Legendre Module (numpy.polynomial.legendre)
This module provides a number of objects (mostly functions) useful for
dealing with Legendre series, including a Legendre class that
encapsulates the usual arithmetic operations. (General information
on how this module represents and works with such polynomials is in the
docstring for its “parent” sub-package, numpy.polynomial).
Legendre Class
| Legendre(coef[, domain, window]) |
A Legendre series class. |
Basics
| legval(x, c[, tensor]) |
Evaluate a Legendre series at points x. |
| legval2d(x, y, c) |
Evaluate a 2-D Legendre series at points (x, y). |
| legval3d(x, y, z, c) |
Evaluate a 3-D Legendre series at points (x, y, z). |
| leggrid2d(x, y, c) |
Evaluate a 2-D Legendre series on the Cartesian product of x and y. |
| leggrid3d(x, y, z, c) |
Evaluate a 3-D Legendre series on the Cartesian product of x, y, and z. |
| legroots(c) |
Compute the roots of a Legendre series. |
| legfromroots(roots) |
Generate a Legendre series with given roots. |
Fitting
| legfit(x, y, deg[, rcond, full, w]) |
Least squares fit of Legendre series to data. |
| legvander(x, deg) |
Pseudo-Vandermonde matrix of given degree. |
| legvander2d(x, y, deg) |
Pseudo-Vandermonde matrix of given degrees. |
| legvander3d(x, y, z, deg) |
Pseudo-Vandermonde matrix of given degrees. |
Calculus
| legder(c[, m, scl, axis]) |
Differentiate a Legendre series. |
| legint(c[, m, k, lbnd, scl, axis]) |
Integrate a Legendre series. |
Algebra
| legadd(c1, c2) |
Add one Legendre series to another. |
| legsub(c1, c2) |
Subtract one Legendre series from another. |
| legmul(c1, c2) |
Multiply one Legendre series by another. |
| legmulx(c) |
Multiply a Legendre series by x. |
| legdiv(c1, c2) |
Divide one Legendre series by another. |
| legpow(c, pow[, maxpower]) |
Raise a Legendre series to a power. |
Quadrature
| leggauss(deg) |
Gauss-Legendre quadrature. |
| legweight(x) |
Weight function of the Legendre polynomials. |
Miscellaneous
| legcompanion(c) |
Return the scaled companion matrix of c. |
| legdomain |
|
| legzero |
|
| legone |
|
| legx |
|
| legtrim(c[, tol]) |
Remove “small” “trailing” coefficients from a polynomial. |
| legline(off, scl) |
Legendre series whose graph is a straight line. |
| leg2poly(c) |
Convert a Legendre series to a polynomial. |
| poly2leg(pol) |
Convert a polynomial to a Legendre series. |