annotate scripts/linear-algebra/rref.m @ 14868:5d3a684236b0

maint: Use Octave coding conventions for cuddling parentheses in scripts directory * lin2mu.m, loadaudio.m, wavread.m, accumarray.m, bicubic.m, celldisp.m, colon.m, cplxpair.m, dblquad.m, divergence.m, genvarname.m, gradient.m, int2str.m, interp1.m, interp1q.m, interp2.m, interpn.m, loadobj.m, nthargout.m, __isequal__.m, __splinen__.m, quadgk.m, quadl.m, quadv.m, rat.m, rot90.m, rotdim.m, saveobj.m, subsindex.m, triplequad.m, delaunay3.m, griddata.m, inpolygon.m, tsearchn.m, voronoi.m, get_first_help_sentence.m, which.m, gray2ind.m, pink.m, dlmwrite.m, strread.m, textread.m, textscan.m, housh.m, ishermitian.m, issymmetric.m, krylov.m, logm.m, null.m, rref.m, compare_versions.m, copyfile.m, dump_prefs.m, edit.m, fileparts.m, getappdata.m, isappdata.m, movefile.m, orderfields.m, parseparams.m, __xzip__.m, rmappdata.m, setappdata.m, swapbytes.m, unpack.m, ver.m, fminbnd.m, fminunc.m, fsolve.m, glpk.m, lsqnonneg.m, qp.m, sqp.m, configure_make.m, copy_files.m, describe.m, get_description.m, get_forge_pkg.m, install.m, installed_packages.m, is_architecture_dependent.m, load_package_dirs.m, print_package_description.m, rebuild.m, repackage.m, save_order.m, shell.m, allchild.m, ancestor.m, area.m, axes.m, axis.m, clabel.m, close.m, colorbar.m, comet.m, comet3.m, contour.m, cylinder.m, ezmesh.m, ezsurf.m, findobj.m, fplot.m, hist.m, isocolors.m, isonormals.m, isosurface.m, isprop.m, legend.m, mesh.m, meshz.m, pareto.m, pcolor.m, peaks.m, plot3.m, plotmatrix.m, plotyy.m, polar.m, print.m, __add_datasource__.m, __add_default_menu__.m, __axes_limits__.m, __bar__.m, __clabel__.m, __contour__.m, __errcomm__.m, __errplot__.m, __ezplot__.m, __file_filter__.m, __fltk_print__.m, __ghostscript__.m, __gnuplot_print__.m, __go_draw_axes__.m, __go_draw_figure__.m, __interp_cube__.m, __marching_cube__.m, __patch__.m, __pie__.m, __plt__.m, __print_parse_opts__.m, __quiver__.m, __scatter__.m, __stem__.m, __tight_eps_bbox__.m, __uigetdir_fltk__.m, __uigetfile_fltk__.m, __uiputfile_fltk__.m, quiver.m, quiver3.m, rectangle.m, refreshdata.m, ribbon.m, scatter.m, semilogy.m, shading.m, slice.m, subplot.m, surface.m, surfl.m, surfnorm.m, text.m, uigetfile.m, uiputfile.m, whitebg.m, deconv.m, mkpp.m, pchip.m, polyaffine.m, polyder.m, polygcd.m, polyout.m, polyval.m, ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, splinefit.m, addpref.m, getpref.m, setpref.m, ismember.m, setxor.m, arch_fit.m, arch_rnd.m, arch_test.m, autoreg_matrix.m, diffpara.m, fftconv.m, filter2.m, hanning.m, hurst.m, periodogram.m, triangle_sw.m, sinc.m, spectral_xdf.m, spencer.m, stft.m, synthesis.m, unwrap.m, yulewalker.m, bicgstab.m, gmres.m, pcg.m, pcr.m, __sprand_impl__.m, speye.m, spfun.m, sprandn.m, spstats.m, svds.m, treelayout.m, treeplot.m, bessel.m, factor.m, legendre.m, perms.m, primes.m, magic.m, toeplitz.m, corr.m, cov.m, mean.m, median.m, mode.m, qqplot.m, quantile.m, ranks.m, zscore.m, logistic_regression_likelihood.m, bartlett_test.m, chisquare_test_homogeneity.m, chisquare_test_independence.m, kolmogorov_smirnov_test.m, run_test.m, u_test.m, wilcoxon_test.m, z_test.m, z_test_2.m, bin2dec.m, dec2base.m, mat2str.m, strcat.m, strchr.m, strjust.m, strtok.m, substr.m, untabify.m, assert.m, demo.m, example.m, fail.m, speed.m, test.m, now.m: Use Octave coding conventions for cuddling parentheses in scripts directory.
author Rik <octave@nomad.inbox5.com>
date Tue, 17 Jul 2012 07:08:39 -0700
parents f3d52523cde1
children
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rev   line source
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72c96de7a403 maint: update copyright notices for 2012
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1 ## Copyright (C) 2000-2012 Paul Kienzle
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} rref (@var{A})
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21 ## @deftypefnx {Function File} {} rref (@var{A}, @var{tol})
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22 ## @deftypefnx {Function File} {[@var{r}, @var{k}] =} rref (@dots{})
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23 ## Return the reduced row echelon form of @var{A}. @var{tol} defaults
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24 ## to @code{eps * max (size (@var{A})) * norm (@var{A}, inf)}.
