Chebyshev Module (numpy.polynomial.chebyshev)

New in version 1.4.0.

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

Chebyshev Class

Chebyshev(coef[, domain, window])

A Chebyshev series class.

Basics

chebval(x, c[, tensor])	Evaluate a Chebyshev series at points x.
chebval2d(x, y, c)	Evaluate a 2-D Chebyshev series at points (x, y).
chebval3d(x, y, z, c)	Evaluate a 3-D Chebyshev series at points (x, y, z).
chebgrid2d(x, y, c)	Evaluate a 2-D Chebyshev series on the Cartesian product of x and y.
chebgrid3d(x, y, z, c)	Evaluate a 3-D Chebyshev series on the Cartesian product of x, y, and z.
chebroots(c)	Compute the roots of a Chebyshev series.
chebfromroots(roots)	Generate a Chebyshev series with given roots.

Fitting

chebfit(x, y, deg[, rcond, full, w])	Least squares fit of Chebyshev series to data.
chebvander(x, deg)	Pseudo-Vandermonde matrix of given degree.
chebvander2d(x, y, deg)	Pseudo-Vandermonde matrix of given degrees.
chebvander3d(x, y, z, deg)	Pseudo-Vandermonde matrix of given degrees.

Calculus

chebder(c[, m, scl, axis])	Differentiate a Chebyshev series.
chebint(c[, m, k, lbnd, scl, axis])	Integrate a Chebyshev series.

Algebra

chebadd(c1, c2)	Add one Chebyshev series to another.
chebsub(c1, c2)	Subtract one Chebyshev series from another.
chebmul(c1, c2)	Multiply one Chebyshev series by another.
chebmulx(c)	Multiply a Chebyshev series by x.
chebdiv(c1, c2)	Divide one Chebyshev series by another.
chebpow(c, pow[, maxpower])	Raise a Chebyshev series to a power.

Quadrature

chebgauss(deg)	Gauss-Chebyshev quadrature.
chebweight(x)	The weight function of the Chebyshev polynomials.

Miscellaneous

chebcompanion(c)	Return the scaled companion matrix of c.
chebdomain
chebzero
chebone
chebx
chebtrim(c[, tol])	Remove “small” “trailing” coefficients from a polynomial.
chebline(off, scl)	Chebyshev series whose graph is a straight line.
cheb2poly(c)	Convert a Chebyshev series to a polynomial.
poly2cheb(pol)	Convert a polynomial to a Chebyshev series.