numpy.polynomial.polynomial.polyval2d

polynomial.polynomial.polyval2d(x, y, c)

Evaluate a 2-D polynomial at points (x, y).

This function returns the value

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

The parameters x and y 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 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 (x, y), where x and y must have the same shape. 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 coefficient of the term of multi-degree i,j is 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 formed with pairs of corresponding values from x and y.

See also

polyval, polygrid2d, polyval3d, polygrid3d

Notes

New in version 1.7.0.

Examples

>>> from numpy.polynomial import polynomial as P
>>> c = ((1, 2, 3), (4, 5, 6))
>>> P.polyval2d(1, 1, c) 
21.0