feat: add dispatch rules for pinv and svd

[alessandrogentili001]

Add Dispatch Rules for pinv and svd

Related to #49

Summary

This PR adds specialized dispatch rules for pinv (pseudoinverse) and svd (singular value decomposition) for structured linear operators. These additions follow the existing patterns used by inv, logdet, and trace to improve performance and numerical stability by exploiting operator structure.

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Changes

1. pinv Dispatch Rules (cola/linalg/inverse/pinv.py)

• BlockDiag: $pinv(\text{BlockDiag}(A, B, \dots)) = \text{BlockDiag}(pinv(A), pinv(B), \dots)$
• Kronecker: $pinv(\text{Kronecker}(A, B)) = \text{Kronecker}(pinv(A), pinv(B))$
• Diagonal (Fix): Updated to handle zero diagonal entries correctly using a mask to avoid division by zero.

2. svd Dispatch Rules (cola/linalg/svd/svd.py)

• ScalarMul: Decomposes into phase, magnitude, and identity components.
• Permutation: Recognizes permutations as unitary (all singular values equal to 1).
• BlockDiag: $svd(\text{BlockDiag}(A, B)) \to \text{BlockDiag}(U_A, U_B), \text{Diag}(\text{concat}(\sigma_A, \sigma_B)), \text{BlockDiag}(V_A, V_B)$
• Kronecker: $svd(\text{Kronecker}(A, B)) \to \text{Kronecker}(U_A, U_B), \text{Kronecker}(S_A, S_B), \text{Kronecker}(V_A, V_B)$

3. Backend Additions

• Added pinv to np_fns.py (np.linalg.pinv) and jax_fns.py (jnp.linalg.pinv) to ensure consistency across all supported backends.

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Tests

I have added two new test files containing 18 tests covering all dispatch rules across NumPy, PyTorch, and JAX backends.

Test File	Cases Covered	Status
tests/linalg/inverse/test_pinv_dispatch.py	BlockDiag, Kronecker (3 backends)	✅ 6 passed
tests/linalg/svd/test_svd_dispatch.py	ScalarMul, Permutation, BlockDiag, Kronecker (3 backends)	✅ 12 passed

Verification Criteria:

• Reconstruction Accuracy: Verified that $U \Sigma V^H \approx A$ with a relative error $< 10^{-5}$.
• Analytical Correctness: Singular values were verified against known analytical solutions where applicable.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 83.64%. Comparing base (2ddcb3d) to head (b501909).
⚠️ Report is 5 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #123      +/-   ##
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+ Coverage   83.09%   83.64%   +0.54%     
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  Files          45       45              
  Lines        3827     3870      +43     
==========================================
+ Hits         3180     3237      +57     
+ Misses        647      633      -14     

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