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

annotate scripts/specfun/legendre.m @ 19697:4197fc428c7d

maint: Update copyright notices for 2015.

author	John W. Eaton <jwe@octave.org>
date	Wed, 11 Feb 2015 14:19:08 -0500
parents	55b613e5183d
children	9fc020886ae9

rev	line source
19697 4197fc428c7d maint: Update copyright notices for 2015. John W. Eaton <jwe@octave.org> parents: 19099 diff changeset	1 ## Copyright (C) 2000-2015 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
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	24 ## @var{m} = 0 @dots{} @var{n}.
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	25 ##
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	26 ## The value @var{n} must be a real non-negative integer. @var{x} is a
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	27 ## vector with real-valued elements in the range [-1, 1].
7508 f501b22c0394 doc fixes for legendre John W. Eaton <jwe@octave.org> parents: 7507 diff changeset	28 ##
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	29 ## The optional argument @var{normalization} may be one of @qcode{"unnorm"},
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	30 ## @qcode{"sch"}, or @qcode{"norm"}. The default if no normalization is given
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	31 ## is @qcode{"unnorm"}.
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	32 ##
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	33 ## When the optional argument @var{normalization} is @qcode{"unnorm"}, compute
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	34 ## the Legendre function of degree @var{n} and order @var{m} and return all
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	35 ## values for @var{m} = 0 @dots{} @var{n}. The return value has one dimension
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	36 ## more than @var{x}.
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	37 ##
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	38 ## 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	39 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	40 ## @tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	41 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	42 ## P^m_n(x) = (-1)^m (1-x^2)^{m/2}{d^m\over {dx^m}}P_n (x)
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	43 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	44 ## @end tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	45 ## @ifnottex
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	46 ##
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	47 ## @example
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	48 ## @group
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	49 ## 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	50 ## P(x) = (-1) * (1-x ) * ---- P(x)
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	51 ## n dx^m n
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	52 ## @end group
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	53 ## @end example
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	54 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	55 ## @end ifnottex
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	56 ##
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	57 ## @noindent
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	58 ## with Legendre polynomial of degree @var{n}:
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	59 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	60 ## @tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	61 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	62 ## P(x) = {1\over{2^n n!}}\biggl({d^n\over{dx^n}}(x^2 - 1)^n\biggr)
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	63 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	64 ## @end tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	65 ## @ifnottex
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	66 ##
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	67 ## @example
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	68 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	69 ## 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	70 ## P(x) = ------ [----(x - 1) ]
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	71 ## n 2^n n! dx^n
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	72 ## @end group
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	73 ## @end example
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	74 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	75 ## @end ifnottex
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	76 ##
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	77 ## @noindent
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	78 ## @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	79 ##
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	80 ## @example
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	81 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	82 ## x \| -1.0 \| -0.9 \| -0.8
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	83 ## ------------------------------------
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	84 ## m=0 \| -1.00000 \| -0.47250 \| -0.08000
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	85 ## m=1 \| 0.00000 \| -1.99420 \| -1.98000
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	86 ## 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	87 ## m=3 \| 0.00000 \| -1.24229 \| -3.24000
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	88 ## @end group
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	89 ## @end example
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	90 ##
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	91 ## When the optional argument @code{normalization} is @qcode{"sch"},
7508 f501b22c0394 doc fixes for legendre John W. Eaton <jwe@octave.org> parents: 7507 diff changeset	92 ## 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	93 ## 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	94 ## 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	95 ##
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	96 ## For Legendre functions of degree @var{n} and order 0:
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	97 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	98 ## @tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	99 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	100 ## SP^0_n (x) = P^0_n (x)
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	101 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	102 ## @end tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	103 ## @ifnottex
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	104 ##
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	105 ## @example
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	106 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	107 ## 0 0
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	108 ## SP(x) = P(x)
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	109 ## n n
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	110 ## @end group
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	111 ## @end example
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	112 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	113 ## @end ifnottex
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	114 ##
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	115 ## 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	116 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	117 ## @tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	118 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	119 ## SP^m_n (x) = P^m_n (x)(-1)^m\biggl({2(n-m)!\over{(n+m)!}}\biggl)^{0.5}
