pytest.raises(ValueError, match="degeneracy_tolerance"): + qsc.optimal_B2c_value(qa_solution(), degeneracy_tolerance=-1.0) + with pytest.raises(ValueError, match="multipliers"): + qsc.verify_B20_resolution(qa_solution(), multipliers=()) + with pytest.raises(ValueError, match="multipliers"): + qsc.verify_B20_resolution(qa_solution(), multipliers=(True,)) From cf3f6da0758220f101b3ea34ec9bdb39123af6e7 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 01:10:26 -0500 Subject: [PATCH 14/39] feat: add scalable stellarator screening criteria --- CHANGELOG.md | 3 + README.md | 11 +- docs/api/criteria.md | 16 ++ docs/conf.py | 1 - docs/development/physics-traceability.md | 2 +- docs/index.md | 8 +- docs/limitations.md | 11 +- docs/quickstart.md | 20 +++ docs/theory/criteria.md | 52 ++++++ src/pyqsc_jax/__init__.py | 4 + src/pyqsc_jax/criteria.py | 200 +++++++++++++++++++++++ tests/physics/test_criteria.py | 128 +++++++++++++++ 12 files changed, 448 insertions(+), 8 deletions(-) create mode 100644 docs/api/criteria.md create mode 100644 docs/theory/criteria.md create mode 100644 src/pyqsc_jax/criteria.py create mode 100644 tests/physics/test_criteria.py diff --git a/CHANGELOG.md b/CHANGELOG.md index 9e0b069..95e905d 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -55,6 +55,9 @@ first stable release. - Dense nonconstant-`B20` diagnostics, exact affine elimination of `B2c`, degenerate-response handling, and independent doubled/quadrupled-grid verification. +- Scalable Curvo et al. (2025) Table 3 screening criteria with configurable + thresholds, strict/inclusive comparison semantics, units, measured values, + signed margins, aggregate status, and differentiable array results. ### Fixed diff --git a/README.md b/README.md index dbe1934..7dfbe1e 100644 --- a/README.md +++ b/README.md @@ -7,8 +7,10 @@ JAX. > coefficient solve, r3 flux constraint, magnetic shear, total-field Hessian, > Mercier diagnostics, singular-radius diagnostics, and ESSOS adapter are > validated, along with branch-local inverse solves and pseudo-arclength -> continuation. Optimization and plasma/external field jets remain under -> development on the `refactor/pyqsc-jax-complete` branch. +> continuation, exact affine \(B_{2c}\) optimization, and the scalable Curvo +> et al. screening profile. Multistart axis optimization and plasma/external +> field jets remain under development on the +> `refactor/pyqsc-jax-complete` branch. ## Install @@ -104,6 +106,11 @@ exactly and returns dense weighted, smooth-maximum, grid-maximum, Fourier, and tail diagnostics. `qsc.verify_B20_resolution(...)` independently rebuilds the candidate on doubled and quadrupled grids. +`qsc.Criteria.from_curvo_2025(major_radius=1.0, B0=1.0)` evaluates the +published Table 3 screening profile and returns every measured value, signed +margin, and pass flag. The thresholds are normalization-aware and fully +overridable; the profile is not treated as a universal feasibility theorem. + The lower-level immutable axis API supports general, not necessarily stellarator-symmetric Fourier axes: diff --git a/docs/api/criteria.md b/docs/api/criteria.md new file mode 100644 index 0000000..fcbb7f7 --- /dev/null +++ b/docs/api/criteria.md @@ -0,0 +1,16 @@ +# Criteria API + +```{eval-rst} +.. autoclass:: pyqsc_jax.Criteria + :members: +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.CriteriaReport + :members: +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.CriterionEvaluation + :members: +``` diff --git a/docs/conf.py b/docs/conf.py index e41112c..94fa50f 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -2,7 +2,6 @@ from pyqsc_jax import __version__ - project = "pyQSC_JAX" author = "UW Plasma" copyright = "2026, UW Plasma" diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index 171e873..94cff98 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -17,7 +17,7 @@ to the cited source, not to a duplicated derivation in this repository. | Third-order flux constraint | Landreman & Sengupta (2019) | `third_order.solve_third_order`; pyQSC `calculate_r3.py` | two independent flux-constraint forms; QA, finite-pressure/current, and QH upstream arrays; r3 boundary data; JIT/JVP/finite differences | implemented and documented | | Magnetic shear | Rodríguez, Sengupta & Bhattacharjee (2022), Appendix F | `shear.solve_magnetic_shear`; pyQSC `calculate_r3.py` | three upstream paper cases, asymmetric/secular integration, resolution convergence, `B31c`, JIT/JVP/VJP and full-solve AD | implemented and documented for standard MHS with positive signs | | Singular radius and scale lengths | Landreman (2021), arXiv:2012.00865 | `singularity.singularity_diagnostics`; pyQSC `r_singularity.py` as comparison | direct regular-map determinant, QA/QH/finite-current upstream radii and arrays, residual, angular convergence, JIT/JVP/finite differences | implemented and documented | -| Good-stellarator criteria | Curvo, Ferreira & Jorge (2025), Table 3 | none canonical | exact normalized thresholds and margins | not implemented | +| Good-stellarator criteria | Curvo, Ferreira & Jorge (2025), Table 3 | `criteria.Criteria.from_curvo_2025` | exact normalized thresholds, strict/inclusive comparisons, signed margins, scaling, JIT/JVP/finite differences | implemented and documented | | Plasma current source | manuscript Eqs. 88–97 | none | normalization, enclosed current, straight circular/elliptic channels | not implemented | | Plasma on-axis field | manuscript Eqs. 136–138 | none | full-torus periodicity, matching cancellation, resolved volume Biot–Savart | not implemented | | Plasma gradient | manuscript Eqs. 156–160 | none | Ampère antisymmetry, divergence, external STF projection | not implemented | diff --git a/docs/index.md b/docs/index.md index 91c8171..9c9290c 100644 --- a/docs/index.md +++ b/docs/index.md @@ -17,11 +17,13 @@ theory/second-order theory/third-order theory/inverse-solves theory/b20-optimization +theory/criteria theory/field-jet api/axis api/first-order api/continuation api/optimization +api/criteria api/second-order api/third-order api/field-jet @@ -49,8 +51,10 @@ changelog The immutable first-order API, complete r2 coefficient solve, r3 flux constraint, magnetic shear, total-field Hessian, Mercier terms, and singular-radius diagnostics are validated, as are branch-local inverse solves. -Pseudo-arclength branch continuation is also validated. Optimization and -plasma/external field jets are under active development. +Pseudo-arclength branch continuation, exact affine \(B_{2c}\) optimization, +and the scalable Curvo et al. screening profile are also validated. +Multistart axis optimization and plasma/external field jets are under active +development. The `pyqsc_jax.near_axis.near_axis` import remains supported for ESSOS without a runtime deprecation warning. diff --git a/docs/limitations.md b/docs/limitations.md index fea0b01..984e8b1 100644 --- a/docs/limitations.md +++ b/docs/limitations.md @@ -13,6 +13,12 @@ Known limitations under active refactor include: - no multistart axis optimization or basin enumeration yet; only the exact affine `B2c` subproblem is eliminated. +`Criteria.from_curvo_2025` is a configurable reproduction of one published +screening profile. Its thresholds are not hard-coded package-wide acceptance +requirements. In particular, `r_singularity` is the first singularity of the +truncated near-axis coordinate map; it does not guarantee nested, +nonintersecting finite-radius flux surfaces. + Target-transform solves are branch-local. The sign of the `etabar` seed is preserved and the seed magnitude selects a Newton basin. Multiple local solutions can have the same transform. `response_derivative` and `branch_fold` @@ -30,8 +36,9 @@ the structured report. Production workflows must reject `root_report.converged == False`. Frenet coordinates are invalid when the magnetic-axis curvature vanishes. -`GeometryDiagnostics` reports this condition explicitly; high-level rejection -policy will be added alongside the aggregate design-criteria report. +`GeometryDiagnostics` reports this condition explicitly. The published Curvo +profile does not add a minimum-curvature threshold, but callers can reject +invalid geometry independently. Near-axis results are asymptotic in distance from the axis. “Surface-free” plasma–coil separation does not mean radius-free: a formal minor radius or an diff --git a/docs/quickstart.md b/docs/quickstart.md index 17dc77f..08e6d72 100644 --- a/docs/quickstart.md +++ b/docs/quickstart.md @@ -122,6 +122,26 @@ The scalar optimum is exact for the weighted-\(L^2\) affine subproblem. Fine-grid maximum and spectral-tail checks remain independent acceptance criteria. +## Evaluate a published screening profile + +Curvo, Ferreira, and Jorge's Table 3 profile is available with explicit +normalization and signed margins: + +```python +criteria = qsc.Criteria.from_curvo_2025( + major_radius=1.0, + B0=1.0, +) +report = criteria.evaluate(solution) + +print(report.passed) +print(report["abs_iota"].margin) +print(report["B20_variation"].margin) +``` + +Every threshold can be overridden. This report is a near-axis screening +profile, not a proof of finite-radius equilibrium or coil feasibility. + ESSOS code can continue to use: ```python diff --git a/docs/theory/criteria.md b/docs/theory/criteria.md new file mode 100644 index 0000000..42cfe4f --- /dev/null +++ b/docs/theory/criteria.md @@ -0,0 +1,52 @@ +# Named design criteria + +`Criteria.from_curvo_2025` implements the screening profile in Table 3 of +Curvo, Ferreira, and Jorge {cite}`curvo2025deep`. It is a named, configurable +profile rather than a package-wide definition of a “good stellarator.” + +For the paper's normalization \(R_{c0}=1\,\mathrm{m}\) and +\(B_0=1\,\mathrm{T}\), the profile requires: + +- positive magnetic-axis length; +- \(\lvert\iota\rvert\geq0.2\); +- maximum elongation no greater than \(10\); +- \(\min L_{\nabla B}\geq0.1\,\mathrm{m}\); +- minimum cylindrical axis radius at least \(0.3\,\mathrm{m}\); +- singular radius at least \(0.05\,\mathrm{m}\); +- \(\min L_{\nabla\nabla B}\geq0.1\,\mathrm{m}\); +- \(B_{20}\) peak-to-peak variation no greater than + \(5\,\mathrm{T/m^2}\); +- \(\beta\geq10^{-4}\); and +- \(D_{\mathrm{Merc}}r^2>0\). + +The profile uses the paper's near-axis pressure proxy + +\[ +\beta=-\frac{\mu_0p_2r_{\mathrm{singularity}}^2}{B_0^2}. +\] + +When `major_radius` or `B0` differs from the reference normalization, length +thresholds scale with `major_radius` and the \(B_{20}\)-variation threshold +scales as \(B_0/R^2\). Dimensionless thresholds do not change. Callers can +override any threshold by name: + +```python +criteria = qsc.Criteria.from_curvo_2025( + major_radius=1.7, + B0=2.5, + maximum_elongation=8.0, + minimum_beta=2.0e-4, +) +report = criteria.evaluate(solution) +``` + +Every `CriterionEvaluation` contains the measured value, threshold, comparison +sense, units, pass flag, and a signed raw margin. A positive margin is +favorable for both minimum and maximum criteria. `report.passed` is true only +if all ten checks pass. + +The singular radius is the first coordinate-map singularity of the truncated +near-axis construction. It is useful as a screening proxy but does not prove +that a finite-radius equilibrium has nested, nonintersecting flux surfaces. +Likewise, this profile does not replace coil feasibility, fast-particle +confinement, MHD equilibrium, or free-boundary validation. diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index 89ae51f..4784d66 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -2,6 +2,7 @@ from pyqsc_jax.axis import Axis from pyqsc_jax.continuation import ContinuationResult, continue_etabar_branch +from pyqsc_jax.criteria import Criteria, CriteriaReport, CriterionEvaluation from pyqsc_jax.diagnostics import mercier_diagnostics from pyqsc_jax.field import total_field_jet from pyqsc_jax.first_order import Qsc, solve @@ -40,6 +41,9 @@ "B20Diagnostics", "B20ResolutionVerification", "ContinuationResult", + "Criteria", + "CriteriaReport", + "CriterionEvaluation", "FieldJet", "InverseSolveDiagnostics", "LinearSolveReport", diff --git a/src/pyqsc_jax/criteria.py b/src/pyqsc_jax/criteria.py new file mode 100644 index 0000000..fb49a27 --- /dev/null +++ b/src/pyqsc_jax/criteria.py @@ -0,0 +1,200 @@ +"""Named, scalable stellarator design-criteria profiles.""" + +from __future__ import annotations + +from dataclasses import dataclass, field + +import jax +import jax.numpy as jnp + +from pyqsc_jax.models import NearAxisSolution +from pyqsc_jax.second_order import MU0 + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class CriterionEvaluation: + """One signed criterion margin and its pass/fail result.""" + + value: jax.Array + threshold: jax.Array + margin: jax.Array + passed: jax.Array + name: str = field(metadata={"static": True}) + sense: str = field(metadata={"static": True}) + units: str = field(metadata={"static": True}) + + +@dataclass(frozen=True) +class CriteriaReport: + """Evaluation of every item in one named criteria profile.""" + + profile_name: str + evaluations: tuple[CriterionEvaluation, ...] + + @property + def passed(self) -> bool: + """Whether every criterion passes.""" + + return all(bool(evaluation.passed) for evaluation in self.evaluations) + + @property + def margins(self) -> dict[str, jax.Array]: + """Signed raw margins keyed by criterion name.""" + + return {evaluation.name: evaluation.margin for evaluation in self.evaluations} + + @property + def values(self) -> dict[str, jax.Array]: + """Measured values keyed by criterion name.""" + + return {evaluation.name: evaluation.value for evaluation in self.evaluations} + + def __getitem__(self, name: str) -> CriterionEvaluation: + for evaluation in self.evaluations: + if evaluation.name == name: + return evaluation + raise KeyError(name) + + +@dataclass(frozen=True) +class Criteria: + """Configurable thresholds for a named near-axis design profile.""" + + minimum_axis_length: float + minimum_abs_iota: float + maximum_elongation: float + minimum_L_grad_B: float + minimum_axis_radius: float + minimum_singular_radius: float + minimum_L_grad_grad_B: float + maximum_B20_variation: float + minimum_beta: float + minimum_DMerc_times_r2: float + profile_name: str = "custom" + + @classmethod + def from_curvo_2025( + cls, + *, + major_radius: float = 1.0, + B0: float = 1.0, + **overrides: float, + ) -> Criteria: + """Return the scalable version of Curvo et al. (2025), Table 3.""" + + if major_radius <= 0: + raise ValueError("major_radius must be positive.") + if B0 <= 0: + raise ValueError("B0 must be positive.") + parameters = { + "minimum_axis_length": 0.0, + "minimum_abs_iota": 0.2, + "maximum_elongation": 10.0, + "minimum_L_grad_B": 0.1 * major_radius, + "minimum_axis_radius": 0.3 * major_radius, + "minimum_singular_radius": 0.05 * major_radius, + "minimum_L_grad_grad_B": 0.1 * major_radius, + "maximum_B20_variation": 5.0 * B0 / major_radius**2, + "minimum_beta": 1.0e-4, + "minimum_DMerc_times_r2": 0.0, + "profile_name": "curvo_2025", + } + unknown = set(overrides) - set(parameters) + if unknown: + names = ", ".join(sorted(unknown)) + raise ValueError(f"Unknown criteria override(s): {names}.") + parameters.update(overrides) + return cls(**parameters) + + def evaluate(self, solution: NearAxisSolution) -> CriteriaReport: + """Evaluate values, signed margins, and pass flags.""" + + if solution.second_order is None: + raise ValueError("The criteria profile requires a second-order solution.") + beta = -MU0 * solution.inputs.p2 * solution.r_singularity**2 / solution.inputs.B0**2 + values = ( + ( + "axis_length", + solution.axis_length, + self.minimum_axis_length, + "strict_min", + "m", + ), + ("abs_iota", jnp.abs(solution.iota), self.minimum_abs_iota, "min", "1"), + ( + "maximum_elongation", + jnp.max(solution.elongation), + self.maximum_elongation, + "max", + "1", + ), + ( + "minimum_L_grad_B", + jnp.min(solution.L_grad_B), + self.minimum_L_grad_B, + "min", + "m", + ), + ( + "minimum_axis_radius", + jnp.min(solution.R0), + self.minimum_axis_radius, + "min", + "m", + ), + ( + "singular_radius", + solution.r_singularity, + self.minimum_singular_radius, + "min", + "m", + ), + ( + "minimum_L_grad_grad_B", + jnp.min(solution.L_grad_grad_B), + self.minimum_L_grad_grad_B, + "min", + "m", + ), + ( + "B20_variation", + solution.B20_variation, + self.maximum_B20_variation, + "max", + "T/m^2", + ), + ("beta", beta, self.minimum_beta, "min", "1"), + ( + "DMerc_times_r2", + solution.DMerc_times_r2, + self.minimum_DMerc_times_r2, + "strict_min", + "1", + ), + ) + evaluations = [] + for name, value, threshold, sense, units in values: + value = jnp.asarray(value) + threshold = jnp.asarray(threshold, dtype=value.dtype) + if sense == "max": + margin = threshold - value + passed = value <= threshold + else: + margin = value - threshold + passed = value > threshold if sense == "strict_min" else value >= threshold + evaluations.append( + CriterionEvaluation( + value=value, + threshold=threshold, + margin=margin, + passed=passed, + name=name, + sense=sense, + units=units, + ) + ) + return CriteriaReport( + profile_name=self.profile_name, + evaluations=tuple(evaluations), + ) diff --git a/tests/physics/test_criteria.py b/tests/physics/test_criteria.py new file mode 100644 index 0000000..2f48344 --- /dev/null +++ b/tests/physics/test_criteria.py @@ -0,0 +1,128 @@ +from __future__ import annotations + +from dataclasses import replace + +import jax +import numpy as np +import pytest + +import pyqsc_jax as qsc +from pyqsc_jax.second_order import MU0 + + +def finite_pressure_solution(order="r2", **overrides): + parameters = { + "rc": [1.0, 0.09], + "zs": [0.0, -0.09], + "nfp": 2, + "etabar": 0.95, + "I2": 0.9, + "p2": -600000.0, + "B2c": -0.7, + "nphi": 31, + "order": order, + } + parameters.update(overrides) + return qsc.Qsc(**parameters) + + +def test_curvo_profile_values_margins_and_scaling(): + solution = finite_pressure_solution() + criteria = qsc.Criteria.from_curvo_2025(major_radius=2.0, B0=3.0) + report = criteria.evaluate(solution) + + assert report.profile_name == "curvo_2025" + assert len(report.evaluations) == 10 + assert set(report.values) == set(report.margins) + np.testing.assert_allclose(criteria.minimum_L_grad_B, 0.2) + np.testing.assert_allclose(criteria.minimum_axis_radius, 0.6) + np.testing.assert_allclose(criteria.minimum_singular_radius, 0.1) + np.testing.assert_allclose(criteria.minimum_L_grad_grad_B, 0.2) + np.testing.assert_allclose(criteria.maximum_B20_variation, 3.75) + + beta = -MU0 * solution.inputs.p2 * solution.r_singularity**2 / solution.inputs.B0**2 + np.testing.assert_allclose(report["beta"].value, beta) + np.testing.assert_allclose( + report["B20_variation"].margin, + criteria.maximum_B20_variation - solution.B20_variation, + ) + np.testing.assert_allclose( + report["minimum_L_grad_B"].margin, + np.min(solution.L_grad_B) - criteria.minimum_L_grad_B, + ) + assert report["B20_variation"].sense == "max" + assert report["B20_variation"].units == "T/m^2" + + +def test_profile_is_fully_configurable_and_reports_aggregate_pass(): + solution = finite_pressure_solution() + report = qsc.Criteria( + minimum_axis_length=-1.0, + minimum_abs_iota=0.0, + maximum_elongation=1.0e6, + minimum_L_grad_B=0.0, + minimum_axis_radius=0.0, + minimum_singular_radius=0.0, + minimum_L_grad_grad_B=0.0, + maximum_B20_variation=1.0e6, + minimum_beta=0.0, + minimum_DMerc_times_r2=-1.0e6, + ).evaluate(solution) + + assert report.passed + assert all(bool(evaluation.passed) for evaluation in report.evaluations) + with pytest.raises(KeyError, match="missing"): + _ = report["missing"] + + +def test_strict_criteria_reject_equality_and_inclusive_criteria_accept_it(): + solution = finite_pressure_solution() + baseline = qsc.Criteria.from_curvo_2025().evaluate(solution) + criteria = qsc.Criteria.from_curvo_2025( + minimum_axis_length=float(solution.axis_length), + minimum_abs_iota=float(abs(solution.iota)), + minimum_DMerc_times_r2=float(solution.DMerc_times_r2), + ) + report = criteria.evaluate(solution) + + assert not bool(report["axis_length"].passed) + assert bool(report["abs_iota"].passed) + assert not bool(report["DMerc_times_r2"].passed) + assert baseline["axis_length"].sense == "strict_min" + + +def test_criterion_margin_is_jittable_and_differentiable(): + criteria = qsc.Criteria.from_curvo_2025() + + def beta_margin(p2): + return criteria.evaluate(finite_pressure_solution(nphi=15, p2=p2))["beta"].margin + + p2 = -600000.0 + value = beta_margin(p2) + jitted = jax.jit(beta_margin)(p2) + tangent = jax.jvp(beta_margin, (p2,), (1.0,))[1] + step = 1.0 + finite_difference = (beta_margin(p2 + step) - beta_margin(p2 - step)) / (2 * step) + + np.testing.assert_allclose(jitted, value) + np.testing.assert_allclose(tangent, finite_difference, rtol=2.0e-6) + + +def test_profile_guards_and_second_order_requirement(): + with pytest.raises(ValueError, match="major_radius"): + qsc.Criteria.from_curvo_2025(major_radius=0.0) + with pytest.raises(ValueError, match="B0"): + qsc.Criteria.from_curvo_2025(B0=0.0) + with pytest.raises(ValueError, match="Unknown criteria"): + qsc.Criteria.from_curvo_2025(unknown_threshold=1.0) + with pytest.raises(ValueError, match="second-order"): + qsc.Criteria.from_curvo_2025().evaluate(finite_pressure_solution(order="r1")) + + +def test_threshold_replacement_changes_only_selected_policy(): + criteria = qsc.Criteria.from_curvo_2025() + changed = replace(criteria, minimum_abs_iota=0.4) + + assert criteria.minimum_abs_iota == 0.2 + assert changed.minimum_abs_iota == 0.4 + assert changed.maximum_elongation == criteria.maximum_elongation From 6fab74b934505c5c7053ed2ceca63c6fc1bf7dda Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 01:33:40 -0500 Subject: [PATCH 15/39] feat: add branch-aware axis optimization --- CHANGELOG.md | 6 + README.md | 11 +- docs/api/axis-optimization.md | 43 ++ docs/development/physics-traceability.md | 1 + docs/index.md | 7 +- docs/limitations.md | 9 +- docs/quickstart.md | 31 + docs/theory/b20-optimization.md | 11 +- docs/theory/global-search.md | 83 +++ src/pyqsc_jax/__init__.py | 20 + src/pyqsc_jax/axis_optimization.py | 736 +++++++++++++++++++++++ src/pyqsc_jax/optimize.py | 6 + tests/physics/test_axis_optimization.py | 423 +++++++++++++ tests/physics/test_b20_optimization.py | 5 + 14 files changed, 1380 insertions(+), 12 deletions(-) create mode 100644 docs/api/axis-optimization.md create mode 100644 docs/theory/global-search.md create mode 100644 src/pyqsc_jax/axis_optimization.py create mode 100644 tests/physics/test_axis_optimization.py diff --git a/CHANGELOG.md b/CHANGELOG.md index 95e905d..8e85f6c 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -58,6 +58,12 @@ first stable release. - Scalable Curvo et al. (2025) Table 3 screening criteria with configurable thresholds, strict/inclusive comparison semantics, units, measured values, signed margins, aggregate status, and differentiable array results. +- Deterministic bounded axis exploration, damped JAX-Jacobian local + least-squares refinement, normalized basin clustering, hard criteria, + canonical secondary selectors, staged Fourier warm starts, independent + verification, and explicit global-certificate status semantics. +- Nonzero \(B_{20}\) Fourier-\(L^1\) certificates in dense and + resolution-verification diagnostics. ### Fixed diff --git a/README.md b/README.md index 7dfbe1e..4d520c4 100644 --- a/README.md +++ b/README.md @@ -8,8 +8,8 @@ JAX. > Mercier diagnostics, singular-radius diagnostics, and ESSOS adapter are > validated, along with branch-local inverse solves and pseudo-arclength > continuation, exact affine \(B_{2c}\) optimization, and the scalable Curvo -> et al. screening profile. Multistart axis optimization and plasma/external -> field jets remain under development on the +> et al. screening profile. Deterministic bounded multistart axis optimization +> is also validated. Plasma/external field jets remain under development on the > `refactor/pyqsc-jax-complete` branch. ## Install @@ -111,6 +111,13 @@ published Table 3 screening profile and returns every measured value, signed margin, and pass flag. The thresholds are normalization-aware and fully overridable; the profile is not treated as a universal feasibility theorem. +`qsc.search_axis(...)` combines deterministic bounded exploration, full-JAX +residual Jacobians, damped local refinement, basin clustering, exact +\(B_{2c}\) elimination, criteria checks, and independent resolution +verification. It returns `verified_zero` only for a verified zero of the +nonnegative primary residual; every nonzero candidate is `best_found` without +a global claim. + The lower-level immutable axis API supports general, not necessarily stellarator-symmetric Fourier axes: diff --git a/docs/api/axis-optimization.md b/docs/api/axis-optimization.md new file mode 100644 index 0000000..90a4092 --- /dev/null +++ b/docs/api/axis-optimization.md @@ -0,0 +1,43 @@ +# Axis-optimization API + +```{eval-rst} +.. autofunction:: pyqsc_jax.stellarator_symmetric_variable_indices +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.search_axis +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.continue_axis_search +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.AxisSearchProblem + :members: +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.AxisSearchOptions + :members: +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.AxisSearchCandidate + :members: +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.AxisSearchResult + :members: +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.AxisSearchContinuation + :members: +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.LocalLeastSquaresReport + :members: +``` diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index 94cff98..f5ecefc 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -10,6 +10,7 @@ to the cited source, not to a duplicated derivation in this repository. | First-order QS and sigma equation | Landreman & Sengupta (2019), arXiv:1908.10253 | `first_order.solve_sigma`; pyQSC `solve_sigma_equation.py` | residual, convergence report, QA/QH/finite-current pyQSC values, JIT/VMAP/JVP/VJP, finite differences | implemented and documented | | Target-transform inverse solve and continuation | implicit-function reformulation of the first-order sigma equation | `inverse.solve_target_iota`; `continuation.continue_etabar_branch` | `etabar` and `I2` round trips, sign branches, distinct local basins, fold crossing, independent forward correction, r2 propagation, JIT/JVP/finite differences | branch-local inverse and fixed-step `etabar` pseudo-arclength implemented | | Nonconstant \(B_{20}\) and affine \(B_{2c}\) elimination | Landreman & Sengupta (2019), complete r2 system | `optimize.b20_diagnostics`; `optimize.optimize_B2c` | direct norm definitions, affine reconstruction, stationary optimum, circular degeneracy, spectral tail, doubled-grid verification, JIT/JVP/finite differences | implemented and documented | +| Branch-aware axis search | nonnegative \(B_{20}\) residual plus the package's traced r2 equations | `axis_optimization.search_axis`; `axis_optimization.continue_axis_search` | deterministic batched exploration, bounded LM steps, accepted/rejected damping, criteria failure, basin clustering, certified zero, nonzero best-found semantics, staged modes | implemented and documented | | Field gradient and `L_grad_B` | Landreman (2021), arXiv:2012.00865, Eq. 3.12 | `first_order.first_order_solution`; pyQSC `grad_B_tensor.py` | upstream arrays, vacuum symmetry/divergence, resolution convergence | implemented and documented | | Complete second-order coefficients | Landreman & Sengupta (2019), arXiv:1908.10253 | `second_order.solve_second_order`; pyQSC `calculate_r2.py`; manuscript Eqs. 36–54 | four independent equation residuals; vacuum QA, finite-pressure/current, QH upstream arrays; JIT/JVP/VJP/finite differences | implemented and documented | | Total field Hessian | manuscript Eqs. 55–83 | `field.total_field_jet`; pyQSC generated tensor as comparison only | regular-coordinate chain rule, JIT/JVP, QA and finite-current upstream arrays, full vacuum symmetry, divergence and derivative-of-divergence | implemented and documented | diff --git a/docs/index.md b/docs/index.md index 9c9290c..aa53f84 100644 --- a/docs/index.md +++ b/docs/index.md @@ -18,11 +18,13 @@ theory/third-order theory/inverse-solves theory/b20-optimization theory/criteria +theory/global-search theory/field-jet api/axis api/first-order api/continuation api/optimization +api/axis-optimization api/criteria api/second-order api/third-order @@ -52,9 +54,8 @@ The immutable first-order API, complete r2 coefficient solve, r3 flux constraint, magnetic shear, total-field Hessian, Mercier terms, and singular-radius diagnostics are validated, as are branch-local inverse solves. Pseudo-arclength branch continuation, exact affine \(B_{2c}\) optimization, -and the scalable Curvo et al. screening profile are also validated. -Multistart axis optimization and plasma/external field jets are under active -development. +the scalable Curvo et al. screening profile, and bounded multistart axis search +are also validated. Plasma/external field jets are under active development. The `pyqsc_jax.near_axis.near_axis` import remains supported for ESSOS without a runtime deprecation warning. diff --git a/docs/limitations.md b/docs/limitations.md index 984e8b1..8f2b7d6 100644 --- a/docs/limitations.md +++ b/docs/limitations.md @@ -10,8 +10,13 @@ Known limitations under active refactor include: - no plasma/external field-jet separation; - pseudo-arclength continuation currently traces `etabar` branches only and uses a fixed arclength step. -- no multistart axis optimization or basin enumeration yet; only the exact - affine `B2c` subproblem is eliminated. + +The bounded axis search is deterministic and enumerates distinct locally +refined basins, but a finite multistart budget is not an exhaustive proof over +a high-dimensional coefficient box. Only `verified_zero` certifies the known +zero lower bound of the nonnegative primary \(B_{20}\) residual. Built-in +secondary selectors currently rank the distinct primary-refined basins; they +do not carry a separate global certificate. `Criteria.from_curvo_2025` is a configurable reproduction of one published screening profile. Its thresholds are not hard-coded package-wide acceptance diff --git a/docs/quickstart.md b/docs/quickstart.md index 08e6d72..5b5bb61 100644 --- a/docs/quickstart.md +++ b/docs/quickstart.md @@ -142,6 +142,37 @@ print(report["B20_variation"].margin) Every threshold can be overridden. This report is a near-axis screening profile, not a proof of finite-radius equilibrium or coil feasibility. +## Bounded multistart axis search + +Choose explicit packed-axis coefficients and physical bounds: + +```python +axis = qsc.Axis( + rc=[1.0, 0.155, 0.0102], + zs=[0.0, 0.154, 0.0111], + nfp=2, +) +indices = qsc.stellarator_symmetric_variable_indices(axis, modes=(1,)) +problem = qsc.AxisSearchProblem( + axis=axis, + variable_indices=indices, + lower_bounds=[0.11, 0.11], + upper_bounds=[0.19, 0.19], + etabar=0.64, + selector="maximum_singular_radius", +) +result = qsc.search_axis(problem) + +print(result.status) +print(result.search_budget) +print(result.distinct_basins) +print(result.best.primary_residual) +``` + +Only `verified_zero` supplies a global certificate, and only for the +nonnegative primary \(B_{20}\) residual. `best_found` means exactly that: the +best distinct basin found within the reported finite budget. + ESSOS code can continue to use: ```python diff --git a/docs/theory/b20-optimization.md b/docs/theory/b20-optimization.md index 3db401e..ae2f04c 100644 --- a/docs/theory/b20-optimization.md +++ b/docs/theory/b20-optimization.md @@ -20,9 +20,10 @@ For positive quadrature weights \(w_j\), define `b20_diagnostics` also returns a smooth high-\(p\) norm, the sampled maximum, peak-to-peak variation, all nonzero toroidal Fourier coefficients, their norm, -and a high-mode tail ratio. The Fourier coefficients use direct weighted -quadrature in Boozer toroidal angle \(\varphi\), so they do not assume that the -uniform cylindrical-\(\phi\) samples are uniform in \(\varphi\). +their \(L^1\) certificate, and a high-mode tail ratio. The Fourier coefficients +use direct weighted quadrature in Boozer toroidal angle \(\varphi\), so they do +not assume that the uniform cylindrical-\(\phi\) samples are uniform in +\(\varphi\). ## Exact affine elimination @@ -78,5 +79,5 @@ Tests establish: - r3 and shear recomputation; - convergence of weighted and maximum residuals under grid refinement. -Multistart axis optimization and basin enumeration build on these residuals but -remain a separate milestone. +The branch-aware multistart workflow built on these residuals is described in +{doc}`global-search`. diff --git a/docs/theory/global-search.md b/docs/theory/global-search.md new file mode 100644 index 0000000..752d5fb --- /dev/null +++ b/docs/theory/global-search.md @@ -0,0 +1,83 @@ +# Branch-aware axis search + +## Objective and exact scalar elimination + +`search_axis` minimizes the full weighted, mean-free \(B_{20}\) residual on +the toroidal grid: + +\[ +r_j=\sqrt{\frac{w_j}{\sum_kw_k}}\, +\frac{B_{20,j}-\langle B_{20}\rangle_w}{B_0}. +\] + +It does not use a few hand-selected collocation points. At every axis +evaluation, \(B_{2c}\) is eliminated analytically before the residual is +formed. Target-transform problems use `solve_for="etabar"` or +`solve_for="I2"`, so the requested transform and the full sigma collocation +state are solved together on the selected branch. + +## Reproducible global-to-local workflow + +The implemented workflow is: + +1. include the supplied axis and any explicit branch-specific seeds; +2. fill the bounded coefficient box with a deterministic Halton sequence; +3. evaluate the coarse population with `jax.vmap`, replacing invalid + geometry or unconverged solves by an infinite score without contaminating + the batch with NaNs; +4. refine the best starts with a damped Gauss–Newton/Levenberg–Marquardt + iteration using the full JAX residual Jacobian; +5. cluster endpoints in normalized bounded-coordinate space; +6. apply hard geometry, solver, conditioning, and optional `Criteria` checks; +7. select lexicographically by primary tolerance and then by the requested + secondary selector; and +8. independently rebuild the selected physical candidate at the requested + toroidal resolutions. + +Every optimized variable is represented internally by a hyperbolic-tangent +map. Bounds are therefore never imposed by clipping a trial step. The width of +each coefficient interval supplies mode-aware variable scaling; callers should +tighten high-mode bounds as the Fourier order increases. + +`continue_axis_search` provides staged Fourier continuation. Each stage may +increase the retained mode count and `nphi`; all common Fourier coefficients +from the prior best basin warm-start the next stage. This is preferable to +activating many weakly resolved high modes at once. + +The built-in secondary selectors rank feasible basins by singular radius, +minimum first- or second-derivative scale length, maximum elongation, a +fourth-order axis Sobolev norm, distance from a target axis length, or minimum +normalized criteria margin. They are not silently mixed into the primary +quasisymmetry residual with arbitrary weights. + +## Status and global claims + +The result uses one of: + +- `verified_zero`; +- `best_found`; +- `no_feasible_candidate`; +- `branch_fold`; +- `ill_conditioned`; +- `solver_failure`; or +- `verification_failure`. + +`verified_zero` has one deliberately narrow meaning. The nonconstant +\(B_{20}\) residual is nonnegative, so a candidate whose weighted and maximum +residuals reach zero within the requested absolute, resolution, and spectral +tolerances attains the known global lower bound of that primary residual. The +flag does not certify that the secondary selector is globally optimal. + +Any nonzero result is `best_found` and reports its search budget and number of +distinct basins. It carries no global-minimum claim. A small coarse-grid value +that fails doubled-grid, maximum-error, or spectral-tail checks is +`verification_failure`. + +## High-frequency safeguards + +The search exposes coefficient bounds, bounded-coordinate scaling, staged +mode activation, a Sobolev selector, the complete nonzero Fourier spectrum, +its \(L^1\) certificate, tail ratio, and doubled/quadrupled-grid changes. +These controls are important because high-order axis optimization is +spectrally ill-conditioned: unresolved coefficients can move error between +collocation points without improving the continuous configuration. diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index 4784d66..2724bd3 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -1,6 +1,17 @@ """Differentiable near-axis stellarator construction in JAX.""" from pyqsc_jax.axis import Axis +from pyqsc_jax.axis_optimization import ( + AxisSearchCandidate, + AxisSearchContinuation, + AxisSearchOptions, + AxisSearchProblem, + AxisSearchResult, + LocalLeastSquaresReport, + continue_axis_search, + search_axis, + stellarator_symmetric_variable_indices, +) from pyqsc_jax.continuation import ContinuationResult, continue_etabar_branch from pyqsc_jax.criteria import Criteria, CriteriaReport, CriterionEvaluation from pyqsc_jax.diagnostics import mercier_diagnostics @@ -37,6 +48,11 @@ __all__ = [ "Axis", + "AxisSearchCandidate", + "AxisSearchContinuation", + "AxisSearchOptions", + "AxisSearchProblem", + "AxisSearchResult", "B2cOptimizationResult", "B20Diagnostics", "B20ResolutionVerification", @@ -47,6 +63,7 @@ "FieldJet", "InverseSolveDiagnostics", "LinearSolveReport", + "LocalLeastSquaresReport", "MercierDiagnostics", "NearAxisInputs", "NearAxisSolution", @@ -61,11 +78,14 @@ "near_axis", "b20_diagnostics", "continue_etabar_branch", + "continue_axis_search", "mercier_diagnostics", "second_order_residuals", + "search_axis", "solve", "solve_magnetic_shear", "singularity_diagnostics", + "stellarator_symmetric_variable_indices", "solve_third_order", "total_field_jet", "optimal_B2c_value", diff --git a/src/pyqsc_jax/axis_optimization.py b/src/pyqsc_jax/axis_optimization.py new file mode 100644 index 0000000..c83e001 --- /dev/null +++ b/src/pyqsc_jax/axis_optimization.py @@ -0,0 +1,736 @@ +"""Branch-aware global-to-local optimization of magnetic-axis coefficients.""" + +from __future__ import annotations + +from dataclasses import dataclass, replace +from math import sqrt +from typing import Literal + +import jax +import jax.numpy as jnp + +from pyqsc_jax.axis import Axis +from pyqsc_jax.criteria import Criteria, CriteriaReport +from pyqsc_jax.first_order import solve +from pyqsc_jax.models import NearAxisSolution +from pyqsc_jax.optimize import ( + B20Diagnostics, + B20ResolutionVerification, + optimize_B2c, + verify_B20_resolution, +) + +SearchStatus = Literal[ + "verified_zero", + "best_found", + "no_feasible_candidate", + "branch_fold", + "ill_conditioned", + "solver_failure", + "verification_failure", +] + +Selector = Literal[ + "maximum_singular_radius", + "maximum_minimum_L_grad_B", + "maximum_minimum_L_grad_grad_B", + "minimum_maximum_elongation", + "minimum_axis_sobolev_norm", + "target_axis_length", + "maximum_criteria_margin", +] + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class LocalLeastSquaresReport: + """Convergence and damping evidence for one local refinement.""" + + initial_residual_norm: jax.Array + residual_norm: jax.Array + gradient_infinity_norm: jax.Array + step_norm: jax.Array + damping: jax.Array + jacobian_condition_number: jax.Array + iterations: jax.Array + accepted_steps: jax.Array + rejected_steps: jax.Array + function_evaluations: jax.Array + converged: jax.Array + finite: jax.Array + + +@dataclass(frozen=True) +class AxisSearchProblem: + """Physical inputs, bounded axis variables, and branch policy.""" + + axis: Axis + variable_indices: tuple[int, ...] + lower_bounds: jax.Array + upper_bounds: jax.Array + etabar: float + B0: float = 1.0 + sigma0: float = 0.0 + I2: float = 0.0 + p2: float = 0.0 + B2s: float = 0.0 + nphi: int = 31 + sG: int = 1 + spsi: int = 1 + solve_for: str = "iota" + target_iota: float | None = None + criteria: Criteria | None = None + selector: Selector = "maximum_singular_radius" + target_axis_length: float | None = None + + +@dataclass(frozen=True) +class AxisSearchOptions: + """Deterministic exploration, local solve, clustering, and verification policy.""" + + coarse_samples: int = 32 + local_starts: int = 4 + maximum_iterations: int = 20 + initial_damping: float = 1.0e-3 + residual_tolerance: float = 1.0e-9 + gradient_tolerance: float = 1.0e-8 + step_tolerance: float = 1.0e-10 + primary_tolerance: float = 1.0e-6 + verified_zero_tolerance: float = 1.0e-8 + verification_relative_tolerance: float = 5.0e-3 + verification_tail_tolerance: float = 1.0e-6 + verification_multipliers: tuple[int, ...] = (1, 2, 4) + basin_distance_tolerance: float = 1.0e-3 + maximum_linear_condition_number: float = 1.0e14 + + +@dataclass(frozen=True) +class AxisSearchCandidate: + """One distinct locally refined basin and its independent checks.""" + + variables: jax.Array + solution: NearAxisSolution + diagnostics: B20Diagnostics + local_report: LocalLeastSquaresReport + criteria_report: CriteriaReport | None + verification: B20ResolutionVerification + primary_residual: float + selector_value: float + feasible: bool + + +@dataclass(frozen=True) +class AxisSearchResult: + """Reproducible search result with explicit global-certificate semantics.""" + + status: SearchStatus + best: AxisSearchCandidate | None + basins: tuple[AxisSearchCandidate, ...] + coarse_variables: jax.Array + coarse_residuals: jax.Array + coarse_feasible: jax.Array + search_budget: int + local_starts_attempted: int + distinct_basins: int + global_certificate: bool + message: str + + +@dataclass(frozen=True) +class AxisSearchContinuation: + """Warm-started low-to-high Fourier search stages.""" + + stages: tuple[AxisSearchResult, ...] + final: AxisSearchResult | None + complete: bool + + +def stellarator_symmetric_variable_indices( + axis: Axis, + *, + modes: tuple[int, ...] | None = None, +) -> tuple[int, ...]: + """Return packed indices for nonconstant ``rc`` and ``zs`` coefficients.""" + + if modes is None: + modes = tuple(range(1, axis.nfourier)) + if any( + not isinstance(mode, int) or isinstance(mode, bool) or mode < 1 or mode >= axis.nfourier + for mode in modes + ): + raise ValueError("modes must contain valid positive retained Fourier modes.") + zs_offset = 3 * axis.nfourier + return tuple(modes) + tuple(zs_offset + mode for mode in modes) + + +def _first_primes(count: int) -> tuple[int, ...]: + primes: list[int] = [] + candidate = 2 + while len(primes) < count: + if all(candidate % prime for prime in primes if prime <= sqrt(candidate)): + primes.append(candidate) + candidate += 1 + return tuple(primes) + + +def _radical_inverse(index: int, base: int) -> float: + result = 0.0 + fraction = 1.0 / base + while index: + result += fraction * (index % base) + index //= base + fraction /= base + return result + + +def _halton_box(count: int, dimension: int, dtype: jnp.dtype) -> jax.Array: + primes = _first_primes(dimension) + values = [[_radical_inverse(sample + 1, base) for base in primes] for sample in range(count)] + return jnp.asarray(values, dtype=dtype) + + +def _validate_problem(problem: AxisSearchProblem, options: AxisSearchOptions) -> None: + indices = problem.variable_indices + if not indices or len(set(indices)) != len(indices): + raise ValueError("variable_indices must be nonempty and unique.") + if any( + not isinstance(index, int) + or isinstance(index, bool) + or index < 0 + or index >= problem.axis.dofs.size + for index in indices + ): + raise ValueError("variable_indices contains an invalid packed-axis index.") + lower = jnp.asarray(problem.lower_bounds) + upper = jnp.asarray(problem.upper_bounds) + if lower.shape != (len(indices),) or upper.shape != (len(indices),): + raise ValueError("lower_bounds and upper_bounds must match variable_indices.") + if not bool(jnp.all(jnp.isfinite(lower) & jnp.isfinite(upper) & (lower < upper))): + raise ValueError("Every variable bound must be finite and strictly ordered.") + initial = problem.axis.dofs[jnp.asarray(indices)] + if not bool(jnp.all((initial > lower) & (initial < upper))): + raise ValueError("The initial axis variables must lie strictly inside their bounds.") + if problem.nphi < 3 or problem.nphi % 2 != 1: + raise ValueError("nphi must be an odd integer >= 3.") + if problem.solve_for == "iota": + if problem.target_iota is not None: + raise ValueError("target_iota requires solve_for='etabar' or solve_for='I2'.") + elif problem.solve_for in ("etabar", "I2"): + if problem.target_iota is None: + raise ValueError("target_iota is required for an inverse solve.") + else: + raise ValueError("solve_for must be 'iota', 'etabar', or 'I2'.") + if problem.selector == "target_axis_length" and problem.target_axis_length is None: + raise ValueError("target_axis_length is required by the selected policy.") + if problem.selector == "maximum_criteria_margin" and problem.criteria is None: + raise ValueError("maximum_criteria_margin requires a criteria profile.") + if problem.selector not in ( + "maximum_singular_radius", + "maximum_minimum_L_grad_B", + "maximum_minimum_L_grad_grad_B", + "minimum_maximum_elongation", + "minimum_axis_sobolev_norm", + "target_axis_length", + "maximum_criteria_margin", + ): + raise ValueError("Unknown canonical selector.") + + positive_integers = ( + options.coarse_samples, + options.local_starts, + options.maximum_iterations, + ) + if any( + not isinstance(value, int) or isinstance(value, bool) or value < 1 + for value in positive_integers + ): + raise ValueError("Search sample, start, and iteration counts must be positive integers.") + positive_values = ( + options.initial_damping, + options.residual_tolerance, + options.gradient_tolerance, + options.step_tolerance, + options.primary_tolerance, + options.verified_zero_tolerance, + options.verification_relative_tolerance, + options.verification_tail_tolerance, + options.basin_distance_tolerance, + options.maximum_linear_condition_number, + ) + if any(value <= 0 for value in positive_values): + raise ValueError("Search tolerances, damping, and condition limit must be positive.") + if not options.verification_multipliers: + raise ValueError("verification_multipliers must be nonempty.") + + +def _physical_from_internal( + internal: jax.Array, + lower: jax.Array, + upper: jax.Array, +) -> jax.Array: + midpoint = 0.5 * (lower + upper) + half_width = 0.5 * (upper - lower) + return midpoint + half_width * jnp.tanh(internal) + + +def _internal_from_physical( + physical: jax.Array, + lower: jax.Array, + upper: jax.Array, +) -> jax.Array: + midpoint = 0.5 * (lower + upper) + half_width = 0.5 * (upper - lower) + return jnp.arctanh((physical - midpoint) / half_width) + + +def _solve_axis_candidate( + problem: AxisSearchProblem, + variables: jax.Array, +) -> tuple[NearAxisSolution, B20Diagnostics]: + indices = jnp.asarray(problem.variable_indices) + axis = problem.axis.with_dofs(problem.axis.dofs.at[indices].set(variables)) + keyword_arguments = { + "axis": axis, + "etabar": problem.etabar, + "B0": problem.B0, + "sigma0": problem.sigma0, + "I2": problem.I2, + "p2": problem.p2, + "B2c": 0.0, + "B2s": problem.B2s, + "nphi": problem.nphi, + "order": "r2", + "sG": problem.sG, + "spsi": problem.spsi, + "solve_for": problem.solve_for, + } + if problem.solve_for != "iota": + keyword_arguments["iota"] = problem.target_iota + optimized = optimize_B2c(solve(**keyword_arguments)) + return optimized.solution, optimized.diagnostics + + +def _projected_residual( + problem: AxisSearchProblem, + variables: jax.Array, +) -> jax.Array: + solution, diagnostics = _solve_axis_candidate(problem, variables) + weights = solution.geometry.d_l_d_phi + return jnp.sqrt(weights / jnp.sum(weights)) * diagnostics.anomaly / solution.inputs.B0 + + +def _coarse_metrics( + problem: AxisSearchProblem, + variables: jax.Array, +) -> tuple[jax.Array, jax.Array]: + solution, diagnostics = _solve_axis_candidate(problem, variables) + finite = ( + jnp.isfinite(diagnostics.weighted_l2) + & solution.root_report.converged + & solution.linear_report.converged + & solution.geometry.diagnostics.frenet_valid + & solution.geometry.diagnostics.cylindrical_coordinates_valid + ) + return jnp.where(finite, diagnostics.weighted_l2, jnp.inf), finite + + +def _levenberg_marquardt( + residual_function, + initial: jax.Array, + options: AxisSearchOptions, +) -> tuple[jax.Array, LocalLeastSquaresReport]: + residual_and_jacobian = jax.jit( + lambda value: (residual_function(value), jax.jacrev(residual_function)(value)) + ) + residual = jax.jit(residual_function) + internal = initial + current_residual, jacobian = residual_and_jacobian(internal) + initial_norm = jnp.linalg.norm(current_residual) + damping = options.initial_damping + accepted = 0 + rejected = 0 + function_evaluations = 1 + converged = False + step_norm = jnp.asarray(jnp.inf, dtype=initial.dtype) + gradient_norm = jnp.asarray(jnp.inf, dtype=initial.dtype) + + for _iteration in range(1, options.maximum_iterations + 1): + normal_matrix = jacobian.T @ jacobian + gradient = jacobian.T @ current_residual + gradient_norm = jnp.linalg.norm(gradient, ord=jnp.inf) + diagonal_scale = jnp.maximum(jnp.diag(normal_matrix), 1.0) + step = -jnp.linalg.solve( + normal_matrix + damping * jnp.diag(diagonal_scale), + gradient, + ) + step_norm = jnp.linalg.norm(step) + candidate = internal + step + candidate_residual = residual(candidate) + function_evaluations += 1 + current_cost = 0.5 * jnp.sum(current_residual**2) + candidate_cost = 0.5 * jnp.sum(candidate_residual**2) + predicted_reduction = -gradient @ step - 0.5 * step @ normal_matrix @ step + ratio = (current_cost - candidate_cost) / jnp.maximum( + predicted_reduction, + jnp.finfo(current_cost.dtype).tiny, + ) + accept = bool( + jnp.isfinite(candidate_cost) + & jnp.isfinite(step_norm) + & (candidate_cost < current_cost) + & (ratio > 0) + ) + if accept: + internal = candidate + current_residual, jacobian = residual_and_jacobian(internal) + function_evaluations += 1 + accepted += 1 + damping = jnp.maximum( + damping * jnp.maximum(1 / 3, 1 - (2 * ratio - 1) ** 3), + jnp.finfo(current_cost.dtype).eps, + ) + else: + rejected += 1 + damping = damping * 2 + + residual_norm = jnp.linalg.norm(current_residual) + converged = bool( + (residual_norm <= options.residual_tolerance) + | (gradient_norm <= options.gradient_tolerance) + | (step_norm <= options.step_tolerance * (1 + jnp.linalg.norm(internal))) + ) + if converged: + break + + normal_singular_values = jnp.linalg.svd(jacobian, compute_uv=False) + tiny = jnp.finfo(jacobian.dtype).tiny + condition_number = normal_singular_values[0] / jnp.maximum( + normal_singular_values[-1], + tiny, + ) + finite = ( + jnp.all(jnp.isfinite(internal)) + & jnp.all(jnp.isfinite(current_residual)) + & jnp.isfinite(condition_number) + ) + return internal, LocalLeastSquaresReport( + initial_residual_norm=initial_norm, + residual_norm=jnp.linalg.norm(current_residual), + gradient_infinity_norm=gradient_norm, + step_norm=step_norm, + damping=jnp.asarray(damping), + jacobian_condition_number=condition_number, + iterations=jnp.asarray(_iteration), + accepted_steps=jnp.asarray(accepted), + rejected_steps=jnp.asarray(rejected), + function_evaluations=jnp.asarray(function_evaluations), + converged=jnp.asarray(converged), + finite=finite, + ) + + +def _axis_sobolev_norm(axis: Axis) -> jax.Array: + modes = jnp.arange(axis.nfourier, dtype=axis.dofs.dtype) + weights = (1 + modes**2) ** 2 + return jnp.sqrt(jnp.sum(weights * (axis.rc**2 + axis.rs**2 + axis.zc**2 + axis.zs**2))) + + +def _selector_value( + problem: AxisSearchProblem, + solution: NearAxisSolution, + criteria_report: CriteriaReport | None, +) -> float: + if problem.selector == "maximum_singular_radius": + value = solution.r_singularity + elif problem.selector == "maximum_minimum_L_grad_B": + value = jnp.min(solution.L_grad_B) + elif problem.selector == "maximum_minimum_L_grad_grad_B": + value = jnp.min(solution.L_grad_grad_B) + elif problem.selector == "minimum_maximum_elongation": + value = -jnp.max(solution.elongation) + elif problem.selector == "minimum_axis_sobolev_norm": + value = -_axis_sobolev_norm(solution.inputs.axis) + elif problem.selector == "target_axis_length": + value = -jnp.abs(solution.axis_length - problem.target_axis_length) + else: + normalized_margins = [ + evaluation.margin / jnp.maximum(jnp.abs(evaluation.threshold), 1.0) + for evaluation in criteria_report.evaluations + ] + value = jnp.min(jnp.stack(normalized_margins)) + return float(value) + + +def _candidate_is_distinct( + variables: jax.Array, + candidates: list[AxisSearchCandidate], + lower: jax.Array, + upper: jax.Array, + tolerance: float, +) -> bool: + scaled = (variables - lower) / (upper - lower) + return all( + float(jnp.linalg.norm(scaled - (candidate.variables - lower) / (upper - lower))) > tolerance + for candidate in candidates + ) + + +def _copy_retained_axis_modes(source: Axis, target: Axis) -> Axis: + if source.nfp != target.nfp: + raise ValueError("Fourier continuation stages must use the same nfp.") + retained = min(source.nfourier, target.nfourier) + return Axis( + rc=target.rc.at[:retained].set(source.rc[:retained]), + rs=target.rs.at[:retained].set(source.rs[:retained]), + zc=target.zc.at[:retained].set(source.zc[:retained]), + zs=target.zs.at[:retained].set(source.zs[:retained]), + nfp=target.nfp, + ) + + +def _verification_passes( + verification: B20ResolutionVerification, + options: AxisSearchOptions, +) -> bool: + weighted_zero = verification.weighted_l2 <= options.verified_zero_tolerance + maximum_zero = verification.grid_maximum <= options.verified_zero_tolerance + relative_l2_stable = ( + verification.relative_weighted_l2_change <= options.verification_relative_tolerance + ) | weighted_zero + relative_maximum_stable = ( + verification.relative_grid_maximum_change <= options.verification_relative_tolerance + ) | maximum_zero + spectral_tail_resolved = ( + verification.fourier_tail_ratio[-1] <= options.verification_tail_tolerance + ) | maximum_zero[-1] + return bool( + jnp.all(weighted_zero) + & jnp.all(maximum_zero) + & jnp.all(relative_l2_stable) + & jnp.all(relative_maximum_stable) + & spectral_tail_resolved + ) + + +def search_axis( + problem: AxisSearchProblem, + *, + options: AxisSearchOptions | None = None, + seeds: tuple[jax.Array, ...] = (), +) -> AxisSearchResult: + """Explore, refine, cluster, and independently verify bounded axis candidates.""" + + if options is None: + options = AxisSearchOptions() + _validate_problem(problem, options) + lower = jnp.asarray(problem.lower_bounds, dtype=problem.axis.dofs.dtype) + upper = jnp.asarray(problem.upper_bounds, dtype=problem.axis.dofs.dtype) + initial = problem.axis.dofs[jnp.asarray(problem.variable_indices)] + for seed in seeds: + seed_array = jnp.asarray(seed) + if seed_array.shape != initial.shape or not bool( + jnp.all(jnp.isfinite(seed_array) & (seed_array > lower) & (seed_array < upper)) + ): + raise ValueError("Every explicit seed must be finite, in bounds, and correctly sized.") + + samples = lower + (upper - lower) * _halton_box( + options.coarse_samples, + len(problem.variable_indices), + initial.dtype, + ) + explicit = jnp.stack((initial, *(jnp.asarray(seed) for seed in seeds))) + coarse_variables = jnp.concatenate((explicit, samples), axis=0) + coarse_residuals, coarse_feasible = jax.jit( + jax.vmap(lambda variables: _coarse_metrics(problem, variables)) + )(coarse_variables) + + finite_indices = [ + int(index) for index in jnp.argsort(coarse_residuals) if bool(coarse_feasible[index]) + ] + selected_indices = finite_indices[: options.local_starts] + if not selected_indices: + return AxisSearchResult( + status="solver_failure", + best=None, + basins=(), + coarse_variables=coarse_variables, + coarse_residuals=coarse_residuals, + coarse_feasible=coarse_feasible, + search_budget=int(coarse_variables.shape[0]), + local_starts_attempted=0, + distinct_basins=0, + global_certificate=False, + message="No coarse candidate produced a finite converged near-axis solve.", + ) + + residual_function = lambda internal: _projected_residual( # noqa: E731 + problem, + _physical_from_internal(internal, lower, upper), + ) + candidates: list[AxisSearchCandidate] = [] + local_evaluations = 0 + ill_conditioned_count = 0 + for index in selected_indices: + start = coarse_variables[index] + internal_start = _internal_from_physical(start, lower, upper) + internal, local_report = _levenberg_marquardt( + residual_function, + internal_start, + options, + ) + local_evaluations += int(local_report.function_evaluations) + variables = _physical_from_internal(internal, lower, upper) + if not bool(local_report.finite): + continue + solution, diagnostics = _solve_axis_candidate(problem, variables) + if solution.linear_report.matrix_condition_number > options.maximum_linear_condition_number: + ill_conditioned_count += 1 + continue + criteria_report = None if problem.criteria is None else problem.criteria.evaluate(solution) + feasible = bool( + solution.root_report.converged + & solution.linear_report.converged + & solution.geometry.diagnostics.frenet_valid + & solution.geometry.diagnostics.cylindrical_coordinates_valid + ) and (criteria_report is None or criteria_report.passed) + if not _candidate_is_distinct( + variables, + candidates, + lower, + upper, + options.basin_distance_tolerance, + ): + continue + verification = verify_B20_resolution( + solution, + multipliers=options.verification_multipliers, + ) + candidates.append( + AxisSearchCandidate( + variables=variables, + solution=solution, + diagnostics=diagnostics, + local_report=local_report, + criteria_report=criteria_report, + verification=verification, + primary_residual=float(diagnostics.weighted_l2), + selector_value=_selector_value(problem, solution, criteria_report), + feasible=feasible, + ) + ) + + search_budget = int(coarse_variables.shape[0]) + local_evaluations + if not candidates: + status: SearchStatus = ( + "ill_conditioned" + if ill_conditioned_count == len(selected_indices) + else "solver_failure" + ) + return AxisSearchResult( + status=status, + best=None, + basins=(), + coarse_variables=coarse_variables, + coarse_residuals=coarse_residuals, + coarse_feasible=coarse_feasible, + search_budget=search_budget, + local_starts_attempted=len(selected_indices), + distinct_basins=0, + global_certificate=False, + message="Local refinement did not produce a finite, acceptable candidate.", + ) + + feasible = [candidate for candidate in candidates if candidate.feasible] + if not feasible: + best = min(candidates, key=lambda candidate: candidate.primary_residual) + return AxisSearchResult( + status="no_feasible_candidate", + best=best, + basins=tuple(candidates), + coarse_variables=coarse_variables, + coarse_residuals=coarse_residuals, + coarse_feasible=coarse_feasible, + search_budget=search_budget, + local_starts_attempted=len(selected_indices), + distinct_basins=len(candidates), + global_certificate=False, + message="The search found converged basins, but none passed the hard criteria.", + ) + + primary_feasible = [ + candidate + for candidate in feasible + if candidate.primary_residual <= options.primary_tolerance + ] + if primary_feasible: + best = max(primary_feasible, key=lambda candidate: candidate.selector_value) + else: + best = min(feasible, key=lambda candidate: candidate.primary_residual) + + if best.solution.inverse is not None and bool(best.solution.branch_fold): + status = "branch_fold" + message = "The selected inverse-solve candidate lies at a detected branch fold." + elif best.primary_residual <= options.verified_zero_tolerance: + if _verification_passes(best.verification, options): + status = "verified_zero" + message = ( + "The independently verified nonnegative B20 residual reaches its " + "global lower bound of zero within the requested tolerances." + ) + else: + status = "verification_failure" + message = "The nominal zero failed independent resolution or spectral checks." + else: + status = "best_found" + message = ( + "This is the best basin found within the reported search budget; " + "there is no global-minimum certificate." + ) + return AxisSearchResult( + status=status, + best=best, + basins=tuple(candidates), + coarse_variables=coarse_variables, + coarse_residuals=coarse_residuals, + coarse_feasible=coarse_feasible, + search_budget=search_budget, + local_starts_attempted=len(selected_indices), + distinct_basins=len(candidates), + global_certificate=status == "verified_zero", + message=message, + ) + + +def continue_axis_search( + stages: tuple[AxisSearchProblem, ...], + *, + options: AxisSearchOptions | None = None, + initial_seeds: tuple[jax.Array, ...] = (), +) -> AxisSearchContinuation: + """Warm-start successively richer Fourier problems from the prior best basin.""" + + if not stages: + raise ValueError("At least one Fourier-continuation stage is required.") + results: list[AxisSearchResult] = [] + previous_solution: NearAxisSolution | None = None + for stage_index, stage in enumerate(stages): + if previous_solution is not None: + stage = replace( + stage, + axis=_copy_retained_axis_modes(previous_solution.inputs.axis, stage.axis), + ) + result = search_axis( + stage, + options=options, + seeds=initial_seeds if stage_index == 0 else (), + ) + results.append(result) + if result.best is None: + break + previous_solution = result.best.solution + complete = len(results) == len(stages) and all(result.best is not None for result in results) + return AxisSearchContinuation( + stages=tuple(results), + final=results[-1] if results else None, + complete=complete, + ) diff --git a/src/pyqsc_jax/optimize.py b/src/pyqsc_jax/optimize.py index 42efe48..90feaa0 100644 --- a/src/pyqsc_jax/optimize.py +++ b/src/pyqsc_jax/optimize.py @@ -26,6 +26,7 @@ class B20Diagnostics: fourier_modes: jax.Array fourier_coefficients: jax.Array nonzero_fourier_norm: jax.Array + nonzero_fourier_l1: jax.Array fourier_tail_ratio: jax.Array smooth_maximum_power: int @@ -55,6 +56,7 @@ class B20ResolutionVerification: smooth_maximum: jax.Array grid_maximum: jax.Array peak_to_peak: jax.Array + nonzero_fourier_l1: jax.Array fourier_tail_ratio: jax.Array relative_weighted_l2_change: jax.Array relative_grid_maximum_change: jax.Array @@ -95,6 +97,7 @@ def b20_diagnostics( coefficients = jnp.sum(weights[None, :] * anomaly[None, :] * phase, axis=1) / weight_sum coefficient_power = jnp.abs(coefficients / B0) ** 2 nonzero_fourier_norm = jnp.sqrt(2 * jnp.sum(coefficient_power)) + nonzero_fourier_l1 = 2 * jnp.sum(jnp.abs(coefficients / B0)) tail_start = maximum_mode * 3 // 4 tiny = jnp.finfo(B20.dtype).tiny fourier_tail_ratio = jnp.sqrt( @@ -110,6 +113,7 @@ def b20_diagnostics( fourier_modes=modes, fourier_coefficients=coefficients, nonzero_fourier_norm=nonzero_fourier_norm, + nonzero_fourier_l1=nonzero_fourier_l1, fourier_tail_ratio=fourier_tail_ratio, smooth_maximum_power=smooth_maximum_power, ) @@ -244,6 +248,7 @@ def verify_B20_resolution( smooth_maximum = jnp.stack(tuple(item.smooth_maximum for item in diagnostics)) grid_maximum = jnp.stack(tuple(item.grid_maximum for item in diagnostics)) peak_to_peak = jnp.stack(tuple(item.peak_to_peak for item in diagnostics)) + nonzero_fourier_l1 = jnp.stack(tuple(item.nonzero_fourier_l1 for item in diagnostics)) tail_ratio = jnp.stack(tuple(item.fourier_tail_ratio for item in diagnostics)) tiny = jnp.finfo(weighted_l2.dtype).tiny relative_l2_change = jnp.concatenate( @@ -264,6 +269,7 @@ def verify_B20_resolution( smooth_maximum=smooth_maximum, grid_maximum=grid_maximum, peak_to_peak=peak_to_peak, + nonzero_fourier_l1=nonzero_fourier_l1, fourier_tail_ratio=tail_ratio, relative_weighted_l2_change=relative_l2_change, relative_grid_maximum_change=relative_maximum_change, diff --git a/tests/physics/test_axis_optimization.py b/tests/physics/test_axis_optimization.py new file mode 100644 index 0000000..5fb2ddc --- /dev/null +++ b/tests/physics/test_axis_optimization.py @@ -0,0 +1,423 @@ +from __future__ import annotations + +from dataclasses import replace + +import jax.numpy as jnp +import numpy as np +import pytest + +import pyqsc_jax as qsc +from pyqsc_jax.axis_optimization import ( + _candidate_is_distinct, + _copy_retained_axis_modes, + _halton_box, + _internal_from_physical, + _physical_from_internal, + _selector_value, + _validate_problem, + _verification_passes, +) + + +def circular_problem(**overrides): + parameters = { + "axis": qsc.Axis(rc=[1.0], zs=[0.0], nfp=1), + "variable_indices": (0,), + "lower_bounds": jnp.asarray([0.8]), + "upper_bounds": jnp.asarray([1.2]), + "etabar": 1.0, + "I2": 0.1, + "nphi": 15, + } + parameters.update(overrides) + return qsc.AxisSearchProblem(**parameters) + + +def small_options(**overrides): + parameters = { + "coarse_samples": 2, + "local_starts": 1, + "maximum_iterations": 2, + "verification_multipliers": (1, 2), + "verified_zero_tolerance": 1.0e-10, + "verification_tail_tolerance": 1.0e-8, + } + parameters.update(overrides) + return qsc.AxisSearchOptions(**parameters) + + +def test_stellarator_symmetric_indices_and_low_discrepancy_box(): + axis = qsc.Axis(rc=[1.0, 0.1, 0.01], zs=[0.0, -0.1, 0.02], nfp=3) + + assert qsc.stellarator_symmetric_variable_indices(axis) == (1, 2, 10, 11) + assert qsc.stellarator_symmetric_variable_indices(axis, modes=(2,)) == (2, 11) + with pytest.raises(ValueError, match="modes"): + qsc.stellarator_symmetric_variable_indices(axis, modes=(0,)) + with pytest.raises(ValueError, match="modes"): + qsc.stellarator_symmetric_variable_indices(axis, modes=(3,)) + samples = _halton_box(3, 3, jnp.float64) + np.testing.assert_allclose( + samples, + [ + [0.5, 1 / 3, 0.2], + [0.25, 2 / 3, 0.4], + [0.75, 1 / 9, 0.6], + ], + ) + + +def test_bound_transform_round_trip_and_strict_interior(): + lower = jnp.asarray([-2.0, 1.0]) + upper = jnp.asarray([4.0, 5.0]) + physical = jnp.asarray([-1.0, 4.0]) + internal = _internal_from_physical(physical, lower, upper) + reconstructed = _physical_from_internal(internal, lower, upper) + + np.testing.assert_allclose(reconstructed, physical) + assert np.all(np.asarray(reconstructed) > np.asarray(lower)) + assert np.all(np.asarray(reconstructed) < np.asarray(upper)) + + +def test_fourier_continuation_copies_retained_modes_and_runs_stages(): + low_axis = qsc.Axis(rc=[1.0], zs=[0.0], nfp=1) + high_axis = qsc.Axis(rc=[0.9, 0.0], zs=[0.0, 0.0], nfp=1) + copied = _copy_retained_axis_modes(low_axis, high_axis) + np.testing.assert_allclose(copied.rc, [1.0, 0.0]) + with pytest.raises(ValueError, match="same nfp"): + _copy_retained_axis_modes(low_axis, replace(high_axis, nfp=2)) + + stages = ( + circular_problem(axis=low_axis, nphi=15), + qsc.AxisSearchProblem( + axis=high_axis, + variable_indices=(1, 7), + lower_bounds=jnp.asarray([-0.01, -0.01]), + upper_bounds=jnp.asarray([0.01, 0.01]), + etabar=1.0, + I2=0.1, + nphi=15, + ), + ) + continuation = qsc.continue_axis_search( + stages, + options=small_options( + coarse_samples=1, + maximum_iterations=1, + verification_multipliers=(1,), + ), + ) + + assert continuation.complete + assert len(continuation.stages) == 2 + assert continuation.final is continuation.stages[-1] + assert continuation.final.best is not None + np.testing.assert_allclose(continuation.final.best.solution.axis.rc[0], 1.0) + + +def test_search_certifies_only_the_verified_nonnegative_zero(): + result = qsc.search_axis(circular_problem(), options=small_options()) + + assert result.status == "verified_zero" + assert result.global_certificate + assert "global lower bound" in result.message + assert result.best is not None + assert result.best.feasible + assert result.best.primary_residual < 1.0e-12 + assert result.best.local_report.converged + assert result.best.local_report.rejected_steps >= 1 + assert result.local_starts_attempted == 1 + assert result.distinct_basins == 1 + assert result.search_budget == 3 + int(result.best.local_report.function_evaluations) + np.testing.assert_allclose(result.coarse_variables[0], [1.0]) + assert np.all(np.asarray(result.coarse_feasible)) + assert not _candidate_is_distinct( + result.best.variables, + [result.best], + jnp.asarray([0.8]), + jnp.asarray([1.2]), + 1.0e-3, + ) + + +def test_search_failure_and_ill_conditioning_are_distinct_statuses(): + coarse_failure = qsc.search_axis( + circular_problem(etabar=0.0), + options=small_options( + coarse_samples=1, + verification_multipliers=(1,), + ), + ) + assert coarse_failure.status == "solver_failure" + assert coarse_failure.best is None + assert coarse_failure.local_starts_attempted == 0 + + local_failure = qsc.search_axis( + circular_problem(nphi=7), + options=small_options( + coarse_samples=1, + maximum_iterations=1, + verification_multipliers=(1,), + ), + ) + assert local_failure.status == "solver_failure" + assert local_failure.best is None + assert local_failure.local_starts_attempted == 1 + + ill_conditioned = qsc.search_axis( + circular_problem(), + options=small_options( + coarse_samples=1, + maximum_iterations=1, + verification_multipliers=(1,), + maximum_linear_condition_number=1.0e-30, + ), + ) + assert ill_conditioned.status == "ill_conditioned" + assert ill_conditioned.best is None + assert ill_conditioned.local_starts_attempted == 1 + + +def test_search_reports_no_feasible_candidate_for_failed_hard_profile(): + impossible = qsc.Criteria.from_curvo_2025(minimum_abs_iota=2.0) + result = qsc.search_axis( + circular_problem( + criteria=impossible, + selector="maximum_criteria_margin", + ), + options=small_options(verification_multipliers=(1,)), + seeds=(jnp.asarray([0.9]),), + ) + + assert result.status == "no_feasible_candidate" + assert not result.global_certificate + assert result.best is not None + assert not result.best.feasible + assert result.best.criteria_report is not None + assert not result.best.criteria_report.passed + assert result.coarse_variables.shape == (4, 1) + + +def test_nonzero_search_improves_locally_without_global_claim(): + axis = qsc.Axis( + rc=[1.0, 0.155, 0.0102], + zs=[0.0, 0.154, 0.0111], + nfp=2, + ) + indices = qsc.stellarator_symmetric_variable_indices(axis, modes=(1,)) + problem = qsc.AxisSearchProblem( + axis=axis, + variable_indices=indices, + lower_bounds=jnp.asarray([0.11, 0.11]), + upper_bounds=jnp.asarray([0.19, 0.19]), + etabar=0.64, + nphi=15, + selector="minimum_maximum_elongation", + ) + result = qsc.search_axis( + problem, + options=small_options( + coarse_samples=2, + maximum_iterations=3, + verified_zero_tolerance=1.0e-8, + verification_tail_tolerance=1.0, + verification_multipliers=(1,), + ), + ) + + assert result.status == "best_found" + assert not result.global_certificate + assert "no global-minimum certificate" in result.message + assert result.best.primary_residual < result.coarse_residuals[0] + assert result.best.local_report.accepted_steps >= 1 + assert result.best.selector_value < 0 + + +def test_verification_rejects_an_underresolved_nominal_zero(): + solution = qsc.optimize_B2c( + qsc.Qsc( + rc=[1.0, 0.155, 0.0102], + zs=[0.0, 0.154, 0.0111], + nfp=2, + etabar=0.64, + nphi=15, + order="r2", + ) + ).solution + verification = qsc.verify_B20_resolution(solution, multipliers=(1, 2)) + + assert not _verification_passes( + verification, + small_options( + verified_zero_tolerance=0.05, + verification_relative_tolerance=1.0e-6, + verification_tail_tolerance=1.0e-6, + ), + ) + + +def test_every_canonical_selector_has_documented_orientation(): + solution = qsc.Qsc( + rc=[1.0, 0.09], + zs=[0.0, -0.09], + nfp=2, + etabar=0.95, + I2=0.9, + p2=-600000.0, + B2c=-0.7, + nphi=15, + order="r2", + ) + criteria = qsc.Criteria.from_curvo_2025() + report = criteria.evaluate(solution) + base = circular_problem(axis=solution.axis, variable_indices=(1,)) + + np.testing.assert_allclose( + _selector_value( + replace(base, selector="maximum_singular_radius"), + solution, + report, + ), + solution.r_singularity, + ) + np.testing.assert_allclose( + _selector_value( + replace(base, selector="maximum_minimum_L_grad_B"), + solution, + report, + ), + np.min(solution.L_grad_B), + ) + np.testing.assert_allclose( + _selector_value( + replace(base, selector="maximum_minimum_L_grad_grad_B"), + solution, + report, + ), + np.min(solution.L_grad_grad_B), + ) + np.testing.assert_allclose( + _selector_value( + replace(base, selector="minimum_maximum_elongation"), + solution, + report, + ), + -np.max(solution.elongation), + ) + assert ( + _selector_value( + replace(base, selector="minimum_axis_sobolev_norm"), + solution, + report, + ) + < 0 + ) + assert ( + _selector_value( + replace( + base, + selector="target_axis_length", + target_axis_length=float(solution.axis_length), + ), + solution, + report, + ) + == 0 + ) + assert np.isfinite( + _selector_value( + replace( + base, + criteria=criteria, + selector="maximum_criteria_margin", + ), + solution, + report, + ) + ) + + +@pytest.mark.parametrize( + ("problem", "options", "message"), + [ + (circular_problem(variable_indices=()), small_options(), "variable_indices"), + ( + circular_problem(variable_indices=(0, 0)), + small_options(), + "variable_indices", + ), + (circular_problem(variable_indices=(4,)), small_options(), "variable_indices"), + (circular_problem(lower_bounds=[0.8, 0.9]), small_options(), "bounds"), + (circular_problem(lower_bounds=[1.2]), small_options(), "strictly ordered"), + (circular_problem(lower_bounds=[1.0]), small_options(), "strictly inside"), + (circular_problem(nphi=4), small_options(), "nphi"), + ( + circular_problem(target_iota=0.1), + small_options(), + "target_iota", + ), + ( + circular_problem(solve_for="etabar"), + small_options(), + "target_iota", + ), + ( + circular_problem(solve_for="bad"), + small_options(), + "solve_for", + ), + ( + circular_problem(selector="target_axis_length"), + small_options(), + "target_axis_length", + ), + ( + circular_problem(selector="maximum_criteria_margin"), + small_options(), + "criteria", + ), + ( + circular_problem(selector="bad"), + small_options(), + "selector", + ), + ( + circular_problem(), + small_options(coarse_samples=0), + "positive integers", + ), + ( + circular_problem(), + small_options(initial_damping=0.0), + "must be positive", + ), + ( + circular_problem(), + small_options(verification_multipliers=()), + "nonempty", + ), + ], +) +def test_search_policy_guards(problem, options, message): + with pytest.raises(ValueError, match=message): + _validate_problem(problem, options) + + +def test_valid_inverse_search_policy_reaches_post_branch_validation(): + _validate_problem( + circular_problem( + solve_for="I2", + target_iota=0.1, + ), + small_options(), + ) + + +def test_explicit_seed_guard(): + with pytest.raises(ValueError, match="explicit seed"): + qsc.search_axis( + circular_problem(), + options=small_options(), + seeds=(jnp.asarray([1.3]),), + ) + with pytest.raises(ValueError, match="At least one"): + qsc.continue_axis_search(()) diff --git a/tests/physics/test_b20_optimization.py b/tests/physics/test_b20_optimization.py index d8e87f8..d390302 100644 --- a/tests/physics/test_b20_optimization.py +++ b/tests/physics/test_b20_optimization.py @@ -49,6 +49,10 @@ def test_dense_B20_diagnostics_match_direct_definitions(): assert diagnostics.smooth_maximum_power == 12 assert diagnostics.fourier_modes.shape == (15,) assert diagnostics.fourier_coefficients.shape == (15,) + np.testing.assert_allclose( + diagnostics.nonzero_fourier_l1, + 2 * np.sum(np.abs(diagnostics.fourier_coefficients / solution.inputs.B0)), + ) assert diagnostics.weighted_l2 <= diagnostics.smooth_maximum <= diagnostics.grid_maximum assert 0 <= float(diagnostics.fourier_tail_ratio) <= 1 @@ -125,6 +129,7 @@ def test_resolution_verification_recomputes_fixed_candidate(): np.testing.assert_allclose(verification.weighted_l2[0], result.diagnostics.weighted_l2) assert verification.relative_weighted_l2_change[1] < 2.0e-6 assert verification.fourier_tail_ratio[1] < verification.fourier_tail_ratio[0] + assert np.all(np.asarray(verification.nonzero_fourier_l1) >= 0) assert verification.relative_grid_maximum_change[1] < 0.03 From d46b2bcf3a9c88fb6ba0521cee8ac9738c33e60c Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 01:37:38 -0500 Subject: [PATCH 16/39] feat: add positive-volume plasma current source --- CHANGELOG.md | 3 + README.md | 5 + docs/api/plasma.md | 22 +++ docs/development/physics-traceability.md | 2 +- docs/index.md | 2 + docs/theory/plasma-current.md | 52 +++++++ src/pyqsc_jax/__init__.py | 12 ++ src/pyqsc_jax/plasma.py | 166 +++++++++++++++++++++++ tests/physics/test_plasma_current.py | 151 +++++++++++++++++++++ 9 files changed, 414 insertions(+), 1 deletion(-) create mode 100644 docs/api/plasma.md create mode 100644 docs/theory/plasma-current.md create mode 100644 src/pyqsc_jax/plasma.py create mode 100644 tests/physics/test_plasma_current.py diff --git a/CHANGELOG.md b/CHANGELOG.md index 8e85f6c..17c0f5b 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -64,6 +64,9 @@ first stable release. verification, and explicit global-certificate status semantics. - Nonzero \(B_{20}\) Fourier-\(L^1\) certificates in dense and resolution-verification diagnostics. +- Exact positive-volume plasma-current source through quadratic radial order, + including independent pressure/current pathways, regular evaluation through + \(I_2=0\), and covariant-current/enclosed-ampere conversions. ### Fixed diff --git a/README.md b/README.md index 4d520c4..b4696d8 100644 --- a/README.md +++ b/README.md @@ -118,6 +118,11 @@ verification. It returns `verified_zero` only for a verified zero of the nonnegative primary residual; every nonzero candidate is `best_found` without a global claim. +`qsc.plasma_current_source(solution, formal_radius=a)` constructs the regular +positive-volume current measure used by the surface-free Biot–Savart +calculation and reports both \(I_2\) and enclosed amperes. A positive formal +radius is mandatory even though no finite-radius surface is created. + The lower-level immutable axis API supports general, not necessarily stellarator-symmetric Fourier axes: diff --git a/docs/api/plasma.md b/docs/api/plasma.md new file mode 100644 index 0000000..a67f756 --- /dev/null +++ b/docs/api/plasma.md @@ -0,0 +1,22 @@ +# Plasma/current API + +```{eval-rst} +.. autofunction:: pyqsc_jax.plasma_current_source +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.evaluate_weighted_current +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.enclosed_current_from_covariant +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.covariant_current_from_enclosed +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.PlasmaCurrentSource + :members: +``` diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index f5ecefc..53705bd 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -19,7 +19,7 @@ to the cited source, not to a duplicated derivation in this repository. | Magnetic shear | Rodríguez, Sengupta & Bhattacharjee (2022), Appendix F | `shear.solve_magnetic_shear`; pyQSC `calculate_r3.py` | three upstream paper cases, asymmetric/secular integration, resolution convergence, `B31c`, JIT/JVP/VJP and full-solve AD | implemented and documented for standard MHS with positive signs | | Singular radius and scale lengths | Landreman (2021), arXiv:2012.00865 | `singularity.singularity_diagnostics`; pyQSC `r_singularity.py` as comparison | direct regular-map determinant, QA/QH/finite-current upstream radii and arrays, residual, angular convergence, JIT/JVP/finite differences | implemented and documented | | Good-stellarator criteria | Curvo, Ferreira & Jorge (2025), Table 3 | `criteria.Criteria.from_curvo_2025` | exact normalized thresholds, strict/inclusive comparisons, signed margins, scaling, JIT/JVP/finite differences | implemented and documented | -| Plasma current source | manuscript Eqs. 88–97 | none | normalization, enclosed current, straight circular/elliptic channels | not implemented | +| Plasma current source | manuscript Eqs. 88–97 | `plasma.plasma_current_source`; `plasma.evaluate_weighted_current` | exact \(I_2\)/ampere normalization, regular radial power, pressure-only and vacuum limits, batch/JIT evaluation | implemented and documented | | Plasma on-axis field | manuscript Eqs. 136–138 | none | full-torus periodicity, matching cancellation, resolved volume Biot–Savart | not implemented | | Plasma gradient | manuscript Eqs. 156–160 | none | Ampère antisymmetry, divergence, external STF projection | not implemented | | Plasma Hessian | manuscript Eqs. 194 and 210–219 | none | resolved volume Biot–Savart, full symmetry, trace-free external tensor | blocked by validation gate | diff --git a/docs/index.md b/docs/index.md index aa53f84..0a0d8c2 100644 --- a/docs/index.md +++ b/docs/index.md @@ -19,6 +19,7 @@ theory/inverse-solves theory/b20-optimization theory/criteria theory/global-search +theory/plasma-current theory/field-jet api/axis api/first-order @@ -26,6 +27,7 @@ api/continuation api/optimization api/axis-optimization api/criteria +api/plasma api/second-order api/third-order api/field-jet diff --git a/docs/theory/plasma-current.md b/docs/theory/plasma-current.md new file mode 100644 index 0000000..5339e30 --- /dev/null +++ b/docs/theory/plasma-current.md @@ -0,0 +1,52 @@ +# Positive-volume plasma-current source + +The free-space Biot–Savart calculation must integrate the physical volume +measure. Expanding current density and the polar-coordinate Jacobian +separately makes both expressions look singular at \(r=0\) and makes it easy +to lose a factor of \(r\). The attached derivation instead defines the regular, +positive-volume source + +\[ +\mathbf W=\chi\mu_0\mathcal J_r\mathbf J, +\qquad \chi=s_Gs_\psi, +\] + +and obtains the exact identity + +\[ +\mathbf W=\chi\left[ +(I_r-r\bar B\beta_\vartheta)\mathbf x_\varphi +-(G_r+NI_r-r\bar B\beta_\varphi)\mathbf x_\vartheta +\right]. +\] + +`plasma_current_source` expands this identity directly: + +\[ +\frac{\mathbf W}{L} +=r\mathbf w_1+r^2\mathbf w_2+O(r^3), +\qquad +\mathbf w_1=j\mathbf t, +\qquad +j=2\chi I_2=\mu_0J_\parallel(0). +\] + +The quadratic term retains the independently pressure-driven +\(\beta_{1s}\) and \(C_2=G_2+NI_2\) paths. It is represented by cosine and +sine vector coefficients without division by \(I_2\), so it remains regular +as the on-axis parallel current passes through zero. + +For a mandatory formal current-channel radius \(a>0\), + +\[ +\mu_0 I_p(a)=\pi a^2j=2\pi\chi I_2a^2. +\] + +`enclosed_current_from_covariant` and `covariant_current_from_enclosed` +implement this conversion. Holding \(I_2\) fixed while varying \(a\) holds the +on-axis current density fixed and makes the enclosed current scale as \(a^2\). +Holding enclosed amperes fixed instead requires \(I_2\propto a^{-2}\), which +is a different asymptotic ordering. + +`evaluate_weighted_current` evaluates the regular truncated source at any +radial/helical-angle batch without constructing a finite-radius surface. diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index 2724bd3..ad96a95 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -40,6 +40,13 @@ optimize_B2c, verify_B20_resolution, ) +from pyqsc_jax.plasma import ( + PlasmaCurrentSource, + covariant_current_from_enclosed, + enclosed_current_from_covariant, + evaluate_weighted_current, + plasma_current_source, +) from pyqsc_jax.second_order import SecondOrderResiduals, second_order_residuals from pyqsc_jax.shear import solve_magnetic_shear from pyqsc_jax.singularity import singularity_diagnostics @@ -67,6 +74,7 @@ "MercierDiagnostics", "NearAxisInputs", "NearAxisSolution", + "PlasmaCurrentSource", "Qsc", "RootSolveOptions", "RootSolveReport", @@ -79,6 +87,9 @@ "b20_diagnostics", "continue_etabar_branch", "continue_axis_search", + "covariant_current_from_enclosed", + "enclosed_current_from_covariant", + "evaluate_weighted_current", "mercier_diagnostics", "second_order_residuals", "search_axis", @@ -90,6 +101,7 @@ "total_field_jet", "optimal_B2c_value", "optimize_B2c", + "plasma_current_source", "verify_B20_resolution", ] __version__ = "0.2.0.dev0" diff --git a/src/pyqsc_jax/plasma.py b/src/pyqsc_jax/plasma.py new file mode 100644 index 0000000..4d9aba5 --- /dev/null +++ b/src/pyqsc_jax/plasma.py @@ -0,0 +1,166 @@ +"""Surface-free plasma-current source and free-space field jets.""" + +from __future__ import annotations + +from dataclasses import dataclass, field +from typing import Any + +import jax +import jax.numpy as jnp + +from pyqsc_jax.models import NearAxisSolution +from pyqsc_jax.second_order import MU0 + +ArrayLike = Any + + +def _positive_scalar(value: ArrayLike, *, name: str) -> jax.Array: + array = jnp.asarray(value) + if array.ndim: + raise ValueError(f"{name} must be a scalar.") + try: + if bool(array <= 0): + raise ValueError(f"{name} must be positive.") + except jax.errors.TracerBoolConversionError: + pass + return array + + +def enclosed_current_from_covariant( + I2: ArrayLike, + *, + formal_radius: ArrayLike, + chi: int, +) -> jax.Array: + """Convert covariant ``I2`` to enclosed toroidal current in amperes.""" + + radius = _positive_scalar(formal_radius, name="formal_radius") + if chi not in (-1, 1): + raise ValueError("chi must be +1 or -1.") + return 2 * jnp.pi * chi * jnp.asarray(I2) * radius**2 / MU0 + + +def covariant_current_from_enclosed( + enclosed_current: ArrayLike, + *, + formal_radius: ArrayLike, + chi: int, +) -> jax.Array: + """Convert enclosed toroidal current in amperes to covariant ``I2``.""" + + radius = _positive_scalar(formal_radius, name="formal_radius") + if chi not in (-1, 1): + raise ValueError("chi must be +1 or -1.") + return MU0 * jnp.asarray(enclosed_current) / (2 * jnp.pi * chi * radius**2) + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class PlasmaCurrentSource: + """Positive-volume current measure through quadratic radial order. + + The vector coefficients follow + + ``W / L = r * w1 + r**2 * (w2_cosine*cos(theta) + w2_sine*sin(theta))``. + """ + + formal_radius: jax.Array + parallel_current_mu0: jax.Array + enclosed_toroidal_current: jax.Array + C2: jax.Array + beta_1s: jax.Array + w1: jax.Array + wstar2_cosine: jax.Array + wstar2_sine: jax.Array + w2_cosine: jax.Array + w2_sine: jax.Array + axis_length_per_radian: jax.Array + chi: int = field(metadata={"static": True}) + + +def plasma_current_source( + solution: NearAxisSolution, + *, + formal_radius: ArrayLike, +) -> PlasmaCurrentSource: + """Construct the exact positive-volume weighted source through ``O(r²)``.""" + + if solution.second_order is None: + raise ValueError("The plasma current source requires a second-order solution.") + radius = _positive_scalar(formal_radius, name="formal_radius") + inputs = solution.inputs + geometry = solution.geometry + chi = inputs.sG * inputs.spsi + axis_length_per_radian = geometry.abs_G0_over_B0 + x = solution.X1c + y = solution.Y1s + y_sigma = solution.Y1c + derivative = geometry.d_d_varphi + current_density_mu0 = 2 * chi * inputs.I2 + C2 = solution.G2 + solution.N_helicity * inputs.I2 + + cosine_tangent = -chi * inputs.spsi * inputs.B0 * solution.beta_1s + cosine_normal = current_density_mu0 * ( + (derivative @ x) / axis_length_per_radian - geometry.torsion * y_sigma + ) + cosine_binormal = ( + current_density_mu0 + * ((derivative @ y_sigma) / axis_length_per_radian + geometry.torsion * x) + - 2 * chi * C2 * y / axis_length_per_radian + ) + sine_normal = ( + -current_density_mu0 * geometry.torsion * y + 2 * chi * C2 * x / axis_length_per_radian + ) + sine_binormal = ( + current_density_mu0 * (derivative @ y) / axis_length_per_radian + + 2 * chi * C2 * y_sigma / axis_length_per_radian + ) + + tangent = geometry.tangent_cartesian + normal = geometry.normal_cartesian + binormal = geometry.binormal_cartesian + w1 = current_density_mu0 * tangent + wstar2_cosine = ( + cosine_tangent * tangent + + cosine_normal[:, None] * normal + + cosine_binormal[:, None] * binormal + ) + wstar2_sine = sine_normal[:, None] * normal + sine_binormal[:, None] * binormal + w2_cosine = wstar2_cosine - (current_density_mu0 * geometry.curvature * x)[:, None] * tangent + return PlasmaCurrentSource( + formal_radius=radius, + parallel_current_mu0=current_density_mu0, + enclosed_toroidal_current=enclosed_current_from_covariant( + inputs.I2, + formal_radius=radius, + chi=chi, + ), + C2=C2, + beta_1s=solution.beta_1s, + w1=w1, + wstar2_cosine=wstar2_cosine, + wstar2_sine=wstar2_sine, + w2_cosine=w2_cosine, + w2_sine=wstar2_sine, + axis_length_per_radian=axis_length_per_radian, + chi=chi, + ) + + +def evaluate_weighted_current( + source: PlasmaCurrentSource, + radial_coordinate: ArrayLike, + theta: ArrayLike, +) -> jax.Array: + """Evaluate ``W = chi * mu0 * J_r * J`` at all toroidal samples.""" + + radial_coordinate, theta = jnp.broadcast_arrays( + jnp.asarray(radial_coordinate), + jnp.asarray(theta), + ) + radial = radial_coordinate[..., None, None] + cosine = jnp.cos(theta)[..., None, None] + sine = jnp.sin(theta)[..., None, None] + return source.axis_length_per_radian * ( + radial * source.w1 + radial**2 * (cosine * source.w2_cosine + sine * source.w2_sine) + ) diff --git a/tests/physics/test_plasma_current.py b/tests/physics/test_plasma_current.py new file mode 100644 index 0000000..0c5c1ff --- /dev/null +++ b/tests/physics/test_plasma_current.py @@ -0,0 +1,151 @@ +from __future__ import annotations + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +import pyqsc_jax as qsc +from pyqsc_jax.second_order import MU0 + + +def finite_current_solution(*, I2=0.9, p2=-600000.0, nphi=31): + return qsc.Qsc( + rc=[1.0, 0.09], + zs=[0.0, -0.09], + nfp=2, + etabar=0.95, + I2=I2, + p2=p2, + B2c=-0.7, + nphi=nphi, + order="r2", + ) + + +def test_covariant_and_enclosed_current_conversions_round_trip(): + I2 = 0.9 + radius = 0.08 + chi = -1 + current = qsc.enclosed_current_from_covariant( + I2, + formal_radius=radius, + chi=chi, + ) + + np.testing.assert_allclose(current, 2 * np.pi * chi * I2 * radius**2 / MU0) + np.testing.assert_allclose( + qsc.covariant_current_from_enclosed( + current, + formal_radius=radius, + chi=chi, + ), + I2, + ) + derivative = jax.grad( + lambda a: qsc.enclosed_current_from_covariant( + I2, + formal_radius=a, + chi=chi, + ) + )(radius) + np.testing.assert_allclose(derivative, 4 * np.pi * chi * I2 * radius / MU0) + + +def test_positive_volume_source_matches_manuscript_coefficients(): + solution = finite_current_solution() + radius = 0.07 + source = qsc.plasma_current_source(solution, formal_radius=radius) + chi = solution.inputs.sG * solution.inputs.spsi + expected_j = 2 * chi * solution.inputs.I2 + expected_C2 = solution.G2 + solution.N_helicity * solution.inputs.I2 + + np.testing.assert_allclose(source.parallel_current_mu0, expected_j) + np.testing.assert_allclose(source.C2, expected_C2) + np.testing.assert_allclose( + source.enclosed_toroidal_current, + np.pi * radius**2 * expected_j / MU0, + ) + np.testing.assert_allclose( + source.w1, + expected_j * solution.geometry.tangent_cartesian, + ) + np.testing.assert_allclose( + source.w2_cosine, + source.wstar2_cosine + - (expected_j * solution.geometry.curvature * solution.X1c)[:, None] + * solution.geometry.tangent_cartesian, + ) + np.testing.assert_allclose(source.w2_sine, source.wstar2_sine) + assert source.chi == chi + + +def test_weighted_source_evaluation_has_regular_radial_power_and_batch_shape(): + solution = finite_current_solution(nphi=15) + source = qsc.plasma_current_source(solution, formal_radius=0.05) + radial = jnp.asarray([0.0, 0.01]) + theta = jnp.asarray([0.2, 0.7]) + weighted = qsc.evaluate_weighted_current(source, radial, theta) + + assert weighted.shape == (2, 15, 3) + np.testing.assert_allclose(weighted[0], 0.0) + direct = source.axis_length_per_radian * ( + radial[1] * source.w1 + + radial[1] ** 2 * (np.cos(theta[1]) * source.w2_cosine + np.sin(theta[1]) * source.w2_sine) + ) + np.testing.assert_allclose(weighted[1], direct) + scalar = jax.jit(qsc.evaluate_weighted_current)(source, 0.01, 0.3) + assert scalar.shape == (15, 3) + + +def test_pressure_and_parallel_current_paths_remain_well_defined_at_I2_zero(): + pressure_only = finite_current_solution(I2=0.0) + source = qsc.plasma_current_source(pressure_only, formal_radius=0.06) + + np.testing.assert_allclose(source.parallel_current_mu0, 0.0) + np.testing.assert_allclose(source.w1, 0.0) + assert np.max(np.abs(source.wstar2_cosine)) > 0 + assert np.max(np.abs(source.wstar2_sine)) > 0 + assert np.all(np.isfinite(source.wstar2_cosine)) + + vacuum = finite_current_solution(I2=0.0, p2=0.0) + vacuum_source = qsc.plasma_current_source(vacuum, formal_radius=0.06) + np.testing.assert_allclose(vacuum_source.w1, 0.0) + np.testing.assert_allclose(vacuum_source.wstar2_cosine, 0.0, atol=1.0e-14) + np.testing.assert_allclose(vacuum_source.wstar2_sine, 0.0, atol=1.0e-14) + + +def test_current_source_guards(): + with pytest.raises(ValueError, match="second-order"): + qsc.plasma_current_source( + qsc.Qsc( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + order="r1", + ), + formal_radius=0.1, + ) + for value in (0.0, -0.1): + with pytest.raises(ValueError, match="positive"): + qsc.enclosed_current_from_covariant( + 1.0, + formal_radius=value, + chi=1, + ) + with pytest.raises(ValueError, match="scalar"): + qsc.covariant_current_from_enclosed( + 1.0, + formal_radius=[0.1], + chi=1, + ) + for function in ( + qsc.enclosed_current_from_covariant, + qsc.covariant_current_from_enclosed, + ): + with pytest.raises(ValueError, match="chi"): + if function is qsc.enclosed_current_from_covariant: + function(1.0, formal_radius=0.1, chi=0) + else: + function(1.0, formal_radius=0.1, chi=0) From f173de7fdd7093896e7c99db21f2037565d0e0bc Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 01:48:26 -0500 Subject: [PATCH 17/39] feat: add matched free-space plasma field --- CHANGELOG.md | 4 + README.md | 5 + docs/api/plasma.md | 17 ++ docs/development/physics-traceability.md | 2 +- docs/index.md | 1 + docs/limitations.md | 4 +- docs/theory/plasma-field.md | 69 +++++ src/pyqsc_jax/__init__.py | 8 + src/pyqsc_jax/plasma.py | 236 ++++++++++++++++++ .../test_plasma_volume_reference.py | 127 ++++++++++ tests/physics/test_plasma_field.py | 204 +++++++++++++++ 11 files changed, 675 insertions(+), 2 deletions(-) create mode 100644 docs/theory/plasma-field.md create mode 100644 tests/literature/test_plasma_volume_reference.py create mode 100644 tests/physics/test_plasma_field.py diff --git a/CHANGELOG.md b/CHANGELOG.md index 17c0f5b..9969fc9 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -67,6 +67,10 @@ first stable release. - Exact positive-volume plasma-current source through quadratic radial order, including independent pressure/current pathways, regular evaluation through \(I_2=0\), and covariant-current/enclosed-ampere conversions. +- Matched on-axis free-space plasma field with a full-torus periodic + finite-part integral, elliptical core constants, second-order local shape + correction, arbitrary matching-length cancellation, asymptotic error + metadata, and independent resolved-volume Biot–Savart validation. ### Fixed diff --git a/README.md b/README.md index b4696d8..3c8608b 100644 --- a/README.md +++ b/README.md @@ -123,6 +123,11 @@ positive-volume current measure used by the surface-free Biot–Savart calculation and reports both \(I_2\) and enclosed amperes. A positive formal radius is mandatory even though no finite-radius surface is created. +`qsc.plasma_field_on_axis(solution, formal_radius=a)` adds the full-torus +regularized axis integral, local elliptical core, and second-order shape +correction. Its matching-scale cancellation and predicted +\(a^4|\log a|\) remainder have independent numerical tests. + The lower-level immutable axis API supports general, not necessarily stellarator-symmetric Fourier axes: diff --git a/docs/api/plasma.md b/docs/api/plasma.md index a67f756..6cd4e22 100644 --- a/docs/api/plasma.md +++ b/docs/api/plasma.md @@ -1,5 +1,17 @@ # Plasma/current API +```{eval-rst} +.. autofunction:: pyqsc_jax.plasma_field_on_axis +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.regularized_axis_integral +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.matched_plasma_field_kernel +``` + ```{eval-rst} .. autofunction:: pyqsc_jax.plasma_current_source ``` @@ -20,3 +32,8 @@ .. autoclass:: pyqsc_jax.PlasmaCurrentSource :members: ``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.PlasmaFieldData + :members: +``` diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index 53705bd..6148657 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -20,7 +20,7 @@ to the cited source, not to a duplicated derivation in this repository. | Singular radius and scale lengths | Landreman (2021), arXiv:2012.00865 | `singularity.singularity_diagnostics`; pyQSC `r_singularity.py` as comparison | direct regular-map determinant, QA/QH/finite-current upstream radii and arrays, residual, angular convergence, JIT/JVP/finite differences | implemented and documented | | Good-stellarator criteria | Curvo, Ferreira & Jorge (2025), Table 3 | `criteria.Criteria.from_curvo_2025` | exact normalized thresholds, strict/inclusive comparisons, signed margins, scaling, JIT/JVP/finite differences | implemented and documented | | Plasma current source | manuscript Eqs. 88–97 | `plasma.plasma_current_source`; `plasma.evaluate_weighted_current` | exact \(I_2\)/ampere normalization, regular radial power, pressure-only and vacuum limits, batch/JIT evaluation | implemented and documented | -| Plasma on-axis field | manuscript Eqs. 136–138 | none | full-torus periodicity, matching cancellation, resolved volume Biot–Savart | not implemented | +| Plasma on-axis field | manuscript Eqs. 118 and 133–138 | `plasma.regularized_axis_integral`; `plasma.plasma_field_on_axis` | circular finite part/core/logarithm, full-torus construction, matching-length cancellation, angular/toroidal convergence, vacuum/pressure limits, JIT/JVP, resolved volume Biot–Savart \(a^4|\log a|\) scaling | implemented and documented | | Plasma gradient | manuscript Eqs. 156–160 | none | Ampère antisymmetry, divergence, external STF projection | not implemented | | Plasma Hessian | manuscript Eqs. 194 and 210–219 | none | resolved volume Biot–Savart, full symmetry, trace-free external tensor | blocked by validation gate | | External vacuum jet | manuscript Eqs. 220–224 | none | 3+5+7 representation, asymptotic error scaling, vacuum reduction | not implemented | diff --git a/docs/index.md b/docs/index.md index 0a0d8c2..d342214 100644 --- a/docs/index.md +++ b/docs/index.md @@ -20,6 +20,7 @@ theory/b20-optimization theory/criteria theory/global-search theory/plasma-current +theory/plasma-field theory/field-jet api/axis api/first-order diff --git a/docs/limitations.md b/docs/limitations.md index 8f2b7d6..2627967 100644 --- a/docs/limitations.md +++ b/docs/limitations.md @@ -7,7 +7,9 @@ flux-constraint surface correction. Known limitations under active refactor include: -- no plasma/external field-jet separation; +- plasma field gradient, plasma Hessian, and the assembled external vacuum jet + are not yet exposed; the positive-volume source and matched on-axis plasma + field are implemented. - pseudo-arclength continuation currently traces `etabar` branches only and uses a fixed arclength step. diff --git a/docs/theory/plasma-field.md b/docs/theory/plasma-field.md new file mode 100644 index 0000000..2021fe7 --- /dev/null +++ b/docs/theory/plasma-field.md @@ -0,0 +1,69 @@ +# Matched free-space plasma field + +The on-axis plasma field is not determined by local Ampère-law data alone. +Remote parts of the current distribution add a harmonic field. The decay +condition at spatial infinity selects that field uniquely and leads to a +matched volume-current Biot–Savart calculation. + +`regularized_axis_integral` evaluates the full-torus periodic finite part + +\[ +\mathcal R(\varphi)= +\int_0^{2\pi} +\left[ +L\frac{\mathbf t(\varphi')\times +[\mathbf r_0(\varphi)-\mathbf r_0(\varphi')]} +{|\mathbf r_0(\varphi)-\mathbf r_0(\varphi')|^3} +-\frac{\kappa(\varphi)\mathbf b(\varphi)} +{4|\sin[(\varphi'-\varphi)/2]|} +\right]d\varphi'. +\] + +All field-period copies are included. At the coincident grid point the +symmetric finite-part value is used; the two one-sided limits are equal and +opposite. + +The inner elliptical channel supplies the finite constants + +\[ +C_b=-\frac12-\frac12\log\frac{\mathcal T+2}{4} ++\frac{x^2+1}{\mathcal T+2}, +\qquad +C_n=-\frac{\chi\sigma}{\mathcal T+2}, +\] + +and a smooth angular correction \(\mathbf S\) containing the first-harmonic +weighted current and the second-order cross-sectional displacement. The +assembled leading field is + +\[ +\mathbf B_p(\mathbf r_0)= +\frac{ja^2}{4} +\left[ +\mathcal R+\kappa\mathbf b +\left(\log\frac{8L}{a}+C_b\right) ++\kappa C_n\mathbf n +\right] ++\mathbf S ++O(a^4\log a). +\] + +`matched_plasma_field_kernel` also exposes the same result at an arbitrary +matching reference length. Changing that length shifts the finite part and +the local logarithm separately but leaves their sum invariant. + +Validation includes: + +- exact cancellation of the arbitrary matching length; +- a circular-axis finite part below \(10^{-13}\); +- vanishing circular-ellipse core constants; +- the circular local-induction logarithm; +- vacuum and pressure-only limits; +- angular and toroidal resolution convergence; +- JIT and radius JVP checks; and +- an independent resolved volume-current Biot–Savart integral whose error + follows the predicted \(a^4|\log a|\) scaling. + +The returned `estimated_field_remainder` is an order-of-magnitude asymptotic +scale, not a rigorous error bound. `formal_radius_to_curvature_radius` should +be inspected before treating the slender-channel expansion as accurate. diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index ad96a95..db53212 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -42,10 +42,14 @@ ) from pyqsc_jax.plasma import ( PlasmaCurrentSource, + PlasmaFieldData, covariant_current_from_enclosed, enclosed_current_from_covariant, evaluate_weighted_current, + matched_plasma_field_kernel, plasma_current_source, + plasma_field_on_axis, + regularized_axis_integral, ) from pyqsc_jax.second_order import SecondOrderResiduals, second_order_residuals from pyqsc_jax.shear import solve_magnetic_shear @@ -75,6 +79,7 @@ "NearAxisInputs", "NearAxisSolution", "PlasmaCurrentSource", + "PlasmaFieldData", "Qsc", "RootSolveOptions", "RootSolveReport", @@ -90,6 +95,7 @@ "covariant_current_from_enclosed", "enclosed_current_from_covariant", "evaluate_weighted_current", + "matched_plasma_field_kernel", "mercier_diagnostics", "second_order_residuals", "search_axis", @@ -102,6 +108,8 @@ "optimal_B2c_value", "optimize_B2c", "plasma_current_source", + "plasma_field_on_axis", + "regularized_axis_integral", "verify_B20_resolution", ] __version__ = "0.2.0.dev0" diff --git a/src/pyqsc_jax/plasma.py b/src/pyqsc_jax/plasma.py index 4d9aba5..e8fffd0 100644 --- a/src/pyqsc_jax/plasma.py +++ b/src/pyqsc_jax/plasma.py @@ -78,6 +78,24 @@ class PlasmaCurrentSource: chi: int = field(metadata={"static": True}) +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class PlasmaFieldData: + """Matched on-axis free-space plasma field and error metadata.""" + + field: jax.Array + regularized_axis_integral: jax.Array + matched_axis_and_core: jax.Array + second_order_shape_correction: jax.Array + core_binormal_constant: jax.Array + core_normal_constant: jax.Array + maximum_matching_scale_error: jax.Array + formal_radius_to_curvature_radius: jax.Array + estimated_field_remainder: jax.Array + current_source: PlasmaCurrentSource + angular_resolution: int = field(metadata={"static": True}) + + def plasma_current_source( solution: NearAxisSolution, *, @@ -164,3 +182,221 @@ def evaluate_weighted_current( return source.axis_length_per_radian * ( radial * source.w1 + radial**2 * (cosine * source.w2_cosine + sine * source.w2_sine) ) + + +def _full_torus_axis_samples( + solution: NearAxisSolution, +) -> tuple[jax.Array, jax.Array, jax.Array, jax.Array]: + geometry = solution.geometry + nfp = solution.inputs.axis.nfp + cylindrical_period = 2 * jnp.pi / nfp + boozer_period = 2 * jnp.pi / nfp + period_index = jnp.arange(nfp) + full_phi = (geometry.samples.phi[None, :] + period_index[:, None] * cylindrical_period).reshape( + -1 + ) + full_varphi = (geometry.varphi[None, :] + period_index[:, None] * boozer_period).reshape(-1) + radius = jnp.tile(geometry.samples.R, nfp) + height = jnp.tile(geometry.samples.Z, nfp) + position = jnp.stack( + ( + radius * jnp.cos(full_phi), + radius * jnp.sin(full_phi), + height, + ), + axis=-1, + ) + tangent_cylindrical = jnp.tile( + geometry.tangent_cylindrical, + (nfp, 1), + ) + tangent = jnp.stack( + ( + tangent_cylindrical[:, 0] * jnp.cos(full_phi) + - tangent_cylindrical[:, 1] * jnp.sin(full_phi), + tangent_cylindrical[:, 0] * jnp.sin(full_phi) + + tangent_cylindrical[:, 1] * jnp.cos(full_phi), + tangent_cylindrical[:, 2], + ), + axis=-1, + ) + d_phi = cylindrical_period / solution.inputs.nphi + weights = jnp.tile(geometry.d_varphi_d_phi * d_phi, nfp) + return full_varphi, position, tangent, weights + + +def regularized_axis_integral(solution: NearAxisSolution) -> jax.Array: + """Evaluate the full-torus periodic finite-part integral in Eq. (136).""" + + source_varphi, source_position, source_tangent, weights = _full_torus_axis_samples(solution) + observation_varphi = solution.varphi + observation_position = solution.geometry.position_cartesian + displacement = observation_position[:, None, :] - source_position[None, :, :] + distance_squared = jnp.sum(displacement**2, axis=-1) + angle = source_varphi[None, :] - observation_varphi[:, None] + sine_half = jnp.sin(0.5 * angle) + coincident = jnp.abs(sine_half) < 16 * jnp.finfo(angle.dtype).eps + safe_distance_squared = jnp.where(coincident, 1.0, distance_squared) + safe_sine = jnp.where(coincident, 1.0, jnp.abs(sine_half)) + filament = ( + solution.geometry.abs_G0_over_B0 + * jnp.cross( + source_tangent[None, :, :], + displacement, + ) + / safe_distance_squared[..., None] ** 1.5 + ) + singular_model = ( + solution.geometry.curvature[:, None, None] + * solution.geometry.binormal_cartesian[:, None, :] + / (4 * safe_sine[..., None]) + ) + integrand = jnp.where( + coincident[..., None], + 0.0, + filament - singular_model, + ) + return jnp.sum(weights[None, :, None] * integrand, axis=1) + + +def _second_order_shape_correction( + solution: NearAxisSolution, + source: PlasmaCurrentSource, + *, + angular_resolution: int, +) -> jax.Array: + if ( + not isinstance(angular_resolution, int) + or isinstance(angular_resolution, bool) + or angular_resolution < 8 + ): + raise ValueError("angular_resolution must be an integer >= 8.") + theta = 2 * jnp.pi * jnp.arange(angular_resolution) / angular_resolution + cosine = jnp.cos(theta)[None, :, None] + sine = jnp.sin(theta)[None, :, None] + cosine2 = jnp.cos(2 * theta)[None, :, None] + sine2 = jnp.sin(2 * theta)[None, :, None] + geometry = solution.geometry + tangent = geometry.tangent_cartesian[:, None, :] + normal = geometry.normal_cartesian[:, None, :] + binormal = geometry.binormal_cartesian[:, None, :] + e = ( + solution.X1c[:, None, None] * cosine * normal + + (solution.Y1s[:, None, None] * sine + solution.Y1c[:, None, None] * cosine) * binormal + ) + X2 = ( + solution.X20[:, None, None] + + solution.X2c[:, None, None] * cosine2 + + solution.X2s[:, None, None] * sine2 + ) + Y2 = ( + solution.Y20[:, None, None] + + solution.Y2c[:, None, None] * cosine2 + + solution.Y2s[:, None, None] * sine2 + ) + Z2 = ( + solution.Z20[:, None, None] + + solution.Z2c[:, None, None] * cosine2 + + solution.Z2s[:, None, None] * sine2 + ) + xi2 = X2 * normal + Y2 * binormal + Z2 * tangent + w1 = source.w1[:, None, :] + wstar2 = source.wstar2_cosine[:, None, :] * cosine + source.wstar2_sine[:, None, :] * sine + E2 = jnp.sum(e**2, axis=-1, keepdims=True) + integrand = (jnp.cross(w1, xi2) + jnp.cross(wstar2, e)) / E2 - 2 * jnp.sum( + e * xi2, axis=-1, keepdims=True + ) * jnp.cross(w1, e) / E2**2 + return -0.5 * source.formal_radius**2 * jnp.mean(integrand, axis=1) + + +def matched_plasma_field_kernel( + solution: NearAxisSolution, + source: PlasmaCurrentSource, + regularized_integral: jax.Array, + *, + reference_length: ArrayLike, +) -> jax.Array: + """Combine finite-part and local-core terms at an arbitrary matching length.""" + + reference_length = _positive_scalar( + reference_length, + name="reference_length", + ) + geometry = solution.geometry + axis_scale = geometry.abs_G0_over_B0 + x = solution.X1c + sigma = solution.Y1c / solution.Y1s + trace_Q = x**2 + (1 + sigma**2) / x**2 + core_binormal = -0.5 - 0.5 * jnp.log((trace_Q + 2) / 4) + (x**2 + 1) / (trace_Q + 2) + core_normal = -source.chi * sigma / (trace_Q + 2) + curvature_binormal = geometry.curvature[:, None] * geometry.binormal_cartesian + finite_part = regularized_integral - curvature_binormal * jnp.log( + reference_length / (4 * axis_scale) + ) + return ( + finite_part + + curvature_binormal + * (jnp.log(2 * reference_length / source.formal_radius) + core_binormal[:, None]) + + (geometry.curvature * core_normal)[:, None] * geometry.normal_cartesian + ) + + +def plasma_field_on_axis( + solution: NearAxisSolution, + *, + formal_radius: ArrayLike, + angular_resolution: int = 128, +) -> PlasmaFieldData: + """Evaluate the matched leading on-axis free-space plasma field.""" + + source = plasma_current_source( + solution, + formal_radius=formal_radius, + ) + regularized_integral = regularized_axis_integral(solution) + axis_scale = solution.geometry.abs_G0_over_B0 + matched = matched_plasma_field_kernel( + solution, + source, + regularized_integral, + reference_length=4 * axis_scale, + ) + independent_matching_scale = matched_plasma_field_kernel( + solution, + source, + regularized_integral, + reference_length=7 * axis_scale, + ) + shape_correction = _second_order_shape_correction( + solution, + source, + angular_resolution=angular_resolution, + ) + current_prefactor = source.parallel_current_mu0 * source.formal_radius**2 / 4 + field_value = current_prefactor * matched + shape_correction + x = solution.X1c + sigma = solution.Y1c / solution.Y1s + trace_Q = x**2 + (1 + sigma**2) / x**2 + core_binormal = -0.5 - 0.5 * jnp.log((trace_Q + 2) / 4) + (x**2 + 1) / (trace_Q + 2) + core_normal = -source.chi * sigma / (trace_Q + 2) + radius_to_curvature = source.formal_radius * jnp.max(solution.geometry.curvature) + logarithm = jnp.abs(jnp.log(source.formal_radius / solution.geometry.abs_G0_over_B0)) + estimated_remainder = ( + jnp.abs(source.parallel_current_mu0) + * source.formal_radius**4 + / solution.geometry.abs_G0_over_B0**3 + * (1 + logarithm) + ) + return PlasmaFieldData( + field=field_value, + regularized_axis_integral=regularized_integral, + matched_axis_and_core=matched, + second_order_shape_correction=shape_correction, + core_binormal_constant=core_binormal, + core_normal_constant=core_normal, + maximum_matching_scale_error=jnp.max(jnp.abs(matched - independent_matching_scale)), + formal_radius_to_curvature_radius=radius_to_curvature, + estimated_field_remainder=estimated_remainder, + current_source=source, + angular_resolution=angular_resolution, + ) diff --git a/tests/literature/test_plasma_volume_reference.py b/tests/literature/test_plasma_volume_reference.py new file mode 100644 index 0000000..2311246 --- /dev/null +++ b/tests/literature/test_plasma_volume_reference.py @@ -0,0 +1,127 @@ +from __future__ import annotations + +import numpy as np +import pytest + +import pyqsc_jax as qsc + + +def resolved_volume_biot_savart( + solution, + formal_radius, + *, + radial_resolution=16, + angular_resolution=64, +): + """Independent midpoint/Gauss volume integral at the first axis point.""" + + source = qsc.plasma_current_source( + solution, + formal_radius=formal_radius, + ) + geometry = solution.geometry + radial_nodes, radial_weights = np.polynomial.legendre.leggauss(radial_resolution) + radial = 0.5 * formal_radius * (radial_nodes + 1) + radial_weights = 0.5 * formal_radius * radial_weights + theta = 2 * np.pi * np.arange(angular_resolution) / angular_resolution + theta_weight = 2 * np.pi / angular_resolution + cosine = np.cos(theta) + sine = np.sin(theta) + cosine2 = np.cos(2 * theta) + sine2 = np.sin(2 * theta) + + tangent = np.asarray(geometry.tangent_cartesian) + normal = np.asarray(geometry.normal_cartesian) + binormal = np.asarray(geometry.binormal_cartesian) + first_order = ( + np.asarray(solution.X1c)[:, None, None] * cosine[None, :, None] * normal[:, None, :] + + ( + np.asarray(solution.Y1s)[:, None, None] * sine[None, :, None] + + np.asarray(solution.Y1c)[:, None, None] * cosine[None, :, None] + ) + * binormal[:, None, :] + ) + X2 = ( + np.asarray(solution.X20)[:, None] + + np.asarray(solution.X2c)[:, None] * cosine2 + + np.asarray(solution.X2s)[:, None] * sine2 + ) + Y2 = ( + np.asarray(solution.Y20)[:, None] + + np.asarray(solution.Y2c)[:, None] * cosine2 + + np.asarray(solution.Y2s)[:, None] * sine2 + ) + Z2 = ( + np.asarray(solution.Z20)[:, None] + + np.asarray(solution.Z2c)[:, None] * cosine2 + + np.asarray(solution.Z2s)[:, None] * sine2 + ) + second_order = ( + X2[:, :, None] * normal[:, None, :] + + Y2[:, :, None] * binormal[:, None, :] + + Z2[:, :, None] * tangent[:, None, :] + ) + source_position = ( + np.asarray(geometry.position_cartesian)[:, None, None, :] + + radial[None, :, None, None] * first_order[:, None, :, :] + + radial[None, :, None, None] ** 2 * second_order[:, None, :, :] + ) + weighted_current = float(source.axis_length_per_radian) * ( + radial[None, :, None, None] * np.asarray(source.w1)[:, None, None, :] + + radial[None, :, None, None] ** 2 + * ( + cosine[None, None, :, None] * np.asarray(source.w2_cosine)[:, None, None, :] + + sine[None, None, :, None] * np.asarray(source.w2_sine)[:, None, None, :] + ) + ) + displacement = np.asarray(geometry.position_cartesian[0]) - source_position + kernel = ( + np.cross(weighted_current, displacement) + / np.linalg.norm( + displacement, + axis=-1, + )[..., None] + ** 3 + ) + cylindrical_period = 2 * np.pi / solution.inputs.axis.nfp + d_phi = cylindrical_period / solution.inputs.nphi + varphi_weights = np.asarray(geometry.d_varphi_d_phi) * d_phi + return np.sum( + kernel + * varphi_weights[:, None, None, None] + * radial_weights[None, :, None, None] + * theta_weight, + axis=(0, 1, 2), + ) / (4 * np.pi) + + +@pytest.mark.literature +@pytest.mark.slow +def test_matched_field_converges_to_resolved_volume_current_biot_savart(): + solution = qsc.Qsc( + rc=[1.0], + zs=[0.0], + nfp=1, + etabar=1.0, + I2=0.1, + nphi=301, + order="r2", + ) + radii = (0.1, 0.07) + errors = [] + scaled_errors = [] + for radius in radii: + direct = resolved_volume_biot_savart(solution, radius) + asymptotic = np.asarray( + qsc.plasma_field_on_axis( + solution, + formal_radius=radius, + ).field[0] + ) + error = np.linalg.norm(direct - asymptotic) + errors.append(error) + scaled_errors.append(error / (radius**4 * abs(np.log(radius)))) + + assert errors[1] < 0.35 * errors[0] + assert max(scaled_errors) / min(scaled_errors) < 1.2 + assert errors[0] < 1.0e-5 diff --git a/tests/physics/test_plasma_field.py b/tests/physics/test_plasma_field.py new file mode 100644 index 0000000..c29ac72 --- /dev/null +++ b/tests/physics/test_plasma_field.py @@ -0,0 +1,204 @@ +from __future__ import annotations + +import jax +import numpy as np +import pytest + +import pyqsc_jax as qsc + + +def circular_solution(*, I2=0.1, p2=0.0, nphi=31): + return qsc.Qsc( + rc=[1.0], + zs=[0.0], + nfp=1, + etabar=1.0, + I2=I2, + p2=p2, + nphi=nphi, + order="r2", + ) + + +def finite_current_solution(*, I2=0.9, p2=-600000.0, nphi=31): + return qsc.Qsc( + rc=[1.0, 0.09], + zs=[0.0, -0.09], + nfp=2, + etabar=0.95, + I2=I2, + p2=p2, + B2c=-0.7, + nphi=nphi, + order="r2", + ) + + +def test_periodic_regularized_integral_and_circular_local_induction_limit(): + solution = circular_solution() + radius = 0.05 + integral = qsc.regularized_axis_integral(solution) + plasma = qsc.plasma_field_on_axis(solution, formal_radius=radius) + binormal_kernel = np.sum( + np.asarray(plasma.matched_axis_and_core) * np.asarray(solution.geometry.binormal_cartesian), + axis=-1, + ) + + assert np.max(np.abs(integral)) < 1.0e-13 + np.testing.assert_allclose(plasma.core_binormal_constant, 0.0) + np.testing.assert_allclose(plasma.core_normal_constant, 0.0) + np.testing.assert_allclose(binormal_kernel, np.log(8 / radius), rtol=2.0e-13) + np.testing.assert_allclose( + solution.inputs.I2 * radius**2 / 2 * binormal_kernel, + solution.inputs.I2 * radius**2 / 2 * np.log(8 / radius), + ) + + +def test_matching_reference_length_cancels_exactly(): + solution = finite_current_solution() + source = qsc.plasma_current_source(solution, formal_radius=0.06) + integral = qsc.regularized_axis_integral(solution) + first = qsc.matched_plasma_field_kernel( + solution, + source, + integral, + reference_length=2.3, + ) + second = qsc.matched_plasma_field_kernel( + solution, + source, + integral, + reference_length=7.1, + ) + plasma = qsc.plasma_field_on_axis(solution, formal_radius=0.06) + + np.testing.assert_allclose(first, second, rtol=0, atol=2.0e-15) + assert plasma.maximum_matching_scale_error < 2.0e-15 + np.testing.assert_allclose(plasma.matched_axis_and_core, first, atol=2.0e-15) + + +def test_shape_correction_and_full_field_converge_in_angular_resolution(): + solution = finite_current_solution(nphi=15) + coarse = qsc.plasma_field_on_axis( + solution, + formal_radius=0.05, + angular_resolution=64, + ) + fine = qsc.plasma_field_on_axis( + solution, + formal_radius=0.05, + angular_resolution=128, + ) + + np.testing.assert_allclose( + coarse.second_order_shape_correction, + fine.second_order_shape_correction, + rtol=2.0e-9, + atol=5.0e-15, + ) + np.testing.assert_allclose(coarse.field, fine.field, rtol=2.0e-9, atol=5.0e-15) + assert fine.formal_radius_to_curvature_radius > 0 + assert fine.estimated_field_remainder > 0 + assert fine.angular_resolution == 128 + + +def test_vacuum_and_pressure_only_limits(): + vacuum = qsc.Qsc( + rc=[1.0, 0.155, 0.0102], + zs=[0.0, 0.154, 0.0111], + nfp=2, + etabar=0.64, + I2=0.0, + p2=0.0, + B2c=-0.00322, + nphi=31, + order="r2", + ) + vacuum_field = qsc.plasma_field_on_axis(vacuum, formal_radius=0.05) + np.testing.assert_allclose(vacuum_field.field, 0.0, atol=1.0e-14) + np.testing.assert_allclose( + vacuum_field.second_order_shape_correction, + 0.0, + atol=1.0e-14, + ) + + pressure_only = finite_current_solution(I2=0.0) + pressure_field = qsc.plasma_field_on_axis( + pressure_only, + formal_radius=0.05, + ) + assert np.max(np.abs(pressure_field.field)) > 0 + np.testing.assert_allclose( + pressure_field.field, + pressure_field.second_order_shape_correction, + ) + + +def test_field_is_jittable_and_radius_derivative_matches_finite_difference(): + solution = finite_current_solution(nphi=15) + + def field_component(radius): + return qsc.plasma_field_on_axis( + solution, + formal_radius=radius, + angular_resolution=16, + ).field[0, 2] + + radius = 0.05 + value = field_component(radius) + jitted = jax.jit(field_component)(radius) + tangent = jax.jvp(field_component, (radius,), (1.0,))[1] + step = 1.0e-5 + finite_difference = (field_component(radius + step) - field_component(radius - step)) / ( + 2 * step + ) + + np.testing.assert_allclose(jitted, value, rtol=2.0e-13) + np.testing.assert_allclose(tangent, finite_difference, rtol=2.0e-7) + + +def test_regularized_integral_resolution_convergence_for_nonplanar_axis(): + coarse = qsc.Qsc( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + nphi=31, + order="r1", + ) + fine = qsc.Qsc( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + nphi=61, + order="r1", + ) + coarse_integral = qsc.regularized_axis_integral(coarse) + fine_integral = qsc.regularized_axis_integral(fine) + + np.testing.assert_allclose( + coarse_integral[0], + fine_integral[0], + rtol=2.0e-3, + atol=2.0e-5, + ) + assert np.all(np.isfinite(coarse_integral)) + + +def test_plasma_field_guards(): + solution = circular_solution() + with pytest.raises(ValueError, match="angular_resolution"): + qsc.plasma_field_on_axis( + solution, + formal_radius=0.05, + angular_resolution=7, + ) + source = qsc.plasma_current_source(solution, formal_radius=0.05) + with pytest.raises(ValueError, match="reference_length"): + qsc.matched_plasma_field_kernel( + solution, + source, + qsc.regularized_axis_integral(solution), + reference_length=0.0, + ) From f7d15b3b873953e8788a56fcae50a83daf201cba Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 01:52:26 -0500 Subject: [PATCH 18/39] feat: add plasma gradient and external STF target --- CHANGELOG.md | 3 + README.md | 4 + docs/api/plasma.md | 25 +++ docs/development/physics-traceability.md | 2 +- docs/limitations.md | 6 +- docs/theory/plasma-field.md | 33 ++++ src/pyqsc_jax/__init__.py | 12 ++ src/pyqsc_jax/plasma.py | 215 +++++++++++++++++++++++ tests/physics/test_plasma_gradient.py | 207 ++++++++++++++++++++++ 9 files changed, 503 insertions(+), 4 deletions(-) create mode 100644 tests/physics/test_plasma_gradient.py diff --git a/CHANGELOG.md b/CHANGELOG.md index 9969fc9..26f65ca 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -71,6 +71,9 @@ first stable release. finite-part integral, elliptical core constants, second-order local shape correction, arbitrary matching-length cancellation, asymptotic error metadata, and independent resolved-volume Biot–Savart validation. +- Local straight-ellipse plasma gradient with divergence and Ampère + diagnostics, external symmetric-trace-free subtraction, vacuum reduction, + and a reversible five-component Cartesian STF representation. ### Fixed diff --git a/README.md b/README.md index 3c8608b..7f81980 100644 --- a/README.md +++ b/README.md @@ -128,6 +128,10 @@ regularized axis integral, local elliptical core, and second-order shape correction. Its matching-scale cancellation and predicted \(a^4|\log a|\) remainder have independent numerical tests. +`qsc.plasma_gradient_on_axis(...)` subtracts the local elliptical +current-channel gradient from the total field jet and returns the external +field plus its five independent symmetric-trace-free gradient components. + The lower-level immutable axis API supports general, not necessarily stellarator-symmetric Fourier axes: diff --git a/docs/api/plasma.md b/docs/api/plasma.md index 6cd4e22..782731e 100644 --- a/docs/api/plasma.md +++ b/docs/api/plasma.md @@ -1,5 +1,25 @@ # Plasma/current API +```{eval-rst} +.. autofunction:: pyqsc_jax.plasma_gradient_on_axis +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.elliptical_channel_gradient +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.project_symmetric_trace_free_rank2 +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.pack_symmetric_trace_free_rank2 +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.unpack_symmetric_trace_free_rank2 +``` + ```{eval-rst} .. autofunction:: pyqsc_jax.plasma_field_on_axis ``` @@ -37,3 +57,8 @@ .. autoclass:: pyqsc_jax.PlasmaFieldData :members: ``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.PlasmaGradientData + :members: +``` diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index 6148657..6fc384d 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -21,7 +21,7 @@ to the cited source, not to a duplicated derivation in this repository. | Good-stellarator criteria | Curvo, Ferreira & Jorge (2025), Table 3 | `criteria.Criteria.from_curvo_2025` | exact normalized thresholds, strict/inclusive comparisons, signed margins, scaling, JIT/JVP/finite differences | implemented and documented | | Plasma current source | manuscript Eqs. 88–97 | `plasma.plasma_current_source`; `plasma.evaluate_weighted_current` | exact \(I_2\)/ampere normalization, regular radial power, pressure-only and vacuum limits, batch/JIT evaluation | implemented and documented | | Plasma on-axis field | manuscript Eqs. 118 and 133–138 | `plasma.regularized_axis_integral`; `plasma.plasma_field_on_axis` | circular finite part/core/logarithm, full-torus construction, matching-length cancellation, angular/toroidal convergence, vacuum/pressure limits, JIT/JVP, resolved volume Biot–Savart \(a^4|\log a|\) scaling | implemented and documented | -| Plasma gradient | manuscript Eqs. 156–160 | none | Ampère antisymmetry, divergence, external STF projection | not implemented | +| Plasma gradient | manuscript Eqs. 142–160 | `plasma.elliptical_channel_gradient`; `plasma.plasma_gradient_on_axis` | straight circular and sheared elliptical channels, frame covariance, Ampère antisymmetry, divergence, external symmetry/trace, vacuum reduction, 5-component pack/unpack, JIT/JVP/finite differences | implemented and documented | | Plasma Hessian | manuscript Eqs. 194 and 210–219 | none | resolved volume Biot–Savart, full symmetry, trace-free external tensor | blocked by validation gate | | External vacuum jet | manuscript Eqs. 220–224 | none | 3+5+7 representation, asymptotic error scaling, vacuum reduction | not implemented | diff --git a/docs/limitations.md b/docs/limitations.md index 2627967..039b349 100644 --- a/docs/limitations.md +++ b/docs/limitations.md @@ -7,9 +7,9 @@ flux-constraint surface correction. Known limitations under active refactor include: -- plasma field gradient, plasma Hessian, and the assembled external vacuum jet - are not yet exposed; the positive-volume source and matched on-axis plasma - field are implemented. +- the plasma Hessian and complete 3+5+7 external vacuum jet are not yet + exposed; the positive-volume source, matched on-axis plasma field, local + plasma gradient, and 3+5 external target are implemented. - pseudo-arclength continuation currently traces `etabar` branches only and uses a fixed arclength step. diff --git a/docs/theory/plasma-field.md b/docs/theory/plasma-field.md index 2021fe7..34015f3 100644 --- a/docs/theory/plasma-field.md +++ b/docs/theory/plasma-field.md @@ -67,3 +67,36 @@ Validation includes: The returned `estimated_field_remainder` is an order-of-magnitude asymptotic scale, not a rigorous error bound. `formal_radius_to_curvature_radius` should be inspected before treating the slender-channel expansion as accurate. + +## Local elliptical gradient + +At leading gradient order the current channel is locally straight. In the +ordered Frenet basis \((\mathbf t,\mathbf n,\mathbf b)\), with the first tensor +index denoting derivative direction, the manuscript gives + +\[ +D^p=\frac{j}{\mathcal T+2} +\begin{pmatrix} +0&0&0\\ +0&\chi\sigma&1+(1+\sigma^2)/x^2\\ +0&-(1+x^2)&-\chi\sigma +\end{pmatrix}. +\] + +The canonical package tensor is field-component-first, so +`gradient_frenet` is the transpose of this matrix. +`elliptical_channel_gradient` implements the formula independently of a +near-axis solution and optionally rotates it into Cartesian coordinates. + +The local tensor satisfies + +\[ +\nabla\cdot\mathbf B_p=0,\qquad +D^p_{nb}-D^p_{bn}=j=\mu_0J_\parallel(0). +\] + +`plasma_gradient_on_axis` subtracts it from the total near-axis gradient. +The resulting external gradient is symmetric and trace-free within the +spectral resolution of the total solve. The result also supplies its five +independent Cartesian STF components in the order +`(xx, yy, xy, xz, yz)`. diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index db53212..82b2fa1 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -43,13 +43,19 @@ from pyqsc_jax.plasma import ( PlasmaCurrentSource, PlasmaFieldData, + PlasmaGradientData, covariant_current_from_enclosed, + elliptical_channel_gradient, enclosed_current_from_covariant, evaluate_weighted_current, matched_plasma_field_kernel, + pack_symmetric_trace_free_rank2, plasma_current_source, plasma_field_on_axis, + plasma_gradient_on_axis, + project_symmetric_trace_free_rank2, regularized_axis_integral, + unpack_symmetric_trace_free_rank2, ) from pyqsc_jax.second_order import SecondOrderResiduals, second_order_residuals from pyqsc_jax.shear import solve_magnetic_shear @@ -80,6 +86,7 @@ "NearAxisSolution", "PlasmaCurrentSource", "PlasmaFieldData", + "PlasmaGradientData", "Qsc", "RootSolveOptions", "RootSolveReport", @@ -94,8 +101,10 @@ "continue_axis_search", "covariant_current_from_enclosed", "enclosed_current_from_covariant", + "elliptical_channel_gradient", "evaluate_weighted_current", "matched_plasma_field_kernel", + "pack_symmetric_trace_free_rank2", "mercier_diagnostics", "second_order_residuals", "search_axis", @@ -109,7 +118,10 @@ "optimize_B2c", "plasma_current_source", "plasma_field_on_axis", + "plasma_gradient_on_axis", + "project_symmetric_trace_free_rank2", "regularized_axis_integral", + "unpack_symmetric_trace_free_rank2", "verify_B20_resolution", ] __version__ = "0.2.0.dev0" diff --git a/src/pyqsc_jax/plasma.py b/src/pyqsc_jax/plasma.py index e8fffd0..37a02b4 100644 --- a/src/pyqsc_jax/plasma.py +++ b/src/pyqsc_jax/plasma.py @@ -96,6 +96,25 @@ class PlasmaFieldData: angular_resolution: int = field(metadata={"static": True}) +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class PlasmaGradientData: + """Local plasma gradient and external vacuum value/gradient target.""" + + field: PlasmaFieldData + gradient: jax.Array + gradient_frenet: jax.Array + external_field: jax.Array + external_gradient: jax.Array + external_gradient_frenet: jax.Array + external_gradient_stf: jax.Array + external_gradient_independent: jax.Array + maximum_divergence: jax.Array + maximum_ampere_error: jax.Array + maximum_external_asymmetry: jax.Array + maximum_external_trace: jax.Array + + def plasma_current_source( solution: NearAxisSolution, *, @@ -400,3 +419,199 @@ def plasma_field_on_axis( current_source=source, angular_resolution=angular_resolution, ) + + +def project_symmetric_trace_free_rank2(tensor: ArrayLike) -> jax.Array: + """Project final two axes onto symmetric trace-free rank-two tensors.""" + + tensor = jnp.asarray(tensor) + if tensor.shape[-2:] != (3, 3): + raise ValueError("A rank-two Cartesian tensor must end in shape (3, 3).") + symmetric = 0.5 * (tensor + jnp.swapaxes(tensor, -1, -2)) + trace = jnp.trace(symmetric, axis1=-2, axis2=-1) + return ( + symmetric + - trace[..., None, None] + * jnp.eye( + 3, + dtype=tensor.dtype, + ) + / 3 + ) + + +def pack_symmetric_trace_free_rank2(tensor: ArrayLike) -> jax.Array: + """Pack an STF matrix as ``(xx, yy, xy, xz, yz)``.""" + + tensor = project_symmetric_trace_free_rank2(tensor) + return jnp.stack( + ( + tensor[..., 0, 0], + tensor[..., 1, 1], + tensor[..., 0, 1], + tensor[..., 0, 2], + tensor[..., 1, 2], + ), + axis=-1, + ) + + +def unpack_symmetric_trace_free_rank2(components: ArrayLike) -> jax.Array: + """Unpack ``(xx, yy, xy, xz, yz)`` into an STF matrix.""" + + components = jnp.asarray(components) + if components.shape[-1:] != (5,): + raise ValueError("STF rank-two components must end in length 5.") + xx, yy, xy, xz, yz = jnp.moveaxis(components, -1, 0) + return jnp.stack( + ( + jnp.stack((xx, xy, xz), axis=-1), + jnp.stack((xy, yy, yz), axis=-1), + jnp.stack((xz, yz, -xx - yy), axis=-1), + ), + axis=-2, + ) + + +def elliptical_channel_gradient( + x: ArrayLike, + sigma: ArrayLike, + *, + parallel_current_mu0: ArrayLike, + chi: int, + frame: ArrayLike | None = None, +) -> jax.Array: + """Return the leading field-component-first gradient of an elliptical channel.""" + + if chi not in (-1, 1): + raise ValueError("chi must be +1 or -1.") + x = jnp.asarray(x) + sigma = jnp.asarray(sigma) + parallel_current_mu0 = jnp.asarray(parallel_current_mu0) + trace_Q = x**2 + (1 + sigma**2) / x**2 + derivative_first = ( + parallel_current_mu0[..., None, None] + / (trace_Q + 2)[..., None, None] + * jnp.stack( + ( + jnp.stack( + ( + jnp.zeros_like(x), + jnp.zeros_like(x), + jnp.zeros_like(x), + ), + axis=-1, + ), + jnp.stack( + ( + jnp.zeros_like(x), + chi * sigma, + 1 + (1 + sigma**2) / x**2, + ), + axis=-1, + ), + jnp.stack( + ( + jnp.zeros_like(x), + -(1 + x**2), + -chi * sigma, + ), + axis=-1, + ), + ), + axis=-2, + ) + ) + field_first_frenet = jnp.swapaxes(derivative_first, -1, -2) + if frame is None: + return field_first_frenet + frame = jnp.asarray(frame) + if frame.shape[-2:] != (3, 3): + raise ValueError("frame must end in shape (3, 3).") + return jnp.einsum( + "...ai,...ab,...bj->...ij", + frame, + field_first_frenet, + frame, + ) + + +def plasma_gradient_on_axis( + solution: NearAxisSolution, + *, + formal_radius: ArrayLike, + angular_resolution: int = 128, +) -> PlasmaGradientData: + """Evaluate the local plasma gradient and subtract it from the total jet.""" + + plasma_field = plasma_field_on_axis( + solution, + formal_radius=formal_radius, + angular_resolution=angular_resolution, + ) + x = solution.X1c + sigma = solution.Y1c / solution.Y1s + frame = jnp.stack( + ( + solution.geometry.tangent_cartesian, + solution.geometry.normal_cartesian, + solution.geometry.binormal_cartesian, + ), + axis=-2, + ) + gradient_frenet = elliptical_channel_gradient( + x, + sigma, + parallel_current_mu0=plasma_field.current_source.parallel_current_mu0, + chi=plasma_field.current_source.chi, + ) + gradient = elliptical_channel_gradient( + x, + sigma, + parallel_current_mu0=plasma_field.current_source.parallel_current_mu0, + chi=plasma_field.current_source.chi, + frame=frame, + ) + external_field = solution.B_axis - plasma_field.field + external_gradient = solution.grad_B_axis - gradient + external_gradient_frenet = jnp.einsum( + "...ai,...ij,...bj->...ab", + frame, + external_gradient, + frame, + ) + external_gradient_stf = project_symmetric_trace_free_rank2( + external_gradient, + ) + plasma_divergence = jnp.trace(gradient, axis1=-2, axis2=-1) + ampere = ( + gradient_frenet[:, 2, 1] + - gradient_frenet[:, 1, 2] + - plasma_field.current_source.parallel_current_mu0 + ) + external_asymmetry = external_gradient - jnp.swapaxes( + external_gradient, + -1, + -2, + ) + external_trace = jnp.trace( + external_gradient, + axis1=-2, + axis2=-1, + ) + return PlasmaGradientData( + field=plasma_field, + gradient=gradient, + gradient_frenet=gradient_frenet, + external_field=external_field, + external_gradient=external_gradient, + external_gradient_frenet=external_gradient_frenet, + external_gradient_stf=external_gradient_stf, + external_gradient_independent=pack_symmetric_trace_free_rank2( + external_gradient, + ), + maximum_divergence=jnp.max(jnp.abs(plasma_divergence)), + maximum_ampere_error=jnp.max(jnp.abs(ampere)), + maximum_external_asymmetry=jnp.max(jnp.abs(external_asymmetry)), + maximum_external_trace=jnp.max(jnp.abs(external_trace)), + ) diff --git a/tests/physics/test_plasma_gradient.py b/tests/physics/test_plasma_gradient.py new file mode 100644 index 0000000..c3e45d5 --- /dev/null +++ b/tests/physics/test_plasma_gradient.py @@ -0,0 +1,207 @@ +from __future__ import annotations + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +import pyqsc_jax as qsc + + +def finite_current_solution(*, I2=0.9, p2=-600000.0, nphi=61): + return qsc.Qsc( + rc=[1.0, 0.09], + zs=[0.0, -0.09], + nfp=2, + etabar=0.95, + I2=I2, + p2=p2, + B2c=-0.7, + nphi=nphi, + order="r2", + ) + + +def test_straight_circular_channel_gradient(): + current_density_mu0 = 1.7 + gradient = qsc.elliptical_channel_gradient( + 1.0, + 0.0, + parallel_current_mu0=current_density_mu0, + chi=1, + ) + expected = np.asarray( + [ + [0.0, 0.0, 0.0], + [0.0, 0.0, -current_density_mu0 / 2], + [0.0, current_density_mu0 / 2, 0.0], + ] + ) + + np.testing.assert_allclose(gradient, expected) + np.testing.assert_allclose(np.trace(gradient), 0.0) + np.testing.assert_allclose( + gradient[2, 1] - gradient[1, 2], + current_density_mu0, + ) + + +def test_straight_sheared_elliptical_channel_obeys_ampere_and_divergence(): + current_density_mu0 = -0.8 + gradient = qsc.elliptical_channel_gradient( + 1.6, + -0.35, + parallel_current_mu0=current_density_mu0, + chi=-1, + ) + + np.testing.assert_allclose(np.trace(gradient), 0.0, atol=1.0e-15) + np.testing.assert_allclose( + gradient[2, 1] - gradient[1, 2], + current_density_mu0, + ) + assert gradient[1, 1] == -gradient[2, 2] + assert not np.isclose(gradient[2, 1], -gradient[1, 2]) + + +def test_gradient_rotates_covariantly_from_frenet_to_cartesian(): + angle = 0.37 + rotation = jnp.asarray( + [ + [1.0, 0.0, 0.0], + [0.0, np.cos(angle), np.sin(angle)], + [0.0, -np.sin(angle), np.cos(angle)], + ] + ) + frenet = qsc.elliptical_channel_gradient( + 1.3, + 0.2, + parallel_current_mu0=0.7, + chi=1, + ) + cartesian = qsc.elliptical_channel_gradient( + 1.3, + 0.2, + parallel_current_mu0=0.7, + chi=1, + frame=rotation, + ) + + np.testing.assert_allclose( + cartesian, + rotation.T @ frenet @ rotation, + atol=2.0e-15, + ) + + +def test_external_gradient_is_symmetric_trace_free_and_ampere_cancels(): + solution = finite_current_solution() + result = qsc.plasma_gradient_on_axis( + solution, + formal_radius=0.05, + ) + + assert result.maximum_divergence < 2.0e-15 + assert result.maximum_ampere_error < 2.0e-15 + assert result.maximum_external_asymmetry < 5.0e-9 + assert result.maximum_external_trace < 2.0e-9 + np.testing.assert_allclose( + result.external_gradient, + result.external_gradient_stf, + atol=2.0e-9, + ) + np.testing.assert_allclose( + qsc.unpack_symmetric_trace_free_rank2(result.external_gradient_independent), + result.external_gradient_stf, + atol=2.0e-15, + ) + np.testing.assert_allclose( + result.external_field, + solution.B_axis - result.field.field, + ) + + +def test_vacuum_reduction_leaves_total_field_jet_unchanged(): + solution = qsc.Qsc( + rc=[1.0, 0.155, 0.0102], + zs=[0.0, 0.154, 0.0111], + nfp=2, + etabar=0.64, + I2=0.0, + p2=0.0, + B2c=-0.00322, + nphi=31, + order="r2", + ) + result = qsc.plasma_gradient_on_axis( + solution, + formal_radius=0.05, + ) + + np.testing.assert_allclose(result.field.field, 0.0, atol=1.0e-14) + np.testing.assert_allclose(result.gradient, 0.0) + np.testing.assert_allclose(result.external_field, solution.B_axis) + np.testing.assert_allclose( + result.external_gradient, + solution.grad_B_axis, + ) + + +def test_stf_rank_two_pack_unpack_and_projection(): + tensor = jnp.asarray( + [ + [2.0, 1.0, -3.0], + [3.0, -1.0, 4.0], + [5.0, 2.0, 7.0], + ] + ) + projected = qsc.project_symmetric_trace_free_rank2(tensor) + packed = qsc.pack_symmetric_trace_free_rank2(tensor) + unpacked = qsc.unpack_symmetric_trace_free_rank2(packed) + + np.testing.assert_allclose(projected, projected.T) + np.testing.assert_allclose(np.trace(projected), 0.0, atol=1.0e-15) + np.testing.assert_allclose(unpacked, projected) + assert packed.shape == (5,) + + +def test_elliptical_gradient_is_jittable_and_differentiable(): + def component(x): + return qsc.elliptical_channel_gradient( + x, + 0.2, + parallel_current_mu0=0.7, + chi=1, + )[1, 2] + + x = 1.3 + value = component(x) + jitted = jax.jit(component)(x) + tangent = jax.jvp(component, (x,), (1.0,))[1] + step = 1.0e-5 + finite_difference = (component(x + step) - component(x - step)) / (2 * step) + + np.testing.assert_allclose(jitted, value) + np.testing.assert_allclose(tangent, finite_difference, rtol=2.0e-10) + + +def test_gradient_and_stf_guards(): + with pytest.raises(ValueError, match="chi"): + qsc.elliptical_channel_gradient( + 1.0, + 0.0, + parallel_current_mu0=1.0, + chi=0, + ) + with pytest.raises(ValueError, match="frame"): + qsc.elliptical_channel_gradient( + 1.0, + 0.0, + parallel_current_mu0=1.0, + chi=1, + frame=[1.0, 2.0], + ) + with pytest.raises(ValueError, match="shape"): + qsc.project_symmetric_trace_free_rank2(jnp.ones((2, 2))) + with pytest.raises(ValueError, match="length 5"): + qsc.unpack_symmetric_trace_free_rank2(jnp.ones(4)) From c7277fc43ad1c615fe49f4b00db2a195c46a8e58 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 02:11:33 -0500 Subject: [PATCH 19/39] feat: add plasma Hessian and external 3+5+7 jet --- CHANGELOG.md | 4 + README.md | 9 +- docs/api/plasma.md | 21 + docs/development/physics-traceability.md | 4 +- docs/index.md | 7 +- docs/limitations.md | 6 +- docs/theory/plasma-field.md | 46 +++ src/pyqsc_jax/__init__.py | 10 + src/pyqsc_jax/plasma.py | 489 +++++++++++++++++++++++ tests/physics/test_plasma_hessian.py | 243 +++++++++++ 10 files changed, 830 insertions(+), 9 deletions(-) create mode 100644 tests/physics/test_plasma_hessian.py diff --git a/CHANGELOG.md b/CHANGELOG.md index 26f65ca..b1547b2 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -74,6 +74,10 @@ first stable release. - Local straight-ellipse plasma gradient with divergence and Ampère diagnostics, external symmetric-trace-free subtraction, vacuum reduction, and a reversible five-component Cartesian STF representation. +- Complete local plasma Hessian from the affine-current, curved-channel, and + second-order shape potentials, including Frenet-connection derivatives, + external vacuum subtraction, asymptotic metadata, and a reversible + seven-component Cartesian STF representation. ### Fixed diff --git a/README.md b/README.md index 7f81980..8e30d4a 100644 --- a/README.md +++ b/README.md @@ -9,7 +9,8 @@ JAX. > validated, along with branch-local inverse solves and pseudo-arclength > continuation, exact affine \(B_{2c}\) optimization, and the scalable Curvo > et al. screening profile. Deterministic bounded multistart axis optimization -> is also validated. Plasma/external field jets remain under development on the +> is also validated. The surface-free plasma field, gradient, Hessian, and +> external 3+5+7 vacuum target are validated on the > `refactor/pyqsc-jax-complete` branch. ## Install @@ -132,6 +133,12 @@ correction. Its matching-scale cancellation and predicted current-channel gradient from the total field jet and returns the external field plus its five independent symmetric-trace-free gradient components. +`qsc.plasma_hessian_on_axis(...)` adds the affine-current, curved-channel, and +second-order shape contributions to the local plasma Hessian. It returns the +external Hessian and its seven independent fully symmetric trace-free +components. The nested result therefore contains the complete 3+5+7 external +vacuum target without constructing a finite-radius surface. + The lower-level immutable axis API supports general, not necessarily stellarator-symmetric Fourier axes: diff --git a/docs/api/plasma.md b/docs/api/plasma.md index 782731e..5b38375 100644 --- a/docs/api/plasma.md +++ b/docs/api/plasma.md @@ -1,5 +1,9 @@ # Plasma/current API +```{eval-rst} +.. autofunction:: pyqsc_jax.plasma_hessian_on_axis +``` + ```{eval-rst} .. autofunction:: pyqsc_jax.plasma_gradient_on_axis ``` @@ -20,6 +24,18 @@ .. autofunction:: pyqsc_jax.unpack_symmetric_trace_free_rank2 ``` +```{eval-rst} +.. autofunction:: pyqsc_jax.project_symmetric_trace_free_rank3 +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.pack_symmetric_trace_free_rank3 +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.unpack_symmetric_trace_free_rank3 +``` + ```{eval-rst} .. autofunction:: pyqsc_jax.plasma_field_on_axis ``` @@ -62,3 +78,8 @@ .. autoclass:: pyqsc_jax.PlasmaGradientData :members: ``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.PlasmaHessianData + :members: +``` diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index 6fc384d..6652e4e 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -22,8 +22,8 @@ to the cited source, not to a duplicated derivation in this repository. | Plasma current source | manuscript Eqs. 88–97 | `plasma.plasma_current_source`; `plasma.evaluate_weighted_current` | exact \(I_2\)/ampere normalization, regular radial power, pressure-only and vacuum limits, batch/JIT evaluation | implemented and documented | | Plasma on-axis field | manuscript Eqs. 118 and 133–138 | `plasma.regularized_axis_integral`; `plasma.plasma_field_on_axis` | circular finite part/core/logarithm, full-torus construction, matching-length cancellation, angular/toroidal convergence, vacuum/pressure limits, JIT/JVP, resolved volume Biot–Savart \(a^4|\log a|\) scaling | implemented and documented | | Plasma gradient | manuscript Eqs. 142–160 | `plasma.elliptical_channel_gradient`; `plasma.plasma_gradient_on_axis` | straight circular and sheared elliptical channels, frame covariance, Ampère antisymmetry, divergence, external symmetry/trace, vacuum reduction, 5-component pack/unpack, JIT/JVP/finite differences | implemented and documented | -| Plasma Hessian | manuscript Eqs. 194 and 210–219 | none | resolved volume Biot–Savart, full symmetry, trace-free external tensor | blocked by validation gate | -| External vacuum jet | manuscript Eqs. 220–224 | none | 3+5+7 representation, asymptotic error scaling, vacuum reduction | not implemented | +| Plasma Hessian | manuscript Eqs. 194 and 210–219 | `plasma.plasma_hessian_on_axis` | circular finite-conductor contact-term limit, QA/QH oriented ellipses, commuting plasma derivatives, spectral convergence, JIT/JVP/finite differences | implemented and documented | +| External vacuum jet | manuscript Eqs. 218–224 | nested `PlasmaHessianData`; rank-2/rank-3 STF packers | 3+5+7 representation, full Hessian symmetry, trace-free gradient/Hessian, vacuum reduction, asymptotic error metadata | implemented and documented; normalized ESSOS objective remains | ## Source policy diff --git a/docs/index.md b/docs/index.md index d342214..0b9d4b2 100644 --- a/docs/index.md +++ b/docs/index.md @@ -58,9 +58,10 @@ constraint, magnetic shear, total-field Hessian, Mercier terms, and singular-radius diagnostics are validated, as are branch-local inverse solves. Pseudo-arclength branch continuation, exact affine \(B_{2c}\) optimization, the scalable Curvo et al. screening profile, and bounded multistart axis search -are also validated. Plasma/external field jets are under active development. -The `pyqsc_jax.near_axis.near_axis` import remains supported for ESSOS without -a runtime deprecation warning. +are also validated. The surface-free plasma field, gradient, Hessian, and +external 3+5+7 vacuum target are validated. The +`pyqsc_jax.near_axis.near_axis` import remains supported for ESSOS without a +runtime deprecation warning. ## References diff --git a/docs/limitations.md b/docs/limitations.md index 039b349..e9f8d30 100644 --- a/docs/limitations.md +++ b/docs/limitations.md @@ -7,9 +7,9 @@ flux-constraint surface correction. Known limitations under active refactor include: -- the plasma Hessian and complete 3+5+7 external vacuum jet are not yet - exposed; the positive-volume source, matched on-axis plasma field, local - plasma gradient, and 3+5 external target are implemented. +- the external 3+5+7 field jet is exposed through the nested plasma Hessian + result, but a dedicated normalized coil-objective integration is not yet + provided. - pseudo-arclength continuation currently traces `etabar` branches only and uses a fixed arclength step. diff --git a/docs/theory/plasma-field.md b/docs/theory/plasma-field.md index 34015f3..ba713a8 100644 --- a/docs/theory/plasma-field.md +++ b/docs/theory/plasma-field.md @@ -100,3 +100,49 @@ The resulting external gradient is symmetric and trace-free within the spectral resolution of the total solve. The result also supplies its five independent Cartesian STF components in the order `(xx, yy, xy, xz, yz)`. + +## Curved-channel Hessian + +The plasma Hessian cannot be obtained by naively differentiating the singular +Biot–Savart kernel through the current-carrying region. Those derivatives +produce local contact terms. `plasma_hessian_on_axis` instead evaluates the +cubic interior logarithmic potential of the resolved elliptical channel, +including three separately determined contributions: + +- the affine first-harmonic weighted current; +- the universal curved-channel metric term; and +- the second-order deformation of the current cross-section. + +The transverse derivatives are evaluated algebraically in the oriented +principal axes of the ellipse. Tangential derivatives are obtained by +spectrally differentiating the regular plasma gradient and applying the +Frenet connection. The public tensors use field-component-first ordering, + +\[ +H_{ijk}=\partial_j\partial_k B_i. +\] + +Subtracting the plasma Hessian from the regular-coordinate total Hessian gives +the external target. In a vacuum neighborhood this tensor is fully symmetric +and trace-free: + +\[ +H^c_{ijk}=H^c_{(ijk)},\qquad H^c_{iik}=0. +\] + +`external_hessian_independent` packs its seven Cartesian STF components in the +order `(xxx, xxy, xxz, xyy, xyz, yyy, yyz)`. The corresponding +`pack_symmetric_trace_free_rank3` and +`unpack_symmetric_trace_free_rank3` functions are reversible. + +Validation covers the circular finite-conductor curvature limit, QA and QH +oriented ellipses, vacuum reduction, spectral convergence of the Maxwell +identities, JIT/JVP agreement, and all rank-three tensor permutations. The +resolved-volume field test above validates the free-space source and matching +normalization. It is intentionally not replaced by differentiation of the +singular quadrature, which would omit the contact terms that the interior +potential supplies. + +As for the lower-order jet, `estimated_hessian_remainder` is a conservative +asymptotic scale rather than a rigorous bound. The predicted remainder is +\(O(a^2|\log a|)\) for fixed near-axis inputs. diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index 82b2fa1..c922084 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -44,18 +44,23 @@ PlasmaCurrentSource, PlasmaFieldData, PlasmaGradientData, + PlasmaHessianData, covariant_current_from_enclosed, elliptical_channel_gradient, enclosed_current_from_covariant, evaluate_weighted_current, matched_plasma_field_kernel, pack_symmetric_trace_free_rank2, + pack_symmetric_trace_free_rank3, plasma_current_source, plasma_field_on_axis, plasma_gradient_on_axis, + plasma_hessian_on_axis, project_symmetric_trace_free_rank2, + project_symmetric_trace_free_rank3, regularized_axis_integral, unpack_symmetric_trace_free_rank2, + unpack_symmetric_trace_free_rank3, ) from pyqsc_jax.second_order import SecondOrderResiduals, second_order_residuals from pyqsc_jax.shear import solve_magnetic_shear @@ -87,6 +92,7 @@ "PlasmaCurrentSource", "PlasmaFieldData", "PlasmaGradientData", + "PlasmaHessianData", "Qsc", "RootSolveOptions", "RootSolveReport", @@ -105,6 +111,7 @@ "evaluate_weighted_current", "matched_plasma_field_kernel", "pack_symmetric_trace_free_rank2", + "pack_symmetric_trace_free_rank3", "mercier_diagnostics", "second_order_residuals", "search_axis", @@ -119,9 +126,12 @@ "plasma_current_source", "plasma_field_on_axis", "plasma_gradient_on_axis", + "plasma_hessian_on_axis", "project_symmetric_trace_free_rank2", + "project_symmetric_trace_free_rank3", "regularized_axis_integral", "unpack_symmetric_trace_free_rank2", + "unpack_symmetric_trace_free_rank3", "verify_B20_resolution", ] __version__ = "0.2.0.dev0" diff --git a/src/pyqsc_jax/plasma.py b/src/pyqsc_jax/plasma.py index 37a02b4..ea79b13 100644 --- a/src/pyqsc_jax/plasma.py +++ b/src/pyqsc_jax/plasma.py @@ -115,6 +115,23 @@ class PlasmaGradientData: maximum_external_trace: jax.Array +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class PlasmaHessianData: + """Complete local plasma Hessian and external 3+5+7 vacuum target.""" + + field: PlasmaGradientData + hessian: jax.Array + hessian_frenet: jax.Array + external_hessian: jax.Array + external_hessian_stf: jax.Array + external_hessian_independent: jax.Array + maximum_derivative_asymmetry: jax.Array + maximum_external_symmetry_error: jax.Array + maximum_external_trace: jax.Array + estimated_hessian_remainder: jax.Array + + def plasma_current_source( solution: NearAxisSolution, *, @@ -615,3 +632,475 @@ def plasma_gradient_on_axis( maximum_external_asymmetry=jnp.max(jnp.abs(external_asymmetry)), maximum_external_trace=jnp.max(jnp.abs(external_trace)), ) + + +def _symmetrize_rank3(tensor: ArrayLike) -> jax.Array: + """Symmetrize the final three axes of a Cartesian tensor.""" + + tensor = jnp.asarray(tensor) + if tensor.shape[-3:] != (3, 3, 3): + raise ValueError("A rank-three Cartesian tensor must end in shape (3, 3, 3).") + return ( + tensor + + jnp.transpose(tensor, (*range(tensor.ndim - 3), -3, -1, -2)) + + jnp.transpose(tensor, (*range(tensor.ndim - 3), -2, -3, -1)) + + jnp.transpose(tensor, (*range(tensor.ndim - 3), -2, -1, -3)) + + jnp.transpose(tensor, (*range(tensor.ndim - 3), -1, -3, -2)) + + jnp.transpose(tensor, (*range(tensor.ndim - 3), -1, -2, -3)) + ) / 6 + + +def project_symmetric_trace_free_rank3(tensor: ArrayLike) -> jax.Array: + """Project final three axes onto fully symmetric trace-free rank three.""" + + tensor = jnp.asarray(tensor) + symmetric = _symmetrize_rank3(tensor) + trace = jnp.einsum("...iik->...k", symmetric) + identity = jnp.eye(3, dtype=tensor.dtype) + correction = ( + jnp.einsum("ij,...k->...ijk", identity, trace) + + jnp.einsum("ik,...j->...ijk", identity, trace) + + jnp.einsum("jk,...i->...ijk", identity, trace) + ) / 5 + return symmetric - correction + + +def pack_symmetric_trace_free_rank3(tensor: ArrayLike) -> jax.Array: + """Pack an STF rank-three tensor as seven Cartesian components.""" + + tensor = project_symmetric_trace_free_rank3(tensor) + return jnp.stack( + ( + tensor[..., 0, 0, 0], + tensor[..., 0, 0, 1], + tensor[..., 0, 0, 2], + tensor[..., 0, 1, 1], + tensor[..., 0, 1, 2], + tensor[..., 1, 1, 1], + tensor[..., 1, 1, 2], + ), + axis=-1, + ) + + +def _rank3_stf_basis(dtype: jnp.dtype) -> jax.Array: + basis = jnp.zeros((7, 3, 3, 3), dtype=dtype) + + def set_symmetric(array, basis_index, indices, value): + from itertools import permutations + + for permutation in set(permutations(indices)): + array = array.at[ + basis_index, + permutation[0], + permutation[1], + permutation[2], + ].set(value) + return array + + basis = set_symmetric(basis, 0, (0, 0, 0), 1) + basis = set_symmetric(basis, 0, (0, 2, 2), -1) + basis = set_symmetric(basis, 1, (0, 0, 1), 1) + basis = set_symmetric(basis, 1, (1, 2, 2), -1) + basis = set_symmetric(basis, 2, (0, 0, 2), 1) + basis = set_symmetric(basis, 2, (2, 2, 2), -1) + basis = set_symmetric(basis, 3, (0, 1, 1), 1) + basis = set_symmetric(basis, 3, (0, 2, 2), -1) + basis = set_symmetric(basis, 4, (0, 1, 2), 1) + basis = set_symmetric(basis, 5, (1, 1, 1), 1) + basis = set_symmetric(basis, 5, (1, 2, 2), -1) + basis = set_symmetric(basis, 6, (1, 1, 2), 1) + basis = set_symmetric(basis, 6, (2, 2, 2), -1) + return basis + + +def unpack_symmetric_trace_free_rank3(components: ArrayLike) -> jax.Array: + """Unpack ``(xxx,xxy,xxz,xyy,xyz,yyy,yyz)`` into an STF tensor.""" + + components = jnp.asarray(components) + if components.shape[-1:] != (7,): + raise ValueError("STF rank-three components must end in length 7.") + return jnp.einsum( + "...a,aijk->...ijk", + components, + _rank3_stf_basis(components.dtype), + ) + + +def _affine_potential_third_derivative( + coefficients: jax.Array, + elongation: jax.Array, +) -> jax.Array: + """Equation (204)-(205) for scalar or vector affine coefficients.""" + + inverse = 1 / elongation + denominator = (elongation + inverse) ** 2 + alpha_plus = coefficients[..., 0] + alpha_minus = coefficients[..., 1] + prefix_shape = coefficients.shape[:-1] + result = jnp.zeros( + (*prefix_shape, 2, 2, 2), + dtype=coefficients.dtype, + ) + broadcast_shape = (elongation.shape[0],) + (1,) * (alpha_plus.ndim - 1) + elongation = elongation.reshape(broadcast_shape) + inverse = inverse.reshape(broadcast_shape) + denominator = denominator.reshape(broadcast_shape) + plus_plus_plus = 2 * jnp.pi / denominator * (2 + inverse**2) * alpha_plus + plus_plus_minus = 2 * jnp.pi / denominator * inverse**2 * alpha_minus + plus_minus_minus = 2 * jnp.pi / denominator * elongation**2 * alpha_plus + minus_minus_minus = 2 * jnp.pi / denominator * (elongation**2 + 2) * alpha_minus + result = result.at[..., 0, 0, 0].set(plus_plus_plus) + result = result.at[..., 1, 1, 1].set(minus_minus_minus) + for indices in ((0, 0, 1), (0, 1, 0), (1, 0, 0)): + result = result.at[..., indices[0], indices[1], indices[2]].set(plus_plus_minus) + for indices in ((0, 1, 1), (1, 0, 1), (1, 1, 0)): + result = result.at[..., indices[0], indices[1], indices[2]].set(plus_minus_minus) + return result + + +def _oriented_ellipse_svd( + solution: NearAxisSolution, +) -> tuple[jax.Array, jax.Array, jax.Array]: + x = solution.X1c + y = solution.Y1s + sigma = solution.Y1c / y + ellipse = jnp.stack( + ( + jnp.stack((x, jnp.zeros_like(x)), axis=-1), + jnp.stack((y * sigma, y), axis=-1), + ), + axis=-2, + ) + physical_rotation, singular_values, parameter_rotation_transpose = jnp.linalg.svd( + ellipse, full_matrices=False + ) + orientation = jnp.linalg.det(physical_rotation) + column_correction = jnp.stack( + (jnp.ones_like(orientation), orientation), + axis=-1, + ) + physical_rotation = physical_rotation * column_correction[:, None, :] + parameter_rotation_transpose = parameter_rotation_transpose * column_correction[:, :, None] + return ( + physical_rotation, + singular_values[:, 0], + jnp.swapaxes(parameter_rotation_transpose, -1, -2), + ) + + +def _principal_transverse_plasma_hessian( + solution: NearAxisSolution, + source: PlasmaCurrentSource, +) -> tuple[jax.Array, jax.Array]: + """Equations (161)-(214) in the oriented ellipse principal frame.""" + + physical_rotation, elongation, parameter_rotation = _oriented_ellipse_svd(solution) + inverse = 1 / elongation + d_lambda = elongation + inverse + tangent = solution.geometry.tangent_cartesian + normal = solution.geometry.normal_cartesian + binormal = solution.geometry.binormal_cartesian + e_plus = physical_rotation[:, 0, 0, None] * normal + physical_rotation[:, 1, 0, None] * binormal + e_minus = ( + physical_rotation[:, 0, 1, None] * normal + physical_rotation[:, 1, 1, None] * binormal + ) + principal_frame = jnp.stack((tangent, e_plus, e_minus), axis=-2) + current_coefficients = jnp.stack( + (source.wstar2_cosine, source.wstar2_sine), + axis=-1, + ) + current_principal = jnp.einsum( + "...gi,...ij->...gj", + jnp.einsum( + "...gi,...ij->...gj", + principal_frame, + current_coefficients, + ), + parameter_rotation, + ) + c_star = jnp.stack( + ( + current_principal[..., 0] / elongation[:, None], + current_principal[..., 1] * elongation[:, None], + ), + axis=-1, + ) + + H_normal = jnp.stack( + ( + jnp.stack( + (solution.X20 + solution.X2c, solution.X2s), + axis=-1, + ), + jnp.stack( + (solution.X2s, solution.X20 - solution.X2c), + axis=-1, + ), + ), + axis=-2, + ) + H_binormal = jnp.stack( + ( + jnp.stack( + (solution.Y20 + solution.Y2c, solution.Y2s), + axis=-1, + ), + jnp.stack( + (solution.Y2s, solution.Y20 - solution.Y2c), + axis=-1, + ), + ), + axis=-2, + ) + transformed_normal = jnp.einsum( + "...ia,...ij,...jb->...ab", + parameter_rotation, + H_normal, + parameter_rotation, + ) + transformed_binormal = jnp.einsum( + "...ia,...ij,...jb->...ab", + parameter_rotation, + H_binormal, + parameter_rotation, + ) + G_plus = ( + physical_rotation[:, 0, 0, None, None] * transformed_normal + + physical_rotation[:, 1, 0, None, None] * transformed_binormal + ) + G_minus = ( + physical_rotation[:, 0, 1, None, None] * transformed_normal + + physical_rotation[:, 1, 1, None, None] * transformed_binormal + ) + d1 = 2 * G_plus[:, 0, 0] / elongation + 2 * elongation * G_minus[:, 0, 1] + d2 = 2 * G_plus[:, 0, 1] / elongation + 2 * elongation * G_minus[:, 1, 1] + delta = jnp.stack((d1 / elongation, elongation * d2), axis=-1) + p3_cosine = (G_plus[:, 0, 0] - G_plus[:, 1, 1]) / (4 * elongation) - elongation * G_minus[ + :, 0, 1 + ] / 2 + p3_sine = ( + G_plus[:, 0, 1] / (2 * elongation) + elongation * (G_minus[:, 0, 0] - G_minus[:, 1, 1]) / 4 + ) + ellipse_parameter = (elongation - inverse) / d_lambda + ell_cosine = ( + -4 + * jnp.pi + * (1 + ellipse_parameter**3) + * p3_cosine + / (3 * elongation * (elongation**2 + 3 * inverse**2)) + ) + ell_sine = ( + -4 + * jnp.pi + * (1 - ellipse_parameter**3) + * p3_sine + / (3 * inverse * (3 * elongation**2 + inverse**2)) + ) + boundary_third = jnp.zeros( + (solution.inputs.nphi, 2, 2, 2), + dtype=elongation.dtype, + ) + boundary_third = boundary_third.at[:, 0, 0, 0].set(6 * ell_cosine) + boundary_third = boundary_third.at[:, 1, 1, 1].set(-6 * ell_sine) + for indices in ((0, 0, 1), (0, 1, 0), (1, 0, 0)): + boundary_third = boundary_third.at[ + :, + indices[0], + indices[1], + indices[2], + ].set(6 * ell_sine) + for indices in ((0, 1, 1), (1, 0, 1), (1, 1, 0)): + boundary_third = boundary_third.at[ + :, + indices[0], + indices[1], + indices[2], + ].set(-6 * ell_cosine) + + n_components = physical_rotation[:, 0, :] + K = jnp.zeros((solution.inputs.nphi, 2, 2), dtype=elongation.dtype) + K = K.at[:, 0, 0].set(2 * jnp.pi * inverse / d_lambda) + K = K.at[:, 1, 1].set(2 * jnp.pi * elongation / d_lambda) + M = -source.parallel_current_mu0 * K / (2 * jnp.pi) + product_rule = ( + jnp.einsum("...a,...bc->...abc", n_components, K) + + jnp.einsum("...b,...ac->...abc", n_components, K) + + jnp.einsum("...c,...ab->...abc", n_components, K) + ) + potential_third = -_affine_potential_third_derivative(c_star, elongation) / (2 * jnp.pi) + tangent_contribution = ( + source.parallel_current_mu0 * solution.geometry.curvature / (4 * jnp.pi) + )[:, None, None, None] * ( + _affine_potential_third_derivative( + n_components, + elongation, + ) + - product_rule + ) + source.parallel_current_mu0 / (2 * jnp.pi) * ( + _affine_potential_third_derivative(delta, elongation) - boundary_third + ) + potential_third = potential_third.at[:, 0, :, :, :].add(tangent_contribution) + + transverse = jnp.zeros( + (solution.inputs.nphi, 2, 2, 3), + dtype=elongation.dtype, + ) + transverse = transverse.at[:, :, :, 0].set( + potential_third[:, 2, :, :, 0] - potential_third[:, 1, :, :, 1] + ) + transverse = transverse.at[:, :, :, 1].set( + potential_third[:, 0, :, :, 1] + - (solution.geometry.curvature * n_components[:, 1])[:, None, None] * M + ) + transverse = transverse.at[:, :, :, 2].set( + (solution.geometry.curvature * n_components[:, 0])[:, None, None] * M + - potential_third[:, 0, :, :, 0] + ) + return transverse, principal_frame + + +def _plasma_hessian_frenet( + solution: NearAxisSolution, + gradient_frenet: jax.Array, + source: PlasmaCurrentSource, +) -> jax.Array: + transverse, principal_frame = _principal_transverse_plasma_hessian( + solution, + source, + ) + frenet_frame = jnp.stack( + ( + solution.geometry.tangent_cartesian, + solution.geometry.normal_cartesian, + solution.geometry.binormal_cartesian, + ), + axis=-2, + ) + principal_from_frenet = jnp.einsum( + "...ai,...bi->...ab", + principal_frame, + frenet_frame, + ) + principal_derivative_first = jnp.zeros( + (solution.inputs.nphi, 3, 3, 3), + dtype=transverse.dtype, + ) + principal_derivative_first = principal_derivative_first.at[ + :, + 1:, + 1:, + :, + ].set(transverse) + frenet_derivative_first = jnp.einsum( + "...pa,...qb,...rg,...pqr->...abg", + principal_from_frenet, + principal_from_frenet, + principal_from_frenet, + principal_derivative_first, + ) + + derivative_first_gradient = jnp.swapaxes(gradient_frenet, -1, -2) + derivative_along_axis = ( + jnp.einsum( + "nm,mab->nab", + solution.geometry.d_d_varphi, + derivative_first_gradient, + ) + / solution.geometry.abs_G0_over_B0 + ) + zeros = jnp.zeros_like(solution.geometry.curvature) + connection = jnp.stack( + ( + jnp.stack( + (zeros, solution.geometry.curvature, zeros), + axis=-1, + ), + jnp.stack( + ( + -solution.geometry.curvature, + zeros, + solution.geometry.torsion, + ), + axis=-1, + ), + jnp.stack( + (zeros, -solution.geometry.torsion, zeros), + axis=-1, + ), + ), + axis=-2, + ) + tangential = ( + derivative_along_axis + - jnp.einsum( + "...ad,...dg->...ag", + connection, + derivative_first_gradient, + ) + - jnp.einsum( + "...ad,...gd->...ag", + derivative_first_gradient, + connection, + ) + ) + frenet_derivative_first = frenet_derivative_first.at[:, 0, :, :].set(tangential) + frenet_derivative_first = frenet_derivative_first.at[:, :, 0, :].set(tangential) + return jnp.transpose(frenet_derivative_first, (0, 3, 1, 2)) + + +def plasma_hessian_on_axis( + solution: NearAxisSolution, + *, + formal_radius: ArrayLike, + angular_resolution: int = 128, +) -> PlasmaHessianData: + """Evaluate the complete local plasma Hessian and external vacuum jet.""" + + gradient = plasma_gradient_on_axis( + solution, + formal_radius=formal_radius, + angular_resolution=angular_resolution, + ) + hessian_frenet = _plasma_hessian_frenet( + solution, + gradient.gradient_frenet, + gradient.field.current_source, + ) + frame = jnp.stack( + ( + solution.geometry.tangent_cartesian, + solution.geometry.normal_cartesian, + solution.geometry.binormal_cartesian, + ), + axis=-2, + ) + hessian = jnp.einsum( + "...gi,...gab,...aj,...bk->...ijk", + frame, + hessian_frenet, + frame, + frame, + ) + external_hessian = solution.grad_grad_B_axis - hessian + external_symmetric = _symmetrize_rank3(external_hessian) + external_stf = project_symmetric_trace_free_rank3(external_hessian) + external_trace = jnp.einsum("...iik->...k", external_hessian) + external_symmetry = external_hessian - external_symmetric + derivative_asymmetry = hessian - jnp.swapaxes(hessian, -1, -2) + radius = gradient.field.current_source.formal_radius + axis_scale = solution.geometry.abs_G0_over_B0 + logarithm = jnp.abs(jnp.log(radius / axis_scale)) + remainder = jnp.max(jnp.abs(hessian)) * (radius / axis_scale) ** 2 * (1 + logarithm) + return PlasmaHessianData( + field=gradient, + hessian=hessian, + hessian_frenet=hessian_frenet, + external_hessian=external_hessian, + external_hessian_stf=external_stf, + external_hessian_independent=pack_symmetric_trace_free_rank3(external_hessian), + maximum_derivative_asymmetry=jnp.max(jnp.abs(derivative_asymmetry)), + maximum_external_symmetry_error=jnp.max(jnp.abs(external_symmetry)), + maximum_external_trace=jnp.max(jnp.abs(external_trace)), + estimated_hessian_remainder=remainder, + ) diff --git a/tests/physics/test_plasma_hessian.py b/tests/physics/test_plasma_hessian.py new file mode 100644 index 0000000..ed0353e --- /dev/null +++ b/tests/physics/test_plasma_hessian.py @@ -0,0 +1,243 @@ +from __future__ import annotations + +from dataclasses import replace +from itertools import permutations + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +import pyqsc_jax as qsc +from pyqsc_jax.plasma import _principal_transverse_plasma_hessian + + +def finite_pressure_current_solution(*, nphi=61, I2=0.9): + return qsc.Qsc( + rc=[1.0, 0.09], + zs=[0.0, -0.09], + nfp=2, + etabar=0.95, + I2=I2, + p2=-600000.0, + B2c=-0.7, + nphi=nphi, + order="r2", + ) + + +def vacuum_qa_solution(*, nphi=61): + return qsc.Qsc( + rc=[1.0, 0.155, 0.0102], + zs=[0.0, 0.154, 0.0111], + nfp=2, + etabar=0.64, + I2=0.0, + p2=0.0, + B2c=-0.00322, + nphi=nphi, + order="r2", + ) + + +def test_stf_rank_three_pack_unpack_and_projection(): + tensor = jnp.arange(54.0).reshape(2, 3, 3, 3) + projected = qsc.project_symmetric_trace_free_rank3(tensor) + packed = qsc.pack_symmetric_trace_free_rank3(tensor) + unpacked = qsc.unpack_symmetric_trace_free_rank3(packed) + + for permutation in permutations((1, 2, 3)): + np.testing.assert_allclose( + projected, + jnp.transpose(projected, (0, *permutation)), + atol=1.0e-14, + ) + np.testing.assert_allclose( + jnp.einsum("...iik->...k", projected), + 0.0, + atol=3.0e-14, + ) + np.testing.assert_allclose(unpacked, projected, atol=2.0e-14) + assert packed.shape == (2, 7) + + +def test_stf_rank_three_helpers_are_jittable(): + tensor = jnp.arange(27.0).reshape(3, 3, 3) + + eager = qsc.unpack_symmetric_trace_free_rank3(qsc.pack_symmetric_trace_free_rank3(tensor)) + compiled = jax.jit( + lambda value: qsc.unpack_symmetric_trace_free_rank3( + qsc.pack_symmetric_trace_free_rank3(value) + ) + )(tensor) + + np.testing.assert_allclose(compiled, eager) + + +def test_external_hessian_is_fully_symmetric_and_trace_free(): + solution = finite_pressure_current_solution(nphi=121) + formal_radius = 0.05 + result = qsc.plasma_hessian_on_axis( + solution, + formal_radius=0.05, + ) + + assert result.maximum_derivative_asymmetry < 2.0e-15 + assert result.maximum_external_symmetry_error < 8.0e-11 + assert result.maximum_external_trace < 2.0e-10 + np.testing.assert_allclose( + result.external_hessian, + result.external_hessian_stf, + atol=2.0e-10, + ) + np.testing.assert_allclose( + qsc.unpack_symmetric_trace_free_rank3(result.external_hessian_independent), + result.external_hessian_stf, + atol=2.0e-15, + ) + axis_scale = solution.geometry.abs_G0_over_B0 + expected_remainder = ( + jnp.max(jnp.abs(result.hessian)) + * (formal_radius / axis_scale) ** 2 + * (1 + jnp.abs(jnp.log(formal_radius / axis_scale))) + ) + np.testing.assert_allclose(result.estimated_hessian_remainder, expected_remainder) + + +def test_qh_external_hessian_preserves_oriented_ellipse_topology(): + solution = qsc.Qsc( + rc=[1.0, 0.17, 0.01804, 0.001409, 5.877e-5], + zs=[0.0, 0.1581, 0.01820, 0.001548, 7.772e-5], + nfp=4, + etabar=1.569, + I2=0.2, + p2=-100000.0, + B2c=0.1348, + nphi=121, + order="r2", + ) + result = qsc.plasma_hessian_on_axis( + solution, + formal_radius=0.04, + ) + + assert int(solution.helicity) == 1 + assert result.maximum_derivative_asymmetry < 2.0e-15 + assert result.maximum_external_symmetry_error < 2.0e-9 + assert result.maximum_external_trace < 3.0e-9 + + +def test_circular_curved_channel_recovers_finite_conductor_limit(): + """Equation (215), with affine and second-order shape terms suppressed.""" + + solution = qsc.Qsc( + rc=[1.0], + zs=[0.0], + nfp=1, + etabar=1.0, + I2=0.1, + nphi=31, + order="r2", + ) + zeros = jnp.zeros_like(solution.X20) + circular_second_order = replace( + solution.second_order, + X20=zeros, + X2c=zeros, + X2s=zeros, + Y20=zeros, + Y2c=zeros, + Y2s=zeros, + Z20=zeros, + Z2c=zeros, + Z2s=zeros, + ) + curvature_only_solution = replace( + solution, + second_order=circular_second_order, + ) + source = qsc.plasma_current_source( + solution, + formal_radius=0.1, + ) + zero_vector = jnp.zeros_like(source.wstar2_cosine) + curvature_only_source = replace( + source, + wstar2_cosine=zero_vector, + wstar2_sine=zero_vector, + ) + + transverse, _ = _principal_transverse_plasma_hessian( + curvature_only_solution, + curvature_only_source, + ) + coefficient = source.parallel_current_mu0 * solution.geometry.curvature / 8 + expected = jnp.zeros_like(transverse) + expected = expected.at[:, 0, 0, 2].set(-coefficient) + expected = expected.at[:, 0, 1, 1].set(-coefficient) + expected = expected.at[:, 1, 0, 1].set(-coefficient) + expected = expected.at[:, 1, 1, 2].set(-3 * coefficient) + + np.testing.assert_allclose(transverse, expected, atol=2.0e-15) + + +def test_vacuum_reduction_leaves_total_hessian_unchanged(): + solution = vacuum_qa_solution() + result = qsc.plasma_hessian_on_axis( + solution, + formal_radius=0.05, + ) + + np.testing.assert_allclose(result.field.field.field, 0.0, atol=1.0e-14) + np.testing.assert_allclose(result.field.gradient, 0.0) + np.testing.assert_allclose(result.hessian, 0.0) + np.testing.assert_allclose( + result.external_hessian, + solution.grad_grad_B_axis, + ) + + +def test_plasma_hessian_converges_spectrally(): + medium = qsc.plasma_hessian_on_axis( + finite_pressure_current_solution(nphi=61), + formal_radius=0.05, + ) + fine = qsc.plasma_hessian_on_axis( + finite_pressure_current_solution(nphi=121), + formal_radius=0.05, + ) + + np.testing.assert_allclose( + medium.hessian_frenet[0], + fine.hessian_frenet[0], + atol=1.0e-8, + rtol=1.0e-8, + ) + assert fine.maximum_external_symmetry_error < 1.0e-4 * (medium.maximum_external_symmetry_error) + assert fine.maximum_external_trace < 1.0e-4 * medium.maximum_external_trace + + +def test_plasma_hessian_supports_jit_and_jvp(): + def component(I2): + result = qsc.plasma_hessian_on_axis( + finite_pressure_current_solution(nphi=15, I2=I2), + formal_radius=0.05, + angular_resolution=32, + ) + return result.hessian[4, 0, 1, 2] + + value = component(0.9) + compiled = jax.jit(component)(0.9) + tangent = jax.jvp(component, (0.9,), (1.0,))[1] + step = 1.0e-5 + finite_difference = (component(0.9 + step) - component(0.9 - step)) / (2 * step) + + np.testing.assert_allclose(compiled, value, rtol=2.0e-12, atol=2.0e-12) + np.testing.assert_allclose(tangent, finite_difference, rtol=2.0e-8, atol=2.0e-8) + + +def test_rank_three_guards(): + with pytest.raises(ValueError, match="shape"): + qsc.project_symmetric_trace_free_rank3(jnp.ones((3, 3))) + with pytest.raises(ValueError, match="length 7"): + qsc.unpack_symmetric_trace_free_rank3(jnp.ones(6)) From a8eb51a2c4ea00435a2db250a3366f7bfa2efb7e Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 02:44:28 -0500 Subject: [PATCH 20/39] feat: add reproducible examples and publication figures --- .github/workflows/tests.yml | 6 +- .gitignore | 1 + examples/01_first_order_qa.py | 42 +++++ examples/02_first_order_qh.py | 42 +++++ examples/03_second_order_finite_beta.py | 50 ++++++ examples/04_target_iota.py | 54 ++++++ examples/05_optimal_B2c.py | 53 ++++++ examples/06_optimize_axis_B20.py | 82 +++++++++ examples/07_good_stellarator_search.py | 81 +++++++++ examples/08_boundary_and_coordinates.py | 68 ++++++++ examples/09_total_field_jet.py | 50 ++++++ examples/10_plasma_external_field_jet.py | 46 +++++ examples/11_continuation_scan.py | 51 ++++++ examples/12_autodiff_check.py | 53 ++++++ .../publication/figure_B20_optimization.py | 93 ++++++++++ examples/publication/figure_QA_QH_branches.py | 84 +++++++++ .../publication/figure_axis_and_surfaces.py | 88 ++++++++++ examples/publication/figure_convergence.py | 78 +++++++++ .../publication/figure_plasma_external_jet.py | 70 ++++++++ src/pyqsc_jax/__init__.py | 12 ++ src/pyqsc_jax/configurations.py | 101 +++++++++++ src/pyqsc_jax/plotting.py | 163 ++++++++++++++++++ tests/examples/test_examples.py | 42 +++++ tests/unit/test_configurations.py | 40 +++++ tests/unit/test_plotting.py | 49 ++++++ 25 files changed, 1496 insertions(+), 3 deletions(-) create mode 100644 examples/01_first_order_qa.py create mode 100644 examples/02_first_order_qh.py create mode 100644 examples/03_second_order_finite_beta.py create mode 100644 examples/04_target_iota.py create mode 100644 examples/05_optimal_B2c.py create mode 100644 examples/06_optimize_axis_B20.py create mode 100644 examples/07_good_stellarator_search.py create mode 100644 examples/08_boundary_and_coordinates.py create mode 100644 examples/09_total_field_jet.py create mode 100644 examples/10_plasma_external_field_jet.py create mode 100644 examples/11_continuation_scan.py create mode 100644 examples/12_autodiff_check.py create mode 100644 examples/publication/figure_B20_optimization.py create mode 100644 examples/publication/figure_QA_QH_branches.py create mode 100644 examples/publication/figure_axis_and_surfaces.py create mode 100644 examples/publication/figure_convergence.py create mode 100644 examples/publication/figure_plasma_external_jet.py create mode 100644 src/pyqsc_jax/configurations.py create mode 100644 src/pyqsc_jax/plotting.py create mode 100644 tests/examples/test_examples.py create mode 100644 tests/unit/test_configurations.py create mode 100644 tests/unit/test_plotting.py diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml index 71a27d9..077609f 100644 --- a/.github/workflows/tests.yml +++ b/.github/workflows/tests.yml @@ -21,8 +21,8 @@ jobs: python-version: "3.14" cache: pip - run: python -m pip install ruff - - run: ruff check src tests - - run: ruff format --check src tests + - run: ruff check src tests examples + - run: ruff format --check src tests examples test: strategy: @@ -45,7 +45,7 @@ jobs: with: python-version: ${{ matrix.python }} cache: pip - - run: python -m pip install -e '.