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annotate src/DLD-FUNCTIONS/mgorth.cc @ 13141:e81ddf9cacd5

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maint: untabify and remove trailing whitespace from source files * bicg.m, gmres.m, pkg.m: Untabify and remove trailing whitespace. * libcruft/Makefile.am, libcruft/blas-xtra/cdotc3.f, libcruft/blas-xtra/cmatm3.f, libcruft/blas-xtra/ddot3.f, libcruft/blas-xtra/dmatm3.f, libcruft/blas-xtra/sdot3.f, libcruft/blas-xtra/smatm3.f, libcruft/blas-xtra/zdotc3.f, libcruft/blas-xtra/zmatm3.f, libcruft/lapack-xtra/crsf2csf.f, libcruft/lapack-xtra/zrsf2csf.f, liboctave/Array.cc, liboctave/DASPK-opts.in, liboctave/DASRT-opts.in, liboctave/DASSL-opts.in, liboctave/LSODE-opts.in, liboctave/Makefile.a,mliboctave/Quad-opts.in, liboctave/Sparse-perm-op-defs.h, scripts/Makefile.a,mscripts/deprecated/glpkmex.m, scripts/general/blkdiag.m, scripts/general/interp1.m, scripts/general/profshow.m, scripts/general/quadl.m, scripts/general/triplequad.m, scripts/help/__makeinfo__.m, scripts/io/strread.m, scripts/io/textread.m, scripts/io/textscan.m, scripts/linear-algebra/rank.m, scripts/miscellaneous/gzip.m, scripts/miscellaneous/private/__xzip__.m, scripts/miscellaneous/tempdir.m, scripts/miscellaneous/unpack.m, scripts/pkg/pkg.m, scripts/plot/allchild.m, scripts/plot/ancestor.m, scripts/plot/cla.m, scripts/plot/clf.m, scripts/plot/findall.m, scripts/plot/findobj.m, scripts/plot/gca.m, scripts/plot/gcf.m, scripts/plot/hggroup.m, scripts/plot/isfigure.m, scripts/plot/ishghandle.m, scripts/plot/legend.m, scripts/plot/line.m, scripts/plot/loglog.m, scripts/plot/patch.m, scripts/plot/print.m, scripts/plot/private/__quiver__.m, scripts/plot/private/__scatter__.m, scripts/plot/rectangle.m, scripts/plot/semilogx.m, scripts/plot/semilogy.m, scripts/plot/surface.m, scripts/plot/text.m, scripts/plot/title.m, scripts/plot/trisurf.m, scripts/plot/view.m, scripts/plot/whitebg.m, scripts/plot/xlabel.m, scripts/plot/xlim.m, scripts/plot/ylabel.m, scripts/plot/ylim.m, scripts/plot/zlabel.m, scripts/plot/zlim.m, scripts/polynomial/mkpp.m, scripts/polynomial/polygcd.m, scripts/polynomial/ppint.m, scripts/polynomial/ppjumps.m, scripts/polynomial/ppval.m, scripts/set/setxor.m, scripts/sparse/bicgstab.m, scripts/sparse/cgs.m, scripts/sparse/spconvert.m, scripts/specfun/nthroot.m, scripts/strings/strmatch.m, scripts/strings/untabify.m, scripts/testfun/demo.m, scripts/testfun/example.m, src/DLD-FUNCTIONS/filter.cc, src/DLD-FUNCTIONS/mgorth.cc, src/DLD-FUNCTIONS/quadcc.cc, src/DLD-FUNCTIONS/str2double.cc, src/Makefile.a,msrc/gl-render.cc, src/gl2ps-renderer.cc, src/graphics.cc, src/octave-config.cc.in, src/octave-config.in, src/ov-class.h, src/ov-fcn.h, src/profiler.cc, src/profiler.h, src/pt-binop.cc, src/pt-unop.cc, src/symtab.cc, src/txt-eng-ft.cc: Remove trailing whitespace.
author John W. Eaton <jwe@octave.org>
date Thu, 15 Sep 2011 12:51:10 -0400
parents e742720c5e71
children 72c96de7a403
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
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1 /*
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2
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3 Copyright (C) 2009-2011 Carlo de Falco
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4 Copyright (C) 2010 VZLU Prague
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5
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6 This file is part of Octave.
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7
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8 Octave is free software; you can redistribute it and/or modify it
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9 under the terms of the GNU General Public License as published by the
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10 Free Software Foundation; either version 3 of the License, or (at your
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11 option) any later version.
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12
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13 Octave is distributed in the hope that it will be useful, but WITHOUT
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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16 for more details.
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17
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18 You should have received a copy of the GNU General Public License
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19 along with Octave; see the file COPYING. If not, see
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20 <http://www.gnu.org/licenses/>.
