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# numpy.polynomial.hermite_e.hermegrid3d

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Evaluate a 3-D HermiteE series on the Cartesian product of x, y, and z.

This function returns the values:

.. math:: p(a,b,c) = \sum_{i,j,k} c_{i,j,k} * He_i(a) * He_j(b) * He_k(c)

where the points (a, b, c) consist of all triples formed by taking
a from x, b from y, and c from z. The resulting points form
a grid with x in the first dimension, y in the second, and z in
the third.(more...)


        def hermegrid3d(x, y, z, c):
"""
Evaluate a 3-D HermiteE series on the Cartesian product of x, y, and z.

This function returns the values:

.. math:: p(a,b,c) = \\sum_{i,j,k} c_{i,j,k} * He_i(a) * He_j(b) * He_k(c)

where the points (a, b, c) consist of all triples formed by taking
a from x, b from y, and c from z. The resulting points form
a grid with x in the first dimension, y in the second, and z in
the third.

The parameters x, y, and z are converted to arrays only if they
are tuples or a lists, otherwise they are treated as a scalars. In
either case, either x, y, and z or their elements must support
multiplication and addition both with themselves and with the elements
of c.

If c has fewer than three dimensions, ones are implicitly appended to
its shape to make it 3-D. The shape of the result will be c.shape[3:] +
x.shape + y.shape + z.shape.

Parameters
----------
x, y, z : array_like, compatible objects
The three dimensional series is evaluated at the points in the
Cartesian product of x, y, and z.  If x,y, or z is a
list or tuple, it is first converted to an ndarray, otherwise it is
left unchanged and, if it isn't an ndarray, it is treated as a
scalar.
c : array_like
Array of coefficients ordered so that the coefficients for terms of
degree i,j are contained in c[i,j]. If c has dimension
greater than two the remaining indices enumerate multiple sets of
coefficients.

Returns
-------
values : ndarray, compatible object
The values of the two dimensional polynomial at points in the Cartesian
product of x and y.

--------
hermeval, hermeval2d, hermegrid2d, hermeval3d

Notes
-----

"""
c = hermeval(x, c)
c = hermeval(y, c)
c = hermeval(z, c)
return c


        #test values
tgt = np.einsum('i,j,k->ijk', y1, y2, y3)
res = herme.hermegrid3d(x1, x2, x3, self.c3d)
assert_almost_equal(res, tgt)

#test shape
z = np.ones((2,3))
res = herme.hermegrid3d(z, z, z, self.c3d)


        #test values