linalg op• Data kinds: matrix × signal → signal
• Call: import mathops; mathops.mat_solve(a, b) (or opsmath.get("mat_solve"))
Solve the square linear system `A x = b (LAPACK gesv`, LU with partial pivoting).
*a* must be square `(n, n); *b* is (n,) or (n, k)` (multiple
right-hand sides). An exactly singular *A* raises `ValueError`.
Do not trust the answer of an ill-conditioned system: a solve loses
about `log10(cond(A)) significant digits, so at cond > 1e12` maybe 3
of float64's ~16 digits survive — and *this function cannot tell you that*,
because a near-singular system still "solves". Check :func:mat_cond
first; for a rank-deficient or noisy system use :func:mat_lstsq /
:func:mat_pinv with an explicit `rcond` instead.
HALCON: `solve_matrix`. Returns float64, same trailing shape as *b*.
Every mathops op validates its input before computing (nothing slips through silently):
• **complex input raises ValueError** — coercing to float64 silently discards the imaginary part (numpy only emits a ComplexWarning and returns a plausible-looking wrong real number). State .real/.imag/abs() explicitly, or use complexops, which handles complex data.
• **masked arrays with masked elements raise ValueError** — the implicit conversion that peels off the mask and uses the raw values underneath is refused. Say explicitly whether to fill or to drop.
• **NaN/Inf raises ValueError on every input** (refused with the count stated — it propagates through the whole result).
• Shapes are strict: 1-D and 2-D are never implicitly promoted or broadcast (a matrix in a vector slot, or a vector in a matrix slot, raises ValueError; reshape explicitly).
• Size cap: ops that take a matrix, and the stat_histogram bins, raise ValueError beyond mathops.MAX_ELEMENTS (2^26 ≈ 67 million elements).
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• math_metrology — py -3.11 examples/math_metrology.py
signal as input)mat_lstsq · stat_describe · stat_histogram · stat_zscore · interp_linear · interp_cubic · poly_fit · poly_eval
linalg)mat_lstsq · mat_svd · mat_eigh · mat_pinv · mat_cond
*Provenance: mathops.py — MATH operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.