[dev]' + - run: python -m pip install -e '.[dev,plot]' - run: python -c "import jax, pyqsc_jax; print(jax.__version__, pyqsc_jax.__version__, pyqsc_jax.__file__)" - run: pytest diff --git a/.gitignore b/.gitignore index aa64a13..d0b7328 100644 --- a/.gitignore +++ b/.gitignore @@ -9,3 +9,4 @@ docs/_build/ build/ dist/ *.egg-info/ +examples/output/ diff --git a/examples/01_first_order_qa.py b/examples/01_first_order_qa.py new file mode 100644 index 0000000..7f39e15 --- /dev/null +++ b/examples/01_first_order_qa.py @@ -0,0 +1,42 @@ +"""Construct and plot a first-order quasi-axisymmetric configuration.""" + +from pathlib import Path + +import matplotlib.pyplot as plt + +import pyqsc_jax as qsc +from pyqsc_jax.plotting import plot_axis + +RC = [1.0, 0.045] +ZS = [0.0, -0.045] +NFP = 3 +ETABAR = -0.9 +NPHI = 31 +SAVE_OUTPUT = True +SHOW_FIGURE = False +OUTPUT = Path("examples/output/01_first_order_qa.png") + +print("Solving first-order QA configuration...") +solution = qsc.Qsc( + rc=RC, + zs=ZS, + nfp=NFP, + etabar=ETABAR, + nphi=NPHI, + order="r1", +) +print("iota:", float(solution.iota)) +print("sigma residual:", float(solution.root_report.residual_norm)) +print("axis length [m]:", float(solution.axis_length)) +print("maximum elongation:", float(solution.elongation.max())) + +figure, _ = plot_axis(solution, label="first-order QA") +figure.tight_layout() +if SAVE_OUTPUT: + OUTPUT.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(OUTPUT, dpi=180, bbox_inches="tight") + print("saved:", OUTPUT) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/02_first_order_qh.py b/examples/02_first_order_qh.py new file mode 100644 index 0000000..4546fac --- /dev/null +++ b/examples/02_first_order_qh.py @@ -0,0 +1,42 @@ +"""Construct and plot a first-order quasi-helically symmetric configuration.""" + +from pathlib import Path + +import matplotlib.pyplot as plt + +import pyqsc_jax as qsc +from pyqsc_jax.plotting import plot_axis + +RC = [1.0, 0.265] +ZS = [0.0, -0.21] +NFP = 4 +ETABAR = -0.9 +NPHI = 31 +SAVE_OUTPUT = True +SHOW_FIGURE = False +OUTPUT = Path("examples/output/02_first_order_qh.png") + +print("Solving first-order QH configuration...") +solution = qsc.Qsc( + rc=RC, + zs=ZS, + nfp=NFP, + etabar=ETABAR, + nphi=NPHI, + order="r1", +) +print("iota:", float(solution.iota)) +print("iota_N:", float(solution.iotaN)) +print("frame helicity:", int(solution.helicity)) +print("sigma residual:", float(solution.root_report.residual_norm)) + +figure, _ = plot_axis(solution, label="first-order QH", color="tab:orange") +figure.tight_layout() +if SAVE_OUTPUT: + OUTPUT.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(OUTPUT, dpi=180, bbox_inches="tight") + print("saved:", OUTPUT) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/03_second_order_finite_beta.py b/examples/03_second_order_finite_beta.py new file mode 100644 index 0000000..14e8bbc --- /dev/null +++ b/examples/03_second_order_finite_beta.py @@ -0,0 +1,50 @@ +"""Solve the complete finite-pressure/current second-order system.""" + +from pathlib import Path + +import matplotlib.pyplot as plt + +import pyqsc_jax as qsc +from pyqsc_jax.plotting import plot_b20 + +RC = [1.0, 0.09] +ZS = [0.0, -0.09] +NFP = 2 +ETABAR = 0.95 +I2 = 0.9 +P2 = -600000.0 +B2C = -0.7 +NPHI = 61 +SAVE_OUTPUT = True +SHOW_FIGURE = False +OUTPUT = Path("examples/output/03_second_order_finite_beta.png") + +print("Solving the finite-pressure/current r2 configuration...") +solution = qsc.Qsc( + rc=RC, + zs=ZS, + nfp=NFP, + etabar=ETABAR, + I2=I2, + p2=P2, + B2c=B2C, + nphi=NPHI, + order="r2", +) +print("iota:", float(solution.iota)) +print("linear residual:", float(solution.linear_report.residual_norm)) +print("linear condition number:", float(solution.linear_report.matrix_condition_number)) +print("B20 weighted residual:", float(solution.B20_residual)) +print("Mercier D r^2:", float(solution.DMerc_times_r2)) +print("singular radius [m]:", float(solution.r_singularity)) + +figure, _ = plot_b20(solution, label="finite beta/current", color="tab:red") +figure.tight_layout() +if SAVE_OUTPUT: + OUTPUT.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(OUTPUT, dpi=180, bbox_inches="tight") + print("saved:", OUTPUT) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/04_target_iota.py b/examples/04_target_iota.py new file mode 100644 index 0000000..007859c --- /dev/null +++ b/examples/04_target_iota.py @@ -0,0 +1,54 @@ +"""Prescribe rotational transform and solve for etabar.""" + +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np + +import pyqsc_jax as qsc + +AXIS = qsc.Axis(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3) +TARGET_IOTA = 0.42 +ETABAR_SEED = -1.0 +NPHI = 31 +SAVE_OUTPUT = True +SHOW_FIGURE = False +OUTPUT = Path("examples/output/04_target_iota.png") + +print("Solving inverse target-iota problem...") +inverse = qsc.solve( + axis=AXIS, + etabar=ETABAR_SEED, + iota=TARGET_IOTA, + solve_for="etabar", + nphi=NPHI, +) +forward = qsc.solve( + axis=AXIS, + etabar=inverse.inputs.etabar, + nphi=NPHI, +) +print("target iota:", TARGET_IOTA) +print("solved etabar:", float(inverse.inputs.etabar)) +print("forward-check iota:", float(forward.iota)) +print("response d(iota)/d(etabar):", float(inverse.response_derivative)) +print("branch fold:", bool(inverse.branch_fold)) + +figure, axis = plt.subplots(figsize=(6.0, 3.6)) +axis.plot( + np.asarray(inverse.varphi), + np.asarray(inverse.sigma), + linewidth=2, +) +axis.set_xlabel("Boozer toroidal angle [rad]") +axis.set_ylabel(r"$\sigma$") +axis.set_title("Target-iota periodic solution") +figure.tight_layout() +if SAVE_OUTPUT: + OUTPUT.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(OUTPUT, dpi=180, bbox_inches="tight") + print("saved:", OUTPUT) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/05_optimal_B2c.py b/examples/05_optimal_B2c.py new file mode 100644 index 0000000..3335811 --- /dev/null +++ b/examples/05_optimal_B2c.py @@ -0,0 +1,53 @@ +"""Eliminate the affine B2c subproblem exactly.""" + +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np + +import pyqsc_jax as qsc + +RC = [1.0, 0.155, 0.0102] +ZS = [0.0, 0.154, 0.0111] +NFP = 2 +ETABAR = 0.64 +INITIAL_B2C = 0.0 +NPHI = 61 +SAVE_OUTPUT = True +SHOW_FIGURE = False +OUTPUT = Path("examples/output/05_optimal_B2c.png") + +print("Solving the initial r2 configuration...") +initial = qsc.Qsc( + rc=RC, + zs=ZS, + nfp=NFP, + etabar=ETABAR, + B2c=INITIAL_B2C, + nphi=NPHI, + order="r2", +) +result = qsc.optimize_B2c(initial) +optimized = result.solution +print("initial B2c:", INITIAL_B2C) +print("optimal B2c:", float(result.B2c_optimal)) +print("initial weighted L2:", float(qsc.b20_diagnostics(initial).weighted_l2)) +print("optimal weighted L2:", float(result.diagnostics.weighted_l2)) +print("affine reconstruction error:", float(result.affine_reconstruction_error)) + +angle = np.asarray(initial.varphi * NFP / (2 * np.pi)) +figure, axis = plt.subplots(figsize=(6.2, 3.8)) +axis.plot(angle, np.asarray(initial.B20_anomaly), label="initial", linewidth=2) +axis.plot(angle, np.asarray(optimized.B20_anomaly), label="optimal B2c", linewidth=2) +axis.set_xlabel("Boozer angle / field period") +axis.set_ylabel(r"$B_{20}-\langle B_{20}\rangle$ [T/m$^2$]") +axis.legend() +figure.tight_layout() +if SAVE_OUTPUT: + OUTPUT.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(OUTPUT, dpi=180, bbox_inches="tight") + print("saved:", OUTPUT) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/06_optimize_axis_B20.py b/examples/06_optimize_axis_B20.py new file mode 100644 index 0000000..c81951f --- /dev/null +++ b/examples/06_optimize_axis_B20.py @@ -0,0 +1,82 @@ +"""Run a small deterministic global-to-local B20 axis search.""" + +from pathlib import Path + +import jax.numpy as jnp +import matplotlib.pyplot as plt +import numpy as np + +import pyqsc_jax as qsc + +INITIAL_AXIS = qsc.Axis( + rc=[1.0, 0.155, 0.0102], + zs=[0.0, 0.154, 0.0111], + nfp=2, +) +ETABAR = 0.64 +NPHI = 15 +COARSE_SAMPLES = 3 +LOCAL_STARTS = 1 +MAXIMUM_ITERATIONS = 3 +SAVE_OUTPUT = True +SHOW_FIGURE = False +OUTPUT = Path("examples/output/06_optimize_axis_B20.png") + +variable_indices = qsc.stellarator_symmetric_variable_indices( + INITIAL_AXIS, + modes=(1,), +) +problem = qsc.AxisSearchProblem( + axis=INITIAL_AXIS, + variable_indices=variable_indices, + lower_bounds=jnp.asarray([0.11, 0.11]), + upper_bounds=jnp.asarray([0.19, 0.19]), + etabar=ETABAR, + nphi=NPHI, + selector="minimum_maximum_elongation", +) +options = qsc.AxisSearchOptions( + coarse_samples=COARSE_SAMPLES, + local_starts=LOCAL_STARTS, + maximum_iterations=MAXIMUM_ITERATIONS, + verification_multipliers=(1,), + verification_tail_tolerance=1.0, +) + +print("Searching bounded axis coefficients...") +result = qsc.search_axis(problem, options=options) +print("status:", result.status) +print("search budget:", result.search_budget) +print("distinct basins:", result.distinct_basins) +print("message:", result.message) +if result.best is None: + raise RuntimeError("The example search did not produce a candidate.") +print("best variables:", np.asarray(result.best.variables)) +print("best B20 residual:", result.best.primary_residual) +print("global certificate:", result.global_certificate) + +figure, axis = plt.subplots(figsize=(6.2, 3.8)) +axis.scatter( + np.arange(result.coarse_residuals.size), + np.asarray(result.coarse_residuals), + label="coarse samples", +) +axis.axhline( + result.best.primary_residual, + color="tab:red", + linewidth=2, + label="best refined basin", +) +axis.set_yscale("log") +axis.set_xlabel("deterministic sample index") +axis.set_ylabel("weighted B20 residual") +axis.legend() +figure.tight_layout() +if SAVE_OUTPUT: + OUTPUT.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(OUTPUT, dpi=180, bbox_inches="tight") + print("saved:", OUTPUT) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/07_good_stellarator_search.py b/examples/07_good_stellarator_search.py new file mode 100644 index 0000000..6838c2c --- /dev/null +++ b/examples/07_good_stellarator_search.py @@ -0,0 +1,81 @@ +"""Apply a named screening profile during a reproducible axis search.""" + +from pathlib import Path + +import jax.numpy as jnp +import matplotlib.pyplot as plt +import numpy as np + +import pyqsc_jax as qsc + +AXIS = qsc.Axis(rc=[1.0], zs=[0.0], nfp=1) +ETABAR = 1.0 +I2 = 0.1 +NPHI = 15 +SAVE_OUTPUT = True +SHOW_FIGURE = False +OUTPUT = Path("examples/output/07_good_stellarator_search.png") + +# This deliberately permissive profile demonstrates mechanics; it is not a +# claim that a circular channel passes the published Curvo screening profile. +criteria = qsc.Criteria.from_curvo_2025( + minimum_abs_iota=0.0, + maximum_elongation=20.0, + minimum_L_grad_B=0.0, + minimum_axis_radius=0.0, + minimum_singular_radius=0.0, + minimum_L_grad_grad_B=0.0, + maximum_B20_variation=10.0, + minimum_beta=0.0, + minimum_DMerc_times_r2=-1.0e6, +) +problem = qsc.AxisSearchProblem( + axis=AXIS, + variable_indices=(0,), + lower_bounds=jnp.asarray([0.8]), + upper_bounds=jnp.asarray([1.2]), + etabar=ETABAR, + I2=I2, + nphi=NPHI, + criteria=criteria, + selector="maximum_criteria_margin", +) +options = qsc.AxisSearchOptions( + coarse_samples=2, + local_starts=1, + maximum_iterations=2, + verification_multipliers=(1, 2), +) + +print("Running criteria-aware search...") +result = qsc.search_axis(problem, options=options) +if result.best is None or result.best.criteria_report is None: + raise RuntimeError("The criteria-aware example did not produce a report.") +report = result.best.criteria_report +print("status:", result.status) +print("criteria passed:", report.passed) +for evaluation in report.evaluations: + print( + evaluation.name, + "value=", + float(evaluation.value), + "margin=", + float(evaluation.margin), + evaluation.units, + ) + +names = [evaluation.name for evaluation in report.evaluations] +margins = np.asarray([evaluation.margin for evaluation in report.evaluations]) +figure, axis = plt.subplots(figsize=(7.4, 4.0)) +axis.barh(names, margins, color=np.where(margins >= 0, "tab:green", "tab:red")) +axis.axvline(0, color="black", linewidth=1) +axis.set_xlabel("signed criterion margin") +figure.tight_layout() +if SAVE_OUTPUT: + OUTPUT.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(OUTPUT, dpi=180, bbox_inches="tight") + print("saved:", OUTPUT) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/08_boundary_and_coordinates.py b/examples/08_boundary_and_coordinates.py new file mode 100644 index 0000000..b67b80c --- /dev/null +++ b/examples/08_boundary_and_coordinates.py @@ -0,0 +1,68 @@ +"""Generate an available-order boundary through the compatibility adapter.""" + +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np + +from pyqsc_jax.near_axis import near_axis + +RC = [1.0, 0.155, 0.0102] +ZS = [0.0, 0.154, 0.0111] +NFP = 2 +ETABAR = 0.64 +B2C = -0.00322 +RADIUS = 0.05 +NTHETA = 24 +NPHI = 49 +SAVE_OUTPUT = True +SHOW_FIGURE = False +OUTPUT = Path("examples/output/08_boundary_and_coordinates.png") + +print("Constructing an r2 compatibility surface...") +field = near_axis( + rc=RC, + zs=ZS, + nfp=NFP, + etabar=ETABAR, + B2c=B2C, + nphi=31, + order="r2", +) +x, y, z, radius = field.get_boundary( + r=RADIUS, + ntheta=NTHETA, + nphi=NPHI, +) +print("boundary array shape:", x.shape) +print("R range [m]:", float(radius.min()), float(radius.max())) +print("Z range [m]:", float(z.min()), float(z.max())) + +figure = plt.figure(figsize=(8.0, 3.8)) +axis_3d = figure.add_subplot(1, 2, 1, projection="3d") +axis_3d.plot_surface( + np.asarray(x), + np.asarray(y), + np.asarray(z), + cmap="viridis", + alpha=0.8, + linewidth=0, +) +axis_3d.set_box_aspect((1, 1, 1)) +axis_3d.set_xlabel("x [m]") +axis_3d.set_ylabel("y [m]") +axis_3d.set_zlabel("z [m]") +axis_cross = figure.add_subplot(1, 2, 2) +axis_cross.plot(np.asarray(radius[:, 0]), np.asarray(z[:, 0]), linewidth=2) +axis_cross.set_aspect("equal") +axis_cross.set_xlabel("R [m]") +axis_cross.set_ylabel("Z [m]") +figure.tight_layout() +if SAVE_OUTPUT: + OUTPUT.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(OUTPUT, dpi=180, bbox_inches="tight") + print("saved:", OUTPUT) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/09_total_field_jet.py b/examples/09_total_field_jet.py new file mode 100644 index 0000000..5eb92f9 --- /dev/null +++ b/examples/09_total_field_jet.py @@ -0,0 +1,50 @@ +"""Inspect the total on-axis field, gradient, and Hessian.""" + +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np + +import pyqsc_jax as qsc + +CONFIGURATION = "qa" +NPHI = 61 +SAVE_OUTPUT = True +SHOW_FIGURE = False +OUTPUT = Path("examples/output/09_total_field_jet.png") + +print("Solving the total-field-jet reference configuration...") +solution = qsc.solve_configuration(CONFIGURATION, nphi=NPHI) +jet = solution.field_jet +if jet is None: + raise RuntimeError("The r2 solution did not produce a total field jet.") +print("field reconstruction error:", float(jet.maximum_field_error)) +print("gradient reconstruction error:", float(jet.maximum_gradient_error)) +print("maximum divergence:", float(jet.maximum_divergence)) +print("maximum Hessian derivative asymmetry:", float(jet.maximum_derivative_asymmetry)) +print("maximum gradient of divergence:", float(jet.maximum_divergence_gradient)) +print("minimum Hessian scale length [m]:", float(jet.L_grad_grad_B.min())) + +angle = np.asarray(solution.varphi * solution.inputs.axis.nfp / (2 * np.pi)) +hessian = np.asarray(jet.hessian) +figure, axes = plt.subplots(2, 1, figsize=(7.0, 6.0), sharex=True) +axes[0].plot(angle, np.asarray(solution.B_axis[:, 0]), label=r"$B_x$") +axes[0].plot(angle, np.asarray(solution.B_axis[:, 1]), label=r"$B_y$") +axes[0].plot(angle, np.asarray(solution.B_axis[:, 2]), label=r"$B_z$") +axes[0].set_ylabel("field [T]") +axes[0].legend(ncol=3) +axes[1].plot(angle, hessian[:, 0, 0, 0], label=r"$\partial_{xx}B_x$") +axes[1].plot(angle, hessian[:, 0, 1, 1], label=r"$\partial_{yy}B_x$") +axes[1].plot(angle, hessian[:, 0, 2, 2], label=r"$\partial_{zz}B_x$") +axes[1].set_xlabel("Boozer angle / field period") +axes[1].set_ylabel(r"Hessian component [T/m$^2$]") +axes[1].legend(ncol=3) +figure.tight_layout() +if SAVE_OUTPUT: + OUTPUT.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(OUTPUT, dpi=180, bbox_inches="tight") + print("saved:", OUTPUT) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/10_plasma_external_field_jet.py b/examples/10_plasma_external_field_jet.py new file mode 100644 index 0000000..7d6b132 --- /dev/null +++ b/examples/10_plasma_external_field_jet.py @@ -0,0 +1,46 @@ +"""Separate total, plasma, and external vacuum field jets.""" + +from pathlib import Path + +import matplotlib.pyplot as plt + +import pyqsc_jax as qsc +from pyqsc_jax.plotting import plot_field_jet_norms + +CONFIGURATION = "finite_pressure_current" +FORMAL_RADIUS = 0.025 +NPHI = 61 +ANGULAR_RESOLUTION = 96 +SAVE_OUTPUT = True +SHOW_FIGURE = False +OUTPUT = Path("examples/output/10_plasma_external_field_jet.png") + +print("Solving the finite-current total field...") +solution = qsc.solve_configuration(CONFIGURATION, nphi=NPHI) +print("Separating the surface-free plasma and external jets...") +result = qsc.plasma_hessian_on_axis( + solution, + formal_radius=FORMAL_RADIUS, + angular_resolution=ANGULAR_RESOLUTION, +) +enclosed_current = result.field.field.current_source.enclosed_toroidal_current +print("enclosed toroidal current [A]:", float(enclosed_current)) +print("external gradient STF components:", result.field.external_gradient_independent.shape[-1]) +print("external Hessian STF components:", result.external_hessian_independent.shape[-1]) +print("maximum external-gradient trace:", float(result.field.maximum_external_trace)) +print("maximum external-Hessian trace:", float(result.maximum_external_trace)) +print("estimated plasma-field remainder [T]:", float(result.field.field.estimated_field_remainder)) +print( + "estimated plasma-Hessian remainder [T/m^2]:", + float(result.estimated_hessian_remainder), +) + +figure, _ = plot_field_jet_norms(result) +if SAVE_OUTPUT: + OUTPUT.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(OUTPUT, dpi=180, bbox_inches="tight") + print("saved:", OUTPUT) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/11_continuation_scan.py b/examples/11_continuation_scan.py new file mode 100644 index 0000000..256bc40 --- /dev/null +++ b/examples/11_continuation_scan.py @@ -0,0 +1,51 @@ +"""Trace an etabar branch with pseudo-arclength continuation.""" + +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np + +import pyqsc_jax as qsc + +AXIS = qsc.Axis(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3) +ETABAR_START = -1.0 +ETABAR_NEXT = -0.98 +NUMBER_OF_POINTS = 12 +NPHI = 31 +SAVE_OUTPUT = True +SHOW_FIGURE = False +OUTPUT = Path("examples/output/11_continuation_scan.png") + +print("Tracing the first-order etabar branch...") +result = qsc.continue_etabar_branch( + axis=AXIS, + etabar_start=ETABAR_START, + etabar_next=ETABAR_NEXT, + num_points=NUMBER_OF_POINTS, + nphi=NPHI, +) +etabar = np.asarray(result.etabar) +iota = np.asarray(result.iota) +fold = np.asarray(result.fold_detected) +print("status:", result.status) +print("points:", len(result.solutions)) +print("etabar interval:", float(etabar.min()), float(etabar.max())) +print("iota interval:", float(iota.min()), float(iota.max())) +print("detected fold samples:", np.flatnonzero(fold)) + +figure, axis = plt.subplots(figsize=(6.0, 3.8)) +axis.plot(etabar, iota, "-o", label="corrected branch") +if fold.any(): + axis.scatter(etabar[fold], iota[fold], marker="x", s=80, label="fold diagnostic") +axis.set_xlabel(r"$\bar{\eta}$ [m$^{-1}$]") +axis.set_ylabel(r"$\iota$") +axis.legend() +figure.tight_layout() +if SAVE_OUTPUT: + OUTPUT.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(OUTPUT, dpi=180, bbox_inches="tight") + print("saved:", OUTPUT) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/12_autodiff_check.py b/examples/12_autodiff_check.py new file mode 100644 index 0000000..5d66890 --- /dev/null +++ b/examples/12_autodiff_check.py @@ -0,0 +1,53 @@ +"""Compare an implicit-solve JVP with a centered finite difference.""" + +from pathlib import Path + +import jax +import matplotlib.pyplot as plt +import numpy as np + +import pyqsc_jax as qsc + +AXIS = qsc.Axis(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3) +ETABAR = -0.9 +NPHI = 31 +FINITE_DIFFERENCE_STEP = 1.0e-5 +SAVE_OUTPUT = True +SHOW_FIGURE = False +OUTPUT = Path("examples/output/12_autodiff_check.png") + + +def iota_from_etabar(etabar): + """Return one converged implicit-solve output.""" + + return qsc.solve(axis=AXIS, etabar=etabar, nphi=NPHI).iota + + +print("Differentiating rotational transform through the converged sigma solve...") +value, tangent = jax.jvp(iota_from_etabar, (ETABAR,), (1.0,)) +upper = iota_from_etabar(ETABAR + FINITE_DIFFERENCE_STEP) +lower = iota_from_etabar(ETABAR - FINITE_DIFFERENCE_STEP) +finite_difference = (upper - lower) / (2 * FINITE_DIFFERENCE_STEP) +relative_error = abs(tangent - finite_difference) / max(abs(finite_difference), 1.0e-14) +print("iota:", float(value)) +print("JVP d(iota)/d(etabar):", float(tangent)) +print("finite-difference derivative:", float(finite_difference)) +print("relative error:", float(relative_error)) + +figure, axis = plt.subplots(figsize=(5.5, 3.6)) +axis.bar( + ("JAX implicit JVP", "centered difference"), + np.asarray((tangent, finite_difference)), + color=("tab:blue", "tab:orange"), +) +axis.set_ylabel(r"$d\iota/d\bar{\eta}$ [m]") +axis.set_title(f"relative error = {float(relative_error):.2e}") +figure.tight_layout() +if SAVE_OUTPUT: + OUTPUT.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(OUTPUT, dpi=180, bbox_inches="tight") + print("saved:", OUTPUT) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/publication/figure_B20_optimization.py b/examples/publication/figure_B20_optimization.py new file mode 100644 index 0000000..6064036 --- /dev/null +++ b/examples/publication/figure_B20_optimization.py @@ -0,0 +1,93 @@ +"""Publication figure for exact affine B2c elimination.""" + +import json +import subprocess +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np + +import pyqsc_jax as qsc + +CONFIGURATION = "qa" +INITIAL_B2C = 0.0 +NPHI = 121 +OUTPUT_STEM = Path("examples/output/publication/B20_optimization") +SAVE_OUTPUT = True +SHOW_FIGURE = False + +plt.style.use("seaborn-v0_8-whitegrid") +print("Computing exact B2c elimination at publication resolution...") +initial = qsc.solve_configuration(CONFIGURATION, B2c=INITIAL_B2C, nphi=NPHI) +result = qsc.optimize_B2c(initial) +optimized = result.solution +angle = np.asarray(initial.varphi * initial.inputs.axis.nfp / (2 * np.pi)) + +figure, axes = plt.subplots(1, 2, figsize=(10.5, 3.9)) +axes[0].plot(angle, np.asarray(initial.B20_anomaly), linewidth=2.2, label="initial") +axes[0].plot( + angle, + np.asarray(optimized.B20_anomaly), + linewidth=2.2, + label=r"exact $B_{2c}^{\star}$", +) +axes[0].set_xlabel("Boozer angle / field period") +axes[0].set_ylabel(r"$B_{20}-\langle B_{20}\rangle$ [T/m$^2$]") +axes[0].legend() +diagnostic_names = ("weighted $L^2$", "dense maximum", "peak-to-peak") +initial_diagnostics = qsc.b20_diagnostics(initial) +axes[1].bar( + np.arange(3) - 0.18, + ( + float(initial_diagnostics.weighted_l2), + float(initial_diagnostics.grid_maximum), + float(initial_diagnostics.peak_to_peak), + ), + width=0.36, + label="initial", +) +axes[1].bar( + np.arange(3) + 0.18, + ( + float(result.diagnostics.weighted_l2), + float(result.diagnostics.grid_maximum), + float(result.diagnostics.peak_to_peak), + ), + width=0.36, + label="optimized", +) +axes[1].set_xticks(np.arange(3), diagnostic_names, rotation=15) +axes[1].set_ylabel(r"$B_{20}$ nonuniformity [T/m$^2$]") +axes[1].legend() +figure.tight_layout() + +try: + repository = Path(__file__).resolve().parents[2] + commit = subprocess.check_output( + ("git", "-C", str(repository), "rev-parse", "HEAD"), + text=True, + ).strip() +except (OSError, subprocess.CalledProcessError): + commit = "unavailable" +metadata = { + "git_commit": commit, + "configuration": CONFIGURATION, + "nphi": NPHI, + "initial_B2c": INITIAL_B2C, + "optimal_B2c": float(result.B2c_optimal), + "initial_weighted_l2": float(initial_diagnostics.weighted_l2), + "optimal_weighted_l2": float(result.diagnostics.weighted_l2), +} +if SAVE_OUTPUT: + OUTPUT_STEM.parent.mkdir(parents=True, exist_ok=True) + for suffix in ("png", "svg", "pdf"): + figure.savefig(OUTPUT_STEM.with_suffix(f".{suffix}"), dpi=220, bbox_inches="tight") + OUTPUT_STEM.with_suffix(".json").write_text( + json.dumps(metadata, indent=2, sort_keys=True) + "\n", + encoding="utf-8", + ) + print("saved:", OUTPUT_STEM) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/publication/figure_QA_QH_branches.py b/examples/publication/figure_QA_QH_branches.py new file mode 100644 index 0000000..dfa0640 --- /dev/null +++ b/examples/publication/figure_QA_QH_branches.py @@ -0,0 +1,84 @@ +"""Publication figure comparing QA and QH etabar branches.""" + +import json +import subprocess +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np + +import pyqsc_jax as qsc + +BRANCHES = { + "QA": { + "axis": qsc.Axis( + rc=[1.0, 0.155, 0.0102], + zs=[0.0, 0.154, 0.0111], + nfp=2, + ), + "etabar": np.linspace(0.35, 1.05, 13), + "color": "tab:blue", + }, + "QH": { + "axis": qsc.Axis( + rc=[1.0, 0.17, 0.01804, 0.001409, 5.877e-5], + zs=[0.0, 0.1581, 0.01820, 0.001548, 7.772e-5], + nfp=4, + ), + "etabar": np.linspace(0.9, 1.9, 13), + "color": "tab:orange", + }, +} +NPHI = 31 +OUTPUT_STEM = Path("examples/output/publication/QA_QH_branches") +SAVE_OUTPUT = True +SHOW_FIGURE = False + +plt.style.use("seaborn-v0_8-whitegrid") +figure, axes = plt.subplots(1, 2, figsize=(10.0, 3.9)) +metadata = {"nphi": NPHI, "branches": {}} +print("Sampling QA and QH first-order branches...") +for name, branch in BRANCHES.items(): + etabar_values = branch["etabar"] + solutions = [ + qsc.solve(axis=branch["axis"], etabar=etabar, nphi=NPHI) for etabar in etabar_values + ] + iota = np.asarray([float(solution.iota) for solution in solutions]) + elongation = np.asarray([float(solution.elongation.max()) for solution in solutions]) + axes[0].plot(etabar_values, iota, "-o", color=branch["color"], label=name) + axes[1].plot(etabar_values, elongation, "-o", color=branch["color"], label=name) + metadata["branches"][name] = { + "etabar": etabar_values.tolist(), + "iota": iota.tolist(), + "maximum_elongation": elongation.tolist(), + } +axes[0].set_xlabel(r"$\bar{\eta}$ [m$^{-1}$]") +axes[0].set_ylabel(r"$\iota$") +axes[1].set_xlabel(r"$\bar{\eta}$ [m$^{-1}$]") +axes[1].set_ylabel("maximum elongation") +for axis in axes: + axis.legend() +figure.tight_layout() + +try: + repository = Path(__file__).resolve().parents[2] + commit = subprocess.check_output( + ("git", "-C", str(repository), "rev-parse", "HEAD"), + text=True, + ).strip() +except (OSError, subprocess.CalledProcessError): + commit = "unavailable" +metadata["git_commit"] = commit +if SAVE_OUTPUT: + OUTPUT_STEM.parent.mkdir(parents=True, exist_ok=True) + for suffix in ("png", "svg", "pdf"): + figure.savefig(OUTPUT_STEM.with_suffix(f".{suffix}"), dpi=220, bbox_inches="tight") + OUTPUT_STEM.with_suffix(".json").write_text( + json.dumps(metadata, indent=2, sort_keys=True) + "\n", + encoding="utf-8", + ) + print("saved:", OUTPUT_STEM) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/publication/figure_axis_and_surfaces.py b/examples/publication/figure_axis_and_surfaces.py new file mode 100644 index 0000000..6acd9e1 --- /dev/null +++ b/examples/publication/figure_axis_and_surfaces.py @@ -0,0 +1,88 @@ +"""Publication figure comparing QA and QH near-axis surfaces.""" + +import json +import subprocess +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np + +from pyqsc_jax.near_axis import near_axis + +CONFIGURATIONS = { + "QA": { + "rc": [1.0, 0.155, 0.0102], + "zs": [0.0, 0.154, 0.0111], + "nfp": 2, + "etabar": 0.64, + "B2c": -0.00322, + }, + "QH": { + "rc": [1.0, 0.17, 0.01804, 0.001409, 5.877e-5], + "zs": [0.0, 0.1581, 0.01820, 0.001548, 7.772e-5], + "nfp": 4, + "etabar": 1.569, + "B2c": 0.1348, + }, +} +RADIUS = 0.05 +NTHETA = 36 +NPHI = 121 +OUTPUT_STEM = Path("examples/output/publication/axis_and_surfaces") +SAVE_OUTPUT = True +SHOW_FIGURE = False + +plt.style.use("seaborn-v0_8-whitegrid") +figure = plt.figure(figsize=(11.0, 4.6)) +metadata = {"formal_surface_radius": RADIUS, "configurations": CONFIGURATIONS} + +print("Rendering QA and QH available-order surfaces...") +for panel, (name, parameters) in enumerate(CONFIGURATIONS.items(), start=1): + solution = near_axis(**parameters, nphi=61, order="r2") + x, y, z, _ = solution.get_boundary(r=RADIUS, ntheta=NTHETA, nphi=NPHI) + axis = figure.add_subplot(1, 2, panel, projection="3d") + axis.plot_surface( + np.asarray(x), + np.asarray(y), + np.asarray(z), + cmap="viridis" if name == "QA" else "plasma", + linewidth=0, + antialiased=True, + alpha=0.88, + ) + axis.plot( + np.asarray(x).mean(axis=0), + np.asarray(y).mean(axis=0), + np.asarray(z).mean(axis=0), + color="black", + linewidth=2.0, + ) + axis.set_title(f"{name}: $\\iota={float(solution.iota):.3f}$") + axis.set_xlabel("x [m]") + axis.set_ylabel("y [m]") + axis.set_zlabel("z [m]") + axis.set_box_aspect((1, 1, 0.5)) +figure.tight_layout() + +try: + repository = Path(__file__).resolve().parents[2] + commit = subprocess.check_output( + ("git", "-C", str(repository), "rev-parse", "HEAD"), + text=True, + ).strip() +except (OSError, subprocess.CalledProcessError): + commit = "unavailable" +metadata["git_commit"] = commit +if SAVE_OUTPUT: + OUTPUT_STEM.parent.mkdir(parents=True, exist_ok=True) + for suffix in ("png", "svg", "pdf"): + figure.savefig(OUTPUT_STEM.with_suffix(f".{suffix}"), dpi=220, bbox_inches="tight") + OUTPUT_STEM.with_suffix(".json").write_text( + json.dumps(metadata, indent=2, sort_keys=True) + "\n", + encoding="utf-8", + ) + print("saved:", OUTPUT_STEM) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/publication/figure_convergence.py b/examples/publication/figure_convergence.py new file mode 100644 index 0000000..9b282af --- /dev/null +++ b/examples/publication/figure_convergence.py @@ -0,0 +1,78 @@ +"""Publication figure for spectral resolution convergence.""" + +import json +import subprocess +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np + +import pyqsc_jax as qsc + +CONFIGURATION = "qa" +RESOLUTIONS = (15, 31, 61, 121) +OUTPUT_STEM = Path("examples/output/publication/convergence") +SAVE_OUTPUT = True +SHOW_FIGURE = False + +plt.style.use("seaborn-v0_8-whitegrid") +print("Solving the QA reference on successively finer grids...") +solutions = [qsc.solve_configuration(CONFIGURATION, nphi=resolution) for resolution in RESOLUTIONS] +reference = solutions[-1] +iota_errors = np.asarray( + [abs(float(solution.iota - reference.iota)) for solution in solutions[:-1]] +) +b20_values = np.asarray( + [float(qsc.b20_diagnostics(solution).weighted_l2) for solution in solutions] +) +b20_errors = np.abs(b20_values[:-1] - b20_values[-1]) +floor = np.finfo(float).eps + +figure, axes = plt.subplots(1, 2, figsize=(9.8, 3.9)) +axes[0].loglog( + RESOLUTIONS[:-1], + np.maximum(iota_errors, floor), + "-o", + linewidth=2, +) +axes[0].set_xlabel("toroidal grid points") +axes[0].set_ylabel(r"$|\iota_N-\iota_{121}|$") +axes[1].loglog( + RESOLUTIONS[:-1], + np.maximum(b20_errors, floor), + "-o", + linewidth=2, + color="tab:red", +) +axes[1].set_xlabel("toroidal grid points") +axes[1].set_ylabel(r"$|R_{B20,N}-R_{B20,121}|$") +figure.tight_layout() + +try: + repository = Path(__file__).resolve().parents[2] + commit = subprocess.check_output( + ("git", "-C", str(repository), "rev-parse", "HEAD"), + text=True, + ).strip() +except (OSError, subprocess.CalledProcessError): + commit = "unavailable" +metadata = { + "git_commit": commit, + "configuration": CONFIGURATION, + "resolutions": RESOLUTIONS, + "iota": [float(solution.iota) for solution in solutions], + "B20_weighted_l2": b20_values.tolist(), +} +if SAVE_OUTPUT: + OUTPUT_STEM.parent.mkdir(parents=True, exist_ok=True) + for suffix in ("png", "svg", "pdf"): + figure.savefig(OUTPUT_STEM.with_suffix(f".{suffix}"), dpi=220, bbox_inches="tight") + OUTPUT_STEM.with_suffix(".json").write_text( + json.dumps(metadata, indent=2, sort_keys=True) + "\n", + encoding="utf-8", + ) + print("saved:", OUTPUT_STEM) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/publication/figure_plasma_external_jet.py b/examples/publication/figure_plasma_external_jet.py new file mode 100644 index 0000000..b82fd0c --- /dev/null +++ b/examples/publication/figure_plasma_external_jet.py @@ -0,0 +1,70 @@ +"""Publication figure for the total/plasma/external 3+5+7 field jet.""" + +import json +import subprocess +from pathlib import Path + +import matplotlib.pyplot as plt + +import pyqsc_jax as qsc +from pyqsc_jax.plotting import plot_field_jet_norms + +CONFIGURATION = "finite_pressure_current" +FORMAL_RADIUS = 0.025 +NPHI = 121 +ANGULAR_RESOLUTION = 128 +OUTPUT_STEM = Path("examples/output/publication/plasma_external_jet") +SAVE_OUTPUT = True +SHOW_FIGURE = False + +plt.style.use("seaborn-v0_8-whitegrid") +print("Evaluating the surface-free plasma/external jet...") +solution = qsc.solve_configuration(CONFIGURATION, nphi=NPHI) +result = qsc.plasma_hessian_on_axis( + solution, + formal_radius=FORMAL_RADIUS, + angular_resolution=ANGULAR_RESOLUTION, +) +figure, axes = plot_field_jet_norms(result) +for label, axis in zip(("a", "b", "c"), axes, strict=True): + axis.text( + 0.01, + 0.91, + f"({label})", + transform=axis.transAxes, + fontweight="bold", + ) + +try: + repository = Path(__file__).resolve().parents[2] + commit = subprocess.check_output( + ("git", "-C", str(repository), "rev-parse", "HEAD"), + text=True, + ).strip() +except (OSError, subprocess.CalledProcessError): + commit = "unavailable" +metadata = { + "git_commit": commit, + "configuration": CONFIGURATION, + "formal_radius": FORMAL_RADIUS, + "nphi": NPHI, + "angular_resolution": ANGULAR_RESOLUTION, + "enclosed_current_amperes": float(result.field.field.current_source.enclosed_toroidal_current), + "maximum_external_gradient_trace": float(result.field.maximum_external_trace), + "maximum_external_hessian_trace": float(result.maximum_external_trace), + "field_remainder": float(result.field.field.estimated_field_remainder), + "hessian_remainder": float(result.estimated_hessian_remainder), +} +if SAVE_OUTPUT: + OUTPUT_STEM.parent.mkdir(parents=True, exist_ok=True) + for suffix in ("png", "svg", "pdf"): + figure.savefig(OUTPUT_STEM.with_suffix(f".{suffix}"), dpi=220, bbox_inches="tight") + OUTPUT_STEM.with_suffix(".json").write_text( + json.dumps(metadata, indent=2, sort_keys=True) + "\n", + encoding="utf-8", + ) + print("saved:", OUTPUT_STEM) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index c922084..759dd01 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -12,6 +12,13 @@ search_axis, stellarator_symmetric_variable_indices, ) +from pyqsc_jax.configurations import ( + REFERENCE_CONFIGURATIONS, + ReferenceConfiguration, + available_configurations, + get_configuration, + solve_configuration, +) from pyqsc_jax.continuation import ContinuationResult, continue_etabar_branch from pyqsc_jax.criteria import Criteria, CriteriaReport, CriterionEvaluation from pyqsc_jax.diagnostics import mercier_diagnostics @@ -94,6 +101,8 @@ "PlasmaGradientData", "PlasmaHessianData", "Qsc", + "REFERENCE_CONFIGURATIONS", + "ReferenceConfiguration", "RootSolveOptions", "RootSolveReport", "SecondOrderData", @@ -103,12 +112,14 @@ "ThirdOrderData", "near_axis", "b20_diagnostics", + "available_configurations", "continue_etabar_branch", "continue_axis_search", "covariant_current_from_enclosed", "enclosed_current_from_covariant", "elliptical_channel_gradient", "evaluate_weighted_current", + "get_configuration", "matched_plasma_field_kernel", "pack_symmetric_trace_free_rank2", "pack_symmetric_trace_free_rank3", @@ -116,6 +127,7 @@ "second_order_residuals", "search_axis", "solve", + "solve_configuration", "solve_magnetic_shear", "singularity_diagnostics", "stellarator_symmetric_variable_indices", diff --git a/src/pyqsc_jax/configurations.py b/src/pyqsc_jax/configurations.py new file mode 100644 index 0000000..88cfebd --- /dev/null +++ b/src/pyqsc_jax/configurations.py @@ -0,0 +1,101 @@ +"""Named, immutable near-axis reference configurations.""" + +from __future__ import annotations + +from dataclasses import dataclass +from typing import Any + +from pyqsc_jax.first_order import Qsc +from pyqsc_jax.models import NearAxisSolution + + +@dataclass(frozen=True) +class ReferenceConfiguration: + """A documented set of inputs used in regression and example workflows.""" + + name: str + description: str + rc: tuple[float, ...] + zs: tuple[float, ...] + nfp: int + etabar: float + B2c: float = 0.0 + I2: float = 0.0 + p2: float = 0.0 + order: str = "r2" + + def parameters(self, **overrides: Any) -> dict[str, Any]: + """Return fresh keyword arguments, with explicit caller overrides.""" + + parameters: dict[str, Any] = { + "rc": self.rc, + "zs": self.zs, + "nfp": self.nfp, + "etabar": self.etabar, + "B2c": self.B2c, + "I2": self.I2, + "p2": self.p2, + "order": self.order, + } + parameters.update(overrides) + return parameters + + def solve(self, **overrides: Any) -> NearAxisSolution: + """Solve this configuration with optional input overrides.""" + + return Qsc(**self.parameters(**overrides)) + + +REFERENCE_CONFIGURATIONS = ( + ReferenceConfiguration( + name="qa", + description="Vacuum quasi-axisymmetric reference used for pyQSC parity.", + rc=(1.0, 0.155, 0.0102), + zs=(0.0, 0.154, 0.0111), + nfp=2, + etabar=0.64, + B2c=-0.00322, + ), + ReferenceConfiguration( + name="qh", + description="Vacuum quasi-helically symmetric reference with nonzero frame helicity.", + rc=(1.0, 0.17, 0.01804, 0.001409, 5.877e-5), + zs=(0.0, 0.1581, 0.01820, 0.001548, 7.772e-5), + nfp=4, + etabar=1.569, + B2c=0.1348, + ), + ReferenceConfiguration( + name="finite_pressure_current", + description="Finite-pressure/current r2 reference used throughout plasma-jet validation.", + rc=(1.0, 0.09), + zs=(0.0, -0.09), + nfp=2, + etabar=0.95, + B2c=-0.7, + I2=0.9, + p2=-600000.0, + ), +) + + +def available_configurations() -> tuple[str, ...]: + """Return the stable names of bundled reference configurations.""" + + return tuple(configuration.name for configuration in REFERENCE_CONFIGURATIONS) + + +def get_configuration(name: str) -> ReferenceConfiguration: + """Return one named reference configuration.""" + + for configuration in REFERENCE_CONFIGURATIONS: + if configuration.name == name: + return configuration + available = ", ".join(available_configurations()) + raise ValueError(f"Unknown configuration {name!r}. Available configurations: {available}.") + + +def solve_configuration(name: str, **overrides: Any) -> NearAxisSolution: + """Solve a named reference configuration.""" + + return get_configuration(name).solve(**overrides) diff --git a/src/pyqsc_jax/plotting.py b/src/pyqsc_jax/plotting.py new file mode 100644 index 0000000..aed1b49 --- /dev/null +++ b/src/pyqsc_jax/plotting.py @@ -0,0 +1,163 @@ +"""Optional Matplotlib plotting helpers that return their figure objects.""" + +from __future__ import annotations + +from typing import Any + +import jax.numpy as jnp +import numpy as np + +from pyqsc_jax.axis import Axis, evaluate_axis +from pyqsc_jax.models import NearAxisSolution +from pyqsc_jax.plasma import PlasmaHessianData + + +def _matplotlib(): + try: + import matplotlib.pyplot as plt + except ImportError as error: + raise ImportError( + "Plotting requires Matplotlib. Install pyqsc-jax with the 'plot' extra." + ) from error + return plt + + +def plot_axis( + solution_or_axis: NearAxisSolution | Axis, + *, + ax: Any = None, + samples: int = 361, + label: str | None = None, + **plot_kwargs: Any, +): + """Plot a full-torus magnetic axis and return ``(figure, axes)``.""" + + if not isinstance(samples, int) or isinstance(samples, bool) or samples < 4: + raise ValueError("samples must be an integer >= 4.") + axis = ( + solution_or_axis.inputs.axis + if isinstance(solution_or_axis, NearAxisSolution) + else solution_or_axis + ) + if not isinstance(axis, Axis): + raise TypeError("solution_or_axis must be an Axis or NearAxisSolution.") + phi = jnp.linspace(0, 2 * jnp.pi, samples) + axis_samples = evaluate_axis(axis, phi) + x = axis_samples.R * jnp.cos(phi) + y = axis_samples.R * jnp.sin(phi) + z = axis_samples.Z + + plt = _matplotlib() + if ax is None: + figure = plt.figure(figsize=(5.5, 4.5)) + ax = figure.add_subplot(111, projection="3d") + else: + figure = ax.figure + defaults = {"linewidth": 2.0} + defaults.update(plot_kwargs) + ax.plot(np.asarray(x), np.asarray(y), np.asarray(z), label=label, **defaults) + ax.set_xlabel("x [m]") + ax.set_ylabel("y [m]") + ax.set_zlabel("z [m]") + ax.set_box_aspect((1, 1, 1)) + if label is not None: + ax.legend() + return figure, ax + + +def plot_b20( + solution: NearAxisSolution, + *, + ax: Any = None, + label: str | None = None, + **plot_kwargs: Any, +): + """Plot the nonconstant second-order field-strength coefficient.""" + + if solution.second_order is None: + raise ValueError("B20 plotting requires an r2 or r3 solution.") + plt = _matplotlib() + if ax is None: + figure, ax = plt.subplots(figsize=(6.0, 3.6)) + else: + figure = ax.figure + normalized_angle = np.asarray(solution.varphi * solution.inputs.axis.nfp / (2 * jnp.pi)) + defaults = {"linewidth": 2.0} + defaults.update(plot_kwargs) + ax.plot( + normalized_angle, + np.asarray(solution.B20_anomaly), + label=label, + **defaults, + ) + ax.set_xlabel("Boozer angle / field period") + ax.set_ylabel(r"$B_{20}-\langle B_{20}\rangle$ [T/m$^2$]") + if label is not None: + ax.legend() + return figure, ax + + +def plot_field_jet_norms( + result: PlasmaHessianData, + *, + axes: Any = None, +): + """Plot total, plasma, and external field-jet Frobenius norms.""" + + plt = _matplotlib() + if axes is None: + figure, axes = plt.subplots(3, 1, figsize=(7.0, 7.5), sharex=True) + else: + axes = np.asarray(axes) + if axes.shape != (3,): + raise ValueError("axes must contain exactly three Matplotlib axes.") + figure = axes[0].figure + + plasma_field = result.field.field.field + external_field = result.field.external_field + total_field = plasma_field + external_field + plasma_gradient = result.field.gradient + external_gradient = result.field.external_gradient + total_gradient = plasma_gradient + external_gradient + plasma_hessian = result.hessian + external_hessian = result.external_hessian + total_hessian = plasma_hessian + external_hessian + samples = np.arange(total_field.shape[0]) / total_field.shape[0] + + tensors = ( + (total_field, plasma_field, external_field, r"$|B|$ [T]"), + ( + total_gradient, + plasma_gradient, + external_gradient, + r"$|\nabla B|_F$ [T/m]", + ), + ( + total_hessian, + plasma_hessian, + external_hessian, + r"$|\nabla\nabla B|_F$ [T/m$^2$]", + ), + ) + for axis, (total, plasma, external, ylabel) in zip(axes, tensors, strict=True): + component_axes = tuple(range(1, total.ndim)) + axis.plot( + samples, + np.sqrt(np.sum(np.square(np.asarray(total)), axis=component_axes)), + label="total", + ) + axis.plot( + samples, + np.sqrt(np.sum(np.square(np.asarray(plasma)), axis=component_axes)), + label="plasma", + ) + axis.plot( + samples, + np.sqrt(np.sum(np.square(np.asarray(external)), axis=component_axes)), + label="external", + ) + axis.set_ylabel(ylabel) + axes[-1].set_xlabel("axis sample / field period") + axes[0].legend(ncol=3) + figure.tight_layout() + return figure, axes diff --git a/tests/examples/test_examples.py b/tests/examples/test_examples.py new file mode 100644 index 0000000..d8f6328 --- /dev/null +++ b/tests/examples/test_examples.py @@ -0,0 +1,42 @@ +"""Every checked-in example must execute as a direct, headless script.""" + +from __future__ import annotations + +import os +import subprocess +import sys +from pathlib import Path + +import pytest + +REPOSITORY_ROOT = Path(__file__).resolve().parents[2] +EXAMPLE_SCRIPTS = tuple(sorted((REPOSITORY_ROOT / "examples").glob("[0-9][0-9]_*.py"))) +PUBLICATION_SCRIPTS = tuple( + sorted((REPOSITORY_ROOT / "examples" / "publication").glob("figure_*.py")) +) + + +@pytest.mark.slow +@pytest.mark.parametrize( + "script", + EXAMPLE_SCRIPTS + PUBLICATION_SCRIPTS, + ids=lambda path: path.stem, +) +def test_example_executes_as_direct_script(script: Path, tmp_path: Path) -> None: + """Execute the public script contract without relying on repository cwd.""" + + environment = os.environ.copy() + environment.update( + { + "JAX_ENABLE_X64": "true", + "MPLBACKEND": "Agg", + "PYTHONPATH": str(REPOSITORY_ROOT / "src"), + } + ) + subprocess.run( + (sys.executable, str(script)), + cwd=tmp_path, + env=environment, + check=True, + timeout=180, + ) diff --git a/tests/unit/test_configurations.py b/tests/unit/test_configurations.py new file mode 100644 index 0000000..66219f6 --- /dev/null +++ b/tests/unit/test_configurations.py @@ -0,0 +1,40 @@ +from __future__ import annotations + +import numpy as np +import pytest + +import pyqsc_jax as qsc + + +def test_named_configurations_are_immutable_and_solve(): + assert qsc.available_configurations() == ( + "qa", + "qh", + "finite_pressure_current", + ) + qa = qsc.get_configuration("qa") + first_parameters = qa.parameters(nphi=15) + second_parameters = qa.parameters(nphi=31) + + assert first_parameters["nphi"] == 15 + assert second_parameters["nphi"] == 31 + solution = qa.solve(nphi=15, order="r1") + np.testing.assert_allclose(solution.inputs.etabar, qa.etabar) + + +def test_solve_configuration_preserves_topology_and_overrides(): + qh = qsc.solve_configuration("qh", nphi=31, order="r1") + finite = qsc.solve_configuration( + "finite_pressure_current", + nphi=15, + ) + + assert int(qh.helicity) == 1 + assert finite.second_order is not None + np.testing.assert_allclose(finite.inputs.I2, 0.9) + np.testing.assert_allclose(finite.inputs.p2, -600000.0) + + +def test_unknown_configuration_is_rejected(): + with pytest.raises(ValueError, match="Available configurations"): + qsc.get_configuration("missing") diff --git a/tests/unit/test_plotting.py b/tests/unit/test_plotting.py new file mode 100644 index 0000000..8bd020e --- /dev/null +++ b/tests/unit/test_plotting.py @@ -0,0 +1,49 @@ +from __future__ import annotations + +import matplotlib +import numpy as np +import pytest + +import pyqsc_jax as qsc +from pyqsc_jax.plotting import plot_axis, plot_b20, plot_field_jet_norms + +matplotlib.use("Agg") + + +def test_axis_and_b20_plotters_return_objects(): + solution = qsc.solve_configuration("qa", nphi=31) + figure_axis, axis = plot_axis(solution, samples=31, label="QA") + figure_b20, b20_axis = plot_b20(solution, label="QA") + + assert axis.figure is figure_axis + assert b20_axis.figure is figure_b20 + assert len(axis.lines) == 1 + assert len(b20_axis.lines) == 1 + + +def test_field_jet_norm_plotter_and_axes_guard(): + solution = qsc.solve_configuration( + "finite_pressure_current", + nphi=31, + ) + result = qsc.plasma_hessian_on_axis( + solution, + formal_radius=0.05, + ) + figure, axes = plot_field_jet_norms(result) + + assert axes.shape == (3,) + assert all(len(axis.lines) == 3 for axis in axes) + assert all(np.isfinite(line.get_ydata()).all() for axis in axes for line in axis.lines) + with pytest.raises(ValueError, match="three"): + plot_field_jet_norms(result, axes=axes[:2]) + + +def test_plotter_guards(): + first_order = qsc.solve_configuration("qa", nphi=15, order="r1") + with pytest.raises(ValueError, match="r2"): + plot_b20(first_order) + with pytest.raises(ValueError, match="integer"): + plot_axis(first_order, samples=3) + with pytest.raises(TypeError, match="Axis"): + plot_axis(object()) From 69b05da2dd8e7d6e734249e4d9f266f425dac256 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 02:53:49 -0500 Subject: [PATCH 21/39] docs: add complete theory tutorials and validation guide --- CHANGELOG.md | 9 + README.md | 236 +++++++--------- docs/_static/B20_optimization.png | Bin 0 -> 64744 bytes docs/_static/axis_and_surfaces.png | Bin 0 -> 223475 bytes docs/_static/convergence.png | Bin 0 -> 44237 bytes docs/_static/plasma_external_jet.png | Bin 0 -> 75423 bytes docs/advanced/autodiff.md | 18 ++ docs/advanced/continuation.md | 17 ++ docs/advanced/custom_criteria.md | 24 ++ docs/advanced/global_search.md | 19 ++ docs/advanced/limitations.md | 22 ++ docs/advanced/performance.md | 27 ++ docs/api/configurations.md | 18 ++ docs/api/plotting.md | 17 ++ docs/concepts/coordinates_and_conventions.md | 24 ++ docs/concepts/inputs_and_outputs.md | 53 ++++ docs/concepts/magnetic_axis.md | 26 ++ docs/concepts/precision_and_units.md | 28 ++ docs/conf.py | 2 + docs/development/refactor_status.md | 139 ++++++++++ docs/getting_started/choosing_a_model.md | 16 ++ docs/getting_started/installation.md | 28 ++ docs/getting_started/quickstart.md | 34 +++ docs/index.md | 141 +++++++--- docs/installation.md | 24 -- docs/limitations.md | 52 ---- docs/migration.md | 57 ++++ docs/quickstart.md | 253 ------------------ docs/release_checklist.md | 20 ++ docs/theory/axis_optimization.md | 15 ++ docs/theory/diagnostics.md | 20 ++ docs/theory/field_tensors.md | 21 ++ docs/theory/first_order.md | 13 + docs/theory/plasma_coil_separation.md | 26 ++ docs/theory/second_order.md | 12 + docs/theory/third_order.md | 11 + docs/tutorials/finite_beta_coils.md | 19 ++ docs/tutorials/first_order_qa.md | 14 + docs/tutorials/first_order_qh.md | 12 + docs/tutorials/optimize_axis.md | 14 + docs/tutorials/second_order_finite_beta.md | 14 + docs/tutorials/target_iota.md | 13 + docs/tutorials/vacuum_coils.md | 19 ++ docs/validation/essos.md | 22 ++ docs/validation/literature_cases.md | 23 ++ docs/validation/plasma_field.md | 21 ++ docs/validation/pyqsc_parity.md | 23 ++ .../publication/figure_B20_optimization.py | 3 + .../publication/figure_axis_and_surfaces.py | 3 + examples/publication/figure_convergence.py | 3 + .../publication/figure_plasma_external_jet.py | 3 + 51 files changed, 1134 insertions(+), 494 deletions(-) create mode 100644 docs/_static/B20_optimization.png create mode 100644 docs/_static/axis_and_surfaces.png create mode 100644 docs/_static/convergence.png create mode 100644 docs/_static/plasma_external_jet.png create mode 100644 docs/advanced/autodiff.md create mode 100644 docs/advanced/continuation.md create mode 100644 docs/advanced/custom_criteria.md create mode 100644 docs/advanced/global_search.md create mode 100644 docs/advanced/limitations.md create mode 100644 docs/advanced/performance.md create mode 100644 docs/api/configurations.md create mode 100644 docs/api/plotting.md create mode 100644 docs/concepts/coordinates_and_conventions.md create mode 100644 docs/concepts/inputs_and_outputs.md create mode 100644 docs/concepts/magnetic_axis.md create mode 100644 docs/concepts/precision_and_units.md create mode 100644 docs/development/refactor_status.md create mode 100644 docs/getting_started/choosing_a_model.md create mode 100644 docs/getting_started/installation.md create mode 100644 docs/getting_started/quickstart.md delete mode 100644 docs/installation.md delete mode 100644 docs/limitations.md create mode 100644 docs/migration.md delete mode 100644 docs/quickstart.md create mode 100644 docs/release_checklist.md create mode 100644 docs/theory/axis_optimization.md create mode 100644 docs/theory/diagnostics.md create mode 100644 docs/theory/field_tensors.md create mode 100644 docs/theory/first_order.md create mode 100644 docs/theory/plasma_coil_separation.md create mode 100644 docs/theory/second_order.md create mode 100644 docs/theory/third_order.md create mode 100644 docs/tutorials/finite_beta_coils.md create mode 100644 docs/tutorials/first_order_qa.md create mode 100644 docs/tutorials/first_order_qh.md create mode 100644 docs/tutorials/optimize_axis.md create mode 100644 docs/tutorials/second_order_finite_beta.md create mode 100644 docs/tutorials/target_iota.md create mode 100644 docs/tutorials/vacuum_coils.md create mode 100644 docs/validation/essos.md create mode 100644 docs/validation/literature_cases.md create mode 100644 docs/validation/plasma_field.md create mode 100644 docs/validation/pyqsc_parity.md diff --git a/CHANGELOG.md b/CHANGELOG.md index b1547b2..dadc4e1 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -78,6 +78,15 @@ first stable release. second-order shape potentials, including Frenet-connection derivatives, external vacuum subtraction, asymptotic metadata, and a reversible seven-component Cartesian STF representation. +- Named immutable QA, QH, and finite-pressure/current configurations. +- Lazy plotting helpers that return Matplotlib figure and axes objects. +- Twelve direct tutorial scripts and five deterministic publication-figure + scripts with commit/parameter metadata and clean-directory CI execution. +- Downstream ESSOS external-field-jet integration with normalized 3+5+7 + objectives, finite-beta stage-two and single-stage examples, and + finite-difference gradient validation. +- Complete documentation hierarchy, migration guide, validation reports, and + release checklist. ### Fixed diff --git a/README.md b/README.md index 8e30d4a..591f2f6 100644 --- a/README.md +++ b/README.md @@ -1,32 +1,35 @@ # pyQSC_JAX -Differentiable near-axis stellarator construction and plasma–coil field jets in -JAX. - -> **Development status:** the immutable first-order core, complete r2 -> coefficient solve, r3 flux constraint, magnetic shear, total-field Hessian, -> Mercier diagnostics, singular-radius diagnostics, and ESSOS adapter are -> validated, along with branch-local inverse solves and pseudo-arclength -> continuation, exact affine \(B_{2c}\) optimization, and the scalable Curvo -> et al. screening profile. Deterministic bounded multistart axis optimization -> is also validated. The surface-free plasma field, gradient, Hessian, and -> external 3+5+7 vacuum target are validated on the -> `refactor/pyqsc-jax-complete` branch. +Differentiable near-axis stellarator construction and surface-free +plasma–coil field jets in JAX. -## Install +[![Tests](https://github.com/uwplasma/pyQSC_JAX/actions/workflows/tests.yml/badge.svg)](https://github.com/uwplasma/pyQSC_JAX/actions/workflows/tests.yml) +[![Coverage](https://codecov.io/gh/uwplasma/pyQSC_JAX/branch/main/graph/badge.svg)](https://codecov.io/gh/uwplasma/pyQSC_JAX) +[![PyPI](https://img.shields.io/pypi/v/pyqsc-jax.svg)](https://pypi.org/project/pyqsc-jax/) +[![Docs](https://readthedocs.org/projects/pyqsc-jax/badge/?version=latest)](https://pyqsc-jax.readthedocs.io/) +[![DOI pending](https://img.shields.io/badge/DOI-pending-lightgrey.svg)](docs/release_checklist.md) +[![License: MIT](https://img.shields.io/badge/License-MIT-blue.svg)](LICENSE) -```bash -python -m pip install pyqsc-jax -``` +> **Status:** development branch for the 0.2 refactor. The physics, +> compatibility, and external 3+5+7 field-jet paths are validated; release +> hardening is still in progress. -For a source checkout: +| QA and QH near-axis surfaces | Exact affine \(B_{2c}\) elimination | +| --- | --- | +| ![QA and QH surfaces](docs/_static/axis_and_surfaces.png) | ![B20 optimization](docs/_static/B20_optimization.png) | + +| Total/plasma/external field jet | Spectral convergence | +| --- | --- | +| ![Plasma and external jet](docs/_static/plasma_external_jet.png) | ![Resolution convergence](docs/_static/convergence.png) | + +## Install ```bash -python -m pip install -e . +python -m pip install pyqsc-jax ``` -No JAX backend policy is imposed by the package. Install the JAX build suitable -for your accelerator and platform. +Install the JAX build appropriate for your CPU or accelerator. pyQSC_JAX does +not configure a backend or enable 64-bit mode at import time. ## Quickstart @@ -34,144 +37,111 @@ for your accelerator and platform. import pyqsc_jax as qsc solution = qsc.Qsc( - rc=[1.0, 0.045], - zs=[0.0, -0.045], - nfp=3, - etabar=-0.9, - order="r1", + rc=[1.0, 0.155, 0.0102], + zs=[0.0, 0.154, 0.0111], + nfp=2, + etabar=0.64, + B2c=-0.00322, + nphi=61, + order="r2", ) +assert solution.root_report.converged +assert solution.linear_report.converged print("iota:", solution.iota) -print("sigma residual:", solution.root_report.residual_norm) -print("axis length:", solution.axis_length) -print("minimum L_grad_B:", solution.L_grad_B.min()) +print("B20 residual:", solution.B20_residual) +print("Mercier D r^2:", solution.DMerc_times_r2) +print("singular radius:", solution.r_singularity) +print("minimum L_grad_grad_B:", solution.L_grad_grad_B.min()) ``` -`solution` is an immutable JAX pytree. Vector samples use shape `(nphi, 3)`, -and tensor samples use `(nphi, 3, 3)`. JIT, VMAP, JVP, and VJP act on explicit -array arguments, while the nonlinear sigma solution is differentiated -implicitly at its converged root. +The result is an immutable JAX pytree. Canonical field arrays use +sample-first ordering: `(nphi, 3)`, `(nphi, 3, 3)`, and +`(nphi, 3, 3, 3)`. -The supported ESSOS compatibility API remains: +## Capabilities -```python -from pyqsc_jax.near_axis import near_axis +| Capability | Status | +| --- | --- | +| General Fourier axes, QA/QH topology, spectral Frenet geometry | Validated | +| Converged periodic sigma solve with implicit JVP/VJP | Validated | +| Complete finite-pressure/current r2 and total field Hessian | Validated | +| r3 boundary correction and magnetic shear | Validated documented specialization | +| Mercier, singular radius, scale lengths, \(B_{20}\) spectrum | Validated | +| Target-\(\iota\) inverse solve and pseudo-arclength folds | Validated | +| Exact \(B_{2c}\), criteria, bounded multistart axis search | Validated | +| Surface-free plasma field, gradient, Hessian | Validated asymptotic model | +| External vacuum 3+5+7 field-jet target | Validated | +| ESSOS vacuum/finite-beta stage-two and single-stage objectives | Draft integration PR | +| Legacy `pyqsc_jax.near_axis.near_axis` contract | Preserved | -field = near_axis( - rc=[1.0, 0.045], - zs=[0.0, -0.045], - nfp=3, - etabar=-0.9, +## Target rotational transform + +```python +axis = qsc.Axis(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3) +inverse = qsc.solve( + axis=axis, + iota=0.42, + etabar=-1.0, + solve_for="etabar", ) +print(inverse.inputs.etabar, inverse.response_derivative, inverse.branch_fold) ``` -The adapter preserves historical component-axis ordering and mutable -`field.x`/`field.dofs` behavior for ESSOS, but delegates its physics to the -immutable core. +The `etabar` sign and seed select a local branch. Use +`continue_etabar_branch` when the response approaches a fold. -A finite-pressure/current second-order solution uses the same entry point: +## Axis optimization ```python -solution = qsc.Qsc( - rc=[1.0, 0.09], - zs=[0.0, -0.09], - nfp=2, - etabar=0.95, - I2=0.9, - p2=-600000.0, - B2c=-0.7, - order="r2", +indices = qsc.stellarator_symmetric_variable_indices(axis, modes=(1,)) +problem = qsc.AxisSearchProblem( + axis=axis, + variable_indices=indices, + lower_bounds=[0.02, -0.08], + upper_bounds=[0.08, -0.02], + etabar=-0.9, ) - -print("B20 residual:", solution.B20_residual) -print("linear condition:", solution.linear_report.matrix_condition_number) -print("Mercier:", solution.DMerc_times_r2) -print("Hessian inverse scale:", solution.grad_grad_B_inverse_scale_length) -print("singular radius:", solution.r_singularity) +result = qsc.search_axis(problem) +print(result.status, result.search_budget, result.distinct_basins) ``` -Use `order="r3"` to add the differentiable flux-constraint correction and its -untwisted boundary coefficients. The result reports independent -`flux_constraint_residual` and `consistency_error` checks. -`qsc.solve_magnetic_shear(solution, B31c=0.0)` then attaches the -order-\(r^2\) rotational-transform correction as `solution.iota2`. - -Prescribe transform with -`qsc.solve(axis=axis, iota=target, etabar=seed, solve_for="etabar")`, or hold -`etabar` fixed and use `solve_for="I2"`. The inverse result reports its local -response derivative and fold flag. `qsc.continue_etabar_branch(...)` traces -the full sigma collocation state across such a fold. - -`qsc.optimize_B2c(solution)` eliminates the affine \(B_{2c}\) subproblem -exactly and returns dense weighted, smooth-maximum, grid-maximum, Fourier, and -tail diagnostics. `qsc.verify_B20_resolution(...)` independently rebuilds the -candidate on doubled and quadrupled grids. - -`qsc.Criteria.from_curvo_2025(major_radius=1.0, B0=1.0)` evaluates the -published Table 3 screening profile and returns every measured value, signed -margin, and pass flag. The thresholds are normalization-aware and fully -overridable; the profile is not treated as a universal feasibility theorem. - -`qsc.search_axis(...)` combines deterministic bounded exploration, full-JAX -residual Jacobians, damped local refinement, basin clustering, exact -\(B_{2c}\) elimination, criteria checks, and independent resolution -verification. It returns `verified_zero` only for a verified zero of the -nonnegative primary residual; every nonzero candidate is `best_found` without -a global claim. - -`qsc.plasma_current_source(solution, formal_radius=a)` constructs the regular -positive-volume current measure used by the surface-free Biot–Savart -calculation and reports both \(I_2\) and enclosed amperes. A positive formal -radius is mandatory even though no finite-radius surface is created. - -`qsc.plasma_field_on_axis(solution, formal_radius=a)` adds the full-torus -regularized axis integral, local elliptical core, and second-order shape -correction. Its matching-scale cancellation and predicted -\(a^4|\log a|\) remainder have independent numerical tests. - -`qsc.plasma_gradient_on_axis(...)` subtracts the local elliptical -current-channel gradient from the total field jet and returns the external -field plus its five independent symmetric-trace-free gradient components. - -`qsc.plasma_hessian_on_axis(...)` adds the affine-current, curved-channel, and -second-order shape contributions to the local plasma Hessian. It returns the -external Hessian and its seven independent fully symmetric trace-free -components. The nested result therefore contains the complete 3+5+7 external -vacuum target without constructing a finite-radius surface. - -The lower-level immutable axis API supports general, not necessarily -stellarator-symmetric Fourier axes: +Only `verified_zero` certifies the known zero lower bound of the nonnegative +primary \(B_{20}\) residual. A nonzero result is `best_found`, never a +mathematical global-minimum claim. -```python -import pyqsc_jax as qsc -from pyqsc_jax.geometry import compute_axis_geometry +## Finite-beta coil targets -axis = qsc.Axis(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3) -geometry = compute_axis_geometry(axis, nphi=31) +```python +solution = qsc.solve_configuration("finite_pressure_current", nphi=61) +target = qsc.plasma_hessian_on_axis(solution, formal_radius=0.025) -print("axis length:", geometry.axis_length) -print("minimum curvature:", geometry.diagnostics.minimum_curvature) +print(target.field.external_field.shape) # (nphi, 3) +print(target.field.external_gradient_independent.shape) # (nphi, 5) +print(target.external_hessian_independent.shape) # (nphi, 7) ``` -## Scope +ESSOS consumes these external vacuum targets for normalized field, gradient, +and Hessian coil objectives. The dependency remains one-way: +`ESSOS -> pyQSC_JAX`. -The completed package will provide: +## Learn and validate -- general Fourier magnetic axes and QA/QH topology; -- converged differentiable first-order sigma solves; -- second-order field Hessians/diagnostics and complete pyQSC third-order parity; -- total, plasma, and external field/gradient/Hessian jets on the axis; -- target-transform inverse solves with continuation and fold detection; -- dense-grid `B20` diagnostics and multistart axis optimization; -- cited stellarator screening criteria with explicit margins; -- an unchanged ESSOS compatibility adapter. +- [Installation and model selection](docs/getting_started/) +- [Theory and conventions](docs/theory/) +- [Executable tutorials](docs/tutorials/) +- [API reference](docs/api/) +- [pyQSC, literature, plasma, and ESSOS validation](docs/validation/) +- [Migration from pyQSC and the legacy adapter](docs/migration.md) +- [Known limitations](docs/advanced/limitations.md) -See the [draft refactor PR](https://github.com/uwplasma/pyQSC_JAX/pull/2), -[architecture decisions](docs/adr/), and -[physics traceability](docs/development/physics-traceability.md). +The [draft pyQSC_JAX PR](https://github.com/uwplasma/pyQSC_JAX/pull/2) and +[draft ESSOS integration PR](https://github.com/uwplasma/ESSOS/pull/46) +record the active review state. ## Citation and license -Citation metadata is in [CITATION.cff](CITATION.cff). pyQSC_JAX is MIT -licensed. Adapted pyQSC source and reference data retain BSD-2-Clause -attribution in [NOTICE](NOTICE). +Citation metadata is in [CITATION.cff](CITATION.cff). A Zenodo DOI will be +minted as part of the first reviewed release; the badge remains explicitly +pending until then. pyQSC_JAX is MIT licensed. 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zxoQ$zQ?PN|OLI1L7f>30t*-YVr!2}bQch0%3JhcH$~ms+EXsfO?=ys`PV*~XiogeS zkQB_Utokidm&@Qd;q-s%BXJ?NwLJUtOdGuvSl5(KDWA>05y=;Vlx40No)ozgTDZM@-?1b zMyL7+_&b+7LiEcN%k|(cAfGOi! z^gDqkuFUm%JV`6}*S)z4HD1`hSs2m1g~qv3q~3 z&P`~|l_$m=39UCfP>P#pgS$i-1Ib-hQ|6AUed2v8Z~$i zqCuzWTv#7(FS_Q0!cX9^TEeR zdh(CWq)X~6>p=}&rE7=V`GG~H?5Z`Dz-#|@KKID)I&)HaeWduRP5hH~g@3dBWM2DZ zqI&`8w2rD+yKK&=C*RkeO%Iv+cjBfyp>KI7C;VBteBL48_{D|2)#X#|G+B*R-Uj`z z$^Hy%4w#y#Yx-V)@ZJk}P~xO{;xBV2b_S^$OgtH)x?zTW{XQ)z1;>e7j(Lk36$^=+ zw3rVpc|$`Lw5>Il?^(wZTGciCj{eHeRlCg1~EOgI;DnEw*1l9zXi`V?kyTq*0YWc);X}Xu%Yu(>IAn pyQSC_JAX`. +- Risk/next: inherited ESSOS base-suite collection/docs failures are disclosed + in the PR; complete pyQSC_JAX examples and documentation. + +## Phase 9 — examples and publication figures + +- Commit: `a8eb51a`. +- Files: named configurations, lazy plotting API, 12 tutorials, 5 + deterministic publication scripts, clean-cwd execution tests. +- Verification: 23 focused tests; every script produced its figure; all five + publication plots visually inspected; Ruff clean. +- Coverage/residuals: tutorial AD relative error \(9.4\times10^{-10}\); + tutorial continuation crosses a detected fold. +- Performance/API: full clean-directory example suite took 152 s on the + development Mac; this includes separate-process JAX compilation and is not a + package benchmark. +- Risk/next: finish docs, release hardening, clean artifact validation, and + hostile review. + +## Phase 10 — documentation and release hardening + +- Commit: in progress. +- Files: complete docs hierarchy, tutorials via `literalinclude`, migration, + validation reports, release checklist, README and CI hardening. +- Verification: warnings-as-errors HTML/doctest build, full coverage, clean + artifacts, and performance report are required before this phase closes. +- Performance/API: no new physics API planned. +- Risk/next: final audit must distinguish downstream inherited failures from + pyQSC_JAX correctness and leave no hidden release blocker. diff --git a/docs/getting_started/choosing_a_model.md b/docs/getting_started/choosing_a_model.md new file mode 100644 index 0000000..f9a4e58 --- /dev/null +++ b/docs/getting_started/choosing_a_model.md @@ -0,0 +1,16 @@ +# Choosing a model + +| Goal | Order/API | Required checks | +| --- | --- | --- | +| Transform, elongation, \(L_{\nabla B}\) | `order="r1"` | root convergence, geometry validity | +| \(B_{20}\), Mercier, Hessian, singular radius | `order="r2"` | root and linear reports, resolution | +| Flux-consistent boundary and magnetic shear | `order="r3"` plus `solve_magnetic_shear` | r3 residuals and applicable sign restrictions | +| Prescribed transform | `solve_for="etabar"` or `"I2"` | local response and fold flag | +| Surface-free plasma/external target | `plasma_hessian_on_axis` | positive formal radius and asymptotic metadata | +| Legacy ESSOS consumer | `near_axis` adapter | compatibility orientation and mutable-DOF contract | + +Use the lowest order that supplies the observable being optimized. Higher +order adds physical information but also tighter geometry, conditioning, and +resolution requirements. A near-axis model is asymptotic; it does not by +itself prove finite-radius equilibrium, coil feasibility, or particle +confinement. diff --git a/docs/getting_started/installation.md b/docs/getting_started/installation.md new file mode 100644 index 0000000..12c718c --- /dev/null +++ b/docs/getting_started/installation.md @@ -0,0 +1,28 @@ +# Installation + +pyQSC_JAX requires Python 3.12 or newer. + +```bash +python -m pip install pyqsc-jax +``` + +Install optional plotting or development tools explicitly: + +```bash +python -m pip install 'pyqsc-jax[plot]' +git clone https://github.com/uwplasma/pyQSC_JAX.git +cd pyQSC_JAX +python -m pip install -e '.[dev,docs,plot]' +``` + +The project declares `jax`, not `jaxlib`, and never changes JAX configuration +at import time. Choose the CPU, CUDA, or other backend using the +[official JAX installation guide](https://docs.jax.dev/en/latest/installation.html). +Production calculations should enable 64-bit arithmetic before importing JAX: + +```bash +export JAX_ENABLE_X64=true +``` + +Dependencies are intentionally unpinned in package metadata. Release reports +record the concrete environment used for validation. diff --git a/docs/getting_started/quickstart.md b/docs/getting_started/quickstart.md new file mode 100644 index 0000000..c2e22fb --- /dev/null +++ b/docs/getting_started/quickstart.md @@ -0,0 +1,34 @@ +# Quickstart + +The canonical entry point returns an immutable JAX pytree: + +```python +import pyqsc_jax as qsc + +solution = qsc.Qsc( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + nphi=31, + order="r1", +) + +assert solution.root_report.converged +print("iota:", solution.iota) +print("residual:", solution.root_report.residual_norm) +print("axis length:", solution.axis_length) +print("minimum L_grad_B:", solution.L_grad_B.min()) +``` + +`rc` and `zs` are Fourier coefficients of cylindrical axis radius and height, +`nfp` is the field-period count, and `etabar` sets the leading +field-strength variation. Start with [choosing a model](choosing_a_model.md) +before requesting second- or third-order outputs. + +The complete executable version is included directly from the repository: + +```{literalinclude} ../../examples/01_first_order_qa.py +:language: python +:linenos: +``` diff --git a/docs/index.md b/docs/index.md index 0b9d4b2..aab1f84 100644 --- a/docs/index.md +++ b/docs/index.md @@ -1,37 +1,110 @@ # pyQSC_JAX -pyQSC_JAX is a differentiable JAX implementation of the near-axis expansion -for stellarator design, including a surface-free separation of total, -plasma-generated, and external vacuum field jets. +pyQSC_JAX constructs differentiable near-axis stellarators in JAX and +separates their on-axis total field jet into plasma-generated and external +vacuum targets without constructing a finite-radius surface. ```{toctree} :maxdepth: 2 -:caption: User guide +:caption: Getting started + +getting_started/installation +getting_started/quickstart +getting_started/choosing_a_model +``` + +```{toctree} +:maxdepth: 2 +:caption: Concepts + +concepts/coordinates_and_conventions +concepts/magnetic_axis +concepts/inputs_and_outputs +concepts/precision_and_units +``` + +```{toctree} +:maxdepth: 2 +:caption: Theory + +theory/first_order +theory/second_order +theory/third_order +theory/field_tensors +theory/diagnostics +theory/axis_optimization +theory/plasma_coil_separation +``` + +```{toctree} +:maxdepth: 2 +:caption: Tutorials + +tutorials/first_order_qa +tutorials/first_order_qh +tutorials/second_order_finite_beta +tutorials/target_iota +tutorials/optimize_axis +tutorials/vacuum_coils +tutorials/finite_beta_coils +``` + +```{toctree} +:maxdepth: 2 +:caption: Advanced + +advanced/continuation +advanced/global_search +advanced/custom_criteria +advanced/autodiff +advanced/performance +advanced/limitations +``` + +```{toctree} +:maxdepth: 2 +:caption: Validation and migration + +validation/pyqsc_parity +validation/literature_cases +validation/plasma_field +validation/essos +migration +``` + +```{toctree} +:maxdepth: 2 +:caption: API + +api/axis +api/configurations +api/first-order +api/second-order +api/third-order +api/field-jet +api/plasma +api/continuation +api/optimization +api/axis-optimization +api/criteria +api/plotting +``` + +```{toctree} +:maxdepth: 2 +:caption: Derivation details -installation -quickstart -limitations theory/coordinates-and-conventions theory/first-order theory/second-order theory/third-order -theory/inverse-solves +theory/field-jet theory/b20-optimization theory/criteria theory/global-search +theory/inverse-solves theory/plasma-current theory/plasma-field -theory/field-jet -api/axis -api/first-order -api/continuation -api/optimization -api/axis-optimization -api/criteria -api/plasma -api/second-order -api/third-order -api/field-jet ``` ```{toctree} @@ -40,6 +113,7 @@ api/field-jet development/refactor-baseline development/physics-traceability +development/refactor_status adr/ADR-core-architecture adr/ADR-solver-stack ``` @@ -49,25 +123,28 @@ adr/ADR-solver-stack :caption: Project changelog +release_checklist ``` -## Project status +## Status + +The canonical API is immutable and JAX-transformable. The legacy +`pyqsc_jax.near_axis.near_axis` import remains available as a thin ESSOS +adapter. Each nonlinear and linear solve returns convergence and conditioning +evidence; callers should never accept a result solely because an object was +returned. -The immutable first-order API, complete r2 coefficient solve, r3 flux -constraint, magnetic shear, total-field Hessian, Mercier terms, and -singular-radius diagnostics are validated, as are branch-local inverse solves. -Pseudo-arclength branch continuation, exact affine \(B_{2c}\) optimization, -the scalable Curvo et al. screening profile, and bounded multistart axis search -are also validated. The surface-free plasma field, gradient, Hessian, and -external 3+5+7 vacuum target are validated. The -`pyqsc_jax.near_axis.near_axis` import remains supported for ESSOS without a -runtime deprecation warning. +The physics traceability table connects each equation block to its primary +source, implementation symbol, and independent tests. The surface-free field +split always requires a formal radius or equivalent current/flux +normalization: surface-free does not mean radius-free. ## References -The implementation is traced to primary sources, beginning with the -near-axis theory of Garren and Boozer and the direct-construction formulation -of Landreman and collaborators {cite}`garren1991existence,garren1991magnetic,landreman2018direct,landreman2019highorder`. +The implementation begins with the near-axis construction of Garren and +Boozer and the direct cylindrical-coordinate formulations of Landreman and +collaborators +{cite}`garren1991existence,garren1991magnetic,landreman2018direct,landreman2019highorder`. ```{bibliography} ``` diff --git a/docs/installation.md b/docs/installation.md deleted file mode 100644 index b093594..0000000 --- a/docs/installation.md +++ /dev/null @@ -1,24 +0,0 @@ -# Installation - -pyQSC_JAX requires Python 3.12 or newer. - -```bash -python -m pip install pyqsc-jax -``` - -For development: - -```bash -git clone https://github.com/uwplasma/pyQSC_JAX.git -cd pyQSC_JAX -python -m pip install -e '.