numpy.polynomial.legendre.legval3d¶
- polynomial.legendre.legval3d(x, y, z, c)[source]¶
Evaluate a 3-D Legendre series at points (x, y, z).
This function returns the values:
\[p(x,y,z) = \sum_{i,j,k} c_{i,j,k} * L_i(x) * L_j(y) * L_k(z)\]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.
Notes
New in version 1.7.0.