`numpy.polynomial.hermite:hermvander`

source: /numpy/polynomial/hermite.py :1123

Signature

def hermvander ( x , deg )

Summary

Pseudo-Vandermonde matrix of given degree.

Extended Summary

Returns the pseudo-Vandermonde matrix of degree deg and sample points x. The pseudo-Vandermonde matrix is defined by

V [..., i] = H_{i} (x),

where 0 <= i <= deg. The leading indices of V index the elements of x and the last index is the degree of the Hermite polynomial.

If c is a 1-D array of coefficients of length n + 1 and V is the array V = hermvander(x, n), then np.dot(V, c) and hermval(x, c) are the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of Hermite series of the same degree and sample points.

Parameters

x : array_like: Array of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If x is scalar it is converted to a 1-D array.
deg : int: Degree of the resulting matrix.

Returns

vander : ndarray: The pseudo-Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1,), where The last index is the degree of the corresponding Hermite polynomial. The dtype will be the same as the converted x.

Examples

import numpy as np
from numpy.polynomial.hermite import hermvander
x = np.array([-1, 0, 1])
hermvander(x, 3)

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Aliases

numpy.polynomial.hermite.hermvander