dynsys op• Data kinds: none → table (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.ode_flow_states(system='lorenz', params=None, x0=None, t_end=40.0, dt=0.005, method='rk4') (to call the implementation directly, import mathops; mathops.ode_flow_states(system='lorenz', params=None, x0=None, t_end=40.0, dt=0.005, method='rk4'); from the registry, opsmath.get("ode_flow_states"))
Integrate a named vector field — the trajectory, with the order you paid for.
Explicit Runge-Kutta on one of the named systems (lorenz, rossler, harmonic, linear). method="rk4" is the classical 4th-order step; method="euler" is there as a control group — the same picture comes out of both, and only the error tells them apart.
★Why the field is a name, not a function: the typed ledger registers inputs by sort and the chain fuzzer builds arguments from data, so a callable can never be reached from there. A name (or, for linear, the matrix itself in params) keeps every op in this family reachable from the ledger.
★Why this earns its place: for system="linear" the exact solution is expm(A t) x0, so the error is known in closed form — and halving dt divides it by 16, which is what "4th order" means. A drawing of an attractor cannot be checked; this can.
system : str
One of DYNSYS_SYSTEMS.
params : floats or None
System parameters (defaults in DYNSYS_SYSTEMS). For linear this is
the matrix A in row-major order (n*n numbers).
x0 : floats or None
Initial state (default: a point on the attractor / unit first coordinate).
t_end, dt : float
Integration window and step. t_end / dt must stay under 4,000,000.
method : "rk4" | "euler"
Returns a states table: t (S,) and x (S, n).
Raises ValueError: unknown system or method; wrong parameter count; non-finite input; dt not positive; a step count over the cap; a trajectory that left float range (the field diverged — reported, never silently clipped).
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_what_a_picture_cannot_check — py -3.11 examples/poc_what_a_picture_cannot_check.py
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
dynsys)ode_vector_field_grid · dynsys_poincare_section · dynsys_lyapunov_spectrum · dynsys_bifurcation_map · dynsys_correlation_dimension
*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.