linalg op• Data kinds: matrix → table
• Call: import fullseye as fs; fs.ledger.mat_lu(a, pivoting='partial') (to call the implementation directly, import mathops; mathops.mat_lu(a, pivoting='partial'); from the registry, opsmath.get("mat_lu"))
LU factorisation P @ A = L @ U (L unit lower, U upper).
pivoting="partial" (default, LAPACK getrf) swaps rows so every multiplier is |l| <= 1. pivoting="none" is plain Gaussian elimination, kept on purpose as the classic failure: on [[1e-20, 1], [1, 1]] the multiplier is 1e20, U[1,1] rounds to −1e20 and L @ U loses the original A[1,1] = 1 entirely (Trefethen & Bau, Lecture 20).
Returns a dict: P, L, U, growth = max|U| / max|A| (the growth factor; huge growth means the factorisation is numerically meaningless) and residual = max|P A − L U| / max|A|.
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).
• blas_threads_and_memory — Why matrix decompositions are slow — BLAS threads, caches, memory layout
• 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.
• (none yet)
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
linalg)mat_solve · mat_lstsq · mat_svd · mat_eigh · mat_pinv · mat_cond · mat_qr · mat_cholesky
*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.