numpy.polynomial.hermite.hermgrid2d

polynomial.hermite.hermgrid2d(x, y, c)

Evaluate a 2-D Hermite series on the Cartesian product of x and y.

This function returns the values:

\[p(a,b) = \sum_{i,j} c_{i,j} * H_i(a) * H_j(b)\]

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

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

If c has fewer than two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape.

Parameters:

x, yarray_like, compatible objects

The two dimensional series is evaluated at the points in the Cartesian product of x and y. If x or y 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.

carray_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:

valuesndarray, compatible object

The values of the two dimensional polynomial at points in the Cartesian product of x and y.

See also

hermval, hermval2d, hermval3d, hermgrid3d

Notes

New in version 1.7.0.

Examples

>>> from numpy.polynomial.hermite import hermgrid2d
>>> x = [1, 2, 3]
>>> y = [4, 5]
>>> c = [[1, 2, 3], [4, 5, 6]]
>>> hermgrid2d(x, y, c)
array([[1035., 1599.],
       [1867., 2883.],
       [2699., 4167.]])