linalg op• Data kinds: matrix → table
• Call: import fullseye as fs; fs.ledger.mat_svd(a, full_matrices=False) (to call the implementation directly, import mathops; mathops.mat_svd(a, full_matrices=False); from the registry, opsmath.get("mat_svd"))
• Return value through the ledger: fullseye.ledger.mat_svd(...) returns only the declared out type table (the underlying function also returns auxiliary values). When you need what was dropped, use fullseye.ledger.mat_svd.raw(...) or call mathops.mat_svd directly.
Singular value decomposition A = U @ diag(s) @ Vt (LAPACK gesdd).
Returns (U, s, Vt) with s descending and non-negative. With the default full_matrices=False the *thin* SVD is returned (U is (m, r), Vt is (r, n), r = min(m, n)) — enough to reconstruct A exactly and what every rank/PCA use wants; pass True for the full orthogonal bases.
Sign trap (honest): each singular-vector pair (u_i, v_i) is defined only up to a simultaneous sign flip, and vectors within a *degenerate* (equal-s) block only up to rotation. Assert on s, on U diag(s) Vt, or on projectors — never on raw U/Vt entries.
HALCON: svd_matrix.
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.
• math_metrology — py -3.11 examples/math_metrology.py
• poc_water_level — py -3.11 examples/poc_water_level.py
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
linalg)mat_solve · mat_lstsq · mat_eigh · mat_pinv · mat_cond · mat_lu · 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.