linalg: add matrix_rank, cond, and polar decomposition - #258
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matrix_rank(A, tol=None): count of singular values above tol, default max(m,n) * eps * sigma_max (numpy convention). cond(A): 2-norm condition number sigma_max / sigma_min via SVD. Returns inf for singular matrices. Works for rectangular A. Closes sbryngelson#125.
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Closes #125. Closes #168.
What
Three new functions in
aneforge/linalg.py, all composed from the existing on-ANE SVD:matrix_rank(A, tol=None)— numerical rank by counting singular values abovetol. Default follows numpy:max(m, n) * eps(fp32) * sigma_max.cond(A)— 2-norm condition numbersigma_max / sigma_min. Returnsinffor singular matrices. Works for rectangular A.polar(A)— polar decompositionA = U @ Pvia randomized SVD. U has orthonormal columns, P is symmetric positive-semidefinite. Oracle:scipy.linalg.polar.Checks
ruff check— cleanpylint 2-space— 10.00/10pyright— 0 errorscompileall— cleanpytest -m "not requires_ane"— all pass (off-device)Notes
condreturnsinfwhen the condition number exceeds ~1e2 (sigma_min underflows to 0 in fp16). Tests use cond ≤ 5 for oracle comparisons.polaruses randomized SVD (not full SVD), so P has ~1e-4 asymmetry from the approximation. Symmetrized in the implementation.