numpy.polynomial.legendre.leggrid3d¶

polynomial.legendre.leggrid3d(x, y, z, c)[source]¶

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

This function returns the values:

\[p(a,b,c) = \sum_{i,j,k} c_{i,j,k} * L_i(a) * L_j(b) * L_k(c)\]

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, zarray_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.
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.