numpy.polynomial.chebyshev.chebvander2d
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numpy.polynomial.chebyshev.chebvander2d(x, y, deg)
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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 bywhere
0 <= i <= deg[0]
and0 <= j <= deg[1]
. The leading indices ofV
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 ofV
correspond to the elements of a 2-D coefficient arrayc
of shape (xdeg + 1, ydeg + 1) in the orderand
np.dot(V, c.flat)
andchebval2d(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, y : array_like
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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.
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deg : list of ints
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List of maximum degrees of the form [x_deg, y_deg].
Returns: -
vander2d : ndarray
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The shape of the returned matrix is
x.shape + (order,)
, where. The dtype will be the same as the converted
x
andy
.
See also
chebvander
,chebvander3d.
,chebval3d
Notes
New in version 1.7.0.
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© 2005–2019 NumPy Developers
Licensed under the 3-clause BSD License.
https://docs.scipy.org/doc/numpy-1.16.1/reference/generated/numpy.polynomial.chebyshev.chebvander2d.html