scipy.interpolate.splev(x, tck, der=0, ext=0)[source]#

Evaluate a B-spline or its derivatives.

Given the knots and coefficients of a B-spline representation, evaluate the value of the smoothing polynomial and its derivatives. This is a wrapper around the FORTRAN routines splev and splder of FITPACK.


An array of points at which to return the value of the smoothed spline or its derivatives. If tck was returned from splprep, then the parameter values, u should be given.

tckBSpline instance or tuple

If a tuple, then it should be a sequence of length 3 returned by splrep or splprep containing the knots, coefficients, and degree of the spline. (Also see Notes.)

derint, optional

The order of derivative of the spline to compute (must be less than or equal to k, the degree of the spline).

extint, optional

Controls the value returned for elements of x not in the interval defined by the knot sequence.

  • if ext=0, return the extrapolated value.

  • if ext=1, return 0

  • if ext=2, raise a ValueError

  • if ext=3, return the boundary value.

The default value is 0.

yndarray or list of ndarrays

An array of values representing the spline function evaluated at the points in x. If tck was returned from splprep, then this is a list of arrays representing the curve in an N-D space.


Manipulating the tck-tuples directly is not recommended. In new code, prefer using BSpline objects.



C. de Boor, “On calculating with b-splines”, J. Approximation Theory, 6, p.50-62, 1972.


M. G. Cox, “The numerical evaluation of b-splines”, J. Inst. Maths Applics, 10, p.134-149, 1972.


P. Dierckx, “Curve and surface fitting with splines”, Monographs on Numerical Analysis, Oxford University Press, 1993.


Examples are given in the tutorial.

A comparison between splev, splder and spalde to compute the derivatives of a B-spline can be found in the spalde examples section.