numpy.polynomial.polynomial.polyvander#
- polynomial.polynomial.polyvander(x, deg)[source]#
Vandermonde matrix of given degree.
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 matrixV = polyvander(x, n)
, thennp.dot(V, c)
andpolyval(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:
- xarray_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.
- degint
Degree of the resulting matrix.
- Returns:
- vanderndarray.
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.
See also
Examples
The Vandermonde matrix of degree
deg = 5
and sample pointsx = [-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.]])