scijit.interpolate.splint¶

scijit.interpolate.splint(a, b, tck, full_output=0)¶

Evaluate the definite integral of a spline.

Parameters:

a, bfloat: Integration limits, the limits first and tck last. They may lie outside the knot range, where the spline is extrapolated; b < a gives the negated integral.
tcktuple of (t, c, k): Spline representation.
full_outputint, optional: Non-zero also returns wrk, the per-B-spline integrals. Default 0. Must be a compile-time constant inside @njit, since it selects the return type.

Returns:

resfloat: The integral of the spline over [a, b].
wrk1-D float64 ndarray, length len(t) - k - 1: The integral of each normalised B-spline over [a, b], so that res == sum(c[:len(wrk)] * wrk). Returned only when full_output is non-zero.

Raises:

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

See also

scipy.interpolate.splint: The scipy routine this mirrors.

Notes

full_output must be a compile-time constant inside @njit: it selects between a bare float and a 2-tuple, and numba compiles one return type per specialization. A bool, an int, a string and the default are read while the call compiles; a float, a container and a runtime variable are not, and raise TypingError naming the argument. From Python every object is read by its truthiness.
full_output=1 returns the wrk array, holding the integrals of the normalized B-splines. scipy 1.18 returns (res, None) there.
A parametric c, the coefficient list scipy.interpolate.splprep returns, makes scipy return a list of integrals. This takes one coefficient array at a time.
tck is a 3-tuple. scipy also accepts a BSpline instance.

prange-safe: yes.

Examples

>>> import numpy as np
>>> from numba import njit
>>> from scijit.interpolate import splrep, splint
>>> x = np.linspace(0, np.pi, 60)
>>> tck = splrep(x, np.sin(x))
>>> @njit
... def area(tck):
...     return splint(0.0, np.pi, tck)
>>> float(np.round(area(tck), 10))
1.9999999783
>>> @njit
... def area_and_parts(tck):
...     res, wrk = splint(0.0, np.pi, tck, 1)
...     return res, len(wrk)
>>> res, nwrk = area_and_parts(tck)
>>> float(np.round(res, 10)), nwrk
(1.9999999783, 60)