SciPy

scipy.interpolate.spalde

scipy.interpolate.spalde(x, tck)[source]

Evaluate all derivatives of a B-spline.

Given the knots and coefficients of a cubic B-spline compute all derivatives up to order k at a point (or set of points).

Parameters:

x : array_like

A point or a set of points at which to evaluate the derivatives. Note that t(k) <= x <= t(n-k+1) must hold for each x.

tck : tuple

A tuple (t, c, k), containing the vector of knots, the B-spline coefficients, and the degree of the spline (see splev).

Returns:

results : {ndarray, list of ndarrays}

An array (or a list of arrays) containing all derivatives up to order k inclusive for each point x.

References

[R74]C. de Boor: On calculating with b-splines, J. Approximation Theory 6 (1972) 50-62.
[R75]M. G. Cox : The numerical evaluation of b-splines, J. Inst. Maths applics 10 (1972) 134-149.
[R76]P. Dierckx : Curve and surface fitting with splines, Monographs on Numerical Analysis, Oxford University Press, 1993.