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numpy.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 matrix V = polyvander(x, n), then, 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.


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.


Degree of the resulting matrix.


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.