octave-antonio: scripts/specfun/legendre.m annotate

annotate scripts/specfun/legendre.m @ 14327:4d917a6a858b stable

doc: Use Octave coding conventions in @example blocks of docstrings. * accumarray.m, accumdim.m, bar.m, base2dec.m, bincoeff.m, bitcmp.m, bitset.m, celldisp.m, chop.m, clabel.m, cloglog.m, colon.m, compass.m, computer.m, contour3.m, contourc.m, corr.m, cstrcat.m, ctime.m, cylinder.m, date.m, dec2base.m, demo.m, dir.m, dlmwrite.m, expm.m, ezcontourf.m, ezcontour.m, ezmeshc.m, ezmesh.m, ezplot.m, ezsurfc.m, ezsurf.m, feather.m, findobj.m, flipdim.m, fplot.m, genvarname.m, getfield.m, hankel.m, hilb.m, hist.m, idivide.m, index.m, int2str.m, interp1.m, is_leap_year.m, ismember.m, isocolors.m, isonormals.m, isosurface.m, kurtosis.m, legendre.m, linkprop.m, logit.m, logm.m, __makeinfo__.m, __marching_cube__.m, median.m, mkoctfile.m, moment.m, mpoles.m, orderfields.m, pcg.m, pcr.m, plot3.m, plotmatrix.m, polyaffine.m, polygcd.m, poly.m, polyout.m, print.m, qp.m, quadgk.m, qzhess.m, randi.m, rat.m, refreshdata.m, residue.m, rose.m, rot90.m, saveas.m, saveobj.m, shiftdim.m, skewness.m, spaugment.m, spdiags.m, sqp.m, stem.m, str2num.m, strcat.m, strjust.m, strread.m, strsplit.m, structfun.m, subplot.m, subsindex.m, substruct.m, surfl.m, surfnorm.m, svds.m, uimenu.m, union.m, voronoi.m, warning_ids.m, wblpdf.m: Use Octave coding conventions in @example blocks of docstrings.

author	Rik <octave@nomad.inbox5.com>
date	Sat, 04 Feb 2012 22:12:50 -0800
parents	72c96de7a403
children	f3d52523cde1

rev	line source
14138 72c96de7a403 maint: update copyright notices for 2012 John W. Eaton <jwe@octave.org> parents: 12893 diff changeset	1 ## Copyright (C) 2000-2012 Kai Habel
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	2 ## Copyright (C) 2008 Marco Caliari
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	3 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	4 ## This file is part of Octave.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	5 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	6 ## Octave is free software; you can redistribute it and/or modify it
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	7 ## under the terms of the GNU General Public License as published by
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7001 diff changeset	8 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7001 diff changeset	9 ## your option) any later version.
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	10 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	11 ## Octave is distributed in the hope that it will be useful, but
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	14 ## General Public License for more details.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	15 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	16 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7001 diff changeset	17 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7001 diff changeset	18 ## <http://www.gnu.org/licenses/>.
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	19
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	20 ## -- texinfo --
10793 be55736a0783 Grammarcheck the documentation from m-files. Rik <octave@nomad.inbox5.com> parents: 10672 diff changeset	21 ## @deftypefn {Function File} {@var{l} =} legendre (@var{n}, @var{x})
7508 f501b22c0394 doc fixes for legendre John W. Eaton <jwe@octave.org> parents: 7507 diff changeset	22 ## @deftypefnx {Function File} {@var{l} =} legendre (@var{n}, @var{x}, @var{normalization})
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	23 ## Compute the Legendre function of degree @var{n} and order
c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	24 ## @var{m} = 0 @dots{} N@. The optional argument, @var{normalization},
7517 f88b720bf254 legendre.m: modified help text. Ben Abbott <bpabbott@mac.com> parents: 7508 diff changeset	25 ## may be one of @code{"unnorm"}, @code{"sch"}, or @code{"norm"}.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	26 ## The default is @code{"unnorm"}. The value of @var{n} must be a
c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	27 ## non-negative scalar integer.
