diff options
Diffstat (limited to 'numpy/polynomial')
| -rw-r--r-- | numpy/polynomial/legendre.py | 89 |
1 files changed, 56 insertions, 33 deletions
diff --git a/numpy/polynomial/legendre.py b/numpy/polynomial/legendre.py index 93ba1d348..f084617b6 100644 --- a/numpy/polynomial/legendre.py +++ b/numpy/polynomial/legendre.py @@ -1,5 +1,8 @@ """ -Objects for dealing with Legendre series. +Legendre Series (:mod: `numpy.polynomial.legendre`) +=================================================== + +.. currentmodule:: numpy.polynomial.polynomial This module provides a number of objects (mostly functions) useful for dealing with Legendre series, including a `Legendre` class that @@ -9,53 +12,73 @@ docstring for its "parent" sub-package, `numpy.polynomial`). Constants --------- -- `legdomain` -- Legendre series default domain, [-1,1]. -- `legzero` -- Legendre series that evaluates identically to 0. -- `legone` -- Legendre series that evaluates identically to 1. -- `legx` -- Legendre series for the identity map, ``f(x) = x``. + +.. autosummary:: + :toctree: generated/ + + legdomain Legendre series default domain, [-1,1]. + legzero Legendre series that evaluates identically to 0. + legone Legendre series that evaluates identically to 1. + legx Legendre series for the identity map, ``f(x) = x``. Arithmetic ---------- -- `legmulx` -- multiply a Legendre series in ``P_i(x)`` by ``x``. -- `legadd` -- add two Legendre series. -- `legsub` -- subtract one Legendre series from another. -- `legmul` -- multiply two Legendre series. -- `legdiv` -- divide one Legendre series by another. -- `legpow` -- raise a Legendre series to an positive integer power -- `legval` -- evaluate a Legendre series at given points. -- `legval2d` -- evaluate a 2D Legendre series at given points. -- `legval3d` -- evaluate a 3D Legendre series at given points. -- `leggrid2d` -- evaluate a 2D Legendre series on a Cartesian product. -- `leggrid3d` -- evaluate a 3D Legendre series on a Cartesian product. + +.. autosummary:: + :toctree: generated/ + + legmulx multiply a Legendre series in P_i(x) by x. + legadd add two Legendre series. + legsub subtract one Legendre series from another. + legmul multiply two Legendre series. + legdiv divide one Legendre series by another. + legpow raise a Legendre series to an positive integer power + legval evaluate a Legendre series at given points. + legval2d evaluate a 2D Legendre series at given points. + legval3d evaluate a 3D Legendre series at given points. + leggrid2d evaluate a 2D Legendre series on a Cartesian product. + leggrid3d evaluate a 3D Legendre series on a Cartesian product. Calculus -------- -- `legder` -- differentiate a Legendre series. -- `legint` -- integrate a Legendre series. + +.. autosummary:: + :toctree: generated/ + + legder differentiate a Legendre series. + legint integrate a Legendre series. Misc Functions -------------- -- `legfromroots` -- create a Legendre series with specified roots. -- `legroots` -- find the roots of a Legendre series. -- `legvander` -- Vandermonde-like matrix for Legendre polynomials. -- `legvander2d` -- Vandermonde-like matrix for 2D power series. -- `legvander3d` -- Vandermonde-like matrix for 3D power series. -- `leggauss` -- Gauss-Legendre quadrature, points and weights. -- `legweight` -- Legendre weight function. -- `legcompanion` -- symmetrized companion matrix in Legendre form. -- `legfit` -- least-squares fit returning a Legendre series. -- `legtrim` -- trim leading coefficients from a Legendre series. -- `legline` -- Legendre series representing given straight line. -- `leg2poly` -- convert a Legendre series to a polynomial. -- `poly2leg` -- convert a polynomial to a Legendre series. + +.. autosummary:: + :toctree: generated/ + + legfromroots create a Legendre series with specified roots. + legroots find the roots of a Legendre series. + legvander Vandermonde-like matrix for Legendre polynomials. + legvander2d Vandermonde-like matrix for 2D power series. + legvander3d Vandermonde-like matrix for 3D power series. + leggauss Gauss-Legendre quadrature, points and weights. + legweight Legendre weight function. + legcompanion symmetrized companion matrix in Legendre form. + legfit least-squares fit returning a Legendre series. + legtrim trim leading coefficients from a Legendre series. + legline Legendre series representing given straight line. + leg2poly convert a Legendre series to a polynomial. + poly2leg convert a polynomial to a Legendre series. Classes ------- -- `Legendre` -- A Legendre series class. + Legendre A Legendre series class. See also -------- -`numpy.polynomial` +numpy.polynomial.polynomial +numpy.polynomial.chebyshev +numpy.polynomial.laguerre +numpy.polynomial.hermite +numpy.polynomial.hermite_e """ from __future__ import division |