Legendre Module (numpy.polynomial.legendre)

New in version 1.6.0.

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.