scipy.interpolate.BSpline.insert_knot#

BSpline.insert_knot(x, m=1)[source]#

Insert a new knot at x of multiplicity m.

Given the knots and coefficients of a B-spline representation, create a new B-spline with a knot inserted m times at point x.

Parameters:

xfloat: The position of the new knot
mint, optional: The number of times to insert the given knot (its multiplicity). Default is 1.

Returns:

splBSpline object: A new BSpline object with the new knot inserted.

See also

scipy.interpolate.insert

Notes

Based on algorithms from [1] and [2].

In case of a periodic spline (self.extrapolate == "periodic") there must be either at least k interior knots t(j) satisfying t(k+1)<t(j)<=x or at least k interior knots t(j) satisfying x<=t(j)<t(n-k).

This routine is functionally equivalent to scipy.interpolate.insert.

Added in version 1.13.

References

[1]

W. Boehm, “Inserting new knots into b-spline curves.”, Computer Aided Design, 12, p.199-201, 1980. DOI:10.1016/0010-4485(80)90154-2.

[2]

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

Examples

You can insert knots into a B-spline:

>>> import numpy as np
>>> from scipy.interpolate import BSpline, make_interp_spline
>>> x = np.linspace(0, 10, 5)
>>> y = np.sin(x)
>>> spl = make_interp_spline(x, y, k=3)
>>> spl.t
array([ 0.,  0.,  0.,  0.,  5., 10., 10., 10., 10.])

Insert a single knot

>>> spl_1 = spl.insert_knot(3)
>>> spl_1.t
array([ 0.,  0.,  0.,  0.,  3.,  5., 10., 10., 10., 10.])

Insert a multiple knot

>>> spl_2 = spl.insert_knot(8, m=3)
>>> spl_2.t
array([ 0.,  0.,  0.,  0.,  5.,  8.,  8.,  8., 10., 10., 10., 10.])