_vander_nd(vander_fs, points, degrees)
The result is built by combining the results of 1d Vandermonde matrices,
$$W[i_0, \ldots, i_M, j_0, \ldots, j_N] = \prod_{k=0}^N{V_k(x_k)[i_0, \ldots, i_M, j_k]}$$where
$$N &= \texttt{len(points)} = \texttt{len(degrees)} = \texttt{len(vander\_fs)} \\ M &= \texttt{points[k].ndim} \\ V_k &= \texttt{vander\_fs[k]} \\ x_k &= \texttt{points[k]} \\ 0 \le j_k &\le \texttt{degrees[k]}$$Expanding the one-dimensional $V_k$ functions gives:
$$W[i_0, \ldots, i_M, j_0, \ldots, j_N] = \prod_{k=0}^N{B_{k, j_k}(x_k[i_0, \ldots, i_M])}$$where $B_{k,m}$ is the m'th basis of the polynomial construction used along dimension $k$ . For a regular polynomial, $B_{k, m}(x) = P_m(x) = x^m$ .
The 1d vander function to use for each axis, such as polyvander
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. This must be the same length as :None:None:`vander_fs`.
The maximum degree (inclusive) to use for each axis. This must be the same length as :None:None:`vander_fs`.
An array of shape points[0].shape + tuple(d + 1 for d in degrees)
.
A generalization of the Vandermonde matrix for N dimensions
The following pages refer to to this document either explicitly or contain code examples using this.
numpy.polynomial.polyutils._vander_nd_flat
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