Hermite Module, “Physicists’” (numpy.polynomial.hermite)

New in version 1.6.0.

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

Hermite Class

Hermite(coef[, domain, window])

An Hermite series class.

Basics

hermval(x, c[, tensor])	Evaluate an Hermite series at points x.
hermval2d(x, y, c)	Evaluate a 2-D Hermite series at points (x, y).
hermval3d(x, y, z, c)	Evaluate a 3-D Hermite series at points (x, y, z).
hermgrid2d(x, y, c)	Evaluate a 2-D Hermite series on the Cartesian product of x and y.
hermgrid3d(x, y, z, c)	Evaluate a 3-D Hermite series on the Cartesian product of x, y, and z.
hermroots(c)	Compute the roots of a Hermite series.
hermfromroots(roots)	Generate a Hermite series with given roots.

Fitting

hermfit(x, y, deg[, rcond, full, w])	Least squares fit of Hermite series to data.
hermvander(x, deg)	Pseudo-Vandermonde matrix of given degree.
hermvander2d(x, y, deg)	Pseudo-Vandermonde matrix of given degrees.
hermvander3d(x, y, z, deg)	Pseudo-Vandermonde matrix of given degrees.

Calculus

hermder(c[, m, scl, axis])	Differentiate a Hermite series.
hermint(c[, m, k, lbnd, scl, axis])	Integrate a Hermite series.

Algebra

hermadd(c1, c2)	Add one Hermite series to another.
hermsub(c1, c2)	Subtract one Hermite series from another.
hermmul(c1, c2)	Multiply one Hermite series by another.
hermmulx(c)	Multiply a Hermite series by x.
hermdiv(c1, c2)	Divide one Hermite series by another.
hermpow(c, pow[, maxpower])	Raise a Hermite series to a power.

Quadrature

hermgauss(deg)	Gauss-Hermite quadrature.
hermweight(x)	Weight function of the Hermite polynomials.

Miscellaneous

hermcompanion(c)	Return the scaled companion matrix of c.
hermdomain
hermzero
hermone
hermx
hermtrim(c[, tol])	Remove “small” “trailing” coefficients from a polynomial.
hermline(off, scl)	Hermite series whose graph is a straight line.
herm2poly(c)	Convert a Hermite series to a polynomial.
poly2herm(pol)	Convert a polynomial to a Hermite series.