7508 f501b22c0394 doc fixes for legendre John W. Eaton <jwe@octave.org> parents: 7507 diff changeset	28 ##
f501b22c0394 doc fixes for legendre John W. Eaton <jwe@octave.org> parents: 7507 diff changeset	29 ## If the optional argument @var{normalization} is missing or is
f501b22c0394 doc fixes for legendre John W. Eaton <jwe@octave.org> parents: 7507 diff changeset	30 ## @code{"unnorm"}, compute the Legendre function of degree @var{n} and
f501b22c0394 doc fixes for legendre John W. Eaton <jwe@octave.org> parents: 7507 diff changeset	31 ## order @var{m} and return all values for @var{m} = 0 @dots{} @var{n}.
f501b22c0394 doc fixes for legendre John W. Eaton <jwe@octave.org> parents: 7507 diff changeset	32 ## The return value has one dimension more than @var{x}.
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	33 ##
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	34 ## The Legendre Function of degree @var{n} and order @var{m}:
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	35 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	36 ## @tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	37 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	38 ## P^m_n(x) = (-1)^m (1-x^2)^{m/2}{d^m\over {dx^m}}P_n (x)
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	39 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	40 ## @end tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	41 ## @ifnottex
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	42 ##
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	43 ## @example
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	44 ## @group
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	45 ## m m 2 m/2 d^m
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	46 ## P(x) = (-1) * (1-x ) * ---- P(x)
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	47 ## n dx^m n
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	48 ## @end group
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	49 ## @end example
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	50 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	51 ## @end ifnottex
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	52 ##
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	53 ## @noindent
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	54 ## with Legendre polynomial of degree @var{n}:
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	55 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	56 ## @tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	57 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	58 ## P(x) = {1\over{2^n n!}}\biggl({d^n\over{dx^n}}(x^2 - 1)^n\biggr)
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	59 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	60 ## @end tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	61 ## @ifnottex
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	62 ##
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	63 ## @example
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	64 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	65 ## 1 d^n 2 n
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	66 ## P(x) = ------ [----(x - 1) ]
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	67 ## n 2^n n! dx^n
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	68 ## @end group
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	69 ## @end example
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	70 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	71 ## @end ifnottex
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	72 ##
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	73 ## @noindent
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	74 ## @code{legendre (3, [-1.0, -0.9, -0.8])} returns the matrix:
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	75 ##
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	76 ## @example
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	77 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	78 ## x \| -1.0 \| -0.9 \| -0.8
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	79 ## ------------------------------------
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	80 ## m=0 \| -1.00000 \| -0.47250 \| -0.08000
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	81 ## m=1 \| 0.00000 \| -1.99420 \| -1.98000
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	82 ## m=2 \| 0.00000 \| -2.56500 \| -4.32000
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	83 ## m=3 \| 0.00000 \| -1.24229 \| -3.24000
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	84 ## @end group
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	85 ## @end example
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	86 ##
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	87 ## If the optional argument @code{normalization} is @code{"sch"},
7508 f501b22c0394 doc fixes for legendre John W. Eaton <jwe@octave.org> parents: 7507 diff changeset	88 ## compute the Schmidt semi-normalized associated Legendre function.
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	89 ## The Schmidt semi-normalized associated Legendre function is related
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	90 ## to the unnormalized Legendre functions by the following:
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	91 ##
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	92 ## For Legendre functions of degree n and order 0:
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	93 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	94 ## @tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	95 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	96 ## SP^0_n (x) = P^0_n (x)
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	97 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	98 ## @end tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	99 ## @ifnottex
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	100 ##
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	101 ## @example
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	102 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	103 ## 0 0
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	104 ## SP(x) = P(x)
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	105 ## n n
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	106 ## @end group
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	107 ## @end example
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	108 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	109 ## @end ifnottex
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	110 ##
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	111 ## For Legendre functions of degree n and order m:
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	112 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	113 ## @tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	114 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	115 ## SP^m_n (x) = P^m_n (x)(-1)^m\biggl({2(n-m)!\over{(n+m)!}}\biggl)^{0.5}
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	116 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	117 ## @end tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	118 ## @ifnottex
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	119 ##
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	120 ## @example
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	121 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	122 ## m m m 2(n-m)! 0.5
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	123 ## SP(x) = P(x) * (-1) * [-------]
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	124 ## n n (n+m)!
