`scipy.interpolate._bsplines:BSpline.insert_knot`

source: build-install/usr/lib/python3.14/site-packages/scipy/interpolate/_bsplines.py:1371

Signature

def insert_knot(self, x, m = 1)

Summary

Insert a new knot at x of multiplicity m.

Extended Summary

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

x : float: The position of the new knot
m : int, optional: The number of times to insert the given knot (its multiplicity). Default is 1.

Returns

spl : `BSpline` object: A new BSpline object with the new knot inserted.

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.

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.])

Aliases

scipy.interpolate.BSpline.insert_knot