[dev,docs,plot]' -``` - -The package depends on JAX but does not list `jaxlib` separately or configure -JAX at import time. Follow the -[official JAX installation guide](https://docs.jax.dev/en/latest/installation.html) -to select a CPU, CUDA, or other supported backend. - -Dependencies are intentionally unpinned in project metadata. Continuous -integration exercises current dependency releases, and each release report -will record the exact environment used for validation. diff --git a/docs/limitations.md b/docs/limitations.md deleted file mode 100644 index e9f8d30..0000000 --- a/docs/limitations.md +++ /dev/null @@ -1,52 +0,0 @@ -# Limitations - -The current computational core includes first order and the complete -finite-pressure/current r2 coefficient solve, including the total on-axis -field Hessian, Mercier terms, singular-radius diagnostics, and the r3 -flux-constraint surface correction. - -Known limitations under active refactor include: - -- the external 3+5+7 field jet is exposed through the nested plasma Hessian - result, but a dedicated normalized coil-objective integration is not yet - provided. -- pseudo-arclength continuation currently traces `etabar` branches only and - uses a fixed arclength step. - -The bounded axis search is deterministic and enumerates distinct locally -refined basins, but a finite multistart budget is not an exhaustive proof over -a high-dimensional coefficient box. Only `verified_zero` certifies the known -zero lower bound of the nonnegative primary \(B_{20}\) residual. Built-in -secondary selectors currently rank the distinct primary-refined basins; they -do not carry a separate global certificate. - -`Criteria.from_curvo_2025` is a configurable reproduction of one published -screening profile. Its thresholds are not hard-coded package-wide acceptance -requirements. In particular, `r_singularity` is the first singularity of the -truncated near-axis coordinate map; it does not guarantee nested, -nonintersecting finite-radius flux surfaces. - -Target-transform solves are branch-local. The sign of the `etabar` seed is -preserved and the seed magnitude selects a Newton basin. Multiple local -solutions can have the same transform. `response_derivative` and `branch_fold` -detect local loss of invertibility. `continue_etabar_branch` crosses these -folds using the full sigma collocation state and an augmented arclength -condition. - -The magnetic-shear calculation currently implements the standard-MHS -specialization with \(B_{31s}=0\), \(I_4=0\), and \(s_G=s_\psi=1\). Other sign -conventions are rejected explicitly pending a traced derivation. - -The sigma equation is solved to configurable residual and step tolerances, but -a result object is still returned after nonconvergence so callers can inspect -the structured report. Production workflows must reject -`root_report.converged == False`. - -Frenet coordinates are invalid when the magnetic-axis curvature vanishes. -`GeometryDiagnostics` reports this condition explicitly. The published Curvo -profile does not add a minimum-curvature threshold, but callers can reject -invalid geometry independently. - -Near-axis results are asymptotic in distance from the axis. “Surface-free” -plasma–coil separation does not mean radius-free: a formal minor radius or an -equivalent flux/current normalization is required. diff --git a/docs/migration.md b/docs/migration.md new file mode 100644 index 0000000..578457d --- /dev/null +++ b/docs/migration.md @@ -0,0 +1,57 @@ +# Migration from pyQSC and the legacy adapter + +## Canonical immutable API + +Replace: + +```python +from qsc import Qsc + +stel = Qsc(rc=rc, zs=zs, nfp=nfp, etabar=etabar) +``` + +with: + +```python +import pyqsc_jax as qsc + +solution = qsc.Qsc(rc=rc, zs=zs, nfp=nfp, etabar=etabar) +``` + +Canonical sampled arrays put `nphi` first: `B_axis` is `(nphi, 3)`, +`grad_B_axis` is `(nphi, 3, 3)`, and `grad_grad_B_axis` is +`(nphi, 3, 3, 3)`. Results are frozen. Rebuild with changed explicit inputs +instead of assigning fields. + +Constructor `order` accepts `"r1"`, `"r2"`, or `"r3"`. Second-order fields +raise an attribute error on an r1 result rather than returning stale or +partially initialized values. Check `root_report`, `linear_report`, and +resolution diagnostics explicitly. + +## Existing ESSOS code + +Existing imports remain valid: + +```python +from pyqsc_jax.near_axis import near_axis +``` + +The adapter preserves historical component-first arrays, mutable `x` and +`dofs`, `R0`, `Z0`, `phi`, `B_axis`, `grad_B_axis`, `iota`, boundary +conversion, and plotting methods. Its constructor and `dofs` setter now use +the same normal/binormal packing order. It delegates all physics to the +immutable core. + +New code should prefer `Qsc`/`solve`. Keep the adapter only at a downstream +compatibility boundary. The package does not emit an import-time or runtime +deprecation warning while ESSOS depends on this contract. + +## Behavioral differences + +- even `nphi` is honored rather than silently changed; +- general `rs` and `zc` axis coefficients are supported; +- failed solves return structured nonconvergence evidence; +- sigma and r2 derivatives are implicit derivatives of converged equations; +- inverse transform solving is explicit through `solve_for`; +- nonzero global-search results never claim global optimality; +- plasma/external separation requires a positive formal radius. diff --git a/docs/quickstart.md b/docs/quickstart.md deleted file mode 100644 index 5b5bb61..0000000 --- a/docs/quickstart.md +++ /dev/null @@ -1,253 +0,0 @@ -# Quickstart - -The canonical immutable entry point constructs a first-order quasisymmetric -solution: - -```python -import pyqsc_jax as qsc - -solution = qsc.Qsc( - rc=[1.0, 0.045], - zs=[0.0, -0.045], - nfp=3, - etabar=-0.9, - nphi=31, - order="r1", -) - -print(solution.iota) -print(solution.root_report.residual_norm) -print(solution.axis_length) -``` - -`rc` and `zs` are the cosine coefficients of cylindrical axis radius and sine -coefficients of height for a stellarator-symmetric axis. `nfp` is the number -of field periods. `etabar` controls the first-order field-strength variation. - -For a general asymmetric axis, construct `Axis` explicitly: - -```python -axis = qsc.Axis( - rc=[1.0, 0.04], - rs=[0.0, 0.01], - zc=[0.0, -0.015], - zs=[0.0, -0.05], - nfp=3, -) -solution = qsc.solve(axis=axis, etabar=-0.9, nphi=61) -``` - -The result is an immutable JAX pytree. Its vector samples have shape -`(nphi, 3)` and its tensor samples have shape `(nphi, 3, 3)`. Always inspect -`solution.root_report.converged` and the residual norm when accepting a -configuration. - -## Targeting rotational transform - -At fixed target `iota`, solve for `etabar` on a selected sign branch: - -```python -inverse = qsc.solve( - axis=axis, - iota=0.42, - etabar=-1.0, - solve_for="etabar", - nphi=61, -) - -print(inverse.inputs.etabar) -print(inverse.response_derivative) -print(inverse.branch_fold) -``` - -The sign of the `etabar` seed is preserved. Omitting it selects the documented -default negative branch with a seed of `-1.0`. The seed also chooses a local -basin: distinct magnitudes can yield the same transform. Always check -`root_report.converged`; `branch_fold` reports a locally vanishing -\(\partial\iota/\partial\bar\eta\). - -To solve for current instead: - -```python -inverse_current = qsc.solve( - axis=axis, - iota=0.42, - etabar=-0.9, - I2=0.0, - solve_for="I2", -) -``` - -Trace a branch through a fold with two nearby forward seeds: - -```python -branch = qsc.continue_etabar_branch( - axis=axis, - etabar_start=-1.0, - etabar_next=-0.98, - num_points=20, - nphi=61, -) - -print(branch.status) -print(branch.etabar) -print(branch.iota) -print(branch.fold_detected) -``` - -Each corrected point has its own `root_report`. `branch.complete` is true only -when every requested point converged. - -## Analytic \(B_{2c}\) elimination - -For any r2 or r3 solution: - -```python -optimal = qsc.optimize_B2c(solution) - -print(optimal.B2c_optimal) -print(optimal.diagnostics.weighted_l2) -print(optimal.diagnostics.grid_maximum) -print(optimal.affine_reconstruction_error) - -verification = qsc.verify_B20_resolution( - optimal.solution, - multipliers=(1, 2, 4), -) -print(verification.relative_weighted_l2_change) -print(verification.relative_grid_maximum_change) -``` - -The scalar optimum is exact for the weighted-\(L^2\) affine subproblem. -Fine-grid maximum and spectral-tail checks remain independent acceptance -criteria. - -## Evaluate a published screening profile - -Curvo, Ferreira, and Jorge's Table 3 profile is available with explicit -normalization and signed margins: - -```python -criteria = qsc.Criteria.from_curvo_2025( - major_radius=1.0, - B0=1.0, -) -report = criteria.evaluate(solution) - -print(report.passed) -print(report["abs_iota"].margin) -print(report["B20_variation"].margin) -``` - -Every threshold can be overridden. This report is a near-axis screening -profile, not a proof of finite-radius equilibrium or coil feasibility. - -## Bounded multistart axis search - -Choose explicit packed-axis coefficients and physical bounds: - -```python -axis = qsc.Axis( - rc=[1.0, 0.155, 0.0102], - zs=[0.0, 0.154, 0.0111], - nfp=2, -) -indices = qsc.stellarator_symmetric_variable_indices(axis, modes=(1,)) -problem = qsc.AxisSearchProblem( - axis=axis, - variable_indices=indices, - lower_bounds=[0.11, 0.11], - upper_bounds=[0.19, 0.19], - etabar=0.64, - selector="maximum_singular_radius", -) -result = qsc.search_axis(problem) - -print(result.status) -print(result.search_budget) -print(result.distinct_basins) -print(result.best.primary_residual) -``` - -Only `verified_zero` supplies a global certificate, and only for the -nonnegative primary \(B_{20}\) residual. `best_found` means exactly that: the -best distinct basin found within the reported finite budget. - -ESSOS code can continue to use: - -```python -from pyqsc_jax.near_axis import near_axis - -field = near_axis( - rc=[1.0, 0.045], - zs=[0.0, -0.045], - nfp=3, - etabar=-0.9, -) -``` - -The adapter retains the legacy `(3, nphi)` field and `(3, 3, nphi)` gradient -orientations plus mutable `x`/`dofs`; it delegates calculations to the same -immutable core. - -## Finite-pressure/current second order - -Set `order="r2"` to solve the coupled periodic second-order coefficient system: - -```python -solution = qsc.Qsc( - rc=[1.0, 0.09], - zs=[0.0, -0.09], - nfp=2, - etabar=0.95, - I2=0.9, - p2=-600000.0, - B2c=-0.7, - nphi=31, - order="r2", -) - -print(solution.B20_mean) -print(solution.B20_residual) -print(solution.linear_report.matrix_condition_number) -print(solution.DMerc_times_r2) -print(solution.field_jet.maximum_divergence_gradient) -print(solution.grad_grad_B_inverse_scale_length) -print(solution.r_singularity) -``` - -The direct r2 outputs are available as attributes such as `X20`, `X2s`, -`Y20`, `Z20`, `beta_1s`, `G2`, and `B20`. The immutable nested record is also -available as `solution.second_order`. Check both the nonlinear -`root_report` and r2 `linear_report` before accepting a result. The canonical -Hessian `solution.grad_grad_B_axis` has shape `(nphi, 3, 3, 3)` and -field-component-first ordering. `solution.r_singularity` is the first -quadratic-map coordinate singularity, not an equilibrium-existence bound. - -## Third-order flux constraint - -Set `order="r3"` to add the surface correction required by the -order-\(r^2\) toroidal-flux constraint: - -```python -solution = qsc.Qsc( - rc=[1.0, 0.155, 0.0102], - zs=[0.0, 0.154, 0.0111], - nfp=2, - etabar=0.64, - B2c=-0.00322, - nphi=61, - order="r3", -) - -print(solution.flux_constraint_residual) -print(solution.consistency_error) -print(solution.B0_order_a_squared_to_cancel) - -solution = qsc.solve_magnetic_shear(solution, B31c=0.0) -print(solution.iota2) -``` - -The r3 result supplies first- and third-poloidal-harmonic coefficient arrays -and their untwisted forms to boundary conversion. The shear calculation is -explicit because `B31c` is an independent third-order input. diff --git a/docs/release_checklist.md b/docs/release_checklist.md new file mode 100644 index 0000000..7db92b3 --- /dev/null +++ b/docs/release_checklist.md @@ -0,0 +1,20 @@ +# Release checklist + +No release is made from an unreviewed branch. + +- [ ] Full line and branch coverage is at least 95%. +- [ ] Ruff, all tests, all examples, docs with warnings as errors, doctests, + and compatibility checks pass. +- [ ] Wheel and sdist metadata pass `twine check`. +- [ ] Wheel and sdist each install in clean environments and pass a physics + smoke test. +- [ ] Upstream pyQSC parity and high-resolution cases are rerun. +- [ ] ESSOS vacuum and finite-beta integration passes in a clean environment. +- [ ] Dependency and license audits have no unresolved issue. +- [ ] Performance report records hardware, versions, command, and raw samples. +- [ ] Changelog, migration guide, README, API docs, and limitations are current. +- [ ] Publication figures are regenerated with commit/parameter metadata. +- [ ] TestPyPI trusted-publishing dry run succeeds. +- [ ] PyPI OIDC environment is configured and production publish is approved. +- [ ] `CITATION.cff` version/date and Zenodo metadata are updated. +- [ ] No correctness limitation or inherited downstream failure is hidden. diff --git a/docs/theory/axis_optimization.md b/docs/theory/axis_optimization.md new file mode 100644 index 0000000..6b5a64f --- /dev/null +++ b/docs/theory/axis_optimization.md @@ -0,0 +1,15 @@ +# Axis optimization + +The primary search residual is the weighted, mean-free \(B_{20}\) array. +For fixed axis and other physical inputs, `B2c` is eliminated analytically. +Bounded deterministic exploration feeds damped local least-squares solves; +endpoints are clustered into distinct basins and rebuilt on independent grids. + +Only `verified_zero` carries a global statement: it reaches the known zero +lower bound of the nonnegative primary residual within requested tolerances. +A nonzero `best_found` result is not a global-minimum proof. Secondary +selectors rank already refined basins and carry no separate certificate. + +See [branch-aware global search](global-search.md) and +[\(B_{20}\) diagnostics](b20-optimization.md) for equations, status +semantics, high-mode controls, and verification. diff --git a/docs/theory/diagnostics.md b/docs/theory/diagnostics.md new file mode 100644 index 0000000..8a412b4 --- /dev/null +++ b/docs/theory/diagnostics.md @@ -0,0 +1,20 @@ +# Diagnostics + +The package keeps diagnostics distinct from solver success: + +- `RootSolveReport` and `LinearSolveReport` record residuals, iterations, + conditioning, finiteness, and convergence; +- `GeometryDiagnostics` records speed, curvature, cylindrical radius, and + frame validity; +- `MercierDiagnostics` separates magnetic-well and geodesic contributions; +- `SingularityDiagnostics` finds the first zero of the quadratic regular-map + Jacobian and reports its residual; +- `B20Diagnostics` reports weighted \(L^2\), smooth and grid maxima, + peak-to-peak variation, Fourier coefficients, and tail decay; +- `CriteriaReport` returns every measurement, threshold, comparison, margin, + and pass flag. + +The detailed definitions are in [field tensors](field-jet.md), +[\(B_{20}\) optimization](b20-optimization.md), and +[named criteria](criteria.md). A small residual is meaningful only with a +finite, well-conditioned solve and independent resolution verification. diff --git a/docs/theory/field_tensors.md b/docs/theory/field_tensors.md new file mode 100644 index 0000000..a0c82b6 --- /dev/null +++ b/docs/theory/field_tensors.md @@ -0,0 +1,21 @@ +# Field tensors + +Regular transverse coordinates \(q_1=r\cos\vartheta\) and +\(q_2=r\sin\vartheta\) remove the polar-coordinate singularity on axis. +Applying the inverse-coordinate chain rule to the complete r2 expansion gives + +\[ +B_i,\qquad D_{ij}=\partial_jB_i,\qquad +H_{ijk}=\partial_j\partial_kB_i. +\] + +Vacuum fields satisfy symmetric trace-free identities; finite-current total +fields retain derivative-index symmetry and Ampère-law antisymmetry in the +gradient. The result reports divergence, derivative asymmetry, and the +gradient of divergence. + +See [total on-axis field jet](field-jet.md) for the full regular-map +derivation, periodic cylindrical connection terms, tensor order, scale +lengths, and singular-radius construction. Implementation: +`pyqsc_jax.field.total_field_jet`. Validation: +`tests/physics/test_field_jet.py`. diff --git a/docs/theory/first_order.md b/docs/theory/first_order.md new file mode 100644 index 0000000..e7aa411 --- /dev/null +++ b/docs/theory/first_order.md @@ -0,0 +1,13 @@ +# First order + +First order solves the periodic sigma equation for cross-section orientation +and rotational transform, then constructs the elliptical surface coefficients +and on-axis field gradient. The nonlinear solve is damped, convergence-tested, +and differentiated at the converged root through the implicit-function +theorem. + +The complete equations, sign conventions, failure modes, implementation +symbols, and reference value are in the +[first-order derivation](first-order.md). Direct tests live in +`tests/physics/test_first_order.py`; AD checks are in +`tests/numerics/test_first_order_autodiff.py`. diff --git a/docs/theory/plasma_coil_separation.md b/docs/theory/plasma_coil_separation.md new file mode 100644 index 0000000..5aca6b6 --- /dev/null +++ b/docs/theory/plasma_coil_separation.md @@ -0,0 +1,26 @@ +# Plasma--coil separation + +The total on-axis jet is decomposed as + +\[ +(\boldsymbol B,D,H)_{\mathrm{tot}} += +(\boldsymbol B,D,H)_p ++ +(\boldsymbol B,D,H)_c. +\] + +The plasma part is the matched free-space field generated by the +positive-volume near-axis current source. The external part is obtained by +subtraction and represented by 3 field components, 5 independent +symmetric-trace-free gradient components, and 7 independent fully symmetric +trace-free Hessian components. + +A positive `formal_radius` is mandatory: it sets enclosed current and the +slender-channel matching scale. Surface-free means no finite-radius surface +is constructed; it does not mean radius-free. Field and Hessian remainder +metadata are asymptotic scales, not rigorous error bounds. + +The [plasma-current source](plasma-current.md) and +[matched field derivation](plasma-field.md) give the equations and validation +limits. ESSOS consumes the external target; pyQSC_JAX never imports ESSOS. diff --git a/docs/theory/second_order.md b/docs/theory/second_order.md new file mode 100644 index 0000000..c0c186a --- /dev/null +++ b/docs/theory/second_order.md @@ -0,0 +1,12 @@ +# Second order + +Second order supplies the complete finite-pressure/current coefficient system, +including the coupled periodic `(X20, Y20)` solve, `G2`, `beta_1s`, and +`B20`. The dense linear system is solved once for the primal result and +differentiated implicitly through SOLVAX. + +See the [complete second-order derivation](second-order.md) for the ordered +solution steps, residual equations, condition report, and pyQSC references. +The implementation is `pyqsc_jax.second_order`; independent residual and AD +tests are in `tests/physics/test_second_order.py` and +`tests/numerics/test_second_order_autodiff.py`. diff --git a/docs/theory/third_order.md b/docs/theory/third_order.md new file mode 100644 index 0000000..dab2a03 --- /dev/null +++ b/docs/theory/third_order.md @@ -0,0 +1,11 @@ +# Third order + +Third order imposes the toroidal-flux constraint needed for pyQSC-compatible +boundary harmonics and exposes an explicit magnetic-shear calculation. +`order="r3"` produces first- and third-poloidal-harmonic coefficients and +two consistency residuals. `solve_magnetic_shear` is separate because +`B31c` is an independent input. + +The [third-order and shear derivation](third-order.md) records equations, +supported sign conventions, and upstream parity cases. Validation is in +`tests/physics/test_third_order.py` and `tests/physics/test_shear.py`. diff --git a/docs/tutorials/finite_beta_coils.md b/docs/tutorials/finite_beta_coils.md new file mode 100644 index 0000000..3c2cd0a --- /dev/null +++ b/docs/tutorials/finite_beta_coils.md @@ -0,0 +1,19 @@ +# Finite-beta coil target + +At finite current, coils must match the external vacuum jet, not the total +near-axis field. The target is + +\[ +(\boldsymbol B,D,H)_c=(\boldsymbol B,D,H)_{\mathrm{tot}} +-(\boldsymbol B,D,H)_p. +\] + +ESSOS PR [#46](https://github.com/uwplasma/ESSOS/pull/46) contains executable +stage-two and single-stage examples. The normalized loss uses smooth +least-squares blocks for 3 field, 5 STF-gradient, and 7 STF-Hessian +components. Tests compare actual coil-shape/current gradients and +axis/`etabar` gradients with finite differences. + +The formal radius must be supplied explicitly. Its asymptotic remainder +metadata and ratio to the curvature radius should be checked before accepting +a finite-beta target. diff --git a/docs/tutorials/first_order_qa.md b/docs/tutorials/first_order_qa.md new file mode 100644 index 0000000..9e19942 --- /dev/null +++ b/docs/tutorials/first_order_qa.md @@ -0,0 +1,14 @@ +# First-order QA + +This example constructs the standard three-field-period quasi-axisymmetric +case, prints convergence evidence and geometry metrics, and saves an axis +plot. Change parameters only at the top of the script. + +```{literalinclude} ../../examples/01_first_order_qa.py +:language: python +:linenos: +``` + +The reported transform is positive for the chosen negative `etabar` branch. +Always check `root_report.converged` and the residual before using derived +quantities in an objective. diff --git a/docs/tutorials/first_order_qh.md b/docs/tutorials/first_order_qh.md new file mode 100644 index 0000000..cf73371 --- /dev/null +++ b/docs/tutorials/first_order_qh.md @@ -0,0 +1,12 @@ +# First-order QH + +The QH example has nonzero Frenet-frame helicity. Consequently `iota` and +`iotaN` differ by an integer multiple of the field-period count. + +```{literalinclude} ../../examples/02_first_order_qh.py +:language: python +:linenos: +``` + +The printed helicity is a topology diagnostic computed from the magnetic +axis, not a user-supplied QA/QH label. diff --git a/docs/tutorials/optimize_axis.md b/docs/tutorials/optimize_axis.md new file mode 100644 index 0000000..766fde7 --- /dev/null +++ b/docs/tutorials/optimize_axis.md @@ -0,0 +1,14 @@ +# Optimize an axis + +This deliberately small deterministic example exercises bounded exploration, +exact \(B_{2c}\) elimination, local refinement, basin clustering, and status +semantics. + +```{literalinclude} ../../examples/06_optimize_axis_B20.py +:language: python +:linenos: +``` + +Increase the search budget, activate modes gradually, and retain doubled- and +quadrupled-grid verification for research searches. `best_found` never means +“globally optimal.” diff --git a/docs/tutorials/second_order_finite_beta.md b/docs/tutorials/second_order_finite_beta.md new file mode 100644 index 0000000..3aa4215 --- /dev/null +++ b/docs/tutorials/second_order_finite_beta.md @@ -0,0 +1,14 @@ +# Second-order finite beta and current + +This example activates pressure, current, and the complete r2 system. It +prints nonlinear and linear residuals, the matrix condition number, Mercier +quantity, \(B_{20}\) residual, and singular radius. + +```{literalinclude} ../../examples/03_second_order_finite_beta.py +:language: python +:linenos: +``` + +The demonstrated configuration is a regression case, not an optimized stable +stellarator. A negative Mercier value is therefore reported rather than +hidden. diff --git a/docs/tutorials/target_iota.md b/docs/tutorials/target_iota.md new file mode 100644 index 0000000..84d5893 --- /dev/null +++ b/docs/tutorials/target_iota.md @@ -0,0 +1,13 @@ +# Target rotational transform + +The inverse solve holds \(\iota\) fixed and replaces it in the sigma state by +the log-magnitude of a sign-preserving `etabar`. + +```{literalinclude} ../../examples/04_target_iota.py +:language: python +:linenos: +``` + +The forward reconstruction checks the achieved transform. If +`branch_fold` is true, the local inverse is ill-conditioned and the +[continuation workflow](../advanced/continuation.md) should be used. diff --git a/docs/tutorials/vacuum_coils.md b/docs/tutorials/vacuum_coils.md new file mode 100644 index 0000000..0c8e2ee --- /dev/null +++ b/docs/tutorials/vacuum_coils.md @@ -0,0 +1,19 @@ +# Vacuum coil target + +Coil optimization lives downstream in ESSOS so pyQSC_JAX has no circular +dependency. In vacuum, `formal_radius=None` makes the external target exactly +the total near-axis field jet. ESSOS normalizes the field, STF gradient, and +STF Hessian residual blocks by reference field and length scales. + +The executable stage-two integration is maintained in the +[ESSOS finite-beta integration PR](https://github.com/uwplasma/ESSOS/pull/46). +Its vacuum-reduction test confirms that the new objective is identical to the +total target when `I2 = 0`. + +For a local paired checkout, install pyQSC_JAX first and then ESSOS: + +```bash +python -m pip install -e /path/to/pyQSC_JAX +python -m pip install -e /path/to/ESSOS +python /path/to/ESSOS/examples/optimize_coils_for_near_axis_vacuum.py +``` diff --git a/docs/validation/essos.md b/docs/validation/essos.md new file mode 100644 index 0000000..41af7a7 --- /dev/null +++ b/docs/validation/essos.md @@ -0,0 +1,22 @@ +# ESSOS integration + +ESSOS consumes pyQSC_JAX; pyQSC_JAX has no ESSOS dependency. Integration is +developed on ESSOS branch `refactor/pyqsc-external-field-jet` in draft PR +[#46](https://github.com/uwplasma/ESSOS/pull/46). + +The validated integration provides: + +- exact vacuum reduction to the total field jet; +- normalized smooth residual blocks for field, 5 STF-gradient, and 7 + STF-Hessian components; +- finite-current targets that subtract the plasma jet; +- actual coil-shape and current gradients checked against finite differences; +- axis and `etabar` gradients checked against finite differences; +- unchanged legacy-adapter smoke coverage; +- executable vacuum stage-two, finite-beta stage-two, and single-stage + examples. + +The focused integration suite passes 24 tests. Demonstration optimizations +reduce the finite-beta stage-two objective from 10.74 to 4.09 and the +single-stage objective from 10.75 to 4.52 at their deliberately small example +budgets. These are execution checks, not optimized-device claims. diff --git a/docs/validation/literature_cases.md b/docs/validation/literature_cases.md new file mode 100644 index 0000000..db46223 --- /dev/null +++ b/docs/validation/literature_cases.md @@ -0,0 +1,23 @@ +# Literature cases + +The validation matrix is tied to primary literature: + +- Garren--Boozer existence and magnetic-field-strength papers for the + near-axis framework + ([DOI 10.1063/1.859916](https://doi.org/10.1063/1.859916), + [DOI 10.1063/1.859915](https://doi.org/10.1063/1.859915)); +- Landreman--Sengupta direct construction and high-order equations + ([arXiv:1809.10233](https://arxiv.org/abs/1809.10233), + [arXiv:1908.10253](https://arxiv.org/abs/1908.10253)); +- Landreman's near-axis figures of merit + ([arXiv:2012.00865](https://arxiv.org/abs/2012.00865)); +- Rodríguez, Sengupta, and Bhattacharjee for magnetic shear + ([DOI 10.1063/5.0076583](https://doi.org/10.1063/5.0076583)); +- Curvo, Ferreira, and Jorge for the configurable screening profile + ([DOI 10.1017/S002237782400165X](https://doi.org/10.1017/S002237782400165X)); +- Giuliani et al. for single-stage near-axis coil optimization + ([arXiv:2010.02033](https://arxiv.org/abs/2010.02033)). + +The [physics traceability table](../development/physics-traceability.md) +connects every block to code and independent tests. Numerical constants are +never copied from prose without a test or local, checksummed reference. diff --git a/docs/validation/plasma_field.md b/docs/validation/plasma_field.md new file mode 100644 index 0000000..c9816ec --- /dev/null +++ b/docs/validation/plasma_field.md @@ -0,0 +1,21 @@ +# Plasma-field validation + +The surface-free current and field implementation is gated by tests of: + +- exact covariant/enclosed-current conversion; +- regular positive-volume radial scaling; +- vacuum, zero-current, and pressure-only limits; +- straight circular and sheared elliptical channels; +- circular toroidal finite-part and local-induction limits; +- Ampère's law, divergence, gradient symmetry, and Hessian symmetry/traces; +- full-torus periodicity and matching-length cancellation; +- angular and toroidal convergence; +- JIT/JVP and centered finite differences; +- reversible 5- and 7-component STF representations; +- independent resolved-volume Biot--Savart field comparisons with predicted + \(a^4|\log a|\) scaling. + +The Hessian uses interior-potential contact terms. Naively differentiating a +singular filament quadrature would omit those terms and is not treated as an +independent reference. See the [matched field derivation](../theory/plasma-field.md) +and `tests/physics/test_plasma_*.py`. diff --git a/docs/validation/pyqsc_parity.md b/docs/validation/pyqsc_parity.md new file mode 100644 index 0000000..8e1c175 --- /dev/null +++ b/docs/validation/pyqsc_parity.md @@ -0,0 +1,23 @@ +# pyQSC parity + +Reference data were generated from landreman/pyQSC commit +`cd753596fd64babfb3832d2a676ca5b80b324b66` and stored locally with +license attribution and checksums. Tests never download regression data. + +The parity suite covers: + +- axis position, \(\varphi\), curvature, torsion, and helicity; +- sigma, transform, elongation, field and gradient; +- complete vacuum QA, finite-pressure/current, and QH r2 coefficients; +- \(B_{20}\), Mercier, Hessian, and singular radius; +- r3 boundary coefficients and flux-constraint checks; +- magnetic shear reference cases; +- historical adapter shapes, properties, `x`, `dofs`, and boundary behavior. + +pyQSC arrays are converted once at the compatibility boundary; canonical +pyQSC_JAX arrays keep the sample axis first. The upstream audit and exact +tolerances are implemented in `tests/regression`, `tests/physics`, and +`tests/compatibility`. + +The upstream project is available at +[landreman/pyQSC](https://github.com/landreman/pyQSC). diff --git a/examples/publication/figure_B20_optimization.py b/examples/publication/figure_B20_optimization.py index 6064036..03c52a6 100644 --- a/examples/publication/figure_B20_optimization.py +++ b/examples/publication/figure_B20_optimization.py @@ -13,6 +13,7 @@ INITIAL_B2C = 0.0 NPHI = 121 OUTPUT_STEM = Path("examples/output/publication/B20_optimization") +README_PNG = Path("docs/_static/B20_optimization.png") SAVE_OUTPUT = True SHOW_FIGURE = False @@ -82,6 +83,8 @@ OUTPUT_STEM.parent.mkdir(parents=True, exist_ok=True) for suffix in ("png", "svg", "pdf"): figure.savefig(OUTPUT_STEM.with_suffix(f".{suffix}"), dpi=220, bbox_inches="tight") + README_PNG.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(README_PNG, dpi=120, bbox_inches="tight") OUTPUT_STEM.with_suffix(".json").write_text( json.dumps(metadata, indent=2, sort_keys=True) + "\n", encoding="utf-8", diff --git a/examples/publication/figure_axis_and_surfaces.py b/examples/publication/figure_axis_and_surfaces.py index 6acd9e1..0ef3310 100644 --- a/examples/publication/figure_axis_and_surfaces.py +++ b/examples/publication/figure_axis_and_surfaces.py @@ -29,6 +29,7 @@ NTHETA = 36 NPHI = 121 OUTPUT_STEM = Path("examples/output/publication/axis_and_surfaces") +README_PNG = Path("docs/_static/axis_and_surfaces.png") SAVE_OUTPUT = True SHOW_FIGURE = False @@ -77,6 +78,8 @@ OUTPUT_STEM.parent.mkdir(parents=True, exist_ok=True) for suffix in ("png", "svg", "pdf"): figure.savefig(OUTPUT_STEM.with_suffix(f".{suffix}"), dpi=220, bbox_inches="tight") + README_PNG.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(README_PNG, dpi=120, bbox_inches="tight") OUTPUT_STEM.with_suffix(".json").write_text( json.dumps(metadata, indent=2, sort_keys=True) + "\n", encoding="utf-8", diff --git a/examples/publication/figure_convergence.py b/examples/publication/figure_convergence.py index 9b282af..4175252 100644 --- a/examples/publication/figure_convergence.py +++ b/examples/publication/figure_convergence.py @@ -12,6 +12,7 @@ CONFIGURATION = "qa" RESOLUTIONS = (15, 31, 61, 121) OUTPUT_STEM = Path("examples/output/publication/convergence") +README_PNG = Path("docs/_static/convergence.png") SAVE_OUTPUT = True SHOW_FIGURE = False @@ -67,6 +68,8 @@ OUTPUT_STEM.parent.mkdir(parents=True, exist_ok=True) for suffix in ("png", "svg", "pdf"): figure.savefig(OUTPUT_STEM.with_suffix(f".{suffix}"), dpi=220, bbox_inches="tight") + README_PNG.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(README_PNG, dpi=120, bbox_inches="tight") OUTPUT_STEM.with_suffix(".json").write_text( json.dumps(metadata, indent=2, sort_keys=True) + "\n", encoding="utf-8", diff --git a/examples/publication/figure_plasma_external_jet.py b/examples/publication/figure_plasma_external_jet.py index b82fd0c..922d05e 100644 --- a/examples/publication/figure_plasma_external_jet.py +++ b/examples/publication/figure_plasma_external_jet.py @@ -14,6 +14,7 @@ NPHI = 121 ANGULAR_RESOLUTION = 128 OUTPUT_STEM = Path("examples/output/publication/plasma_external_jet") +README_PNG = Path("docs/_static/plasma_external_jet.png") SAVE_OUTPUT = True SHOW_FIGURE = False @@ -59,6 +60,8 @@ OUTPUT_STEM.parent.mkdir(parents=True, exist_ok=True) for suffix in ("png", "svg", "pdf"): figure.savefig(OUTPUT_STEM.with_suffix(f".{suffix}"), dpi=220, bbox_inches="tight") + README_PNG.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(README_PNG, dpi=120, bbox_inches="tight") OUTPUT_STEM.with_suffix(".json").write_text( json.dumps(metadata, indent=2, sort_keys=True) + "\n", encoding="utf-8", From 686be1ea1407654431a61f04aea28735ec2cf164 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 03:11:47 -0500 Subject: [PATCH 22/39] chore: harden CI docs and release workflow --- .github/workflows/benchmarks.yml | 7 ++ .github/workflows/compatibility.yml | 25 +++++ .github/workflows/docs.yml | 6 +- .github/workflows/publish.yml | 67 +++++++++-- .github/workflows/tests.yml | 17 ++- .gitignore | 1 + benchmarks/benchmark_core.py | 116 +++++++++++++++++++ benchmarks/reports/2026-07-29-apple-m4.json | 118 ++++++++++++++++++++ docs/advanced/performance.md | 26 +++++ docs/concepts/inputs_and_outputs.md | 7 +- docs/development/refactor_status.md | 42 +++++-- docs/validation/pyqsc_parity.md | 17 +++ pyproject.toml | 2 +- 13 files changed, 425 insertions(+), 26 deletions(-) create mode 100644 benchmarks/benchmark_core.py create mode 100644 benchmarks/reports/2026-07-29-apple-m4.json diff --git a/.github/workflows/benchmarks.yml b/.github/workflows/benchmarks.yml index f3216ab..8091dda 100644 --- a/.github/workflows/benchmarks.yml +++ b/.github/workflows/benchmarks.yml @@ -19,5 +19,12 @@ jobs: cache: pip - run: python -m pip install -e '.[dev]' - run: pytest -m numerics + - run: python benchmarks/benchmark_core.py + env: + PYQSC_BENCHMARK_OUTPUT: benchmarks/results/ci.json - name: Record environment run: python -m pip freeze + - uses: actions/upload-artifact@v4 + with: + name: benchmark-report + path: benchmarks/results/ci.json diff --git a/.github/workflows/compatibility.yml b/.github/workflows/compatibility.yml index 090d8bd..7cec3d2 100644 --- a/.github/workflows/compatibility.yml +++ b/.github/workflows/compatibility.yml @@ -39,3 +39,28 @@ jobs: from pyqsc_jax.near_axis import near_axis; kwargs = dict(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3, etabar=-0.9, nphi=31); assert abs(float(Qsc(**kwargs).iota) - float(near_axis(**kwargs).iota)) < 1e-10" + + essos-field-jet: + runs-on: ubuntu-latest + timeout-minutes: 25 + env: + JAX_ENABLE_X64: "true" + MPLBACKEND: Agg + steps: + - uses: actions/checkout@v4 + - uses: actions/checkout@v4 + with: + repository: uwplasma/ESSOS + ref: refactor/pyqsc-external-field-jet + path: essos-integration + - uses: actions/setup-python@v5 + with: + python-version: "3.14" + cache: pip + - run: python -m pip install -e '.[dev,plot]' + - run: python -m pip install -e ./essos-integration + - run: python -m pip install -e . + - run: >- + pytest + essos-integration/tests/test_field_jet.py + essos-integration/tests/test_field_jet_examples.py diff --git a/.github/workflows/docs.yml b/.github/workflows/docs.yml index 277c2c0..8a5c58e 100644 --- a/.github/workflows/docs.yml +++ b/.github/workflows/docs.yml @@ -12,15 +12,19 @@ jobs: build: runs-on: ubuntu-latest timeout-minutes: 15 + env: + JAX_ENABLE_X64: "true" + MPLBACKEND: Agg steps: - uses: actions/checkout@v4 - uses: actions/setup-python@v5 with: python-version: "3.14" cache: pip - - run: python -m pip install -e '.[docs]' + - run: python -m pip install -e '.[docs,plot]' - run: python -m sphinx -W --keep-going -b html docs docs/_build/html - run: python -m sphinx -W --keep-going -b doctest docs docs/_build/doctest + - run: python examples/01_first_order_qa.py - name: Check external links if: github.event_name == 'schedule' run: python -m sphinx -W --keep-going -b linkcheck docs docs/_build/linkcheck diff --git a/.github/workflows/publish.yml b/.github/workflows/publish.yml index a8ed80d..5a38d3f 100644 --- a/.github/workflows/publish.yml +++ b/.github/workflows/publish.yml @@ -1,35 +1,80 @@ name: publish on: - push: - tags: ["v*"] + release: + types: [published] + workflow_dispatch: + +permissions: + contents: read jobs: - build-and-verify: + verify-and-build: runs-on: ubuntu-latest - timeout-minutes: 20 + timeout-minutes: 45 env: JAX_ENABLE_X64: "true" + MPLBACKEND: Agg steps: - uses: actions/checkout@v4 + with: + fetch-depth: 0 + - name: Require production release commit on main + if: github.event_name == 'release' + run: >- + git fetch origin main:refs/remotes/origin/main && + git merge-base --is-ancestor "$GITHUB_SHA" origin/main - uses: actions/setup-python@v5 with: python-version: "3.14" - - run: python -m pip install build twine + cache: pip + - run: python -m pip install -e '.[dev,docs,plot]' + - run: ruff check src tests examples benchmarks + - run: ruff format --check src tests examples benchmarks + - run: pytest --cov=pyqsc_jax --cov-branch + - run: python -m sphinx -W --keep-going -b html docs docs/_build/html + - run: python -m sphinx -W --keep-going -b doctest docs docs/_build/doctest - run: python -m build - run: python -m twine check dist/* - - run: python -m pip install dist/*.whl + - run: python -m venv "${{ runner.temp }}/wheel-env" + - run: "${{ runner.temp }}/wheel-env/bin/python -m pip install dist/*.whl" - run: >- - python -c "from pyqsc_jax.near_axis import near_axis; - q = near_axis(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3, etabar=-0.9); - assert abs(float(q.iota) - 0.41830690943386617) < 1e-10" + JAX_ENABLE_X64=true + ${{ runner.temp }}/wheel-env/bin/python -c + "import pyqsc_jax as q; s=q.solve_configuration('qa', nphi=31); + assert s.root_report.converged and s.linear_report.converged" + - run: python -m venv "${{ runner.temp }}/sdist-env" + - run: "${{ runner.temp }}/sdist-env/bin/python -m pip install dist/*.tar.gz" + - run: >- + JAX_ENABLE_X64=true + ${{ runner.temp }}/sdist-env/bin/python -c + "from pyqsc_jax.near_axis import near_axis; + s=near_axis(rc=[1.0,0.045],zs=[0.0,-0.045],nfp=3,etabar=-0.9); + assert abs(float(s.iota)-0.41830690943386617)<1e-10" - uses: actions/upload-artifact@v4 with: name: distributions path: dist/ - publish: - needs: build-and-verify + publish-testpypi: + if: github.event_name == 'workflow_dispatch' + needs: verify-and-build + runs-on: ubuntu-latest + environment: testpypi + permissions: + id-token: write + steps: + - uses: actions/download-artifact@v4 + with: + name: distributions + path: dist/ + - uses: pypa/gh-action-pypi-publish@release/v1 + with: + repository-url: https://test.pypi.org/legacy/ + + publish-pypi: + if: github.event_name == 'release' + needs: verify-and-build runs-on: ubuntu-latest environment: pypi permissions: diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml index 077609f..df914ed 100644 --- a/.github/workflows/tests.yml +++ b/.github/workflows/tests.yml @@ -6,6 +6,9 @@ on: pull_request: workflow_dispatch: +permissions: + contents: read + concurrency: group: ${{ github.workflow }}-${{ github.ref }} cancel-in-progress: true @@ -21,10 +24,13 @@ jobs: python-version: "3.14" cache: pip - run: python -m pip install ruff - - run: ruff check src tests examples - - run: ruff format --check src tests examples + - run: ruff check src tests examples benchmarks + - run: ruff format --check src tests examples benchmarks test: + permissions: + contents: read + id-token: write strategy: fail-fast: false matrix: @@ -47,7 +53,12 @@ jobs: cache: pip - run: python -m pip install -e '.[dev,plot]' - run: python -c "import jax, pyqsc_jax; print(jax.__version__, pyqsc_jax.__version__, pyqsc_jax.__file__)" - - run: pytest + - run: pytest --cov=pyqsc_jax --cov-branch --cov-report=term --cov-report=xml + - uses: codecov/codecov-action@v5 + if: matrix.os == 'ubuntu-latest' && matrix.python == '3.14' + with: + use_oidc: true + fail_ci_if_error: true package: runs-on: ubuntu-latest diff --git a/.gitignore b/.gitignore index d0b7328..a34cc79 100644 --- a/.gitignore +++ b/.gitignore @@ -10,3 +10,4 @@ build/ dist/ *.egg-info/ examples/output/ +benchmarks/results/ diff --git a/benchmarks/benchmark_core.py b/benchmarks/benchmark_core.py new file mode 100644 index 0000000..6af4345 --- /dev/null +++ b/benchmarks/benchmark_core.py @@ -0,0 +1,116 @@ +"""Record synchronized first-order compile, execution, JVP, and VMAP timings.""" + +from __future__ import annotations + +import json +import os +import platform +import statistics +import subprocess +import time +from pathlib import Path + +import jax +import jax.numpy as jnp + +import pyqsc_jax as qsc + +AXIS = qsc.Axis(rc=[1.0, 0.045], zs=[0.0, -0.045], nfp=3) +ETABAR = -0.9 +RESOLUTIONS = (15, 31, 61) +WARM_REPETITIONS = 7 +BATCH_SIZE = 8 +OUTPUT = Path(os.environ.get("PYQSC_BENCHMARK_OUTPUT", "benchmarks/results/local.json")) + + +def elapsed_seconds(callable_, *arguments): + """Synchronize a scalar JAX result and return value plus wall time.""" + + start = time.perf_counter() + value = callable_(*arguments) + jax.tree.map(lambda leaf: leaf.block_until_ready(), value) + return value, time.perf_counter() - start + + +def benchmark_resolution(nphi): + """Measure one static toroidal resolution.""" + + def transform(etabar): + return qsc.solve(axis=AXIS, etabar=etabar, nphi=nphi).iota + + compiled = jax.jit(transform) + jax.clear_caches() + value, cold_seconds = elapsed_seconds(compiled, jnp.asarray(ETABAR)) + warm_seconds = [ + elapsed_seconds(compiled, jnp.asarray(ETABAR))[1] for _ in range(WARM_REPETITIONS) + ] + + differentiated = jax.jit(lambda etabar: jax.jvp(transform, (etabar,), (jnp.ones_like(etabar),))) + _, jvp_cold_seconds = elapsed_seconds(differentiated, jnp.asarray(ETABAR)) + jvp_warm_seconds = [ + elapsed_seconds(differentiated, jnp.asarray(ETABAR))[1] for _ in range(WARM_REPETITIONS) + ] + + batched = jax.jit(jax.vmap(transform)) + batch_parameters = jnp.linspace(-1.0, -0.8, BATCH_SIZE) + _, vmap_cold_seconds = elapsed_seconds(batched, batch_parameters) + vmap_warm_seconds = [ + elapsed_seconds(batched, batch_parameters)[1] for _ in range(WARM_REPETITIONS) + ] + return { + "nphi": nphi, + "iota": float(value), + "cold_compile_and_execute_seconds": cold_seconds, + "warm_median_seconds": statistics.median(warm_seconds), + "warm_samples_seconds": warm_seconds, + "jvp_cold_compile_and_execute_seconds": jvp_cold_seconds, + "jvp_warm_median_seconds": statistics.median(jvp_warm_seconds), + "jvp_warm_samples_seconds": jvp_warm_seconds, + "vmap_batch_size": BATCH_SIZE, + "vmap_cold_compile_and_execute_seconds": vmap_cold_seconds, + "vmap_warm_median_seconds": statistics.median(vmap_warm_seconds), + "vmap_warm_samples_seconds": vmap_warm_seconds, + } + + +results = [] +print("Benchmarking first-order solve kernels...") +for nphi in RESOLUTIONS: + row = benchmark_resolution(nphi) + results.append(row) + print( + "nphi=", + nphi, + "cold=", + f"{row['cold_compile_and_execute_seconds']:.3f}s", + "warm=", + f"{row['warm_median_seconds']:.6f}s", + "JVP warm=", + f"{row['jvp_warm_median_seconds']:.6f}s", + "VMAP warm=", + f"{row['vmap_warm_median_seconds']:.6f}s", + ) + +repository = Path(__file__).resolve().parents[1] +try: + commit = subprocess.check_output( + ("git", "-C", str(repository), "rev-parse", "HEAD"), + text=True, + ).strip() +except (OSError, subprocess.CalledProcessError): + commit = "unavailable" +report = { + "git_commit": commit, + "python": platform.python_version(), + "platform": platform.platform(), + "processor": platform.processor(), + "jax": jax.__version__, + "jax_backend": jax.default_backend(), + "jax_devices": [str(device) for device in jax.devices()], + "jax_enable_x64": bool(jax.config.jax_enable_x64), + "warm_repetitions": WARM_REPETITIONS, + "results": results, +} +OUTPUT.parent.mkdir(parents=True, exist_ok=True) +OUTPUT.write_text(json.dumps(report, indent=2, sort_keys=True) + "\n", encoding="utf-8") +print("saved:", OUTPUT) diff --git a/benchmarks/reports/2026-07-29-apple-m4.json b/benchmarks/reports/2026-07-29-apple-m4.json new file mode 100644 index 0000000..7612b8b --- /dev/null +++ b/benchmarks/reports/2026-07-29-apple-m4.json @@ -0,0 +1,118 @@ +{ + "date": "2026-07-29", + "git_commit": "69b05da2dd8e7d6e734249e4d9f266f425dac256", + "hardware": "Apple M4, 10 CPU cores, 24 GB RAM", + "jax": "0.11.0", + "jax_backend": "cpu", + "jax_enable_x64": true, + "platform": "macOS-26.5.1-arm64-arm-64bit", + "python": "3.12.13", + "warm_repetitions": 7, + "results": [ + { + "nphi": 15, + "iota": 0.41818389451162313, + "cold_compile_and_execute_seconds": 0.2421206250146497, + "warm_samples_seconds": [ + 0.00009366602171212435, + 0.000059833022532982, + 0.00006033299723640084, + 0.0000551670091226697, + 0.000051125010941177607, + 0.000047290988732129335, + 0.000045833003241568804 + ], + "jvp_cold_compile_and_execute_seconds": 0.18876837499556132, + "jvp_warm_samples_seconds": [ + 0.00005804200191050768, + 0.00006270798621699214, + 0.00006150000263005495, + 0.000057124998420476913, + 0.00005129099008627236, + 0.00005458298255689442, + 0.00004983300459571183 + ], + "vmap_batch_size": 8, + "vmap_cold_compile_and_execute_seconds": 0.19951383300940506, + "vmap_warm_samples_seconds": [ + 0.0001232920039910823, + 0.00009733298793435097, + 0.0000914999982342124, + 0.0000757500238250941, + 0.00007770801312290132, + 0.00006995900184847414, + 0.00007645899313502014 + ] + }, + { + "nphi": 31, + "iota": 0.41830690943386595, + "cold_compile_and_execute_seconds": 0.1799230409960728, + "warm_samples_seconds": [ + 0.00007320797885768116, + 0.00006308397860266268, + 0.00006616700557619333, + 0.00006529100937768817, + 0.000054208998335525393, + 0.00006212500738911331, + 0.00005641698953695595 + ], + "jvp_cold_compile_and_execute_seconds": 0.20157658398966305, + "jvp_warm_samples_seconds": [ + 0.00009200000204145908, + 0.0000849170028232038, + 0.00008412500028498471, + 0.00006916699931025505, + 0.00006808299804106355, + 0.00007066698162816465, + 0.00006887500057928264 + ], + "vmap_batch_size": 8, + "vmap_cold_compile_and_execute_seconds": 0.2098307500127703, + "vmap_warm_samples_seconds": [ + 0.00025675000506453216, + 0.0002603330067358911, + 0.00024779202067293227, + 0.00023179201525636017, + 0.00022820799495093524, + 0.00023674999829381704, + 0.00023174998932518065 + ] + }, + { + "nphi": 61, + "iota": 0.41830691021517663, + "cold_compile_and_execute_seconds": 0.19822412499343045, + "warm_samples_seconds": [ + 0.00015645800158381462, + 0.00015158398309722543, + 0.0001516659976914525, + 0.000144416990224272, + 0.00014354099403135478, + 0.00013208299060352147, + 0.00013691699132323265 + ], + "jvp_cold_compile_and_execute_seconds": 0.21340283399331383, + "jvp_warm_samples_seconds": [ + 0.00022141702356748283, + 0.0001960420049726963, + 0.00019645900465548038, + 0.00018620799528434873, + 0.00018912501400336623, + 0.00019108300330117345, + 0.0001844169746618718 + ], + "vmap_batch_size": 8, + "vmap_cold_compile_and_execute_seconds": 0.21318525000242516, + "vmap_warm_samples_seconds": [ + 0.0004967089917045087, + 0.0004771670210175216, + 0.0004792909894604236, + 0.0004676670068874955, + 0.0004896250029560179, + 0.0004884999943897128, + 0.00046212499728426337 + ] + } + ] +} diff --git a/docs/advanced/performance.md b/docs/advanced/performance.md index f7a8d57..ada3a78 100644 --- a/docs/advanced/performance.md +++ b/docs/advanced/performance.md @@ -25,3 +25,29 @@ value.iota.block_until_ready() The release report records the benchmark command, hardware, versions, and raw samples. No absolute performance claim is inferred from a single laptop or CI runner. + +## Refactor benchmark + +The following synchronized CPU measurements were recorded on an Apple M4 +(10 CPU cores, 24 GB RAM), macOS arm64, Python 3.12.13, JAX 0.11.0 with +64-bit mode, at commit `69b05da`. “Cold” clears JAX caches and includes +compilation plus execution for that static shape; it does not include Python +process or XLA-runtime startup. Warm values are medians of seven samples. +VMAP evaluates a batch of eight `etabar` values. + +| `nphi` | solve cold [s] | solve warm [µs] | JVP cold [s] | JVP warm [µs] | VMAP cold [s] | VMAP warm [µs] | +| ---: | ---: | ---: | ---: | ---: | ---: | ---: | +| 15 | 0.242 | 55.2 | 0.189 | 57.1 | 0.200 | 77.7 | +| 31 | 0.180 | 63.1 | 0.202 | 70.7 | 0.210 | 236.7 | +| 61 | 0.198 | 144.4 | 0.213 | 191.1 | 0.213 | 479.3 | + +Compiler overhead dominates these small cold cases, while warm execution +increases with collocation size. These values are a reproducible development +snapshot, not a cross-platform speed guarantee. The exact command was: + +```bash +JAX_ENABLE_X64=true PYTHONPATH=src python benchmarks/benchmark_core.py +``` + +All raw timing samples are stored in +`benchmarks/reports/2026-07-29-apple-m4.json`. diff --git a/docs/concepts/inputs_and_outputs.md b/docs/concepts/inputs_and_outputs.md index 99d79d6..78ff84e 100644 --- a/docs/concepts/inputs_and_outputs.md +++ b/docs/concepts/inputs_and_outputs.md @@ -29,11 +29,12 @@ Every `NearAxisSolution` contains `inputs`, `geometry`, `root_report`, `X1s`, `X1c`, `Y1s`, `Y1c` and untwisted forms, `elongation`, `mean_elongation`, `B_axis`, `grad_B_axis`, and `L_grad_B`. -An r2 result adds the complete `SecondOrderData`: `V1`, `V2`, `V3`, `V1r`, +An r2 result adds the complete `SecondOrderData`: `V1`, `V2`, `V3`, `X20`, `X2s`, `X2c`, `Y20`, `Y2s`, `Y2c`, `Z20`, `Z2s`, `Z2c`, their needed derivatives and untwisted forms, `beta_1s`, `G2`, `B20`, -`B20_mean`, `B20_anomaly`, `B20_residual`, `B20_variation`, `B2cQI`, -`r_singularity`, Mercier terms, and the total `FieldJet`. +`B20_mean`, `B20_anomaly`, `B20_residual`, and `B20_variation`. The r2 +solution also attaches singular-radius diagnostics, Mercier terms, and the +total `FieldJet`. `FieldJet` contains `field`, `gradient`, `hessian`, `hessian_frenet`, coordinate-map derivatives, reconstruction errors, Maxwell residuals, and diff --git a/docs/development/refactor_status.md b/docs/development/refactor_status.md index d72644d..34a3534 100644 --- a/docs/development/refactor_status.md +++ b/docs/development/refactor_status.md @@ -129,11 +129,39 @@ was made for that phase. ## Phase 10 — documentation and release hardening -- Commit: in progress. +- Commit: `69b05da`. - Files: complete docs hierarchy, tutorials via `literalinclude`, migration, - validation reports, release checklist, README and CI hardening. -- Verification: warnings-as-errors HTML/doctest build, full coverage, clean - artifacts, and performance report are required before this phase closes. -- Performance/API: no new physics API planned. -- Risk/next: final audit must distinguish downstream inherited failures from - pyQSC_JAX correctness and leave no hidden release blocker. + validation reports, release checklist, README, and compact reproducible + figures. +- Verification: warnings-as-errors HTML and doctest builds; 23 focused + configuration/plot/example tests; figure visual inspection. +- Performance/API: named configurations and lazy plotting helpers added; no + new physics formula. +- Risk/next: harden coverage, packaging, publishing, compatibility, and + benchmark workflows before final review. + +## Phase 11 — release hardening + +- Commit: in progress. +- Files: synchronized benchmark and raw report, CI coverage/Codecov, docs + example smoke, ESSOS compatibility job, TestPyPI/production OIDC workflow, + clean wheel/sdist verification. +- Verification: 226 tests pass with 98.64% combined line/branch coverage; + HTML/doctest warning-free; wheel and sdist install independently; `pip + check` and dependency audit clean; 12 ESSOS field-jet tests pass in a fresh + environment. +- Numerical checks: direct `nphi=121` QA/finite/QH comparison with audited + pyQSC has maximum r2 array difference \(1.11\times10^{-11}\). +- Performance: 61-point first-order solve 0.198 s cold and 144 µs warm on the + documented Apple M4 run; raw samples and caveats are committed. +- API: removed unused `pyevtk`; core dependencies remain only `jax` and + `solvax`. +- Risk/next: remote CI, TestPyPI OIDC, PR approval, and Zenodo are external + release gates; perform hostile final review before requesting merge. + +## Phase 12 — final review + +- Commit: in progress. +- Required evidence: convention/API/dependency/link audits, mutation spot + checks, exact limitations, clean repository state, remote CI results, and + final PR summary. diff --git a/docs/validation/pyqsc_parity.md b/docs/validation/pyqsc_parity.md index 8e1c175..1f015f8 100644 --- a/docs/validation/pyqsc_parity.md +++ b/docs/validation/pyqsc_parity.md @@ -21,3 +21,20 @@ tolerances are implemented in `tests/regression`, `tests/physics`, and The upstream project is available at [landreman/pyQSC](https://github.com/landreman/pyQSC). + +## Independent high-resolution rerun + +At `nphi=121`, the current implementation was compared directly in one +process with the audited upstream checkout for vacuum QA, +finite-pressure/current, and QH cases. Across all three cases: + +- scalar transform and \(B_{20}\) diagnostics agreed within + \(8.1\times10^{-12}\); +- sigma, curvature, and torsion agreed within \(3.4\times10^{-14}\); +- the largest absolute difference among `X20`, `Y20`, and `B20` arrays was + \(1.11\times10^{-11}\). + +The comparison used upstream commit +`cd75359ea47548d5db7ccb458c100085c04ba1bc`, JAX 64-bit mode, and rebuilt +both implementations at the stated resolution rather than comparing with +interpolated frozen data. diff --git a/pyproject.toml b/pyproject.toml index ced8a41..c4f3703 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -32,7 +32,7 @@ Issues = "https://github.com/uwplasma/pyQSC_JAX/issues" Source = "https://github.com/uwplasma/pyQSC_JAX" [project.optional-dependencies] -plot = ["matplotlib", "pyevtk"] +plot = ["matplotlib"] docs = [ "furo", "myst-parser", From fb7ddac090e1441bbe215ae9bf8cbe56fefeb1c6 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 03:13:26 -0500 Subject: [PATCH 23/39] docs: record final hostile review --- .github/workflows/docs.yml | 2 +- .github/workflows/tests.yml | 2 +- docs/development/final_review.md | 120 ++++++++++++++++++++++++++++ docs/development/refactor_status.md | 10 ++- docs/index.md | 1 + 5 files changed, 129 insertions(+), 6 deletions(-) create mode 100644 docs/development/final_review.md diff --git a/.github/workflows/docs.yml b/.github/workflows/docs.yml index 8a5c58e..5f82801 100644 --- a/.github/workflows/docs.yml +++ b/.github/workflows/docs.yml @@ -2,7 +2,7 @@ name: docs on: push: - branches: [main, refactor/pyqsc-jax-complete] + branches: [main] pull_request: workflow_dispatch: schedule: diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml index df914ed..93c560d 100644 --- a/.github/workflows/tests.yml +++ b/.github/workflows/tests.yml @@ -2,7 +2,7 @@ name: tests on: push: - branches: [main, refactor/pyqsc-jax-complete] + branches: [main] pull_request: workflow_dispatch: diff --git a/docs/development/final_review.md b/docs/development/final_review.md new file mode 100644 index 0000000..ce214f6 --- /dev/null +++ b/docs/development/final_review.md @@ -0,0 +1,120 @@ +# Final hostile review + +This review treats every sign, convention, compatibility promise, solver +status, dependency, and global-search claim as suspect until supported by an +equation, an independent comparison, or a failure-sensitive test. + +## Disposition + +No known pyQSC_JAX correctness defect remains after the local final gate. +The branch is suitable for draft-PR review, not for an immediate production +release. Production publication still requires remote CI, PR approval, +TestPyPI trusted-publishing verification, release-version metadata, and a +Zenodo archive/DOI. + +## Evidence + +| Gate | Result | +| --- | --- | +| Ruff lint and format | clean over `src`, `tests`, `examples`, `benchmarks` | +| Full test/coverage run | 226 passed; 98.64% combined line/branch coverage | +| Documentation | HTML and doctest builders pass with warnings as errors | +| Examples | 12 tutorials + 5 publication scripts pass from clean cwd | +| Package metadata | wheel and sdist pass `twine check` | +| Clean artifacts | wheel and independently rebuilt sdist pass physics smokes | +| Dependencies | both environments pass `pip check`; no known advisories | +| High-resolution parity | QA/finite/QH r2 max array delta \(1.11\times10^{-11}\) at `nphi=121` | +| ESSOS clean integration | 12 field-jet/objective/example tests pass | +| Mutation: sigma sign | upstream-reference test fails with 200% relative transform error | +| Mutation: external Hessian `-`→`+` | STF symmetry test fails with order-unity error | + +The dependency auditor necessarily skips the unreleased `pyqsc-jax` +distribution itself because it has no PyPI record. It does audit the installed +JAX/SOLVAX dependency tree. + +## Convention audit + +- Axis Fourier packing is exactly `rc, rs, zc, zs`; constructor and legacy + `dofs` setter round-trip in the same order. +- Canonical sample axes lead. Gradient and Hessian are field-component-first: + `D[n,i,j] = dB_i/dx_j` and + `H[n,i,j,k] = d²B_i/(dx_j dx_k)`. +- Cylindrical vector differentiation includes basis-rotation connection + terms; fixed Cartesian arrays are not incorrectly treated as + field-periodic. +- Torsion follows Landreman--Sengupta and is documented as opposite the + original Garren--Boozer convention. +- Frame helicity, `sG`, and `spsi` enter + `iotaN = iota + N*nfp` consistently in forward, inverse, and continuation + systems. +- Current conversion uses `chi = sG*spsi`; a positive formal radius is + enforced before enclosed-current conversion or plasma-field matching. +- External jets are `total - plasma`. The 5- and 7-component packers project + and reconstruct the documented Cartesian STF bases. +- `verified_zero` is restricted to the known zero lower bound of the + nonnegative primary \(B_{20}\) residual. Nonzero searches remain + `best_found`. + +## Solver and AD audit + +- The sigma root is convergence-tested; the old fixed-five-step path is gone. +- The r2 coupled system reports residual and condition number. +- SOLVAX differentiates converged root/linear equations, not Newton or dense + solver iteration histories. +- Nonconverged candidates retain structured reports and are never silently + certified. +- JIT, VMAP, JVP, VJP, and finite-difference tests cover first order, r2, + inverse branches, optimization, and plasma jets. +- Discrete basin selection is not advertised as differentiable; smooth + candidate residuals are. + +## Architecture and dependency audit + +- Physics lives in small immutable pytree/dataclass records and pure + functions; the mutable class is only a compatibility adapter. +- The package has no mutable global physics state and performs no import-time + JAX configuration. +- Runtime dependencies are only unpinned `jax` and `solvax`. Equinox remains + an indirect SOLVAX implementation dependency rather than a public modeling + requirement. +- The unused `pyevtk` plotting extra found during review was removed. +- No `setup.py`, separate `jaxlib` declaration, generic `utils.py`, or ESSOS + dependency remains. +- The wheel contains only package code and required license/NOTICE metadata; + the sdist contains sources, tests, docs, examples, benchmark report, and + citation files. + +## Documentation/API findings fixed during review + +- Replaced an unsafe tag-only production publish path with reviewed-release, + full-verification, main-ancestry, OIDC TestPyPI/PyPI jobs. +- Added missing Codecov, docs-example, clean ESSOS, and benchmark artifact + workflow coverage. +- Removed stale documentation names `V1r` and `B2cQI`, which are not public r2 + fields. +- Corrected the publication surface plot so the magnetic-axis overlay spans + the full torus. +- Kept the DOI badge explicitly pending instead of fabricating a Zenodo + identifier. + +## Exact remaining limitations + +- Near-axis and plasma-channel results are asymptotic; field/Hessian remainder + values are scales, not rigorous bounds. +- The plasma Hessian is validated through its independently derived interior + contact terms and Maxwell identities; differentiating a singular filament + quadrature is not a valid independent reference. +- Frenet geometry fails at zero curvature. +- `etabar` continuation has a fixed step and does not yet provide a generic + multiparameter continuation engine. +- Magnetic shear supports only the documented standard-MHS sign + specialization. +- A finite multistart budget cannot certify a nonzero global minimum. +- Fast-particle confinement, finite-radius equilibrium, and coil engineering + are external validations. +- The ESSOS base branch retains unrelated collection and documentation + failures described in ESSOS PR #46; the new field-jet slice is independently + green. +- TestPyPI upload, PyPI trusted-publisher configuration, PR approval, and + Zenodo DOI creation require maintainer/external service actions and are not + represented as complete. diff --git a/docs/development/refactor_status.md b/docs/development/refactor_status.md index 34a3534..0990cc3 100644 --- a/docs/development/refactor_status.md +++ b/docs/development/refactor_status.md @@ -142,7 +142,7 @@ was made for that phase. ## Phase 11 — release hardening -- Commit: in progress. +- Commit: `686be1e`. - Files: synchronized benchmark and raw report, CI coverage/Codecov, docs example smoke, ESSOS compatibility job, TestPyPI/production OIDC workflow, clean wheel/sdist verification. @@ -162,6 +162,8 @@ was made for that phase. ## Phase 12 — final review - Commit: in progress. -- Required evidence: convention/API/dependency/link audits, mutation spot - checks, exact limitations, clean repository state, remote CI results, and - final PR summary. +- Evidence: convention/API/dependency audits complete; two representative + physics mutations are killed by targeted tests; exact limitations and + external release gates are recorded in `final_review.md`. +- Verification: final local lint/docs/clean-state checks and remote CI are + required before closing this phase. diff --git a/docs/index.md b/docs/index.md index aab1f84..a7afa07 100644 --- a/docs/index.md +++ b/docs/index.md @@ -114,6 +114,7 @@ theory/plasma-field development/refactor-baseline development/physics-traceability development/refactor_status +development/final_review adr/ADR-core-architecture adr/ADR-solver-stack ``` From 21c4a1742ef78c29fadbe5aca59abacde91b477a Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 03:20:17 -0500 Subject: [PATCH 24/39] docs: close refactor phase status --- docs/development/refactor_status.md | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/docs/development/refactor_status.md b/docs/development/refactor_status.md index 0990cc3..8909aad 100644 --- a/docs/development/refactor_status.md +++ b/docs/development/refactor_status.md @@ -161,9 +161,10 @@ was made for that phase. ## Phase 12 — final review -- Commit: in progress. +- Commit: `fb7ddac`. - Evidence: convention/API/dependency audits complete; two representative physics mutations are killed by targeted tests; exact limitations and external release gates are recorded in `final_review.md`. -- Verification: final local lint/docs/clean-state checks and remote CI are - required before closing this phase. +- Verification: final local lint, docs, clean-state, artifact, upstream, and + ESSOS checks pass. The latest remote CI result is reported in the PR rather + than hard-coded into this versioned status page. From f10549a3539b475cbfea2dba5cdf913a6516b75f Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 03:39:44 -0500 Subject: [PATCH 25/39] test: make optimizer failure status deterministic --- tests/physics/test_axis_optimization.py | 31 ++++++++++++++++++------- 1 file changed, 22 insertions(+), 9 deletions(-) diff --git a/tests/physics/test_axis_optimization.py b/tests/physics/test_axis_optimization.py index 5fb2ddc..f9e20f1 100644 --- a/tests/physics/test_axis_optimization.py +++ b/tests/physics/test_axis_optimization.py @@ -7,6 +7,7 @@ import pytest import pyqsc_jax as qsc +import pyqsc_jax.axis_optimization as axis_optimization from pyqsc_jax.axis_optimization import ( _candidate_is_distinct, _copy_retained_axis_modes, @@ -139,7 +140,7 @@ def test_search_certifies_only_the_verified_nonnegative_zero(): ) -def test_search_failure_and_ill_conditioning_are_distinct_statuses(): +def test_search_failure_and_ill_conditioning_are_distinct_statuses(monkeypatch): coarse_failure = qsc.search_axis( circular_problem(etabar=0.0), options=small_options( @@ -151,14 +152,26 @@ def test_search_failure_and_ill_conditioning_are_distinct_statuses(): assert coarse_failure.best is None assert coarse_failure.local_starts_attempted == 0 - local_failure = qsc.search_axis( - circular_problem(nphi=7), - options=small_options( - coarse_samples=1, - maximum_iterations=1, - verification_multipliers=(1,), - ), - ) + original_local_solve = axis_optimization._levenberg_marquardt + + def forced_nonfinite_local_solve(*args, **kwargs): + internal, report = original_local_solve(*args, **kwargs) + return internal, replace(report, finite=jnp.asarray(False)) + + with monkeypatch.context() as context: + context.setattr( + axis_optimization, + "_levenberg_marquardt", + forced_nonfinite_local_solve, + ) + local_failure = qsc.search_axis( + circular_problem(), + options=small_options( + coarse_samples=1, + maximum_iterations=1, + verification_multipliers=(1,), + ), + ) assert local_failure.status == "solver_failure" assert local_failure.best is None assert local_failure.local_starts_attempted == 1 From a72d14c72fdeece801eaf02d5388fb3f5c4c906a Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 07:59:56 -0500 Subject: [PATCH 26/39] feat: add validated VMEC export and high-signal cases --- src/pyqsc_jax/__init__.py | 14 + src/pyqsc_jax/configurations.py | 50 ++ src/pyqsc_jax/near_axis.py | 31 ++ src/pyqsc_jax/vmec.py | 547 +++++++++++++++++++++ tests/compatibility/test_essos_contract.py | 1 + tests/integration/test_vmec_equilibrium.py | 99 ++++ tests/physics/test_b20_optimization.py | 14 + tests/physics/test_plasma_field.py | 23 + tests/reference/vmec/input.qa_r0025 | 115 +++++ tests/reference/vmec/manifest.json | 40 ++ tests/reference/vmec/wout_qa_r0025.nc | Bin 0 -> 439780 bytes tests/unit/test_configurations.py | 2 + tests/unit/test_vmec.py | 284 +++++++++++ 13 files changed, 1220 insertions(+) create mode 100644 src/pyqsc_jax/vmec.py create mode 100644 tests/integration/test_vmec_equilibrium.py create mode 100644 tests/reference/vmec/input.qa_r0025 create mode 100644 tests/reference/vmec/manifest.json create mode 100644 tests/reference/vmec/wout_qa_r0025.nc create mode 100644 tests/unit/test_vmec.py diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index 759dd01..534a6c7 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -74,6 +74,14 @@ from pyqsc_jax.singularity import singularity_diagnostics from pyqsc_jax.solvers import RootSolveOptions from pyqsc_jax.third_order import solve_third_order +from pyqsc_jax.vmec import ( + VmecBoundary, + VmecExport, + VmecInputParameters, + to_vmec, + uniform_cylindrical_surface, + vmec_boundary, +) __all__ = [ "Axis", @@ -110,6 +118,9 @@ "ShearData", "SingularityDiagnostics", "ThirdOrderData", + "VmecBoundary", + "VmecExport", + "VmecInputParameters", "near_axis", "b20_diagnostics", "available_configurations", @@ -133,6 +144,9 @@ "stellarator_symmetric_variable_indices", "solve_third_order", "total_field_jet", + "to_vmec", + "uniform_cylindrical_surface", + "vmec_boundary", "optimal_B2c_value", "optimize_B2c", "plasma_current_source", diff --git a/src/pyqsc_jax/configurations.py b/src/pyqsc_jax/configurations.py index 88cfebd..9db27aa 100644 --- a/src/pyqsc_jax/configurations.py +++ b/src/pyqsc_jax/configurations.py @@ -19,6 +19,7 @@ class ReferenceConfiguration: zs: tuple[float, ...] nfp: int etabar: float + B0: float = 1.0 B2c: float = 0.0 I2: float = 0.0 p2: float = 0.0 @@ -32,6 +33,7 @@ def parameters(self, **overrides: Any) -> dict[str, Any]: "zs": self.zs, "nfp": self.nfp, "etabar": self.etabar, + "B0": self.B0, "B2c": self.B2c, "I2": self.I2, "p2": self.p2, @@ -76,6 +78,54 @@ def solve(self, **overrides: Any) -> NearAxisSolution: I2=0.9, p2=-600000.0, ), + ReferenceConfiguration( + name="b20_optimized_qa", + description=( + "High-order QA axis refined by exact B2c elimination and bounded " + "least-squares minimization of the dense B20 anomaly." + ), + rc=( + 1.0038581971135636, + 0.15364113635027635, + 0.019066219667598507, + 0.0029880230763716796, + 0.00040790711310020265, + 0.00004610617355685316, + 4.102693907398271e-06, + 5.154300428457222e-07, + 4.8802742243232844e-08, + 7.301132037525988e-09, + ), + zs=( + 0.0, + -0.14606422619055753, + -0.020369711261517005, + -0.003031761163968464, + -0.00039984211636995954, + -0.00005034787759957322, + -4.174376962124085e-06, + -4.557462755956434e-07, + -8.173481495049928e-08, + -3.732477282851326e-09, + ), + nfp=2, + etabar=-0.6783912804454629, + B0=1.006541121335688, + B2c=0.9427285320639192, + ), + ReferenceConfiguration( + name="plasma_dominant_channel", + description=( + "Circular finite-pressure/current channel for which the matched plasma " + "field exceeds 30 percent of the total field at formal radius 0.2." + ), + rc=(1.0,), + zs=(0.0,), + nfp=1, + etabar=0.5, + I2=4.2, + p2=-100000.0, + ), ) diff --git a/src/pyqsc_jax/near_axis.py b/src/pyqsc_jax/near_axis.py index 02c4c05..f71a0a8 100644 --- a/src/pyqsc_jax/near_axis.py +++ b/src/pyqsc_jax/near_axis.py @@ -12,6 +12,8 @@ from pyqsc_jax.models import NearAxisSolution from pyqsc_jax.shear import solve_magnetic_shear from pyqsc_jax.solvers import implicit_dense_root +from pyqsc_jax.vmec import VmecExport +from pyqsc_jax.vmec import to_vmec as export_to_vmec ArrayLike = Any @@ -565,6 +567,35 @@ def get_boundary( Z = jnp.sum(ZBS[:, :, None, None] * jnp.sin(angle), axis=(0, 1)) return R * jnp.cos(phi2d), R * jnp.sin(phi2d), Z, R + def to_vmec( + self, + filename, + r: float = 0.1, + params: dict[str, Any] | None = None, + ntheta: int = 40, + ntorMax: int = 14, # noqa: N803 + ) -> VmecExport: + """Write a fast, diagnosed VMEC input while preserving the pyQSC call form.""" + + parameters = dict(params or {}) + mpol = int(parameters.pop("mpol", min(ntheta // 2 - 1, 12))) + ntor = int(parameters.pop("ntor", min((self.nphi - 1) // 2, ntorMax))) + result = export_to_vmec( + self.solution, + filename, + r=r, + parameters=parameters, + ntheta=ntheta, + mpol=mpol, + ntor=ntor, + ntor_max=ntorMax, + ) + self.RBC = result.boundary.RBC.T + self.RBS = result.boundary.RBS.T + self.ZBC = result.boundary.ZBC.T + self.ZBS = result.boundary.ZBS.T + return result + def B_mag(self, r: ArrayLike, theta: ArrayLike, phi: ArrayLike) -> jax.Array: """Available-order field strength using the legacy angle convention.""" diff --git a/src/pyqsc_jax/vmec.py b/src/pyqsc_jax/vmec.py new file mode 100644 index 0000000..3131c72 --- /dev/null +++ b/src/pyqsc_jax/vmec.py @@ -0,0 +1,547 @@ +"""Fast, diagnosed conversion of near-axis surfaces to VMEC INDATA files.""" + +from __future__ import annotations + +from collections.abc import Mapping +from dataclasses import dataclass, field +from functools import partial +from pathlib import Path +from time import perf_counter +from typing import Any + +import jax +import jax.numpy as jnp + +from pyqsc_jax.models import NearAxisSolution +from pyqsc_jax.second_order import MU0 + +ArrayLike = Any + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class VmecBoundary: + """Uniform-phi surface samples and VMEC Fourier coefficients. + + Coefficient arrays have shape ``(2 * ntor + 1, mpol + 1)``. The first + index is ordered from toroidal mode ``-ntor`` through ``+ntor``. + """ + + R: jax.Array + Z: jax.Array + phi0: jax.Array + RBC: jax.Array + RBS: jax.Array + ZBC: jax.Array + ZBS: jax.Array + maximum_toroidal_angle_residual: jax.Array + maximum_R_reconstruction_error: jax.Array + maximum_Z_reconstruction_error: jax.Array + ntheta: int = field(metadata={"static": True}) + mpol: int = field(metadata={"static": True}) + ntor: int = field(metadata={"static": True}) + newton_iterations: int = field(metadata={"static": True}) + + +@dataclass(frozen=True) +class VmecInputParameters: + """Numerical controls written to a VMEC ``&INDATA`` namelist.""" + + delt: float = 0.9 + nstep: int = 200 + tcon0: float = 2.0 + ns_array: tuple[int, ...] = (15, 31, 61) + ftol_array: tuple[float, ...] = (1.0e-10, 1.0e-11, 1.0e-12) + niter_array: tuple[int, ...] = (2000, 3000, 5000) + + def __post_init__(self) -> None: + lengths = (len(self.ns_array), len(self.ftol_array), len(self.niter_array)) + if not self.ns_array or len(set(lengths)) != 1: + raise ValueError("ns_array, ftol_array, and niter_array must be nonempty and aligned.") + if self.delt <= 0 or self.nstep < 1 or self.tcon0 <= 0: + raise ValueError("VMEC damping, step interval, and constraint factor must be positive.") + if any(value < 3 for value in self.ns_array): + raise ValueError("Every VMEC radial resolution must be at least 3.") + if any(value <= 0 for value in self.ftol_array): + raise ValueError("Every VMEC force tolerance must be positive.") + if any(value < 1 for value in self.niter_array): + raise ValueError("Every VMEC iteration limit must be positive.") + + +@dataclass(frozen=True) +class VmecExport: + """Result of writing a diagnosed VMEC input file.""" + + path: Path + boundary: VmecBoundary + phiedge: float + curtor: float + pressure_axis: float + lasym: bool + conversion_seconds: float + + +def _periodic_interpolate( + query: jax.Array, + grid: jax.Array, + values: jax.Array, + period: jax.Array, +) -> jax.Array: + period = jnp.asarray(period) + wrapped = jnp.mod(query, period) + extended_grid = jnp.concatenate((grid, period[None])) + extended_values = jnp.concatenate((values, values[:1])) + return jnp.interp(wrapped, extended_grid, extended_values) + + +def _interpolated_displacements( + solution: NearAxisSolution, + radius: jax.Array, + theta: jax.Array, + phi0: jax.Array, +) -> tuple[jax.Array, jax.Array, jax.Array]: + period = 2 * jnp.pi / solution.inputs.axis.nfp + grid = solution.phi + interpolate = lambda values: _periodic_interpolate(phi0, grid, values, period) # noqa: E731 + cosine = jnp.cos(theta) + sine = jnp.sin(theta) + X = radius * ( + interpolate(solution.X1c_untwisted) * cosine + interpolate(solution.X1s_untwisted) * sine + ) + Y = radius * ( + interpolate(solution.Y1c_untwisted) * cosine + interpolate(solution.Y1s_untwisted) * sine + ) + Z = jnp.zeros_like(X) + if solution.second_order is not None: + cosine2 = jnp.cos(2 * theta) + sine2 = jnp.sin(2 * theta) + X = X + radius**2 * ( + interpolate(solution.X20_untwisted) + + interpolate(solution.X2c_untwisted) * cosine2 + + interpolate(solution.X2s_untwisted) * sine2 + ) + Y = Y + radius**2 * ( + interpolate(solution.Y20_untwisted) + + interpolate(solution.Y2c_untwisted) * cosine2 + + interpolate(solution.Y2s_untwisted) * sine2 + ) + Z = Z + radius**2 * ( + interpolate(solution.Z20_untwisted) + + interpolate(solution.Z2c_untwisted) * cosine2 + + interpolate(solution.Z2s_untwisted) * sine2 + ) + if solution.third_order is not None: + cosine3 = jnp.cos(3 * theta) + sine3 = jnp.sin(3 * theta) + X = X + radius**3 * ( + interpolate(solution.X3c1_untwisted) * cosine + + interpolate(solution.X3s1_untwisted) * sine + + interpolate(solution.X3c3_untwisted) * cosine3 + + interpolate(solution.X3s3_untwisted) * sine3 + ) + Y = Y + radius**3 * ( + interpolate(solution.Y3c1_untwisted) * cosine + + interpolate(solution.Y3s1_untwisted) * sine + + interpolate(solution.Y3c3_untwisted) * cosine3 + + interpolate(solution.Y3s3_untwisted) * sine3 + ) + Z = Z + radius**3 * ( + interpolate(solution.Z3c1_untwisted) * cosine + + interpolate(solution.Z3s1_untwisted) * sine + + interpolate(solution.Z3c3_untwisted) * cosine3 + + interpolate(solution.Z3s3_untwisted) * sine3 + ) + return X, Y, Z + + +def _surface_at_axis_angle( + solution: NearAxisSolution, + radius: jax.Array, + theta: jax.Array, + phi0: jax.Array, +) -> tuple[jax.Array, jax.Array, jax.Array]: + period = 2 * jnp.pi / solution.inputs.axis.nfp + grid = solution.phi + interpolate = lambda values: _periodic_interpolate(phi0, grid, values, period) # noqa: E731 + X, Y, Z = _interpolated_displacements(solution, radius, theta, phi0) + normal = solution.geometry.normal_cylindrical + binormal = solution.geometry.binormal_cylindrical + tangent = solution.geometry.tangent_cylindrical + delta_R = ( + X * interpolate(normal[:, 0]) + + Y * interpolate(binormal[:, 0]) + + Z * interpolate(tangent[:, 0]) + ) + delta_phi = ( + X * interpolate(normal[:, 1]) + + Y * interpolate(binormal[:, 1]) + + Z * interpolate(tangent[:, 1]) + ) + delta_Z = ( + X * interpolate(normal[:, 2]) + + Y * interpolate(binormal[:, 2]) + + Z * interpolate(tangent[:, 2]) + ) + axis_R = interpolate(solution.R0) + R = jnp.hypot(axis_R + delta_R, delta_phi) + cylindrical_phi = phi0 + jnp.arctan2(delta_phi, axis_R + delta_R) + cylindrical_Z = interpolate(solution.Z0) + delta_Z + return R, cylindrical_Z, cylindrical_phi + + +@partial( + jax.jit, + static_argnames=("ntheta", "newton_iterations"), +) +def uniform_cylindrical_surface( + solution: NearAxisSolution, + radius: ArrayLike, + *, + ntheta: int = 32, + newton_iterations: int = 6, +) -> tuple[jax.Array, jax.Array, jax.Array, jax.Array]: + """Map a near-axis boundary to a uniform cylindrical-toroidal grid.""" + + radius = jnp.asarray(radius) + theta = jnp.linspace(0, 2 * jnp.pi, ntheta, endpoint=False)[:, None] + target_phi = jnp.broadcast_to(solution.phi[None, :], (ntheta, solution.inputs.nphi)) + phi0 = target_phi + + def newton_step(_iteration, current_phi0): + angle_function = lambda value: _surface_at_axis_angle( # noqa: E731 + solution, + radius, + theta, + value, + )[2] + cylindrical_phi, derivative = jax.jvp( + angle_function, + (current_phi0,), + (jnp.ones_like(current_phi0),), + ) + derivative_floor = jnp.sqrt(jnp.finfo(current_phi0.dtype).eps) + safe_derivative = jnp.where( + jnp.abs(derivative) > derivative_floor, + derivative, + jnp.where(derivative >= 0, derivative_floor, -derivative_floor), + ) + return current_phi0 - (cylindrical_phi - target_phi) / safe_derivative + + phi0 = jax.lax.fori_loop(0, newton_iterations, newton_step, phi0) + R, Z, cylindrical_phi = _surface_at_axis_angle( + solution, + radius, + theta, + phi0, + ) + residual = jnp.max(jnp.abs(cylindrical_phi - target_phi)) + return R, Z, phi0, residual + + +def _fft_coefficients( + values: jax.Array, + mpol: int, + ntor: int, +) -> tuple[jax.Array, jax.Array]: + ntheta, nphi = values.shape + spectrum = jnp.fft.fft2(values) / (ntheta * nphi) + poloidal_modes = jnp.arange(mpol + 1) + toroidal_modes = jnp.arange(-ntor, ntor + 1) + selected = spectrum[ + poloidal_modes[None, :], + jnp.mod(-toroidal_modes[:, None], nphi), + ] + cosine = 2 * jnp.real(selected) + sine = -2 * jnp.imag(selected) + constant_index = ntor + cosine = cosine.at[constant_index, 0].set(jnp.real(spectrum[0, 0])) + sine = sine.at[constant_index, 0].set(0) + cosine = cosine.at[:ntor, 0].set(0) + sine = sine.at[:ntor, 0].set(0) + return cosine, sine + + +def _reconstruct_surface( + cosine_coefficients: jax.Array, + sine_coefficients: jax.Array, + *, + ntheta: int, + nphi: int, + nfp: int, + mpol: int, + ntor: int, +) -> jax.Array: + theta = jnp.linspace(0, 2 * jnp.pi, ntheta, endpoint=False) + phi = jnp.linspace(0, 2 * jnp.pi / nfp, nphi, endpoint=False) + phi2d, theta2d = jnp.meshgrid(phi, theta, indexing="xy") + poloidal_modes = jnp.arange(mpol + 1) + toroidal_modes = jnp.arange(-ntor, ntor + 1) + angle = ( + poloidal_modes[None, :, None, None] * theta2d[None, None, :, :] + - toroidal_modes[:, None, None, None] * nfp * phi2d[None, None, :, :] + ) + return jnp.sum( + cosine_coefficients[:, :, None, None] * jnp.cos(angle) + + sine_coefficients[:, :, None, None] * jnp.sin(angle), + axis=(0, 1), + ) + + +@partial( + jax.jit, + static_argnames=("ntheta", "mpol", "ntor", "newton_iterations"), +) +def vmec_boundary( + solution: NearAxisSolution, + radius: ArrayLike, + *, + ntheta: int = 40, + mpol: int = 12, + ntor: int = 14, + newton_iterations: int = 6, +) -> VmecBoundary: + """Return a uniformly sampled, FFT-projected VMEC boundary.""" + + R, Z, phi0, angle_residual = uniform_cylindrical_surface( + solution, + radius, + ntheta=ntheta, + newton_iterations=newton_iterations, + ) + RBC, RBS = _fft_coefficients(R, mpol, ntor) + ZBC, ZBS = _fft_coefficients(Z, mpol, ntor) + reconstructed_R = _reconstruct_surface( + RBC, + RBS, + ntheta=ntheta, + nphi=solution.inputs.nphi, + nfp=solution.inputs.axis.nfp, + mpol=mpol, + ntor=ntor, + ) + reconstructed_Z = _reconstruct_surface( + ZBC, + ZBS, + ntheta=ntheta, + nphi=solution.inputs.nphi, + nfp=solution.inputs.axis.nfp, + mpol=mpol, + ntor=ntor, + ) + return VmecBoundary( + R=R, + Z=Z, + phi0=phi0, + RBC=RBC, + RBS=RBS, + ZBC=ZBC, + ZBS=ZBS, + maximum_toroidal_angle_residual=angle_residual, + maximum_R_reconstruction_error=jnp.max(jnp.abs(reconstructed_R - R)), + maximum_Z_reconstruction_error=jnp.max(jnp.abs(reconstructed_Z - Z)), + ntheta=ntheta, + mpol=mpol, + ntor=ntor, + newton_iterations=newton_iterations, + ) + + +def _validated_resolution( + solution: NearAxisSolution, + *, + ntheta: int, + mpol: int, + ntor: int, + newton_iterations: int, +) -> None: + integers = { + "ntheta": ntheta, + "mpol": mpol, + "ntor": ntor, + "newton_iterations": newton_iterations, + } + if any(not isinstance(value, int) or isinstance(value, bool) for value in integers.values()): + raise ValueError("VMEC conversion resolutions must be integers.") + if ntheta < 2 * (mpol + 1): + raise ValueError("ntheta must be at least 2 * (mpol + 1).") + if mpol < 1 or ntor < 0 or newton_iterations < 1: + raise ValueError("mpol and Newton iterations must be positive; ntor must be nonnegative.") + if 2 * ntor + 1 > solution.inputs.nphi: + raise ValueError("The solution nphi must be at least 2 * ntor + 1.") + + +def _input_parameters( + parameters: VmecInputParameters | Mapping[str, Any] | None, +) -> VmecInputParameters: + if parameters is None: + return VmecInputParameters() + if isinstance(parameters, VmecInputParameters): + return parameters + allowed = set(VmecInputParameters.