New in version 1.6.0.

Laguerre Series (numpy.polynomial.laguerre)¶

This module provides a number of objects (mostly functions) useful for dealing with Laguerre series, including a Laguerre 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).

Classes¶

 Laguerre(coef[, domain, window]) A Laguerre series class.

Constants¶

 lagdomain An array object represents a multidimensional, homogeneous array of fixed-size items. lagzero An array object represents a multidimensional, homogeneous array of fixed-size items. lagone An array object represents a multidimensional, homogeneous array of fixed-size items. lagx An array object represents a multidimensional, homogeneous array of fixed-size items.

Arithmetic¶

 lagadd(c1, c2) Add one Laguerre series to another. lagsub(c1, c2) Subtract one Laguerre series from another. lagmulx(c) Multiply a Laguerre series by x. lagmul(c1, c2) Multiply one Laguerre series by another. lagdiv(c1, c2) Divide one Laguerre series by another. lagpow(c, pow[, maxpower]) Raise a Laguerre series to a power. lagval(x, c[, tensor]) Evaluate a Laguerre series at points x. lagval2d(x, y, c) Evaluate a 2-D Laguerre series at points (x, y). lagval3d(x, y, z, c) Evaluate a 3-D Laguerre series at points (x, y, z). laggrid2d(x, y, c) Evaluate a 2-D Laguerre series on the Cartesian product of x and y. laggrid3d(x, y, z, c) Evaluate a 3-D Laguerre series on the Cartesian product of x, y, and z.

Calculus¶

 lagder(c[, m, scl, axis]) Differentiate a Laguerre series. lagint(c[, m, k, lbnd, scl, axis]) Integrate a Laguerre series.

Misc Functions¶

 lagfromroots(roots) Generate a Laguerre series with given roots. lagroots(c) Compute the roots of a Laguerre series. lagvander(x, deg) Pseudo-Vandermonde matrix of given degree. lagvander2d(x, y, deg) Pseudo-Vandermonde matrix of given degrees. lagvander3d(x, y, z, deg) Pseudo-Vandermonde matrix of given degrees. laggauss(deg) Gauss-Laguerre quadrature. lagweight(x) Weight function of the Laguerre polynomials. lagcompanion(c) Return the companion matrix of c. lagfit(x, y, deg[, rcond, full, w]) Least squares fit of Laguerre series to data. lagtrim(c[, tol]) Remove "small" "trailing" coefficients from a polynomial. lagline(off, scl) Laguerre series whose graph is a straight line. lag2poly(c) Convert a Laguerre series to a polynomial. poly2lag(pol) Convert a polynomial to a Laguerre series.