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annotate scripts/specfun/legendre.m @ 17281:bc924baa2c4e

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doc: Add new @qcode macro for code samples which are quoted. Macro handles options ("on") or properties ("position") more elegantly than @code{"text"}. * doc/interpreter/macros.texi: Add new @qcode macro. * doc/interpreter/tips.txi: Add documentation about @qcode macro. * doc/interpreter/basics.txi, doc/interpreter/container.txi, doc/interpreter/emacs.txi, doc/interpreter/errors.txi, doc/interpreter/eval.txi, doc/interpreter/expr.txi, doc/interpreter/external.txi, doc/interpreter/func.txi, doc/interpreter/grammar.txi, doc/interpreter/image.txi, doc/interpreter/install.txi, doc/interpreter/interp.txi, doc/interpreter/io.txi, doc/interpreter/matrix.txi, doc/interpreter/numbers.txi, doc/interpreter/oop.txi, doc/interpreter/package.txi, doc/interpreter/plot.txi, doc/interpreter/quad.txi, doc/interpreter/sparse.txi, doc/interpreter/strings.txi, doc/interpreter/system.txi, doc/interpreter/vectorize.txi, libinterp/corefcn/balance.cc, libinterp/corefcn/bitfcns.cc, libinterp/corefcn/cellfun.cc, libinterp/corefcn/conv2.cc, libinterp/corefcn/data.cc, libinterp/corefcn/debug.cc, libinterp/corefcn/defaults.cc, libinterp/corefcn/dirfns.cc, libinterp/corefcn/dlmread.cc, libinterp/corefcn/error.cc, libinterp/corefcn/file-io.cc, libinterp/corefcn/find.cc, libinterp/corefcn/gammainc.cc, libinterp/corefcn/graphics.cc, libinterp/corefcn/help.cc, libinterp/corefcn/hex2num.cc, libinterp/corefcn/input.cc, libinterp/corefcn/load-path.cc, libinterp/corefcn/load-save.cc, libinterp/corefcn/ls-oct-ascii.cc, libinterp/corefcn/lu.cc, libinterp/corefcn/luinc.cc, libinterp/corefcn/matrix_type.cc, libinterp/corefcn/oct-hist.cc, libinterp/corefcn/pager.cc, libinterp/corefcn/pr-output.cc, libinterp/corefcn/pt-jit.cc, libinterp/corefcn/qz.cc, libinterp/corefcn/rand.cc, libinterp/corefcn/regexp.cc, libinterp/corefcn/schur.cc, libinterp/corefcn/sighandlers.cc, libinterp/corefcn/sparse.cc, libinterp/corefcn/spparms.cc, libinterp/corefcn/str2double.cc, libinterp/corefcn/svd.cc, libinterp/corefcn/symtab.cc, libinterp/corefcn/syscalls.cc, libinterp/corefcn/toplev.cc, libinterp/corefcn/tril.cc, libinterp/corefcn/typecast.cc, libinterp/corefcn/utils.cc, libinterp/corefcn/variables.cc, libinterp/dldfcn/__init_fltk__.cc, libinterp/dldfcn/chol.cc, libinterp/dldfcn/colamd.cc, libinterp/dldfcn/fftw.cc, libinterp/dldfcn/qr.cc, libinterp/dldfcn/symbfact.cc, libinterp/octave-value/ov-base.cc, libinterp/octave-value/ov-fcn-handle.cc, libinterp/octave-value/ov-fcn-inline.cc, libinterp/octave-value/ov-java.cc, libinterp/octave-value/ov-range.cc, libinterp/octave-value/ov-struct.cc, libinterp/octave-value/ov-usr-fcn.cc, libinterp/parse-tree/oct-parse.in.yy, libinterp/parse-tree/pt-binop.cc, libinterp/parse-tree/pt-eval.cc, libinterp/parse-tree/pt-mat.cc, scripts/@ftp/ftp.m, scripts/deprecated/java_convert_matrix.m, scripts/deprecated/java_debug.m, scripts/deprecated/java_unsigned_conversion.m, scripts/deprecated/shell_cmd.m, scripts/general/dblquad.m, scripts/general/display.m, scripts/general/genvarname.m, scripts/general/idivide.m, scripts/general/interp1.m, scripts/general/interp2.m, scripts/general/interp3.m, scripts/general/interpn.m, scripts/general/isa.m, scripts/general/profexplore.m, scripts/general/profile.m, scripts/general/quadgk.m, scripts/general/randi.m, scripts/general/structfun.m, scripts/general/subsindex.m, scripts/general/triplequad.m, scripts/geometry/griddata.m, scripts/geometry/griddata3.m, scripts/geometry/griddatan.m, scripts/geometry/voronoi.m, scripts/help/help.m, scripts/help/lookfor.m, scripts/image/cmpermute.m, scripts/image/colormap.m, scripts/image/image.m, scripts/image/imagesc.m, scripts/image/imfinfo.m, scripts/image/imformats.m, scripts/image/imread.m, scripts/image/imshow.m, scripts/image/imwrite.m, scripts/image/ind2gray.m, scripts/image/lines.m, scripts/image/rgb2ind.m, scripts/image/spinmap.m, scripts/io/dlmwrite.m, scripts/io/strread.m, scripts/io/textread.m, scripts/io/textscan.m, scripts/java/javaclasspath.m, scripts/java/usejava.m, scripts/miscellaneous/bzip2.m, scripts/miscellaneous/computer.m, scripts/miscellaneous/copyfile.m, scripts/miscellaneous/debug.m, scripts/miscellaneous/dos.m, scripts/miscellaneous/edit.m, scripts/miscellaneous/gzip.m, scripts/miscellaneous/license.m, scripts/miscellaneous/mkoctfile.m, scripts/miscellaneous/movefile.m, scripts/miscellaneous/parseparams.m, scripts/miscellaneous/unix.m, scripts/optimization/fminbnd.m, scripts/optimization/fminsearch.m, scripts/optimization/fminunc.m, scripts/optimization/fsolve.m, scripts/optimization/fzero.m, scripts/optimization/glpk.m, scripts/optimization/lsqnonneg.m, scripts/optimization/optimset.m, scripts/optimization/pqpnonneg.m, scripts/pkg/pkg.m, scripts/plot/allchild.m, scripts/plot/ancestor.m, scripts/plot/area.m, scripts/plot/axis.m, scripts/plot/bar.m, scripts/plot/barh.m, scripts/plot/box.m, scripts/plot/caxis.m, scripts/plot/cla.m, scripts/plot/clabel.m, scripts/plot/clf.m, scripts/plot/close.m, scripts/plot/colorbar.m, scripts/plot/daspect.m, scripts/plot/ezmesh.m, scripts/plot/ezmeshc.m, scripts/plot/ezsurf.m, scripts/plot/ezsurfc.m, scripts/plot/findall.m, scripts/plot/findobj.m, scripts/plot/gcbo.m, scripts/plot/gcf.m, scripts/plot/gco.m, scripts/plot/grid.m, scripts/plot/guihandles.m, scripts/plot/hdl2struct.m, scripts/plot/hidden.m, scripts/plot/hold.m, scripts/plot/isonormals.m, scripts/plot/isosurface.m, scripts/plot/legend.m, scripts/plot/mesh.m, scripts/plot/meshc.m, scripts/plot/meshz.m, scripts/plot/newplot.m, scripts/plot/orient.m, scripts/plot/pareto.m, scripts/plot/patch.m, scripts/plot/pbaspect.m, scripts/plot/pcolor.m, scripts/plot/plot.m, scripts/plot/print.m, scripts/plot/private/__add_default_menu__.m, scripts/plot/quiver.m, scripts/plot/quiver3.m, scripts/plot/refreshdata.m, scripts/plot/saveas.m, scripts/plot/scatter.m, scripts/plot/scatter3.m, scripts/plot/shading.m, scripts/plot/shrinkfaces.m, scripts/plot/slice.m, scripts/plot/stem.m, scripts/plot/stem3.m, scripts/plot/struct2hdl.m, scripts/plot/subplot.m, scripts/plot/surf.m, scripts/plot/surfc.m, scripts/plot/surfl.m, scripts/plot/tetramesh.m, scripts/plot/uigetfile.m, scripts/plot/uimenu.m, scripts/plot/uiputfile.m, scripts/plot/waterfall.m, scripts/plot/whitebg.m, scripts/plot/xlim.m, scripts/plot/ylim.m, scripts/plot/zlim.m, scripts/polynomial/conv.m, scripts/polynomial/polyout.m, scripts/polynomial/splinefit.m, scripts/set/ismember.m, scripts/set/powerset.m, scripts/set/setdiff.m, scripts/set/union.m, scripts/set/unique.m, scripts/signal/detrend.m, scripts/signal/filter2.m, scripts/signal/freqz.m, scripts/signal/periodogram.m, scripts/signal/spectral_adf.m, scripts/signal/spectral_xdf.m, scripts/sparse/eigs.m, scripts/sparse/svds.m, scripts/specfun/legendre.m, scripts/special-matrix/gallery.m, scripts/statistics/base/mean.m, scripts/statistics/base/moment.m, scripts/statistics/tests/cor_test.m, scripts/statistics/tests/kolmogorov_smirnov_test.m, scripts/statistics/tests/kolmogorov_smirnov_test_2.m, scripts/statistics/tests/kruskal_wallis_test.m, scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/sign_test.m, scripts/statistics/tests/t_test.m, scripts/statistics/tests/t_test_2.m, scripts/statistics/tests/t_test_regression.m, scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m, scripts/statistics/tests/welch_test.m, scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m, scripts/statistics/tests/z_test_2.m, scripts/strings/base2dec.m, scripts/strings/index.m, scripts/strings/isstrprop.m, scripts/strings/mat2str.m, scripts/strings/regexptranslate.m, scripts/strings/rindex.m, scripts/strings/str2num.m, scripts/strings/strcat.m, scripts/strings/strjust.m, scripts/strings/strmatch.m, scripts/strings/validatestring.m, scripts/testfun/demo.m, scripts/testfun/example.m, scripts/testfun/test.m, scripts/time/addtodate.m, scripts/time/asctime.m, scripts/time/datestr.m, scripts/time/datetick.m, scripts/time/weekday.m, scripts/ui/errordlg.m, scripts/ui/helpdlg.m, scripts/ui/inputdlg.m, scripts/ui/listdlg.m, scripts/ui/msgbox.m, scripts/ui/questdlg.m, scripts/ui/warndlg.m: Use new @qcode macro.
author Rik <rik@octave.org>
date Mon, 19 Aug 2013 20:46:38 -0700
parents 5d3a684236b0
children d63878346099
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72c96de7a403 maint: update copyright notices for 2012
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1 ## Copyright (C) 2000-2012 Kai Habel
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2 ## Copyright (C) 2008 Marco Caliari
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {Function File} {@var{l} =} legendre (@var{n}, @var{x})
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22 ## @deftypefnx {Function File} {@var{l} =} legendre (@var{n}, @var{x}, @var{normalization})
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23 ## Compute the Legendre function of degree @var{n} and order
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24 ## @var{m} = 0 @dots{} N@. The optional argument, @var{normalization},
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25 ## may be one of @qcode{"unnorm"}, @qcode{"sch"}, or @qcode{"norm"}.
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26 ## The default is @qcode{"unnorm"}. The value of @var{n} must be a
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27 ## non-negative scalar integer.