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	120 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	121 ## @end tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	122 ## @ifnottex
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	123 ##
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	124 ## @example
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	125 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	126 ## 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	127 ## 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	128 ## n n (n+m)!
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	129 ## @end group
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	130 ## @end example
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	131 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	132 ## @end ifnottex
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	133 ##
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	134 ## When the optional argument @var{normalization} is @qcode{"norm"},
7508 f501b22c0394 doc fixes for legendre John W. Eaton <jwe@octave.org> parents: 7507 diff changeset	135 ## 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	136 ## 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	137 ## 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	138 ##
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	139 ## 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	140 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	141 ## @tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	142 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	143 ## NP^m_n (x) = P^m_n (x)(-1)^m\biggl({(n+0.5)(n-m)!\over{(n+m)!}}\biggl)^{0.5}
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	144 ## $$
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	145 ## @end tex
e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	146 ## @ifnottex
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	147 ##
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	148 ## @example
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	149 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	150 ## 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	151 ## 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	152 ## n n (n+m)!
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	153 ## @end group
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	154 ## @end example
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	155 ##
11415 e7ed20f87e82 Add @tex blocks to gammainc and legendre docstrings. Michael Godfrey <godfrey@isl.stanford.edu> parents: 10793 diff changeset	156 ## @end ifnottex
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	157 ## @end deftypefn
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	158
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	159 ## Author: Marco Caliari <marco.caliari@univr.it>
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	160
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	161 function retval = legendre (n, x, normalization)
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	162
8255 3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	163 persistent warned_overflow = false;
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	164
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	165 if (nargin < 2 \|\| nargin > 3)
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	166 print_usage ();
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	167 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	168
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	169 if (! isreal (n) \|\| ! isscalar (n) \|\| n < 0 \|\| n != fix (n))
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	170 error ("legendre: N must be a real non-negative integer");
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	171 elseif (! 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	172 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	173 endif
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	174
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	175 if (nargin == 3)
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	176 normalization = lower (normalization);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	177 else
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	178 normalization = "unnorm";
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	179 endif
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	180
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	181 unnorm = false;
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	182 switch (normalization)
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	183 case "unnorm"
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	184 scale = 1;
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	185 unnorm = true;
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	186 case "norm"
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	187 scale = sqrt (n+0.5);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	188 case "sch"
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	189 scale = sqrt (2);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	190 otherwise
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	191 error ('legendre: NORMALIZATION option must be "unnorm", "norm", or "sch"');
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	192 endswitch
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	193
12893 72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	194 scale = scale * ones (size (x));
8255 3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	195
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	196 ## Based on the recurrence relation below
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	197 ## m m m
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	198 ## (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	199 ## n+1 n n-1
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	200 ## http://en.wikipedia.org/wiki/Associated_Legendre_function
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	201
8255 3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	202 overflow = false;
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	203 retval = zeros ([n+1, size(x)]);
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	204 for m = 1:n
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	205 lpm1 = scale;
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	206 lpm2 = (2m-1) . x .* scale;
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	207 lpm3 = lpm2;
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	208 for k = m+1:n
8255 3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	209 lpm3a = (2k-1) . x .* lpm2;
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	210 lpm3b = (k+m-2) .* lpm1;
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	211 lpm3 = (lpm3a - lpm3b) / (k-m+1);
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	212 lpm1 = lpm2;
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	213 lpm2 = lpm3;
8255 3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	214 if (! warned_overflow)
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	215 if ( any (abs (lpm3a) > realmax)
8255 3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	216 \|\| any (abs (lpm3b) > realmax)
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	217 \|\| any (abs (lpm3) > realmax))
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	218 overflow = true;
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	219 endif
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	220 endif
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	221 endfor
12893 72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	222 retval(m,:) = lpm3(:);
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	223 if (unnorm)
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	224 scale = -(2m-1);
