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# numpy.polynomial.polynomial.polygrid3d

polynomial.polynomial.polygrid3d(x, y, z, c)

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

  This function returns the values:

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

  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, z array_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.

    c array_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:
    values ndarray, compatible object

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

  See also

  `polyval`, `polyval2d`, `polygrid2d`, `polyval3d`

  Examples

      >>> from numpy.polynomial import polynomial as P
      >>> c = ((1, 2, 3), (4, 5, 6), (7, 8, 9))
      >>> P.polygrid3d([0, 1], [0, 1], [0, 1], c)
      array([[ 1., 13.],
             [ 6., 51.]])