`scipy.interpolate._fitpack_repro:disc`

source: /scipy/interpolate/_fitpack_repro.py :439

Signature

def disc ( t , k )

Summary

Discontinuity matrix: jumps of k-th derivatives of b-splines at internal knots.

Extended Summary

See Eqs. (9)-(10) of Ref. [1], or, equivalently, Eq. (3.43) of Ref. [2].

This routine assumes internal knots are all simple (have multiplicity =1).

Parameters

t : ndarray, 1D, shape(n,): Knots.
k : int: The spline degree

Returns

disc : ndarray, shape(n-2*k-1, k+2): The jumps of the k-th derivatives of b-splines at internal knots, t[k+1], ...., t[n-k-1].
offset : ndarray, shape(2-2*k-1,): Offsets
nc : int

Notes

The normalization here follows FITPACK: (https://github.com/scipy/scipy/blob/maintenance/1.11.x/scipy/interpolate/fitpack/fpdisc.f#L36)

The k-th derivative jumps are multiplied by a factor

(delta / nrint)**k / k!

where delta is the length of the interval spanned by internal knots, and nrint is one less the number of internal knots (i.e., the number of subintervals between them).

Aliases

scipy.interpolate._fitpack_repro.disc