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Diffstat (limited to 'numpy/polynomial/chebyshev.py')
| -rw-r--r-- | numpy/polynomial/chebyshev.py | 108 |
1 files changed, 62 insertions, 46 deletions
diff --git a/numpy/polynomial/chebyshev.py b/numpy/polynomial/chebyshev.py index 093eb0048..1329ba07d 100644 --- a/numpy/polynomial/chebyshev.py +++ b/numpy/polynomial/chebyshev.py @@ -1,5 +1,7 @@ """ -Objects for dealing with Chebyshev series. +==================================================== +Chebyshev Series (:mod:`numpy.polynomial.chebyshev`) +==================================================== This module provides a number of objects (mostly functions) useful for dealing with Chebyshev series, including a `Chebyshev` class that @@ -7,57 +9,75 @@ 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 +------- + +.. autosummary:: + :toctree: generated/ + + Chebyshev + + Constants --------- -- `chebdomain` -- Chebyshev series default domain, [-1,1]. -- `chebzero` -- (Coefficients of the) Chebyshev series that evaluates - identically to 0. -- `chebone` -- (Coefficients of the) Chebyshev series that evaluates - identically to 1. -- `chebx` -- (Coefficients of the) Chebyshev series for the identity map, - ``f(x) = x``. + +.. autosummary:: + :toctree: generated/ + + chebdomain + chebzero + chebone + chebx Arithmetic ---------- -- `chebadd` -- add two Chebyshev series. -- `chebsub` -- subtract one Chebyshev series from another. -- `chebmulx` -- multiply a Chebyshev series in ``P_i(x)`` by ``x``. -- `chebmul` -- multiply two Chebyshev series. -- `chebdiv` -- divide one Chebyshev series by another. -- `chebpow` -- raise a Chebyshev series to a positive integer power. -- `chebval` -- evaluate a Chebyshev series at given points. -- `chebval2d` -- evaluate a 2D Chebyshev series at given points. -- `chebval3d` -- evaluate a 3D Chebyshev series at given points. -- `chebgrid2d` -- evaluate a 2D Chebyshev series on a Cartesian product. -- `chebgrid3d` -- evaluate a 3D Chebyshev series on a Cartesian product. + +.. autosummary:: + :toctree: generated/ + + chebadd + chebsub + chebmulx + chebmul + chebdiv + chebpow + chebval + chebval2d + chebval3d + chebgrid2d + chebgrid3d Calculus -------- -- `chebder` -- differentiate a Chebyshev series. -- `chebint` -- integrate a Chebyshev series. + +.. autosummary:: + :toctree: generated/ + + chebder + chebint Misc Functions -------------- -- `chebfromroots` -- create a Chebyshev series with specified roots. -- `chebroots` -- find the roots of a Chebyshev series. -- `chebvander` -- Vandermonde-like matrix for Chebyshev polynomials. -- `chebvander2d` -- Vandermonde-like matrix for 2D power series. -- `chebvander3d` -- Vandermonde-like matrix for 3D power series. -- `chebgauss` -- Gauss-Chebyshev quadrature, points and weights. -- `chebweight` -- Chebyshev weight function. -- `chebcompanion` -- symmetrized companion matrix in Chebyshev form. -- `chebfit` -- least-squares fit returning a Chebyshev series. -- `chebpts1` -- Chebyshev points of the first kind. -- `chebpts2` -- Chebyshev points of the second kind. -- `chebtrim` -- trim leading coefficients from a Chebyshev series. -- `chebline` -- Chebyshev series representing given straight line. -- `cheb2poly` -- convert a Chebyshev series to a polynomial. -- `poly2cheb` -- convert a polynomial to a Chebyshev series. -- `chebinterpolate` -- interpolate a function at the Chebyshev points. -Classes -------- -- `Chebyshev` -- A Chebyshev series class. +.. autosummary:: + :toctree: generated/ + + chebfromroots + chebroots + chebvander + chebvander2d + chebvander3d + chebgauss + chebweight + chebcompanion + chebfit + chebpts1 + chebpts2 + chebtrim + chebline + cheb2poly + poly2cheb + chebinterpolate See also -------- @@ -87,9 +107,6 @@ References (preprint: https://www.math.hmc.edu/~benjamin/papers/CombTrig.pdf, pg. 4) """ -from __future__ import division, absolute_import, print_function - -import warnings import numpy as np import numpy.linalg as la from numpy.core.multiarray import normalize_axis_index @@ -1060,7 +1077,6 @@ def chebint(c, m=1, k=[], lbnd=0, scl=1, axis=0): if n > 1: tmp[2] = c[1]/4 for j in range(2, n): - t = c[j]/(2*j + 1) # FIXME: t never used tmp[j + 1] = c[j]/(2*(j + 1)) tmp[j - 1] -= c[j]/(2*(j - 1)) tmp[0] += k[i] - chebval(lbnd, tmp) @@ -1468,7 +1484,7 @@ def chebvander2d(x, y, deg): .. versionadded:: 1.7.0 """ - return pu._vander2d(chebvander, x, y, deg) + return pu._vander_nd_flat((chebvander, chebvander), (x, y), deg) def chebvander3d(x, y, z, deg): @@ -1522,7 +1538,7 @@ def chebvander3d(x, y, z, deg): .. versionadded:: 1.7.0 """ - return pu._vander3d(chebvander, x, y, z, deg) + return pu._vander_nd_flat((chebvander, chebvander, chebvander), (x, y, z), deg) def chebfit(x, y, deg, rcond=None, full=False, w=None): |