wave op• Data kinds: none → matrix (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.wave_membrane_mode(kind='rectangular', m=2, n=3, shape=(256, 256), aspect=1.0, free_edge=True) (to call the implementation directly, import mathops; mathops.wave_membrane_mode(kind='rectangular', m=2, n=3, shape=(256, 256), aspect=1.0, free_edge=True); from the registry, opsmath.get("wave_membrane_mode"))
One eigenmode of a vibrating membrane — the shape the sand draws.
★This is a membrane, not a plate. The familiar Chladni pattern cos(m pi x) cos(n pi y) - cos(n pi x) cos(m pi y) solves the Helmholtz equation with free (Neumann) edges; a real Chladni *plate* obeys the biharmonic equation and has a different frequency ladder. The pictures look alike, the frequencies do not — so this op says membrane and is checked against membrane truth only.
kind="rectangular" returns the (possibly combined) cosine mode over a rectangle of the given *aspect*; kind="circular" returns J_m(k r) cos(m theta) with k from the Bessel zero, zero outside the disc.
★Why this earns its place: the nodal lines of a rectangular mode are known by count — a simple (m, n) mode has m-1 interior vertical and n-1 horizontal nodal lines — and the circular mode's nodal circles are at the ratios of successive Bessel zeros. The drawing can therefore be graded.
Returns a matrix (signed displacement, peak scaled to 1). Use wave_nodal_lines for the zero set.
Raises ValueError: unknown kind; m/n below the valid range; a grid over the cap; non-positive aspect; free_edge=False combined with m == n for the combined mode (the difference vanishes identically).
HALCON: no operator.
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
matrix as input)mat_solve · mat_lstsq · mat_svd · mat_eigh · mat_pinv · mat_cond · mat_lu · mat_qr
wave)wave_mode_frequencies · 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.