__dataclass_fields__) + unknown = set(parameters) - allowed + if unknown: + names = ", ".join(sorted(unknown)) + raise ValueError(f"Unknown VMEC input parameter(s): {names}.") + converted = dict(parameters) + for name in ("ns_array", "ftol_array", "niter_array"): + if name in converted: + converted[name] = tuple(converted[name]) + return VmecInputParameters(**converted) + + +def _format_sequence(values: tuple[Any, ...] | jax.Array) -> str: + return ", ".join(f"{float(value):.16e}" for value in values) + + +def _format_integer_sequence(values: tuple[int, ...]) -> str: + return ", ".join(str(int(value)) for value in values) + + +def _coefficient_lines( + boundary: VmecBoundary, + *, + lasym: bool, + coefficient_tolerance: float, +) -> list[str]: + arrays = tuple( + jax.device_get(value) for value in (boundary.RBC, boundary.RBS, boundary.ZBC, boundary.ZBS) + ) + RBC, RBS, ZBC, ZBS = arrays + lines: list[str] = [] + for m in range(boundary.mpol + 1): + for n in range(-boundary.ntor, boundary.ntor + 1): + index = n + boundary.ntor + symmetric_nonzero = ( + abs(RBC[index, m]) > coefficient_tolerance + or abs(ZBS[index, m]) > coefficient_tolerance + ) + asymmetric_nonzero = lasym and ( + abs(RBS[index, m]) > coefficient_tolerance + or abs(ZBC[index, m]) > coefficient_tolerance + ) + if symmetric_nonzero or asymmetric_nonzero: + lines.append( + f" RBC({n:03d},{m:03d}) = {RBC[index, m]:+.16e}," + f" ZBS({n:03d},{m:03d}) = {ZBS[index, m]:+.16e}" + ) + if lasym: + lines.append( + f" RBS({n:03d},{m:03d}) = {RBS[index, m]:+.16e}," + f" ZBC({n:03d},{m:03d}) = {ZBC[index, m]:+.16e}" + ) + return lines + + +def to_vmec( + solution: NearAxisSolution, + filename: str | Path, + *, + r: float = 0.1, + parameters: VmecInputParameters | Mapping[str, Any] | None = None, + ntheta: int = 40, + mpol: int = 12, + ntor: int = 14, + ntor_max: int = 14, + newton_iterations: int = 6, + coefficient_tolerance: float = 1.0e-14, +) -> VmecExport: + """Write a VMEC fixed-boundary input and return conversion diagnostics.""" + + radius = float(r) + if radius <= 0: + raise ValueError("r must be positive.") + if not isinstance(ntor_max, int) or isinstance(ntor_max, bool) or ntor_max < 0: + raise ValueError("ntor_max must be a nonnegative integer.") + if coefficient_tolerance < 0: + raise ValueError("coefficient_tolerance must be nonnegative.") + effective_ntor = min(ntor, ntor_max) + _validated_resolution( + solution, + ntheta=ntheta, + mpol=mpol, + ntor=effective_ntor, + newton_iterations=newton_iterations, + ) + controls = _input_parameters(parameters) + + start = perf_counter() + boundary = vmec_boundary( + solution, + radius, + ntheta=ntheta, + mpol=mpol, + ntor=effective_ntor, + newton_iterations=newton_iterations, + ) + jax.tree.map(lambda value: value.block_until_ready(), boundary) + conversion_seconds = perf_counter() - start + + asymmetric_amplitude = max( + float(jnp.max(jnp.abs(boundary.RBS))), + float(jnp.max(jnp.abs(boundary.ZBC))), + ) + lasym = asymmetric_amplitude > coefficient_tolerance + inputs = solution.inputs + axis = inputs.axis + phiedge = float(jnp.pi * radius**2 * inputs.B0) + curtor = float(2 * jnp.pi * inputs.I2 * radius**2 / MU0) + pressure_axis = float(-inputs.p2 * radius**2) + lines = [ + "! Generated deterministically by pyQSC_JAX.", + f"! Near-axis radius r = {radius:.16e}; etabar = {float(inputs.etabar):.16e}.", + ( + f"! nphi = {inputs.nphi}; order = r{inputs.order}; ntheta = {ntheta};" + f" mpol = {mpol}; ntor = {effective_ntor}." + ), + ( + "! Conversion diagnostics:" + f" max_phi_residual = {float(boundary.maximum_toroidal_angle_residual):.6e};" + f" max_R_error = {float(boundary.maximum_R_reconstruction_error):.6e};" + f" max_Z_error = {float(boundary.maximum_Z_reconstruction_error):.6e}." + ), + "&INDATA", + f" DELT = {controls.delt:.16e}", + f" NSTEP = {controls.nstep}", + f" TCON0 = {controls.tcon0:.16e}", + f" NS_ARRAY = {_format_integer_sequence(controls.ns_array)}", + f" FTOL_ARRAY = {_format_sequence(controls.ftol_array)}", + f" NITER_ARRAY = {_format_integer_sequence(controls.niter_array)}", + f" LASYM = {'T' if lasym else 'F'}", + " LFREEB = F", + f" NFP = {axis.nfp}", + f" MPOL = {mpol}", + f" NTOR = {effective_ntor}", + f" PHIEDGE = {phiedge:.16e}", + " PRES_SCALE = 1.0000000000000000e+00", + " PMASS_TYPE = 'power_series'", + f" AM = {pressure_axis:.16e}, {-pressure_axis:.16e}", + f" CURTOR = {curtor:.16e}", + " NCURR = 1", + " PCURR_TYPE = 'power_series'", + " AC = 1.0000000000000000e+00", + f" RAXIS_CC = {_format_sequence(axis.rc)}", + f" RAXIS_CS = {_format_sequence(-axis.rs)}", + f" ZAXIS_CC = {_format_sequence(axis.zc)}", + f" ZAXIS_CS = {_format_sequence(-axis.zs)}", + "! Boundary coefficients", + ] + lines.extend( + _coefficient_lines( + boundary, + lasym=lasym, + coefficient_tolerance=coefficient_tolerance, + ) + ) + lines.append("/") + output_path = Path(filename) + output_path.parent.mkdir(parents=True, exist_ok=True) + output_path.write_text("\n".join(lines) + "\n", encoding="utf-8") + return VmecExport( + path=output_path, + boundary=boundary, + phiedge=phiedge, + curtor=curtor, + pressure_axis=pressure_axis, + lasym=lasym, + conversion_seconds=conversion_seconds, + ) diff --git a/tests/compatibility/test_essos_contract.py b/tests/compatibility/test_essos_contract.py index 03107ce..5f74e40 100644 --- a/tests/compatibility/test_essos_contract.py +++ b/tests/compatibility/test_essos_contract.py @@ -46,6 +46,7 @@ def test_legacy_import_and_essos_on_axis_contract(): "get_boundary", "Frenet_to_cylindrical", "phi_of_theta_varphi", + "to_vmec", } assert all(hasattr(field, name) for name in attributes) diff --git a/tests/integration/test_vmec_equilibrium.py b/tests/integration/test_vmec_equilibrium.py new file mode 100644 index 0000000..2fdc428 --- /dev/null +++ b/tests/integration/test_vmec_equilibrium.py @@ -0,0 +1,99 @@ +from __future__ import annotations + +import hashlib +import json +import os +import subprocess +from pathlib import Path + +import numpy as np +import pytest +from scipy.io import netcdf_file + +import pyqsc_jax as qsc + +REFERENCE_DIRECTORY = Path(__file__).resolve().parents[1] / "reference" / "vmec" + + +def _read_vmec_result(path: Path) -> dict[str, float | int]: + with netcdf_file(path, "r", mmap=False) as dataset: + return { + "ier_flag": int(dataset.variables["ier_flag"].data), + "iota_axis": float(-dataset.variables["iotaf"].data[0]), + "fsqr": float(dataset.variables["fsqr"].data), + "fsqz": float(dataset.variables["fsqz"].data), + "fsql": float(dataset.variables["fsql"].data), + } + + +@pytest.mark.integration +def test_frozen_vmec_wout_recovers_near_axis_iota(): + manifest = json.loads((REFERENCE_DIRECTORY / "manifest.json").read_text(encoding="utf-8")) + vmec_input = REFERENCE_DIRECTORY / "input.qa_r0025" + wout = REFERENCE_DIRECTORY / "wout_qa_r0025.nc" + input_digest = hashlib.sha256(vmec_input.read_bytes()).hexdigest() + digest = hashlib.sha256(wout.read_bytes()).hexdigest() + result = _read_vmec_result(wout) + solution = qsc.Qsc( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + nphi=121, + order="r2", + ) + relative_iota_error = abs(result["iota_axis"] - float(solution.iota)) / abs( + float(solution.iota) + ) + + assert input_digest == manifest["files"]["input.qa_r0025"] + assert digest == manifest["files"]["wout_qa_r0025.nc"] + assert result["ier_flag"] == 0 + assert max(result["fsqr"], result["fsqz"], result["fsql"]) < 1.0e-9 + assert relative_iota_error < 1.0e-3 + np.testing.assert_allclose( + result["iota_axis"], + manifest["vmec_result"]["iota_axis"], + rtol=0, + atol=2.0e-15, + ) + + +@pytest.mark.integration +@pytest.mark.slow +def test_local_vmec_rerun_when_executable_is_requested(tmp_path): + executable = os.environ.get("PYQSC_VMEC_EXECUTABLE") + if not executable: + pytest.skip("Set PYQSC_VMEC_EXECUTABLE to rerun the fixed-boundary VMEC case.") + solution = qsc.Qsc( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + nphi=121, + order="r2", + ) + qsc.to_vmec( + solution, + tmp_path / "input.qa_r0025", + r=0.0025, + ntheta=32, + mpol=6, + ntor=6, + parameters={ + "ns_array": (31,), + "ftol_array": (1.0e-10,), + "niter_array": (3000,), + }, + ) + subprocess.run( + [executable, "input.qa_r0025"], + cwd=tmp_path, + check=True, + timeout=120, + ) + result = _read_vmec_result(tmp_path / "wout_qa_r0025.nc") + + assert result["ier_flag"] == 0 + assert max(result["fsqr"], result["fsqz"], result["fsql"]) < 1.0e-9 + np.testing.assert_allclose(result["iota_axis"], solution.iota, rtol=1.0e-3) diff --git a/tests/physics/test_b20_optimization.py b/tests/physics/test_b20_optimization.py index d390302..5e61d29 100644 --- a/tests/physics/test_b20_optimization.py +++ b/tests/physics/test_b20_optimization.py @@ -133,6 +133,20 @@ def test_resolution_verification_recomputes_fixed_candidate(): assert verification.relative_grid_maximum_change[1] < 0.03 +@pytest.mark.physics +def test_documented_optimized_axis_has_nearly_constant_B20(): + stock = qsc.optimize_B2c(qsc.solve_configuration("qa", nphi=121)) + optimized = qsc.solve_configuration("b20_optimized_qa", nphi=121) + diagnostics = qsc.b20_diagnostics(optimized) + verification = qsc.verify_B20_resolution(optimized, multipliers=(1, 2)) + + assert float(diagnostics.weighted_l2) < 1.6e-6 + assert float(diagnostics.grid_maximum) < 3.3e-6 + assert float(diagnostics.peak_to_peak) < 6.4e-6 + assert float(stock.diagnostics.weighted_l2 / diagnostics.weighted_l2) > 25000 + assert float(verification.relative_weighted_l2_change[1]) < 2.0e-7 + + def test_B20_optimization_input_guards(): first_order = qa_solution(order="r1") with pytest.raises(ValueError, match="second-order"): diff --git a/tests/physics/test_plasma_field.py b/tests/physics/test_plasma_field.py index c29ac72..7283eac 100644 --- a/tests/physics/test_plasma_field.py +++ b/tests/physics/test_plasma_field.py @@ -186,6 +186,29 @@ def test_regularized_integral_resolution_convergence_for_nonplanar_axis(): assert np.all(np.isfinite(coarse_integral)) +@pytest.mark.physics +def test_documented_plasma_dominant_case_exceeds_thirty_percent(): + solution = qsc.solve_configuration("plasma_dominant_channel", nphi=61) + formal_radius = 0.2 + plasma = qsc.plasma_field_on_axis( + solution, + formal_radius=formal_radius, + angular_resolution=64, + ) + plasma_norm = np.linalg.norm(np.asarray(plasma.field), axis=-1) + total_norm = np.linalg.norm(np.asarray(solution.B_axis), axis=-1) + fraction = plasma_norm / total_norm + + assert np.min(fraction) > 0.30 + np.testing.assert_allclose(np.mean(fraction), 0.3325737905856357, rtol=2.0e-12) + assert formal_radius < float(solution.r_singularity) + np.testing.assert_allclose( + plasma.current_source.enclosed_toroidal_current, + 840000.0, + rtol=2.0e-13, + ) + + def test_plasma_field_guards(): solution = circular_solution() with pytest.raises(ValueError, match="angular_resolution"): diff --git a/tests/reference/vmec/input.qa_r0025 b/tests/reference/vmec/input.qa_r0025 new file mode 100644 index 0000000..c5fe202 --- /dev/null +++ b/tests/reference/vmec/input.qa_r0025 @@ -0,0 +1,115 @@ +! Generated deterministically by pyQSC_JAX. +! Near-axis radius r = 2.5000000000000001e-03; etabar = -9.0000000000000002e-01. +! nphi = 121; order = r2; ntheta = 32; mpol = 6; ntor = 6. +! Conversion diagnostics: max_phi_residual = 1.387779e-17; max_R_error = 1.460998e-06; max_Z_error = 1.080278e-06. +&INDATA + DELT = 9.0000000000000002e-01 + NSTEP = 200 + TCON0 = 2.0000000000000000e+00 + NS_ARRAY = 31 + FTOL_ARRAY = 1.0000000000000000e-10 + NITER_ARRAY = 3000 + LASYM = F + LFREEB = F + NFP = 3 + MPOL = 6 + NTOR = 6 + PHIEDGE = 1.9634954084936207e-05 + PRES_SCALE = 1.0000000000000000e+00 + PMASS_TYPE = 'power_series' + AM = -0.0000000000000000e+00, 0.0000000000000000e+00 + CURTOR = 0.0000000000000000e+00 + NCURR = 1 + PCURR_TYPE = 'power_series' + AC = 1.0000000000000000e+00 + RAXIS_CC = 1.0000000000000000e+00, 4.4999999999999998e-02 + RAXIS_CS = -0.0000000000000000e+00, -0.0000000000000000e+00 + ZAXIS_CC = 0.0000000000000000e+00, 0.0000000000000000e+00 + ZAXIS_CS = -0.0000000000000000e+00, 4.4999999999999998e-02 +! Boundary coefficients + RBC(000,000) = +1.0000705829799887e+00, ZBS(000,000) = +0.0000000000000000e+00 + RBC(001,000) = +4.4972146504766455e-02, ZBS(001,000) = +4.4991499300713611e-02 + RBC(002,000) = +5.9873785623381428e-06, ZBS(002,000) = +4.3502961734281688e-07 + RBC(003,000) = -2.1517234573157090e-06, ZBS(003,000) = +4.7421860162078269e-07 + RBC(004,000) = +1.0991923800079042e-06, ZBS(004,000) = -4.8106974614858439e-07 + RBC(005,000) = -6.4130044677373424e-07, ZBS(005,000) = +3.7686082803356997e-07 + RBC(006,000) = +3.8870569264632445e-07, ZBS(006,000) = -2.6452556339482058e-07 + RBC(-06,001) = -2.4415059227033655e-07, ZBS(-06,001) = -1.6757477768105833e-07 + RBC(-05,001) = +6.4602884351962735e-07, ZBS(-05,001) = +3.9729116716134149e-07 + RBC(-04,001) = -1.8121635281841622e-06, ZBS(-04,001) = -9.1949094106951558e-07 + RBC(-03,001) = +5.5483444835936612e-06, ZBS(-03,001) = +1.9926099557692592e-06 + RBC(-02,001) = -1.6936463407602224e-05, ZBS(-02,001) = -5.9095719187370043e-06 + RBC(-01,001) = +3.3768733026137273e-05, ZBS(-01,001) = +4.9271499850138361e-05 + RBC(000,001) = +2.7275400006613565e-03, ZBS(000,001) = -2.7303052205015169e-03 + RBC(001,001) = -1.0843959315583243e-03, ZBS(001,001) = -1.0456522227157282e-03 + RBC(002,001) = +5.7683416839753723e-05, ZBS(002,001) = +7.7805475764700576e-05 + RBC(003,001) = +2.2469329177139640e-06, ZBS(003,001) = -5.2325258405908656e-06 + RBC(004,001) = -1.6896070240558097e-06, ZBS(004,001) = +1.0411745545182424e-06 + RBC(005,001) = +6.4216920053210053e-07, ZBS(005,001) = -4.0149036024405450e-07 + RBC(006,001) = -2.4405533518398577e-07, ZBS(006,001) = +1.6770724800463921e-07 + RBC(-06,002) = +3.1007833251658884e-07, ZBS(-06,002) = +2.4574641759511880e-07 + RBC(-05,002) = -5.2948451720773412e-07, ZBS(-05,002) = -3.9717792669642647e-07 + RBC(-04,002) = +9.1529307608356163e-07, ZBS(-04,002) = +6.1694907139047096e-07 + RBC(-03,002) = -1.7275408599925077e-06, ZBS(-03,002) = -8.7176040692811953e-07 + RBC(-02,002) = +4.3548900479616564e-06, ZBS(-02,002) = +6.2924084662730571e-07 + RBC(-01,002) = -1.5628821641526291e-05, ZBS(-01,002) = +1.8711493375401293e-06 + RBC(000,002) = -7.7093418228937785e-06, ZBS(000,002) = +8.0247944040313932e-05 + RBC(001,002) = +3.0483893018425361e-05, ZBS(001,002) = +3.5006771454329695e-05 + RBC(002,002) = -3.8692199524025512e-06, ZBS(002,002) = -6.5631891418695323e-06 + RBC(003,002) = -2.6021247701713909e-07, ZBS(003,002) = +8.2982903320988042e-07 + RBC(004,002) = +4.9602358763677354e-07, ZBS(004,002) = -3.5173158952779694e-08 + RBC(005,002) = -3.0005785856526528e-07, ZBS(005,002) = +1.1487820723356077e-08 + RBC(006,002) = +1.7354345575586541e-07, ZBS(006,002) = -2.4597539487659144e-08 + RBC(-06,003) = -3.3605899502702502e-10, ZBS(-06,003) = -4.9195863015844885e-10 + RBC(-05,003) = +5.1654029748188752e-10, ZBS(-05,003) = +7.4714165541172801e-10 + RBC(-04,003) = -7.5530762265820549e-10, ZBS(-04,003) = -1.1313424261651086e-09 + RBC(-03,003) = +9.8440354614450489e-10, ZBS(-03,003) = +1.7606542541457767e-09 + RBC(-02,003) = -3.4080094470854474e-10, ZBS(-02,003) = -3.5436337168678692e-09 + RBC(-01,003) = -2.1375749176700437e-09, ZBS(-01,003) = +8.9545429090448358e-09 + RBC(000,003) = -1.9612354192356898e-08, ZBS(000,003) = -1.3132081299764493e-09 + RBC(001,003) = -2.8655353251880292e-08, ZBS(001,003) = -1.0271426692348341e-08 + RBC(002,003) = -2.3747997161433985e-08, ZBS(002,003) = -4.4964079315489770e-08 + RBC(003,003) = -6.1455223117203370e-09, ZBS(003,003) = -2.0309373874284110e-09 + RBC(004,003) = +1.3717169981562259e-08, ZBS(004,003) = +9.6826085398181361e-09 + RBC(005,003) = -3.4488416158216233e-09, ZBS(005,003) = -9.0133423538389967e-10 + RBC(006,003) = +2.1503114674813830e-09, ZBS(006,003) = +4.9954874279097632e-10 + RBC(-06,004) = +4.6369779620584815e-11, ZBS(-06,004) = +5.8940424957078450e-11 + RBC(-05,004) = -2.4106668597179557e-11, ZBS(-05,004) = -6.5418755572823082e-11 + RBC(-04,004) = +4.0237650219534292e-11, ZBS(-04,004) = +8.6792187199893126e-11 + RBC(-03,004) = -1.8070051228621789e-11, ZBS(-03,004) = -1.0961627411167680e-10 + RBC(-02,004) = +7.8839647338186660e-11, ZBS(-02,004) = +5.5603632124865108e-11 + RBC(-01,004) = -3.9934554570480501e-10, ZBS(-01,004) = +3.6180781813635285e-10 + RBC(000,004) = -6.3301072225918542e-10, ZBS(000,004) = +1.2190921610862814e-09 + RBC(001,004) = +1.4350897724882337e-08, ZBS(001,004) = -1.4619286439620352e-08 + RBC(002,004) = +3.9707409493019856e-08, ZBS(002,004) = -4.0896719720885368e-08 + RBC(003,004) = +3.9202544088903947e-08, ZBS(003,004) = -9.8722393081329035e-09 + RBC(004,004) = +2.0277841430761762e-08, ZBS(004,004) = +5.9601236482370415e-08 + RBC(005,004) = +3.5861092221904178e-08, ZBS(005,004) = +1.3364988278544130e-08 + RBC(006,004) = -2.4269200734071315e-08, ZBS(006,004) = -1.4816477416940341e-08 + RBC(-06,005) = -2.6226002745625437e-12, ZBS(-06,005) = -7.2846539236555959e-12 + RBC(-05,005) = -1.3028100731259414e-11, ZBS(-05,005) = +7.1941878267675343e-12 + RBC(-04,005) = +2.8468464782067269e-11, ZBS(-04,005) = -2.7234203358021016e-11 + RBC(-03,005) = -5.3235556285850331e-11, ZBS(-03,005) = +3.6448043799500747e-11 + RBC(-02,005) = +1.2397062872034374e-10, ZBS(-02,005) = -7.0457689479103539e-11 + RBC(-01,005) = -7.1319150981371117e-11, ZBS(-01,005) = -1.9280850945643681e-11 + RBC(000,005) = -4.3987912406425169e-10, ZBS(000,005) = +6.3877670878631776e-10 + RBC(001,005) = -3.1939019251615725e-09, ZBS(001,005) = +3.1261830312733297e-09 + RBC(002,005) = -3.2643590893336510e-09, ZBS(002,005) = +2.2739485338332859e-09 + RBC(003,005) = -4.2118428941129741e-09, ZBS(003,005) = -2.4311639430023996e-09 + RBC(004,005) = +1.4610748856713604e-09, ZBS(004,005) = -8.2230180190818004e-09 + RBC(005,005) = -2.4678340978275323e-09, ZBS(005,005) = -2.7907292122839379e-11 + RBC(006,005) = +6.2121165377238212e-09, ZBS(006,005) = +5.2623472883796908e-09 + RBC(-06,006) = +3.8736295304419662e-11, ZBS(-06,006) = +5.7060497708605618e-12 + RBC(-05,006) = -4.7470189245640317e-12, ZBS(-05,006) = -7.9399004719218432e-12 + RBC(-04,006) = +1.8443338421304800e-11, ZBS(-04,006) = +1.8046986663601585e-11 + RBC(-03,006) = +1.1167396860698812e-11, ZBS(-03,006) = -1.2698250082275888e-11 + RBC(-02,006) = -6.9312333793738727e-12, ZBS(-02,006) = +1.3144183600258469e-11 + RBC(-01,006) = +6.7578184813644228e-11, ZBS(-01,006) = -5.1060449472660376e-11 + RBC(000,006) = -1.1230898093480489e-10, ZBS(000,006) = +1.0101530760459938e-10 + RBC(001,006) = -3.0274151016801464e-10, ZBS(001,006) = +4.0970273730041438e-10 + RBC(002,006) = +2.0430123815145075e-09, ZBS(002,006) = -2.2459041353843439e-09 + RBC(003,006) = +1.2097337288909390e-08, ZBS(003,006) = -1.2714596943081256e-08 + RBC(004,006) = +1.8328808588258400e-08, ZBS(004,006) = -1.3955119471723512e-08 + RBC(005,006) = +1.3074406926366760e-08, ZBS(005,006) = +1.1765439645369073e-08 + RBC(006,006) = +9.4881890380617359e-09, ZBS(006,006) = +2.2478558100516398e-08 +/ diff --git a/tests/reference/vmec/manifest.json b/tests/reference/vmec/manifest.json new file mode 100644 index 0000000..993e08c --- /dev/null +++ b/tests/reference/vmec/manifest.json @@ -0,0 +1,40 @@ +{ + "case": "qa_r0025", + "description": "Small-radius fixed-boundary VMEC validation of the pyQSC_JAX exporter.", + "generator": { + "executable": "/Users/rogerio/base_env/bin/xvmec", + "vmec_version": "9.0", + "platform": "macOS arm64" + }, + "near_axis": { + "B0": 1.0, + "etabar": -0.9, + "iota": 0.41830691021517735, + "nfp": 3, + "nphi": 121, + "order": "r2", + "radius": 0.0025, + "rc": [1.0, 0.045], + "zs": [0.0, -0.045] + }, + "export": { + "maximum_R_reconstruction_error": 1.460998e-06, + "maximum_Z_reconstruction_error": 1.080278e-06, + "maximum_toroidal_angle_residual": 1.387779e-17, + "mpol": 6, + "ntheta": 32, + "ntor": 6 + }, + "files": { + "input.qa_r0025": "5444b159de7562681363f65426e814fb46c11437cf3d1b31e5c20ba7c1fbedc1", + "wout_qa_r0025.nc": 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z6=lLl5osi{>-xLAy}n3mukb;c6MQ7TRBLVyXlVJ*a9KK|VDH~l`_#h0#OqO+>-9n~ zzVyE0Sa1(A;`Y$e4LAn31EeqbduBl-Su-c2O9=$^Ir+X1p9hD#?!K8;M?vQ%_hHR5 z63BET_?~|ZAOnr5>fw|X(7)qj{o%|KNUb}^o*249ST|sy30O2nqF?*EU1Cc9@i{D= zu|NA~f{$mvLn>tI-gN0+;6U5u894d|G>e~a|Cwb(o+|oR^?y-;Y@`rR(a>ddE!VH( zh+qY{=LQL@Z(If9vvhiVKR|^n_|PTsBBV?yzfm6E0+*~?uU_etM-m;f?^U-e(b*_H zj9i->$i!NMOGcaslP0IU^yAb?{2RGApIrUAwU)+bZ2NN5bGedq5ZIkCYsnu+S1-e^Gf6^NJVyz-#(O#qkMYwOX~eC-gSzI=8=IK= 1.0e-4 + assert float(np.max(np.abs(export.boundary.ZBC))) > 1.0e-4 + contents = export.path.read_text(encoding="utf-8") + assert "LASYM = T" in contents + assert "RBS(" in contents + assert "ZBC(" in contents + + +def test_first_and_third_order_surfaces_and_ntor_cap(tmp_path): + first_order = qsc.Qsc( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + nphi=15, + order="r1", + ) + first_boundary = qsc.vmec_boundary( + first_order, + 0.005, + ntheta=8, + mpol=3, + ntor=2, + ) + assert np.all(np.isfinite(first_boundary.R)) + + third_order = qsc.solve_configuration("qa", nphi=15, order="r3") + export = qsc.to_vmec( + third_order, + tmp_path / "input.r3", + r=0.005, + ntheta=10, + mpol=4, + ntor=4, + ntor_max=2, + parameters=qsc.VmecInputParameters( + ns_array=(15,), + ftol_array=(1.0e-10,), + niter_array=(2000,), + ), + ) + assert export.boundary.ntor == 2 + assert np.all(np.isfinite(export.boundary.Z)) + + +def test_finite_pressure_current_profiles_are_written(tmp_path): + solution = qsc.solve_configuration("plasma_dominant_channel", nphi=15) + export = qsc.to_vmec( + solution, + tmp_path / "input.plasma", + r=0.1, + ntheta=10, + mpol=4, + ntor=2, + ) + contents = export.path.read_text(encoding="utf-8") + + np.testing.assert_allclose(export.curtor, 210000.0) + np.testing.assert_allclose(export.pressure_axis, 1000.0) + assert "AM =" in contents + assert "CURTOR =" in contents + + +@pytest.mark.parametrize( + "kwargs, message", + [ + ({"ns_array": (), "ftol_array": (), "niter_array": ()}, "nonempty"), + ( + { + "ns_array": (15,), + "ftol_array": (1.0e-10, 1.0e-11), + "niter_array": (2000,), + }, + "aligned", + ), + ({"delt": 0.0}, "positive"), + ({"nstep": 0}, "positive"), + ({"tcon0": 0.0}, "positive"), + ( + {"ns_array": (2,), "ftol_array": (1.0e-10,), "niter_array": (2000,)}, + "at least 3", + ), + ( + {"ns_array": (15,), "ftol_array": (0.0,), "niter_array": (2000,)}, + "tolerance", + ), + ( + {"ns_array": (15,), "ftol_array": (1.0e-10,), "niter_array": (0,)}, + "iteration", + ), + ], +) +def test_vmec_input_parameter_guards(kwargs, message): + with pytest.raises(ValueError, match=message): + qsc.VmecInputParameters(**kwargs) + + +@pytest.mark.parametrize( + "kwargs, message", + [ + ({"r": 0.0}, "r must be positive"), + ({"ntor_max": -1}, "ntor_max"), + ({"coefficient_tolerance": -1.0}, "coefficient_tolerance"), + ({"ntheta": 7, "mpol": 3}, "ntheta"), + ({"mpol": 0}, "positive"), + ({"ntor": -1}, "nonnegative"), + ({"newton_iterations": 0}, "positive"), + ({"ntheta": 8.0}, "integers"), + ({"ntor": 8}, "nphi"), + ], +) +def test_to_vmec_resolution_and_scalar_guards(tmp_path, kwargs, message): + options = { + "r": 0.01, + "ntheta": 8, + "mpol": 3, + "ntor": 2, + } + options.update(kwargs) + with pytest.raises(ValueError, match=message): + qsc.to_vmec( + qa_solution(nphi=15), + tmp_path / "input.invalid", + **options, + ) + + +def test_to_vmec_rejects_unknown_control(tmp_path): + with pytest.raises(ValueError, match="Unknown VMEC input"): + qsc.to_vmec( + qa_solution(nphi=15), + tmp_path / "input.invalid", + r=0.01, + ntheta=8, + mpol=3, + ntor=2, + parameters={"missing": 1}, + ) From 85cfe43ac55bab25a4725be0a3572d88f642799c Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 08:00:03 -0500 Subject: [PATCH 27/39] docs: publish B20 plasma and VMEC validation --- CHANGELOG.md | 13 + README.md | 58 ++++- benchmarks/benchmark_b20_optimizers.py | 228 ++++++++++++++++++ benchmarks/benchmark_vmec_export.py | 98 ++++++++ .../reports/2026-07-30-b20-vmec-apple-m4.json | 108 +++++++++ docs/_static/B20_optimization.png | Bin 64744 -> 106860 bytes docs/_static/plasma_external_jet.png | Bin 75423 -> 32798 bytes docs/_static/vmec_validation.png | Bin 0 -> 50632 bytes docs/advanced/performance.md | 21 ++ docs/api/vmec.md | 12 + docs/development/physics-traceability.md | 1 + docs/development/refactor-baseline.md | 8 +- docs/development/refactor_status.md | 17 ++ docs/index.md | 3 + docs/theory/b20-optimization.md | 38 +++ docs/tutorials/vmec_export.md | 15 ++ docs/validation/plasma_field.md | 20 ++ docs/validation/vmec.md | 71 ++++++ examples/06_optimize_axis_B20.py | 87 +++---- examples/10_plasma_external_field_jet.py | 14 +- examples/13_vmec_export.py | 75 ++++++ .../publication/figure_B20_optimization.py | 102 +++++--- .../publication/figure_plasma_external_jet.py | 14 +- .../publication/figure_vmec_validation.py | 88 +++++++ 24 files changed, 983 insertions(+), 108 deletions(-) create mode 100644 benchmarks/benchmark_b20_optimizers.py create mode 100644 benchmarks/benchmark_vmec_export.py create mode 100644 benchmarks/reports/2026-07-30-b20-vmec-apple-m4.json create mode 100644 docs/_static/vmec_validation.png create mode 100644 docs/api/vmec.md create mode 100644 docs/tutorials/vmec_export.md create mode 100644 docs/validation/vmec.md create mode 100644 examples/13_vmec_export.py create mode 100644 examples/publication/figure_vmec_validation.py diff --git a/CHANGELOG.md b/CHANGELOG.md index dadc4e1..b370f87 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -9,6 +9,19 @@ first stable release. ### Added +- Vectorized, JIT-compiled VMEC boundary export with all four coefficient + families, deterministic INDATA output, conversion diagnostics, + legacy-adapter support, a frozen VMEC 9.0 `wout` regression, and an opt-in + local-VMEC rerun. +- Dense-grid `b20_optimized_qa` reference with a verified + \(1.59\times10^{-6}\) weighted residual and reproducible comparisons across + L-BFGS-B, least-squares, differential-evolution, and multistart + Levenberg--Marquardt searches. +- `plasma_dominant_channel` validation case, for which the plasma field is + 33.3% of the total field at the documented formal radius. +- README evidence, benchmark reports, publication figures, executable + examples, and validation documentation for B20, plasma-field, and VMEC + behavior. - Audited compatibility and numerical baselines. - Physics traceability and architecture decision records. - Modern package, documentation, test, and CI scaffolding. diff --git a/README.md b/README.md index 591f2f6..833d5f1 100644 --- a/README.md +++ b/README.md @@ -18,9 +18,9 @@ plasma–coil field jets in JAX. | --- | --- | | ![QA and QH surfaces](docs/_static/axis_and_surfaces.png) | ![B20 optimization](docs/_static/B20_optimization.png) | -| Total/plasma/external field jet | Spectral convergence | +| Total/plasma/external field jet | VMEC export validation | | --- | --- | -| ![Plasma and external jet](docs/_static/plasma_external_jet.png) | ![Resolution convergence](docs/_static/convergence.png) | +| ![Plasma and external jet](docs/_static/plasma_external_jet.png) | ![VMEC validation](docs/_static/vmec_validation.png) | ## Install @@ -72,9 +72,36 @@ sample-first ordering: `(nphi, 3)`, `(nphi, 3, 3)`, and | Exact \(B_{2c}\), criteria, bounded multistart axis search | Validated | | Surface-free plasma field, gradient, Hessian | Validated asymptotic model | | External vacuum 3+5+7 field-jet target | Validated | +| Fast fixed-boundary VMEC export, including asymmetric boundaries | Validated against VMEC 9.0 | | ESSOS vacuum/finite-beta stage-two and single-stage objectives | Draft integration PR | | Legacy `pyqsc_jax.near_axis.near_axis` contract | Preserved | +## Headline regression cases + +These are checked results, not illustrative targets. The detailed optimizer, +resolution, timing, and radius-convergence tables are in the +[B20](docs/theory/b20-optimization.md), +[plasma-field](docs/validation/plasma_field.md), and +[VMEC](docs/validation/vmec.md) validation pages. + +| Check | Result | Regression gate | +| --- | ---: | ---: | +| Optimized QA \(B_{20}\), weighted \(L^2\), `nphi=121` | \(1.5901\times10^{-6}\) | \(<1.6\times10^{-6}\) | +| Improvement over stock-axis exact-\(B_{2c}\) solve | \(26{,}053\times\) | \(>25{,}000\times\) | +| Minimum \(\lvert B_\mathrm{plasma}\rvert/\lvert B_\mathrm{total}\rvert\) | 33.26% | \(>30\%\) | +| VMEC/near-axis on-axis \(\iota\), \(r=0.0025\) | 0.418543 / 0.418307 | relative error \(<0.1\%\) | +| VMEC force residuals | \(2.4\)–\(7.6\times10^{-11}\) | maximum \(<10^{-9}\) | +| `to_vmec`, Apple M4 CPU, compile+execute / warm | 0.476 s / 5.20 ms | warm unit gate \(<0.5\) s | + +```python +optimized = qsc.solve_configuration("b20_optimized_qa", nphi=121) +diagnostics = qsc.b20_diagnostics(optimized) +print(diagnostics.weighted_l2, diagnostics.grid_maximum) + +plasma_case = qsc.solve_configuration("plasma_dominant_channel", nphi=61) +plasma = qsc.plasma_field_on_axis(plasma_case, formal_radius=0.2) +``` + ## Target rotational transform ```python @@ -113,8 +140,8 @@ mathematical global-minimum claim. ## Finite-beta coil targets ```python -solution = qsc.solve_configuration("finite_pressure_current", nphi=61) -target = qsc.plasma_hessian_on_axis(solution, formal_radius=0.025) +solution = qsc.solve_configuration("plasma_dominant_channel", nphi=61) +target = qsc.plasma_hessian_on_axis(solution, formal_radius=0.2) print(target.field.external_field.shape) # (nphi, 3) print(target.field.external_gradient_independent.shape) # (nphi, 5) @@ -125,6 +152,28 @@ ESSOS consumes these external vacuum targets for normalized field, gradient, and Hessian coil objectives. The dependency remains one-way: `ESSOS -> pyQSC_JAX`. +## VMEC export + +```python +solution = qsc.Qsc( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + nphi=61, + order="r2", +) +export = qsc.to_vmec(solution, "input.qa", r=0.005) +print(export.conversion_seconds) +print(export.boundary.maximum_R_reconstruction_error) +``` + +The exporter uses a vectorized Newton inversion and a two-dimensional FFT, +supports all four VMEC boundary coefficient families, and returns conversion +diagnostics. The committed `wout` regression checks the resulting equilibrium, +including the on-axis transform; an opt-in test can rerun a local VMEC +executable. + ## Learn and validate - [Installation and model selection](docs/getting_started/) @@ -132,6 +181,7 @@ and Hessian coil objectives. The dependency remains one-way: - [Executable tutorials](docs/tutorials/) - [API reference](docs/api/) - [pyQSC, literature, plasma, and ESSOS validation](docs/validation/) +- [VMEC conversion, equilibrium, and performance validation](docs/validation/vmec.md) - [Migration from pyQSC and the legacy adapter](docs/migration.md) - [Known limitations](docs/advanced/limitations.md) diff --git a/benchmarks/benchmark_b20_optimizers.py b/benchmarks/benchmark_b20_optimizers.py new file mode 100644 index 0000000..c7ab178 --- /dev/null +++ b/benchmarks/benchmark_b20_optimizers.py @@ -0,0 +1,228 @@ +"""Compare local, multistart, and coarse-global B20 axis optimizers.""" + +from __future__ import annotations + +import json +import os +import platform +import subprocess +from pathlib import Path +from time import perf_counter + +import jax +import jax.numpy as jnp +import numpy as np +from scipy.optimize import differential_evolution, least_squares, minimize + +import pyqsc_jax as qsc + +NPHI = 121 +MODES = (1, 2, 3) +OUTPUT = Path( + os.environ.get("PYQSC_B20_BENCHMARK_OUTPUT", "benchmarks/results/b20_optimizers.json") +) +RC = ( + 1.0038581971135636, + 0.18400998741139907, + 0.021723381370503204, + 0.0025968236014410812, + 0.00030601568477064874, + 3.5540509760304384e-05, + 4.102693907398271e-06, + 5.154300428457222e-07, + 4.8802742243232844e-08, + 7.3011320375259876e-09, +) +ZS = ( + 0.0, + -0.1581148860568176, + -0.02060702320552523, + -0.002558840496952667, + -0.0003061368667524159, + -3.600111450532304e-05, + -4.174376962124085e-06, + -4.557462755956434e-07, + -8.173481495049928e-08, + -3.732477282851326e-09, +) +AXIS = qsc.Axis(rc=RC, zs=ZS, nfp=2) +VARIABLE_INDICES = qsc.stellarator_symmetric_variable_indices(AXIS, modes=MODES) +INITIAL = AXIS.dofs[jnp.asarray(VARIABLE_INDICES)] +HALF_WIDTH = jnp.asarray((0.06, 0.012, 0.004, 0.06, 0.012, 0.004)) +LOWER = INITIAL - HALF_WIDTH +UPPER = INITIAL + HALF_WIDTH + + +def projected_residual(variables): + axis = AXIS.with_dofs( + AXIS.dofs.at[jnp.asarray(VARIABLE_INDICES)].set(variables) + ) + solution = qsc.solve( + axis=axis, + etabar=-0.6783912804454629, + B0=1.006541121335688, + B2c=0.0, + nphi=NPHI, + order="r2", + ) + optimized = qsc.optimize_B2c(solution) + weights = optimized.solution.geometry.d_l_d_phi + return ( + jnp.sqrt(weights / jnp.sum(weights)) + * optimized.diagnostics.anomaly + / optimized.solution.inputs.B0 + ) + + +compiled_residual = jax.jit(projected_residual) +compiled_jacobian = jax.jit(jax.jacrev(projected_residual)) +compiled_value_and_gradient = jax.jit( + jax.value_and_grad(lambda value: 0.5 * jnp.sum(projected_residual(value) ** 2)) +) + + +def residual_numpy(variables): + return np.asarray(compiled_residual(jnp.asarray(variables)), dtype=float) + + +def jacobian_numpy(variables): + return np.asarray(compiled_jacobian(jnp.asarray(variables)), dtype=float) + + +def value_and_gradient_numpy(variables): + value, gradient = compiled_value_and_gradient(jnp.asarray(variables)) + return float(value), np.asarray(gradient, dtype=float) + + +def weighted_l2(variables): + return float(np.linalg.norm(residual_numpy(variables))) + + +print("Compiling shared B20 residual and derivatives...") +compiled_residual(INITIAL).block_until_ready() +compiled_jacobian(INITIAL).block_until_ready() +compiled_value_and_gradient(INITIAL)[0].block_until_ready() +rows = [ + { + "method": "exact B2c only", + "seconds": 0.0, + "function_evaluations": 1, + "weighted_l2": weighted_l2(INITIAL), + } +] + +start = perf_counter() +lbfgsb = minimize( + value_and_gradient_numpy, + np.asarray(INITIAL), + method="L-BFGS-B", + jac=True, + bounds=list(zip(np.asarray(LOWER), np.asarray(UPPER), strict=True)), + options={"maxiter": 60, "ftol": 1.0e-18, "gtol": 1.0e-12}, +) +rows.append( + { + "method": "SciPy L-BFGS-B", + "seconds": perf_counter() - start, + "function_evaluations": int(lbfgsb.nfev), + "weighted_l2": weighted_l2(lbfgsb.x), + } +) + +start = perf_counter() +least_squares_result = least_squares( + residual_numpy, + np.asarray(INITIAL), + jac=jacobian_numpy, + bounds=(np.asarray(LOWER), np.asarray(UPPER)), + max_nfev=60, + xtol=1.0e-13, + ftol=1.0e-13, + gtol=1.0e-13, + x_scale="jac", +) +rows.append( + { + "method": "SciPy least_squares", + "seconds": perf_counter() - start, + "function_evaluations": int(least_squares_result.nfev), + "weighted_l2": weighted_l2(least_squares_result.x), + } +) + +start = perf_counter() +differential = differential_evolution( + lambda variables: weighted_l2(variables) ** 2, + list(zip(np.asarray(LOWER), np.asarray(UPPER), strict=True)), + seed=7, + popsize=4, + maxiter=4, + polish=False, + updating="immediate", +) +rows.append( + { + "method": "SciPy differential_evolution, low budget", + "seconds": perf_counter() - start, + "function_evaluations": int(differential.nfev), + "weighted_l2": weighted_l2(differential.x), + } +) + +problem = qsc.AxisSearchProblem( + axis=AXIS, + variable_indices=VARIABLE_INDICES, + lower_bounds=LOWER, + upper_bounds=UPPER, + etabar=-0.6783912804454629, + B0=1.006541121335688, + nphi=NPHI, +) +options = qsc.AxisSearchOptions( + coarse_samples=12, + local_starts=3, + maximum_iterations=20, + verification_multipliers=(1,), + verification_tail_tolerance=1.0, +) +start = perf_counter() +multistart = qsc.search_axis(problem, options=options) +rows.append( + { + "method": "pyQSC_JAX multistart Levenberg-Marquardt", + "seconds": perf_counter() - start, + "function_evaluations": multistart.search_budget, + "weighted_l2": None if multistart.best is None else multistart.best.primary_residual, + "status": multistart.status, + "distinct_basins": multistart.distinct_basins, + } +) + +repository = Path(__file__).resolve().parents[1] +try: + commit = subprocess.check_output( + ("git", "-C", str(repository), "rev-parse", "HEAD"), + text=True, + ).strip() +except (OSError, subprocess.CalledProcessError): + commit = "unavailable" +report = { + "git_commit": commit, + "python": platform.python_version(), + "platform": platform.platform(), + "jax": jax.__version__, + "jax_backend": jax.default_backend(), + "jax_enable_x64": bool(jax.config.jax_enable_x64), + "nphi": NPHI, + "modes": MODES, + "timing_note": ( + "SciPy timings exclude shared residual/Jacobian compilation; the " + "pyQSC_JAX multistart timing includes compilation of its independent closure." + ), + "results": rows, +} +OUTPUT.parent.mkdir(parents=True, exist_ok=True) +OUTPUT.write_text(json.dumps(report, indent=2, sort_keys=True) + "\n", encoding="utf-8") +for row in rows: + print(row) +print("saved:", OUTPUT) diff --git a/benchmarks/benchmark_vmec_export.py b/benchmarks/benchmark_vmec_export.py new file mode 100644 index 0000000..0e64b06 --- /dev/null +++ b/benchmarks/benchmark_vmec_export.py @@ -0,0 +1,98 @@ +"""Record synchronized cold and warm VMEC boundary-export timings.""" + +from __future__ import annotations + +import json +import os +import platform +import statistics +import subprocess +import tempfile +from pathlib import Path + +import jax + +import pyqsc_jax as qsc + +RADIUS = 0.03 +NPHI = 61 +NTHETA = 40 +MPOL = 12 +NTOR = 14 +WARM_REPETITIONS = 7 +OUTPUT = Path( + os.environ.get("PYQSC_VMEC_BENCHMARK_OUTPUT", "benchmarks/results/vmec_export.json") +) + +solution = qsc.Qsc( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + nphi=NPHI, + order="r2", +) +with tempfile.TemporaryDirectory() as temporary_directory: + destination = Path(temporary_directory) / "input.benchmark" + jax.clear_caches() + cold = qsc.to_vmec( + solution, + destination, + r=RADIUS, + ntheta=NTHETA, + mpol=MPOL, + ntor=NTOR, + ) + warm = [ + qsc.to_vmec( + solution, + destination, + r=RADIUS, + ntheta=NTHETA, + mpol=MPOL, + ntor=NTOR, + ).conversion_seconds + for _ in range(WARM_REPETITIONS) + ] + +repository = Path(__file__).resolve().parents[1] +try: + commit = subprocess.check_output( + ("git", "-C", str(repository), "rev-parse", "HEAD"), + text=True, + ).strip() +except (OSError, subprocess.CalledProcessError): + commit = "unavailable" +report = { + "git_commit": commit, + "python": platform.python_version(), + "platform": platform.platform(), + "processor": platform.processor(), + "jax": jax.__version__, + "jax_backend": jax.default_backend(), + "jax_enable_x64": bool(jax.config.jax_enable_x64), + "case": { + "radius": RADIUS, + "nphi": NPHI, + "ntheta": NTHETA, + "mpol": MPOL, + "ntor": NTOR, + }, + "cold_compile_and_execute_seconds": cold.conversion_seconds, + "warm_median_seconds": statistics.median(warm), + "warm_samples_seconds": warm, + "maximum_toroidal_angle_residual": float( + cold.boundary.maximum_toroidal_angle_residual + ), + "maximum_R_reconstruction_error": float( + cold.boundary.maximum_R_reconstruction_error + ), + "maximum_Z_reconstruction_error": float( + cold.boundary.maximum_Z_reconstruction_error + ), +} +OUTPUT.parent.mkdir(parents=True, exist_ok=True) +OUTPUT.write_text(json.dumps(report, indent=2, sort_keys=True) + "\n", encoding="utf-8") +print("cold compile + execution [s]:", cold.conversion_seconds) +print("warm median [s]:", report["warm_median_seconds"]) +print("saved:", OUTPUT) diff --git a/benchmarks/reports/2026-07-30-b20-vmec-apple-m4.json b/benchmarks/reports/2026-07-30-b20-vmec-apple-m4.json new file mode 100644 index 0000000..19c6bbf --- /dev/null +++ b/benchmarks/reports/2026-07-30-b20-vmec-apple-m4.json @@ -0,0 +1,108 @@ +{ + "date": "2026-07-30", + "source_tree_base_commit": "f10549a3539b475cbfea2dba5cdf913a6516b75f", + "hardware": "Apple M4, 10 CPU cores, 24 GB RAM", + "jax": "0.11.0", + "jax_backend": "cpu", + "jax_enable_x64": true, + "platform": "macOS-26.5.1-arm64-arm-64bit-Mach-O", + "python": "3.13.7", + "b20_optimizer_comparison": { + "common_case": "Landreman-Paul precise-QA seed; Fourier modes 1-3 varied; exact B2c eliminated at every evaluation; nphi=121 verification", + "timing_note": "SciPy timings exclude shared residual/Jacobian compilation; the pyQSC_JAX multistart timing includes compilation of its independent closure.", + "results": [ + { + "function_evaluations": 1, + "method": "exact B2c only", + "seconds": 0.0, + "weighted_l2": 0.0003748334323839126 + }, + { + "function_evaluations": 72, + "method": "SciPy L-BFGS-B", + "seconds": 0.14576879201922566, + "weighted_l2": 0.0001923145250044151 + }, + { + "function_evaluations": 60, + "method": "SciPy least_squares", + "seconds": 2.7433434999838937, + "weighted_l2": 0.00019145867839143548 + }, + { + "function_evaluations": 120, + "method": "SciPy differential_evolution, low budget", + "seconds": 0.13656237500254065, + "weighted_l2": 0.10281099494870141 + }, + { + "distinct_basins": 3, + "function_evaluations": 129, + "method": "pyQSC_JAX multistart Levenberg-Marquardt", + "seconds": 20.765741583018098, + "status": "best_found", + "weighted_l2": 0.00012441235529252347 + } + ], + "selected_refinement": { + "function_evaluations": 75, + "method": "bounded SciPy least_squares, Fourier modes 1-5", + "seconds": null, + "verification_nphi": [61, 121, 241, 481], + "verification_weighted_l2": [ + 1.590064943168028e-06, + 1.5900649311201347e-06, + 1.5900649186197967e-06, + 1.590064906e-06 + ] + } + }, + "vmec_export": { + "case": "QA r2, radius=0.03, nphi=61, ntheta=40, mpol=12, ntor=14", + "cold_compile_and_execute_seconds": 0.4759971250023227, + "warm_median_seconds": 0.005203832988627255, + "warm_samples_seconds": [ + 0.005135457991855219, + 0.005203832988627255, + 0.005606082995655015, + 0.005212290998315439, + 0.005193958000745624, + 0.0052505840139929205, + 0.0050905829994007945 + ], + "maximum_R_reconstruction_error_m": 3.4204787844327456e-06, + "maximum_Z_reconstruction_error_m": 2.261107830789366e-06, + "maximum_toroidal_angle_residual": 2.22e-16 + }, + "vmec_radius_convergence": { + "near_axis_iota": 0.41830691021517735, + "vmec_version": "9.0", + "results": [ + { + "radius": 0.0025, + "relative_iota_error": 0.0005645603050142573, + "vmec_iota_axis": 0.418543069691998 + }, + 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b/docs/advanced/performance.md index ada3a78..bc3f5fc 100644 --- a/docs/advanced/performance.md +++ b/docs/advanced/performance.md @@ -51,3 +51,24 @@ JAX_ENABLE_X64=true PYTHONPATH=src python benchmarks/benchmark_core.py All raw timing samples are stored in `benchmarks/reports/2026-07-29-apple-m4.json`. + +## VMEC boundary export + +The VMEC converter is separately benchmarked because its old scalar +point-by-point root solves obscured the cost of the actual Fourier projection. +The replacement performs one JIT-compiled, vectorized Newton inversion and a +two-dimensional FFT. + +| grid and spectrum | compile + execute | warm median | max \(R\) error | max \(Z\) error | +| --- | ---: | ---: | ---: | ---: | +| `nphi=61`, `ntheta=40`, `mpol=12`, `ntor=14` | 0.476 s | 5.20 ms | 3.42 µm | 2.26 µm | + +The command is: + +```bash +JAX_ENABLE_X64=true PYTHONPATH=src python benchmarks/benchmark_vmec_export.py +``` + +The reported conversion timer excludes the near-axis solve and file-system +startup. Both cold and warm calls synchronize the boundary arrays before +stopping the timer. diff --git a/docs/api/vmec.md b/docs/api/vmec.md new file mode 100644 index 0000000..fc96262 --- /dev/null +++ b/docs/api/vmec.md @@ -0,0 +1,12 @@ +# VMEC export + +```{eval-rst} +.. automodule:: pyqsc_jax.vmec + :members: + :undoc-members: + :show-inheritance: +``` + +`to_vmec` is also available as a method on the legacy +`pyqsc_jax.near_axis.near_axis` adapter. That method preserves the upstream +call form and populates `RBC`, `RBS`, `ZBC`, and `ZBS` compatibility arrays. diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index 6652e4e..31e07ec 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -24,6 +24,7 @@ to the cited source, not to a duplicated derivation in this repository. | Plasma gradient | manuscript Eqs. 142–160 | `plasma.elliptical_channel_gradient`; `plasma.plasma_gradient_on_axis` | straight circular and sheared elliptical channels, frame covariance, Ampère antisymmetry, divergence, external symmetry/trace, vacuum reduction, 5-component pack/unpack, JIT/JVP/finite differences | implemented and documented | | Plasma Hessian | manuscript Eqs. 194 and 210–219 | `plasma.plasma_hessian_on_axis` | circular finite-conductor contact-term limit, QA/QH oriented ellipses, commuting plasma derivatives, spectral convergence, JIT/JVP/finite differences | implemented and documented | | External vacuum jet | manuscript Eqs. 218–224 | nested `PlasmaHessianData`; rank-2/rank-3 STF packers | 3+5+7 representation, full Hessian symmetry, trace-free gradient/Hessian, vacuum reduction, asymptotic error metadata | implemented and documented; normalized ESSOS objective remains | +| VMEC fixed-boundary conversion | near-axis surface expansion plus VMEC Fourier boundary convention | `vmec.uniform_cylindrical_surface`; `vmec.vmec_boundary`; upstream pyQSC `to_vmec.py` as an independent comparison | vectorized/legacy surface agreement, Fourier reconstruction, asymmetric coefficients, deterministic input, warm timing, frozen and live VMEC on-axis iota and force residuals, radius convergence | implemented and documented | ## Source policy diff --git a/docs/development/refactor-baseline.md b/docs/development/refactor-baseline.md index 282fcee..4f55ee2 100644 --- a/docs/development/refactor-baseline.md +++ b/docs/development/refactor-baseline.md @@ -110,9 +110,11 @@ but remains part of the final definition of done. ## Upstream test audit -At pyQSC commit `cd75359`, 31 tests pass in 22.80 seconds when -`test_to_vmec.py` is excluded because its optional MPI/VMEC runtime is absent. -The tests cover: +At pyQSC commit `cd75359`, 31 tests passed in 22.80 seconds during the initial +audit when upstream `test_to_vmec.py` was excluded because its optional +MPI/VMEC runtime was absent from that audit environment. The refactored +package now has its own frozen-wout equilibrium regression and an opt-in local +VMEC rerun; see {doc}`../validation/vmec`. The audited upstream tests cover: - Newton convergence, Fourier differentiation, interpolation, and utilities; - axis geometry, helicity, sigma, iota, field gradient, and scale lengths; diff --git a/docs/development/refactor_status.md b/docs/development/refactor_status.md index 8909aad..511e767 100644 --- a/docs/development/refactor_status.md +++ b/docs/development/refactor_status.md @@ -168,3 +168,20 @@ was made for that phase. - Verification: final local lint, docs, clean-state, artifact, upstream, and ESSOS checks pass. The latest remote CI result is reported in the PR rather than hard-coded into this versioned status page. + +## Phase 13 — high-signal examples and VMEC equilibrium validation + +- Files: vectorized VMEC exporter, deterministic INDATA writer, frozen VMEC + 9.0 equilibrium, B20/plasma-dominant named cases, optimizer/export + benchmarks, publication figures, and expanded validation docs. +- Verification: 255 tests pass with 98.74% combined line/branch coverage; + `vmec.py` has 100% line/branch coverage; warnings-as-errors documentation + builds; both frozen and live local-VMEC equilibrium checks pass. +- Numerical checks: optimized QA weighted B20 residual + \(1.5901\times10^{-6}\) at `nphi=121` and stable through `nphi=481`; + plasma-field fraction 33.26%; VMEC on-axis-iota error 0.0565% at radius + 0.0025 with force residuals below \(7.6\times10^{-11}\). +- Performance: synchronized VMEC conversion is 0.476 s including compilation + and 5.20 ms warm at the documented high-resolution boundary setting. +- Risk/next: on-axis-iota agreement is asymptotic and degrades at larger + export radius as documented; remote CI and review remain external gates. diff --git a/docs/index.md b/docs/index.md index a7afa07..fcb920f 100644 --- a/docs/index.md +++ b/docs/index.md @@ -45,6 +45,7 @@ tutorials/first_order_qh tutorials/second_order_finite_beta tutorials/target_iota tutorials/optimize_axis +tutorials/vmec_export tutorials/vacuum_coils tutorials/finite_beta_coils ``` @@ -68,6 +69,7 @@ advanced/limitations validation/pyqsc_parity validation/literature_cases validation/plasma_field +validation/vmec validation/essos migration ``` @@ -88,6 +90,7 @@ api/optimization api/axis-optimization api/criteria api/plotting +api/vmec ``` ```{toctree} diff --git a/docs/theory/b20-optimization.md b/docs/theory/b20-optimization.md index ae2f04c..49e262b 100644 --- a/docs/theory/b20-optimization.md +++ b/docs/theory/b20-optimization.md @@ -81,3 +81,41 @@ Tests establish: The branch-aware multistart workflow built on these residuals is described in {doc}`global-search`. + +## Optimizer comparison and selected case + +Several optimizers were tested from the Landreman--Paul precise-QA axis. For +the common comparison, Fourier modes 1--3 were varied and \(B_{2c}\) was +eliminated exactly at every objective evaluation. Timings are warm local +measurements and exclude the shared JAX compilation. + +| method | evaluations | time [s] | independently evaluated weighted \(L^2\) | +| --- | ---: | ---: | ---: | +| exact \(B_{2c}\) only | 1 | — | \(3.7483\times10^{-4}\) | +| SciPy L-BFGS-B | 72 | 0.146 | \(1.9231\times10^{-4}\) | +| SciPy `least_squares` | 60 | 2.743 | \(1.9146\times10^{-4}\) | +| low-budget differential evolution | 120 | 0.137 | \(1.0281\times10^{-1}\) | +| pyQSC_JAX multistart Levenberg--Marquardt | 129 | 20.766* | \(1.2441\times10^{-4}\) | + +The SciPy timings exclude the shared JAX residual/Jacobian compilation; the +asterisked multistart timing includes compilation of its independent closure. +The coarse differential-evolution budget is included to show why a method +label alone does not establish global quality. It did not locate the narrow +good basin. The selected `b20_optimized_qa` case used bounded +`least_squares` on modes 1--5 after exact \(B_{2c}\) elimination, followed by +independent resolution checks: + +| `nphi` | weighted \(L^2\) | +| ---: | ---: | +| 61 | \(1.5900649432\times10^{-6}\) | +| 121 | \(1.5900649311\times10^{-6}\) | +| 241 | \(1.5900649186\times10^{-6}\) | +| 481 | \(1.5900649060\times10^{-6}\) | + +At `nphi=121`, its dense maximum is \(3.20\times10^{-6}\) and peak-to-peak +variation is \(6.27\times10^{-6}\). This is 26,053 times smaller in weighted +residual than exact \(B_{2c}\) optimization of the stock README QA axis. The +result is a verified numerical basin, not a proof that no other basin is +better. The runnable comparison is +`benchmarks/benchmark_b20_optimizers.py`; its frozen report records the full +environment and raw values. diff --git a/docs/tutorials/vmec_export.md b/docs/tutorials/vmec_export.md new file mode 100644 index 0000000..84c9c57 --- /dev/null +++ b/docs/tutorials/vmec_export.md @@ -0,0 +1,15 @@ +# Export a fixed-boundary VMEC input + +The exporter does not require VMEC. It constructs the near-axis surface, +inverts cylindrical toroidal angle on a uniform grid, projects all four +boundary coefficient families with a two-dimensional FFT, writes a +deterministic `&INDATA` file, and returns accuracy and timing diagnostics. + +```{literalinclude} ../../examples/13_vmec_export.py +:language: python +``` + +For an asymptotic transform check, start at a small radius. Increasing the +radius tests finite-radius behavior of the truncated near-axis surface as well +as the exporter. The measured convergence is documented in +{doc}`../validation/vmec`. diff --git a/docs/validation/plasma_field.md b/docs/validation/plasma_field.md index c9816ec..ae1105e 100644 --- a/docs/validation/plasma_field.md +++ b/docs/validation/plasma_field.md @@ -19,3 +19,23 @@ The Hessian uses interior-potential contact terms. Naively differentiating a singular filament quadrature would omit those terms and is not treated as an independent reference. See the [matched field derivation](../theory/plasma-field.md) and `tests/physics/test_plasma_*.py`. + +## Plasma-dominant regression case + +The public `plasma_dominant_channel` case is a circular finite-pressure/current +channel with `I2=4.2`, `p2=-1e5`, `B0=1`, and formal radius 0.2 m. It is used +to keep the plasma/external split visually and numerically consequential: + +| quantity | value | +| --- | ---: | +| minimum/mean/maximum \(\lvert B_p\rvert/\lvert B_\mathrm{tot}\rvert\) | 0.332574 / 0.332574 / 0.332574 | +| enclosed toroidal current | 0.84 MA | +| formal radius | 0.2 m | +| computed singular radius | 0.4034 m | +| formal/singular radius | 0.496 | +| estimated field remainder | 0.0351 T | + +The \(>30\%\) fraction, finite current, and radius margin are regression +assertions. This case is intentionally transparent rather than a claim of an +optimized stellarator: its role is to validate that the plasma contribution +cannot silently collapse to a negligible plotting scale. diff --git a/docs/validation/vmec.md b/docs/validation/vmec.md new file mode 100644 index 0000000..83966f5 --- /dev/null +++ b/docs/validation/vmec.md @@ -0,0 +1,71 @@ +# VMEC validation + +## Conversion algorithm + +`uniform_cylindrical_surface` solves the cylindrical-toroidal angle inversion +for the entire poloidal/toroidal grid with six JAX Newton steps. Its derivative +is obtained by JVP, so no finite-difference step is selected. `vmec_boundary` +then computes `RBC`, `RBS`, `ZBC`, and `ZBS` simultaneously with a +two-dimensional FFT. This replaces the legacy scalar dense-root solve at every +surface point and the direct Fourier quadrature over every retained mode. + +At `nphi=61`, `ntheta=40`, `mpol=12`, and `ntor=14`, the new surface agrees +with the independent legacy root-based conversion to \(1.6\times10^{-14}\) m. +At radius 0.03 m, its retained-spectrum reconstruction errors are +\(3.42\times10^{-6}\) m in \(R\) and \(2.26\times10^{-6}\) m in \(Z\); +the maximum toroidal-angle residual is \(2.22\times10^{-16}\) rad. + +## Local equilibrium check + +The checked-in validation case was run with local VMEC2000 9.0 on macOS +arm64. It uses + +- `rc=[1.0, 0.045]`, `zs=[0.0, -0.045]`, `nfp=3`; +- `etabar=-0.9`, `B0=1`, `nphi=121`, order `r2`; +- export radius \(r=0.0025\) m; +- `ntheta=32`, `mpol=6`, `ntor=6`, `ns=31`. + +| Quantity | Near axis | VMEC | +| --- | ---: | ---: | +| on-axis \(\iota\) | 0.4183069102 | 0.4185430697 | +| relative difference | — | 0.05646% | +| `fsqr` | — | \(7.59\times10^{-11}\) | +| `fsqz` | — | \(4.21\times10^{-11}\) | +| `fsql` | — | \(2.40\times10^{-11}\) | + +The fixed +[`wout_qa_r0025.nc`](../../tests/reference/vmec/wout_qa_r0025.nc) +and its [manifest](../../tests/reference/vmec/manifest.json) are read on every +test run. The test checks the checksum, normal termination, force residuals, +and on-axis transform. Set +`PYQSC_VMEC_EXECUTABLE=/path/to/xvmec` to enable the second integration test, +which regenerates the input and reruns VMEC in a temporary directory. + +## Radius convergence + +The on-axis transform comparison is asymptotic. The same low-resolution VMEC +setup gives: + +| radius [m] | VMEC on-axis \(\iota\) | relative difference | +| ---: | ---: | ---: | +| 0.0025 | 0.41854307 | 0.0565% | +| 0.0050 | 0.41922558 | 0.2196% | +| 0.0100 | 0.42224025 | 0.9403% | +| 0.0200 | 0.43955604 | 5.0798% | +| 0.0300 | 0.49070165 | 17.3066% | + +The first three points show the expected approximately \(O(r^2)\) error. The +larger-radius results are intentionally retained: agreement at a small radius +does not imply that a truncated near-axis boundary is accurate arbitrarily far +from the axis. + +## Performance + +On the Apple M4 development machine, conversion at the higher +`40 × 61`, `mpol=12`, `ntor=14` resolution took 0.476 s including JAX +compilation and 5.20 ms after compilation. These are synchronized local +measurements, not cross-platform pass/fail promises. The unit test uses a +generous 0.5 s warm-call ceiling to catch a return to per-point root solving. +Raw data and the runnable command are in +`benchmarks/reports/2026-07-30-b20-vmec-apple-m4.json` and +`benchmarks/benchmark_vmec_export.py`. diff --git a/examples/06_optimize_axis_B20.py b/examples/06_optimize_axis_B20.py index c81951f..36dbc1c 100644 --- a/examples/06_optimize_axis_B20.py +++ b/examples/06_optimize_axis_B20.py @@ -1,76 +1,49 @@ -"""Run a small deterministic global-to-local B20 axis search.""" +"""Compare a stock QA axis with a dense-grid B20-optimized QA axis.""" from pathlib import Path -import jax.numpy as jnp import matplotlib.pyplot as plt import numpy as np import pyqsc_jax as qsc -INITIAL_AXIS = qsc.Axis( - rc=[1.0, 0.155, 0.0102], - zs=[0.0, 0.154, 0.0111], - nfp=2, -) -ETABAR = 0.64 -NPHI = 15 -COARSE_SAMPLES = 3 -LOCAL_STARTS = 1 -MAXIMUM_ITERATIONS = 3 +STOCK_CONFIGURATION = "qa" +OPTIMIZED_CONFIGURATION = "b20_optimized_qa" +NPHI = 121 SAVE_OUTPUT = True SHOW_FIGURE = False OUTPUT = Path("examples/output/06_optimize_axis_B20.png") -variable_indices = qsc.stellarator_symmetric_variable_indices( - INITIAL_AXIS, - modes=(1,), -) -problem = qsc.AxisSearchProblem( - axis=INITIAL_AXIS, - variable_indices=variable_indices, - lower_bounds=jnp.asarray([0.11, 0.11]), - upper_bounds=jnp.asarray([0.19, 0.19]), - etabar=ETABAR, - nphi=NPHI, - selector="minimum_maximum_elongation", -) -options = qsc.AxisSearchOptions( - coarse_samples=COARSE_SAMPLES, - local_starts=LOCAL_STARTS, - maximum_iterations=MAXIMUM_ITERATIONS, - verification_multipliers=(1,), - verification_tail_tolerance=1.0, -) +print("Eliminating B2c exactly for the stock QA axis...") +stock = qsc.optimize_B2c(qsc.solve_configuration(STOCK_CONFIGURATION, nphi=NPHI)) +print("Loading the independently optimized Fourier axis...") +optimized = qsc.solve_configuration(OPTIMIZED_CONFIGURATION, nphi=NPHI) +optimized_diagnostics = qsc.b20_diagnostics(optimized) +verification = qsc.verify_B20_resolution(optimized, multipliers=(1, 2)) +improvement = float(stock.diagnostics.weighted_l2 / optimized_diagnostics.weighted_l2) -print("Searching bounded axis coefficients...") -result = qsc.search_axis(problem, options=options) -print("status:", result.status) -print("search budget:", result.search_budget) -print("distinct basins:", result.distinct_basins) -print("message:", result.message) -if result.best is None: - raise RuntimeError("The example search did not produce a candidate.") -print("best variables:", np.asarray(result.best.variables)) -print("best B20 residual:", result.best.primary_residual) -print("global certificate:", result.global_certificate) +print("stock exact-B2c weighted L2:", float(stock.diagnostics.weighted_l2)) +print("optimized-axis weighted L2:", float(optimized_diagnostics.weighted_l2)) +print("optimized-axis dense maximum:", float(optimized_diagnostics.grid_maximum)) +print("improvement factor:", improvement) +print("nphi verification:", np.asarray(verification.resolutions)) +print("verified weighted L2:", np.asarray(verification.weighted_l2)) -figure, axis = plt.subplots(figsize=(6.2, 3.8)) -axis.scatter( - np.arange(result.coarse_residuals.size), - np.asarray(result.coarse_residuals), - label="coarse samples", -) -axis.axhline( - result.best.primary_residual, - color="tab:red", +stock_angle = np.asarray(stock.solution.varphi * stock.solution.inputs.axis.nfp / (2 * np.pi)) +optimized_angle = np.asarray(optimized.varphi * optimized.inputs.axis.nfp / (2 * np.pi)) +figure, axes = plt.subplots(1, 2, figsize=(9.4, 3.8)) +axes[0].plot(stock_angle, np.asarray(stock.diagnostics.anomaly), linewidth=2) +axes[0].set_title(r"stock axis + exact $B_{2c}$") +axes[0].set_xlabel("Boozer angle / field period") +axes[0].set_ylabel(r"$B_{20}-\langle B_{20}\rangle$ [T/m$^2$]") +axes[1].plot( + optimized_angle, + np.asarray(optimized_diagnostics.anomaly), linewidth=2, - label="best refined basin", + color="tab:green", ) -axis.set_yscale("log") -axis.set_xlabel("deterministic sample index") -axis.set_ylabel("weighted B20 residual") -axis.legend() +axes[1].set_title(f"optimized axis ({improvement:,.0f}x smaller)") +axes[1].set_xlabel("Boozer angle / field period") figure.tight_layout() if SAVE_OUTPUT: OUTPUT.parent.mkdir(parents=True, exist_ok=True) diff --git a/examples/10_plasma_external_field_jet.py b/examples/10_plasma_external_field_jet.py index 7d6b132..040b28d 100644 --- a/examples/10_plasma_external_field_jet.py +++ b/examples/10_plasma_external_field_jet.py @@ -7,8 +7,8 @@ import pyqsc_jax as qsc from pyqsc_jax.plotting import plot_field_jet_norms -CONFIGURATION = "finite_pressure_current" -FORMAL_RADIUS = 0.025 +CONFIGURATION = "plasma_dominant_channel" +FORMAL_RADIUS = 0.2 NPHI = 61 ANGULAR_RESOLUTION = 96 SAVE_OUTPUT = True @@ -24,7 +24,17 @@ angular_resolution=ANGULAR_RESOLUTION, ) enclosed_current = result.field.field.current_source.enclosed_toroidal_current +plasma_fraction = ( + ( + (result.field.field.field**2).sum(axis=-1) + / (solution.B_axis**2).sum(axis=-1) + ) + ** 0.5 +) print("enclosed toroidal current [A]:", float(enclosed_current)) +print("minimum |B_plasma| / |B_total|:", float(plasma_fraction.min())) +print("mean |B_plasma| / |B_total|:", float(plasma_fraction.mean())) +print("formal radius / singular radius:", float(FORMAL_RADIUS / solution.r_singularity)) print("external gradient STF components:", result.field.external_gradient_independent.shape[-1]) print("external Hessian STF components:", result.external_hessian_independent.shape[-1]) print("maximum external-gradient trace:", float(result.field.maximum_external_trace)) diff --git a/examples/13_vmec_export.py b/examples/13_vmec_export.py new file mode 100644 index 0000000..63a9293 --- /dev/null +++ b/examples/13_vmec_export.py @@ -0,0 +1,75 @@ +"""Export a diagnosed VMEC boundary without invoking VMEC.""" + +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np + +import pyqsc_jax as qsc + +RADIUS = 0.005 +NPHI = 61 +NTHETA = 40 +MPOL = 12 +NTOR = 14 +SAVE_OUTPUT = True +SHOW_FIGURE = False +VMEC_INPUT = Path("examples/output/input.pyqsc_jax_qa") +FIGURE_OUTPUT = Path("examples/output/13_vmec_export.png") + +solution = qsc.Qsc( + rc=[1.0, 0.045], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + nphi=NPHI, + order="r2", +) +print("Writing the fixed-boundary VMEC input...") +export = qsc.to_vmec( + solution, + VMEC_INPUT, + r=RADIUS, + ntheta=NTHETA, + mpol=MPOL, + ntor=NTOR, +) +boundary = export.boundary +print("input:", export.path) +print("conversion seconds (compile + first execution):", export.conversion_seconds) +print("maximum toroidal-angle residual:", float(boundary.maximum_toroidal_angle_residual)) +print("maximum R reconstruction error [m]:", float(boundary.maximum_R_reconstruction_error)) +print("maximum Z reconstruction error [m]:", float(boundary.maximum_Z_reconstruction_error)) +print("run with: xvmec", export.path.name) + +figure, axes = plt.subplots(1, 2, figsize=(9.4, 3.8)) +phi_indices = np.linspace(0, NPHI - 1, 7, dtype=int) +for index in phi_indices: + axes[0].plot( + np.asarray(boundary.R[:, index]), + np.asarray(boundary.Z[:, index]), + linewidth=1.3, + ) +axes[0].set_aspect("equal") +axes[0].set_xlabel("R [m]") +axes[0].set_ylabel("Z [m]") +axes[0].set_title("uniform cylindrical-toroidal sections") +mode_amplitude = np.sqrt( + np.asarray(boundary.RBC) ** 2 + + np.asarray(boundary.RBS) ** 2 + + np.asarray(boundary.ZBC) ** 2 + + np.asarray(boundary.ZBS) ** 2 +) +axes[1].semilogy(np.sort(mode_amplitude.ravel())[::-1], marker=".", linewidth=1) +axes[1].set_xlabel("coefficient rank") +axes[1].set_ylabel("combined Fourier amplitude [m]") +axes[1].set_title("VMEC boundary spectrum") +figure.tight_layout() +if SAVE_OUTPUT: + FIGURE_OUTPUT.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(FIGURE_OUTPUT, dpi=180, bbox_inches="tight") + print("saved:", FIGURE_OUTPUT) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/publication/figure_B20_optimization.py b/examples/publication/figure_B20_optimization.py index 03c52a6..66d6430 100644 --- a/examples/publication/figure_B20_optimization.py +++ b/examples/publication/figure_B20_optimization.py @@ -1,4 +1,4 @@ -"""Publication figure for exact affine B2c elimination.""" +"""Publication figure for exact B2c elimination and full-axis B20 optimization.""" import json import subprocess @@ -9,8 +9,8 @@ import pyqsc_jax as qsc -CONFIGURATION = "qa" -INITIAL_B2C = 0.0 +STOCK_CONFIGURATION = "qa" +OPTIMIZED_CONFIGURATION = "b20_optimized_qa" NPHI = 121 OUTPUT_STEM = Path("examples/output/publication/B20_optimization") README_PNG = Path("docs/_static/B20_optimization.png") @@ -18,48 +18,63 @@ SHOW_FIGURE = False plt.style.use("seaborn-v0_8-whitegrid") -print("Computing exact B2c elimination at publication resolution...") -initial = qsc.solve_configuration(CONFIGURATION, B2c=INITIAL_B2C, nphi=NPHI) -result = qsc.optimize_B2c(initial) -optimized = result.solution -angle = np.asarray(initial.varphi * initial.inputs.axis.nfp / (2 * np.pi)) +print("Comparing exact B2c elimination with the optimized Fourier axis...") +stock = qsc.optimize_B2c(qsc.solve_configuration(STOCK_CONFIGURATION, nphi=NPHI)) +optimized = qsc.solve_configuration(OPTIMIZED_CONFIGURATION, nphi=NPHI) +optimized_diagnostics = qsc.b20_diagnostics(optimized) +verification = qsc.verify_B20_resolution(optimized, multipliers=(1, 2)) +improvement = float(stock.diagnostics.weighted_l2 / optimized_diagnostics.weighted_l2) +stock_angle = np.asarray(stock.solution.varphi * stock.solution.inputs.axis.nfp / (2 * np.pi)) +optimized_angle = np.asarray(optimized.varphi * optimized.inputs.axis.nfp / (2 * np.pi)) -figure, axes = plt.subplots(1, 2, figsize=(10.5, 3.9)) -axes[0].plot(angle, np.asarray(initial.B20_anomaly), linewidth=2.2, label="initial") -axes[0].plot( - angle, - np.asarray(optimized.B20_anomaly), - linewidth=2.2, - label=r"exact $B_{2c}^{\star}$", -) +figure, axes = plt.subplots(1, 3, figsize=(12.8, 3.8)) +axes[0].plot(stock_angle, np.asarray(stock.diagnostics.anomaly), linewidth=2.2) +axes[0].set_title(r"stock axis + exact $B_{2c}$") axes[0].set_xlabel("Boozer angle / field period") axes[0].set_ylabel(r"$B_{20}-\langle B_{20}\rangle$ [T/m$^2$]") -axes[0].legend() +axes[1].plot( + optimized_angle, + np.asarray(optimized_diagnostics.anomaly), + linewidth=2.2, + color="tab:green", +) +axes[1].set_title("optimized Fourier axis") +axes[1].set_xlabel("Boozer angle / field period") diagnostic_names = ("weighted $L^2$", "dense maximum", "peak-to-peak") -initial_diagnostics = qsc.b20_diagnostics(initial) -axes[1].bar( +stock_values = ( + float(stock.diagnostics.weighted_l2), + float(stock.diagnostics.grid_maximum), + float(stock.diagnostics.peak_to_peak), +) +optimized_values = ( + float(optimized_diagnostics.weighted_l2), + float(optimized_diagnostics.grid_maximum), + float(optimized_diagnostics.peak_to_peak), +) +axes[2].bar( np.arange(3) - 0.18, - ( - float(initial_diagnostics.weighted_l2), - float(initial_diagnostics.grid_maximum), - float(initial_diagnostics.peak_to_peak), - ), + stock_values, width=0.36, - label="initial", + label=r"exact $B_{2c}$ only", ) -axes[1].bar( +axes[2].bar( np.arange(3) + 0.18, - ( - float(result.diagnostics.weighted_l2), - float(result.diagnostics.grid_maximum), - float(result.diagnostics.peak_to_peak), - ), + optimized_values, width=0.36, - label="optimized", + label="axis + $B_{2c}$", + color="tab:green", +) +axes[2].set_xticks(np.arange(3), diagnostic_names, rotation=15) +axes[2].set_yscale("log") +axes[2].set_ylabel(r"$B_{20}$ nonuniformity [T/m$^2$]") +axes[2].legend(fontsize=8) +axes[2].text( + 0.04, + 0.05, + f"{improvement:,.0f}x lower weighted residual", + transform=axes[2].transAxes, + fontweight="bold", ) -axes[1].set_xticks(np.arange(3), diagnostic_names, rotation=15) -axes[1].set_ylabel(r"$B_{20}$ nonuniformity [T/m$^2$]") -axes[1].legend() figure.tight_layout() try: @@ -72,12 +87,19 @@ commit = "unavailable" metadata = { "git_commit": commit, - "configuration": CONFIGURATION, + "stock_configuration": STOCK_CONFIGURATION, + "optimized_configuration": OPTIMIZED_CONFIGURATION, "nphi": NPHI, - "initial_B2c": INITIAL_B2C, - "optimal_B2c": float(result.B2c_optimal), - "initial_weighted_l2": float(initial_diagnostics.weighted_l2), - "optimal_weighted_l2": float(result.diagnostics.weighted_l2), + "stock_exact_B2c": float(stock.B2c_optimal), + "optimized_B2c": float(optimized.inputs.B2c), + "stock_weighted_l2": float(stock.diagnostics.weighted_l2), + "optimized_weighted_l2": float(optimized_diagnostics.weighted_l2), + "optimized_grid_maximum": float(optimized_diagnostics.grid_maximum), + "optimized_peak_to_peak": float(optimized_diagnostics.peak_to_peak), + "improvement_factor": improvement, + "verification_nphi": np.asarray(verification.resolutions).tolist(), + "verification_weighted_l2": np.asarray(verification.weighted_l2).tolist(), + "optimizer": "bounded scipy least_squares after exact B2c elimination", } if SAVE_OUTPUT: OUTPUT_STEM.parent.mkdir(parents=True, exist_ok=True) diff --git a/examples/publication/figure_plasma_external_jet.py b/examples/publication/figure_plasma_external_jet.py index 922d05e..34f474f 100644 --- a/examples/publication/figure_plasma_external_jet.py +++ b/examples/publication/figure_plasma_external_jet.py @@ -9,8 +9,8 @@ import pyqsc_jax as qsc from pyqsc_jax.plotting import plot_field_jet_norms -CONFIGURATION = "finite_pressure_current" -FORMAL_RADIUS = 0.025 +CONFIGURATION = "plasma_dominant_channel" +FORMAL_RADIUS = 0.2 NPHI = 121 ANGULAR_RESOLUTION = 128 OUTPUT_STEM = Path("examples/output/publication/plasma_external_jet") @@ -26,6 +26,13 @@ formal_radius=FORMAL_RADIUS, angular_resolution=ANGULAR_RESOLUTION, ) +plasma_fraction = ( + ( + (result.field.field.field**2).sum(axis=-1) + / (solution.B_axis**2).sum(axis=-1) + ) + ** 0.5 +) figure, axes = plot_field_jet_norms(result) for label, axis in zip(("a", "b", "c"), axes, strict=True): axis.text( @@ -51,6 +58,9 @@ "nphi": NPHI, "angular_resolution": ANGULAR_RESOLUTION, "enclosed_current_amperes": float(result.field.field.current_source.enclosed_toroidal_current), + "minimum_plasma_field_fraction": float(plasma_fraction.min()), + "mean_plasma_field_fraction": float(plasma_fraction.mean()), + "formal_radius_to_singular_radius": float(FORMAL_RADIUS / solution.r_singularity), "maximum_external_gradient_trace": float(result.field.maximum_external_trace), "maximum_external_hessian_trace": float(result.maximum_external_trace), "field_remainder": float(result.field.field.estimated_field_remainder), diff --git a/examples/publication/figure_vmec_validation.py b/examples/publication/figure_vmec_validation.py new file mode 100644 index 0000000..e33e49b --- /dev/null +++ b/examples/publication/figure_vmec_validation.py @@ -0,0 +1,88 @@ +"""Publication figure for VMEC export timing and on-axis-iota convergence.""" + +import json +import subprocess +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np + +REPORT = ( + Path(__file__).resolve().parents[2] + / "benchmarks" + / "reports" + / "2026-07-30-b20-vmec-apple-m4.json" +) +OUTPUT_STEM = Path("examples/output/publication/vmec_validation") +README_PNG = Path("docs/_static/vmec_validation.png") +SAVE_OUTPUT = True +SHOW_FIGURE = False + +print("Loading the frozen VMEC validation report...") +report = json.loads(REPORT.read_text(encoding="utf-8")) +convergence = report["vmec_radius_convergence"] +radii = np.asarray([row["radius"] for row in convergence["results"]]) +errors = np.asarray([row["relative_iota_error"] for row in convergence["results"]]) +timing = report["vmec_export"] + +plt.style.use("seaborn-v0_8-whitegrid") +figure, axes = plt.subplots(1, 2, figsize=(9.8, 3.8)) +axes[0].loglog(radii, errors, "o-", linewidth=2.2, label="VMEC") +axes[0].loglog( + radii, + errors[0] * (radii / radii[0]) ** 2, + "--", + linewidth=1.7, + label=r"$O(r^2)$", +) +axes[0].set_xlabel("export radius [m]") +axes[0].set_ylabel("relative on-axis iota error") +axes[0].set_title("near-axis convergence") +axes[0].legend() +cold_ms = 1000 * timing["cold_compile_and_execute_seconds"] +warm_ms = 1000 * timing["warm_median_seconds"] +axes[1].bar(("compile + execute", "warm execute"), (cold_ms, warm_ms), color=("0.45", "tab:blue")) +axes[1].set_yscale("log") +axes[1].set_ylabel("conversion time [ms]") +axes[1].set_title("vectorized JAX exporter") +axes[1].text( + 0.5, + 0.07, + f"{timing['maximum_R_reconstruction_error_m'] * 1e6:.2f} µm max R error\n" + f"{timing['maximum_Z_reconstruction_error_m'] * 1e6:.2f} µm max Z error", + ha="center", + transform=axes[1].transAxes, +) +figure.tight_layout() + +try: + repository = Path(__file__).resolve().parents[2] + commit = subprocess.check_output( + ("git", "-C", str(repository), "rev-parse", "HEAD"), + text=True, + ).strip() +except (OSError, subprocess.CalledProcessError): + commit = "unavailable" +metadata = { + "git_commit": commit, + "source_report": str(REPORT), + "near_axis_iota": convergence["near_axis_iota"], + "radius_convergence": convergence["results"], + "vmec_version": convergence["vmec_version"], + "export": timing, +} +if SAVE_OUTPUT: + OUTPUT_STEM.parent.mkdir(parents=True, exist_ok=True) + for suffix in ("png", "svg", "pdf"): + figure.savefig(OUTPUT_STEM.with_suffix(f".{suffix}"), dpi=220, bbox_inches="tight") + README_PNG.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(README_PNG, dpi=120, bbox_inches="tight") + OUTPUT_STEM.with_suffix(".json").write_text( + json.dumps(metadata, indent=2, sort_keys=True) + "\n", + encoding="utf-8", + ) + print("saved:", OUTPUT_STEM) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) From 70330a612e2c968eb0edde327235be4eb662600c Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 08:03:28 -0500 Subject: [PATCH 28/39] style: match current Ruff formatting --- benchmarks/benchmark_b20_optimizers.py | 4 +--- benchmarks/benchmark_vmec_export.py | 16 ++++------------ examples/10_plasma_external_field_jet.py | 8 ++------ .../publication/figure_plasma_external_jet.py | 8 ++------ 4 files changed, 9 insertions(+), 27 deletions(-) diff --git a/benchmarks/benchmark_b20_optimizers.py b/benchmarks/benchmark_b20_optimizers.py index c7ab178..7d5ebb2 100644 --- a/benchmarks/benchmark_b20_optimizers.py +++ b/benchmarks/benchmark_b20_optimizers.py @@ -54,9 +54,7 @@ def projected_residual(variables): - axis = AXIS.with_dofs( - AXIS.dofs.at[jnp.asarray(VARIABLE_INDICES)].set(variables) - ) + axis = AXIS.with_dofs(AXIS.dofs.at[jnp.asarray(VARIABLE_INDICES)].set(variables)) solution = qsc.solve( axis=axis, etabar=-0.6783912804454629, diff --git a/benchmarks/benchmark_vmec_export.py b/benchmarks/benchmark_vmec_export.py index 0e64b06..547a354 100644 --- a/benchmarks/benchmark_vmec_export.py +++ b/benchmarks/benchmark_vmec_export.py @@ -20,9 +20,7 @@ MPOL = 12 NTOR = 14 WARM_REPETITIONS = 7 -OUTPUT = Path( - os.environ.get("PYQSC_VMEC_BENCHMARK_OUTPUT", "benchmarks/results/vmec_export.json") -) +OUTPUT = Path(os.environ.get("PYQSC_VMEC_BENCHMARK_OUTPUT", "benchmarks/results/vmec_export.json")) solution = qsc.Qsc( rc=[1.0, 0.045], @@ -81,15 +79,9 @@ "cold_compile_and_execute_seconds": cold.conversion_seconds, "warm_median_seconds": statistics.median(warm), "warm_samples_seconds": warm, - "maximum_toroidal_angle_residual": float( - cold.boundary.maximum_toroidal_angle_residual - ), - "maximum_R_reconstruction_error": float( - cold.boundary.maximum_R_reconstruction_error - ), - "maximum_Z_reconstruction_error": float( - cold.boundary.maximum_Z_reconstruction_error - ), + "maximum_toroidal_angle_residual": float(cold.boundary.maximum_toroidal_angle_residual), + "maximum_R_reconstruction_error": float(cold.boundary.maximum_R_reconstruction_error), + "maximum_Z_reconstruction_error": float(cold.boundary.maximum_Z_reconstruction_error), } OUTPUT.parent.mkdir(parents=True, exist_ok=True) OUTPUT.write_text(json.dumps(report, indent=2, sort_keys=True) + "\n", encoding="utf-8") diff --git a/examples/10_plasma_external_field_jet.py b/examples/10_plasma_external_field_jet.py index 040b28d..7c95906 100644 --- a/examples/10_plasma_external_field_jet.py +++ b/examples/10_plasma_external_field_jet.py @@ -25,12 +25,8 @@ ) enclosed_current = result.field.field.current_source.enclosed_toroidal_current plasma_fraction = ( - ( - (result.field.field.field**2).sum(axis=-1) - / (solution.B_axis**2).sum(axis=-1) - ) - ** 0.5 -) + (result.field.field.field**2).sum(axis=-1) / (solution.B_axis**2).sum(axis=-1) +) ** 0.5 print("enclosed toroidal current [A]:", float(enclosed_current)) print("minimum |B_plasma| / |B_total|:", float(plasma_fraction.min())) print("mean |B_plasma| / |B_total|:", float(plasma_fraction.mean())) diff --git a/examples/publication/figure_plasma_external_jet.py b/examples/publication/figure_plasma_external_jet.py index 34f474f..3f9aedc 100644 --- a/examples/publication/figure_plasma_external_jet.py +++ b/examples/publication/figure_plasma_external_jet.py @@ -27,12 +27,8 @@ angular_resolution=ANGULAR_RESOLUTION, ) plasma_fraction = ( - ( - (result.field.field.field**2).sum(axis=-1) - / (solution.B_axis**2).sum(axis=-1) - ) - ** 0.5 -) + (result.field.field.field**2).sum(axis=-1) / (solution.B_axis**2).sum(axis=-1) +) ** 0.5 figure, axes = plot_field_jet_norms(result) for label, axis in zip(("a", "b", "c"), axes, strict=True): axis.text( From 6dd0cadc6ba50f96dd9590953dc0446033660004 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 10:17:28 -0500 Subject: [PATCH 29/39] feat: add differentiable VMEX radial equilibria --- .github/workflows/compatibility.yml | 22 ++ benchmarks/benchmark_vmex_interface.py | 95 ++++++ pyproject.toml | 1 + src/pyqsc_jax/__init__.py | 18 ++ src/pyqsc_jax/configurations.py | 14 + src/pyqsc_jax/plotting.py | 130 ++++++++ src/pyqsc_jax/vmex.py | 404 +++++++++++++++++++++++++ tests/integration/test_vmex_live.py | 69 +++++ tests/physics/test_plasma_field.py | 20 ++ tests/unit/test_configurations.py | 1 + tests/unit/test_plotting.py | 33 +- tests/unit/test_vmex_interface.py | 253 ++++++++++++++++ 12 files changed, 1059 insertions(+), 1 deletion(-) create mode 100644 benchmarks/benchmark_vmex_interface.py create mode 100644 src/pyqsc_jax/vmex.py create mode 100644 tests/integration/test_vmex_live.py create mode 100644 tests/unit/test_vmex_interface.py diff --git a/.github/workflows/compatibility.yml b/.github/workflows/compatibility.yml index 7cec3d2..7983651 100644 --- a/.github/workflows/compatibility.yml +++ b/.github/workflows/compatibility.yml @@ -64,3 +64,25 @@ jobs: pytest essos-integration/tests/test_field_jet.py essos-integration/tests/test_field_jet_examples.py + + vmex-implicit: + runs-on: ubuntu-latest + timeout-minutes: 20 + env: + JAX_ENABLE_X64: "true" + PYQSC_RUN_VMEX: "1" + steps: + - uses: actions/checkout@v4 + - uses: actions/checkout@v4 + with: + repository: uwplasma/vmex + ref: main + path: vmex-integration + - uses: actions/setup-python@v5 + with: + python-version: "3.12" + cache: pip + - run: python -m pip install -e '.[dev]' + - run: python -m pip install -e ./vmex-integration + - run: python -m pip install -e . + - run: pytest tests/integration/test_vmex_live.py diff --git a/benchmarks/benchmark_vmex_interface.py b/benchmarks/benchmark_vmex_interface.py new file mode 100644 index 0000000..117079a --- /dev/null +++ b/benchmarks/benchmark_vmex_interface.py @@ -0,0 +1,95 @@ +"""Record synchronized VMEX forward and implicit-gradient timings.""" + +from __future__ import annotations + +import json +import os +import platform +import subprocess +from pathlib import Path +from time import perf_counter + +import jax +import numpy as np + +import pyqsc_jax as qsc + +CONFIGURATION = "plasma_stellarator" +RADIUS = 0.02 +OUTPUT = Path( + os.environ.get( + "PYQSC_VMEX_BENCHMARK_OUTPUT", + "benchmarks/results/vmex_interface.json", + ) +) + +near_axis = qsc.solve_configuration(CONFIGURATION, nphi=31) +problem = qsc.to_vmex_problem( + near_axis, + r=RADIUS, + qs_surfaces=(0.2, 0.4, 0.6, 0.8, 1.0), + ntheta=8, + mpol=3, + ntor=2, + ns_array=(7,), + ftol=1.0e-7, + max_iterations=1200, + multigrid=False, +) + +jax.clear_caches() +start = perf_counter() +equilibrium = problem.solve() +jax.block_until_ready(equilibrium.quantities) +forward_seconds = perf_counter() - start + + +def objective(parameters): + """Return the scalar used to benchmark VMEX's implicit gradient.""" + + return qsc.vmex_radial_quantities(problem, parameters).magnetic_well + + +start = perf_counter() +well, gradient = jax.value_and_grad(objective)(problem.parameters) +jax.block_until_ready((well, gradient)) +value_and_gradient_seconds = perf_counter() - start + +repository = Path(__file__).resolve().parents[1] +try: + commit = subprocess.check_output( + ("git", "-C", str(repository), "rev-parse", "HEAD"), + text=True, + ).strip() +except (OSError, subprocess.CalledProcessError): + commit = "unavailable" +report = { + "git_commit": commit, + "python": platform.python_version(), + "platform": platform.platform(), + "processor": platform.processor(), + "jax": jax.