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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`.

    See Also
    --------
    hermeval, hermeval2d, hermegrid2d, hermeval3d

    Notes
    -----

    .. versionadded::1.7.0

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


src/n/u/nupic-linux64-HEAD/lib64/python2.6/site-packages/numpy/polynomial/tests/test_hermite_e.py   nupic-linux64(Download)
        #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)

src/n/u/numpy-1.8.1/numpy/polynomial/tests/test_hermite_e.py   numpy(Download)
        #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)