spectral op• Data kinds: matrix → table
• Call: import fullseye as fs; fs.ledger.music_doa(X, n_sources: 'int | None' = None, *, spacing: 'float' = 0.5, grid_deg=None) -> 'dict' (to call the implementation directly, import mathspectral; mathspectral.music_doa(X, n_sources: 'int | None' = None, *, spacing: 'float' = 0.5, grid_deg=None) -> 'dict'; from the registry, opsmath.get("music_doa"))
MUSIC (Schmidt 1986): searches for the directions orthogonal to the noise subspace of the covariance.
P(θ) = 1 / ‖E_nᴴ a(θ)‖². In the true direction the denominator becomes almost 0 and a sharp peak rises.
Assumptions: the number of sources is correct, and the sources are mutually uncorrelated (with correlated waves = multipath, the subspace collapses and the peaks vanish). If n_sources=None, it is estimated with n_sources_mdl and n_sources_estimated in the return value is set to True. Returns {"grid_deg", "pseudo_spectrum_db", "doa_deg", "eigenvalues"} (doa is n values in order of peak size, at the grid's resolution).
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.
• spectral_tour — py -3.11 examples/spectral_tour.py
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
spectral)lomb_scargle · ula_snapshots · esprit_doa · n_sources_mdl · hilbert_analytic
*Provenance: mathspectral.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.