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21
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22 */
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23
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24 #ifdef HAVE_CONFIG_H
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25 #include <config.h>
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26 #endif
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27
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28 #include "oct-norm.h"
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29 #include "defun-dld.h"
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30 #include "error.h"
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31 #include "gripes.h"
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32
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33 template <class ColumnVector, class Matrix, class RowVector>
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34 static void
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35 do_mgorth (ColumnVector& x, const Matrix& V, RowVector& h)
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36 {
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37 octave_idx_type Vc = V.columns ();
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38 h = RowVector (Vc + 1);
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39 for (octave_idx_type j = 0; j < Vc; j++)
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40 {
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41 ColumnVector Vcj = V.column (j);
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42 h(j) = RowVector (Vcj.hermitian ()) * x;
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43 x -= h(j) * Vcj;
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44 }
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45
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46 h(Vc) = xnorm (x);
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47 if (real (h(Vc)) > 0)
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48 x = x / h(Vc);
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49 }
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50
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51 DEFUN_DLD (mgorth, args, nargout,
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52 "-*- texinfo -*-\n\
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53 @deftypefn {Loadable Function} {[@var{y}, @var{h}] =} mgorth (@var{x}, @var{v})\n\
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54 Orthogonalize a given column vector @var{x} with respect to a given\n\
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55 orthonormal basis @var{v} using a modified Gram-Schmidt orthogonalization. \n\
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56 On exit, @var{y} is a unit vector such that:\n\
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57 \n\
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58 @example\n\
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59 @group\n\
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60 norm (@var{y}) = 1\n\
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61 @var{v}' * @var{y} = 0\n\
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62 @var{x} = @var{h}*[@var{v}, @var{y}]\n\
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63 @end group\n\
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64 @end example\n\
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65 \n\
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66 @end deftypefn")
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67 {
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68 octave_value_list retval;
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69
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70 int nargin = args.length();
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71
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72 if (nargin != 2 || nargout > 2)
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73 {
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74 print_usage ();
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75 return retval;
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76 }
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77
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78 octave_value arg_x = args(0);
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79 octave_value arg_v = args(1);
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80
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81 if (arg_v.ndims () != 2 || arg_x.ndims () != 2 || arg_x.columns () != 1
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82 || arg_v.rows () != arg_x.rows ())
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83 {
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84 error ("mgorth: V should me a matrix, and X a column vector with"
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85 " the same number of rows as V.");
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86 return retval;
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87 }
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88
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89 if (! arg_x.is_numeric_type () && ! arg_v.is_numeric_type ())
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90 {
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91 error ("mgorth: X and V must be numeric");
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92 }
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93
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94 bool iscomplex = (arg_x.is_complex_type () || arg_v.is_complex_type ());
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95 if (arg_x.is_single_type () || arg_v.is_single_type ())
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96 {
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97 if (iscomplex)
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98 {
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99 FloatComplexColumnVector x = arg_x.float_complex_column_vector_value ();
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100 FloatComplexMatrix V = arg_v.float_complex_matrix_value ();
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101 FloatComplexRowVector h;
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102 do_mgorth (x, V, h);
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103 retval(1) = h;
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104 retval(0) = x;
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105 }
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106 else
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107 {
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108 FloatColumnVector x = arg_x.float_column_vector_value ();
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109 FloatMatrix V = arg_v.float_matrix_value ();
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110 FloatRowVector h;
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111 do_mgorth (x, V, h);
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112 retval(1) = h;
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113 retval(0) = x;
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114 }
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115 }
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116 else
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117 {
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118 if (iscomplex)
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119 {
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120 ComplexColumnVector x = arg_x.complex_column_vector_value ();
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121 ComplexMatrix V = arg_v.complex_matrix_value ();
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122 ComplexRowVector h;
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123 do_mgorth (x, V, h);
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124 retval(1) = h;
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125 retval(0) = x;
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126 }
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127 else
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128 {
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129 ColumnVector x = arg_x.column_vector_value ();
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130 Matrix V = arg_v.matrix_value ();
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131 RowVector h;
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132 do_mgorth (x, V, h);
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133 retval(1) = h;
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134 retval(0) = x;
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135 }
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136 }
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137
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138 return retval;
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139 }
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140
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Carlo de Falco <kingcrimson@tiscali.it>
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141 /*
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 12509
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142
12509
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143 %!test
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144 %! for ii=1:100; assert (abs (mgorth (randn (5, 1), eye (5, 4))), [0 0 0 0 1]', eps); endfor
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145
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146 %!test
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147 %! a = hilb (5);
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148 %! a(:, 1) /= norm (a(:, 1));
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149 %! for ii = 1:5
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150 %! a(:, ii) = mgorth (a(:, ii), a(:, 1:ii-1));
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151 %! endfor
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152 %! assert (a' * a, eye (5), 1e10);
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153
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154 */