Pseudo-Vandermonde matrix of given degrees.
Returns the pseudo-Vandermonde matrix of degrees deg and sample
points (x, y, z). If l, m, n are the given degrees in x, y, z,
then Hehe pseudo-Vandermonde matrix is defined by
System Message: WARNING/2 (V[..., (m+1)(n+1)i + (n+1)j + k] = He_i(x)*He_j(y)*He_k(z),
)
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where 0 <= i <= l, 0 <= j <= m, and 0 <= j <= n. The leading
indices of V index the points (x, y, z) and the last index encodes
the degrees of the HermiteE polynomials.
If V = hermevander3d(x, y, z, [xdeg, ydeg, zdeg]), then the columns
of V correspond to the elements of a 3-D coefficient array c of
shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order
System Message: WARNING/2 (c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},...
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This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/TeX Live for SUSE Linux)
restricted \write18 enabled.
entering extended mode
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and np.dot(V, c.flat) and hermeval3d(x, y, z, 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 3-D HermiteE
series of the same degrees and sample points.
Parameters : | x, y, z : 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, z_deg].
|
Returns : | vander3d : ndarray
The shape of the returned matrix is x.shape + (order,), where
System Message: WARNING/2 (order = (deg[0]+1)*(deg([1]+1)*(deg[2]+1))
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This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/TeX Live for SUSE Linux)
restricted \write18 enabled.
entering extended mode
(./math.tex
LaTeX2e <2011/06/27>
Babel <3.9f> and hyphenation patterns for 78 languages loaded.
(/usr/share/texmf/tex/latex/base/article.cls
Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
(/usr/share/texmf/tex/latex/base/size12.clo))
(/usr/share/texmf/tex/latex/base/inputenc.sty
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l.131 \endinput
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Transcript written on math.log.
. The dtype will
be the same as the converted x, y, and z.
|
Notes