__version__, + "jax_backend": jax.default_backend(), + "jax_enable_x64": bool(jax.config.jax_enable_x64), + "vmex": problem.vmex_version, + "vmex_validated_commit": problem.validated_commit, + "case": { + "configuration": CONFIGURATION, + "radius": RADIUS, + "nphi": near_axis.inputs.nphi, + "ntheta": problem.ntheta, + "mpol_maximum": problem.mpol, + "ntor": problem.ntor, + "ns_array": np.asarray(problem.input.ns_array).tolist(), + }, + "forward_seconds": forward_seconds, + "value_and_gradient_seconds": value_and_gradient_seconds, + "magnetic_well": float(well), + "gradient_pres_scale": float(gradient.pres_scale), + "gradient_rbc_norm": float(np.linalg.norm(np.asarray(gradient.rbc))), +} +OUTPUT.parent.mkdir(parents=True, exist_ok=True) +OUTPUT.write_text(json.dumps(report, indent=2, sort_keys=True) + "\n", encoding="utf-8") +print("VMEX forward [s]:", forward_seconds) +print("VMEX magnetic-well value + gradient [s]:", value_and_gradient_seconds) +print("saved:", OUTPUT) diff --git a/pyproject.toml b/pyproject.toml index c4f3703..634245b 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -33,6 +33,7 @@ Source = "https://github.com/uwplasma/pyQSC_JAX" [project.optional-dependencies] plot = ["matplotlib"] +vmex = ["vmex"] docs = [ "furo", "myst-parser", diff --git a/src/pyqsc_jax/__init__.py b/src/pyqsc_jax/__init__.py index 534a6c7..a5732ca 100644 --- a/src/pyqsc_jax/__init__.py +++ b/src/pyqsc_jax/__init__.py @@ -82,6 +82,16 @@ uniform_cylindrical_surface, vmec_boundary, ) +from pyqsc_jax.vmex import ( + VMEX_VALIDATED_COMMIT, + VmexEquilibrium, + VmexProblem, + VmexRadialQuantities, + solve_vmex, + to_vmex_problem, + vmex_parameters_from_solution, + vmex_radial_quantities, +) __all__ = [ "Axis", @@ -121,6 +131,10 @@ "VmecBoundary", "VmecExport", "VmecInputParameters", + "VmexEquilibrium", + "VmexProblem", + "VmexRadialQuantities", + "VMEX_VALIDATED_COMMIT", "near_axis", "b20_diagnostics", "available_configurations", @@ -145,8 +159,12 @@ "solve_third_order", "total_field_jet", "to_vmec", + "to_vmex_problem", "uniform_cylindrical_surface", "vmec_boundary", + "vmex_parameters_from_solution", + "vmex_radial_quantities", + "solve_vmex", "optimal_B2c_value", "optimize_B2c", "plasma_current_source", diff --git a/src/pyqsc_jax/configurations.py b/src/pyqsc_jax/configurations.py index 9db27aa..563b49f 100644 --- a/src/pyqsc_jax/configurations.py +++ b/src/pyqsc_jax/configurations.py @@ -126,6 +126,20 @@ def solve(self, **overrides: Any) -> NearAxisSolution: I2=4.2, p2=-100000.0, ), + ReferenceConfiguration( + name="plasma_stellarator", + description=( + "Two-field-period finite-pressure/current stellarator with an " + "angle-dependent plasma/external split and more than 30 percent " + "plasma field at formal radius 0.2." + ), + rc=(1.0, 0.008), + zs=(0.0, -0.008), + nfp=2, + etabar=0.5, + I2=4.2, + p2=-100000.0, + ), ) diff --git a/src/pyqsc_jax/plotting.py b/src/pyqsc_jax/plotting.py index aed1b49..0a89899 100644 --- a/src/pyqsc_jax/plotting.py +++ b/src/pyqsc_jax/plotting.py @@ -4,12 +4,14 @@ from typing import Any +import jax import jax.numpy as jnp import numpy as np from pyqsc_jax.axis import Axis, evaluate_axis from pyqsc_jax.models import NearAxisSolution from pyqsc_jax.plasma import PlasmaHessianData +from pyqsc_jax.vmec import uniform_cylindrical_surface def _matplotlib(): @@ -65,6 +67,80 @@ def plot_axis( return figure, ax +def surface_coordinates( + solution: NearAxisSolution, + *, + radius: float = 0.05, + ntheta: int = 32, +) -> tuple[jax.Array, jax.Array, jax.Array]: + """Return full-torus Cartesian coordinates of a near-axis surface.""" + + if radius <= 0: + raise ValueError("radius must be positive.") + if not isinstance(ntheta, int) or isinstance(ntheta, bool) or ntheta < 4: + raise ValueError("ntheta must be an integer >= 4.") + R, Z, _, _ = uniform_cylindrical_surface(solution, radius, ntheta=ntheta) + period = 2 * jnp.pi / solution.inputs.axis.nfp + phi_periods = tuple( + solution.phi + period_index * period for period_index in range(solution.inputs.axis.nfp) + ) + phi = jnp.concatenate(phi_periods) + R = jnp.concatenate((R,) * solution.inputs.axis.nfp, axis=1) + Z = jnp.concatenate((Z,) * solution.inputs.axis.nfp, axis=1) + x = R * jnp.cos(phi[None, :]) + y = R * jnp.sin(phi[None, :]) + return ( + jnp.concatenate((x, x[:, :1]), axis=1), + jnp.concatenate((y, y[:, :1]), axis=1), + jnp.concatenate((Z, Z[:, :1]), axis=1), + ) + + +def plot_surface_3d( + solution: NearAxisSolution, + *, + radius: float = 0.05, + ntheta: int = 32, + ax: Any = None, + cmap: str = "viridis", + alpha: float = 0.9, + plot_axis_line: bool = True, + **surface_kwargs: Any, +): + """Plot a full-torus near-axis surface and return ``(figure, axes)``.""" + + x, y, z = surface_coordinates(solution, radius=radius, ntheta=ntheta) + plt = _matplotlib() + if ax is None: + figure = plt.figure(figsize=(6.0, 4.8)) + ax = figure.add_subplot(111, projection="3d") + else: + figure = ax.figure + defaults = { + "cmap": cmap, + "linewidth": 0, + "antialiased": True, + "alpha": alpha, + } + defaults.update(surface_kwargs) + ax.plot_surface(np.asarray(x), np.asarray(y), np.asarray(z), **defaults) + if plot_axis_line: + phi = jnp.linspace(0, 2 * jnp.pi, 361) + axis_samples = evaluate_axis(solution.inputs.axis, phi) + ax.plot( + np.asarray(axis_samples.R * jnp.cos(phi)), + np.asarray(axis_samples.R * jnp.sin(phi)), + np.asarray(axis_samples.Z), + color="black", + linewidth=1.8, + ) + ax.set_xlabel("x [m]") + ax.set_ylabel("y [m]") + ax.set_zlabel("z [m]") + ax.set_box_aspect((1, 1, 0.5)) + return figure, ax + + def plot_b20( solution: NearAxisSolution, *, @@ -161,3 +237,57 @@ def plot_field_jet_norms( axes[0].legend(ncol=3) figure.tight_layout() return figure, axes + + +def field_split_frenet_components( + result: PlasmaHessianData, + solution: NearAxisSolution, +) -> jax.Array: + """Return total/plasma/external field components in the Frenet frame. + + The result has shape ``(3, 3, nphi)``. The first index orders + ``(total, plasma, external)`` and the second orders + ``(tangent, normal, binormal)``. + """ + + plasma = result.field.field.field + external = result.field.external_field + fields = jnp.stack((plasma + external, plasma, external)) + frames = jnp.stack( + ( + solution.geometry.tangent_cartesian, + solution.geometry.normal_cartesian, + solution.geometry.binormal_cartesian, + ) + ) + return jnp.einsum("fpi,cpi->fcp", fields, frames) + + +def plot_field_split_components( + result: PlasmaHessianData, + solution: NearAxisSolution, + *, + axes: Any = None, +): + """Plot angle-dependent total/plasma/external Frenet field components.""" + + plt = _matplotlib() + if axes is None: + figure, axes = plt.subplots(3, 1, figsize=(7.0, 7.2), sharex=True) + else: + axes = np.asarray(axes) + if axes.shape != (3,): + raise ValueError("axes must contain exactly three Matplotlib axes.") + figure = axes[0].figure + components = np.asarray(field_split_frenet_components(result, solution)) + angle = np.asarray(solution.varphi * solution.inputs.axis.nfp / (2 * jnp.pi)) + contributions = ("total", "plasma", "external") + component_labels = (r"$B_t$ [T]", r"$B_n$ [T]", r"$B_b$ [T]") + for component_index, (axis, ylabel) in enumerate(zip(axes, component_labels, strict=True)): + for field_index, label in enumerate(contributions): + axis.plot(angle, components[field_index, component_index], label=label) + axis.set_ylabel(ylabel) + axes[-1].set_xlabel("Boozer angle / field period") + axes[0].legend(ncol=3) + figure.tight_layout() + return figure, axes diff --git a/src/pyqsc_jax/vmex.py b/src/pyqsc_jax/vmex.py new file mode 100644 index 0000000..100324b --- /dev/null +++ b/src/pyqsc_jax/vmex.py @@ -0,0 +1,404 @@ +"""Optional differentiable fixed-boundary equilibrium interface to VMEX.""" + +from __future__ import annotations + +import dataclasses +import importlib +from dataclasses import dataclass +from typing import Any + +import jax +import jax.numpy as jnp +import numpy as np + +from pyqsc_jax.models import NearAxisSolution +from pyqsc_jax.second_order import MU0 +from pyqsc_jax.vmec import VmecBoundary, vmec_boundary + +VMEX_VALIDATED_COMMIT = "2a40d7566be083070ea3ea534fa5d1fc44ad733a" + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class VmexRadialQuantities: + """Differentiable radial and scalar quantities from a converged VMEX state. + + ``iota_vmec`` retains VMEC's native sign convention. ``iota`` uses the + pyQSC_JAX toroidal-angle convention, which is the negative of VMEC's for + boundaries produced by :func:`pyqsc_jax.vmec_boundary`. + """ + + s: jax.Array + iota: jax.Array + iota_vmec: jax.Array + qs_surfaces: jax.Array + quasisymmetry: jax.Array + magnetic_well: jax.Array + aspect: jax.Array + volume: jax.Array + magnetic_energy: jax.Array + thermal_energy: jax.Array + + +@dataclass(frozen=True) +class VmexEquilibrium: + """A VMEX implicit solution together with user-facing radial quantities.""" + + solution: Any + quantities: VmexRadialQuantities + + +@dataclass(frozen=True) +class VmexProblem: + """Reusable static VMEX problem and its differentiable parameter pytree.""" + + input: Any + parameters: Any + boundary: VmecBoundary + radius: float + qs_surfaces: tuple[float, ...] + helicity_m: int + helicity_n: int + ntheta: int + mpol: int + ntor: int + newton_iterations: int + ftol: float + max_iterations: int + multigrid: bool + device: Any + vmex_version: str + validated_commit: str = VMEX_VALIDATED_COMMIT + + @property + def finite_beta(self) -> bool: + """Whether the static reference input has a nonzero pressure profile.""" + + return bool(np.any(np.asarray(self.input.am))) + + def parameters_for( + self, + solution: NearAxisSolution, + *, + radius: Any | None = None, + ) -> Any: + """Map another near-axis solution into this problem's parameter pytree.""" + + return vmex_parameters_from_solution(self, solution, radius=radius) + + def quantities(self, parameters: Any | None = None) -> VmexRadialQuantities: + """Solve and return differentiable radial quantities.""" + + return vmex_radial_quantities(self, parameters) + + def solve(self, parameters: Any | None = None) -> VmexEquilibrium: + """Solve the fixed-boundary equilibrium and retain the raw VMEX result.""" + + return solve_vmex(self, parameters) + + +def _import_vmex(): + try: + module = importlib.import_module("vmex") + except ImportError as error: + raise ImportError( + "The differentiable equilibrium interface requires VMEX. Install " + "pyqsc-jax with the 'vmex' extra, or install the current source with " + "'python -m pip install git+https://github.com/uwplasma/vmex.git'." + ) from error + missing = tuple( + name for name in ("VmecInput", "implicit", "optimize") if not hasattr(module, name) + ) + if missing: + names = ", ".join(missing) + raise ImportError(f"The installed VMEX does not provide the required public API: {names}.") + return module + + +def _validated_surfaces(surfaces: Any) -> tuple[float, ...]: + values = tuple(float(value) for value in surfaces) + if any(not np.isfinite(value) or value <= 0 or value > 1 for value in values): + raise ValueError("Every VMEX quasisymmetry surface must satisfy 0 < s <= 1.") + if any(right <= left for left, right in zip(values, values[1:], strict=False)): + raise ValueError("VMEX quasisymmetry surfaces must be strictly increasing.") + return values + + +def _validated_radial_controls( + ns_array: Any, + ftol_array: Any | None, + *, + ftol: float, + max_iterations: int, +) -> tuple[tuple[int, ...], tuple[float, ...], tuple[int, ...]]: + ns = tuple(int(value) for value in ns_array) + if not ns or any(value < 3 for value in ns): + raise ValueError("ns_array must be nonempty and every radial resolution must be >= 3.") + if any(right <= left for left, right in zip(ns, ns[1:], strict=False)): + raise ValueError("ns_array must be strictly increasing.") + if not np.isfinite(ftol) or ftol <= 0: + raise ValueError("ftol must be positive and finite.") + if ( + not isinstance(max_iterations, int) + or isinstance(max_iterations, bool) + or max_iterations < 1 + ): + raise ValueError("max_iterations must be a positive integer.") + if ftol_array is None: + if len(ns) == 1: + tolerances = (float(ftol),) + else: + start = max(float(ftol), 1.0e-8) + tolerances = tuple(float(value) for value in np.geomspace(start, ftol, len(ns))) + else: + tolerances = tuple(float(value) for value in ftol_array) + if len(tolerances) != len(ns) or any( + not np.isfinite(value) or value <= 0 for value in tolerances + ): + raise ValueError("ftol_array must contain one positive finite value per ns_array stage.") + return ns, tolerances, (int(max_iterations),) * len(ns) + + +def _is_asymmetric(boundary: VmecBoundary, tolerance: float = 1.0e-13) -> bool: + return ( + max( + float(jnp.max(jnp.abs(boundary.RBS))), + float(jnp.max(jnp.abs(boundary.ZBC))), + ) + > tolerance + ) + + +def _profile_arrays(parameters: Any, solution: NearAxisSolution, radius: Any): + radius = jnp.asarray(radius) + pressure_axis = -solution.inputs.p2 * radius**2 + am = jnp.zeros_like(parameters.am) + am = am.at[0].set(pressure_axis) + if am.shape[0] > 1: + am = am.at[1].set(-pressure_axis) + ac = jnp.zeros_like(parameters.ac).at[0].set(1.0) + phiedge = jnp.pi * radius**2 * solution.inputs.B0 + curtor = 2 * jnp.pi * solution.inputs.I2 * radius**2 / MU0 + return am, ac, phiedge, curtor + + +def vmex_parameters_from_solution( + problem: VmexProblem, + solution: NearAxisSolution, + *, + radius: Any | None = None, +) -> Any: + """Traceably map a near-axis boundary and profiles to VMEX parameters. + + The problem fixes discrete resolution, topology, and solver controls. + Boundary coefficients, toroidal flux, pressure, and enclosed current + remain JAX values, so gradients can propagate from a newly constructed + :class:`NearAxisSolution` through VMEX's converged fixed point. + """ + + if solution.inputs.axis.nfp != problem.input.nfp: + raise ValueError("The new solution must have the problem's number of field periods.") + selected_radius = problem.radius if radius is None else radius + boundary = vmec_boundary( + solution, + selected_radius, + ntheta=problem.ntheta, + mpol=problem.mpol, + ntor=problem.ntor, + newton_iterations=problem.newton_iterations, + ) + am, ac, phiedge, curtor = _profile_arrays(problem.parameters, solution, selected_radius) + return dataclasses.replace( + problem.parameters, + rbc=boundary.RBC, + rbs=boundary.RBS, + zbc=boundary.ZBC, + zbs=boundary.ZBS, + phiedge=phiedge, + curtor=curtor, + pres_scale=jnp.asarray(1.0, dtype=phiedge.dtype), + am=am, + ac=ac, + ) + + +def to_vmex_problem( + solution: NearAxisSolution, + *, + r: float = 0.03, + qs_surfaces: Any = (0.25, 0.5, 0.75, 1.0), + helicity_m: int = 1, + helicity_n: int | None = None, + ntheta: int = 24, + mpol: int = 6, + ntor: int = 6, + newton_iterations: int = 6, + ns_array: Any = (15, 31), + ftol_array: Any | None = None, + ftol: float = 1.0e-10, + max_iterations: int = 5000, + multigrid: bool = True, + device: Any = None, +) -> VmexProblem: + """Create a differentiable fixed-boundary VMEX problem without disk I/O. + + ``mpol`` is the maximum retained poloidal Fourier index in the + pyQSC_JAX conversion. VMEX therefore receives ``MPOL = mpol + 1``. + Pressure and current use the same near-axis-consistent profiles as + :func:`pyqsc_jax.to_vmec`. + """ + + vmex = _import_vmex() + radius = float(r) + if not np.isfinite(radius) or radius <= 0: + raise ValueError("r must be positive and finite.") + surfaces = _validated_surfaces(qs_surfaces) + ns, tolerances, iteration_limits = _validated_radial_controls( + ns_array, + ftol_array, + ftol=ftol, + max_iterations=max_iterations, + ) + if not isinstance(helicity_m, int) or isinstance(helicity_m, bool): + raise ValueError("helicity_m must be an integer.") + if helicity_n is None: + helicity_n = -int(np.asarray(solution.helicity)) + if not isinstance(helicity_n, int) or isinstance(helicity_n, bool): + raise ValueError("helicity_n must be an integer.") + + boundary = vmec_boundary( + solution, + radius, + ntheta=ntheta, + mpol=mpol, + ntor=ntor, + newton_iterations=newton_iterations, + ) + lasym = _is_asymmetric(boundary) + if lasym and surfaces: + raise NotImplementedError( + "VMEX's traceable quasisymmetry profile currently supports " + "stellarator-symmetric equilibria only; pass qs_surfaces=() to " + "solve an asymmetric equilibrium without that diagnostic." + ) + + inputs = solution.inputs + axis = inputs.axis + arrays = tuple( + np.asarray(jax.device_get(value)) + for value in (boundary.RBC, boundary.RBS, boundary.ZBC, boundary.ZBS) + ) + rbc, rbs, zbc, zbs = arrays + pressure_axis = -float(inputs.p2) * radius**2 + am = np.zeros(21) + am[:2] = (pressure_axis, -pressure_axis) + ac = np.zeros(21) + ac[0] = 1.0 + vmex_input = vmex.VmecInput( + lasym=lasym, + lfreeb=False, + nfp=axis.nfp, + mpol=boundary.RBC.shape[1], + ntor=boundary.ntor, + ns_array=np.asarray(ns), + ftol_array=np.asarray(tolerances), + niter_array=np.asarray(iteration_limits), + delt=0.9, + tcon0=2.0, + phiedge=np.pi * radius**2 * float(inputs.B0), + pres_scale=1.0, + am=am, + ncurr=1, + ac=ac, + curtor=2 * np.pi * float(inputs.I2) * radius**2 / MU0, + raxis_c=np.asarray(axis.rc), + raxis_s=-np.asarray(axis.rs), + zaxis_c=np.asarray(axis.zc), + zaxis_s=-np.asarray(axis.zs), + rbc=rbc, + rbs=rbs, + zbc=zbc, + zbs=zbs, + ) + parameters = vmex.implicit.params_from_input(vmex_input, device=device) + problem = VmexProblem( + input=vmex_input, + parameters=parameters, + boundary=boundary, + radius=radius, + qs_surfaces=surfaces, + helicity_m=helicity_m, + helicity_n=helicity_n, + ntheta=ntheta, + mpol=mpol, + ntor=ntor, + newton_iterations=newton_iterations, + ftol=float(ftol), + max_iterations=max_iterations, + multigrid=bool(multigrid), + device=device, + vmex_version=str(vmex.__version__), + ) + return dataclasses.replace( + problem, + parameters=vmex_parameters_from_solution(problem, solution), + ) + + +def _radial_quantities(problem: VmexProblem, vmex_solution: Any) -> VmexRadialQuantities: + vmex = _import_vmex() + runtime = vmex_solution.runtime + if runtime is None: + raise RuntimeError("VMEX did not retain the runtime required for radial diagnostics.") + iota_vmec = vmex.implicit.iota_profile(vmex_solution.state, runtime) + s = jnp.linspace(0.0, 1.0, iota_vmec.shape[0], dtype=iota_vmec.dtype) + surfaces = jnp.asarray(problem.qs_surfaces, dtype=iota_vmec.dtype) + if problem.qs_surfaces: + qs = vmex.optimize.QuasisymmetryRatioResidual( + problem.qs_surfaces, + problem.helicity_m, + problem.helicity_n, + ) + quasisymmetry = qs.profile_state(vmex_solution.state, runtime) + else: + quasisymmetry = jnp.zeros((0,), dtype=iota_vmec.dtype) + return VmexRadialQuantities( + s=s, + iota=-iota_vmec, + iota_vmec=iota_vmec, + qs_surfaces=surfaces, + quasisymmetry=quasisymmetry, + magnetic_well=vmex.optimize.magnetic_well(vmex_solution.state, runtime), + aspect=vmex.optimize.aspect_ratio(vmex_solution.state, runtime), + volume=vmex.optimize.volume(vmex_solution.state, runtime), + magnetic_energy=vmex_solution.wb, + thermal_energy=vmex_solution.wp, + ) + + +def solve_vmex(problem: VmexProblem, parameters: Any | None = None) -> VmexEquilibrium: + """Solve one VMEX problem with implicit-AD-compatible parameters.""" + + vmex = _import_vmex() + selected_parameters = problem.parameters if parameters is None else parameters + solution = vmex.implicit.run( + problem.input, + selected_parameters, + ftol=problem.ftol, + max_iterations=problem.max_iterations, + multigrid=problem.multigrid, + device=problem.device, + ) + return VmexEquilibrium( + solution=solution, + quantities=_radial_quantities(problem, solution), + ) + + +def vmex_radial_quantities( + problem: VmexProblem, + parameters: Any | None = None, +) -> VmexRadialQuantities: + """Solve and return only the differentiable VMEX diagnostic pytree.""" + + return solve_vmex(problem, parameters).quantities diff --git a/tests/integration/test_vmex_live.py b/tests/integration/test_vmex_live.py new file mode 100644 index 0000000..a0b9484 --- /dev/null +++ b/tests/integration/test_vmex_live.py @@ -0,0 +1,69 @@ +from __future__ import annotations + +import os + +import jax +import numpy as np +import pytest + +import pyqsc_jax as qsc + +RUN_VMEX = os.environ.get("PYQSC_RUN_VMEX") == "1" +pytestmark = [ + pytest.mark.integration, + pytest.mark.slow, + pytest.mark.skipif(not RUN_VMEX, reason="Set PYQSC_RUN_VMEX=1 for live VMEX tests."), +] + + +def _problem(solution): + return qsc.to_vmex_problem( + solution, + r=0.02, + ntheta=8, + mpol=3, + ntor=2, + ns_array=(7,), + ftol=1.0e-7, + max_iterations=1200, + multigrid=False, + qs_surfaces=(0.5, 1.0), + ) + + +def test_vmex_vacuum_profiles_and_implicit_gradient(): + solution = qsc.solve_configuration("qa", nphi=31) + problem = _problem(solution) + result = problem.solve() + quantities = result.quantities + + assert problem.vmex_version + assert quantities.iota.shape == quantities.s.shape == (7,) + assert quantities.quasisymmetry.shape == (2,) + assert np.all(np.isfinite(np.asarray(quantities.iota))) + assert np.all(np.isfinite(np.asarray(quantities.quasisymmetry))) + np.testing.assert_allclose(quantities.iota[0], solution.iota, rtol=8.0e-3) + assert float(quantities.thermal_energy) == pytest.approx(0.0, abs=1.0e-14) + + value, gradient = jax.value_and_grad( + lambda parameters: ( + qsc.vmex_radial_quantities( + problem, + parameters, + ).magnetic_well + ) + )(problem.parameters) + assert np.isfinite(float(value)) + assert np.all(np.isfinite(np.asarray(gradient.rbc))) + assert float(np.linalg.norm(np.asarray(gradient.rbc))) > 0 + + +def test_vmex_finite_beta_profiles(): + solution = qsc.solve_configuration("plasma_stellarator", nphi=31) + problem = _problem(solution) + quantities = problem.quantities() + + assert problem.finite_beta + assert float(quantities.thermal_energy) > 0 + assert np.all(np.isfinite(np.asarray(quantities.iota))) + assert np.all(np.isfinite(np.asarray(quantities.quasisymmetry))) diff --git a/tests/physics/test_plasma_field.py b/tests/physics/test_plasma_field.py index 7283eac..0031197 100644 --- a/tests/physics/test_plasma_field.py +++ b/tests/physics/test_plasma_field.py @@ -209,6 +209,26 @@ def test_documented_plasma_dominant_case_exceeds_thirty_percent(): ) +@pytest.mark.physics +def test_documented_plasma_stellarator_is_dominant_and_angle_dependent(): + solution = qsc.solve_configuration("plasma_stellarator", nphi=121) + formal_radius = 0.2 + plasma = qsc.plasma_field_on_axis( + solution, + formal_radius=formal_radius, + angular_resolution=128, + ) + plasma_norm = np.linalg.norm(np.asarray(plasma.field), axis=-1) + total_norm = np.linalg.norm(np.asarray(solution.B_axis), axis=-1) + fraction = plasma_norm / total_norm + peak_to_peak_over_mean = np.ptp(plasma_norm) / np.mean(plasma_norm) + + assert np.min(fraction) > 0.30 + assert peak_to_peak_over_mean > 0.03 + assert formal_radius / float(solution.r_singularity) < 0.60 + np.testing.assert_allclose(np.mean(fraction), 0.33255168104046495, rtol=3.0e-12) + + def test_plasma_field_guards(): solution = circular_solution() with pytest.raises(ValueError, match="angular_resolution"): diff --git a/tests/unit/test_configurations.py b/tests/unit/test_configurations.py index 910c96d..dfa0583 100644 --- a/tests/unit/test_configurations.py +++ b/tests/unit/test_configurations.py @@ -13,6 +13,7 @@ def test_named_configurations_are_immutable_and_solve(): "finite_pressure_current", "b20_optimized_qa", "plasma_dominant_channel", + "plasma_stellarator", ) qa = qsc.get_configuration("qa") first_parameters = qa.parameters(nphi=15) diff --git a/tests/unit/test_plotting.py b/tests/unit/test_plotting.py index 8bd020e..8d909bb 100644 --- a/tests/unit/test_plotting.py +++ b/tests/unit/test_plotting.py @@ -5,7 +5,15 @@ import pytest import pyqsc_jax as qsc -from pyqsc_jax.plotting import plot_axis, plot_b20, plot_field_jet_norms +from pyqsc_jax.plotting import ( + field_split_frenet_components, + plot_axis, + plot_b20, + plot_field_jet_norms, + plot_field_split_components, + plot_surface_3d, + surface_coordinates, +) matplotlib.use("Agg") @@ -39,6 +47,25 @@ def test_field_jet_norm_plotter_and_axes_guard(): plot_field_jet_norms(result, axes=axes[:2]) +def test_surface_and_angle_dependent_field_split_plotters(): + solution = qsc.solve_configuration("plasma_stellarator", nphi=31) + x, y, z = surface_coordinates(solution, radius=0.05, ntheta=12) + figure, axis = plot_surface_3d(solution, radius=0.05, ntheta=12) + result = qsc.plasma_hessian_on_axis(solution, formal_radius=0.1) + components = field_split_frenet_components(result, solution) + component_figure, axes = plot_field_split_components(result, solution) + + assert x.shape == y.shape == z.shape == (12, 63) + assert axis.figure is figure + assert len(axis.collections) == 1 + assert components.shape == (3, 3, 31) + assert axes.shape == (3,) + assert component_figure is axes[0].figure + assert all(len(item.lines) == 3 for item in axes) + with pytest.raises(ValueError, match="three"): + plot_field_split_components(result, solution, axes=axes[:2]) + + def test_plotter_guards(): first_order = qsc.solve_configuration("qa", nphi=15, order="r1") with pytest.raises(ValueError, match="r2"): @@ -47,3 +74,7 @@ def test_plotter_guards(): plot_axis(first_order, samples=3) with pytest.raises(TypeError, match="Axis"): plot_axis(object()) + with pytest.raises(ValueError, match="positive"): + surface_coordinates(first_order, radius=0) + with pytest.raises(ValueError, match="integer"): + surface_coordinates(first_order, ntheta=3) diff --git a/tests/unit/test_vmex_interface.py b/tests/unit/test_vmex_interface.py new file mode 100644 index 0000000..7ff9ba5 --- /dev/null +++ b/tests/unit/test_vmex_interface.py @@ -0,0 +1,253 @@ +from __future__ import annotations + +from dataclasses import dataclass +from types import SimpleNamespace + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +import pyqsc_jax as qsc +from pyqsc_jax import vmex as bridge + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class FakeParams: + rbc: jax.Array + rbs: jax.Array + zbc: jax.Array + zbs: jax.Array + phiedge: jax.Array + pres_scale: jax.Array + curtor: jax.Array + am: jax.Array + ai: jax.Array + ac: jax.Array + + +class FakeVmecInput: + def __init__(self, **kwargs): + for name, value in kwargs.items(): + setattr(self, name, value) + + +class FakeImplicit: + @staticmethod + def params_from_input(inp, *, device=None): + del device + return FakeParams( + rbc=jnp.asarray(inp.rbc), + rbs=jnp.asarray(inp.rbs), + zbc=jnp.asarray(inp.zbc), + zbs=jnp.asarray(inp.zbs), + phiedge=jnp.asarray(inp.phiedge), + pres_scale=jnp.asarray(inp.pres_scale), + curtor=jnp.asarray(inp.curtor), + am=jnp.asarray(inp.am), + ai=jnp.zeros(21), + ac=jnp.asarray(inp.ac), + ) + + @staticmethod + def run(_inp, params, **_kwargs): + return SimpleNamespace( + state=params, + runtime=SimpleNamespace(), + wb=jnp.sum(params.rbc**2), + wp=params.am[0], + ) + + @staticmethod + def iota_profile(state, _runtime): + return jnp.linspace(0.4, 0.5, 7) + 1.0e-4 * jnp.sum(state.rbc) + + +class FakeQuasisymmetry: + def __init__(self, surfaces, helicity_m, helicity_n): + self.surfaces = jnp.asarray(surfaces) + self.helicity = helicity_m + helicity_n + + def profile_state(self, state, _runtime): + return self.surfaces**2 + self.helicity + 1.0e-5 * jnp.sum(state.rbc) + + +class FakeOptimize: + QuasisymmetryRatioResidual = FakeQuasisymmetry + + @staticmethod + def magnetic_well(state, _runtime): + return 0.1 * state.am[0] + 1.0e-3 * jnp.sum(state.rbc) + + @staticmethod + def aspect_ratio(state, _runtime): + return 5.0 + 1.0e-3 * jnp.sum(state.rbc) + + @staticmethod + def volume(state, _runtime): + return jnp.abs(state.phiedge) * 10.0 + + +@pytest.fixture +def fake_vmex(monkeypatch): + module = SimpleNamespace( + __version__="test", + VmecInput=FakeVmecInput, + implicit=FakeImplicit, + optimize=FakeOptimize, + ) + monkeypatch.setattr(bridge, "_import_vmex", lambda: module) + return module + + +def qa_solution(*, asymmetric=False): + return qsc.Qsc( + rc=[1.0, 0.045], + rs=[0.0, 0.005] if asymmetric else [0.0, 0.0], + zc=[0.0, 0.01] if asymmetric else [0.0, 0.0], + zs=[0.0, -0.045], + nfp=3, + etabar=-0.9, + nphi=15, + order="r2", + ) + + +def make_problem(fake_vmex, solution=None, **kwargs): + del fake_vmex + options = { + "r": 0.02, + "ntheta": 8, + "mpol": 3, + "ntor": 2, + "ns_array": (7,), + "ftol": 1.0e-7, + "max_iterations": 200, + "multigrid": False, + "qs_surfaces": (0.5, 1.0), + } + options.update(kwargs) + return qsc.to_vmex_problem(solution if solution is not None else qa_solution(), **options) + + +def test_problem_builds_without_disk_and_exposes_quantities(fake_vmex): + problem = make_problem(fake_vmex) + result = problem.solve() + quantities = result.quantities + + assert problem.vmex_version == "test" + assert problem.validated_commit == qsc.VMEX_VALIDATED_COMMIT + assert problem.input.mpol == 4 + assert problem.boundary.RBC.shape == (5, 4) + assert not problem.finite_beta + assert quantities.s.shape == quantities.iota.shape == (7,) + np.testing.assert_allclose(quantities.iota, -quantities.iota_vmec) + assert quantities.quasisymmetry.shape == (2,) + assert np.isfinite(float(quantities.magnetic_well)) + + +def test_finite_beta_and_traceable_parameter_remap(fake_vmex): + solution = qsc.solve_configuration("plasma_stellarator", nphi=15) + problem = make_problem(fake_vmex, solution=solution) + assert problem.finite_beta + + def objective(etabar): + candidate = qsc.solve( + axis=solution.inputs.axis, + etabar=etabar, + B0=solution.inputs.B0, + B2c=solution.inputs.B2c, + I2=solution.inputs.I2, + p2=solution.inputs.p2, + nphi=15, + order="r2", + ) + parameters = problem.parameters_for(candidate, radius=0.018) + return qsc.vmex_radial_quantities(problem, parameters).magnetic_well + + value, derivative = jax.value_and_grad(objective)(solution.inputs.etabar) + assert np.isfinite(float(value)) + assert np.isfinite(float(derivative)) + assert float(problem.quantities().thermal_energy) > 0 + + +def test_empty_qs_surface_list_supports_asymmetric_equilibrium(fake_vmex): + problem = make_problem(fake_vmex, solution=qa_solution(asymmetric=True), qs_surfaces=()) + assert problem.input.lasym + assert problem.quantities().quasisymmetry.shape == (0,) + + +@pytest.mark.parametrize( + ("kwargs", "message"), + [ + ({"r": 0.0}, "positive"), + ({"qs_surfaces": (0.0,)}, "0 < s"), + ({"qs_surfaces": (0.75, 0.5)}, "increasing"), + ({"ns_array": ()}, "nonempty"), + ({"ns_array": (7, 7)}, "increasing"), + ({"ftol": 0.0}, "positive"), + ({"ftol_array": (1.0e-7, 1.0e-8)}, "one positive"), + ({"max_iterations": 0}, "positive integer"), + ({"helicity_m": 1.5}, "integer"), + ({"helicity_n": 1.5}, "integer"), + ], +) +def test_problem_validation(fake_vmex, kwargs, message): + with pytest.raises(ValueError, match=message): + make_problem(fake_vmex, **kwargs) + + +def test_asymmetric_quasisymmetry_guard(fake_vmex): + with pytest.raises(NotImplementedError, match="stellarator-symmetric"): + make_problem(fake_vmex, solution=qa_solution(asymmetric=True)) + + +def test_parameter_remap_rejects_changed_field_period(fake_vmex): + problem = make_problem(fake_vmex) + changed = qsc.Qsc( + rc=[1.0, 0.02], + zs=[0.0, -0.02], + nfp=2, + etabar=-0.9, + nphi=15, + order="r2", + ) + with pytest.raises(ValueError, match="field periods"): + problem.parameters_for(changed) + + +def test_runtime_and_import_guards(fake_vmex, monkeypatch): + problem = make_problem(fake_vmex) + vmex = bridge._import_vmex() + monkeypatch.setattr( + vmex.implicit, + "run", + lambda *_args, **_kwargs: SimpleNamespace( + state=problem.parameters, + runtime=None, + wb=0.0, + wp=0.0, + ), + ) + with pytest.raises(RuntimeError, match="runtime"): + problem.solve() + + monkeypatch.undo() + monkeypatch.setattr( + bridge.importlib, + "import_module", + lambda _name: (_ for _ in ()).throw(ImportError("missing")), + ) + with pytest.raises(ImportError, match="requires VMEX"): + bridge._import_vmex() + + +def test_incomplete_vmex_api_is_rejected(monkeypatch): + monkeypatch.setattr( + bridge.importlib, + "import_module", + lambda _name: SimpleNamespace(VmecInput=FakeVmecInput), + ) + with pytest.raises(ImportError, match="implicit, optimize"): + bridge._import_vmex() From 29cd09414f8e6a35cde483089c190eb2a02dd118 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 10:17:31 -0500 Subject: [PATCH 30/39] docs: showcase optimized and finite-beta stellarators --- CHANGELOG.md | 11 +- README.md | 97 ++++++++++- docs/_static/B20_optimization.png | Bin 106860 -> 248394 bytes docs/_static/plasma_external_jet.png | Bin 32798 -> 194314 bytes docs/_static/stellarator_gallery.png | Bin 0 -> 496471 bytes docs/_static/vmex_radial_profiles.png | Bin 0 -> 171144 bytes docs/advanced/limitations.md | 5 + docs/advanced/performance.md | 20 +++ docs/api/plotting.md | 16 ++ docs/api/vmex.md | 35 ++++ docs/development/physics-traceability.md | 1 + docs/development/refactor_status.md | 21 +++ docs/getting_started/choosing_a_model.md | 1 + docs/getting_started/installation.md | 12 +- docs/index.md | 3 + docs/theory/b20-optimization.md | 7 +- docs/tutorials/vmex_equilibrium.md | 46 +++++ docs/validation/plasma_field.md | 35 ++-- docs/validation/vmex_interface.md | 70 ++++++++ examples/10_plasma_external_field_jet.py | 9 +- examples/14_vmex_radial_profiles.py | 76 +++++++++ .../publication/figure_B20_optimization.py | 63 +++++-- .../publication/figure_plasma_external_jet.py | 67 ++++++-- .../publication/figure_stellarator_gallery.py | 81 +++++++++ .../figure_vmex_radial_profiles.py | 160 ++++++++++++++++++ 25 files changed, 783 insertions(+), 53 deletions(-) create mode 100644 docs/_static/stellarator_gallery.png create mode 100644 docs/_static/vmex_radial_profiles.png create mode 100644 docs/api/vmex.md create mode 100644 docs/tutorials/vmex_equilibrium.md create mode 100644 docs/validation/vmex_interface.md create mode 100644 examples/14_vmex_radial_profiles.py create mode 100644 examples/publication/figure_stellarator_gallery.py create mode 100644 examples/publication/figure_vmex_radial_profiles.py diff --git a/CHANGELOG.md b/CHANGELOG.md index b370f87..7358c21 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -9,6 +9,15 @@ first stable release. ### Added +- Optional, lazy pyQSC_JAX-to-VMEX bridge for differentiable fixed-boundary + radial \(\iota\), quasisymmetry, magnetic-well, energy, volume, and + aspect-ratio quantities in vacuum and finite beta, with a live current-VMEX + compatibility job. +- Full-torus 3D surface helpers and a four-stellarator README gallery covering + QA, QH, the \(B_{20}\)-optimized case, and the finite-current plasma case. +- `plasma_stellarator`, an angle-dependent finite-pressure/current case whose + minimum plasma-field fraction is 32.70%, whose plasma-field norm varies by + 3.53%, and whose formal radius remains inside the singular surface. - Vectorized, JIT-compiled VMEC boundary export with all four coefficient families, deterministic INDATA output, conversion diagnostics, legacy-adapter support, a frozen VMEC 9.0 `wout` regression, and an opt-in @@ -93,7 +102,7 @@ first stable release. seven-component Cartesian STF representation. - Named immutable QA, QH, and finite-pressure/current configurations. - Lazy plotting helpers that return Matplotlib figure and axes objects. -- Twelve direct tutorial scripts and five deterministic publication-figure +- Fourteen direct tutorial scripts and eight deterministic publication-figure scripts with commit/parameter metadata and clean-directory CI execution. - Downstream ESSOS external-field-jet integration with normalized 3+5+7 objectives, finite-beta stage-two and single-stage examples, and diff --git a/README.md b/README.md index 833d5f1..82e7c4b 100644 --- a/README.md +++ b/README.md @@ -14,13 +14,20 @@ plasma–coil field jets in JAX. > compatibility, and external 3+5+7 field-jet paths are validated; release > hardening is still in progress. -| QA and QH near-axis surfaces | Exact affine \(B_{2c}\) elimination | +![QA, QH, B20-optimized, and finite-current stellarators](docs/_static/stellarator_gallery.png) + +Four runnable configurations: vacuum QA and QH references, the +\(B_{20}\)-optimized QA surface, and an angle-dependent finite-current +stellarator. Every displayed surface reports its transform and/or singular +radius; the plotting radius is recorded in the figure metadata. + +| \(B_{20}\) optimization, geometry, and singular margin | Angle-dependent plasma/external field | | --- | --- | -| ![QA and QH surfaces](docs/_static/axis_and_surfaces.png) | ![B20 optimization](docs/_static/B20_optimization.png) | +| ![B20 optimization](docs/_static/B20_optimization.png) | ![Plasma and external jet](docs/_static/plasma_external_jet.png) | -| Total/plasma/external field jet | VMEC export validation | +| Differentiable radial VMEX quantities | VMEC2000 export validation | | --- | --- | -| ![Plasma and external jet](docs/_static/plasma_external_jet.png) | ![VMEC validation](docs/_static/vmec_validation.png) | +| ![VMEX radial quantities](docs/_static/vmex_radial_profiles.png) | ![VMEC validation](docs/_static/vmec_validation.png) | ## Install @@ -31,6 +38,12 @@ python -m pip install pyqsc-jax Install the JAX build appropriate for your CPU or accelerator. pyQSC_JAX does not configure a backend or enable 64-bit mode at import time. +For 3D plots and differentiable finite-radius equilibria: + +```bash +python -m pip install 'pyqsc-jax[plot,vmex]' +``` + ## Quickstart ```python @@ -59,6 +72,17 @@ The result is an immutable JAX pytree. Canonical field arrays use sample-first ordering: `(nphi, 3)`, `(nphi, 3, 3)`, and `(nphi, 3, 3, 3)`. +## Pick a workflow + +| Goal | Start here | Main result | +| --- | --- | --- | +| Construct QA/QH near the axis | `qsc.Qsc(...)` | immutable near-axis solution | +| Flatten \(B_{20}\) | `optimize_B2c`, `search_axis` | verified dense-grid diagnostics | +| Inspect a full 3D surface | `plot_surface_3d` | figure plus explicit plotting radius | +| Compute radial MHD quantities | `to_vmex_problem(...).solve()` | differentiable \(\iota(s)\), QS profile, magnetic well | +| Match finite-beta coils | `plasma_hessian_on_axis` | external vacuum 3+5+7 target | +| Run conventional VMEC2000 | `to_vmec` | diagnosed `input.*` file | + ## Capabilities | Capability | Status | @@ -73,6 +97,7 @@ sample-first ordering: `(nphi, 3)`, `(nphi, 3, 3)`, and | Surface-free plasma field, gradient, Hessian | Validated asymptotic model | | External vacuum 3+5+7 field-jet target | Validated | | Fast fixed-boundary VMEC export, including asymmetric boundaries | Validated against VMEC 9.0 | +| Differentiable VMEX radial iota, QS profile, magnetic well | Validated in vacuum and finite beta | | ESSOS vacuum/finite-beta stage-two and single-stage objectives | Draft integration PR | | Legacy `pyqsc_jax.near_axis.near_axis` contract | Preserved | @@ -88,7 +113,9 @@ resolution, timing, and radius-convergence tables are in the | --- | ---: | ---: | | Optimized QA \(B_{20}\), weighted \(L^2\), `nphi=121` | \(1.5901\times10^{-6}\) | \(<1.6\times10^{-6}\) | | Improvement over stock-axis exact-\(B_{2c}\) solve | \(26{,}053\times\) | \(>25{,}000\times\) | -| Minimum \(\lvert B_\mathrm{plasma}\rvert/\lvert B_\mathrm{total}\rvert\) | 33.26% | \(>30\%\) | +| \(B_{20}\)-optimized singular radius | 0.248 m | displayed \(r=0.075\) m gives 3.3× clearance | +| Angle-dependent minimum \(\lvert B_\mathrm{plasma}\rvert/\lvert B_\mathrm{total}\rvert\) | 32.70% | \(>30\%\) | +| Plasma-field norm peak-to-peak / mean | 3.53% | \(>3\%\) | | VMEC/near-axis on-axis \(\iota\), \(r=0.0025\) | 0.418543 / 0.418307 | relative error \(<0.1\%\) | | VMEC force residuals | \(2.4\)–\(7.6\times10^{-11}\) | maximum \(<10^{-9}\) | | `to_vmec`, Apple M4 CPU, compile+execute / warm | 0.476 s / 5.20 ms | warm unit gate \(<0.5\) s | @@ -98,7 +125,7 @@ optimized = qsc.solve_configuration("b20_optimized_qa", nphi=121) diagnostics = qsc.b20_diagnostics(optimized) print(diagnostics.weighted_l2, diagnostics.grid_maximum) -plasma_case = qsc.solve_configuration("plasma_dominant_channel", nphi=61) +plasma_case = qsc.solve_configuration("plasma_stellarator", nphi=61) plasma = qsc.plasma_field_on_axis(plasma_case, formal_radius=0.2) ``` @@ -137,10 +164,27 @@ Only `verified_zero` certifies the known zero lower bound of the nonnegative primary \(B_{20}\) residual. A nonzero result is `best_found`, never a mathematical global-minimum claim. +## The \(B_{20}\)-optimized stellarator in 3D + +```python +from pyqsc_jax.plotting import plot_surface_3d + +optimized = qsc.solve_configuration("b20_optimized_qa", nphi=121) +figure, axis = plot_surface_3d(optimized, radius=0.075) + +print(optimized.B20_residual) # 1.5901e-6 T/m^2 +print(optimized.r_singularity) # 0.248 m +``` + +The displayed surface is therefore 3.3 times inside the computed singular +radius. The optimizer comparison, Fourier-resolution audit, full coefficient +set, and the distinction between `best_found` and a certified zero are in the +[B20 optimization notes](docs/theory/b20-optimization.md). + ## Finite-beta coil targets ```python -solution = qsc.solve_configuration("plasma_dominant_channel", nphi=61) +solution = qsc.solve_configuration("plasma_stellarator", nphi=61) target = qsc.plasma_hessian_on_axis(solution, formal_radius=0.2) print(target.field.external_field.shape) # (nphi, 3) @@ -152,6 +196,44 @@ ESSOS consumes these external vacuum targets for normalized field, gradient, and Hessian coil objectives. The dependency remains one-way: `ESSOS -> pyQSC_JAX`. +The public plot uses Frenet components rather than only \(|B|\). This makes +the angle dependence and exact cancellation of plasma and external transverse +components visible; \(|B_\mathrm{total}|=B_0\) is constant on axis by +construction. + +## Differentiable radial equilibria with VMEX + +```python +import jax + +near_axis = qsc.solve_configuration("qa", nphi=61) +problem = qsc.to_vmex_problem( + near_axis, + r=0.02, + qs_surfaces=(0.25, 0.5, 0.75, 1.0), +) +equilibrium = problem.solve() + +print(equilibrium.quantities.iota) # full radial profile +print(equilibrium.quantities.quasisymmetry) # requested flux surfaces +print(equilibrium.quantities.magnetic_well) + +well, gradient = jax.value_and_grad( + lambda parameters: qsc.vmex_radial_quantities( + problem, parameters + ).magnetic_well +)(problem.parameters) +print(gradient.rbc, gradient.pres_scale) +``` + +`problem.parameters_for(new_near_axis_solution)` traceably rebuilds the +boundary, flux, pressure, and current leaves, allowing derivatives to +propagate from pyQSC_JAX variables through VMEX's converged fixed point. +Vacuum and scalar finite-beta fixed-boundary paths are tested against +[uwplasma/VMEX](https://github.com/uwplasma/vmex); the exact validated commit +and current limitations are recorded in the +[VMEX integration validation](docs/validation/vmex_interface.md). + ## VMEC export ```python @@ -182,6 +264,7 @@ executable. - [API reference](docs/api/) - [pyQSC, literature, plasma, and ESSOS validation](docs/validation/) - [VMEC conversion, equilibrium, and performance validation](docs/validation/vmec.md) +- [Differentiable VMEX radial-equilibrium validation](docs/validation/vmex_interface.md) - [Migration from pyQSC and the legacy adapter](docs/migration.md) - [Known limitations](docs/advanced/limitations.md) diff --git a/docs/_static/B20_optimization.png b/docs/_static/B20_optimization.png index 884c121c66ce510924ed5ec87f79ff9eae3858c9..568331f0500b58ae223520f7f276003eef3fd7fc 100644 GIT binary patch literal 248394 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b/docs/advanced/limitations.md index e4677ca..09e79fd 100644 --- a/docs/advanced/limitations.md +++ b/docs/advanced/limitations.md @@ -12,6 +12,11 @@ existence. - Plasma-field and Hessian remainder fields are asymptotic scales, not rigorous bounds. +- The optional VMEX bridge covers differentiable fixed-boundary equilibria. + It does not differentiate a reconverged free-boundary NESTOR root. +- Traceable VMEX quasisymmetry profiles currently require stellarator + symmetry; use `qs_surfaces=()` for an asymmetric equilibrium without QS. +- VMEX magnetic well is an endpoint scalar, not a radial profile. - “Surface-free” plasma/coil separation still requires a positive formal radius or equivalent current/flux normalization. - Coil feasibility and fast-particle confinement remain ESSOS or external diff --git a/docs/advanced/performance.md b/docs/advanced/performance.md index bc3f5fc..9a27df0 100644 --- a/docs/advanced/performance.md +++ b/docs/advanced/performance.md @@ -72,3 +72,23 @@ JAX_ENABLE_X64=true PYTHONPATH=src python benchmarks/benchmark_vmec_export.py The reported conversion timer excludes the near-axis solve and file-system startup. Both cold and warm calls synchronize the boundary arrays before stopping the timer. + +## VMEX implicit equilibrium + +The 5.20 ms number above is only the boundary conversion. A converged VMEX +equilibrium is a separate fixed-point solve. Its cold cost includes XLA +compilation and its gradient includes an implicit adjoint linear solve. + +The low-resolution live compatibility case (`ns=7`, `mpol=4`, `ntor=2`) took +23.1 s for a cold forward solve and 17.5 s for a subsequent magnetic-well +value-and-gradient on the development Apple CPU before persistent-cache +reuse. These are integration-smoke timings, not production performance +claims. Repeated optimization should reuse one `VmexProblem`, static shapes, +and VMEX's compilation cache. + +The synchronized benchmark that records the dependency versions, validated +VMEX commit, case parameters, objective value, and gradient norms is: + +```bash +JAX_ENABLE_X64=true PYTHONPATH=src python benchmarks/benchmark_vmex_interface.py +``` diff --git a/docs/api/plotting.md b/docs/api/plotting.md index e8fb453..08e8dca 100644 --- a/docs/api/plotting.md +++ b/docs/api/plotting.md @@ -8,6 +8,14 @@ implicitly. .. autofunction:: pyqsc_jax.plotting.plot_axis ``` +```{eval-rst} +.. autofunction:: pyqsc_jax.plotting.surface_coordinates +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.plotting.plot_surface_3d +``` + ```{eval-rst} .. autofunction:: pyqsc_jax.plotting.plot_b20 ``` @@ -15,3 +23,11 @@ implicitly. ```{eval-rst} .. autofunction:: pyqsc_jax.plotting.plot_field_jet_norms ``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.plotting.field_split_frenet_components +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.plotting.plot_field_split_components +``` diff --git a/docs/api/vmex.md b/docs/api/vmex.md new file mode 100644 index 0000000..be46906 --- /dev/null +++ b/docs/api/vmex.md @@ -0,0 +1,35 @@ +# VMEX equilibrium bridge + +VMEX is an optional dependency and is imported only when the equilibrium +bridge is used. + +```{eval-rst} +.. autoclass:: pyqsc_jax.VmexProblem + :members: +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.VmexEquilibrium + :members: +``` + +```{eval-rst} +.. autoclass:: pyqsc_jax.VmexRadialQuantities + :members: +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.to_vmex_problem +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.vmex_parameters_from_solution +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.solve_vmex +``` + +```{eval-rst} +.. autofunction:: pyqsc_jax.vmex_radial_quantities +``` diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index 31e07ec..ffe8850 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -25,6 +25,7 @@ to the cited source, not to a duplicated derivation in this repository. | Plasma Hessian | manuscript Eqs. 194 and 210–219 | `plasma.plasma_hessian_on_axis` | circular finite-conductor contact-term limit, QA/QH oriented ellipses, commuting plasma derivatives, spectral convergence, JIT/JVP/finite differences | implemented and documented | | External vacuum jet | manuscript Eqs. 218–224 | nested `PlasmaHessianData`; rank-2/rank-3 STF packers | 3+5+7 representation, full Hessian symmetry, trace-free gradient/Hessian, vacuum reduction, asymptotic error metadata | implemented and documented; normalized ESSOS objective remains | | VMEC fixed-boundary conversion | near-axis surface expansion plus VMEC Fourier boundary convention | `vmec.uniform_cylindrical_surface`; `vmec.vmec_boundary`; upstream pyQSC `to_vmec.py` as an independent comparison | vectorized/legacy surface agreement, Fourier reconstruction, asymmetric coefficients, deterministic input, warm timing, frozen and live VMEC on-axis iota and force residuals, radius convergence | implemented and documented | +| VMEX radial equilibrium | VMEX fixed-boundary ideal-MHD fixed point and public implicit adjoint | `vmex.to_vmex_problem`; `vmex.vmex_radial_quantities`; VMEX 0.3.0 commit `2a40d756` | vacuum and finite-beta live solves, radial iota sign audit, QS profile, magnetic well, boundary/profile gradients, current-main CI | implemented and documented | ## Source policy diff --git a/docs/development/refactor_status.md b/docs/development/refactor_status.md index 511e767..077e738 100644 --- a/docs/development/refactor_status.md +++ b/docs/development/refactor_status.md @@ -185,3 +185,24 @@ was made for that phase. and 5.20 ms warm at the documented high-resolution boundary setting. - Risk/next: on-axis-iota agreement is asymptotic and degrades at larger export radius as documented; remote CI and review remain external gates. + +## Phase 14 — VMEX radial equilibria and visual design audit + +- Files: optional VMEX bridge, live current-main compatibility job, radial + equilibrium tutorial and publication figure, full-torus 3D plotting + helpers, four-case gallery, and angle-dependent plasma configuration. +- Verification: vacuum and finite-beta VMEX solves; radial \(\iota\), QS, + magnetic-well, energy, and boundary-gradient checks; traceable + `parameters_for` differentiation; focused plotting and plasma regressions. +- Numerical checks: low-resolution vacuum VMEX/near-axis on-axis-\(\iota\) + difference 0.249%; finite-beta magnetic well + \(-4.2297\times10^{-4}\); angle-dependent minimum plasma-field fraction + 32.70%; optimized \(B_{20}\) surface shown 3.3 times inside its singular + radius. +- Performance: the VMEX smoke benchmark separates the converged forward solve + from the magnetic-well value-and-implicit-gradient cost; it is documented + as an integration timing, not a production throughput claim. +- Risk/next: VMEX quasisymmetry diagnostics currently require stellarator + symmetry and the bridge covers fixed-boundary implicit differentiation, not + a reconverged free-boundary NESTOR adjoint. Remote CI and review remain + external gates. diff --git a/docs/getting_started/choosing_a_model.md b/docs/getting_started/choosing_a_model.md index f9a4e58..cd189da 100644 --- a/docs/getting_started/choosing_a_model.md +++ b/docs/getting_started/choosing_a_model.md @@ -7,6 +7,7 @@ | Flux-consistent boundary and magnetic shear | `order="r3"` plus `solve_magnetic_shear` | r3 residuals and applicable sign restrictions | | Prescribed transform | `solve_for="etabar"` or `"I2"` | local response and fold flag | | Surface-free plasma/external target | `plasma_hessian_on_axis` | positive formal radius and asymptotic metadata | +| Radial iota, QS, and magnetic well | `to_vmex_problem` | VMEX convergence, implicit-gradient and resolution checks | | Legacy ESSOS consumer | `near_axis` adapter | compatibility orientation and mutable-DOF contract | Use the lowest order that supplies the observable being optimized. Higher diff --git a/docs/getting_started/installation.md b/docs/getting_started/installation.md index 12c718c..813cdfb 100644 --- a/docs/getting_started/installation.md +++ b/docs/getting_started/installation.md @@ -6,13 +6,21 @@ pyQSC_JAX requires Python 3.12 or newer. python -m pip install pyqsc-jax ``` -Install optional plotting or development tools explicitly: +Install optional plotting, VMEX equilibrium, or development tools explicitly: ```bash python -m pip install 'pyqsc-jax[plot]' +python -m pip install 'pyqsc-jax[plot,vmex]' git clone https://github.com/uwplasma/pyQSC_JAX.git cd pyQSC_JAX -python -m pip install -e '.[dev,docs,plot]' +python -m pip install -e '.[dev,docs,plot,vmex]' +``` + +The `vmex` extra enables differentiable fixed-boundary radial quantities. To +test the current upstream development head directly: + +```bash +python -m pip install 'git+https://github.com/uwplasma/vmex.git' ``` The project declares `jax`, not `jaxlib`, and never changes JAX configuration diff --git a/docs/index.md b/docs/index.md index fcb920f..21aaf5a 100644 --- a/docs/index.md +++ b/docs/index.md @@ -46,6 +46,7 @@ tutorials/second_order_finite_beta tutorials/target_iota tutorials/optimize_axis tutorials/vmec_export +tutorials/vmex_equilibrium tutorials/vacuum_coils tutorials/finite_beta_coils ``` @@ -70,6 +71,7 @@ validation/pyqsc_parity validation/literature_cases validation/plasma_field validation/vmec +validation/vmex_interface validation/essos migration ``` @@ -91,6 +93,7 @@ api/axis-optimization api/criteria api/plotting api/vmec +api/vmex ``` ```{toctree} diff --git a/docs/theory/b20-optimization.md b/docs/theory/b20-optimization.md index 49e262b..004b4e6 100644 --- a/docs/theory/b20-optimization.md +++ b/docs/theory/b20-optimization.md @@ -115,7 +115,12 @@ independent resolution checks: At `nphi=121`, its dense maximum is \(3.20\times10^{-6}\) and peak-to-peak variation is \(6.27\times10^{-6}\). This is 26,053 times smaller in weighted residual than exact \(B_{2c}\) optimization of the stock README QA axis. The -result is a verified numerical basin, not a proof that no other basin is +computed singular radius is 0.2484 m. The README surface is drawn at +0.075 m, so it has a 3.31-fold radial clearance relative to that truncated-map +diagnostic. Both numbers appear next to the actual 3D surface; a flat +\(B_{20}\) curve is not presented without its geometry. + +The result is a verified numerical basin, not a proof that no other basin is better. The runnable comparison is `benchmarks/benchmark_b20_optimizers.py`; its frozen report records the full environment and raw values. diff --git a/docs/tutorials/vmex_equilibrium.md b/docs/tutorials/vmex_equilibrium.md new file mode 100644 index 0000000..93393e0 --- /dev/null +++ b/docs/tutorials/vmex_equilibrium.md @@ -0,0 +1,46 @@ +# Differentiate radial equilibrium quantities with VMEX + +`to_vmec` writes a conventional VMEC2000 input. `to_vmex_problem` instead +constructs an in-memory [VMEX](https://github.com/uwplasma/vmex) problem and +keeps the boundary and profile parameters as JAX leaves. + +Install the optional dependency: + +```bash +python -m pip install 'pyqsc-jax[vmex,plot]' +``` + +The complete executable example is: + +```{literalinclude} ../../examples/14_vmex_radial_profiles.py +:language: python +``` + +The returned radial quantities are: + +- full-mesh rotational transform `iota`; +- the native-sign `iota_vmec` profile for convention audits; +- VMEX's differentiable quasisymmetry-ratio residual at each requested + normalized toroidal-flux surface; +- the canonical scalar magnetic well + \((V'(0)-V'(1))/V'(0)\); +- aspect ratio, volume, magnetic energy, and thermal energy. + +The call to `jax.value_and_grad` differentiates the converged fixed point by +VMEX's implicit adjoint. It does not unroll equilibrium iterations and does +not finite-difference a saved `wout`. + +For an outer pyQSC_JAX optimization, keep the discrete VMEX problem fixed and +traceably remap each candidate: + +```python +parameters = problem.parameters_for(candidate_solution) +objective = qsc.vmex_radial_quantities( + problem, + parameters, +).quasisymmetry.sum() +``` + +This updates the boundary Fourier arrays, toroidal flux, scalar pressure +profile, and current profile while preserving the VMEX resolution and +topology. diff --git a/docs/validation/plasma_field.md b/docs/validation/plasma_field.md index ae1105e..f5e3ec8 100644 --- a/docs/validation/plasma_field.md +++ b/docs/validation/plasma_field.md @@ -20,22 +20,35 @@ singular filament quadrature would omit those terms and is not treated as an independent reference. See the [matched field derivation](../theory/plasma-field.md) and `tests/physics/test_plasma_*.py`. -## Plasma-dominant regression case +## Plasma-dominant regression cases -The public `plasma_dominant_channel` case is a circular finite-pressure/current -channel with `I2=4.2`, `p2=-1e5`, `B0=1`, and formal radius 0.2 m. It is used -to keep the plasma/external split visually and numerically consequential: +`plasma_dominant_channel` remains the circular analytic regression: it makes +the current normalization transparent and produces the same 33.2574% fraction +at every angle. + +The README and example use `plasma_stellarator`, a gently shaped +two-field-period case with `I2=4.2`, `p2=-1e5`, `B0=1`, and formal radius +0.2 m. It retains the \(>30\%\) plasma contribution while making the split +angle dependent: | quantity | value | | --- | ---: | -| minimum/mean/maximum \(\lvert B_p\rvert/\lvert B_\mathrm{tot}\rvert\) | 0.332574 / 0.332574 / 0.332574 | +| minimum/mean/maximum \(\lvert B_p\rvert/\lvert B_\mathrm{tot}\rvert\) | 0.326967 / 0.332552 / 0.338719 | +| plasma \(\lvert B\rvert\) peak-to-peak / mean | 0.03534 | +| external \(\lvert B\rvert\) peak-to-peak / mean | 0.02663 | | enclosed toroidal current | 0.84 MA | | formal radius | 0.2 m | -| computed singular radius | 0.4034 m | -| formal/singular radius | 0.496 | +| computed singular radius | 0.3351 m | +| formal/singular radius | 0.597 | | estimated field remainder | 0.0351 T | -The \(>30\%\) fraction, finite current, and radius margin are regression -assertions. This case is intentionally transparent rather than a claim of an -optimized stellarator: its role is to validate that the plasma contribution -cannot silently collapse to a negligible plotting scale. +The minimum fraction, nonzero angular variation, finite current, and radius +margin are regression assertions. The publication plot shows total, plasma, +and external Frenet components; plotting only their norms would hide both the +constant-\(B_0\) total-field construction and the exact cancellation of +transverse plasma/external components. + +This is a field-split demonstration rather than a device-quality optimum. Its +role is to ensure that the plasma contribution cannot silently collapse to a +negligible plotting scale while retaining explicit asymptotic-error and +singular-radius metadata. diff --git a/docs/validation/vmex_interface.md b/docs/validation/vmex_interface.md new file mode 100644 index 0000000..b7cff32 --- /dev/null +++ b/docs/validation/vmex_interface.md @@ -0,0 +1,70 @@ +# Differentiable VMEX integration + +The bridge was audited and exercised against +[uwplasma/VMEX](https://github.com/uwplasma/vmex) version 0.3.0 at commit +`2a40d7566be083070ea3ea534fa5d1fc44ad733a`. A compatibility CI job checks +the interface against current VMEX `main` on every pyQSC_JAX pull request. + +## Tested contract + +The integration uses VMEX's public APIs: + +- `VmecInput`; +- `implicit.params_from_input` and `implicit.run`; +- `implicit.iota_profile`; +- `optimize.QuasisymmetryRatioResidual.profile_state`; +- `optimize.magnetic_well`, `aspect_ratio`, and `volume`. + +The fixed-boundary solve and derived quantities remain inside the JAX +transformation. Unit tests also differentiate through +`problem.parameters_for(candidate_solution)`, which includes pyQSC_JAX's +surface conversion and pressure/current normalization. + +The live compatibility test covers: + +| Case | Pressure | Current | Checked quantities | +| --- | ---: | ---: | --- | +| vacuum QA | zero | zero | \(\iota(s)\), QS profile, well, implicit boundary gradient | +| `plasma_stellarator` | finite | finite | \(\iota(s)\), QS profile, well, nonzero thermal energy | + +At the deliberately small `ns=7`, `mpol=4`, `ntor=2` smoke resolution, the +vacuum VMEX axis value in the pyQSC_JAX sign convention is `-0.421520`, +compared with the near-axis value `-0.420473`. This is a 0.249% difference; +the test gate is 0.8%. The purpose of this low-resolution job is cross-package +AD compatibility, not a production equilibrium accuracy claim. + +The publication example records finite-beta values of: + +| Quantity | Value | +| --- | ---: | +| magnetic well | \(-4.22969\times10^{-4}\) | +| \(\partial W/\partial p_\mathrm{scale}\) | \(+5.24435\times10^{-5}\) | +| \(\|\partial W/\partial RBC\|_2\) | \(2.01871\) | + +These values are finite, nonzero regression evidence that the pressure and +boundary adjoint paths are active. + +## Coordinate convention + +VMEC's native transform for boundaries written by pyQSC_JAX has the opposite +sign from pyQSC_JAX's toroidal-angle convention. `VmexRadialQuantities` +therefore exposes both: + +- `iota_vmec`: VMEX native sign; +- `iota`: the sign aligned with `NearAxisSolution.iota`. + +The conversion is explicit and covered by tests. + +## Scope limits + +- The bridge differentiates VMEX's fixed-boundary equilibrium. It does not + claim an adjoint of the reconverged free-boundary NESTOR root. +- VMEX's traceable quasisymmetry profile currently requires stellarator + symmetry. Asymmetric equilibria can be solved with `qs_surfaces=()`. +- The magnetic well is VMEX's canonical endpoint scalar. No undocumented + radial “well profile” is invented. +- Pressure/current profiles are the simple near-axis-consistent profiles used + by `to_vmec`; users can replace the returned VMEX parameter leaves when a + different finite-radius profile model is intended. +- Production results require radial, angular, and Fourier-resolution studies + beyond the fast compatibility settings above. diff --git a/examples/10_plasma_external_field_jet.py b/examples/10_plasma_external_field_jet.py index 7c95906..352166d 100644 --- a/examples/10_plasma_external_field_jet.py +++ b/examples/10_plasma_external_field_jet.py @@ -3,11 +3,12 @@ from pathlib import Path import matplotlib.pyplot as plt +import numpy as np import pyqsc_jax as qsc -from pyqsc_jax.plotting import plot_field_jet_norms +from pyqsc_jax.plotting import plot_field_split_components -CONFIGURATION = "plasma_dominant_channel" +CONFIGURATION = "plasma_stellarator" FORMAL_RADIUS = 0.2 NPHI = 61 ANGULAR_RESOLUTION = 96 @@ -30,6 +31,8 @@ print("enclosed toroidal current [A]:", float(enclosed_current)) print("minimum |B_plasma| / |B_total|:", float(plasma_fraction.min())) print("mean |B_plasma| / |B_total|:", float(plasma_fraction.mean())) +plasma_norm = np.linalg.norm(np.asarray(result.field.field.field), axis=-1) +print("plasma |B| peak-to-peak / mean:", float(np.ptp(plasma_norm) / np.mean(plasma_norm))) print("formal radius / singular radius:", float(FORMAL_RADIUS / solution.r_singularity)) print("external gradient STF components:", result.field.external_gradient_independent.shape[-1]) print("external Hessian STF components:", result.external_hessian_independent.shape[-1]) @@ -41,7 +44,7 @@ float(result.estimated_hessian_remainder), ) -figure, _ = plot_field_jet_norms(result) +figure, _ = plot_field_split_components(result, solution) if SAVE_OUTPUT: OUTPUT.parent.mkdir(parents=True, exist_ok=True) figure.savefig(OUTPUT, dpi=180, bbox_inches="tight") diff --git a/examples/14_vmex_radial_profiles.py b/examples/14_vmex_radial_profiles.py new file mode 100644 index 0000000..fe47d32 --- /dev/null +++ b/examples/14_vmex_radial_profiles.py @@ -0,0 +1,76 @@ +"""Solve differentiable radial equilibrium quantities with optional VMEX.""" + +from pathlib import Path + +import jax +import matplotlib.pyplot as plt +import numpy as np + +import pyqsc_jax as qsc + +CONFIGURATION = "qa" +RADIUS = 0.02 +QS_SURFACES = (0.25, 0.5, 0.75, 1.0) +OUTPUT = Path("examples/output/14_vmex_radial_profiles.png") +SAVE_FIGURE = True +SHOW_FIGURE = False + +print("Constructing the near-axis boundary...") +solution = qsc.solve_configuration(CONFIGURATION, nphi=31) +try: + problem = qsc.to_vmex_problem( + solution, + r=RADIUS, + qs_surfaces=QS_SURFACES, + ntheta=8, + mpol=3, + ntor=2, + ns_array=(7,), + ftol=1.0e-7, + max_iterations=1200, + multigrid=False, + ) +except ImportError as error: + print(error) + print("Skipping the optional VMEX equilibrium example.") + raise SystemExit(0) from None + +print("Solving the converged fixed-boundary equilibrium with VMEX...") +result = problem.solve() +quantities = result.quantities +print("VMEX version:", problem.vmex_version) +print("iota(s):", np.asarray(quantities.iota)) +print("quasisymmetry profile:", np.asarray(quantities.quasisymmetry)) +print("magnetic well:", float(quantities.magnetic_well)) + +print("Differentiating magnetic well through the converged VMEX fixed point...") +well, gradient = jax.value_and_grad( + lambda parameters: qsc.vmex_radial_quantities(problem, parameters).magnetic_well +)(problem.parameters) +print("magnetic well:", float(well)) +print("d(well)/d(pres_scale):", float(gradient.pres_scale)) +print("||d(well)/d(RBC)||:", float(np.linalg.norm(np.asarray(gradient.rbc)))) + +figure, axes = plt.subplots(1, 2, figsize=(9.4, 3.8)) +axes[0].plot(np.asarray(quantities.s), np.asarray(quantities.iota), "-o") +axes[0].axhline(float(solution.iota), color="black", linestyle="--", label="near axis") +axes[0].set_xlabel(r"normalized toroidal flux $s$") +axes[0].set_ylabel(r"$\iota(s)$") +axes[0].legend() +axes[1].semilogy( + np.asarray(quantities.qs_surfaces), + np.asarray(quantities.quasisymmetry), + "-o", +) +axes[1].set_xlabel(r"normalized toroidal flux $s$") +axes[1].set_ylabel("VMEX QS residual") +figure.tight_layout() + +if SAVE_FIGURE: + OUTPUT.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(OUTPUT, dpi=180, bbox_inches="tight") + print("saved:", OUTPUT) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/publication/figure_B20_optimization.py b/examples/publication/figure_B20_optimization.py index 66d6430..e13aa04 100644 --- a/examples/publication/figure_B20_optimization.py +++ b/examples/publication/figure_B20_optimization.py @@ -8,10 +8,12 @@ import numpy as np import pyqsc_jax as qsc +from pyqsc_jax.plotting import plot_surface_3d STOCK_CONFIGURATION = "qa" OPTIMIZED_CONFIGURATION = "b20_optimized_qa" NPHI = 121 +SURFACE_RADIUS = 0.075 OUTPUT_STEM = Path("examples/output/publication/B20_optimization") README_PNG = Path("docs/_static/B20_optimization.png") SAVE_OUTPUT = True @@ -27,19 +29,38 @@ stock_angle = np.asarray(stock.solution.varphi * stock.solution.inputs.axis.nfp / (2 * np.pi)) optimized_angle = np.asarray(optimized.varphi * optimized.inputs.axis.nfp / (2 * np.pi)) -figure, axes = plt.subplots(1, 3, figsize=(12.8, 3.8)) -axes[0].plot(stock_angle, np.asarray(stock.diagnostics.anomaly), linewidth=2.2) -axes[0].set_title(r"stock axis + exact $B_{2c}$") -axes[0].set_xlabel("Boozer angle / field period") -axes[0].set_ylabel(r"$B_{20}-\langle B_{20}\rangle$ [T/m$^2$]") -axes[1].plot( +figure = plt.figure(figsize=(13.2, 8.2)) +surface_axis = figure.add_subplot(2, 2, 1, projection="3d") +plot_surface_3d( + optimized, + radius=SURFACE_RADIUS, + ntheta=36, + ax=surface_axis, + cmap="viridis", +) +surface_axis.view_init(elev=24, azim=38) +surface_axis.set_title( + "optimized QA surface\n" + rf"$\iota={float(optimized.iota):.3f}$, " + rf"$r_\mathrm{{sing}}={float(optimized.r_singularity):.3f}$ m" +) + +stock_axis = figure.add_subplot(2, 2, 2) +stock_axis.plot(stock_angle, np.asarray(stock.diagnostics.anomaly), linewidth=2.2) +stock_axis.set_title(r"stock axis + exact $B_{2c}$") +stock_axis.set_xlabel("Boozer angle / field period") +stock_axis.set_ylabel(r"$B_{20}-\langle B_{20}\rangle$ [T/m$^2$]") + +optimized_axis = figure.add_subplot(2, 2, 3) +optimized_axis.plot( optimized_angle, np.asarray(optimized_diagnostics.anomaly), linewidth=2.2, color="tab:green", ) -axes[1].set_title("optimized Fourier axis") -axes[1].set_xlabel("Boozer angle / field period") +optimized_axis.set_title("optimized Fourier axis") +optimized_axis.set_xlabel("Boozer angle / field period") +optimized_axis.set_ylabel(r"$B_{20}-\langle B_{20}\rangle$ [T/m$^2$]") diagnostic_names = ("weighted $L^2$", "dense maximum", "peak-to-peak") stock_values = ( float(stock.diagnostics.weighted_l2), @@ -51,29 +72,34 @@ float(optimized_diagnostics.grid_maximum), float(optimized_diagnostics.peak_to_peak), ) -axes[2].bar( +summary_axis = figure.add_subplot(2, 2, 4) +summary_axis.bar( np.arange(3) - 0.18, stock_values, width=0.36, label=r"exact $B_{2c}$ only", ) -axes[2].bar( +summary_axis.bar( np.arange(3) + 0.18, optimized_values, width=0.36, label="axis + $B_{2c}$", color="tab:green", ) -axes[2].set_xticks(np.arange(3), diagnostic_names, rotation=15) -axes[2].set_yscale("log") -axes[2].set_ylabel(r"$B_{20}$ nonuniformity [T/m$^2$]") -axes[2].legend(fontsize=8) -axes[2].text( +summary_axis.set_xticks(np.arange(3), diagnostic_names, rotation=12) +summary_axis.set_yscale("log") +summary_axis.set_ylabel(r"$B_{20}$ nonuniformity [T/m$^2$]") +summary_axis.legend(fontsize=8) +clearance = float(optimized.r_singularity) / SURFACE_RADIUS +summary_axis.text( 0.04, 0.05, - f"{improvement:,.0f}x lower weighted residual", - transform=axes[2].transAxes, + f"{improvement:,.0f}x lower residual\n" + rf"shown surface: $r={SURFACE_RADIUS:.3f}$ m" + f" ({clearance:.1f}x inside singular radius)", + transform=summary_axis.transAxes, fontweight="bold", + bbox={"facecolor": "white", "edgecolor": "0.7", "alpha": 0.9}, ) figure.tight_layout() @@ -96,6 +122,9 @@ "optimized_weighted_l2": float(optimized_diagnostics.weighted_l2), "optimized_grid_maximum": float(optimized_diagnostics.grid_maximum), "optimized_peak_to_peak": float(optimized_diagnostics.peak_to_peak), + "optimized_singular_radius": float(optimized.r_singularity), + "surface_radius": SURFACE_RADIUS, + "singular_radius_clearance": clearance, "improvement_factor": improvement, "verification_nphi": np.asarray(verification.resolutions).tolist(), "verification_weighted_l2": np.asarray(verification.weighted_l2).tolist(), diff --git a/examples/publication/figure_plasma_external_jet.py b/examples/publication/figure_plasma_external_jet.py index 3f9aedc..577e821 100644 --- a/examples/publication/figure_plasma_external_jet.py +++ b/examples/publication/figure_plasma_external_jet.py @@ -5,12 +5,14 @@ from pathlib import Path import matplotlib.pyplot as plt +import numpy as np import pyqsc_jax as qsc -from pyqsc_jax.plotting import plot_field_jet_norms +from pyqsc_jax.plotting import field_split_frenet_components, plot_surface_3d -CONFIGURATION = "plasma_dominant_channel" +CONFIGURATION = "plasma_stellarator" FORMAL_RADIUS = 0.2 +DISPLAY_RADIUS = 0.12 NPHI = 121 ANGULAR_RESOLUTION = 128 OUTPUT_STEM = Path("examples/output/publication/plasma_external_jet") @@ -29,15 +31,53 @@ plasma_fraction = ( (result.field.field.field**2).sum(axis=-1) / (solution.B_axis**2).sum(axis=-1) ) ** 0.5 -figure, axes = plot_field_jet_norms(result) -for label, axis in zip(("a", "b", "c"), axes, strict=True): - axis.text( - 0.01, - 0.91, - f"({label})", - transform=axis.transAxes, - fontweight="bold", - ) +components = np.asarray(field_split_frenet_components(result, solution)) +angle = np.asarray(solution.varphi * solution.inputs.axis.nfp / (2 * np.pi)) +plasma_norm = np.linalg.norm(np.asarray(result.field.field.field), axis=1) +external_norm = np.linalg.norm(np.asarray(result.field.external_field), axis=1) + +figure = plt.figure(figsize=(12.8, 8.0)) +surface_axis = figure.add_subplot(2, 2, 1, projection="3d") +plot_surface_3d( + solution, + radius=DISPLAY_RADIUS, + ntheta=32, + ax=surface_axis, + cmap="plasma", +) +surface_axis.view_init(elev=25, azim=35) +surface_axis.set_title( + "finite-current stellarator\n" + rf"$r_\mathrm{{sing}}={float(solution.r_singularity):.3f}$ m" +) + +fraction_axis = figure.add_subplot(2, 2, 2) +fraction_axis.plot(angle, np.asarray(plasma_fraction), color="tab:red", linewidth=2.3) +fraction_axis.axhline(0.30, color="black", linestyle="--", linewidth=1.2, label="30% gate") +fraction_axis.fill_between(angle, 0.30, np.asarray(plasma_fraction), alpha=0.18, color="tab:red") +fraction_axis.set_xlabel("Boozer angle / field period") +fraction_axis.set_ylabel(r"$|B_\mathrm{plasma}|/|B_\mathrm{total}|$") +fraction_axis.set_title("plasma contribution varies with angle") +fraction_axis.legend() + +tangent_axis = figure.add_subplot(2, 2, 3) +for field_index, label in enumerate(("total", "plasma", "external")): + tangent_axis.plot(angle, components[field_index, 0], label=label) +tangent_axis.set_xlabel("Boozer angle / field period") +tangent_axis.set_ylabel(r"$B_t$ [T]") +tangent_axis.set_title("tangent field component") +tangent_axis.legend(ncol=3) + +transverse_axis = figure.add_subplot(2, 2, 4) +transverse_axis.plot(angle, components[1, 1], label=r"plasma $B_n$") +transverse_axis.plot(angle, components[2, 1], "--", label=r"external $B_n$") +transverse_axis.plot(angle, components[1, 2], label=r"plasma $B_b$") +transverse_axis.plot(angle, components[2, 2], "--", label=r"external $B_b$") +transverse_axis.set_xlabel("Boozer angle / field period") +transverse_axis.set_ylabel("transverse field [T]") +transverse_axis.set_title("plasma and external parts cancel to the total") +transverse_axis.legend(ncol=2, fontsize=8) +figure.tight_layout() try: repository = Path(__file__).resolve().parents[2] @@ -51,11 +91,16 @@ "git_commit": commit, "configuration": CONFIGURATION, "formal_radius": FORMAL_RADIUS, + "display_radius": DISPLAY_RADIUS, "nphi": NPHI, "angular_resolution": ANGULAR_RESOLUTION, "enclosed_current_amperes": float(result.field.field.current_source.enclosed_toroidal_current), "minimum_plasma_field_fraction": float(plasma_fraction.min()), "mean_plasma_field_fraction": float(plasma_fraction.mean()), + "maximum_plasma_field_fraction": float(plasma_fraction.max()), + "plasma_norm_peak_to_peak_over_mean": float(np.ptp(plasma_norm) / np.mean(plasma_norm)), + "external_norm_peak_to_peak_over_mean": float(np.ptp(external_norm) / np.mean(external_norm)), + "singular_radius": float(solution.r_singularity), "formal_radius_to_singular_radius": float(FORMAL_RADIUS / solution.r_singularity), "maximum_external_gradient_trace": float(result.field.maximum_external_trace), "maximum_external_hessian_trace": float(result.maximum_external_trace), diff --git a/examples/publication/figure_stellarator_gallery.py b/examples/publication/figure_stellarator_gallery.py new file mode 100644 index 0000000..ebb8f8f --- /dev/null +++ b/examples/publication/figure_stellarator_gallery.py @@ -0,0 +1,81 @@ +"""Publication gallery of the bundled QA, QH, B20, and plasma stellarators.""" + +import json +import subprocess +from pathlib import Path + +import matplotlib.pyplot as plt + +import pyqsc_jax as qsc +from pyqsc_jax.plotting import plot_surface_3d + +CASES = ( + ("qa", "QA reference", 0.055, "viridis"), + ("qh", "QH reference", 0.055, "plasma"), + ("b20_optimized_qa", r"$B_{20}$-optimized QA", 0.075, "cividis"), + ("plasma_stellarator", "finite-current plasma case", 0.12, "magma"), +) +NPHI = 121 +OUTPUT_STEM = Path("examples/output/publication/stellarator_gallery") +README_PNG = Path("docs/_static/stellarator_gallery.png") +SAVE_OUTPUT = True +SHOW_FIGURE = False + +plt.style.use("seaborn-v0_8-whitegrid") +figure = plt.figure(figsize=(12.0, 9.2)) +metadata = {"nphi": NPHI, "configurations": {}} + +print("Rendering the bundled stellarator gallery...") +for panel, (name, title, radius, cmap) in enumerate(CASES, start=1): + solution = qsc.solve_configuration(name, nphi=NPHI) + axis = figure.add_subplot(2, 2, panel, projection="3d") + plot_surface_3d( + solution, + radius=radius, + ntheta=36, + ax=axis, + cmap=cmap, + ) + axis.view_init(elev=24, azim=35) + if name == "b20_optimized_qa": + diagnostic = rf"$\|P B_{{20}}\|_2={float(solution.B20_residual):.2e}$" + elif name == "plasma_stellarator": + diagnostic = r"$\min |B_p|/|B|=32.7\%$ at $a=0.2$ m" + else: + diagnostic = rf"$\iota={float(solution.iota):.3f}$" + axis.set_title( + title + "\n" + diagnostic + rf", $r_\mathrm{{sing}}={float(solution.r_singularity):.3f}$ m" + ) + metadata["configurations"][name] = { + "surface_radius": radius, + "iota": float(solution.iota), + "B20_residual": float(solution.B20_residual), + "singular_radius": float(solution.r_singularity), + "surface_to_singular_radius": radius / float(solution.r_singularity), + } +figure.tight_layout() + +try: + repository = Path(__file__).resolve().parents[2] + commit = subprocess.check_output( + ("git", "-C", str(repository), "rev-parse", "HEAD"), + text=True, + ).strip() +except (OSError, subprocess.CalledProcessError): + commit = "unavailable" +metadata["git_commit"] = commit +if SAVE_OUTPUT: + OUTPUT_STEM.parent.mkdir(parents=True, exist_ok=True) + for suffix in ("png", "svg", "pdf"): + figure.savefig(OUTPUT_STEM.with_suffix(f".{suffix}"), dpi=220, bbox_inches="tight") + README_PNG.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(README_PNG, dpi=130, bbox_inches="tight") + OUTPUT_STEM.with_suffix(".json").write_text( + json.dumps(metadata, indent=2, sort_keys=True) + "\n", + encoding="utf-8", + ) + print("saved:", OUTPUT_STEM) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/publication/figure_vmex_radial_profiles.py b/examples/publication/figure_vmex_radial_profiles.py new file mode 100644 index 0000000..8cc09b0 --- /dev/null +++ b/examples/publication/figure_vmex_radial_profiles.py @@ -0,0 +1,160 @@ +"""Publication figure for the differentiable pyQSC_JAX-to-VMEX bridge.""" + +import json +import subprocess +from pathlib import Path + +import jax +import matplotlib.pyplot as plt +import numpy as np + +import pyqsc_jax as qsc +from pyqsc_jax.plotting import plot_surface_3d + +CASES = ( + ("qa", "vacuum QA"), + ("plasma_stellarator", "finite beta/current"), +) +RADIUS = 0.02 +QS_SURFACES = (0.2, 0.4, 0.6, 0.8, 1.0) +OUTPUT_STEM = Path("examples/output/publication/vmex_radial_profiles") +README_PNG = Path("docs/_static/vmex_radial_profiles.png") +SAVE_OUTPUT = True +SHOW_FIGURE = False + +print("Solving vacuum and finite-beta radial equilibria with VMEX...") +records = [] +try: + for configuration, label in CASES: + near_axis = qsc.solve_configuration(configuration, nphi=31) + problem = qsc.to_vmex_problem( + near_axis, + r=RADIUS, + qs_surfaces=QS_SURFACES, + ntheta=8, + mpol=3, + ntor=2, + ns_array=(7,), + ftol=1.0e-7, + max_iterations=1200, + multigrid=False, + ) + equilibrium = problem.solve() + records.append((label, near_axis, problem, equilibrium.quantities)) +except ImportError as error: + print(error) + print("Skipping the optional VMEX publication figure.") + raise SystemExit(0) from None + +finite_label, finite_axis, finite_problem, finite_quantities = records[-1] +print("Differentiating the finite-beta magnetic well...") +well, gradient = jax.value_and_grad( + lambda parameters: ( + qsc.vmex_radial_quantities( + finite_problem, + parameters, + ).magnetic_well + ) +)(finite_problem.parameters) + +plt.style.use("seaborn-v0_8-whitegrid") +figure = plt.figure(figsize=(12.8, 8.0)) +surface_axis = figure.add_subplot(2, 2, 1, projection="3d") +plot_surface_3d( + finite_axis, + radius=0.08, + ntheta=32, + ax=surface_axis, + cmap="magma", +) +surface_axis.view_init(elev=25, azim=35) +surface_axis.set_title("VMEX source boundary\nfinite pressure and current") + +iota_axis = figure.add_subplot(2, 2, 2) +qs_axis = figure.add_subplot(2, 2, 3) +well_axis = figure.add_subplot(2, 2, 4) +for label, near_axis, _problem, quantities in records: + iota_axis.plot( + np.asarray(quantities.s), + np.asarray(quantities.iota), + "-o", + label=label, + ) + iota_axis.scatter( + [0], + [float(near_axis.iota)], + marker="x", + s=55, + ) + qs_axis.semilogy( + np.asarray(quantities.qs_surfaces), + np.asarray(quantities.quasisymmetry), + "-o", + label=label, + ) +iota_axis.set_xlabel(r"normalized toroidal flux $s$") +iota_axis.set_ylabel(r"$\iota(s)$ in pyQSC convention") +iota_axis.set_title("on-axis construction → radial equilibrium") +iota_axis.legend() +qs_axis.set_xlabel(r"normalized toroidal flux $s$") +qs_axis.set_ylabel("VMEX QS residual") +qs_axis.set_title("differentiable quasisymmetry profile") +qs_axis.legend() + +wells = [float(item[3].magnetic_well) for item in records] +well_axis.bar([item[0] for item in records], wells, color=("tab:blue", "tab:red")) +well_axis.axhline(0, color="black", linewidth=1) +well_axis.set_ylabel(r"$(V'(0)-V'(1))/V'(0)$") +well_axis.set_title("magnetic well + implicit gradient") +well_axis.text( + 0.04, + 0.06, + rf"$\partial W/\partial p_\mathrm{{scale}}={float(gradient.pres_scale):+.2e}$" + "\n" + rf"$\|\partial W/\partial RBC\|={float(np.linalg.norm(np.asarray(gradient.rbc))):.2e}$", + transform=well_axis.transAxes, + fontsize=9, +) +figure.tight_layout() + +try: + repository = Path(__file__).resolve().parents[2] + commit = subprocess.check_output( + ("git", "-C", str(repository), "rev-parse", "HEAD"), + text=True, + ).strip() +except (OSError, subprocess.CalledProcessError): + commit = "unavailable" +metadata = { + "git_commit": commit, + "vmex_version": finite_problem.vmex_version, + "vmex_validated_commit": finite_problem.validated_commit, + "radius": RADIUS, + "cases": { + label: { + "iota": np.asarray(quantities.iota).tolist(), + "quasisymmetry": np.asarray(quantities.quasisymmetry).tolist(), + "magnetic_well": float(quantities.magnetic_well), + "thermal_energy": float(quantities.thermal_energy), + } + for label, _near_axis, _problem, quantities in records + }, + "finite_beta_well": float(well), + "finite_beta_well_gradient_pres_scale": float(gradient.pres_scale), + "finite_beta_well_gradient_rbc_norm": float(np.linalg.norm(np.asarray(gradient.rbc))), +} +if SAVE_OUTPUT: + OUTPUT_STEM.parent.mkdir(parents=True, exist_ok=True) + for suffix in ("png", "svg", "pdf"): + figure.savefig(OUTPUT_STEM.with_suffix(f".{suffix}"), dpi=220, bbox_inches="tight") + README_PNG.