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	125 ## @end group
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	126 ## @end example
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	127 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	128 ## @end ifnottex
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	129 ##
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	130 ## If the optional argument @var{normalization} is @code{"norm"},
7508 f501b22c0394 doc fixes for legendre John W. Eaton <jwe@octave.org> parents: 7507 diff changeset	131 ## compute the fully normalized associated Legendre function.
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	132 ## The fully normalized associated Legendre function is related
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	133 ## to the unnormalized Legendre functions by the following:
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	134 ##
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	135 ## For Legendre functions of degree @var{n} and order @var{m}
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	136 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	137 ## @tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	138 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	139 ## NP^m_n (x) = P^m_n (x)(-1)^m\biggl({(n+0.5)(n-m)!\over{(n+m)!}}\biggl)^{0.5}
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	140 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	141 ## @end tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	142 ## @ifnottex
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	143 ##
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	144 ## @example
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	145 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	146 ## m m m (n+0.5)(n-m)! 0.5
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	147 ## NP(x) = P(x) * (-1) * [-------------]
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	148 ## n n (n+m)!
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	149 ## @end group
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	150 ## @end example
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	151 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	152 ## @end ifnottex
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	153 ## @end deftypefn
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	154
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	155 ## Author: Marco Caliari <marco.caliari@univr.it>
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	156
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	157 function retval = legendre (n, x, normalization)
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	158
8255 3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	159 persistent warned_overflow = false;
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	160
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	161 if (nargin < 2 \|\| nargin > 3)
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	162 print_usage ();
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	163 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	164
10672 1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	165 if (!isscalar (n) \|\| n < 0 \|\| n != fix (n))
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	166 error ("legendre: N must be a non-negative scalar integer");
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	167 endif
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	168
12893 72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	169 if (!isreal (x) \|\| any (x(:) < -1 \| x(:) > 1))
10672 1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	170 error ("legendre: X must be real-valued vector in the range -1 <= X <= 1");
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	171 endif
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	172
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	173 if (nargin == 3)
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	174 normalization = lower (normalization);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	175 else
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	176 normalization = "unnorm";
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	177 endif
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	178
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	179 switch (normalization)
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	180 case "norm"
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	181 scale = sqrt (n+0.5);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	182 case "sch"
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	183 scale = sqrt (2);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	184 case "unnorm"
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	185 scale = 1;
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	186 otherwise
11472 1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done. Rik <octave@nomad.inbox5.com> parents: 11415 diff changeset	187 error ('legendre: expecting NORMALIZATION option to be "norm", "sch", or "unnorm"');
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	188 endswitch
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	189
12893 72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	190 scale = scale * ones (size (x));
8255 3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	191
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	192 ## Based on the recurrence relation below
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	193 ## m m m
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	194 ## (n-m+1) * P (x) = (2n+1)xP (x) - (n+1)P (x)
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	195 ## n+1 n n-1
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	196 ## http://en.wikipedia.org/wiki/Associated_Legendre_function
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	197
8255 3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	198 overflow = false;
12893 72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	199 retval = zeros([n+1, size(x)]);
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	200 for m = 1:n
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	201 lpm1 = scale;
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	202 lpm2 = (2m-1) . x .* scale;
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	203 lpm3 = lpm2;
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	204 for k = m+1:n
8255 3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	205 lpm3a = (2k-1) . x .* lpm2;
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	206 lpm3b = (k+m-2) .* lpm1;
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	207 lpm3 = (lpm3a - lpm3b)/(k-m+1);
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	208 lpm1 = lpm2;
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	209 lpm2 = lpm3;
8255 3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	210 if (! warned_overflow)
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	211 if (any (abs (lpm3a) > realmax)
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	212 \|\| any (abs (lpm3b) > realmax)
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	213 \|\| any (abs (lpm3) > realmax))
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	214 overflow = true;
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	215 endif
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	216 endif
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	217 endfor
12893 72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	218 retval(m,:) = lpm3(:);
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	219 if (strcmp (normalization, "unnorm"))
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	220 scale = -scale * (2*m-1);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	221 else