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	225 else # normalization = "sch" or "norm"
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	226 scale = (2m-1) / sqrt ((n-m+1)*(n+m));
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	227 endif
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	228 scale .*= sqrt (1-x.^2);
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	229 endfor
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	230
12893 72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	231 retval(n+1,:) = scale(:);
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	232
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	233 if (isvector (x))
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	234 ## vector case is special
12893 72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	235 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	236 endif
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	237
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	238 if (strcmp (normalization, "sch"))
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	239 retval(1,:) ./= sqrt (2);
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	240 endif
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	241
8255 3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	242 if (overflow && ! warned_overflow)
8664 e07e93c04080 style fixes John W. Eaton <jwe@octave.org> parents: 8255 diff changeset	243 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	244 warned_overflow = true;
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	245 endif
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	246
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	247 endfunction
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	248
12893 72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	249
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	250 %!test
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	251 %! result = legendre (3, [-1.0 -0.9 -0.8]);
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	252 %! expected = [
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	253 %! -1.00000 -0.47250 -0.08000
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	254 %! 0.00000 -1.99420 -1.98000
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	255 %! 0.00000 -2.56500 -4.32000
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	256 %! 0.00000 -1.24229 -3.24000
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	257 %! ];
7507 bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	258 %! assert (result, expected, 1e-5);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	259
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	260 %!test
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	261 %! 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	262 %! expected = [
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	263 %! -1.00000 -0.47250 -0.08000
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	264 %! 0.00000 0.81413 0.80833
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	265 %! -0.00000 -0.33114 -0.55771
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	266 %! 0.00000 0.06547 0.17076
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	267 %! ];
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	268 %! assert (result, expected, 1e-5);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	269
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	270 %!test
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	271 %! 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	272 %! expected = [
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	273 %! -1.87083 -0.88397 -0.14967
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	274 %! 0.00000 1.07699 1.06932
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	275 %! -0.00000 -0.43806 -0.73778
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	276 %! 0.00000 0.08661 0.22590
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	277 %! ];
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	278 %! assert (result, expected, 1e-5);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	279
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	280 %!test
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	281 %! result = legendre (151, 0);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	282 %! ## 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	283 %! 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	284
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	285 %!test
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	286 %! result = legendre (150, 0);
bc6573d2fa40 legendre.m: Added normalization and improved stability. Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	287 %! ## 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	288 %! 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	289
8255 3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	290 %!test
3f1199ad212f legendre.m: Warn once on under/overflow. Ben Abbott <bpabbott@mac.com> parents: 7517 diff changeset	291 %! result = legendre (0, 0:0.1:1);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	292 %! assert (result, full (ones (1,11)));
12893 72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	293
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	294 %!test
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	295 %! ## Test matrix input
12893 72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	296 %! 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	297 %! 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	298 %! 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	299 %! 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	300 %! assert (result, expected);
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	301
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	302 %!test
72ffa81a68d4 legendre.m: Allow ND-array inputs (Bug #33526). Marco Caliari <marco.caliari@univr.it> parents: 11587 diff changeset	303 %! 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	304 %! 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	305 %! 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	306 %! assert (result, expected);
10672 1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	307
1cd7c39a96ee legendre.m: Orient row vector correctly (bug #29997). Rik <octave@nomad.inbox5.com> parents: 9051 diff changeset	308 %% Check correct invocation
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	309 %!error legendre ()
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	310 %!error legendre (1)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	311 %!error legendre (1,2,3,4)
19099 55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	312 %!error <must be a real non-negative integer> legendre (i, [-1, 0, 1])
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	313 %!error <must be a real non-negative integer> legendre ([1, 2], [-1, 0, 1])
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	314 %!error <must be a real non-negative integer> legendre (-1, [-1, 0, 1])
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	315 %!error <must be a real non-negative integer> legendre (1.1, [-1, 0, 1])
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	316 %!error <must be real-valued vector> legendre (1, [-1+i, 0, 1])
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	317 %!error <in the range -1 .= X .= 1> legendre (1, [-2, 0, 1])
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	318 %!error <in the range -1 .= X .= 1> legendre (1, [-1, 0, 2])
55b613e5183d legendre.m: Overhaul function. Rik <rik@octave.org> parents: 17744 diff changeset	319 %!error <NORMALIZATION option must be> legendre (1, [-1, 0, 1], "badnorm")
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	320

Mercurial > octave-antonio

annotate scripts/specfun/legendre.m @ 19697:4197fc428c7d