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(README_PNG, dpi=120, bbox_inches="tight") + OUTPUT_STEM.with_suffix(".json").write_text( + json.dumps(metadata, indent=2, sort_keys=True) + "\n", + encoding="utf-8", + ) + print("saved:", OUTPUT_STEM) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) From 57767aaf87bc36134e6e14c3c1151ac6c4f78c17 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 11:31:10 -0500 Subject: [PATCH 31/39] fix: accept finite rank-deficient optimizer zeros --- src/pyqsc_jax/axis_optimization.py | 19 +++++++++++++------ tests/physics/test_axis_optimization.py | 14 ++++++++++++++ 2 files changed, 27 insertions(+), 6 deletions(-) diff --git a/src/pyqsc_jax/axis_optimization.py b/src/pyqsc_jax/axis_optimization.py index c83e001..9f8a922 100644 --- a/src/pyqsc_jax/axis_optimization.py +++ b/src/pyqsc_jax/axis_optimization.py @@ -402,16 +402,23 @@ def _levenberg_marquardt( if converged: break - normal_singular_values = jnp.linalg.svd(jacobian, compute_uv=False) - tiny = jnp.finfo(jacobian.dtype).tiny - condition_number = normal_singular_values[0] / jnp.maximum( - normal_singular_values[-1], - tiny, + normal_eigenvalues = jnp.maximum( + jnp.linalg.eigvalsh(jacobian.T @ jacobian), + 0, ) + largest_eigenvalue = normal_eigenvalues[-1] + smallest_eigenvalue = normal_eigenvalues[0] + rank_deficient = smallest_eigenvalue <= (jnp.finfo(jacobian.dtype).eps * largest_eigenvalue) + condition_number = jnp.where( + rank_deficient, + jnp.inf, + jnp.sqrt(largest_eigenvalue / smallest_eigenvalue), + ) + condition_number = jnp.where(jnp.isnan(condition_number), jnp.inf, condition_number) finite = ( jnp.all(jnp.isfinite(internal)) & jnp.all(jnp.isfinite(current_residual)) - & jnp.isfinite(condition_number) + & jnp.all(jnp.isfinite(jacobian)) ) return internal, LocalLeastSquaresReport( initial_residual_norm=initial_norm, diff --git a/tests/physics/test_axis_optimization.py b/tests/physics/test_axis_optimization.py index f9e20f1..f33012a 100644 --- a/tests/physics/test_axis_optimization.py +++ b/tests/physics/test_axis_optimization.py @@ -13,6 +13,7 @@ _copy_retained_axis_modes, _halton_box, _internal_from_physical, + _levenberg_marquardt, _physical_from_internal, _selector_value, _validate_problem, @@ -79,6 +80,19 @@ def test_bound_transform_round_trip_and_strict_interior(): assert np.all(np.asarray(reconstructed) < np.asarray(upper)) +def test_local_solve_accepts_a_finite_rank_deficient_exact_zero(): + options = small_options(maximum_iterations=1) + initial = jnp.asarray([0.0, 0.0]) + residual = lambda value: jnp.zeros((3,), dtype=value.dtype) # noqa: E731 + + internal, report = _levenberg_marquardt(residual, initial, options) + + np.testing.assert_allclose(internal, initial) + assert report.converged + assert report.finite + assert np.isinf(float(report.jacobian_condition_number)) + + def test_fourier_continuation_copies_retained_modes_and_runs_stages(): low_axis = qsc.Axis(rc=[1.0], zs=[0.0], nfp=1) high_axis = qsc.Axis(rc=[0.9, 0.0], zs=[0.0, 0.0], nfp=1) From aa1534d27df09b6948f1585da825579b7f2a2c23 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 11:47:47 -0500 Subject: [PATCH 32/39] feat: showcase screened database stellarators --- README.md | 81 ++++++++------- benchmarks/benchmark_b20_optimizers.py | 49 +++++---- .../reports/2026-07-30-b20-vmec-apple-m4.json | 47 +++++---- docs/_static/B20_optimization.png | Bin 248394 -> 255390 bytes docs/_static/plasma_external_jet.png | Bin 194314 -> 177243 bytes docs/_static/stellarator_gallery.png | Bin 496471 -> 522661 bytes docs/_static/vmex_radial_profiles.png | Bin 171144 -> 173345 bytes docs/development/refactor_status.md | 19 ++++ docs/theory/b20-optimization.md | 61 +++++++---- docs/validation/literature_cases.md | 21 ++++ docs/validation/plasma_field.md | 38 ++++--- docs/validation/vmex_interface.md | 6 +- examples/06_optimize_axis_B20.py | 14 ++- examples/10_plasma_external_field_jet.py | 2 +- .../publication/figure_B20_optimization.py | 19 ++-- .../publication/figure_plasma_external_jet.py | 7 +- .../publication/figure_stellarator_gallery.py | 33 ++++-- src/pyqsc_jax/configurations.py | 97 +++++++++++++++++- src/pyqsc_jax/plotting.py | 47 +++++++-- src/pyqsc_jax/vmec.py | 6 +- tests/physics/test_b20_optimization.py | 19 ++-- tests/physics/test_plasma_field.py | 7 +- tests/unit/test_configurations.py | 26 +++++ tests/unit/test_plotting.py | 19 ++++ 24 files changed, 445 insertions(+), 173 deletions(-) diff --git a/README.md b/README.md index 82e7c4b..a6f5deb 100644 --- a/README.md +++ b/README.md @@ -14,12 +14,16 @@ plasma–coil field jets in JAX. > compatibility, and external 3+5+7 field-jet paths are validated; release > hardening is still in progress. -![QA, QH, B20-optimized, and finite-current stellarators](docs/_static/stellarator_gallery.png) +![Four independently screened stellarators](docs/_static/stellarator_gallery.png) -Four runnable configurations: vacuum QA and QH references, the -\(B_{20}\)-optimized QA surface, and an angle-dependent finite-current -stellarator. Every displayed surface reports its transform and/or singular -radius; the plotting radius is recorded in the figure metadata. +Four runnable, independently re-evaluated designs: [database ID 3](https://stellarator.physics.wisc.edu/app/plot/3), +an eight-mode refinement of [database ID 57409](https://stellarator.physics.wisc.edu/app/plot/57409), +the large-clearance [database ID 107579](https://stellarator.physics.wisc.edu/app/plot/107579), +and an angle-dependent finite-current case. Every displayed design passes the +configurable Curvo/Table-3 profile with the stricter +\(\lvert\iota\rvert\geq0.4\); each panel reports transform, singular radius, +and its defining diagnostic. Plotting radii and database provenance are in +the adjacent JSON metadata. | \(B_{20}\) optimization, geometry, and singular margin | Angle-dependent plasma/external field | | --- | --- | @@ -49,19 +53,15 @@ python -m pip install 'pyqsc-jax[plot,vmex]' ```python import pyqsc_jax as qsc -solution = qsc.Qsc( - rc=[1.0, 0.155, 0.0102], - zs=[0.0, 0.154, 0.0111], - nfp=2, - etabar=0.64, - B2c=-0.00322, - nphi=61, - order="r2", -) +configuration = qsc.get_configuration("database_example_3") +solution = configuration.solve(nphi=81) +criteria = qsc.Criteria.from_curvo_2025(minimum_abs_iota=0.4) assert solution.root_report.converged assert solution.linear_report.converged -print("iota:", solution.iota) +assert criteria.evaluate(solution).passed +print("source:", configuration.source_url) +print("|iota|:", abs(solution.iota)) print("B20 residual:", solution.B20_residual) print("Mercier D r^2:", solution.DMerc_times_r2) print("singular radius:", solution.r_singularity) @@ -111,22 +111,24 @@ resolution, timing, and radius-convergence tables are in the | Check | Result | Regression gate | | --- | ---: | ---: | -| Optimized QA \(B_{20}\), weighted \(L^2\), `nphi=121` | \(1.5901\times10^{-6}\) | \(<1.6\times10^{-6}\) | -| Improvement over stock-axis exact-\(B_{2c}\) solve | \(26{,}053\times\) | \(>25{,}000\times\) | -| \(B_{20}\)-optimized singular radius | 0.248 m | displayed \(r=0.075\) m gives 3.3× clearance | -| Angle-dependent minimum \(\lvert B_\mathrm{plasma}\rvert/\lvert B_\mathrm{total}\rvert\) | 32.70% | \(>30\%\) | -| Plasma-field norm peak-to-peak / mean | 3.53% | \(>3\%\) | +| Database-seeded QH \(B_{20}\), weighted \(L^2\), `nphi=121` | \(1.2743\times10^{-10}\) | \(<1.4\times10^{-10}\) | +| Improvement over ID-57409 exact-\(B_{2c}\) solve | \(2.4321\times10^8\)× | \(>2.0\times10^8\)× | +| \(B_{20}\)-optimized singular radius | 0.249 m | displayed \(r=0.075\) m gives 3.3× clearance | +| Largest showcased singular radius, database ID 107579 | 0.432 m | \(>0.4\) m | +| Four-case showcase design screen | all pass | Curvo profile with \(\lvert\iota\rvert\ge0.4\) | +| Angle-dependent minimum \(\lvert B_\mathrm{plasma}\rvert/\lvert B_\mathrm{total}\rvert\) | 32.99% at \(a=0.45\) m | \(>30\%\) | +| Plasma-field norm peak-to-peak / mean | 4.43% | \(>3\%\) | | VMEC/near-axis on-axis \(\iota\), \(r=0.0025\) | 0.418543 / 0.418307 | relative error \(<0.1\%\) | | VMEC force residuals | \(2.4\)–\(7.6\times10^{-11}\) | maximum \(<10^{-9}\) | | `to_vmec`, Apple M4 CPU, compile+execute / warm | 0.476 s / 5.20 ms | warm unit gate \(<0.5\) s | ```python -optimized = qsc.solve_configuration("b20_optimized_qa", nphi=121) +optimized = qsc.solve_configuration("b20_optimized_good", nphi=121) diagnostics = qsc.b20_diagnostics(optimized) print(diagnostics.weighted_l2, diagnostics.grid_maximum) plasma_case = qsc.solve_configuration("plasma_stellarator", nphi=61) -plasma = qsc.plasma_field_on_axis(plasma_case, formal_radius=0.2) +plasma = qsc.plasma_field_on_axis(plasma_case, formal_radius=0.45) ``` ## Target rotational transform @@ -169,23 +171,27 @@ mathematical global-minimum claim. ```python from pyqsc_jax.plotting import plot_surface_3d -optimized = qsc.solve_configuration("b20_optimized_qa", nphi=121) +optimized = qsc.solve_configuration("b20_optimized_good", nphi=121) figure, axis = plot_surface_3d(optimized, radius=0.075) -print(optimized.B20_residual) # 1.5901e-6 T/m^2 -print(optimized.r_singularity) # 0.248 m +print(abs(optimized.iota)) # 2.9636 +print(optimized.B20_residual) # 1.2743e-10 T/m^2 +print(optimized.r_singularity) # 0.249 m ``` -The displayed surface is therefore 3.3 times inside the computed singular -radius. The optimizer comparison, Fourier-resolution audit, full coefficient -set, and the distinction between `best_found` and a certified zero are in the +This configuration is a staged eight-mode refinement of public database ID +57409, not an unconstrained toy optimum. It passes every named design +criterion with \(\lvert\iota\rvert=2.964\); the displayed surface is 3.3 times +inside the computed singular radius. The optimizer comparison, +Fourier-resolution audit, full coefficient set, provenance, and the +distinction between `best_found` and a certified zero are in the [B20 optimization notes](docs/theory/b20-optimization.md). ## Finite-beta coil targets ```python solution = qsc.solve_configuration("plasma_stellarator", nphi=61) -target = qsc.plasma_hessian_on_axis(solution, formal_radius=0.2) +target = qsc.plasma_hessian_on_axis(solution, formal_radius=0.45) print(target.field.external_field.shape) # (nphi, 3) print(target.field.external_gradient_independent.shape) # (nphi, 5) @@ -196,17 +202,20 @@ ESSOS consumes these external vacuum targets for normalized field, gradient, and Hessian coil objectives. The dependency remains one-way: `ESSOS -> pyQSC_JAX`. -The public plot uses Frenet components rather than only \(|B|\). This makes -the angle dependence and exact cancellation of plasma and external transverse -components visible; \(|B_\mathrm{total}|=B_0\) is constant on axis by -construction. +This case independently passes the Curvo profile with +\(\lvert\iota\rvert=0.730\) and \(r_\mathrm{sing}=0.992\) m. The stated +formal radius \(a=0.45\) m is mandatory model metadata and remains inside that +singular-radius estimate. The public plot uses Frenet components rather than +only \(|B|\), making the angle dependence and exact cancellation of plasma +and external transverse components visible; +\(|B_\mathrm{total}|=B_0\) is constant on axis by construction. ## Differentiable radial equilibria with VMEX ```python import jax -near_axis = qsc.solve_configuration("qa", nphi=61) +near_axis = qsc.solve_configuration("plasma_stellarator", nphi=61) problem = qsc.to_vmex_problem( near_axis, r=0.02, @@ -250,7 +259,9 @@ print(export.conversion_seconds) print(export.boundary.maximum_R_reconstruction_error) ``` -The exporter uses a vectorized Newton inversion and a two-dimensional FFT, +This small-radius QA input is a conversion-validation reference, not one of +the screened finite-beta showcase devices above. The exporter uses a +vectorized Newton inversion and a two-dimensional FFT, supports all four VMEC boundary coefficient families, and returns conversion diagnostics. The committed `wout` regression checks the resulting equilibrium, including the on-axis transform; an opt-in test can rerun a local VMEC diff --git a/benchmarks/benchmark_b20_optimizers.py b/benchmarks/benchmark_b20_optimizers.py index 7d5ebb2..51bc2eb 100644 --- a/benchmarks/benchmark_b20_optimizers.py +++ b/benchmarks/benchmark_b20_optimizers.py @@ -1,4 +1,4 @@ -"""Compare local, multistart, and coarse-global B20 axis optimizers.""" +"""Compare optimizers from screened stellarator-database configuration 57409.""" from __future__ import annotations @@ -22,44 +22,36 @@ os.environ.get("PYQSC_B20_BENCHMARK_OUTPUT", "benchmarks/results/b20_optimizers.json") ) RC = ( - 1.0038581971135636, - 0.18400998741139907, - 0.021723381370503204, - 0.0025968236014410812, - 0.00030601568477064874, - 3.5540509760304384e-05, - 4.102693907398271e-06, - 5.154300428457222e-07, - 4.8802742243232844e-08, - 7.3011320375259876e-09, + 1.0, + -0.51677144, + -0.009499784, + -0.005914526, ) ZS = ( 0.0, - -0.1581148860568176, - -0.02060702320552523, - -0.002558840496952667, - -0.0003061368667524159, - -3.600111450532304e-05, - -4.174376962124085e-06, - -4.557462755956434e-07, - -8.173481495049928e-08, - -3.732477282851326e-09, + -0.5420635, + -0.012225689, + -0.0059485724, ) -AXIS = qsc.Axis(rc=RC, zs=ZS, nfp=2) +AXIS = qsc.Axis(rc=RC, zs=ZS, nfp=4) VARIABLE_INDICES = qsc.stellarator_symmetric_variable_indices(AXIS, modes=MODES) INITIAL = AXIS.dofs[jnp.asarray(VARIABLE_INDICES)] -HALF_WIDTH = jnp.asarray((0.06, 0.012, 0.004, 0.06, 0.012, 0.004)) +HALF_WIDTH = jnp.asarray((0.14, 0.07, 0.03, 0.14, 0.07, 0.03)) LOWER = INITIAL - HALF_WIDTH UPPER = INITIAL + HALF_WIDTH +ETABAR = -1.3295174 +P2 = -23501.281 +SOURCE_DATABASE_ID = 57409 def projected_residual(variables): axis = AXIS.with_dofs(AXIS.dofs.at[jnp.asarray(VARIABLE_INDICES)].set(variables)) solution = qsc.solve( axis=axis, - etabar=-0.6783912804454629, - B0=1.006541121335688, + etabar=ETABAR, + B0=1.0, B2c=0.0, + p2=P2, nphi=NPHI, order="r2", ) @@ -172,9 +164,11 @@ def weighted_l2(variables): variable_indices=VARIABLE_INDICES, lower_bounds=LOWER, upper_bounds=UPPER, - etabar=-0.6783912804454629, - B0=1.006541121335688, + etabar=ETABAR, + B0=1.0, + p2=P2, nphi=NPHI, + criteria=qsc.Criteria.from_curvo_2025(minimum_abs_iota=0.4), ) options = qsc.AxisSearchOptions( coarse_samples=12, @@ -213,6 +207,9 @@ def weighted_l2(variables): "jax_enable_x64": bool(jax.config.jax_enable_x64), "nphi": NPHI, "modes": MODES, + "source_database_id": SOURCE_DATABASE_ID, + "source_url": (f"https://stellarator.physics.wisc.edu/app/plot/{SOURCE_DATABASE_ID}"), + "selected_configuration": "b20_optimized_good", "timing_note": ( "SciPy timings exclude shared residual/Jacobian compilation; the " "pyQSC_JAX multistart timing includes compilation of its independent closure." diff --git a/benchmarks/reports/2026-07-30-b20-vmec-apple-m4.json b/benchmarks/reports/2026-07-30-b20-vmec-apple-m4.json index 19c6bbf..3a26ae8 100644 --- a/benchmarks/reports/2026-07-30-b20-vmec-apple-m4.json +++ b/benchmarks/reports/2026-07-30-b20-vmec-apple-m4.json @@ -8,52 +8,57 @@ "platform": "macOS-26.5.1-arm64-arm-64bit-Mach-O", "python": "3.13.7", "b20_optimizer_comparison": { - "common_case": "Landreman-Paul precise-QA seed; Fourier modes 1-3 varied; exact B2c eliminated at every evaluation; nphi=121 verification", + "common_case": "Curvo stellarator-database configuration 57409; Fourier modes 1-3 varied; exact B2c eliminated at every evaluation; nphi=121 verification", + "source_database_id": 57409, + "source_url": "https://stellarator.physics.wisc.edu/app/plot/57409", "timing_note": "SciPy timings exclude shared residual/Jacobian compilation; the pyQSC_JAX multistart timing includes compilation of its independent closure.", "results": [ { "function_evaluations": 1, "method": "exact B2c only", "seconds": 0.0, - "weighted_l2": 0.0003748334323839126 + "weighted_l2": 0.030992772869247103 }, { - "function_evaluations": 72, + "function_evaluations": 70, "method": "SciPy L-BFGS-B", - "seconds": 0.14576879201922566, - "weighted_l2": 0.0001923145250044151 + "seconds": 0.18148858298081905, + "weighted_l2": 0.00020139241185160374 }, { - "function_evaluations": 60, + "function_evaluations": 28, "method": "SciPy least_squares", - "seconds": 2.7433434999838937, - "weighted_l2": 0.00019145867839143548 + "seconds": 1.309102333005285, + "weighted_l2": 0.00010250101789370511 }, { "function_evaluations": 120, "method": "SciPy differential_evolution, low budget", - "seconds": 0.13656237500254065, - "weighted_l2": 0.10281099494870141 + "seconds": 0.11324654199415818, + "weighted_l2": 0.2657663516222627 }, { "distinct_basins": 3, - "function_evaluations": 129, + "function_evaluations": 130, "method": "pyQSC_JAX multistart Levenberg-Marquardt", - "seconds": 20.765741583018098, + "seconds": 21.91377937499783, "status": "best_found", - "weighted_l2": 0.00012441235529252347 + "weighted_l2": 0.00010827903169153683 } ], 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index 077e738..2bbcaef 100644 --- a/docs/development/refactor_status.md +++ b/docs/development/refactor_status.md @@ -206,3 +206,22 @@ was made for that phase. symmetry and the bridge covers fixed-boundary implicit differentiation, not a reconverged free-boundary NESTOR adjoint. Remote CI and review remain external gates. + +## Phase 15 — screened database showcase and constrained \(B_{20}\) + +- Files: traceable configurations from Wisconsin database IDs 3, 57409, and + 107579; an eight-mode constrained refinement of ID 57409; direct-Frenet 3D + surface plotting; regenerated README figures and optimizer report. +- Verification: every showcased design independently passes the Curvo profile + with \(\lvert\iota\rvert\ge0.4\); the database source ID and URL are frozen + in configuration and figure metadata; strong-axis surface smoothness is a + regression test. +- Numerical checks: the derived ID-57409 case has + \(\lvert\iota\rvert=2.964\), \(r_\mathrm{sing}=0.249\) m, and weighted + \(B_{20}\) residual \(1.2743\times10^{-10}\) at `nphi=121`, stable through + `nphi=481`. The finite-current showcase has a 32.99% minimum plasma + fraction and 4.43% angular variation while passing the same screen. +- Limitation: the current-visible split uses formal radius 0.45 m and carries + a 0.2286 T estimated field remainder. It is explicitly a field-jet + demonstration; smaller-radius production studies require radius + convergence and current/geometry re-optimization. diff --git a/docs/theory/b20-optimization.md b/docs/theory/b20-optimization.md index 004b4e6..5c03be2 100644 --- a/docs/theory/b20-optimization.md +++ b/docs/theory/b20-optimization.md @@ -84,41 +84,60 @@ The branch-aware multistart workflow built on these residuals is described in ## Optimizer comparison and selected case -Several optimizers were tested from the Landreman--Paul precise-QA axis. For -the common comparison, Fourier modes 1--3 were varied and \(B_{2c}\) was +The public [Curvo stellarator database](https://stellarator.physics.wisc.edu/) +was screened before optimization. Configuration +[57409](https://stellarator.physics.wisc.edu/app/plot/57409) was selected as +the traceable low-\(B_{20}\) seed: pyQSC_JAX independently reproduces +\(\lvert\iota\rvert=2.833\), \(r_\mathrm{sing}=0.238\) m, and a complete +Curvo/Table-3 pass when the minimum-transform threshold is tightened to 0.4. + +Several optimizers were then tested from exactly that downloaded axis. For the +common comparison, Fourier modes 1--3 were varied and \(B_{2c}\) was eliminated exactly at every objective evaluation. Timings are warm local measurements and exclude the shared JAX compilation. | method | evaluations | time [s] | independently evaluated weighted \(L^2\) | | --- | ---: | ---: | ---: | -| exact \(B_{2c}\) only | 1 | — | \(3.7483\times10^{-4}\) | -| SciPy L-BFGS-B | 72 | 0.146 | \(1.9231\times10^{-4}\) | -| SciPy `least_squares` | 60 | 2.743 | \(1.9146\times10^{-4}\) | -| low-budget differential evolution | 120 | 0.137 | \(1.0281\times10^{-1}\) | -| pyQSC_JAX multistart Levenberg--Marquardt | 129 | 20.766* | \(1.2441\times10^{-4}\) | +| exact \(B_{2c}\) only | 1 | — | \(3.09928\times10^{-2}\) | +| SciPy L-BFGS-B | 70 | 0.181 | \(2.01392\times10^{-4}\) | +| SciPy `least_squares` | 28 | 1.309 | \(1.02501\times10^{-4}\) | +| low-budget differential evolution | 120 | 0.113 | \(2.65766\times10^{-1}\) | +| pyQSC_JAX multistart Levenberg--Marquardt | 130 | 21.914* | \(1.08279\times10^{-4}\) | The SciPy timings exclude the shared JAX residual/Jacobian compilation; the asterisked multistart timing includes compilation of its independent closure. The coarse differential-evolution budget is included to show why a method label alone does not establish global quality. It did not locate the narrow -good basin. The selected `b20_optimized_qa` case used bounded -`least_squares` on modes 1--5 after exact \(B_{2c}\) elimination, followed by +good basin. Bounded `least_squares` was then continued one Fourier mode at a +time, re-eliminating \(B_{2c}\) at every evaluation: + +| highest varied mode | independently evaluated weighted \(L^2\) | +| ---: | ---: | +| 3 | \(1.02501\times10^{-4}\) | +| 4 | \(1.13643\times10^{-6}\) | +| 5 | \(5.58886\times10^{-7}\) | +| 6 | \(2.75804\times10^{-7}\) | +| 7 | \(3.02110\times10^{-8}\) | +| 8 | \(1.27645\times10^{-10}\) | + +The resulting `b20_optimized_good` configuration was held fixed for the independent resolution checks: | `nphi` | weighted \(L^2\) | | ---: | ---: | -| 61 | \(1.5900649432\times10^{-6}\) | -| 121 | \(1.5900649311\times10^{-6}\) | -| 241 | \(1.5900649186\times10^{-6}\) | -| 481 | \(1.5900649060\times10^{-6}\) | - -At `nphi=121`, its dense maximum is \(3.20\times10^{-6}\) and peak-to-peak -variation is \(6.27\times10^{-6}\). This is 26,053 times smaller in weighted -residual than exact \(B_{2c}\) optimization of the stock README QA axis. The -computed singular radius is 0.2484 m. The README surface is drawn at -0.075 m, so it has a 3.31-fold radial clearance relative to that truncated-map -diagnostic. Both numbers appear next to the actual 3D surface; a flat -\(B_{20}\) curve is not presented without its geometry. +| 121 | \(1.27431807\times10^{-10}\) | +| 241 | \(1.27645060\times10^{-10}\) | +| 481 | \(1.28075313\times10^{-10}\) | + +At `nphi=121`, its dense maximum is \(2.62\times10^{-10}\) and peak-to-peak +variation is \(5.23\times10^{-10}\). This is \(2.4321\times10^8\) times +smaller in weighted residual than exact \(B_{2c}\) optimization of its public +database seed. The independently recomputed design has +\(\lvert\iota\rvert=2.964\), \(r_\mathrm{sing}=0.2493\) m, maximum elongation +2.95, minimum \(L_{\nabla B}=0.437\) m, minimum +\(L_{\nabla\nabla B}=0.340\) m, positive Mercier margin, and a complete +Curvo-profile pass. The README surface is drawn at 0.075 m, giving 3.32-fold +radial clearance relative to the truncated-map singularity diagnostic. The result is a verified numerical basin, not a proof that no other basin is better. The runnable comparison is diff --git a/docs/validation/literature_cases.md b/docs/validation/literature_cases.md index db46223..1d9cb1c 100644 --- a/docs/validation/literature_cases.md +++ b/docs/validation/literature_cases.md @@ -21,3 +21,24 @@ The validation matrix is tied to primary literature: The [physics traceability table](../development/physics-traceability.md) connects every block to code and independent tests. Numerical constants are never copied from prose without a test or local, checksummed reference. + +## Public stellarator-database cases + +The README design gallery is traceable to the +[University of Wisconsin stellarator database](https://stellarator.physics.wisc.edu/) +and its [interactive application](https://stellarator.physics.wisc.edu/app). +The app reports transform magnitude, while the JSON downloads retain the +signed convention. pyQSC_JAX therefore states the showcase gate as +\(\lvert\iota\rvert\ge0.4\). + +| bundled name | public source | role | +| --- | --- | --- | +| `database_example_3` | [ID 3](https://stellarator.physics.wisc.edu/app/plot/3) | documented API/download example | +| `database_low_b20_57409` | [ID 57409](https://stellarator.physics.wisc.edu/app/plot/57409) | low-\(B_{20}\) optimization seed | +| `b20_optimized_good` | derived from [ID 57409](https://stellarator.physics.wisc.edu/app/plot/57409) | constrained eight-mode refinement | +| `database_large_singularity_107579` | [ID 107579](https://stellarator.physics.wisc.edu/app/plot/107579) | large-singular-radius example | + +Every case is solved again rather than trusting displayed database metrics. +Regression tests require all four to pass the full configurable Curvo profile +with the stricter transform threshold. The derived ID-57409 refinement also +retains the source ID and URL in `ReferenceConfiguration` metadata. diff --git a/docs/validation/plasma_field.md b/docs/validation/plasma_field.md index f5e3ec8..b685c5c 100644 --- a/docs/validation/plasma_field.md +++ b/docs/validation/plasma_field.md @@ -27,20 +27,23 @@ the current normalization transparent and produces the same 33.2574% fraction at every angle. The README and example use `plasma_stellarator`, a gently shaped -two-field-period case with `I2=4.2`, `p2=-1e5`, `B0=1`, and formal radius -0.2 m. It retains the \(>30\%\) plasma contribution while making the split -angle dependent: +two-field-period case with `I2=1.55`, `p2=-1e3`, `B0=1`, and formal radius +0.45 m. Unlike the earlier high-current demonstration, this pressure/current +balance passes every configurable Curvo criterion with the stricter +\(\lvert\iota\rvert\ge0.4\). It retains the \(>30\%\) plasma contribution +while making the split angle dependent: | quantity | value | | --- | ---: | -| minimum/mean/maximum \(\lvert B_p\rvert/\lvert B_\mathrm{tot}\rvert\) | 0.326967 / 0.332552 / 0.338719 | -| plasma \(\lvert B\rvert\) peak-to-peak / mean | 0.03534 | -| external \(\lvert B\rvert\) peak-to-peak / mean | 0.02663 | -| enclosed toroidal current | 0.84 MA | -| formal radius | 0.2 m | -| computed singular radius | 0.3351 m | -| formal/singular radius | 0.597 | -| estimated field remainder | 0.0351 T | +| minimum/mean/maximum \(\lvert B_p\rvert/\lvert B_\mathrm{tot}\rvert\) | 0.329933 / 0.337868 / 0.344899 | +| plasma \(\lvert B\rvert\) peak-to-peak / mean | 0.04429 | +| external \(\lvert B\rvert\) peak-to-peak / mean | 0.01042 | +| enclosed toroidal current | 1.569375 MA | +| \(\lvert\iota\rvert\) | 0.730286 | +| formal radius | 0.45 m | +| computed singular radius | 0.9916 m | +| formal/singular radius | 0.454 | +| estimated field remainder | 0.2286 T | The minimum fraction, nonzero angular variation, finite current, and radius margin are regression assertions. The publication plot shows total, plasma, @@ -48,7 +51,12 @@ and external Frenet components; plotting only their norms would hide both the constant-\(B_0\) total-field construction and the exact cancellation of transverse plasma/external components. -This is a field-split demonstration rather than a device-quality optimum. Its -role is to ensure that the plasma contribution cannot silently collapse to a -negligible plotting scale while retaining explicit asymptotic-error and -singular-radius metadata. +The underlying near-axis stellarator passes the named device-screening +profile; the \(a=0.45\) field split is deliberately a current-visible +demonstration, not a high-accuracy finite-radius claim. Its relatively large +0.2286 T remainder estimate is displayed here rather than hidden. Production +use should reduce the formal radius and perform the documented asymptotic +radius convergence, which will also reduce the plasma fraction unless the +current/geometry is re-optimized. The regression's role is to ensure that the +plasma contribution cannot silently collapse to a negligible plotting scale +while retaining explicit asymptotic-error and singular-radius metadata. diff --git a/docs/validation/vmex_interface.md b/docs/validation/vmex_interface.md index b7cff32..5f302ff 100644 --- a/docs/validation/vmex_interface.md +++ b/docs/validation/vmex_interface.md @@ -37,9 +37,9 @@ The publication example records finite-beta values of: | Quantity | Value | | --- | ---: | -| magnetic well | \(-4.22969\times10^{-4}\) | -| \(\partial W/\partial p_\mathrm{scale}\) | \(+5.24435\times10^{-5}\) | -| \(\|\partial W/\partial RBC\|_2\) | \(2.01871\) | +| magnetic well | \(-7.70343\times10^{-5}\) | +| \(\partial W/\partial p_\mathrm{scale}\) | \(+6.55641\times10^{-7}\) | +| \(\|\partial W/\partial RBC\|_2\) | \(1.85853\) | These values are finite, nonzero regression evidence that the pressure and boundary adjoint paths are active. diff --git a/examples/06_optimize_axis_B20.py b/examples/06_optimize_axis_B20.py index 36dbc1c..c889be8 100644 --- a/examples/06_optimize_axis_B20.py +++ b/examples/06_optimize_axis_B20.py @@ -1,4 +1,4 @@ -"""Compare a stock QA axis with a dense-grid B20-optimized QA axis.""" +"""Refine a screened database axis into a nearly constant-B20 stellarator.""" from pathlib import Path @@ -7,14 +7,14 @@ import pyqsc_jax as qsc -STOCK_CONFIGURATION = "qa" -OPTIMIZED_CONFIGURATION = "b20_optimized_qa" +STOCK_CONFIGURATION = "database_low_b20_57409" +OPTIMIZED_CONFIGURATION = "b20_optimized_good" NPHI = 121 SAVE_OUTPUT = True SHOW_FIGURE = False OUTPUT = Path("examples/output/06_optimize_axis_B20.png") -print("Eliminating B2c exactly for the stock QA axis...") +print("Eliminating B2c exactly for database configuration 57409...") stock = qsc.optimize_B2c(qsc.solve_configuration(STOCK_CONFIGURATION, nphi=NPHI)) print("Loading the independently optimized Fourier axis...") optimized = qsc.solve_configuration(OPTIMIZED_CONFIGURATION, nphi=NPHI) @@ -28,12 +28,16 @@ print("improvement factor:", improvement) print("nphi verification:", np.asarray(verification.resolutions)) print("verified weighted L2:", np.asarray(verification.weighted_l2)) +criteria = qsc.Criteria.from_curvo_2025(minimum_abs_iota=0.4) +print("Curvo profile passed:", criteria.evaluate(optimized).passed) +print("|iota|:", abs(float(optimized.iota))) +print("singular radius:", float(optimized.r_singularity)) stock_angle = np.asarray(stock.solution.varphi * stock.solution.inputs.axis.nfp / (2 * np.pi)) optimized_angle = np.asarray(optimized.varphi * optimized.inputs.axis.nfp / (2 * np.pi)) figure, axes = plt.subplots(1, 2, figsize=(9.4, 3.8)) axes[0].plot(stock_angle, np.asarray(stock.diagnostics.anomaly), linewidth=2) -axes[0].set_title(r"stock axis + exact $B_{2c}$") +axes[0].set_title(r"database ID 57409 + exact $B_{2c}$") axes[0].set_xlabel("Boozer angle / field period") axes[0].set_ylabel(r"$B_{20}-\langle B_{20}\rangle$ [T/m$^2$]") axes[1].plot( diff --git a/examples/10_plasma_external_field_jet.py b/examples/10_plasma_external_field_jet.py index 352166d..7850c8d 100644 --- a/examples/10_plasma_external_field_jet.py +++ b/examples/10_plasma_external_field_jet.py @@ -9,7 +9,7 @@ from pyqsc_jax.plotting import plot_field_split_components CONFIGURATION = "plasma_stellarator" -FORMAL_RADIUS = 0.2 +FORMAL_RADIUS = 0.45 NPHI = 61 ANGULAR_RESOLUTION = 96 SAVE_OUTPUT = True diff --git a/examples/publication/figure_B20_optimization.py b/examples/publication/figure_B20_optimization.py index e13aa04..47e9a93 100644 --- a/examples/publication/figure_B20_optimization.py +++ b/examples/publication/figure_B20_optimization.py @@ -10,8 +10,8 @@ import pyqsc_jax as qsc from pyqsc_jax.plotting import plot_surface_3d -STOCK_CONFIGURATION = "qa" -OPTIMIZED_CONFIGURATION = "b20_optimized_qa" +STOCK_CONFIGURATION = "database_low_b20_57409" +OPTIMIZED_CONFIGURATION = "b20_optimized_good" NPHI = 121 SURFACE_RADIUS = 0.075 OUTPUT_STEM = Path("examples/output/publication/B20_optimization") @@ -20,7 +20,7 @@ SHOW_FIGURE = False plt.style.use("seaborn-v0_8-whitegrid") -print("Comparing exact B2c elimination with the optimized Fourier axis...") +print("Refining the traceable low-B20 database configuration 57409...") stock = qsc.optimize_B2c(qsc.solve_configuration(STOCK_CONFIGURATION, nphi=NPHI)) optimized = qsc.solve_configuration(OPTIMIZED_CONFIGURATION, nphi=NPHI) optimized_diagnostics = qsc.b20_diagnostics(optimized) @@ -40,14 +40,14 @@ ) surface_axis.view_init(elev=24, azim=38) surface_axis.set_title( - "optimized QA surface\n" - rf"$\iota={float(optimized.iota):.3f}$, " + "database-seeded optimized QH surface\n" + rf"$|\iota|={abs(float(optimized.iota)):.3f}$, " rf"$r_\mathrm{{sing}}={float(optimized.r_singularity):.3f}$ m" ) stock_axis = figure.add_subplot(2, 2, 2) stock_axis.plot(stock_angle, np.asarray(stock.diagnostics.anomaly), linewidth=2.2) -stock_axis.set_title(r"stock axis + exact $B_{2c}$") +stock_axis.set_title(r"database ID 57409 + exact $B_{2c}$") stock_axis.set_xlabel("Boozer angle / field period") stock_axis.set_ylabel(r"$B_{20}-\langle B_{20}\rangle$ [T/m$^2$]") @@ -95,6 +95,7 @@ 0.04, 0.05, f"{improvement:,.0f}x lower residual\n" + "all Curvo criteria pass\n" rf"shown surface: $r={SURFACE_RADIUS:.3f}$ m" f" ({clearance:.1f}x inside singular radius)", transform=summary_axis.transAxes, @@ -129,6 +130,12 @@ "verification_nphi": np.asarray(verification.resolutions).tolist(), "verification_weighted_l2": np.asarray(verification.weighted_l2).tolist(), "optimizer": "bounded scipy least_squares after exact B2c elimination", + "source_database_id": 57409, + "source_url": "https://stellarator.physics.wisc.edu/app/plot/57409", + "curvo_profile_minimum_abs_iota": 0.4, + "curvo_profile_passed": qsc.Criteria.from_curvo_2025(minimum_abs_iota=0.4) + .evaluate(optimized) + .passed, } if SAVE_OUTPUT: OUTPUT_STEM.parent.mkdir(parents=True, exist_ok=True) diff --git a/examples/publication/figure_plasma_external_jet.py b/examples/publication/figure_plasma_external_jet.py index 577e821..0e34ffb 100644 --- a/examples/publication/figure_plasma_external_jet.py +++ b/examples/publication/figure_plasma_external_jet.py @@ -11,8 +11,8 @@ from pyqsc_jax.plotting import field_split_frenet_components, plot_surface_3d CONFIGURATION = "plasma_stellarator" -FORMAL_RADIUS = 0.2 -DISPLAY_RADIUS = 0.12 +FORMAL_RADIUS = 0.45 +DISPLAY_RADIUS = 0.18 NPHI = 121 ANGULAR_RESOLUTION = 128 OUTPUT_STEM = Path("examples/output/publication/plasma_external_jet") @@ -47,7 +47,8 @@ ) surface_axis.view_init(elev=25, azim=35) surface_axis.set_title( - "finite-current stellarator\n" + "screened finite-current stellarator\n" + rf"$|\iota|={abs(float(solution.iota)):.3f}$, " rf"$r_\mathrm{{sing}}={float(solution.r_singularity):.3f}$ m" ) diff --git a/examples/publication/figure_stellarator_gallery.py b/examples/publication/figure_stellarator_gallery.py index ebb8f8f..9a9e559 100644 --- a/examples/publication/figure_stellarator_gallery.py +++ b/examples/publication/figure_stellarator_gallery.py @@ -1,4 +1,4 @@ -"""Publication gallery of the bundled QA, QH, B20, and plasma stellarators.""" +"""Publication gallery of independently screened stellarator designs.""" import json import subprocess @@ -10,10 +10,15 @@ from pyqsc_jax.plotting import plot_surface_3d CASES = ( - ("qa", "QA reference", 0.055, "viridis"), - ("qh", "QH reference", 0.055, "plasma"), - ("b20_optimized_qa", r"$B_{20}$-optimized QA", 0.075, "cividis"), - ("plasma_stellarator", "finite-current plasma case", 0.12, "magma"), + ("database_example_3", "database ID 3", 0.075, "viridis"), + ("b20_optimized_good", r"database-seeded flat $B_{20}$", 0.075, "cividis"), + ( + "database_large_singularity_107579", + r"database ID 107579: large $r_\mathrm{sing}$", + 0.15, + "plasma", + ), + ("plasma_stellarator", "finite-current 33% plasma case", 0.18, "magma"), ) NPHI = 121 OUTPUT_STEM = Path("examples/output/publication/stellarator_gallery") @@ -28,6 +33,8 @@ print("Rendering the bundled stellarator gallery...") for panel, (name, title, radius, cmap) in enumerate(CASES, start=1): solution = qsc.solve_configuration(name, nphi=NPHI) + criteria = qsc.Criteria.from_curvo_2025(minimum_abs_iota=0.4) + assert criteria.evaluate(solution).passed axis = figure.add_subplot(2, 2, panel, projection="3d") plot_surface_3d( solution, @@ -37,14 +44,18 @@ cmap=cmap, ) axis.view_init(elev=24, azim=35) - if name == "b20_optimized_qa": + if name == "b20_optimized_good": diagnostic = rf"$\|P B_{{20}}\|_2={float(solution.B20_residual):.2e}$" elif name == "plasma_stellarator": - diagnostic = r"$\min |B_p|/|B|=32.7\%$ at $a=0.2$ m" + diagnostic = r"$\min |B_p|/|B|=33.0\%$ at $a=0.45$ m" else: - diagnostic = rf"$\iota={float(solution.iota):.3f}$" + diagnostic = rf"$|\iota|={abs(float(solution.iota)):.3f}$" axis.set_title( - title + "\n" + diagnostic + rf", $r_\mathrm{{sing}}={float(solution.r_singularity):.3f}$ m" + title + + "\n" + + diagnostic + + rf", $r_\mathrm{{sing}}={float(solution.r_singularity):.3f}$ m" + + "\nCurvo profile: pass" ) metadata["configurations"][name] = { "surface_radius": radius, @@ -52,6 +63,10 @@ "B20_residual": float(solution.B20_residual), "singular_radius": float(solution.r_singularity), "surface_to_singular_radius": radius / float(solution.r_singularity), + "curvo_profile_minimum_abs_iota": 0.4, + "curvo_profile_passed": True, + "source_database_id": qsc.get_configuration(name).source_database_id, + "source_url": qsc.get_configuration(name).source_url, } figure.tight_layout() diff --git a/src/pyqsc_jax/configurations.py b/src/pyqsc_jax/configurations.py index 563b49f..8cedd21 100644 --- a/src/pyqsc_jax/configurations.py +++ b/src/pyqsc_jax/configurations.py @@ -24,6 +24,8 @@ class ReferenceConfiguration: I2: float = 0.0 p2: float = 0.0 order: str = "r2" + source_database_id: int | None = None + source_url: str | None = None def parameters(self, **overrides: Any) -> dict[str, Any]: """Return fresh keyword arguments, with explicit caller overrides.""" @@ -113,6 +115,91 @@ def solve(self, **overrides: Any) -> NearAxisSolution: B0=1.006541121335688, B2c=0.9427285320639192, ), + ReferenceConfiguration( + name="database_example_3", + description=( + "Curvo stellarator-database configuration 3, retained as the " + "documented download/API example." + ), + rc=(1.0, -0.53677857, -0.046455786, -0.0070183445), + zs=(0.0, -0.5888703, -0.04447083, -0.009581006), + nfp=4, + etabar=1.4014399, + B2c=-0.7512066, + p2=-74635.375, + order="r3", + source_database_id=3, + source_url="https://stellarator.physics.wisc.edu/app/plot/3", + ), + ReferenceConfiguration( + name="database_low_b20_57409", + description=( + "Low-B20 Curvo stellarator-database configuration 57409, used as " + "the traceable seed for the bundled constrained refinement." + ), + rc=(1.0, -0.51677144, -0.009499784, -0.005914526), + zs=(0.0, -0.5420635, -0.012225689, -0.0059485724), + nfp=4, + etabar=-1.3295174, + B2c=-0.7577404, + p2=-23501.281, + order="r3", + source_database_id=57409, + source_url="https://stellarator.physics.wisc.edu/app/plot/57409", + ), + ReferenceConfiguration( + name="b20_optimized_good", + description=( + "Eight-mode QH refinement of database configuration 57409. Exact " + "B2c elimination and staged bounded least-squares flatten B20 while " + "retaining every Curvo Table-3 margin with |iota| above 0.4." + ), + rc=( + 1.0, + -0.5039436500066075, + -0.043965867334349464, + -0.00654919263283669, + -3.047898633100702e-06, + 2.7519909478191202e-05, + 6.071324626161564e-06, + 8.46692978641554e-07, + 5.99743474381913e-08, + ), + zs=( + 0.0, + -0.5050020451312105, + -0.045010140721391825, + -0.006585874304053245, + -1.5550078876295003e-05, + 2.6653739413147386e-05, + 5.978859527401134e-06, + 8.327402553082346e-07, + 5.9109366390399247e-08, + ), + nfp=4, + etabar=-1.3295174, + B2c=-1.132420959333329, + p2=-23501.281, + order="r3", + source_database_id=57409, + source_url="https://stellarator.physics.wisc.edu/app/plot/57409", + ), + ReferenceConfiguration( + name="database_large_singularity_107579", + description=( + "Curvo stellarator-database configuration 107579, selected for its " + "large independently recomputed singular radius." + ), + rc=(1.0, -0.54465365, 0.005908036, 0.0054288576), + zs=(0.0, 0.540987, -0.009328544, -0.003327578), + nfp=3, + etabar=-0.95917624, + B2c=0.10977107, + p2=-19211.062, + order="r3", + source_database_id=107579, + source_url="https://stellarator.physics.wisc.edu/app/plot/107579", + ), ReferenceConfiguration( name="plasma_dominant_channel", description=( @@ -129,16 +216,16 @@ def solve(self, **overrides: Any) -> NearAxisSolution: ReferenceConfiguration( name="plasma_stellarator", description=( - "Two-field-period finite-pressure/current stellarator with an " - "angle-dependent plasma/external split and more than 30 percent " - "plasma field at formal radius 0.2." + "Curvo-screened two-field-period finite-pressure/current " + "stellarator with an angle-dependent plasma/external split and " + "more than 30 percent plasma field at formal radius 0.45." ), rc=(1.0, 0.008), zs=(0.0, -0.008), nfp=2, etabar=0.5, - I2=4.2, - p2=-100000.0, + I2=1.55, + p2=-1000.0, ), ) diff --git a/src/pyqsc_jax/plotting.py b/src/pyqsc_jax/plotting.py index 0a89899..b1e65cd 100644 --- a/src/pyqsc_jax/plotting.py +++ b/src/pyqsc_jax/plotting.py @@ -11,7 +11,7 @@ from pyqsc_jax.axis import Axis, evaluate_axis from pyqsc_jax.models import NearAxisSolution from pyqsc_jax.plasma import PlasmaHessianData -from pyqsc_jax.vmec import uniform_cylindrical_surface +from pyqsc_jax.vmec import frenet_displacements def _matplotlib(): @@ -79,20 +79,47 @@ def surface_coordinates( raise ValueError("radius must be positive.") if not isinstance(ntheta, int) or isinstance(ntheta, bool) or ntheta < 4: raise ValueError("ntheta must be an integer >= 4.") - R, Z, _, _ = uniform_cylindrical_surface(solution, radius, ntheta=ntheta) + theta = jnp.linspace(0, 2 * jnp.pi, ntheta, endpoint=False)[:, None] + phi0 = solution.phi[None, :] + X, Y, Z = frenet_displacements( + solution, + jnp.asarray(radius), + theta, + phi0, + ) + axis_position = jnp.stack( + ( + solution.R0 * jnp.cos(solution.phi), + solution.R0 * jnp.sin(solution.phi), + solution.Z0, + ), + axis=-1, + ) + period_position = ( + axis_position[None, :, :] + + X[..., None] * solution.geometry.normal_cartesian[None, :, :] + + Y[..., None] * solution.geometry.binormal_cartesian[None, :, :] + + Z[..., None] * solution.geometry.tangent_cartesian[None, :, :] + ) period = 2 * jnp.pi / solution.inputs.axis.nfp - phi_periods = tuple( - solution.phi + period_index * period for period_index in range(solution.inputs.axis.nfp) + period_angles = jnp.arange(solution.inputs.axis.nfp) * period + cosine = jnp.cos(period_angles)[None, :, None] + sine = jnp.sin(period_angles)[None, :, None] + x_period = period_position[..., 0][:, None, :] + y_period = period_position[..., 1][:, None, :] + x = x_period * cosine - y_period * sine + y = x_period * sine + y_period * cosine + z = jnp.broadcast_to( + period_position[..., 2][:, None, :], + x.shape, ) - phi = jnp.concatenate(phi_periods) - R = jnp.concatenate((R,) * solution.inputs.axis.nfp, axis=1) - Z = jnp.concatenate((Z,) * solution.inputs.axis.nfp, axis=1) - x = R * jnp.cos(phi[None, :]) - y = R * jnp.sin(phi[None, :]) + x = x.reshape(ntheta, -1) + y = y.reshape(ntheta, -1) + z = z.reshape(ntheta, -1) return ( jnp.concatenate((x, x[:, :1]), axis=1), jnp.concatenate((y, y[:, :1]), axis=1), - jnp.concatenate((Z, Z[:, :1]), axis=1), + jnp.concatenate((z, z[:, :1]), axis=1), ) diff --git a/src/pyqsc_jax/vmec.py b/src/pyqsc_jax/vmec.py index 3131c72..fec3c84 100644 --- a/src/pyqsc_jax/vmec.py +++ b/src/pyqsc_jax/vmec.py @@ -94,12 +94,14 @@ def _periodic_interpolate( return jnp.interp(wrapped, extended_grid, extended_values) -def _interpolated_displacements( +def frenet_displacements( solution: NearAxisSolution, radius: jax.Array, theta: jax.Array, phi0: jax.Array, ) -> tuple[jax.Array, jax.Array, jax.Array]: + """Evaluate all available near-axis Frenet displacements.""" + period = 2 * jnp.pi / solution.inputs.axis.nfp grid = solution.phi interpolate = lambda values: _periodic_interpolate(phi0, grid, values, period) # noqa: E731 @@ -163,7 +165,7 @@ def _surface_at_axis_angle( period = 2 * jnp.pi / solution.inputs.axis.nfp grid = solution.phi interpolate = lambda values: _periodic_interpolate(phi0, grid, values, period) # noqa: E731 - X, Y, Z = _interpolated_displacements(solution, radius, theta, phi0) + X, Y, Z = frenet_displacements(solution, radius, theta, phi0) normal = solution.geometry.normal_cylindrical binormal = solution.geometry.binormal_cylindrical tangent = solution.geometry.tangent_cylindrical diff --git a/tests/physics/test_b20_optimization.py b/tests/physics/test_b20_optimization.py index 5e61d29..661bfd4 100644 --- a/tests/physics/test_b20_optimization.py +++ b/tests/physics/test_b20_optimization.py @@ -135,16 +135,19 @@ def test_resolution_verification_recomputes_fixed_candidate(): @pytest.mark.physics def test_documented_optimized_axis_has_nearly_constant_B20(): - stock = qsc.optimize_B2c(qsc.solve_configuration("qa", nphi=121)) - optimized = qsc.solve_configuration("b20_optimized_qa", nphi=121) + stock = qsc.optimize_B2c(qsc.solve_configuration("database_low_b20_57409", nphi=121)) + optimized = qsc.solve_configuration("b20_optimized_good", nphi=121) diagnostics = qsc.b20_diagnostics(optimized) verification = qsc.verify_B20_resolution(optimized, multipliers=(1, 2)) - - assert float(diagnostics.weighted_l2) < 1.6e-6 - assert float(diagnostics.grid_maximum) < 3.3e-6 - assert float(diagnostics.peak_to_peak) < 6.4e-6 - assert float(stock.diagnostics.weighted_l2 / diagnostics.weighted_l2) > 25000 - assert float(verification.relative_weighted_l2_change[1]) < 2.0e-7 + criteria = qsc.Criteria.from_curvo_2025(minimum_abs_iota=0.4) + + assert float(diagnostics.weighted_l2) < 1.4e-10 + assert float(diagnostics.grid_maximum) < 3.0e-10 + assert float(diagnostics.peak_to_peak) < 6.0e-10 + assert float(stock.diagnostics.weighted_l2 / diagnostics.weighted_l2) > 2.0e8 + assert float(verification.relative_weighted_l2_change[1]) < 2.0e-3 + assert criteria.evaluate(optimized).passed + assert abs(float(optimized.iota)) > 0.4 def test_B20_optimization_input_guards(): diff --git a/tests/physics/test_plasma_field.py b/tests/physics/test_plasma_field.py index 0031197..78c79c6 100644 --- a/tests/physics/test_plasma_field.py +++ b/tests/physics/test_plasma_field.py @@ -212,7 +212,7 @@ def test_documented_plasma_dominant_case_exceeds_thirty_percent(): @pytest.mark.physics def test_documented_plasma_stellarator_is_dominant_and_angle_dependent(): solution = qsc.solve_configuration("plasma_stellarator", nphi=121) - formal_radius = 0.2 + formal_radius = 0.45 plasma = qsc.plasma_field_on_axis( solution, formal_radius=formal_radius, @@ -225,8 +225,9 @@ def test_documented_plasma_stellarator_is_dominant_and_angle_dependent(): assert np.min(fraction) > 0.30 assert peak_to_peak_over_mean > 0.03 - assert formal_radius / float(solution.r_singularity) < 0.60 - np.testing.assert_allclose(np.mean(fraction), 0.33255168104046495, rtol=3.0e-12) + assert formal_radius / float(solution.r_singularity) < 0.46 + assert qsc.Criteria.from_curvo_2025(minimum_abs_iota=0.4).evaluate(solution).passed + np.testing.assert_allclose(np.mean(fraction), 0.3378675182784863, rtol=3.0e-12) def test_plasma_field_guards(): diff --git a/tests/unit/test_configurations.py b/tests/unit/test_configurations.py index dfa0583..dbb2443 100644 --- a/tests/unit/test_configurations.py +++ b/tests/unit/test_configurations.py @@ -12,6 +12,10 @@ def test_named_configurations_are_immutable_and_solve(): "qh", "finite_pressure_current", "b20_optimized_qa", + "database_example_3", + "database_low_b20_57409", + "b20_optimized_good", + "database_large_singularity_107579", "plasma_dominant_channel", "plasma_stellarator", ) @@ -38,6 +42,28 @@ def test_solve_configuration_preserves_topology_and_overrides(): np.testing.assert_allclose(finite.inputs.p2, -600000.0) +@pytest.mark.physics +def test_database_showcase_configurations_are_traceable_and_screened(): + criteria = qsc.Criteria.from_curvo_2025(minimum_abs_iota=0.4) + expected_sources = { + "database_example_3": 3, + "database_low_b20_57409": 57409, + "b20_optimized_good": 57409, + "database_large_singularity_107579": 107579, + } + + for name, database_id in expected_sources.items(): + configuration = qsc.get_configuration(name) + solution = configuration.solve(nphi=61) + + assert configuration.source_database_id == database_id + assert configuration.source_url == ( + f"https://stellarator.physics.wisc.edu/app/plot/{database_id}" + ) + assert criteria.evaluate(solution).passed + assert abs(float(solution.iota)) >= 0.4 + + def test_unknown_configuration_is_rejected(): with pytest.raises(ValueError, match="Available configurations"): qsc.get_configuration("missing") diff --git a/tests/unit/test_plotting.py b/tests/unit/test_plotting.py index 8d909bb..8bbc8c8 100644 --- a/tests/unit/test_plotting.py +++ b/tests/unit/test_plotting.py @@ -66,6 +66,25 @@ def test_surface_and_angle_dependent_field_split_plotters(): plot_field_split_components(result, solution, axes=axes[:2]) +@pytest.mark.physics +@pytest.mark.parametrize( + ("configuration", "radius"), + ( + ("database_example_3", 0.075), + ("b20_optimized_good", 0.075), + ("database_large_singularity_107579", 0.15), + ), +) +def test_database_surface_coordinates_are_finite_and_smooth(configuration, radius): + solution = qsc.solve_configuration(configuration, nphi=121) + x, y, z = surface_coordinates(solution, radius=radius, ntheta=36) + points = np.stack((x, y, z), axis=-1) + toroidal_edges = np.linalg.norm(np.diff(points, axis=1), axis=-1) + + assert np.all(np.isfinite(points)) + assert np.max(toroidal_edges) < 0.25 + + def test_plotter_guards(): first_order = qsc.solve_configuration("qa", nphi=15, order="r1") with pytest.raises(ValueError, match="r2"): From 2c31d85e8c9b821e5e32d0eb8c3be857fa2527c1 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 12:02:29 -0500 Subject: [PATCH 33/39] test: cover reusable plotting axes --- tests/unit/test_plotting.py | 21 ++++++++++++++++++--- 1 file changed, 18 insertions(+), 3 deletions(-) diff --git a/tests/unit/test_plotting.py b/tests/unit/test_plotting.py index 8bbc8c8..2d0740b 100644 --- a/tests/unit/test_plotting.py +++ b/tests/unit/test_plotting.py @@ -22,11 +22,17 @@ def test_axis_and_b20_plotters_return_objects(): solution = qsc.solve_configuration("qa", nphi=31) figure_axis, axis = plot_axis(solution, samples=31, label="QA") figure_b20, b20_axis = plot_b20(solution, label="QA") + reused_axis_figure, reused_axis = plot_axis(solution, ax=axis, samples=31) + reused_b20_figure, reused_b20_axis = plot_b20(solution, ax=b20_axis) assert axis.figure is figure_axis assert b20_axis.figure is figure_b20 - assert len(axis.lines) == 1 - assert len(b20_axis.lines) == 1 + assert reused_axis_figure is figure_axis + assert reused_axis is axis + assert reused_b20_figure is figure_b20 + assert reused_b20_axis is b20_axis + assert len(axis.lines) == 2 + assert len(b20_axis.lines) == 2 def test_field_jet_norm_plotter_and_axes_guard(): @@ -51,13 +57,22 @@ def test_surface_and_angle_dependent_field_split_plotters(): solution = qsc.solve_configuration("plasma_stellarator", nphi=31) x, y, z = surface_coordinates(solution, radius=0.05, ntheta=12) figure, axis = plot_surface_3d(solution, radius=0.05, ntheta=12) + reused_figure, reused_axis = plot_surface_3d( + solution, + radius=0.05, + ntheta=12, + ax=axis, + plot_axis_line=False, + ) result = qsc.plasma_hessian_on_axis(solution, formal_radius=0.1) components = field_split_frenet_components(result, solution) component_figure, axes = plot_field_split_components(result, solution) assert x.shape == y.shape == z.shape == (12, 63) assert axis.figure is figure - assert len(axis.collections) == 1 + assert reused_figure is figure + assert reused_axis is axis + assert len(axis.collections) == 2 assert components.shape == (3, 3, 31) assert axes.shape == (3,) assert component_figure is axes[0].figure From da7d7753c0e169b39ee4e68f2bf8e38e3901ddd6 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 12:24:01 -0500 Subject: [PATCH 34/39] ci: allow screened physics suite to complete --- .github/workflows/tests.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml index 93c560d..522afc4 100644 --- a/.github/workflows/tests.yml +++ b/.github/workflows/tests.yml @@ -42,7 +42,7 @@ jobs: - os: macos-latest python: "3.14" runs-on: ${{ matrix.os }} - timeout-minutes: 20 + timeout-minutes: 30 env: JAX_ENABLE_X64: "true" steps: From f316e113c58c3f9bc4fd0e34745314380527a668 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 14:12:36 -0500 Subject: [PATCH 35/39] fix: showcase zero-current finite-beta stellarators --- README.md | 39 +++++++--- benchmarks/benchmark_vmex_interface.py | 2 + docs/_static/plasma_external_jet.png | Bin 177243 -> 211741 bytes docs/_static/stellarator_gallery.png | Bin 522661 -> 539630 bytes docs/_static/vmex_radial_profiles.png | Bin 173345 -> 179067 bytes docs/development/refactor_status.md | 14 ++-- docs/validation/plasma_field.md | 70 +++++++++--------- docs/validation/vmex_interface.md | 20 +++-- examples/03_second_order_finite_beta.py | 27 +++---- examples/07_good_stellarator_search.py | 49 ++++++------ examples/10_plasma_external_field_jet.py | 7 +- .../publication/figure_plasma_external_jet.py | 27 ++++--- .../publication/figure_stellarator_gallery.py | 13 +++- .../figure_vmex_radial_profiles.py | 6 +- src/pyqsc_jax/configurations.py | 22 +++--- src/pyqsc_jax/vmex.py | 6 ++ tests/integration/test_vmex_live.py | 15 ++++ tests/physics/test_plasma_field.py | 18 +++-- tests/unit/test_configurations.py | 5 ++ tests/unit/test_plotting.py | 3 +- tests/unit/test_vmex_interface.py | 2 + 21 files changed, 209 insertions(+), 136 deletions(-) diff --git a/README.md b/README.md index a6f5deb..01d11cf 100644 --- a/README.md +++ b/README.md @@ -19,8 +19,9 @@ plasma–coil field jets in JAX. Four runnable, independently re-evaluated designs: [database ID 3](https://stellarator.physics.wisc.edu/app/plot/3), an eight-mode refinement of [database ID 57409](https://stellarator.physics.wisc.edu/app/plot/57409), the large-clearance [database ID 107579](https://stellarator.physics.wisc.edu/app/plot/107579), -and an angle-dependent finite-current case. Every displayed design passes the -configurable Curvo/Table-3 profile with the stricter +and the finite-pressure, zero-current [database ID 52521](https://stellarator.physics.wisc.edu/app/plot/52521). +Every displayed design is a nonplanar stellarator and passes the configurable +Curvo/Table-3 profile with the stricter \(\lvert\iota\rvert\geq0.4\); each panel reports transform, singular radius, and its defining diagnostic. Plotting radii and database provenance are in the adjacent JSON metadata. @@ -116,8 +117,9 @@ resolution, timing, and radius-convergence tables are in the | \(B_{20}\)-optimized singular radius | 0.249 m | displayed \(r=0.075\) m gives 3.3× clearance | | Largest showcased singular radius, database ID 107579 | 0.432 m | \(>0.4\) m | | Four-case showcase design screen | all pass | Curvo profile with \(\lvert\iota\rvert\ge0.4\) | -| Angle-dependent minimum \(\lvert B_\mathrm{plasma}\rvert/\lvert B_\mathrm{total}\rvert\) | 32.99% at \(a=0.45\) m | \(>30\%\) | -| Plasma-field norm peak-to-peak / mean | 4.43% | \(>3\%\) | +| Pressure-only \(I_2=0\) plasma fraction, min/mean/max at \(a=0.15\) m | 0.1761% / 0.1890% / 0.2026% | nonzero and resolved | +| Pressure-driven plasma-field norm peak-to-peak / mean | 14.04% | \(>10\%\) | +| Finite-beta showcase axis torsion, RMS | \(0.979\ \mathrm{m}^{-1}\) | \(>0.5\ \mathrm{m}^{-1}\) | | VMEC/near-axis on-axis \(\iota\), \(r=0.0025\) | 0.418543 / 0.418307 | relative error \(<0.1\%\) | | VMEC force residuals | \(2.4\)–\(7.6\times10^{-11}\) | maximum \(<10^{-9}\) | | `to_vmec`, Apple M4 CPU, compile+execute / warm | 0.476 s / 5.20 ms | warm unit gate \(<0.5\) s | @@ -128,7 +130,8 @@ diagnostics = qsc.b20_diagnostics(optimized) print(diagnostics.weighted_l2, diagnostics.grid_maximum) plasma_case = qsc.solve_configuration("plasma_stellarator", nphi=61) -plasma = qsc.plasma_field_on_axis(plasma_case, formal_radius=0.45) +assert plasma_case.inputs.I2 == 0 +plasma = qsc.plasma_field_on_axis(plasma_case, formal_radius=0.15) ``` ## Target rotational transform @@ -191,7 +194,9 @@ distinction between `best_found` and a certified zero are in the ```python solution = qsc.solve_configuration("plasma_stellarator", nphi=61) -target = qsc.plasma_hessian_on_axis(solution, formal_radius=0.45) +assert solution.inputs.I2 == 0 +assert solution.inputs.p2 != 0 +target = qsc.plasma_hessian_on_axis(solution, formal_radius=0.15) print(target.field.external_field.shape) # (nphi, 3) print(target.field.external_gradient_independent.shape) # (nphi, 5) @@ -202,24 +207,34 @@ ESSOS consumes these external vacuum targets for normalized field, gradient, and Hessian coil objectives. The dependency remains one-way: `ESSOS -> pyQSC_JAX`. -This case independently passes the Curvo profile with -\(\lvert\iota\rvert=0.730\) and \(r_\mathrm{sing}=0.992\) m. The stated -formal radius \(a=0.45\) m is mandatory model metadata and remains inside that -singular-radius estimate. The public plot uses Frenet components rather than -only \(|B|\), making the angle dependence and exact cancellation of plasma -and external transverse components visible; +This is public stellarator-database configuration 52521, with exactly +\(I_2=0\), finite \(p_2=-2.8248\times10^4\ \mathrm{Pa/m^2}\), +\(\lvert\iota\rvert=2.809\), \(r_\mathrm{sing}=0.392\) m, and RMS axis +torsion \(0.979\ \mathrm{m}^{-1}\). It independently passes the Curvo profile. +The stated formal radius \(a=0.15\) m is mandatory model metadata and remains +inside the singular-radius estimate. The public plot uses Frenet components +and a percent scale, making the pressure-driven angle dependence and exact +cancellation of plasma and external transverse components visible; \(|B_\mathrm{total}|=B_0\) is constant on axis by construction. +The pressure-only contribution is approximately \(0.19\%\), not 30%. The +larger fraction previously shown came from finite \(I_2\) and produced an +essentially tokamak-like example; it is intentionally excluded from the +showcase. Current-driven cases remain supported and validated by the library, +but all user-facing finite-beta examples use \(I_2=0\). + ## Differentiable radial equilibria with VMEX ```python import jax near_axis = qsc.solve_configuration("plasma_stellarator", nphi=61) +assert near_axis.inputs.I2 == 0 problem = qsc.to_vmex_problem( near_axis, r=0.02, qs_surfaces=(0.25, 0.5, 0.75, 1.0), + adjoint_tol=1e-8, ) equilibrium = problem.solve() diff --git a/benchmarks/benchmark_vmex_interface.py b/benchmarks/benchmark_vmex_interface.py index 117079a..1987797 100644 --- a/benchmarks/benchmark_vmex_interface.py +++ b/benchmarks/benchmark_vmex_interface.py @@ -34,6 +34,7 @@ ns_array=(7,), ftol=1.0e-7, max_iterations=1200, + adjoint_tol=1.0e-8, multigrid=False, ) @@ -81,6 +82,7 @@ def objective(parameters): "mpol_maximum": problem.mpol, "ntor": problem.ntor, "ns_array": np.asarray(problem.input.ns_array).tolist(), + "adjoint_tolerance": problem.adjoint_tol, }, "forward_seconds": forward_seconds, 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z!j^Nqk+;@o4^t)!&cO}(b)+)U4tT^dpn%Fsc{DcvTiF|Vi^0WD(}AHVhl8NmQ~#WU zAm(e7qB^xLc{2J&1iy1tZ6#K$musuEE_pR9Wy%h0I<{DPu<k z0^I`$@w3QUx=3|*|AW71%P#sk4A zBfWv8ujY-D?x5*(q&LK?ohpN8rKN6m>j1{roN}O=$6s-@@Ebn9j`grFF}4V$gPKWz z*il*|$8Hi{WI3K5yaVMWW~Mx0PvlE<;|)#3)yfcDoD=g3*S`&c&<0Hxd!XrvXTib< zdPNkPjI6QoaFzJBh>ywD8mQDBc6)r-FUan_4@{fdqrTc5#jasR+TLaKF5Z}PKn8B! zd|>vi`LomwanVP;8jIRSbKQKAJc#gBQ(}yOuPTt}8PSKC3Eb?4VAa@I}>u*!=%N76t diff --git a/docs/development/refactor_status.md b/docs/development/refactor_status.md index 2bbcaef..80c8a70 100644 --- a/docs/development/refactor_status.md +++ b/docs/development/refactor_status.md @@ -219,9 +219,11 @@ was made for that phase. - Numerical checks: the derived ID-57409 case has \(\lvert\iota\rvert=2.964\), \(r_\mathrm{sing}=0.249\) m, and weighted \(B_{20}\) residual \(1.2743\times10^{-10}\) at `nphi=121`, stable through - `nphi=481`. The finite-current showcase has a 32.99% minimum plasma - fraction and 4.43% angular variation while passing the same screen. -- Limitation: the current-visible split uses formal radius 0.45 m and carries - a 0.2286 T estimated field remainder. It is explicitly a field-jet - demonstration; smaller-radius production studies require radius - convergence and current/geometry re-optimization. + `nphi=481`. The finite-beta showcase is database ID 52521 with exactly + \(I_2=0\), finite \(p_2\), RMS axis torsion \(0.979\ \mathrm{m}^{-1}\), + and 14.04% relative angular variation of the pressure-driven plasma-field + norm while passing the same screen. +- Limitation: at formal radius 0.15 m the pressure-only plasma contribution is + approximately 0.19% of the total field. The former 30% showcase relied on + finite \(I_2\) and was removed because its nearly planar geometry presented + as a tokamak rather than a representative stellarator. diff --git a/docs/validation/plasma_field.md b/docs/validation/plasma_field.md index b685c5c..2f9c678 100644 --- a/docs/validation/plasma_field.md +++ b/docs/validation/plasma_field.md @@ -20,43 +20,41 @@ singular filament quadrature would omit those terms and is not treated as an independent reference. See the [matched field derivation](../theory/plasma-field.md) and `tests/physics/test_plasma_*.py`. -## Plasma-dominant regression cases +## Pressure-only stellarator showcase -`plasma_dominant_channel` remains the circular analytic regression: it makes -the current normalization transparent and produces the same 33.2574% fraction -at every angle. - -The README and example use `plasma_stellarator`, a gently shaped -two-field-period case with `I2=1.55`, `p2=-1e3`, `B0=1`, and formal radius -0.45 m. Unlike the earlier high-current demonstration, this pressure/current -balance passes every configurable Curvo criterion with the stricter -\(\lvert\iota\rvert\ge0.4\). It retains the \(>30\%\) plasma contribution -while making the split angle dependent: +The README and every finite-beta example use `plasma_stellarator`, the public +[Wisconsin stellarator-database configuration 52521](https://stellarator.physics.wisc.edu/app/plot/52521). +It has exactly `I2=0`, finite `p2=-28248.188`, four field periods, and a +strongly nonplanar magnetic axis. At `nphi=121`, its RMS torsion is +\(0.978864\ \mathrm{m}^{-1}\), so this case cannot silently regress to a +planar tokamak axis. It passes every configurable Curvo criterion with the +stricter \(\lvert\iota\rvert\ge0.4\). | quantity | value | | --- | ---: | -| minimum/mean/maximum \(\lvert B_p\rvert/\lvert B_\mathrm{tot}\rvert\) | 0.329933 / 0.337868 / 0.344899 | -| plasma \(\lvert B\rvert\) peak-to-peak / mean | 0.04429 | -| external \(\lvert B\rvert\) peak-to-peak / mean | 0.01042 | -| enclosed toroidal current | 1.569375 MA | -| \(\lvert\iota\rvert\) | 0.730286 | -| formal radius | 0.45 m | -| computed singular radius | 0.9916 m | -| formal/singular radius | 0.454 | -| estimated field remainder | 0.2286 T | - -The minimum fraction, nonzero angular variation, finite current, and radius -margin are regression assertions. The publication plot shows total, plasma, -and external Frenet components; plotting only their norms would hide both the -constant-\(B_0\) total-field construction and the exact cancellation of -transverse plasma/external components. - -The underlying near-axis stellarator passes the named device-screening -profile; the \(a=0.45\) field split is deliberately a current-visible -demonstration, not a high-accuracy finite-radius claim. Its relatively large -0.2286 T remainder estimate is displayed here rather than hidden. Production -use should reduce the formal radius and perform the documented asymptotic -radius convergence, which will also reduce the plasma fraction unless the -current/geometry is re-optimized. The regression's role is to ensure that the -plasma contribution cannot silently collapse to a negligible plotting scale -while retaining explicit asymptotic-error and singular-radius metadata. +| \(I_2\) | exactly 0 | +| \(p_2\) | \(-2.82482\times10^4\ \mathrm{Pa/m^2}\) | +| minimum/mean/maximum \(\lvert B_p\rvert/\lvert B_\mathrm{tot}\rvert\) | 0.00176059 / 0.00188960 / 0.00202583 | +| plasma \(\lvert B\rvert\) peak-to-peak / mean | 0.140368 | +| enclosed toroidal current | exactly 0 A | +| \(\lvert\iota\rvert\) | 2.809271 | +| RMS axis torsion | \(0.978864\ \mathrm{m}^{-1}\) | +| formal radius | 0.15 m | +| computed singular radius | 0.391608 m | +| formal/singular radius | 0.383 | +| estimated Hessian remainder | \(5.54\times10^{-3}\ \mathrm{T/m^2}\) | + +The zero current, finite pressure, nonzero torsion, nonzero plasma field, +angular variation, and radius margin are regression assertions. The +publication plot shows total, plasma, and external Frenet components; +plotting only their norms would hide both the constant-\(B_0\) total-field +construction and the cancellation of transverse plasma/external components. + +The pressure-only plasma contribution is about \(0.19\%\), not 30%. A scan +over screened database configurations and pressure multipliers found that +forcing a current-visible 30% fraction with \(I_2=0\) is incompatible with +the regular, criterion-passing near-axis examples considered here. The +earlier 30% showcase obtained its scale from finite \(I_2\) and appeared +tokamak-like, so it has been removed. `plasma_dominant_channel` is retained +only as a circular analytic current-normalization regression; it is not a +showcase stellarator or a recommended design. diff --git a/docs/validation/vmex_interface.md b/docs/validation/vmex_interface.md index 5f302ff..572caec 100644 --- a/docs/validation/vmex_interface.md +++ b/docs/validation/vmex_interface.md @@ -22,10 +22,10 @@ surface conversion and pressure/current normalization. The live compatibility test covers: -| Case | Pressure | Current | Checked quantities | -| --- | ---: | ---: | --- | -| vacuum QA | zero | zero | \(\iota(s)\), QS profile, well, implicit boundary gradient | -| `plasma_stellarator` | finite | finite | \(\iota(s)\), QS profile, well, nonzero thermal energy | +| Case | Pressure | Current | Axis | Checked quantities | +| --- | ---: | ---: | --- | --- | +| vacuum QA | zero | zero | nonplanar QA | \(\iota(s)\), QS profile, well, implicit boundary gradient | +| `plasma_stellarator` (database ID 52521) | finite | exactly zero | nonplanar, RMS torsion \(0.979\ \mathrm{m}^{-1}\) | \(\iota(s)\), QS profile, well, nonzero thermal energy, implicit pressure/boundary gradients | At the deliberately small `ns=7`, `mpol=4`, `ntor=2` smoke resolution, the vacuum VMEX axis value in the pyQSC_JAX sign convention is `-0.421520`, @@ -33,13 +33,19 @@ compared with the near-axis value `-0.420473`. This is a 0.249% difference; the test gate is 0.8%. The purpose of this low-resolution job is cross-package AD compatibility, not a production equilibrium accuracy claim. +The strongly shaped finite-beta adjoint uses an explicit +`adjoint_tol=1e-8`; the public API retains VMEX's stricter \(10^{-11}\) +default unless the caller makes that tradeoff explicitly. VMEX enforces the +selected residual tolerance and raises rather than returning an unconverged +adjoint. + The publication example records finite-beta values of: | Quantity | Value | | --- | ---: | -| magnetic well | \(-7.70343\times10^{-5}\) | -| \(\partial W/\partial p_\mathrm{scale}\) | \(+6.55641\times10^{-7}\) | -| \(\|\partial W/\partial RBC\|_2\) | \(1.85853\) | +| magnetic well | \(1.84561\times10^{-2}\) | +| \(\partial W/\partial p_\mathrm{scale}\) | \(+6.22590\times10^{-5}\) | +| \(\|\partial W/\partial RBC\|_2\) | \(9.78080\times10^1\) | These values are finite, nonzero regression evidence that the pressure and boundary adjoint paths are active. diff --git a/examples/03_second_order_finite_beta.py b/examples/03_second_order_finite_beta.py index 14e8bbc..88bdf85 100644 --- a/examples/03_second_order_finite_beta.py +++ b/examples/03_second_order_finite_beta.py @@ -1,4 +1,4 @@ -"""Solve the complete finite-pressure/current second-order system.""" +"""Solve the complete finite-pressure, zero-current second-order system.""" from pathlib import Path @@ -7,38 +7,29 @@ import pyqsc_jax as qsc from pyqsc_jax.plotting import plot_b20 -RC = [1.0, 0.09] -ZS = [0.0, -0.09] -NFP = 2 -ETABAR = 0.95 -I2 = 0.9 -P2 = -600000.0 -B2C = -0.7 +CONFIGURATION = "plasma_stellarator" NPHI = 61 SAVE_OUTPUT = True SHOW_FIGURE = False OUTPUT = Path("examples/output/03_second_order_finite_beta.png") -print("Solving the finite-pressure/current r2 configuration...") -solution = qsc.Qsc( - rc=RC, - zs=ZS, - nfp=NFP, - etabar=ETABAR, - I2=I2, - p2=P2, - B2c=B2C, +print("Solving the finite-pressure, zero-current stellarator...") +solution = qsc.solve_configuration( + CONFIGURATION, nphi=NPHI, order="r2", ) +assert float(solution.inputs.I2) == 0.0 +assert float(solution.inputs.p2) != 0.0 print("iota:", float(solution.iota)) +print("torsion RMS [1/m]:", float((solution.torsion**2).mean() ** 0.5)) print("linear residual:", float(solution.linear_report.residual_norm)) print("linear condition number:", float(solution.linear_report.matrix_condition_number)) print("B20 weighted residual:", float(solution.B20_residual)) print("Mercier D r^2:", float(solution.DMerc_times_r2)) print("singular radius [m]:", float(solution.r_singularity)) -figure, _ = plot_b20(solution, label="finite beta/current", color="tab:red") +figure, _ = plot_b20(solution, label="finite pressure, zero current", color="tab:red") figure.tight_layout() if SAVE_OUTPUT: OUTPUT.parent.mkdir(parents=True, exist_ok=True) diff --git a/examples/07_good_stellarator_search.py b/examples/07_good_stellarator_search.py index 6838c2c..a498584 100644 --- a/examples/07_good_stellarator_search.py +++ b/examples/07_good_stellarator_search.py @@ -1,4 +1,4 @@ -"""Apply a named screening profile during a reproducible axis search.""" +"""Apply the Curvo screen during a reproducible zero-current stellarator search.""" from pathlib import Path @@ -8,52 +8,53 @@ import pyqsc_jax as qsc -AXIS = qsc.Axis(rc=[1.0], zs=[0.0], nfp=1) -ETABAR = 1.0 -I2 = 0.1 -NPHI = 15 +CONFIGURATION = "plasma_stellarator" +I2 = 0.0 +NPHI = 31 SAVE_OUTPUT = True SHOW_FIGURE = False OUTPUT = Path("examples/output/07_good_stellarator_search.png") -# This deliberately permissive profile demonstrates mechanics; it is not a -# claim that a circular channel passes the published Curvo screening profile. -criteria = qsc.Criteria.from_curvo_2025( - minimum_abs_iota=0.0, - maximum_elongation=20.0, - minimum_L_grad_B=0.0, - minimum_axis_radius=0.0, - minimum_singular_radius=0.0, - minimum_L_grad_grad_B=0.0, - maximum_B20_variation=10.0, - minimum_beta=0.0, - minimum_DMerc_times_r2=-1.0e6, +configuration = qsc.get_configuration(CONFIGURATION) +axis = qsc.Axis( + rc=configuration.rc, + zs=configuration.zs, + nfp=configuration.nfp, ) +variable_indices = qsc.stellarator_symmetric_variable_indices(axis, modes=(3,)) +criteria = qsc.Criteria.from_curvo_2025(minimum_abs_iota=0.4) problem = qsc.AxisSearchProblem( - axis=AXIS, - variable_indices=(0,), - lower_bounds=jnp.asarray([0.8]), - upper_bounds=jnp.asarray([1.2]), - etabar=ETABAR, + axis=axis, + variable_indices=variable_indices, + lower_bounds=jnp.asarray([0.002, 0.002]), + upper_bounds=jnp.asarray([0.008, 0.008]), + etabar=configuration.etabar, I2=I2, + p2=configuration.p2, nphi=NPHI, criteria=criteria, - selector="maximum_criteria_margin", + selector="maximum_singular_radius", ) options = qsc.AxisSearchOptions( coarse_samples=2, local_starts=1, maximum_iterations=2, verification_multipliers=(1, 2), + verification_tail_tolerance=1.0, ) -print("Running criteria-aware search...") +print("Running criteria-aware search from database ID 52521...") result = qsc.search_axis(problem, options=options) if result.best is None or result.best.criteria_report is None: raise RuntimeError("The criteria-aware example did not produce a report.") report = result.best.criteria_report print("status:", result.status) print("criteria passed:", report.passed) +print("I2:", float(result.best.solution.inputs.I2)) +print("p2:", float(result.best.solution.inputs.p2)) +print("iota:", float(result.best.solution.iota)) +print("singular radius [m]:", float(result.best.solution.r_singularity)) +print("torsion RMS [1/m]:", float((result.best.solution.torsion**2).mean() ** 0.5)) for evaluation in report.evaluations: print( evaluation.name, diff --git a/examples/10_plasma_external_field_jet.py b/examples/10_plasma_external_field_jet.py index 7850c8d..7b02ac3 100644 --- a/examples/10_plasma_external_field_jet.py +++ b/examples/10_plasma_external_field_jet.py @@ -9,15 +9,18 @@ from pyqsc_jax.plotting import plot_field_split_components CONFIGURATION = "plasma_stellarator" -FORMAL_RADIUS = 0.45 +FORMAL_RADIUS = 0.15 NPHI = 61 ANGULAR_RESOLUTION = 96 SAVE_OUTPUT = True SHOW_FIGURE = False OUTPUT = Path("examples/output/10_plasma_external_field_jet.png") -print("Solving the finite-current total field...") +print("Solving the finite-pressure, zero-current stellarator...") solution = qsc.solve_configuration(CONFIGURATION, nphi=NPHI) +assert float(solution.inputs.I2) == 0.0 +assert float(solution.inputs.p2) != 0.0 +print("torsion RMS [1/m]:", float((solution.torsion**2).mean() ** 0.5)) print("Separating the surface-free plasma and external jets...") result = qsc.plasma_hessian_on_axis( solution, diff --git a/examples/publication/figure_plasma_external_jet.py b/examples/publication/figure_plasma_external_jet.py index 0e34ffb..6bb9730 100644 --- a/examples/publication/figure_plasma_external_jet.py +++ b/examples/publication/figure_plasma_external_jet.py @@ -11,8 +11,8 @@ from pyqsc_jax.plotting import field_split_frenet_components, plot_surface_3d CONFIGURATION = "plasma_stellarator" -FORMAL_RADIUS = 0.45 -DISPLAY_RADIUS = 0.18 +FORMAL_RADIUS = 0.15 +DISPLAY_RADIUS = 0.12 NPHI = 121 ANGULAR_RESOLUTION = 128 OUTPUT_STEM = Path("examples/output/publication/plasma_external_jet") @@ -23,6 +23,8 @@ plt.style.use("seaborn-v0_8-whitegrid") print("Evaluating the surface-free plasma/external jet...") solution = qsc.solve_configuration(CONFIGURATION, nphi=NPHI) +assert float(solution.inputs.I2) == 0.0 +assert float(solution.inputs.p2) != 0.0 result = qsc.plasma_hessian_on_axis( solution, formal_radius=FORMAL_RADIUS, @@ -47,19 +49,19 @@ ) surface_axis.view_init(elev=25, azim=35) surface_axis.set_title( - "screened finite-current stellarator\n" + r"database stellarator: finite $p_2$, exactly $I_2=0$" + "\n" rf"$|\iota|={abs(float(solution.iota)):.3f}$, " - rf"$r_\mathrm{{sing}}={float(solution.r_singularity):.3f}$ m" + rf"$\tau_\mathrm{{rms}}={float((solution.torsion**2).mean() ** 0.5):.3f}$ m$^{{-1}}$" ) fraction_axis = figure.add_subplot(2, 2, 2) -fraction_axis.plot(angle, np.asarray(plasma_fraction), color="tab:red", linewidth=2.3) -fraction_axis.axhline(0.30, color="black", linestyle="--", linewidth=1.2, label="30% gate") -fraction_axis.fill_between(angle, 0.30, np.asarray(plasma_fraction), alpha=0.18, color="tab:red") +fraction_percent = 100.0 * np.asarray(plasma_fraction) +fraction_axis.plot(angle, fraction_percent, color="tab:red", linewidth=2.3) +fraction_axis.fill_between(angle, 0.0, fraction_percent, alpha=0.18, color="tab:red") fraction_axis.set_xlabel("Boozer angle / field period") -fraction_axis.set_ylabel(r"$|B_\mathrm{plasma}|/|B_\mathrm{total}|$") -fraction_axis.set_title("plasma contribution varies with angle") -fraction_axis.legend() +fraction_axis.set_ylabel(r"$100|B_\mathrm{plasma}|/|B_\mathrm{total}|$ [%]") +fraction_axis.set_title("pressure-driven plasma contribution") tangent_axis = figure.add_subplot(2, 2, 3) for field_index, label in enumerate(("total", "plasma", "external")): @@ -95,6 +97,11 @@ "display_radius": DISPLAY_RADIUS, "nphi": NPHI, "angular_resolution": ANGULAR_RESOLUTION, + "I2": float(solution.inputs.I2), + "p2": float(solution.inputs.p2), + "torsion_minimum": float(solution.torsion.min()), + "torsion_maximum": float(solution.torsion.max()), + "torsion_rms": float((solution.torsion**2).mean() ** 0.5), "enclosed_current_amperes": float(result.field.field.current_source.enclosed_toroidal_current), "minimum_plasma_field_fraction": float(plasma_fraction.min()), "mean_plasma_field_fraction": float(plasma_fraction.mean()), diff --git a/examples/publication/figure_stellarator_gallery.py b/examples/publication/figure_stellarator_gallery.py index 9a9e559..fc7edb0 100644 --- a/examples/publication/figure_stellarator_gallery.py +++ b/examples/publication/figure_stellarator_gallery.py @@ -18,7 +18,12 @@ 0.15, "plasma", ), - ("plasma_stellarator", "finite-current 33% plasma case", 0.18, "magma"), + ( + "plasma_stellarator", + r"database ID 52521: finite $p_2$, $I_2=0$", + 0.12, + "magma", + ), ) NPHI = 121 OUTPUT_STEM = Path("examples/output/publication/stellarator_gallery") @@ -47,7 +52,8 @@ if name == "b20_optimized_good": diagnostic = rf"$\|P B_{{20}}\|_2={float(solution.B20_residual):.2e}$" elif name == "plasma_stellarator": - diagnostic = r"$\min |B_p|/|B|=33.0\%$ at $a=0.45$ m" + torsion_rms = float((solution.torsion**2).mean() ** 0.5) + diagnostic = rf"$\tau_\mathrm{{rms}}={torsion_rms:.3f}\ \mathrm{{m}}^{{-1}}$" else: diagnostic = rf"$|\iota|={abs(float(solution.iota)):.3f}$" axis.set_title( @@ -67,6 +73,9 @@ "curvo_profile_passed": True, "source_database_id": qsc.get_configuration(name).source_database_id, "source_url": qsc.get_configuration(name).source_url, + "I2": float(solution.inputs.I2), + "p2": float(solution.inputs.p2), + "torsion_rms": float((solution.torsion**2).mean() ** 0.5), } figure.tight_layout() diff --git a/examples/publication/figure_vmex_radial_profiles.py b/examples/publication/figure_vmex_radial_profiles.py index 8cc09b0..8fbe76f 100644 --- a/examples/publication/figure_vmex_radial_profiles.py +++ b/examples/publication/figure_vmex_radial_profiles.py @@ -13,7 +13,7 @@ CASES = ( ("qa", "vacuum QA"), - ("plasma_stellarator", "finite beta/current"), + ("plasma_stellarator", r"finite $p_2$, $I_2=0$"), ) RADIUS = 0.02 QS_SURFACES = (0.2, 0.4, 0.6, 0.8, 1.0) @@ -37,6 +37,7 @@ ns_array=(7,), ftol=1.0e-7, max_iterations=1200, + adjoint_tol=1.0e-8, multigrid=False, ) equilibrium = problem.solve() @@ -68,7 +69,7 @@ cmap="magma", ) surface_axis.view_init(elev=25, azim=35) -surface_axis.set_title("VMEX source boundary\nfinite pressure and current") +surface_axis.set_title(r"VMEX source boundary" "\n" r"finite $p_2$, exactly $I_2=0$") iota_axis = figure.add_subplot(2, 2, 2) qs_axis = figure.add_subplot(2, 2, 3) @@ -130,6 +131,7 @@ "vmex_version": finite_problem.vmex_version, "vmex_validated_commit": finite_problem.validated_commit, "radius": RADIUS, + "adjoint_tolerance": finite_problem.adjoint_tol, "cases": { label: { "iota": np.asarray(quantities.iota).tolist(), diff --git a/src/pyqsc_jax/configurations.py b/src/pyqsc_jax/configurations.py index 8cedd21..5878d01 100644 --- a/src/pyqsc_jax/configurations.py +++ b/src/pyqsc_jax/configurations.py @@ -216,16 +216,20 @@ def solve(self, **overrides: Any) -> NearAxisSolution: ReferenceConfiguration( name="plasma_stellarator", description=( - "Curvo-screened two-field-period finite-pressure/current " - "stellarator with an angle-dependent plasma/external split and " - "more than 30 percent plasma field at formal radius 0.45." + "Curvo stellarator-database configuration 52521: a strongly " + "nonplanar finite-pressure, zero-current stellarator used for " + "the plasma/external and VMEX showcases." ), - rc=(1.0, 0.008), - zs=(0.0, -0.008), - nfp=2, - etabar=0.5, - I2=1.55, - p2=-1000.0, + rc=(1.0, -0.5415884, 0.029195854, 0.0048646266), + zs=(0.0, -0.57113713, 0.029922731, 0.0041398546), + nfp=4, + etabar=1.1396117, + B2c=-0.050057083, + I2=0.0, + p2=-28248.188, + order="r3", + source_database_id=52521, + source_url="https://stellarator.physics.wisc.edu/app/plot/52521", ), ) diff --git a/src/pyqsc_jax/vmex.py b/src/pyqsc_jax/vmex.py index 100324b..9c8edbf 100644 --- a/src/pyqsc_jax/vmex.py +++ b/src/pyqsc_jax/vmex.py @@ -65,6 +65,7 @@ class VmexProblem: newton_iterations: int ftol: float max_iterations: int + adjoint_tol: float multigrid: bool device: Any vmex_version: str @@ -237,6 +238,7 @@ def to_vmex_problem( ftol_array: Any | None = None, ftol: float = 1.0e-10, max_iterations: int = 5000, + adjoint_tol: float = 1.0e-11, multigrid: bool = True, device: Any = None, ) -> VmexProblem: @@ -265,6 +267,8 @@ def to_vmex_problem( helicity_n = -int(np.asarray(solution.helicity)) if not isinstance(helicity_n, int) or isinstance(helicity_n, bool): raise ValueError("helicity_n must be an integer.") + if not np.isfinite(adjoint_tol) or adjoint_tol <= 0: + raise ValueError("adjoint_tol must be positive and finite.") boundary = vmec_boundary( solution, @@ -335,6 +339,7 @@ def to_vmex_problem( newton_iterations=newton_iterations, ftol=float(ftol), max_iterations=max_iterations, + adjoint_tol=float(adjoint_tol), multigrid=bool(multigrid), device=device, vmex_version=str(vmex.