polynomial.polynomial.polyval2d(x, y, c)[source]#

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.

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.


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.

valuesndarray, compatible object

The values of the two dimensional polynomial at points formed with pairs of corresponding values from x and y.


New in version 1.7.0.


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