`numpy.ma.extras:vander`

source: /numpy/ma/extras.py :2216

Signature

def vander ( x , n = None )

Summary

Generate a Vandermonde matrix.

Extended Summary

The columns of the output matrix are powers of the input vector. The order of the powers is determined by the increasing boolean argument. Specifically, when increasing is False, the i-th output column is the input vector raised element-wise to the power of N - i - 1. Such a matrix with a geometric progression in each row is named for Alexandre- Theophile Vandermonde.

Parameters

x : array_like: 1-D input array.
N : int, optional: Number of columns in the output. If N is not specified, a square array is returned (N = len(x)).
increasing : bool, optional: Order of the powers of the columns. If True, the powers increase from left to right, if False (the default) they are reversed.

Returns

out : ndarray: Vandermonde matrix. If increasing is False, the first column is x^(N-1), the second x^(N-2) and so forth. If increasing is True, the columns are x^0, x^1, ..., x^(N-1).

Notes

Masked values in the input array result in rows of zeros.

Examples

import numpy as np
x = np.array([1, 2, 3, 5])
N = 3
np.vander(x, N)

✓

np.column_stack([x**(N-1-i) for i in range(N)])

✓

x = np.array([1, 2, 3, 5])
np.vander(x)
np.vander(x, increasing=True)

✓

The determinant of a square Vandermonde matrix is the product of the differences between the values of the input vector:

np.linalg.det(np.vander(x))

✗

(5-3)*(5-2)*(5-1)*(3-2)*(3-1)*(2-1)

✓

Aliases

numpy.ma.vander