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25 ##
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26 ## Called with two return arguments, @var{k} returns the vector of
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27 ## "bound variables", which are those columns on which elimination
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28 ## has been performed.
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29 ##
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30 ## @end deftypefn
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31
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32 ## Author: Paul Kienzle <pkienzle@users.sf.net>
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33 ## (based on an anonymous source from the public domain)
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34
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35 function [A, k] = rref (A, tol)
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36
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37 if (nargin < 1 || nargin > 2)
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38 print_usage ();
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39 endif
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40
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41 if (ndims (A) > 2)
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42 error ("rref: expecting matrix argument");
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43 endif
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44
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45 [rows, cols] = size (A);
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46
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47 if (nargin < 2)
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48 if (isa (A, "single"))
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49 tol = eps ("single") * max (rows, cols) * norm (A, inf ("single"));
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50 else
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51 tol = eps * max (rows, cols) * norm (A, inf);
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52 endif
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53 endif
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54
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55 used = zeros (1, cols);
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56 r = 1;
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57 for c = 1:cols
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58 ## Find the pivot row
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59 [m, pivot] = max (abs (A(r:rows,c)));
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60 pivot = r + pivot - 1;
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61
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62 if (m <= tol)
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63 ## Skip column c, making sure the approximately zero terms are
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64 ## actually zero.
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65 A(r:rows, c) = zeros (rows-r+1, 1);
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66 else
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67 ## keep track of bound variables
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68 used (1, c) = 1;
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69
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70 ## Swap current row and pivot row
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71 A([pivot, r], c:cols) = A([r, pivot], c:cols);
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72
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73 ## Normalize pivot row
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74 A(r, c:cols) = A(r, c:cols) / A(r, c);
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75
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76 ## Eliminate the current column
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77 ridx = [1:r-1, r+1:rows];
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78 A(ridx, c:cols) = A(ridx, c:cols) - A(ridx, c) * A(r, c:cols);
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79
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80 ## Check if done
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81 if (r++ == rows)
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82 break;
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83 endif
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84 endif
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85 endfor
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86 k = find (used);
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87
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88 endfunction
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89
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90
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91 %!test
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92 %! a = [1];
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93 %! [r k] = rref (a);
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94 %! assert (r, [1], 2e-8);
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95 %! assert (k, [1], 2e-8);
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96
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97 %!test
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98 %! a = [1 3; 4 5];
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99 %! [r k] = rref (a);
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100 %! assert (rank (a), rank (r), 2e-8);
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101 %! assert (r, eye (2), 2e-8);
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102 %! assert (k == [1, 2] || k == [2, 1]);
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103
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104 %!test
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105 %! a = [1 3; 4 5; 7 9];
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106 %! [r k] = rref (a);
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107 %! assert (rank (a), rank (r), 2e-8);
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108 %! assert (r, eye(3)(:,1:2), 2e-8);
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109 %! assert (k, [1 2], 2e-8);
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110
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111 %!test
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112 %! a = [1 2 3; 2 4 6; 7 2 0];
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113 %! [r k] = rref (a);
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114 %! assert (rank (a), rank (r), 2e-8);
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115 %! assert (r, [1 0 (3-7/2); 0 1 (7/4); 0 0 0], 2e-8);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
116 %! assert (k, [1 2], 2e-8);
13048
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 12584
diff changeset
117
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 12584
diff changeset
118 %!test
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 12584
diff changeset
119 %! a = [1 2 1; 2 4 2.01; 2 4 2.1];
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 12584
diff changeset
120 %! tol = 0.02;
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
121 %! [r k] = rref (a, tol);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
122 %! assert (rank (a, tol), rank (r, tol), 2e-8);
13048
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 12584
diff changeset
123 %! tol = 0.2;
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
124 %! [r k] = rref (a, tol);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
125 %! assert (rank (a, tol), rank (r, tol), 2e-8);
13048
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 12584
diff changeset
126
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
127 %!error rref ();
13048
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 12584
diff changeset
128