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. |