numpy.polynomial.chebyshev.
chebvander2d
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
System Message: WARNING/2 (V[..., (deg[1] + 1)*i + j] = T_i(x) * T_j(y), )
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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 degrees of the Chebyshev polynomials.
If V = chebvander2d(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
V = chebvander2d(x, y, [xdeg, ydeg])
System Message: WARNING/2 (c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ... )
and np.dot(V, c.flat) and chebval2d(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 Chebyshev series of the same degrees and sample points.
np.dot(V, c.flat)
chebval2d(x, y, c)
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.
List of maximum degrees of the form [x_deg, y_deg].
The shape of the returned matrix is x.shape + (order,), where
x.shape + (order,)
System Message: WARNING/2 (order = (deg[0]+1)*(deg([1]+1))
See also
chebvander, chebvander3d, chebval2d, chebval3d
chebvander
chebvander3d
chebval2d
chebval3d
Notes
New in version 1.7.0.
