wave op• Data kinds: none → signal (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.wave_mode_frequencies(kind='rectangular', count=10, aspect=1.0) (to call the implementation directly, import mathops; mathops.wave_mode_frequencies(kind='rectangular', count=10, aspect=1.0); from the registry, opsmath.get("wave_mode_frequencies"))
The eigenvalue ladder of a membrane — a closed form you can check against.
`kind="rectangular"`: the Dirichlet eigenvalues of a rectangle are
`pi**2 * (m**2 + n**2 / aspect**2) for m, n >= 1 — **not** m n pi`,
which is the usual slip. `kind="circular"`: the free-edge (Neumann) circular
membrane's eigenvalues are the squares of the zeros of `J'_m`.
★Why this earns its place: this ladder is what separates a membrane from a
plate, and it is exactly computable. The square drum's ratios start
2, 5, 5, 8, 10, 10, 13 (in units of `pi**2`) — the repeated 5 and 10 are the
famous degeneracies that make the square drum's modes ambiguous, and a wrong
implementation loses them.
Returns a `signal`: the eigenvalues, ascending.
Raises `ValueError`: unknown kind; non-positive count or aspect; a
circular request without scipy.
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.
• poc_beats_fringes_and_screens — py -3.11 examples/poc_beats_fringes_and_screens.py
signal as input)mat_solve · mat_lstsq · stat_describe · stat_histogram · stat_zscore · interp_linear · interp_cubic · interp_scattered
wave)wave_membrane_mode · wave_nodal_lines · wave_two_slit · wave_fringe_period · wave_grating_orders
*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.