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28 ##
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29 ## If the optional argument @var{normalization} is missing or is
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30 ## @qcode{"unnorm"}, compute the Legendre function of degree @var{n} and
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31 ## order @var{m} and return all values for @var{m} = 0 @dots{} @var{n}.
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32 ## The return value has one dimension more than @var{x}.
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33 ##
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34 ## The Legendre Function of degree @var{n} and order @var{m}:
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35 ##
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36 ## @tex
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37 ## $$
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38 ## P^m_n(x) = (-1)^m (1-x^2)^{m/2}{d^m\over {dx^m}}P_n (x)
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39 ## $$
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40 ## @end tex
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41 ## @ifnottex
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42 ##
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43 ## @example
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44 ## @group
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45 ## m m 2 m/2 d^m
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46 ## P(x) = (-1) * (1-x ) * ---- P(x)
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47 ## n dx^m n
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48 ## @end group
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49 ## @end example
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50 ##
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51 ## @end ifnottex
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52 ##
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53 ## @noindent
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54 ## with Legendre polynomial of degree @var{n}:
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55 ##
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56 ## @tex
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57 ## $$
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58 ## P(x) = {1\over{2^n n!}}\biggl({d^n\over{dx^n}}(x^2 - 1)^n\biggr)
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59 ## $$
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60 ## @end tex
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61 ## @ifnottex
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62 ##
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63 ## @example
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64 ## @group
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65 ## 1 d^n 2 n
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66 ## P(x) = ------ [----(x - 1) ]
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67 ## n 2^n n! dx^n
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68 ## @end group
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69 ## @end example
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70 ##
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71 ## @end ifnottex
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72 ##
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73 ## @noindent
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74 ## @code{legendre (3, [-1.0, -0.9, -0.8])} returns the matrix:
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75 ##
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76 ## @example
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77 ## @group
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78 ## x | -1.0 | -0.9 | -0.8
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79 ## ------------------------------------
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80 ## m=0 | -1.00000 | -0.47250 | -0.08000
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81 ## m=1 | 0.00000 | -1.99420 | -1.98000
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82 ## m=2 | 0.00000 | -2.56500 | -4.32000
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83 ## m=3 | 0.00000 | -1.24229 | -3.24000
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84 ## @end group
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85 ## @end example
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86 ##
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87 ## If the optional argument @code{normalization} is @qcode{"sch"},
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88 ## compute the Schmidt semi-normalized associated Legendre function.
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89 ## The Schmidt semi-normalized associated Legendre function is related
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90 ## to the unnormalized Legendre functions by the following:
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91 ##
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92 ## For Legendre functions of degree n and order 0:
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93 ##
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94 ## @tex
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95 ## $$
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96 ## SP^0_n (x) = P^0_n (x)
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97 ## $$
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98 ## @end tex
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99 ## @ifnottex
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100 ##
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101 ## @example
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102 ## @group
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103 ## 0 0
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104 ## SP(x) = P(x)
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105 ## n n
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106 ## @end group
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107 ## @end example
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108 ##
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109 ## @end ifnottex
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110 ##
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111 ## For Legendre functions of degree n and order m:
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112 ##
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113 ## @tex
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114 ## $$
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115 ## SP^m_n (x) = P^m_n (x)(-1)^m\biggl({2(n-m)!\over{(n+m)!}}\biggl)^{0.5}
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116 ## $$
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117 ## @end tex
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118 ## @ifnottex
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119 ##
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120 ## @example
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121 ## @group
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122 ## m m m 2(n-m)! 0.5
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123 ## SP(x) = P(x) * (-1) * [-------]
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124 ## n n (n+m)!
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125 ## @end group
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126 ## @end example
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127 ##
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128 ## @end ifnottex
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129 ##
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130 ## If the optional argument @var{normalization} is @qcode{"norm"},
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131 ## compute the fully normalized associated Legendre function.