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	222 ## normalization == "sch" or normalization == "norm"
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	223 scale = scale / sqrt ((n-m+1)(n+m))(2*m-1);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	224 endif
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	225 scale = scale .* sqrt(1-x.^2);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	226 endfor
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	227
12893 72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	228 retval(n+1,:) = scale(:);
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	229
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	230 if (isvector (x))
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	231 ## vector case is special
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	232 retval = reshape (retval, n + 1, length (x));
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	233 endif
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	234
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	235 if (strcmp (normalization, "sch"))
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	236 retval(1,:) = retval(1,:) / sqrt (2);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	237 endif
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	238
8255 3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	239 if (overflow && ! warned_overflow)
8664 e07e93c04080 style fixes John W. Eaton <jwe@octave.org> parents: 8255 diff changeset	240 warning ("legendre: overflow - results may be unstable for high orders");
8255 3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	241 warned_overflow = true;
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	242 endif
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	243
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	244 endfunction
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	245
12893 72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	246
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	247 %!test
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	248 %! result = legendre (3, [-1.0 -0.9 -0.8]);
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	249 %! expected = [
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	250 %! -1.00000 -0.47250 -0.08000
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	251 %! 0.00000 -1.99420 -1.98000
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	252 %! 0.00000 -2.56500 -4.32000
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	253 %! 0.00000 -1.24229 -3.24000
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	254 %! ];
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	255 %! assert (result, expected, 1e-5);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	256
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	257 %!test
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	258 %! result = legendre (3, [-1.0 -0.9 -0.8], "sch");
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	259 %! expected = [
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	260 %! -1.00000 -0.47250 -0.08000
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	261 %! 0.00000 0.81413 0.80833
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	262 %! -0.00000 -0.33114 -0.55771
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	263 %! 0.00000 0.06547 0.17076
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	264 %! ];
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	265 %! assert (result, expected, 1e-5);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	266
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	267 %!test
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	268 %! result = legendre (3, [-1.0 -0.9 -0.8], "norm");
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	269 %! expected = [
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	270 %! -1.87083 -0.88397 -0.14967
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	271 %! 0.00000 1.07699 1.06932
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	272 %! -0.00000 -0.43806 -0.73778
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	273 %! 0.00000 0.08661 0.22590
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	274 %! ];
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	275 %! assert (result, expected, 1e-5);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	276
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	277 %!test
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	278 %! result = legendre (151, 0);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	279 %! ## Don't compare to "-Inf" since it would fail on 64 bit systems.
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	280 %! assert (result(end) < -1.7976e308 && all (isfinite (result(1:end-1))));
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	281
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	282 %!test
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	283 %! result = legendre (150, 0);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	284 %! ## This agrees with Matlab's result.
12893 72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	285 %! assert (result(end), 3.7532741115719e+306, 0.0000000000001e+306);
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	286
8255 3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	287 %!test
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	288 %! result = legendre (0, 0:0.1:1);
12893 72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	289 %! assert (result, full(ones(1,11)));
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	290
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	291 %!test
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	292 %! result = legendre (3, [-1,0,1;1,0,-1]);
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	293 %! ## Test matrix input
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	294 %! expected(:,:,1) = [-1,1;0,0;0,0;0,0];
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	295 %! expected(:,:,2) = [0,0;1.5,1.5;0,0;-15,-15];
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	296 %! expected(:,:,3) = [1,-1;0,0;0,0;0,0];
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	297 %! assert (result, expected);
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	298
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	299 %!test
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	300 %! result = legendre (3, [-1,0,1;1,0,-1]');
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	301 %! expected(:,:,1) = [-1,0,1;0,1.5,0;0,0,0;0,-15,0];
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	302 %! expected(:,:,2) = [1,0,-1;0,1.5,0;0,0,0;0,-15,0];
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	303 %! assert (result, expected);
10672 1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	304
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	305 %% Check correct invocation
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	306 %!error legendre ();
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	307 %!error legendre (1);
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	308 %!error legendre (1,2,3,4);
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	309 %!error legendre ([1, 2], [-1, 0, 1]);
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	310 %!error legendre (-1, [-1, 0, 1]);
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	311 %!error legendre (1.1, [-1, 0, 1]);
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	312 %!error legendre (1, [-1+i, 0, 1]);
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	313 %!error legendre (1, [-2, 0, 1]);
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	314 %!error legendre (1, [-1, 0, 2]);
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	315 %!error legendre (1, [-1, 0, 1], "badnorm");

Mercurial > octave-antonio

annotate scripts/specfun/legendre.m @ 14327:4d917a6a858b stable