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.
numpy.polynomial.chebyshev.poly2cheb numpy.polynomial.legendre.Legendre