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Evaluate a 3-D Hermite 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} * H_i(a) * H_j(b) * H_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 hermgrid3d(x, y, z, c): """ Evaluate a 3-D Hermite 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} * H_i(a) * H_j(b) * H_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 -------- hermval, hermval2d, hermgrid2d, hermval3d Notes ----- .. versionadded::1.7.0 """ c = hermval(x, c) c = hermval(y, c) c = hermval(z, c) return c

**nupic-linux64**(Download)

#test values tgt = np.einsum('i,j,k->ijk', y1, y2, y3) res = herm.hermgrid3d(x1, x2, x3, self.c3d) assert_almost_equal(res, tgt) #test shape z = np.ones((2,3)) res = herm.hermgrid3d(z, z, z, self.c3d)

src/n/u/numpy-1.8.1/numpy/polynomial/tests/test_hermite.py

**numpy**(Download)

#test values tgt = np.einsum('i,j,k->ijk', y1, y2, y3) res = herm.hermgrid3d(x1, x2, x3, self.c3d) assert_almost_equal(res, tgt) #test shape z = np.ones((2, 3)) res = herm.hermgrid3d(z, z, z, self.c3d)