Add cqr_mkl_?syrk_compact: batched symmetric rank-k update

[ivan-pi]

Summary

Implement cqr_mkl_?syrk_compact and dsyrk_compact/ssyrk_compact, a portable batched symmetric rank-k update (C := alpha A op(A)^T + beta C) in Intel MKL's Compact (interleaved-batch) format. This completes the compact BLAS-3 set and provides the missing mkl_?syrk_compact that MKL does not ship, enabling end-to-end Cholesky QR factorization without MKL compute kernels.

Key Changes

• Core kernel (src/cqr_syrk_compact.hpp): Templated vectorized dot-product rank-k update supporting all combinations of:

  • Precisions: double and single
  • Layouts: column-major (tuned) and row-major
  • Transpose modes: A*A^T and A^T*A
  • Triangle selection: upper and lower
  • Interleave widths: V ∈ {2, 4, 8, 16}

  The tuned path (column-major, trans='T') uses contiguous column vectors with JB=4 register blocking for efficient reuse. Other combinations dispatch through a general strided path using BatchView abstractions.

• Dispatch layer (src/cqr_syrk_compact_dispatch.cpp): LAPACK/BLAS-style argument validation with info = -j error reporting; runtime dispatch on interleave width V to compile-time instantiations.

• MKL adapter (src/cqr_mkl_syrk.cpp): C-linkage wrapper cqr_mkl_?syrk_compact that unwraps MKL enums and MKL_COMPACT_PACK format to call the templated kernel. Follows MKL's Compact convention: no workspace, no info return, no argument validation.

• Portable C API (src/cqr_compact.h): dsyrk_compact / ssyrk_compact entry points with full LAPACK/BLAS-style validation for users not using MKL enums.

• Comprehensive testing:

  • src/test_cqr_syrk_compact.cpp: Self-contained validation with no BLAS dependency; tests argument validation and numerical correctness over the full feature matrix (uplo × trans × layout × precision × interleave widths, including padded partial groups). Reference uses rank-1 outer-product summation (different order than kernel) to catch shared arithmetic bugs.
  • src/test_cqr_mkl_syrk.cpp: Three independent validation suites against real Intel MKL:
    • Suite A: vs. dense per-matrix cblas_?syrk (whole matrix, gates active triangle + opposite untouched)
    • Suite B: vs. mkl_?gemm_compact (triangle comparison, same compact pipeline)
    • Suite C: end-to-end Cholesky QR (G = A^T A → R = chol(G) → Q = A R^{-1}; verify Q R = A and Q^T Q = I)

• Design documentation (cqr_mkl_dsyrk_compact_design.md): Full API specification, algorithm description, layout/transpose handling, and compatibility notes with MKL and Arm Performance Libraries.

Implementation Details

• Algorithm: Dot-product (inner-product) form, accumulating each output C(i,j) as a length-k inner product of two vectors along the contraction axis. Preferred over rank-1 form because: (1) C is written exactly once (minimal traffic, beta fold on single store), (2) branch-free arithmetic, (3) blocks cleanly against the triangle (no diagonal-corner peeling).

• Register blocking: JB=4 reuses each A-vector load across four output columns, halving dominant A traffic—the same reuse strategy applied in `ormqr

https://claude.ai/code/session_01Wne41CWggMhAxiggVUhCwv