numpy.polynomial.polynomial.polyvander2d — NumPy v1.11 Manual (original) (raw)

numpy.polynomial.polynomial.polyvander2d(x, y, deg)[source]¶

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

![V[..., deg[1]*i + j] = x^i * y^j,](http://docs.scipy.org/doc/numpy-1.11.0/_images/math/471f61264a5c59a0a2a86a5628e354d5642f9a3f.png)

where 0 <= i <= deg[0] and 0 <= j <= deg[1]. The leading indices of_V_ index the points (x, y) and the last index encodes the powers of_x_ and y.

If V = polyvander2d(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 polyval2d(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 polynomials of the same degrees and sample points.

Parameters:	x, y : array_like Arrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays. deg : list of ints List of maximum degrees of the form [x_deg, y_deg].
Returns:	vander2d : ndarray The shape of the returned matrix is x.shape + (order,), where. The dtype will be the same as the converted x and y.