numpy.polynomial.polynomial.polyvander3d(x, y, z, deg)
[source]
PseudoVandermonde matrix of given degrees.
Returns the pseudoVandermonde matrix of degrees deg
and sample points (x, y, z)
. If l, m, n
are the given degrees in x, y, z
, then The pseudoVandermonde matrix is defined by
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 powers of x
, y
, and z
.
If V = polyvander3d(x, y, z, [xdeg, ydeg, zdeg])
, then the columns of V
correspond to the elements of a 3D coefficient array c
of shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order
and np.dot(V, c.flat)
and polyval3d(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 3D polynomials of the same degrees and sample points.
Parameters: 


Returns: 

See also
New in version 1.7.0.
© 2005–2019 NumPy Developers
Licensed under the 3clause BSD License.
https://docs.scipy.org/doc/numpy1.17.0/reference/generated/numpy.polynomial.polynomial.polyvander3d.html