linalg op• Data kinds: matrix → table
• Call: import fullseye as fs; fs.ledger.mat_eigh(a) (to call the implementation directly, import mathops; mathops.mat_eigh(a); from the registry, opsmath.get("mat_eigh"))
• Return value through the ledger: fullseye.ledger.mat_eigh(...) returns only the declared out type table (the underlying function also returns auxiliary values). When you need what was dropped, use fullseye.ledger.mat_eigh.raw(...) or call mathops.mat_eigh directly.
Eigen-decomposition of a symmetric matrix (LAPACK syevd).
Returns (w, V): eigenvalues w in ascending order (all real — guaranteed by symmetry) and orthonormal eigenvectors as the columns of V (A @ V[:, i] == w[i] * V[:, i]).
Symmetric input only, verified: max|A - A.T| above 1e-10 of the matrix scale raises ValueError. This is deliberate fail-closing of two traps at once — a symmetric solver fed a non-symmetric matrix silently reads one triangle and returns a *plausible wrong* answer, and a general matrix has complex eigenvalues this real-valued API cannot even represent. For a covariance / Hessian / Gram matrix (the metrology cases) symmetry holds by construction; symmetrise explicitly ((A + A.T) / 2) if yours is symmetric-up-to-noise.
Sign trap (honest): each eigenvector is defined only up to sign, and eigenvectors of a *repeated* eigenvalue only up to rotation in that subspace. Compare |v·w| or subspaces, never raw columns.
HALCON: eigenvalues_symmetric_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_thermal_radiometry — py -3.11 examples/poc_thermal_radiometry.py
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
linalg)mat_solve · mat_lstsq · mat_svd · 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.