Pseudo-Vandermonde matrix of given degrees.
Returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y). The pseudo-Vandermonde matrix is defined by
where 0 <= i <= deg and 0 <= j <= deg. The leading indices of V index the points (x, y) and the last index encodes the degrees of the Legendre polynomials.
If V = legvander2d(x, y, [xdeg, ydeg]), then the columns of V correspond to the elements of a 2-D coefficient array c of shape (xdeg + 1, ydeg + 1) in the order
and np.dot(V, c.flat) and legval2d(x, y, c) will be the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of 2-D Legendre series of the same degrees and sample points.
x, y : array_like
deg : list of ints
vander2d : ndarray