spectral op• Data kinds: matrix → table
• Call: import fullseye as fs; fs.ledger.esprit_doa(X, n_sources: 'int | None' = None, *, spacing: 'float' = 0.5) -> 'dict' (to call the implementation directly, import mathspectral; mathspectral.esprit_doa(X, n_sources: 'int | None' = None, *, spacing: 'float' = 0.5) -> 'dict'; from the registry, opsmath.get("esprit_doa"))
ESPRIT (Roy & Kailath 1989): solves for the directions without a grid, from the array's invariance under a "shift by 1 element".
From the eigenvalues λ_k = exp(−2πi d sin θ_k) of Φ, which links the top M−1 rows and the bottom M−1 rows of the signal subspace E_s by least squares, θ_k = arcsin(−arg λ_k / (2π d)). Exact without noise and with uncorrelated sources (not bound by the grid resolution). If n_sources=None, it is estimated by MDL. Returns {"doa_deg", "eigenvalues", "n_sources", "n_sources_estimated"}.
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 · music_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.