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132 ## The fully normalized associated Legendre function is related
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133 ## to the unnormalized Legendre functions by the following:
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134 ##
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135 ## For Legendre functions of degree @var{n} and order @var{m}
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136 ##
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137 ## @tex
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138 ## $$
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139 ## NP^m_n (x) = P^m_n (x)(-1)^m\biggl({(n+0.5)(n-m)!\over{(n+m)!}}\biggl)^{0.5}
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140 ## $$
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141 ## @end tex
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142 ## @ifnottex
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143 ##
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144 ## @example
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145 ## @group
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146 ## m m m (n+0.5)(n-m)! 0.5
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147 ## NP(x) = P(x) * (-1) * [-------------]
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148 ## n n (n+m)!
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149 ## @end group
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150 ## @end example
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151 ##
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152 ## @end ifnottex
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153 ## @end deftypefn
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154
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155 ## Author: Marco Caliari <marco.caliari@univr.it>
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156
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157 function retval = legendre (n, x, normalization)
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158
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159 persistent warned_overflow = false;
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160
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161 if (nargin < 2 || nargin > 3)
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162 print_usage ();
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163 endif
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164
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165 if (!isscalar (n) || n < 0 || n != fix (n))
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166 error ("legendre: N must be a non-negative scalar integer");
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167 endif
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168
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169 if (!isreal (x) || any (x(:) < -1 | x(:) > 1))
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170 error ("legendre: X must be real-valued vector in the range -1 <= X <= 1");
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171 endif
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172
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173 if (nargin == 3)
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174 normalization = lower (normalization);
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175 else
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176 normalization = "unnorm";
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177 endif
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178
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179 switch (normalization)
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180 case "norm"
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181 scale = sqrt (n+0.5);
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182 case "sch"
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183 scale = sqrt (2);
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184 case "unnorm"
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185 scale = 1;
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186 otherwise
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187 error ('legendre: expecting NORMALIZATION option to be "norm", "sch", or "unnorm"');
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188 endswitch
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189
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190 scale = scale * ones (size (x));
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191
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192 ## Based on the recurrence relation below
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193 ## m m m
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194 ## (n-m+1) * P (x) = (2*n+1)*x*P (x) - (n+1)*P (x)
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195 ## n+1 n n-1
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196 ## http://en.wikipedia.org/wiki/Associated_Legendre_function
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197
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198 overflow = false;
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199 retval = zeros ([n+1, size(x)]);
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200 for m = 1:n
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201 lpm1 = scale;
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202 lpm2 = (2*m-1) .* x .* scale;
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203 lpm3 = lpm2;
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204 for k = m+1:n
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205 lpm3a = (2*k-1) .* x .* lpm2;
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206 lpm3b = (k+m-2) .* lpm1;
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207 lpm3 = (lpm3a - lpm3b)/(k-m+1);
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208 lpm1 = lpm2;
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209 lpm2 = lpm3;
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210 if (! warned_overflow)
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211 if (any (abs (lpm3a) > realmax)
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212 || any (abs (lpm3b) > realmax)
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213 || any (abs (lpm3) > realmax))
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214 overflow = true;
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215 endif
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216 endif
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217 endfor
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218 retval(m,:) = lpm3(:);
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219 if (strcmp (normalization, "unnorm"))
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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
14868
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory
Rik <octave@nomad.inbox5.com>
parents: 14363
diff changeset
225 scale = scale .* sqrt (1-x.^2);
7507
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);
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
289 %! 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
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
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
306 %!error legendre ()
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
307 %!error legendre (1)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
308 %!error legendre (1,2,3,4)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
309 %!error legendre ([1, 2], [-1, 0, 1])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
310 %!error legendre (-1, [-1, 0, 1])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
311 %!error legendre (1.1, [-1, 0, 1])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
312 %!error legendre (1, [-1+i, 0, 1])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
313 %!error legendre (1, [-2, 0, 1])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
314 %!error legendre (1, [-1, 0, 2])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
315 %!error legendre (1, [-1, 0, 1], "badnorm")
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
316