numpy.polynomial.chebyshev.chebvander2d   polynomial.chebyshev.chebvander2d(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  \[V[..., (deg[1] + 1)*i + j] = T_i(x) * T_j(y),\] 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  \[c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ...\] 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.  Parameters 
 
x, yarray_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.  
deglist of ints


List of maximum degrees of the form [x_deg, y_deg].    Returns 
 
vander2dndarray


The shape of the returned matrix is x.shape + (order,), where \(order = (deg[0]+1)*(deg[1]+1)\). The dtype will be the same as the converted x and y.      See also  
chebvander, chebvander3d, chebval2d, chebval3d

  Notes  New in version 1.7.0.  


    
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