__version__), @@ -386,6 +391,7 @@ def solve_vmex(problem: VmexProblem, parameters: Any | None = None) -> VmexEquil selected_parameters, ftol=problem.ftol, max_iterations=problem.max_iterations, + adjoint_tol=problem.adjoint_tol, multigrid=problem.multigrid, device=problem.device, ) diff --git a/tests/integration/test_vmex_live.py b/tests/integration/test_vmex_live.py index a0b9484..d86b8bb 100644 --- a/tests/integration/test_vmex_live.py +++ b/tests/integration/test_vmex_live.py @@ -26,6 +26,7 @@ def _problem(solution): ns_array=(7,), ftol=1.0e-7, max_iterations=1200, + adjoint_tol=1.0e-8, multigrid=False, qs_surfaces=(0.5, 1.0), ) @@ -67,3 +68,17 @@ def test_vmex_finite_beta_profiles(): assert float(quantities.thermal_energy) > 0 assert np.all(np.isfinite(np.asarray(quantities.iota))) assert np.all(np.isfinite(np.asarray(quantities.quasisymmetry))) + + value, gradient = jax.value_and_grad( + lambda parameters: ( + qsc.vmex_radial_quantities( + problem, + parameters, + ).magnetic_well + ) + )(problem.parameters) + assert np.isfinite(float(value)) + assert np.isfinite(float(gradient.pres_scale)) + assert float(abs(gradient.pres_scale)) > 0 + assert np.all(np.isfinite(np.asarray(gradient.rbc))) + assert float(np.linalg.norm(np.asarray(gradient.rbc))) > 0 diff --git a/tests/physics/test_plasma_field.py b/tests/physics/test_plasma_field.py index 78c79c6..fdc8f43 100644 --- a/tests/physics/test_plasma_field.py +++ b/tests/physics/test_plasma_field.py @@ -210,9 +210,9 @@ def test_documented_plasma_dominant_case_exceeds_thirty_percent(): @pytest.mark.physics -def test_documented_plasma_stellarator_is_dominant_and_angle_dependent(): +def test_documented_plasma_stellarator_is_pressure_only_nonplanar_and_angle_dependent(): solution = qsc.solve_configuration("plasma_stellarator", nphi=121) - formal_radius = 0.45 + formal_radius = 0.15 plasma = qsc.plasma_field_on_axis( solution, formal_radius=formal_radius, @@ -222,12 +222,16 @@ def test_documented_plasma_stellarator_is_dominant_and_angle_dependent(): total_norm = np.linalg.norm(np.asarray(solution.B_axis), axis=-1) fraction = plasma_norm / total_norm peak_to_peak_over_mean = np.ptp(plasma_norm) / np.mean(plasma_norm) - - assert np.min(fraction) > 0.30 - assert peak_to_peak_over_mean > 0.03 - assert formal_radius / float(solution.r_singularity) < 0.46 + torsion_rms = np.sqrt(np.mean(np.asarray(solution.torsion) ** 2)) + + assert float(solution.inputs.I2) == 0.0 + assert float(solution.inputs.p2) != 0.0 + assert torsion_rms > 0.5 + assert np.min(fraction) > 1.7e-3 + assert peak_to_peak_over_mean > 0.1 + assert formal_radius / float(solution.r_singularity) < 0.4 assert qsc.Criteria.from_curvo_2025(minimum_abs_iota=0.4).evaluate(solution).passed - np.testing.assert_allclose(np.mean(fraction), 0.3378675182784863, rtol=3.0e-12) + np.testing.assert_allclose(np.mean(fraction), 0.0018895978020422664, rtol=3.0e-12) def test_plasma_field_guards(): diff --git a/tests/unit/test_configurations.py b/tests/unit/test_configurations.py index dbb2443..b2ea637 100644 --- a/tests/unit/test_configurations.py +++ b/tests/unit/test_configurations.py @@ -50,6 +50,7 @@ def test_database_showcase_configurations_are_traceable_and_screened(): "database_low_b20_57409": 57409, "b20_optimized_good": 57409, "database_large_singularity_107579": 107579, + "plasma_stellarator": 52521, } for name, database_id in expected_sources.items(): @@ -62,6 +63,10 @@ def test_database_showcase_configurations_are_traceable_and_screened(): ) assert criteria.evaluate(solution).passed assert abs(float(solution.iota)) >= 0.4 + if name == "plasma_stellarator": + assert float(solution.inputs.I2) == 0.0 + assert float(solution.inputs.p2) != 0.0 + assert float(np.sqrt(np.mean(np.asarray(solution.torsion) ** 2))) > 0.5 def test_unknown_configuration_is_rejected(): diff --git a/tests/unit/test_plotting.py b/tests/unit/test_plotting.py index 2d0740b..bdda3c2 100644 --- a/tests/unit/test_plotting.py +++ b/tests/unit/test_plotting.py @@ -68,7 +68,8 @@ def test_surface_and_angle_dependent_field_split_plotters(): components = field_split_frenet_components(result, solution) component_figure, axes = plot_field_split_components(result, solution) - assert x.shape == y.shape == z.shape == (12, 63) + expected_toroidal_points = solution.inputs.axis.nfp * solution.inputs.nphi + 1 + assert x.shape == y.shape == z.shape == (12, expected_toroidal_points) assert axis.figure is figure assert reused_figure is figure assert reused_axis is axis diff --git a/tests/unit/test_vmex_interface.py b/tests/unit/test_vmex_interface.py index 7ff9ba5..ce8a1e8 100644 --- a/tests/unit/test_vmex_interface.py +++ b/tests/unit/test_vmex_interface.py @@ -138,6 +138,7 @@ def test_problem_builds_without_disk_and_exposes_quantities(fake_vmex): assert problem.vmex_version == "test" assert problem.validated_commit == qsc.VMEX_VALIDATED_COMMIT + assert problem.adjoint_tol == 1.0e-11 assert problem.input.mpol == 4 assert problem.boundary.RBC.shape == (5, 4) assert not problem.finite_beta @@ -189,6 +190,7 @@ def test_empty_qs_surface_list_supports_asymmetric_equilibrium(fake_vmex): ({"ftol": 0.0}, "positive"), ({"ftol_array": (1.0e-7, 1.0e-8)}, "one positive"), ({"max_iterations": 0}, "positive integer"), + ({"adjoint_tol": 0.0}, "positive and finite"), ({"helicity_m": 1.5}, "integer"), ({"helicity_n": 1.5}, "integer"), ], From 8fb457deeb8b71dca0bc3d06d2da5fd9cbc99c4f Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 14:34:23 -0500 Subject: [PATCH 36/39] fix: accept converged residuals with undefined derivatives --- src/pyqsc_jax/axis_optimization.py | 4 +++- tests/physics/test_axis_optimization.py | 24 ++++++++++++++++++++++++ 2 files changed, 27 insertions(+), 1 deletion(-) diff --git a/src/pyqsc_jax/axis_optimization.py b/src/pyqsc_jax/axis_optimization.py index 9f8a922..06a9b45 100644 --- a/src/pyqsc_jax/axis_optimization.py +++ b/src/pyqsc_jax/axis_optimization.py @@ -415,10 +415,12 @@ def _levenberg_marquardt( jnp.sqrt(largest_eigenvalue / smallest_eigenvalue), ) condition_number = jnp.where(jnp.isnan(condition_number), jnp.inf, condition_number) + residual_converged = jnp.linalg.norm(current_residual) <= options.residual_tolerance + derivative_finite = jnp.all(jnp.isfinite(jacobian)) finite = ( jnp.all(jnp.isfinite(internal)) & jnp.all(jnp.isfinite(current_residual)) - & jnp.all(jnp.isfinite(jacobian)) + & (derivative_finite | residual_converged) ) return internal, LocalLeastSquaresReport( initial_residual_norm=initial_norm, diff --git a/tests/physics/test_axis_optimization.py b/tests/physics/test_axis_optimization.py index f33012a..142718a 100644 --- a/tests/physics/test_axis_optimization.py +++ b/tests/physics/test_axis_optimization.py @@ -2,6 +2,7 @@ from dataclasses import replace +import jax import jax.numpy as jnp import numpy as np import pytest @@ -93,6 +94,29 @@ def test_local_solve_accepts_a_finite_rank_deficient_exact_zero(): assert np.isinf(float(report.jacobian_condition_number)) +def test_local_solve_accepts_a_finite_converged_residual_with_nan_derivative(): + @jax.custom_vjp + def residual(_value): + return jnp.zeros((3,), dtype=_value.dtype) + + def residual_forward(value): + return jnp.zeros((3,), dtype=value.dtype), value.shape + + def residual_backward(shape, cotangent): + return (jnp.full(shape, jnp.nan, dtype=cotangent.dtype),) + + residual.defvjp(residual_forward, residual_backward) + options = small_options(maximum_iterations=1) + initial = jnp.asarray([0.0, 0.0]) + + internal, report = _levenberg_marquardt(residual, initial, options) + + np.testing.assert_allclose(internal, initial) + assert report.converged + assert report.finite + assert np.isinf(float(report.jacobian_condition_number)) + + def test_fourier_continuation_copies_retained_modes_and_runs_stages(): low_axis = qsc.Axis(rc=[1.0], zs=[0.0], nfp=1) high_axis = qsc.Axis(rc=[0.9, 0.0], zs=[0.0, 0.0], nfp=1) From ccb7c451c3085512ea415fb173db47432750ee2b Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 17:28:22 -0500 Subject: [PATCH 37/39] docs: showcase distinct QA and optimization evidence --- CHANGELOG.md | 14 +- README.md | 43 ++++-- .../2026-07-30-b20-optimizers-apple-m4.json | 52 +++++++ docs/_static/QA_QH_branches.png | Bin 0 -> 46850 bytes docs/_static/convergence.png | Bin 44237 -> 49454 bytes docs/_static/core_performance.png | Bin 0 -> 66572 bytes docs/_static/optimizer_comparison.png | Bin 0 -> 95339 bytes docs/_static/stellarator_gallery.png | Bin 539630 -> 519079 bytes docs/development/final_review.md | 4 +- docs/development/refactor_status.md | 25 ++- docs/theory/b20-optimization.md | 11 +- docs/validation/literature_cases.md | 13 +- examples/publication/figure_QA_QH_branches.py | 22 ++- examples/publication/figure_convergence.py | 5 +- .../publication/figure_core_performance.py | 145 ++++++++++++++++++ .../figure_optimizer_comparison.py | 136 ++++++++++++++++ .../publication/figure_stellarator_gallery.py | 71 +++++++-- src/pyqsc_jax/configurations.py | 18 +++ tests/unit/test_configurations.py | 15 +- tests/unit/test_plotting.py | 1 + 20 files changed, 510 insertions(+), 65 deletions(-) create mode 100644 benchmarks/reports/2026-07-30-b20-optimizers-apple-m4.json create mode 100644 docs/_static/QA_QH_branches.png create mode 100644 docs/_static/core_performance.png create mode 100644 docs/_static/optimizer_comparison.png create mode 100644 examples/publication/figure_core_performance.py create mode 100644 examples/publication/figure_optimizer_comparison.py diff --git a/CHANGELOG.md b/CHANGELOG.md index 7358c21..a69388c 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -14,10 +14,14 @@ first stable release. aspect-ratio quantities in vacuum and finite beta, with a live current-VMEX compatibility job. - Full-torus 3D surface helpers and a four-stellarator README gallery covering - QA, QH, the \(B_{20}\)-optimized case, and the finite-current plasma case. -- `plasma_stellarator`, an angle-dependent finite-pressure/current case whose - minimum plasma-field fraction is 32.70%, whose plasma-field norm varies by - 3.53%, and whose formal radius remains inside the singular surface. + database QA ID 139524, database QH ID 3, the \(B_{20}\)-optimized case, and + the large-singular-radius database case 107579. +- `plasma_stellarator`, an angle-dependent finite-pressure, exactly + zero-current database case whose pressure-driven plasma-field norm varies + by 14.04% and whose formal radius remains inside the singular surface. +- Reproducible README figures for QA/QH topology branches, resolution + convergence, synchronized JIT/JVP/VMAP timings, and five-way \(B_{20}\) + optimizer screening followed by staged eight-mode refinement. - Vectorized, JIT-compiled VMEC boundary export with all four coefficient families, deterministic INDATA output, conversion diagnostics, legacy-adapter support, a frozen VMEC 9.0 `wout` regression, and an opt-in @@ -102,7 +106,7 @@ first stable release. seven-component Cartesian STF representation. - Named immutable QA, QH, and finite-pressure/current configurations. - Lazy plotting helpers that return Matplotlib figure and axes objects. -- Fourteen direct tutorial scripts and eight deterministic publication-figure +- Fourteen direct tutorial scripts and ten deterministic publication-figure scripts with commit/parameter metadata and clean-directory CI execution. - Downstream ESSOS external-field-jet integration with normalized 3+5+7 objectives, finite-beta stage-two and single-stage examples, and diff --git a/README.md b/README.md index 01d11cf..ea2339b 100644 --- a/README.md +++ b/README.md @@ -14,22 +14,33 @@ plasma–coil field jets in JAX. > compatibility, and external 3+5+7 field-jet paths are validated; release > hardening is still in progress. -![Four independently screened stellarators](docs/_static/stellarator_gallery.png) - -Four runnable, independently re-evaluated designs: [database ID 3](https://stellarator.physics.wisc.edu/app/plot/3), -an eight-mode refinement of [database ID 57409](https://stellarator.physics.wisc.edu/app/plot/57409), -the large-clearance [database ID 107579](https://stellarator.physics.wisc.edu/app/plot/107579), -and the finite-pressure, zero-current [database ID 52521](https://stellarator.physics.wisc.edu/app/plot/52521). -Every displayed design is a nonplanar stellarator and passes the configurable -Curvo/Table-3 profile with the stricter -\(\lvert\iota\rvert\geq0.4\); each panel reports transform, singular radius, -and its defining diagnostic. Plotting radii and database provenance are in -the adjacent JSON metadata. +![A visually diverse gallery of screened QA, QH, optimized, and large-clearance stellarators](docs/_static/stellarator_gallery.png) + +Four geometries with four distinct jobs: the one-period QA +[database ID 139524](https://stellarator.physics.wisc.edu/app/plot/139524), +the four-period QH [database ID 3](https://stellarator.physics.wisc.edu/app/plot/3), +an eight-mode flat-\(B_{20}\) refinement of +[database ID 57409](https://stellarator.physics.wisc.edu/app/plot/57409), and +the large-clearance [database ID 107579](https://stellarator.physics.wisc.edu/app/plot/107579). +Every panel is independently re-solved and screened. The lead QA stellarator +has helicity zero, \(\lvert\iota\rvert=0.355\), finite pressure, exactly +\(I_2=0\), and nonzero torsion; it passes the Curvo/Table-3 profile with the +requested \(\lvert\iota\rvert\geq0.3\) gate. The other three pass at +\(\lvert\iota\rvert\geq0.4\). Plot radii and provenance are saved beside the +runnable figure as JSON. | \(B_{20}\) optimization, geometry, and singular margin | Angle-dependent plasma/external field | | --- | --- | | ![B20 optimization](docs/_static/B20_optimization.png) | ![Plasma and external jet](docs/_static/plasma_external_jet.png) | +| QA versus QH topology branches | Resolution audit catches under-resolved \(B_{20}\) | +| --- | --- | +| ![QA and QH topology branches](docs/_static/QA_QH_branches.png) | ![Spectral resolution convergence](docs/_static/convergence.png) | + +| Measured JIT, JVP, and VMAP speedups | Five optimizers plus staged refinement | +| --- | --- | +| ![Measured JAX core performance](docs/_static/core_performance.png) | ![B20 optimizer comparison](docs/_static/optimizer_comparison.png) | + | Differentiable radial VMEX quantities | VMEC2000 export validation | | --- | --- | | ![VMEX radial quantities](docs/_static/vmex_radial_profiles.png) | ![VMEC validation](docs/_static/vmec_validation.png) | @@ -54,13 +65,15 @@ python -m pip install 'pyqsc-jax[plot,vmex]' ```python import pyqsc_jax as qsc -configuration = qsc.get_configuration("database_example_3") +configuration = qsc.get_configuration("database_qa_139524") solution = configuration.solve(nphi=81) -criteria = qsc.Criteria.from_curvo_2025(minimum_abs_iota=0.4) +criteria = qsc.Criteria.from_curvo_2025(minimum_abs_iota=0.3) assert solution.root_report.converged assert solution.linear_report.converged assert criteria.evaluate(solution).passed +assert int(solution.helicity) == 0 +assert solution.inputs.I2 == 0 print("source:", configuration.source_url) print("|iota|:", abs(solution.iota)) print("B20 residual:", solution.B20_residual) @@ -116,13 +129,15 @@ resolution, timing, and radius-convergence tables are in the | Improvement over ID-57409 exact-\(B_{2c}\) solve | \(2.4321\times10^8\)× | \(>2.0\times10^8\)× | | \(B_{20}\)-optimized singular radius | 0.249 m | displayed \(r=0.075\) m gives 3.3× clearance | | Largest showcased singular radius, database ID 107579 | 0.432 m | \(>0.4\) m | -| Four-case showcase design screen | all pass | Curvo profile with \(\lvert\iota\rvert\ge0.4\) | +| Showcase QA, database ID 139524 | helicity 0, \(\lvert\iota\rvert=0.355\), \(\tau_\mathrm{RMS}=1.199\ \mathrm{m}^{-1}\) | Curvo profile with \(\lvert\iota\rvert\ge0.3\) | +| Four-case showcase design screen | all pass | QA gate 0.3; other cases \(\lvert\iota\rvert\ge0.4\) | | Pressure-only \(I_2=0\) plasma fraction, min/mean/max at \(a=0.15\) m | 0.1761% / 0.1890% / 0.2026% | nonzero and resolved | | Pressure-driven plasma-field norm peak-to-peak / mean | 14.04% | \(>10\%\) | | Finite-beta showcase axis torsion, RMS | \(0.979\ \mathrm{m}^{-1}\) | \(>0.5\ \mathrm{m}^{-1}\) | | VMEC/near-axis on-axis \(\iota\), \(r=0.0025\) | 0.418543 / 0.418307 | relative error \(<0.1\%\) | | VMEC force residuals | \(2.4\)–\(7.6\times10^{-11}\) | maximum \(<10^{-9}\) | | `to_vmec`, Apple M4 CPU, compile+execute / warm | 0.476 s / 5.20 ms | warm unit gate \(<0.5\) s | +| First-order solve, `nphi=61`, Apple CPU, compile+execute / warm | 198.2 ms / 0.144 ms | synchronized median; 1,373× amortized speedup | ```python optimized = qsc.solve_configuration("b20_optimized_good", nphi=121) diff --git a/benchmarks/reports/2026-07-30-b20-optimizers-apple-m4.json b/benchmarks/reports/2026-07-30-b20-optimizers-apple-m4.json new file mode 100644 index 0000000..17704dd --- /dev/null +++ b/benchmarks/reports/2026-07-30-b20-optimizers-apple-m4.json @@ -0,0 +1,52 @@ +{ + "git_commit": "8fb457deeb8b71dca0bc3d06d2da5fd9cbc99c4f", + "jax": "0.11.0", + "jax_backend": "cpu", + "jax_enable_x64": true, + "modes": [ + 1, + 2, + 3 + ], + "nphi": 121, + "platform": "macOS-26.5.1-arm64-arm-64bit-Mach-O", + "python": "3.13.7", + "results": [ + { + "function_evaluations": 1, + "method": "exact B2c only", + "seconds": 0.0, + "weighted_l2": 0.030992772869247103 + }, + { + "function_evaluations": 70, + "method": "SciPy L-BFGS-B", + "seconds": 0.1407689999905415, + "weighted_l2": 0.00020139241185160374 + }, + { + "function_evaluations": 28, + "method": "SciPy least_squares", + "seconds": 1.3488249160000123, + "weighted_l2": 0.00010250101789370511 + }, + { + "function_evaluations": 120, + "method": "SciPy differential_evolution, low budget", + "seconds": 0.10409141599666327, + "weighted_l2": 0.2657663516222627 + }, + { + "distinct_basins": 3, + "function_evaluations": 130, + "method": "pyQSC_JAX multistart Levenberg-Marquardt", + "seconds": 21.77209062501788, + "status": "best_found", + "weighted_l2": 0.00010827903169153683 + } + ], + "selected_configuration": "b20_optimized_good", + "source_database_id": 57409, + "source_url": "https://stellarator.physics.wisc.edu/app/plot/57409", + "timing_note": "SciPy timings exclude shared residual/Jacobian compilation; the pyQSC_JAX multistart timing includes compilation of its independent closure." +} diff --git a/docs/_static/QA_QH_branches.png 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UdOU;_*kCbKl{8RgNYl{&1$jNBssI20 diff --git a/docs/development/final_review.md b/docs/development/final_review.md index ce214f6..38e510e 100644 --- a/docs/development/final_review.md +++ b/docs/development/final_review.md @@ -17,9 +17,9 @@ Zenodo archive/DOI. | Gate | Result | | --- | --- | | Ruff lint and format | clean over `src`, `tests`, `examples`, `benchmarks` | -| Full test/coverage run | 226 passed; 98.64% combined line/branch coverage | +| Full test/coverage run | 287 passed, 3 integration skips; 98.79% combined line/branch coverage | | Documentation | HTML and doctest builders pass with warnings as errors | -| Examples | 12 tutorials + 5 publication scripts pass from clean cwd | +| Examples | 14 tutorials + 10 publication scripts pass from clean cwd | | Package metadata | wheel and sdist pass `twine check` | | Clean artifacts | wheel and independently rebuilt sdist pass physics smokes | | Dependencies | both environments pass `pip check`; no known advisories | diff --git a/docs/development/refactor_status.md b/docs/development/refactor_status.md index 80c8a70..dfb7179 100644 --- a/docs/development/refactor_status.md +++ b/docs/development/refactor_status.md @@ -209,13 +209,16 @@ was made for that phase. ## Phase 15 — screened database showcase and constrained \(B_{20}\) -- Files: traceable configurations from Wisconsin database IDs 3, 57409, and - 107579; an eight-mode constrained refinement of ID 57409; direct-Frenet 3D - surface plotting; regenerated README figures and optimizer report. -- Verification: every showcased design independently passes the Curvo profile - with \(\lvert\iota\rvert\ge0.4\); the database source ID and URL are frozen - in configuration and figure metadata; strong-axis surface smoothness is a - regression test. +- Files: traceable configurations from Wisconsin database IDs 3, 57409, + 107579, and the one-period QA ID 139524; an eight-mode constrained + refinement of ID 57409; direct-Frenet 3D surface plotting; topology, + convergence, measured-performance, and optimizer-comparison README figures. +- Verification: every showcased design independently passes the Curvo profile. + The QA lead passes with helicity zero and + \(\lvert\iota\rvert\ge0.3\); the other displayed cases pass with + \(\lvert\iota\rvert\ge0.4\). Database source IDs and URLs are frozen in + configuration and figure metadata, and every displayed surface has a + smoothness regression. - Numerical checks: the derived ID-57409 case has \(\lvert\iota\rvert=2.964\), \(r_\mathrm{sing}=0.249\) m, and weighted \(B_{20}\) residual \(1.2743\times10^{-10}\) at `nphi=121`, stable through @@ -223,6 +226,14 @@ was made for that phase. \(I_2=0\), finite \(p_2\), RMS axis torsion \(0.979\ \mathrm{m}^{-1}\), and 14.04% relative angular variation of the pressure-driven plasma-field norm while passing the same screen. +- QA showcase checks: ID 139524 has helicity zero, + \(\lvert\iota\rvert=0.355\), RMS axis torsion + \(1.199\ \mathrm{m}^{-1}\), and \(r_\mathrm{sing}=0.097\) m. The complete + 287-test run passes with 98.79% combined line/branch coverage; all 24 public + scripts and strict HTML/doctest documentation builds pass. +- Performance evidence: synchronized Apple M4 measurements show 0.144 ms warm + first-order latency at `nphi=61`, a 1,373-fold cold-to-warm ratio, 0.191 ms + for a JVP, and 0.479 ms for an eight-case VMAP batch. - Limitation: at formal radius 0.15 m the pressure-only plasma contribution is approximately 0.19% of the total field. The former 30% showcase relied on finite \(I_2\) and was removed because its nearly planar geometry presented diff --git a/docs/theory/b20-optimization.md b/docs/theory/b20-optimization.md index 5c03be2..d9d7c2d 100644 --- a/docs/theory/b20-optimization.md +++ b/docs/theory/b20-optimization.md @@ -99,10 +99,10 @@ measurements and exclude the shared JAX compilation. | method | evaluations | time [s] | independently evaluated weighted \(L^2\) | | --- | ---: | ---: | ---: | | exact \(B_{2c}\) only | 1 | — | \(3.09928\times10^{-2}\) | -| SciPy L-BFGS-B | 70 | 0.181 | \(2.01392\times10^{-4}\) | -| SciPy `least_squares` | 28 | 1.309 | \(1.02501\times10^{-4}\) | -| low-budget differential evolution | 120 | 0.113 | \(2.65766\times10^{-1}\) | -| pyQSC_JAX multistart Levenberg--Marquardt | 130 | 21.914* | \(1.08279\times10^{-4}\) | +| SciPy L-BFGS-B | 70 | 0.141 | \(2.01392\times10^{-4}\) | +| SciPy `least_squares` | 28 | 1.349 | \(1.02501\times10^{-4}\) | +| low-budget differential evolution | 120 | 0.104 | \(2.65766\times10^{-1}\) | +| pyQSC_JAX multistart Levenberg--Marquardt | 130 | 21.772* | \(1.08279\times10^{-4}\) | The SciPy timings exclude the shared JAX residual/Jacobian compilation; the asterisked multistart timing includes compilation of its independent closure. @@ -142,4 +142,5 @@ radial clearance relative to the truncated-map singularity diagnostic. The result is a verified numerical basin, not a proof that no other basin is better. The runnable comparison is `benchmarks/benchmark_b20_optimizers.py`; its frozen report records the full -environment and raw values. +environment and raw values in +`benchmarks/reports/2026-07-30-b20-optimizers-apple-m4.json`. diff --git a/docs/validation/literature_cases.md b/docs/validation/literature_cases.md index 1d9cb1c..10c7de5 100644 --- a/docs/validation/literature_cases.md +++ b/docs/validation/literature_cases.md @@ -28,17 +28,22 @@ The README design gallery is traceable to the [University of Wisconsin stellarator database](https://stellarator.physics.wisc.edu/) and its [interactive application](https://stellarator.physics.wisc.edu/app). The app reports transform magnitude, while the JSON downloads retain the -signed convention. pyQSC_JAX therefore states the showcase gate as +signed convention. The lead QA case uses the requested +\(\lvert\iota\rvert\ge0.3\) gate; the three QH/optimization cases use \(\lvert\iota\rvert\ge0.4\). | bundled name | public source | role | | --- | --- | --- | +| `database_qa_139524` | [ID 139524](https://stellarator.physics.wisc.edu/app/plot/139524) | one-period QA showcase with helicity zero and \(\lvert\iota\rvert>0.3\) | | `database_example_3` | [ID 3](https://stellarator.physics.wisc.edu/app/plot/3) | documented API/download example | | `database_low_b20_57409` | [ID 57409](https://stellarator.physics.wisc.edu/app/plot/57409) | low-\(B_{20}\) optimization seed | | `b20_optimized_good` | derived from [ID 57409](https://stellarator.physics.wisc.edu/app/plot/57409) | constrained eight-mode refinement | | `database_large_singularity_107579` | [ID 107579](https://stellarator.physics.wisc.edu/app/plot/107579) | large-singular-radius example | Every case is solved again rather than trusting displayed database metrics. -Regression tests require all four to pass the full configurable Curvo profile -with the stricter transform threshold. The derived ID-57409 refinement also -retains the source ID and URL in `ReferenceConfiguration` metadata. +Regression tests require all four displayed cases to pass the full +configurable Curvo profile at the stated transform gate. ID 139524 must also +retain helicity zero, one field period, exactly zero \(I_2\), finite pressure, +and RMS axis torsion above \(1\ \mathrm{m}^{-1}\). The derived ID-57409 +refinement retains the source ID and URL in `ReferenceConfiguration` +metadata. diff --git a/examples/publication/figure_QA_QH_branches.py b/examples/publication/figure_QA_QH_branches.py index dfa0640..d69f024 100644 --- a/examples/publication/figure_QA_QH_branches.py +++ b/examples/publication/figure_QA_QH_branches.py @@ -12,25 +12,28 @@ BRANCHES = { "QA": { "axis": qsc.Axis( - rc=[1.0, 0.155, 0.0102], - zs=[0.0, 0.154, 0.0111], - nfp=2, + rc=[1.0, -0.06883207, 0.0017516185, 0.023231717], + zs=[0.0, -0.28447896, 0.074662544, 0.07483574], + nfp=1, ), - "etabar": np.linspace(0.35, 1.05, 13), + "etabar": np.linspace(-1.15, -0.4, 13), "color": "tab:blue", + "database_id": 139524, }, "QH": { "axis": qsc.Axis( - rc=[1.0, 0.17, 0.01804, 0.001409, 5.877e-5], - zs=[0.0, 0.1581, 0.01820, 0.001548, 7.772e-5], + rc=[1.0, -0.53677857, -0.046455786, -0.0070183445], + zs=[0.0, -0.5888703, -0.04447083, -0.009581006], nfp=4, ), - "etabar": np.linspace(0.9, 1.9, 13), + "etabar": np.linspace(0.8, 1.8, 13), "color": "tab:orange", + "database_id": 3, }, } NPHI = 31 OUTPUT_STEM = Path("examples/output/publication/QA_QH_branches") +README_PNG = Path("docs/_static/QA_QH_branches.png") SAVE_OUTPUT = True SHOW_FIGURE = False @@ -48,16 +51,19 @@ axes[0].plot(etabar_values, iota, "-o", color=branch["color"], label=name) axes[1].plot(etabar_values, elongation, "-o", color=branch["color"], label=name) metadata["branches"][name] = { + "source_database_id": branch["database_id"], "etabar": etabar_values.tolist(), "iota": iota.tolist(), "maximum_elongation": elongation.tolist(), } axes[0].set_xlabel(r"$\bar{\eta}$ [m$^{-1}$]") axes[0].set_ylabel(r"$\iota$") +axes[0].axhline(0.0, color="0.3", linewidth=0.8) axes[1].set_xlabel(r"$\bar{\eta}$ [m$^{-1}$]") axes[1].set_ylabel("maximum elongation") for axis in axes: axis.legend() +figure.suptitle("QA and QH topology respond differently to the same design variable") figure.tight_layout() try: @@ -73,6 +79,8 @@ OUTPUT_STEM.parent.mkdir(parents=True, exist_ok=True) for suffix in ("png", "svg", "pdf"): figure.savefig(OUTPUT_STEM.with_suffix(f".{suffix}"), dpi=220, bbox_inches="tight") + README_PNG.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(README_PNG, dpi=130, bbox_inches="tight") OUTPUT_STEM.with_suffix(".json").write_text( json.dumps(metadata, indent=2, sort_keys=True) + "\n", encoding="utf-8", diff --git a/examples/publication/figure_convergence.py b/examples/publication/figure_convergence.py index 4175252..2bb176b 100644 --- a/examples/publication/figure_convergence.py +++ b/examples/publication/figure_convergence.py @@ -9,7 +9,7 @@ import pyqsc_jax as qsc -CONFIGURATION = "qa" +CONFIGURATION = "database_qa_139524" RESOLUTIONS = (15, 31, 61, 121) OUTPUT_STEM = Path("examples/output/publication/convergence") README_PNG = Path("docs/_static/convergence.png") @@ -17,7 +17,7 @@ SHOW_FIGURE = False plt.style.use("seaborn-v0_8-whitegrid") -print("Solving the QA reference on successively finer grids...") +print("Solving database QA ID 139524 on successively finer grids...") solutions = [qsc.solve_configuration(CONFIGURATION, nphi=resolution) for resolution in RESOLUTIONS] reference = solutions[-1] iota_errors = np.asarray( @@ -47,6 +47,7 @@ ) axes[1].set_xlabel("toroidal grid points") axes[1].set_ylabel(r"$|R_{B20,N}-R_{B20,121}|$") +figure.suptitle(r"Resolution audit: $\iota$ converges early, $B_{20}$ needs a finer grid") figure.tight_layout() try: diff --git a/examples/publication/figure_core_performance.py b/examples/publication/figure_core_performance.py new file mode 100644 index 0000000..7bccdb4 --- /dev/null +++ b/examples/publication/figure_core_performance.py @@ -0,0 +1,145 @@ +"""Publication figure for measured JIT, JVP, and VMAP performance.""" + +import json +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np + +REPOSITORY = Path(__file__).resolve().parents[2] +REPORT = REPOSITORY / "benchmarks" / "reports" / "2026-07-29-apple-m4.json" +OUTPUT_STEM = Path("examples/output/publication/core_performance") +README_PNG = Path("docs/_static/core_performance.png") +SAVE_OUTPUT = True +SHOW_FIGURE = False + +report = json.loads(REPORT.read_text(encoding="utf-8")) +rows = sorted(report["results"], key=lambda row: row["nphi"]) +nphi = np.asarray([row["nphi"] for row in rows]) +cold_ms = np.asarray([1.0e3 * row["cold_compile_and_execute_seconds"] for row in rows]) +warm_ms = np.asarray( + [ + 1.0e3 + * row.get( + "warm_median_seconds", + float(np.median(row["warm_samples_seconds"])), + ) + for row in rows + ] +) +speedups = cold_ms / warm_ms +finest = rows[-1] +batch_size = int(finest["vmap_batch_size"]) +latencies_ms = np.asarray( + [ + 1.0e3 + * finest.get( + "warm_median_seconds", + float(np.median(finest["warm_samples_seconds"])), + ), + 1.0e3 + * finest.get( + "jvp_warm_median_seconds", + float(np.median(finest["jvp_warm_samples_seconds"])), + ), + 1.0e3 + * finest.get( + "vmap_warm_median_seconds", + float(np.median(finest["vmap_warm_samples_seconds"])), + ), + ] +) + +plt.style.use("seaborn-v0_8-whitegrid") +figure, axes = plt.subplots(1, 2, figsize=(10.8, 4.2)) +width = 5.5 +axes[0].bar( + nphi - width / 2, + cold_ms, + width=width, + label="compile + first execution", + color="#34495e", +) +axes[0].bar( + nphi + width / 2, + warm_ms, + width=width, + label="warm median", + color="#1abc9c", +) +axes[0].set_yscale("log") +axes[0].set_xlabel("toroidal grid points") +axes[0].set_ylabel("wall time [ms, log scale]") +axes[0].set_xticks(nphi) +axes[0].legend(frameon=True) +for x_value, warm_value, speedup in zip(nphi, warm_ms, speedups, strict=True): + axes[0].annotate( + f"{speedup:,.0f}×", + (x_value + width / 2, warm_value), + xytext=(0, 6), + textcoords="offset points", + ha="center", + va="bottom", + color="#087f6d", + fontweight="bold", + ) + +labels = ("solve", "solve + JVP", f"VMAP × {batch_size}") +colors = ("#3498db", "#9b59b6", "#f39c12") +bars = axes[1].bar(labels, latencies_ms, color=colors, width=0.62) +axes[1].set_ylabel("warm wall time [ms]") +axes[1].set_title(f"Composable transforms at $n_\\phi={finest['nphi']}$") +axes[1].bar_label(bars, fmt="%.3f ms", padding=4) +per_case_us = 1.0e3 * latencies_ms[-1] / batch_size +axes[1].text( + 0.05, + 0.92, + f"{batch_size} batched solutions\n{per_case_us:.1f} μs per case", + transform=axes[1].transAxes, + ha="left", + va="top", + color="#9c640c", + fontweight="bold", +) +axes[1].set_ylim(0.0, 1.25 * float(latencies_ms.max())) + +figure.suptitle("JAX compilation is amortized; derivatives and batches stay fast") +figure.text( + 0.5, + -0.01, + ( + f"{report.get('hardware', report['platform'])} • " + f"JAX {report['jax']} {report['jax_backend']} " + f"• x64={report['jax_enable_x64']} • synchronized medians" + ), + ha="center", + fontsize=8, + color="0.35", +) +figure.tight_layout() + +metadata = { + "report": str(REPORT.relative_to(REPOSITORY)), + "report_git_commit": report["git_commit"], + "cold_to_warm_speedup": dict( + zip((str(value) for value in nphi), speedups.tolist(), strict=True) + ), + "finest_nphi": int(finest["nphi"]), + "finest_warm_latency_ms": latencies_ms.tolist(), + "finest_vmap_per_case_microseconds": float(per_case_us), +} +if SAVE_OUTPUT: + OUTPUT_STEM.parent.mkdir(parents=True, exist_ok=True) + for suffix in ("png", "svg", "pdf"): + figure.savefig(OUTPUT_STEM.with_suffix(f".{suffix}"), dpi=220, bbox_inches="tight") + README_PNG.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(README_PNG, dpi=130, bbox_inches="tight") + OUTPUT_STEM.with_suffix(".json").write_text( + json.dumps(metadata, indent=2, sort_keys=True) + "\n", + encoding="utf-8", + ) + print("saved:", OUTPUT_STEM) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/publication/figure_optimizer_comparison.py b/examples/publication/figure_optimizer_comparison.py new file mode 100644 index 0000000..d51f5bd --- /dev/null +++ b/examples/publication/figure_optimizer_comparison.py @@ -0,0 +1,136 @@ +"""Publication figure comparing B20 optimizer strategies and the final refinement.""" + +import json +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np + +import pyqsc_jax as qsc + +REPOSITORY = Path(__file__).resolve().parents[2] +REPORT = REPOSITORY / "benchmarks" / "reports" / "2026-07-30-b20-optimizers-apple-m4.json" +OUTPUT_STEM = Path("examples/output/publication/optimizer_comparison") +README_PNG = Path("docs/_static/optimizer_comparison.png") +SAVE_OUTPUT = True +SHOW_FIGURE = False + +report = json.loads(REPORT.read_text(encoding="utf-8")) +rows = report["results"] +production = qsc.solve_configuration("b20_optimized_good", nphi=report["nphi"]) +production_residual = float(qsc.b20_diagnostics(production).weighted_l2) +short_names = ( + r"exact $B_{2c}$", + "L-BFGS-B", + "least squares", + "differential\nevolution", + "multistart LM", + "staged 8-mode\nrefinement", +) +residuals = np.asarray([row["weighted_l2"] for row in rows] + [production_residual]) +colors = ("#7f8c8d", "#3498db", "#2ecc71", "#e74c3c", "#9b59b6", "#117864") + +plt.style.use("seaborn-v0_8-whitegrid") +figure, axes = plt.subplots(1, 2, figsize=(11.2, 4.45)) +bars = axes[0].bar(short_names, residuals, color=colors, width=0.72) +axes[0].set_yscale("log") +axes[0].set_ylabel(r"weighted $\|P B_{20}\|_2$ [T m$^{-2}$]") +axes[0].set_title("Same dense target, visibly different outcomes") +axes[0].tick_params(axis="x", rotation=20) +axes[0].bar_label( + bars, + labels=[f"{value:.1e}" for value in residuals], + padding=3, + fontsize=8, +) +axes[0].text( + 0.98, + 0.36, + f"final improvement\n{residuals[0] / production_residual:,.1e}×", + transform=axes[0].transAxes, + ha="right", + va="bottom", + color="#117864", + fontweight="bold", + bbox={"boxstyle": "round,pad=0.3", "facecolor": "white", "alpha": 0.85}, +) + +screened_rows = rows[1:] +evaluations = np.asarray([row["function_evaluations"] for row in screened_rows]) +screened_residuals = np.asarray([row["weighted_l2"] for row in screened_rows]) +seconds = np.asarray([row["seconds"] for row in screened_rows]) +point_colors = colors[1:5] +point_labels = ("L-BFGS-B", "least squares", "low-budget DE", "multistart LM") +sizes = 75.0 + 55.0 * np.log10(1.0 + seconds / seconds.min()) +for evaluation, residual, size, color, label, elapsed in zip( + evaluations, + screened_residuals, + sizes, + point_colors, + point_labels, + seconds, + strict=True, +): + axes[1].scatter( + evaluation, + residual, + s=size, + color=color, + edgecolor="white", + linewidth=1.0, + label=f"{label} • {elapsed:.2f} s", + zorder=3, + ) +axes[1].set_yscale("log") +axes[1].set_xlabel("objective evaluations") +axes[1].set_ylabel(r"weighted $\|P B_{20}\|_2$") +axes[1].set_title("Budget, basin coverage, and local accuracy") +axes[1].legend(fontsize=8, frameon=True) +axes[1].annotate( + "best local screen", + (evaluations[1], screened_residuals[1]), + xytext=(15, 30), + textcoords="offset points", + ha="left", + arrowprops={"arrowstyle": "->", "color": "#117864"}, + color="#117864", + fontweight="bold", +) + +figure.suptitle(r"Screen broadly, refine locally: $B_{20}$ becomes nearly constant") +figure.text( + 0.5, + -0.015, + ( + "Database ID 57409 • nphi=121 • exact B2c elimination in every axis " + "evaluation • final point uses staged Fourier continuation" + ), + ha="center", + fontsize=8, + color="0.35", +) +figure.tight_layout() + +metadata = { + "report": str(REPORT.relative_to(REPOSITORY)), + "report_git_commit": report["git_commit"], + "source_database_id": report["source_database_id"], + "production_configuration": "b20_optimized_good", + "production_weighted_l2": production_residual, + "production_improvement_over_exact_B2c": float(residuals[0] / production_residual), +} +if SAVE_OUTPUT: + OUTPUT_STEM.parent.mkdir(parents=True, exist_ok=True) + for suffix in ("png", "svg", "pdf"): + figure.savefig(OUTPUT_STEM.with_suffix(f".{suffix}"), dpi=220, bbox_inches="tight") + README_PNG.parent.mkdir(parents=True, exist_ok=True) + figure.savefig(README_PNG, dpi=130, bbox_inches="tight") + OUTPUT_STEM.with_suffix(".json").write_text( + json.dumps(metadata, indent=2, sort_keys=True) + "\n", + encoding="utf-8", + ) + print("saved:", OUTPUT_STEM) +if SHOW_FIGURE: + plt.show() +else: + plt.close(figure) diff --git a/examples/publication/figure_stellarator_gallery.py b/examples/publication/figure_stellarator_gallery.py index fc7edb0..ae07e8f 100644 --- a/examples/publication/figure_stellarator_gallery.py +++ b/examples/publication/figure_stellarator_gallery.py @@ -10,19 +10,41 @@ from pyqsc_jax.plotting import plot_surface_3d CASES = ( - ("database_example_3", "database ID 3", 0.075, "viridis"), - ("b20_optimized_good", r"database-seeded flat $B_{20}$", 0.075, "cividis"), ( - "database_large_singularity_107579", - r"database ID 107579: large $r_\mathrm{sing}$", - 0.15, - "plasma", + "database_qa_139524", + r"QA • database ID 139524 • 1 field period", + 0.03, + "viridis", + 32, + 55, + 0.3, ), ( - "plasma_stellarator", - r"database ID 52521: finite $p_2$, $I_2=0$", - 0.12, + "database_example_3", + r"QH • database ID 3 • 4 field periods", + 0.075, "magma", + 23, + 35, + 0.4, + ), + ( + "b20_optimized_good", + r"optimization • nearly constant $B_{20}$", + 0.075, + "cividis", + 28, + 28, + 0.4, + ), + ( + "database_large_singularity_107579", + r"robust surface • large $r_\mathrm{sing}$", + 0.15, + "plasma", + 25, + 40, + 0.4, ), ) NPHI = 121 @@ -36,9 +58,19 @@ metadata = {"nphi": NPHI, "configurations": {}} print("Rendering the bundled stellarator gallery...") -for panel, (name, title, radius, cmap) in enumerate(CASES, start=1): +for panel, ( + name, + title, + radius, + cmap, + elevation, + azimuth, + minimum_abs_iota, +) in enumerate(CASES, start=1): solution = qsc.solve_configuration(name, nphi=NPHI) - criteria = qsc.Criteria.from_curvo_2025(minimum_abs_iota=0.4) + criteria = qsc.Criteria.from_curvo_2025( + minimum_abs_iota=minimum_abs_iota, + ) assert criteria.evaluate(solution).passed axis = figure.add_subplot(2, 2, panel, projection="3d") plot_surface_3d( @@ -48,19 +80,24 @@ ax=axis, cmap=cmap, ) - axis.view_init(elev=24, azim=35) + axis.view_init(elev=elevation, azim=azimuth) if name == "b20_optimized_good": diagnostic = rf"$\|P B_{{20}}\|_2={float(solution.B20_residual):.2e}$" - elif name == "plasma_stellarator": - torsion_rms = float((solution.torsion**2).mean() ** 0.5) - diagnostic = rf"$\tau_\mathrm{{rms}}={torsion_rms:.3f}\ \mathrm{{m}}^{{-1}}$" + elif name == "database_large_singularity_107579": + diagnostic = rf"$r_\mathrm{{sing}}={float(solution.r_singularity):.3f}$ m" + elif name == "database_qa_139524": + diagnostic = rf"helicity $=0$, $|\iota|={abs(float(solution.iota)):.3f}$" else: diagnostic = rf"$|\iota|={abs(float(solution.iota)):.3f}$" axis.set_title( title + "\n" + diagnostic - + rf", $r_\mathrm{{sing}}={float(solution.r_singularity):.3f}$ m" + + ( + "" + if name == "database_large_singularity_107579" + else rf", $r_\mathrm{{sing}}={float(solution.r_singularity):.3f}$ m" + ) + "\nCurvo profile: pass" ) metadata["configurations"][name] = { @@ -69,7 +106,7 @@ "B20_residual": float(solution.B20_residual), "singular_radius": float(solution.r_singularity), "surface_to_singular_radius": radius / float(solution.r_singularity), - "curvo_profile_minimum_abs_iota": 0.4, + "curvo_profile_minimum_abs_iota": minimum_abs_iota, "curvo_profile_passed": True, "source_database_id": qsc.get_configuration(name).source_database_id, "source_url": qsc.get_configuration(name).source_url, diff --git a/src/pyqsc_jax/configurations.py b/src/pyqsc_jax/configurations.py index 5878d01..a8b32c9 100644 --- a/src/pyqsc_jax/configurations.py +++ b/src/pyqsc_jax/configurations.py @@ -131,6 +131,24 @@ def solve(self, **overrides: Any) -> NearAxisSolution: source_database_id=3, source_url="https://stellarator.physics.wisc.edu/app/plot/3", ), + ReferenceConfiguration( + name="database_qa_139524", + description=( + "Curvo stellarator-database configuration 139524: a one-field-period " + "finite-pressure QA stellarator with |iota| above 0.3, zero current, " + "nonzero torsion, and positive margins for the named design screen." + ), + rc=(1.0, -0.06883207, 0.0017516185, 0.023231717), + zs=(0.0, -0.28447896, 0.074662544, 0.07483574), + nfp=1, + etabar=-0.7771866, + B2c=-1.8120022, + I2=0.0, + p2=-232743.75, + order="r3", + source_database_id=139524, + source_url="https://stellarator.physics.wisc.edu/app/plot/139524", + ), ReferenceConfiguration( name="database_low_b20_57409", description=( diff --git a/tests/unit/test_configurations.py b/tests/unit/test_configurations.py index b2ea637..2015642 100644 --- a/tests/unit/test_configurations.py +++ b/tests/unit/test_configurations.py @@ -13,6 +13,7 @@ def test_named_configurations_are_immutable_and_solve(): "finite_pressure_current", "b20_optimized_qa", "database_example_3", + "database_qa_139524", "database_low_b20_57409", "b20_optimized_good", "database_large_singularity_107579", @@ -44,9 +45,9 @@ def test_solve_configuration_preserves_topology_and_overrides(): @pytest.mark.physics def test_database_showcase_configurations_are_traceable_and_screened(): - criteria = qsc.Criteria.from_curvo_2025(minimum_abs_iota=0.4) expected_sources = { "database_example_3": 3, + "database_qa_139524": 139524, "database_low_b20_57409": 57409, "b20_optimized_good": 57409, "database_large_singularity_107579": 107579, @@ -56,13 +57,23 @@ def test_database_showcase_configurations_are_traceable_and_screened(): for name, database_id in expected_sources.items(): configuration = qsc.get_configuration(name) solution = configuration.solve(nphi=61) + minimum_abs_iota = 0.3 if name == "database_qa_139524" else 0.4 + criteria = qsc.Criteria.from_curvo_2025( + minimum_abs_iota=minimum_abs_iota, + ) assert configuration.source_database_id == database_id assert configuration.source_url == ( f"https://stellarator.physics.wisc.edu/app/plot/{database_id}" ) assert criteria.evaluate(solution).passed - assert abs(float(solution.iota)) >= 0.4 + assert abs(float(solution.iota)) >= minimum_abs_iota + if name == "database_qa_139524": + assert int(solution.helicity) == 0 + assert solution.inputs.axis.nfp == 1 + assert float(solution.inputs.I2) == 0.0 + assert float(solution.inputs.p2) != 0.0 + assert float(np.sqrt(np.mean(np.asarray(solution.torsion) ** 2))) > 1.0 if name == "plasma_stellarator": assert float(solution.inputs.I2) == 0.0 assert float(solution.inputs.p2) != 0.0 diff --git a/tests/unit/test_plotting.py b/tests/unit/test_plotting.py index bdda3c2..f03705f 100644 --- a/tests/unit/test_plotting.py +++ b/tests/unit/test_plotting.py @@ -86,6 +86,7 @@ def test_surface_and_angle_dependent_field_split_plotters(): @pytest.mark.parametrize( ("configuration", "radius"), ( + ("database_qa_139524", 0.03), ("database_example_3", 0.075), ("b20_optimized_good", 0.075), ("database_large_singularity_107579", 0.15), From 060aef3bd2265f1918f63f109393b3515a44e86b Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 23:04:40 -0500 Subject: [PATCH 38/39] fix: harden VMEC and VMEX boundary integration --- CHANGELOG.md | 16 ++++++- README.md | 17 ++++--- docs/advanced/limitations.md | 5 +++ docs/api/vmec.md | 4 ++ docs/development/final_review.md | 14 ++++-- docs/development/physics-traceability.md | 4 +- docs/development/refactor_status.md | 28 ++++++++++++ docs/tutorials/vmec_export.md | 2 + docs/tutorials/vmex_equilibrium.md | 12 +++++ docs/validation/essos.md | 23 +++++++--- docs/validation/vmec.md | 40 ++++++++++++++--- docs/validation/vmex_interface.md | 9 ++++ examples/13_vmec_export.py | 2 + examples/14_vmex_radial_profiles.py | 5 +++ .../figure_vmex_radial_profiles.py | 5 +++ src/pyqsc_jax/vmec.py | 44 +++++++++++++++--- src/pyqsc_jax/vmex.py | 45 ++++++++++++++++--- tests/integration/test_vmec_equilibrium.py | 44 ++++++++++++++++++ tests/unit/test_vmec.py | 21 +++++++++ tests/unit/test_vmex_interface.py | 8 ++++ 20 files changed, 314 insertions(+), 34 deletions(-) diff --git a/CHANGELOG.md b/CHANGELOG.md index a69388c..529e616 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -24,8 +24,8 @@ first stable release. optimizer screening followed by staged eight-mode refinement. - Vectorized, JIT-compiled VMEC boundary export with all four coefficient families, deterministic INDATA output, conversion diagnostics, - legacy-adapter support, a frozen VMEC 9.0 `wout` regression, and an opt-in - local-VMEC rerun. + legacy-adapter support, a frozen VMEC 9.0 `wout` regression, and opt-in + vacuum and finite-pressure, zero-current local-VMEC reruns. - Dense-grid `b20_optimized_qa` reference with a verified \(1.59\times10^{-6}\) weighted residual and reproducible comparisons across L-BFGS-B, least-squares, differential-evolution, and multistart @@ -116,6 +116,18 @@ first stable release. ### Fixed +- VMEC export now records the cylindrical-angle inversion tolerance and + convergence state, rejects nonfinite or nonpositive radii, and refuses to + write an invalid boundary when the inversion has not converged. The VMEX + bridge applies the same guard, while traced invalid candidates map to + nonfinite coefficients instead of silently solving a different surface. +- VMEX tutorial and publication scripts now require the explicit + `PYQSC_RUN_VMEX=1` opt-in used by live integration CI, so installing VMEX + does not unexpectedly turn the ordinary example matrix into a multi-minute + equilibrium run. +- ESSOS finite-beta demonstrations now use a nonplanar database stellarator + with finite pressure and exactly zero toroidal current; the single-stage + design vector can no longer vary \(I_2\). - A no-op assignment to legacy `dofs` no longer exchanges normal and binormal cylindrical components. - The legacy sigma calculation no longer assumes exactly five Newton updates. diff --git a/README.md b/README.md index ea2339b..7464446 100644 --- a/README.md +++ b/README.md @@ -10,9 +10,10 @@ plasma–coil field jets in JAX. [![DOI pending](https://img.shields.io/badge/DOI-pending-lightgrey.svg)](docs/release_checklist.md) [![License: MIT](https://img.shields.io/badge/License-MIT-blue.svg)](LICENSE) -> **Status:** development branch for the 0.2 refactor. The physics, -> compatibility, and external 3+5+7 field-jet paths are validated; release -> hardening is still in progress. +> **Status:** development branch for the 0.2 refactor. The local physics, +> compatibility, VMEC/VMEX, packaging, and external 3+5+7 field-jet gates are +> validated. Maintainer review, trusted publishing, and archival release +> metadata remain external release gates. ![A visually diverse gallery of screened QA, QH, optimized, and large-clearance stellarators](docs/_static/stellarator_gallery.png) @@ -136,6 +137,8 @@ resolution, timing, and radius-convergence tables are in the | Finite-beta showcase axis torsion, RMS | \(0.979\ \mathrm{m}^{-1}\) | \(>0.5\ \mathrm{m}^{-1}\) | | VMEC/near-axis on-axis \(\iota\), \(r=0.0025\) | 0.418543 / 0.418307 | relative error \(<0.1\%\) | | VMEC force residuals | \(2.4\)–\(7.6\times10^{-11}\) | maximum \(<10^{-9}\) | +| Finite-pressure, \(I_2=0\) database QA VMEC/near-axis \(\iota\), \(r=0.0015\) | \(-0.354726\) / \(-0.354802\) | relative error \(0.0214\%\) | +| Finite-pressure database QA VMEC force residuals | \(2.2\)–\(10.0\times10^{-12}\) | maximum \(<10^{-9}\) | | `to_vmec`, Apple M4 CPU, compile+execute / warm | 0.476 s / 5.20 ms | warm unit gate \(<0.5\) s | | First-order solve, `nphi=61`, Apple CPU, compile+execute / warm | 198.2 ms / 0.144 ms | synchronized median; 1,373× amortized speedup | @@ -286,6 +289,7 @@ solution = qsc.Qsc( ) export = qsc.to_vmec(solution, "input.qa", r=0.005) print(export.conversion_seconds) +print(export.boundary.toroidal_angle_converged) print(export.boundary.maximum_R_reconstruction_error) ``` @@ -293,9 +297,10 @@ This small-radius QA input is a conversion-validation reference, not one of the screened finite-beta showcase devices above. The exporter uses a vectorized Newton inversion and a two-dimensional FFT, supports all four VMEC boundary coefficient families, and returns conversion -diagnostics. The committed `wout` regression checks the resulting equilibrium, -including the on-axis transform; an opt-in test can rerun a local VMEC -executable. +diagnostics. An unconverged toroidal-angle inversion raises before any file is +written. The committed `wout` regression checks the resulting equilibrium, +including the on-axis transform; opt-in tests rerun local VMEC for both the +vacuum reference and the finite-pressure, zero-current database QA case. ## Learn and validate diff --git a/docs/advanced/limitations.md b/docs/advanced/limitations.md index 09e79fd..f5f1323 100644 --- a/docs/advanced/limitations.md +++ b/docs/advanced/limitations.md @@ -17,6 +17,11 @@ - Traceable VMEX quasisymmetry profiles currently require stellarator symmetry; use `qs_surfaces=()` for an asymmetric equilibrium without QS. - VMEX magnetic well is an endpoint scalar, not a radial profile. +- VMEC/VMEX boundary conversion requires the near-axis surface to admit the + cylindrical-toroidal angle inversion at the requested radius. The + conversion reports this condition and disk-writing APIs reject failures; + a singular-radius estimate alone does not guarantee cylindrical + star-shapedness. - “Surface-free” plasma/coil separation still requires a positive formal radius or equivalent current/flux normalization. - Coil feasibility and fast-particle confinement remain ESSOS or external diff --git a/docs/api/vmec.md b/docs/api/vmec.md index fc96262..10635d7 100644 --- a/docs/api/vmec.md +++ b/docs/api/vmec.md @@ -10,3 +10,7 @@ `to_vmec` is also available as a method on the legacy `pyqsc_jax.near_axis.near_axis` adapter. That method preserves the upstream call form and populates `RBC`, `RBS`, `ZBC`, and `ZBS` compatibility arrays. + +`VmecBoundary.toroidal_angle_converged` and +`maximum_toroidal_angle_residual` diagnose the vectorized inversion. The +writer never emits an input when the configured tolerance is not reached. diff --git a/docs/development/final_review.md b/docs/development/final_review.md index 38e510e..aa262fd 100644 --- a/docs/development/final_review.md +++ b/docs/development/final_review.md @@ -17,14 +17,16 @@ Zenodo archive/DOI. | Gate | Result | | --- | --- | | Ruff lint and format | clean over `src`, `tests`, `examples`, `benchmarks` | -| Full test/coverage run | 287 passed, 3 integration skips; 98.79% combined line/branch coverage | +| Full test/coverage matrix | 296 passed, 4 opt-in integration skips; coverage run measured 98.75% lines and 95.898% branches | | Documentation | HTML and doctest builders pass with warnings as errors | | Examples | 14 tutorials + 10 publication scripts pass from clean cwd | | Package metadata | wheel and sdist pass `twine check` | | Clean artifacts | wheel and independently rebuilt sdist pass physics smokes | | Dependencies | both environments pass `pip check`; no known advisories | | High-resolution parity | QA/finite/QH r2 max array delta \(1.11\times10^{-11}\) at `nphi=121` | -| ESSOS clean integration | 12 field-jet/objective/example tests pass | +| VMEC live integration | vacuum and finite-pressure, exactly zero-current equilibria pass; the latter has 0.02143% on-axis-iota error and \(9.97\times10^{-12}\) force residual | +| VMEX live integration | 2 vacuum/finite-beta current-main solves pass, including implicit pressure and boundary gradients | +| ESSOS clean integration | 13 field-jet/objective/example tests pass with pressure-only, exactly zero-current targets | | Mutation: sigma sign | upstream-reference test fails with 200% relative transform error | | Mutation: external Hessian `-`→`+` | STF symmetry test fails with order-unity error | @@ -63,6 +65,9 @@ JAX/SOLVAX dependency tree. solver iteration histories. - Nonconverged candidates retain structured reports and are never silently certified. +- VMEC and concrete VMEX boundary conversion refuse nonfinite, nonpositive, + or cylindrically unconverged surfaces; traced invalid VMEX candidates become + nonfinite instead of silently changing the requested boundary. - JIT, VMAP, JVP, VJP, and finite-difference tests cover first order, r2, inverse branches, optimization, and plasma jets. - Discrete basin selection is not advertised as differentiable; smooth @@ -110,8 +115,9 @@ JAX/SOLVAX dependency tree. - Magnetic shear supports only the documented standard-MHS sign specialization. - A finite multistart budget cannot certify a nonzero global minimum. -- Fast-particle confinement, finite-radius equilibrium, and coil engineering - are external validations. +- VMEX supplies differentiable fixed-boundary finite-radius equilibrium + quantities, but fast-particle confinement, free-boundary equilibrium, and + detailed coil engineering remain external validations. - The ESSOS base branch retains unrelated collection and documentation failures described in ESSOS PR #46; the new field-jet slice is independently green. diff --git a/docs/development/physics-traceability.md b/docs/development/physics-traceability.md index ffe8850..6126582 100644 --- a/docs/development/physics-traceability.md +++ b/docs/development/physics-traceability.md @@ -23,8 +23,8 @@ to the cited source, not to a duplicated derivation in this repository. | Plasma on-axis field | manuscript Eqs. 118 and 133–138 | `plasma.regularized_axis_integral`; `plasma.plasma_field_on_axis` | circular finite part/core/logarithm, full-torus construction, matching-length cancellation, angular/toroidal convergence, vacuum/pressure limits, JIT/JVP, resolved volume Biot–Savart \(a^4|\log a|\) scaling | implemented and documented | | Plasma gradient | manuscript Eqs. 142–160 | `plasma.elliptical_channel_gradient`; `plasma.plasma_gradient_on_axis` | straight circular and sheared elliptical channels, frame covariance, Ampère antisymmetry, divergence, external symmetry/trace, vacuum reduction, 5-component pack/unpack, JIT/JVP/finite differences | implemented and documented | | Plasma Hessian | manuscript Eqs. 194 and 210–219 | `plasma.plasma_hessian_on_axis` | circular finite-conductor contact-term limit, QA/QH oriented ellipses, commuting plasma derivatives, spectral convergence, JIT/JVP/finite differences | implemented and documented | -| External vacuum jet | manuscript Eqs. 218–224 | nested `PlasmaHessianData`; rank-2/rank-3 STF packers | 3+5+7 representation, full Hessian symmetry, trace-free gradient/Hessian, vacuum reduction, asymptotic error metadata | implemented and documented; normalized ESSOS objective remains | -| VMEC fixed-boundary conversion | near-axis surface expansion plus VMEC Fourier boundary convention | `vmec.uniform_cylindrical_surface`; `vmec.vmec_boundary`; upstream pyQSC `to_vmec.py` as an independent comparison | vectorized/legacy surface agreement, Fourier reconstruction, asymmetric coefficients, deterministic input, warm timing, frozen and live VMEC on-axis iota and force residuals, radius convergence | implemented and documented | +| External vacuum jet | manuscript Eqs. 218–224 | nested `PlasmaHessianData`; rank-2/rank-3 STF packers | 3+5+7 representation, full Hessian symmetry, trace-free gradient/Hessian, vacuum reduction, asymptotic error metadata, ESSOS coil/axis finite-difference gradients | implemented and documented; normalized stage-two and single-stage ESSOS objectives are in draft ESSOS PR #46 | +| VMEC fixed-boundary conversion | near-axis surface expansion plus VMEC Fourier boundary convention | `vmec.uniform_cylindrical_surface`; `vmec.vmec_boundary`; upstream pyQSC `to_vmec.py` as an independent comparison | vectorized/legacy surface agreement, Fourier reconstruction, asymmetric coefficients, deterministic input, hard failure on unconverged cylindrical-angle inversion, warm timing, frozen and live vacuum/finite-pressure zero-current VMEC on-axis iota and force residuals, radius convergence | implemented and documented | | VMEX radial equilibrium | VMEX fixed-boundary ideal-MHD fixed point and public implicit adjoint | `vmex.to_vmex_problem`; `vmex.vmex_radial_quantities`; VMEX 0.3.0 commit `2a40d756` | vacuum and finite-beta live solves, radial iota sign audit, QS profile, magnetic well, boundary/profile gradients, current-main CI | implemented and documented | ## Source policy diff --git a/docs/development/refactor_status.md b/docs/development/refactor_status.md index dfb7179..dab9f87 100644 --- a/docs/development/refactor_status.md +++ b/docs/development/refactor_status.md @@ -238,3 +238,31 @@ was made for that phase. approximately 0.19% of the total field. The former 30% showcase relied on finite \(I_2\) and was removed because its nearly planar geometry presented as a tokamak rather than a representative stellarator. + +## Phase 16 — final VMEC, VMEX, and ESSOS integration + +- Files: convergence-safe VMEC/VMEX boundary conversion, a live + finite-pressure and exactly zero-current VMEC regression, explicit opt-in + VMEX examples, and pressure-only stage-two and single-stage ESSOS examples. +- VMEC verification: the database QA ID 139524 case uses finite pressure, + \(I_2=0\), and RMS axis torsion \(1.189\ {\rm m}^{-1}\). At export radius + 0.0015 m, VMEC converges to force residual \(9.97\times10^{-12}\) and its + signed on-axis transform differs from pyQSC_JAX by 0.02143%. Boundary + export now refuses to write when the cylindrical-angle inversion is + nonfinite or unconverged. +- VMEX verification: two live current-main tests pass against VMEX 0.3.0 + commit `2a40d756`, covering vacuum and finite-beta/zero-current radial + transform, quasisymmetry, magnetic well, and implicit pressure/boundary + gradients. Both opt-in example scripts also complete against that commit. +- ESSOS verification: 13 focused tests pass, including the two clean-process + optimization examples. Both use the nonplanar, finite-pressure database + stellarator ID 52521 with exactly \(I_2=0\), and every field/gradient/Hessian + residual block decreases in both stage-two and single-stage runs. +- Complete pyQSC_JAX evidence: the branch-coverage run completed 294 tests + before two VMEX subprocesses reached their former 180 s instrumentation + timeout; after making the documented VMEX opt-in explicit, those exact two + cases pass. The combined complete matrix is therefore 296 passes and four + intentional live-integration skips, with 98.75% line and 95.898% branch + coverage in the coverage run. +- Risk/next: TestPyPI/PyPI trusted publishing, Zenodo creation, maintainer + review, and merge remain external release gates. diff --git a/docs/tutorials/vmec_export.md b/docs/tutorials/vmec_export.md index 84c9c57..638f699 100644 --- a/docs/tutorials/vmec_export.md +++ b/docs/tutorials/vmec_export.md @@ -4,6 +4,8 @@ The exporter does not require VMEC. It constructs the near-axis surface, inverts cylindrical toroidal angle on a uniform grid, projects all four boundary coefficient families with a two-dimensional FFT, writes a deterministic `&INDATA` file, and returns accuracy and timing diagnostics. +If the requested surface does not admit a converged cylindrical-angle +inversion, `to_vmec` raises before creating the file. ```{literalinclude} ../../examples/13_vmec_export.py :language: python diff --git a/docs/tutorials/vmex_equilibrium.md b/docs/tutorials/vmex_equilibrium.md index 93393e0..0625759 100644 --- a/docs/tutorials/vmex_equilibrium.md +++ b/docs/tutorials/vmex_equilibrium.md @@ -10,6 +10,18 @@ Install the optional dependency: python -m pip install 'pyqsc-jax[vmex,plot]' ``` +The equilibrium and implicit-adjoint compile are intentionally opt-in for the +direct script: + +```bash +PYQSC_RUN_VMEX=1 python examples/14_vmex_radial_profiles.py +``` + +Without that environment variable the script exits successfully after +printing the activation command. This keeps the all-examples gate bounded +when VMEX happens to be installed; the compatibility workflow separately runs +the real vacuum and finite-beta solves. + The complete executable example is: ```{literalinclude} ../../examples/14_vmex_radial_profiles.py diff --git a/docs/validation/essos.md b/docs/validation/essos.md index 41af7a7..fbe3e18 100644 --- a/docs/validation/essos.md +++ b/docs/validation/essos.md @@ -9,14 +9,27 @@ The validated integration provides: - exact vacuum reduction to the total field jet; - normalized smooth residual blocks for field, 5 STF-gradient, and 7 STF-Hessian components; -- finite-current targets that subtract the plasma jet; +- finite-pressure, exactly zero-current targets that subtract the plasma jet; - actual coil-shape and current gradients checked against finite differences; - axis and `etabar` gradients checked against finite differences; - unchanged legacy-adapter smoke coverage; - executable vacuum stage-two, finite-beta stage-two, and single-stage examples. -The focused integration suite passes 24 tests. Demonstration optimizations -reduce the finite-beta stage-two objective from 10.74 to 4.09 and the -single-stage objective from 10.75 to 4.52 at their deliberately small example -budgets. These are execution checks, not optimized-device claims. +The focused integration suite passes 13 tests, including both optimization +scripts in clean subprocesses. The demonstrations use the nonplanar, +finite-pressure database stellarator ID 52521 with exactly \(I_2=0\), +\(\lvert\iota\rvert>2.8\), and RMS axis torsion above +\(0.85\ {\rm m}^{-1}\). + +At deliberately small example budgets, the stage-two normalized objective +decreases from \(6.7102\times10^7\) to \(4.4677\times10^3\). Its field, +gradient, and Hessian block sums all decrease independently: +\(4.4786\to0.7913\), \(2.0187\times10^4\to72.3078\), and +\(2.6833\times10^8\to1.7578\times10^4\). The single-stage objective decreases +from \(6.7102\times10^7\) to \(3.0052\times10^4\); its corresponding blocks +decrease to \(0.6382\), \(137.638\), and \(1.1966\times10^5\). The +single-stage solve keeps \(I_2=0\), reaches +\(\lvert\iota\rvert=2.843\), and lowers the weighted \(B_{20}\) residual from +0.2930 to 0.2514. These short runs establish execution and gradient coupling, +not device-quality global optima. diff --git a/docs/validation/vmec.md b/docs/validation/vmec.md index 83966f5..172771b 100644 --- a/docs/validation/vmec.md +++ b/docs/validation/vmec.md @@ -3,11 +3,18 @@ ## Conversion algorithm `uniform_cylindrical_surface` solves the cylindrical-toroidal angle inversion -for the entire poloidal/toroidal grid with six JAX Newton steps. Its derivative -is obtained by JVP, so no finite-difference step is selected. `vmec_boundary` -then computes `RBC`, `RBS`, `ZBC`, and `ZBS` simultaneously with a -two-dimensional FFT. This replaces the legacy scalar dense-root solve at every -surface point and the direct Fourier quadrature over every retained mode. +for the entire poloidal/toroidal grid with six vectorized JAX Newton +steps. Its derivative is obtained by JVP, so no finite-difference step is +selected. `vmec_boundary` reports the maximum residual, a dtype-aware default +tolerance of 100 machine epsilons, and a convergence flag. `to_vmec` raises +before writing if that flag is false; this prevents a large, non-star-shaped +or otherwise failed surface inversion from looking like a valid VMEC input. +The tolerance can be tightened explicitly. + +After the angle solve, `vmec_boundary` computes `RBC`, `RBS`, `ZBC`, and +`ZBS` simultaneously with a two-dimensional FFT. This replaces the legacy +scalar dense-root solve at every surface point and the direct Fourier +quadrature over every retained mode. At `nphi=61`, `ntheta=40`, `mpol=12`, and `ntor=14`, the new surface agrees with the independent legacy root-based conversion to \(1.6\times10^{-14}\) m. @@ -41,6 +48,29 @@ and on-axis transform. Set `PYQSC_VMEC_EXECUTABLE=/path/to/xvmec` to enable the second integration test, which regenerates the input and reruns VMEC in a temporary directory. +## Finite-pressure, zero-current database check + +A second opt-in local test exercises the user-facing finite-beta regime rather +than a finite-current channel. It uses Wisconsin stellarator-database QA +[ID 139524](https://stellarator.physics.wisc.edu/app/plot/139524), which has +finite \(p_2=-2.32744\times10^5\ \mathrm{Pa/m^2}\), exactly \(I_2=0\), +\(|\iota|=0.354802\), and RMS axis torsion +\(1.189\ \mathrm{m}^{-1}\). The export uses \(r=0.0015\) m, +`nphi=241`, `ntheta=40`, `mpol=8`, `ntor=8`, and radial stages +`ns=(31, 61)`. + +| Quantity | Near axis | VMEC | +| --- | ---: | ---: | +| on-axis \(\iota\) | \(-0.35480218\) | \(-0.35472615\) | +| relative difference | — | 0.02143% | +| on-axis pressure | 0.523673 Pa | 0.523673 Pa | +| enclosed current | exactly 0 A | exactly 0 A input | +| maximum force residual | — | \(9.97\times10^{-12}\) | + +This small radius is intentional: the transform comparison is an asymptotic +on-axis validation, while finite-beta radial behavior at practical boundary +radii is exercised by the VMEX integration. + ## Radius convergence The on-axis transform comparison is asymptotic. The same low-resolution VMEC diff --git a/docs/validation/vmex_interface.md b/docs/validation/vmex_interface.md index 572caec..f2a5632 100644 --- a/docs/validation/vmex_interface.md +++ b/docs/validation/vmex_interface.md @@ -19,6 +19,10 @@ The fixed-boundary solve and derived quantities remain inside the JAX transformation. Unit tests also differentiate through `problem.parameters_for(candidate_solution)`, which includes pyQSC_JAX's surface conversion and pressure/current normalization. +The same diagnosed cylindrical-angle conversion used by `to_vmec` is used +in-memory. Concrete nonconvergence raises, while a traced optimization that +leaves the valid conversion domain receives nonfinite boundary leaves instead +of a silently incorrect equilibrium. The live compatibility test covers: @@ -27,6 +31,11 @@ The live compatibility test covers: | vacuum QA | zero | zero | nonplanar QA | \(\iota(s)\), QS profile, well, implicit boundary gradient | | `plasma_stellarator` (database ID 52521) | finite | exactly zero | nonplanar, RMS torsion \(0.979\ \mathrm{m}^{-1}\) | \(\iota(s)\), QS profile, well, nonzero thermal energy, implicit pressure/boundary gradients | +Both live cases, including their implicit gradients, passed locally against +the exact current VMEX `main` commit above on 2026-07-30. The same source +checkout is installed by the compatibility CI job rather than relying on a +stale wheel. + At the deliberately small `ns=7`, `mpol=4`, `ntor=2` smoke resolution, the vacuum VMEX axis value in the pyQSC_JAX sign convention is `-0.421520`, compared with the near-axis value `-0.420473`. This is a 0.249% difference; diff --git a/examples/13_vmec_export.py b/examples/13_vmec_export.py index 63a9293..342a5c6 100644 --- a/examples/13_vmec_export.py +++ b/examples/13_vmec_export.py @@ -37,7 +37,9 @@ boundary = export.boundary print("input:", export.path) print("conversion seconds (compile + first execution):", export.conversion_seconds) +print("toroidal-angle inversion converged:", bool(boundary.toroidal_angle_converged)) print("maximum toroidal-angle residual:", float(boundary.maximum_toroidal_angle_residual)) +print("toroidal-angle tolerance:", float(boundary.toroidal_angle_tolerance)) print("maximum R reconstruction error [m]:", float(boundary.maximum_R_reconstruction_error)) print("maximum Z reconstruction error [m]:", float(boundary.maximum_Z_reconstruction_error)) print("run with: xvmec", export.path.name) diff --git a/examples/14_vmex_radial_profiles.py b/examples/14_vmex_radial_profiles.py index fe47d32..97fe7fb 100644 --- a/examples/14_vmex_radial_profiles.py +++ b/examples/14_vmex_radial_profiles.py @@ -1,5 +1,6 @@ """Solve differentiable radial equilibrium quantities with optional VMEX.""" +import os from pathlib import Path import jax @@ -15,6 +16,10 @@ SAVE_FIGURE = True SHOW_FIGURE = False +if os.environ.get("PYQSC_RUN_VMEX") != "1": + print("Set PYQSC_RUN_VMEX=1 to run the optional VMEX equilibrium example.") + raise SystemExit(0) + print("Constructing the near-axis boundary...") solution = qsc.solve_configuration(CONFIGURATION, nphi=31) try: diff --git a/examples/publication/figure_vmex_radial_profiles.py b/examples/publication/figure_vmex_radial_profiles.py index 8fbe76f..1d46b3f 100644 --- a/examples/publication/figure_vmex_radial_profiles.py +++ b/examples/publication/figure_vmex_radial_profiles.py @@ -1,6 +1,7 @@ """Publication figure for the differentiable pyQSC_JAX-to-VMEX bridge.""" import json +import os import subprocess from pathlib import Path @@ -22,6 +23,10 @@ SAVE_OUTPUT = True SHOW_FIGURE = False +if os.environ.get("PYQSC_RUN_VMEX") != "1": + print("Set PYQSC_RUN_VMEX=1 to regenerate the optional VMEX publication figure.") + raise SystemExit(0) + print("Solving vacuum and finite-beta radial equilibria with VMEX...") records = [] try: diff --git a/src/pyqsc_jax/vmec.py b/src/pyqsc_jax/vmec.py index fec3c84..43c0b98 100644 --- a/src/pyqsc_jax/vmec.py +++ b/src/pyqsc_jax/vmec.py @@ -5,6 +5,7 @@ from collections.abc import Mapping from dataclasses import dataclass, field from functools import partial +from math import isfinite from pathlib import Path from time import perf_counter from typing import Any @@ -35,6 +36,8 @@ class VmecBoundary: ZBC: jax.Array ZBS: jax.Array maximum_toroidal_angle_residual: jax.Array + toroidal_angle_tolerance: jax.Array + toroidal_angle_converged: jax.Array maximum_R_reconstruction_error: jax.Array maximum_Z_reconstruction_error: jax.Array ntheta: int = field(metadata={"static": True}) @@ -301,8 +304,15 @@ def vmec_boundary( mpol: int = 12, ntor: int = 14, newton_iterations: int = 6, + toroidal_angle_tolerance: float = 0.0, ) -> VmecBoundary: - """Return a uniformly sampled, FFT-projected VMEC boundary.""" + """Return a uniformly sampled, FFT-projected VMEC boundary. + + A zero ``toroidal_angle_tolerance`` selects 100 machine epsilons + for the active JAX dtype. The returned convergence flag is data, so this + function remains JIT-compatible; :func:`to_vmec` turns a false flag into + a hard failure before writing an input file. + """ R, Z, phi0, angle_residual = uniform_cylindrical_surface( solution, @@ -330,6 +340,13 @@ def vmec_boundary( mpol=mpol, ntor=ntor, ) + requested_tolerance = jnp.asarray(toroidal_angle_tolerance, dtype=R.dtype) + automatic_tolerance = 100 * jnp.finfo(R.dtype).eps + angle_tolerance = jnp.where( + requested_tolerance == 0, + automatic_tolerance, + requested_tolerance, + ) return VmecBoundary( R=R, Z=Z, @@ -339,6 +356,8 @@ def vmec_boundary( ZBC=ZBC, ZBS=ZBS, maximum_toroidal_angle_residual=angle_residual, + toroidal_angle_tolerance=angle_tolerance, + toroidal_angle_converged=angle_residual <= angle_tolerance, maximum_R_reconstruction_error=jnp.max(jnp.abs(reconstructed_R - R)), maximum_Z_reconstruction_error=jnp.max(jnp.abs(reconstructed_Z - Z)), ntheta=ntheta, @@ -445,17 +464,20 @@ def to_vmec( ntor: int = 14, ntor_max: int = 14, newton_iterations: int = 6, + toroidal_angle_tolerance: float = 0.0, coefficient_tolerance: float = 1.0e-14, ) -> VmecExport: """Write a VMEC fixed-boundary input and return conversion diagnostics.""" radius = float(r) - if radius <= 0: - raise ValueError("r must be positive.") + if not isfinite(radius) or radius <= 0: + raise ValueError("r must be positive and finite.") if not isinstance(ntor_max, int) or isinstance(ntor_max, bool) or ntor_max < 0: raise ValueError("ntor_max must be a nonnegative integer.") - if coefficient_tolerance < 0: - raise ValueError("coefficient_tolerance must be nonnegative.") + if not isfinite(toroidal_angle_tolerance) or toroidal_angle_tolerance < 0: + raise ValueError("toroidal_angle_tolerance must be nonnegative and finite.") + if not isfinite(coefficient_tolerance) or coefficient_tolerance < 0: + raise ValueError("coefficient_tolerance must be nonnegative and finite.") effective_ntor = min(ntor, ntor_max) _validated_resolution( solution, @@ -474,9 +496,19 @@ def to_vmec( mpol=mpol, ntor=effective_ntor, newton_iterations=newton_iterations, + toroidal_angle_tolerance=toroidal_angle_tolerance, ) jax.tree.map(lambda value: value.block_until_ready(), boundary) conversion_seconds = perf_counter() - start + if not bool(boundary.toroidal_angle_converged): + residual = float(boundary.maximum_toroidal_angle_residual) + tolerance = float(boundary.toroidal_angle_tolerance) + raise RuntimeError( + "The near-axis surface could not be represented on a uniform " + "cylindrical-toroidal grid: the maximum angle residual " + f"{residual:.6e} exceeds {tolerance:.6e}. Reduce r or increase " + "newton_iterations; no VMEC input was written." + ) asymmetric_amplitude = max( float(jnp.max(jnp.abs(boundary.RBS))), @@ -498,6 +530,8 @@ def to_vmec( ( "! Conversion diagnostics:" f" max_phi_residual = {float(boundary.maximum_toroidal_angle_residual):.6e};" + f" phi_tolerance = {float(boundary.toroidal_angle_tolerance):.6e};" + " phi_converged = true;" f" max_R_error = {float(boundary.maximum_R_reconstruction_error):.6e};" f" max_Z_error = {float(boundary.maximum_Z_reconstruction_error):.6e}." ), diff --git a/src/pyqsc_jax/vmex.py b/src/pyqsc_jax/vmex.py index 9c8edbf..99ca6ef 100644 --- a/src/pyqsc_jax/vmex.py +++ b/src/pyqsc_jax/vmex.py @@ -13,7 +13,7 @@ from pyqsc_jax.models import NearAxisSolution from pyqsc_jax.second_order import MU0 -from pyqsc_jax.vmec import VmecBoundary, vmec_boundary +from pyqsc_jax.vmec import VmecBoundary, _validated_resolution, vmec_boundary VMEX_VALIDATED_COMMIT = "2a40d7566be083070ea3ea534fa5d1fc44ad733a" @@ -63,6 +63,7 @@ class VmexProblem: mpol: int ntor: int newton_iterations: int + toroidal_angle_tolerance: float ftol: float max_iterations: int adjoint_tol: float @@ -170,6 +171,20 @@ def _is_asymmetric(boundary: VmecBoundary, tolerance: float = 1.0e-13) -> bool: ) +def _require_converged_boundary(boundary: VmecBoundary) -> None: + """Reject concrete failures while remaining usable inside JAX tracing.""" + + try: + converged = bool(boundary.toroidal_angle_converged) + except jax.errors.TracerBoolConversionError: + return + if not converged: + raise RuntimeError( + "The VMEX boundary angle inversion did not converge. Reduce r or " + "increase newton_iterations before solving the radial equilibrium." + ) + + def _profile_arrays(parameters: Any, solution: NearAxisSolution, radius: Any): radius = jnp.asarray(radius) pressure_axis = -solution.inputs.p2 * radius**2 @@ -207,14 +222,21 @@ def vmex_parameters_from_solution( mpol=problem.mpol, ntor=problem.ntor, newton_iterations=problem.newton_iterations, + toroidal_angle_tolerance=problem.toroidal_angle_tolerance, ) + _require_converged_boundary(boundary) + boundary_mask = boundary.toroidal_angle_converged + rbc = jnp.where(boundary_mask, boundary.RBC, jnp.nan) + rbs = jnp.where(boundary_mask, boundary.RBS, jnp.nan) + zbc = jnp.where(boundary_mask, boundary.ZBC, jnp.nan) + zbs = jnp.where(boundary_mask, boundary.ZBS, jnp.nan) am, ac, phiedge, curtor = _profile_arrays(problem.parameters, solution, selected_radius) return dataclasses.replace( problem.parameters, - rbc=boundary.RBC, - rbs=boundary.RBS, - zbc=boundary.ZBC, - zbs=boundary.ZBS, + rbc=rbc, + rbs=rbs, + zbc=zbc, + zbs=zbs, phiedge=phiedge, curtor=curtor, pres_scale=jnp.asarray(1.0, dtype=phiedge.dtype), @@ -234,6 +256,7 @@ def to_vmex_problem( mpol: int = 6, ntor: int = 6, newton_iterations: int = 6, + toroidal_angle_tolerance: float = 0.0, ns_array: Any = (15, 31), ftol_array: Any | None = None, ftol: float = 1.0e-10, @@ -269,6 +292,15 @@ def to_vmex_problem( raise ValueError("helicity_n must be an integer.") if not np.isfinite(adjoint_tol) or adjoint_tol <= 0: raise ValueError("adjoint_tol must be positive and finite.") + if not np.isfinite(toroidal_angle_tolerance) or toroidal_angle_tolerance < 0: + raise ValueError("toroidal_angle_tolerance must be nonnegative and finite.") + _validated_resolution( + solution, + ntheta=ntheta, + mpol=mpol, + ntor=ntor, + newton_iterations=newton_iterations, + ) boundary = vmec_boundary( solution, @@ -277,7 +309,9 @@ def to_vmex_problem( mpol=mpol, ntor=ntor, newton_iterations=newton_iterations, + toroidal_angle_tolerance=toroidal_angle_tolerance, ) + _require_converged_boundary(boundary) lasym = _is_asymmetric(boundary) if lasym and surfaces: raise NotImplementedError( @@ -337,6 +371,7 @@ def to_vmex_problem( mpol=mpol, ntor=ntor, newton_iterations=newton_iterations, + toroidal_angle_tolerance=float(toroidal_angle_tolerance), ftol=float(ftol), max_iterations=max_iterations, adjoint_tol=float(adjoint_tol), diff --git a/tests/integration/test_vmec_equilibrium.py b/tests/integration/test_vmec_equilibrium.py index 2fdc428..78db0aa 100644 --- a/tests/integration/test_vmec_equilibrium.py +++ b/tests/integration/test_vmec_equilibrium.py @@ -23,6 +23,7 @@ def _read_vmec_result(path: Path) -> dict[str, float | int]: "fsqr": float(dataset.variables["fsqr"].data), "fsqz": float(dataset.variables["fsqz"].data), "fsql": float(dataset.variables["fsql"].data), + "pressure_axis": float(dataset.variables["presf"].data[0]), } @@ -97,3 +98,46 @@ def test_local_vmec_rerun_when_executable_is_requested(tmp_path): assert result["ier_flag"] == 0 assert max(result["fsqr"], result["fsqz"], result["fsql"]) < 1.0e-9 np.testing.assert_allclose(result["iota_axis"], solution.iota, rtol=1.0e-3) + + +@pytest.mark.integration +@pytest.mark.slow +def test_local_vmec_finite_pressure_zero_current_database_case(tmp_path): + executable = os.environ.get("PYQSC_VMEC_EXECUTABLE") + if not executable: + pytest.skip("Set PYQSC_VMEC_EXECUTABLE to rerun the finite-beta VMEC case.") + solution = qsc.solve_configuration("database_qa_139524", nphi=241, order="r3") + export = qsc.to_vmec( + solution, + tmp_path / "input.qa139524_beta_r0015", + r=0.0015, + ntheta=40, + mpol=8, + ntor=8, + parameters={ + "ns_array": (31, 61), + "ftol_array": (1.0e-9, 1.0e-11), + "niter_array": (3000, 5000), + }, + ) + subprocess.run( + [executable, "input.qa139524_beta_r0015"], + cwd=tmp_path, + check=True, + timeout=120, + ) + result = _read_vmec_result(tmp_path / "wout_qa139524_beta_r0015.nc") + torsion_rms = np.sqrt( + np.sum(np.asarray(solution.torsion**2 * solution.geometry.d_l_d_phi)) + / np.sum(np.asarray(solution.geometry.d_l_d_phi)) + ) + + assert solution.inputs.I2 == 0 + assert solution.inputs.p2 != 0 + assert export.curtor == 0 + assert export.pressure_axis > 0 + assert result["pressure_axis"] == pytest.approx(export.pressure_axis) + assert torsion_rms > 1.0 + assert result["ier_flag"] == 0 + assert max(result["fsqr"], result["fsqz"], result["fsql"]) < 1.0e-9 + np.testing.assert_allclose(result["iota_axis"], solution.iota, rtol=5.0e-4) diff --git a/tests/unit/test_vmec.py b/tests/unit/test_vmec.py index 248edf8..5cd7628 100644 --- a/tests/unit/test_vmec.py +++ b/tests/unit/test_vmec.py @@ -61,6 +61,8 @@ def test_vmec_boundary_is_accurate_and_fast_after_compilation(tmp_path): total_warm_seconds = perf_counter() - start assert float(boundary.maximum_toroidal_angle_residual) < 2.0e-15 + assert bool(boundary.toroidal_angle_converged) + assert float(boundary.toroidal_angle_tolerance) > 0 assert float(boundary.maximum_R_reconstruction_error) < 5.0e-6 assert float(boundary.maximum_Z_reconstruction_error) < 5.0e-6 assert warm_seconds < 0.5 @@ -245,8 +247,12 @@ def test_vmec_input_parameter_guards(kwargs, message): "kwargs, message", [ ({"r": 0.0}, "r must be positive"), + ({"r": float("nan")}, "r must be positive"), ({"ntor_max": -1}, "ntor_max"), ({"coefficient_tolerance": -1.0}, "coefficient_tolerance"), + ({"coefficient_tolerance": float("nan")}, "coefficient_tolerance"), + ({"toroidal_angle_tolerance": -1.0}, "toroidal_angle_tolerance"), + ({"toroidal_angle_tolerance": float("nan")}, "toroidal_angle_tolerance"), ({"ntheta": 7, "mpol": 3}, "ntheta"), ({"mpol": 0}, "positive"), ({"ntor": -1}, "nonnegative"), @@ -271,6 +277,21 @@ def test_to_vmec_resolution_and_scalar_guards(tmp_path, kwargs, message): ) +def test_to_vmec_rejects_unconverged_angle_inversion_without_writing(tmp_path): + output = tmp_path / "input.unconverged" + with pytest.raises(RuntimeError, match="no VMEC input was written"): + qsc.to_vmec( + qa_solution(), + output, + r=0.03, + ntheta=40, + mpol=12, + ntor=14, + newton_iterations=1, + ) + assert not output.exists() + + def test_to_vmec_rejects_unknown_control(tmp_path): with pytest.raises(ValueError, match="Unknown VMEC input"): qsc.to_vmec( diff --git a/tests/unit/test_vmex_interface.py b/tests/unit/test_vmex_interface.py index ce8a1e8..7b73f60 100644 --- a/tests/unit/test_vmex_interface.py +++ b/tests/unit/test_vmex_interface.py @@ -191,6 +191,9 @@ def test_empty_qs_surface_list_supports_asymmetric_equilibrium(fake_vmex): ({"ftol_array": (1.0e-7, 1.0e-8)}, "one positive"), ({"max_iterations": 0}, "positive integer"), ({"adjoint_tol": 0.0}, "positive and finite"), + ({"toroidal_angle_tolerance": -1.0}, "nonnegative and finite"), + ({"newton_iterations": 0}, "positive"), + ({"ntheta": 7}, "ntheta"), ({"helicity_m": 1.5}, "integer"), ({"helicity_n": 1.5}, "integer"), ], @@ -205,6 +208,11 @@ def test_asymmetric_quasisymmetry_guard(fake_vmex): make_problem(fake_vmex, solution=qa_solution(asymmetric=True)) +def test_unconverged_vmex_boundary_is_rejected(fake_vmex): + with pytest.raises(RuntimeError, match="angle inversion did not converge"): + make_problem(fake_vmex, newton_iterations=1) + + def test_parameter_remap_rejects_changed_field_period(fake_vmex): problem = make_problem(fake_vmex) changed = qsc.Qsc( From dcacea215d337321aaa0b84c395c9a8cf0bfe2a2 Mon Sep 17 00:00:00 2001 From: Rogerio Jorge Date: Thu, 30 Jul 2026 23:17:53 -0500 Subject: [PATCH 39/39] docs: record final integration evidence --- docs/development/refactor_status.md | 5 +++++ docs/release_checklist.md | 22 +++++++++++----------- 2 files changed, 16 insertions(+), 11 deletions(-) diff --git a/docs/development/refactor_status.md b/docs/development/refactor_status.md index dab9f87..64a8ae0 100644 --- a/docs/development/refactor_status.md +++ b/docs/development/refactor_status.md @@ -241,6 +241,7 @@ was made for that phase. ## Phase 16 — final VMEC, VMEX, and ESSOS integration +- Commits: pyQSC_JAX `060aef3`; ESSOS `da66774`. - Files: convergence-safe VMEC/VMEX boundary conversion, a live finite-pressure and exactly zero-current VMEC regression, explicit opt-in VMEX examples, and pressure-only stage-two and single-stage ESSOS examples. @@ -258,6 +259,10 @@ was made for that phase. optimization examples. Both use the nonplanar, finite-pressure database stellarator ID 52521 with exactly \(I_2=0\), and every field/gradient/Hessian residual block decreases in both stage-two and single-stage runs. +- Publication verification: all ten scripts were regenerated from + `060aef3`. Physics figures record that exact source commit; performance + figures retain the exact commit of their synchronized raw benchmark report. + The committed README PNGs were byte-stable and visually re-inspected. - Complete pyQSC_JAX evidence: the branch-coverage run completed 294 tests before two VMEX subprocesses reached their former 180 s instrumentation timeout; after making the documented VMEX opt-in explicit, those exact two diff --git a/docs/release_checklist.md b/docs/release_checklist.md index 7db92b3..d497a2d 100644 --- a/docs/release_checklist.md +++ b/docs/release_checklist.md @@ -2,19 +2,19 @@ No release is made from an unreviewed branch. -- [ ] Full line and branch coverage is at least 95%. -- [ ] Ruff, all tests, all examples, docs with warnings as errors, doctests, +- [x] Full line and branch coverage is at least 95%. +- [x] Ruff, all tests, all examples, docs with warnings as errors, doctests, and compatibility checks pass. -- [ ] Wheel and sdist metadata pass `twine check`. -- [ ] Wheel and sdist each install in clean environments and pass a physics +- [x] Wheel and sdist metadata pass `twine check`. +- [x] Wheel and sdist each install in clean environments and pass a physics smoke test. -- [ ] Upstream pyQSC parity and high-resolution cases are rerun. -- [ ] ESSOS vacuum and finite-beta integration passes in a clean environment. -- [ ] Dependency and license audits have no unresolved issue. -- [ ] Performance report records hardware, versions, command, and raw samples. -- [ ] Changelog, migration guide, README, API docs, and limitations are current. -- [ ] Publication figures are regenerated with commit/parameter metadata. +- [x] Upstream pyQSC parity and high-resolution cases are rerun. +- [x] ESSOS vacuum and finite-beta integration passes in a clean environment. +- [x] Dependency and license audits have no unresolved issue. +- [x] Performance report records hardware, versions, command, and raw samples. +- [x] Changelog, migration guide, README, API docs, and limitations are current. +- [x] Publication figures are regenerated with commit/parameter metadata. - [ ] TestPyPI trusted-publishing dry run succeeds. - [ ] PyPI OIDC environment is configured and production publish is approved. - [ ] `CITATION.cff` version/date and Zenodo metadata are updated. -- [ ] No correctness limitation or inherited downstream failure is hidden. +- [x] No correctness limitation or inherited downstream failure is hidden.

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