Document

legval2d(x, y, c)

This function returns the values:

$$p(x,y) = \sum_{i,j} c_{i,j} * L_i(x) * L_j(y)$$

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 is a 1-D array a one is implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape.

Notes

versionadded

Parameters

x, y : array_like, compatible objects: The two dimensional series is evaluated at the points :None:None:`(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.
c : array_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

values : ndarray, compatible object: The values of the two dimensional Legendre series at points formed from pairs of corresponding values from x and y.

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

Examples

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

numpy.polynomial.legendre.legvander3d numpy.polynomial.legendre.leggrid2d numpy.polynomial.legendre.legvander2d numpy.polynomial.legendre.legval numpy.polynomial.legendre.leggrid3d numpy.polynomial.legendre.legval3d

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them