`scipy.interpolate._bsplines:BSpline.basis_element`

source: /scipy/interpolate/_bsplines.py :307

Summary

Return a B-spline basis element B(x | t[0], ..., t[k+1]).

Parameters

t : ndarray, shape (k+2,): internal knots
extrapolate : bool or 'periodic', optional: whether to extrapolate beyond the base interval, t[0] .. t[k+1], or to return nans. If 'periodic', periodic extrapolation is used. Default is True.

Returns

basis_element : callable: A callable representing a B-spline basis element for the knot vector t.

Notes

The degree of the B-spline, k, is inferred from the length of t as len(t)-2. The knot vector is constructed by appending and prepending k+1 elements to internal knots t.

Examples

Construct a cubic B-spline:

import numpy as np
from scipy.interpolate import BSpline
b = BSpline.basis_element([0, 1, 2, 3, 4])
k = b.k

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b.t[k:-k]

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Construct a quadratic B-spline on ``[0, 1, 1, 2]``, and compare to its explicit form:

t = [0, 1, 1, 2]
b = BSpline.basis_element(t)
def f(x):
    return np.where(x < 1, x*x, (2. - x)**2)

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import matplotlib.pyplot as plt
fig, ax = plt.subplots()
x = np.linspace(0, 2, 51)

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ax.plot(x, b(x), 'g', lw=3)
ax.plot(x, f(x), 'r', lw=8, alpha=0.4)

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ax.grid(True)
plt.show()

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Aliases

scipy.interpolate.BSpline.basis_element