numpy.polynomial.polynomial.polyval3d

polynomial.polynomial.polyval3d(x, y, z, c)

Evaluate a 3-D polynomial at points (x, y, z).

This function returns the values:

\[p(x,y,z) = \sum_{i,j,k} c_{i,j,k} * x^i * y^j * z^k\]

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 and they must have the same shape after conversion. 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 3 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.

Parameters:

x, y, zarray_like, compatible object

The three dimensional series is evaluated at the points (x, y, z), where x, y, and z must have the same shape. If any of 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 coefficient of the term of multi-degree i,j,k is contained in c[i,j,k]. If c has dimension greater than 3 the remaining indices enumerate multiple sets of coefficients.

Returns:

valuesndarray, compatible object

The values of the multidimensional polynomial on points formed with triples of corresponding values from x, y, and z.

See also

polyval, polyval2d, polygrid2d, polygrid3d

Notes

New in version 1.7.0.

Examples

>>> from numpy.polynomial import polynomial as P
>>> c = ((1, 2, 3), (4, 5, 6), (7, 8, 9))
>>> P.polyval3d(1, 1, 1, c)
45.0