scijit.interpolate.spalde

scijit.interpolate.spalde(x, tck)

Evaluate all derivatives of a spline at one point.

Parameters:

xfloat

A SCALAR evaluation point, inside the knot range.

tcktuple of (t, c, k)

Spline representation.

Returns:

d1-D float64 ndarray, length k + 1

d[j] is the j-th derivative at x, with d[0] the value itself.

Raises:

TypeError

If x lies outside [t[k], t[n-k-1]], or a knot interval is degenerate.

ValueError

If c holds fewer than len(t) - k - 1 coefficients.

See also

scipy.interpolate.spalde

The scipy routine this mirrors.

Notes

• x is one point. scipy also accepts an array of m points and returns a LIST of m arrays for m > 1, a bare array for m == 1. The return type there follows a run-time length, which a compiled body cannot do. Call it once per point in a loop; inside @njit the loop is compiled, so it carries no per-iteration overhead.

prange-safe: yes.

Examples

>>> import numpy as np
>>> from numba import njit
>>> from scijit.interpolate import splrep, spalde
>>> x = np.linspace(0, 4, 40)
>>> tck = splrep(x, np.sin(x))
>>> @njit
... def derivs(tck):
...     return spalde(0.0, tck)
>>> np.round(derivs(tck), 6)
array([-0.000000e+00,  1.000019e+00, -6.700000e-04, -9.908410e-01])