mat_pinv — MATH `linalg` op

• Data kinds: matrix → matrix

• Call: import fullseye as fs; fs.ledger.mat_pinv(a, rcond=1e-12) (to call the implementation directly, import mathops; mathops.mat_pinv(a, rcond=1e-12); from the registry, opsmath.get("mat_pinv"))

Usage

Moore-Penrose pseudo-inverse via SVD, with the cutoff explicit.

Singular values below rcond * s_max are treated as zero — that cutoff *is* the regularisation, so it is a named, documented parameter here (default 1e-12) rather than a hidden library default: raising it discards noisy directions (stabler, more biased), lowering it keeps them (exact for well-conditioned *A*, explosive near rank deficiency).

Works for any (m, n): pinv(A) @ b is the least-squares solution for m > n and the minimum-norm solution for m < n.

HALCON: no direct operator — HALCON reaches the same result through svd_matrix + reciprocal singular values.

Family-wide input contract (fail-closed)

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).

Detailed usage guide

• math_metrology family guide

Background guides (the physics and conventions behind this op)

• blas_threads_and_memory — Why matrix decompositions are slow — BLAS threads, caches, memory layout

References (sample data, literature)

• 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.

Runnable examples (verified samples that actually call this op)

• math_metrology — py -3.11 examples/math_metrology.py

• poc_machine_condition_fusion — py -3.11 examples/poc_machine_condition_fusion.py

Ops the type connects to (they accept `matrix` as input)

mat_solve · mat_lstsq · mat_svd · mat_eigh · mat_cond · mat_lu · mat_qr · mat_cholesky

Same category (`linalg`)