numpy.polynomial.polynomial.polyvander3d()
numpy.polynomial.polynomial.polyvander3d
-
numpy.polynomial.polynomial.polyvander3d(x, y, z, deg)
[source] -
Pseudo-Vandermonde matrix of given degrees.
Returns the pseudo-Vandermonde matrix of degrees
deg
and sample points(x, y, z)
. Ifl, m, n
are the given degrees inx, y, z
, then The pseudo-Vandermonde matrix is defined bywhere
0 <= i <= l
,0 <= j <= m
, and0 <= j <= n
. The leading indices ofV
index the points(x, y, z)
and the last index encodes the powers ofx
,y
, andz
.If
V = polyvander3d(x, y, z, [xdeg, ydeg, zdeg])
, then the columns ofV
correspond to the elements of a 3-D coefficient arrayc
of shape (xdeg + 1, ydeg + 1, zdeg + 1) in the orderand
np.dot(V, c.flat)
andpolyval3d(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 polynomials 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. The dtype will be the same as the converted
x
,y
, andz
.See also
polyvander
,polyvander3d.
,polyval3d
Notes
New in version 1.7.0.
© 2008–2017 NumPy Developers
Licensed under the NumPy License.
https://docs.scipy.org/doc/numpy-1.12.0/reference/generated/numpy.polynomial.polynomial.polyvander3d.html