`numpy.polynomial.polynomial:polyvander`

source: build-install/usr/lib/python3.14/site-packages/numpy/polynomial/polynomial.py:1074

Signature

def polyvander(x, deg)

Summary

Vandermonde matrix of given degree.

Extended Summary

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

V [..., i] = x^{i},

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

If c is a 1-D array of coefficients of length n + 1 and V is the matrix V = polyvander(x, n), then np.dot(V, c) and polyval(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 polynomials 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 Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1,), where the last index is the power of x. The dtype will be the same as the converted x.

Examples

The Vandermonde matrix of degree ``deg = 5`` and sample points ``x = [-1, 2, 3]`` contains the element-wise powers of `x` from 0 to 5 as its columns.

from numpy.polynomial import polynomial as P
x, deg = [-1, 2, 3], 5
P.polyvander(x=x, deg=deg)

✓

array([[  1.,  -1.,   1.,  -1.,   1.,  -1.],
       [  1.,   2.,   4.,   8.,  16.,  32.],
       [  1.,   3.,   9.,  27.,  81., 243.]])

Aliases

numpy.polynomial.polynomial.polyvander