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# scipy.interpolate.splev

`scipy.interpolate.``splev`(x, tck, der=0, ext=0)

  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.

  Parameters:

  x : array_like

  > 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.

  tck : 3-tuple or a BSpline object

  > 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.)

  der : int, optional

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

  ext : int, 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.

  Returns:

  y : ndarray 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 N-dimensional space.

  See also

  `splprep`, `splrep`, `sproot`, `spalde`, `splint`, `bisplrep`, `bisplev`, `BSpline`

  Notes

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

  References

  [R78] | C. de Boor, “On calculating with b-splines”, J. Approximation Theory, 6, p.50-62, 1972.

  [R79] | M. G. Cox, “The numerical evaluation of b-splines”, J. Inst. Maths Applics, 10, p.134-149, 1972.

  [R80] | P. Dierckx, “Curve and surface fitting with splines”, Monographs on Numerical Analysis, Oxford University Press, 1993.