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update Octave Project Developers copyright for the new year In files that have the "Octave Project Developers" copyright notice, update for 2021. In all .txi and .texi files except gpl.txi and gpl.texi in the doc/liboctave and doc/interpreter directories, change the copyright to "Octave Project Developers", the same as used for other source files. Update copyright notices for 2022 (not done since 2019). For gpl.txi and gpl.texi, change the copyright notice to be "Free Software Foundation, Inc." and leave the date at 2007 only because this file only contains the text of the GPL, not anything created by the Octave Project Developers. Add Paul Thomas to contributors.in.
author John W. Eaton <jwe@octave.org>
date Tue, 28 Dec 2021 18:22:40 -0500
parents 4f8284dee449
children e88a07dec498
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 ////////////////////////////////////////////////////////////////////////
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2 //
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3 // Copyright (C) 2009-2022 The Octave Project Developers
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4 //
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5 // See the file COPYRIGHT.md in the top-level directory of this
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6 // distribution or <https://octave.org/copyright/>.
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7 //
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8 // This file is part of Octave.
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9 //
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10 // Octave is free software: you can redistribute it and/or modify it
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11 // under the terms of the GNU General Public License as published by
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12 // the Free Software Foundation, either version 3 of the License, or
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13 // (at your option) any later version.
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14 //
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15 // Octave is distributed in the hope that it will be useful, but
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 // GNU General Public License for more details.
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19 //
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20 // You should have received a copy of the GNU General Public License
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21 // along with Octave; see the file COPYING. If not, see
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22 // <https://www.gnu.org/licenses/>.
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23 //
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24 ////////////////////////////////////////////////////////////////////////
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25
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26 #if defined (HAVE_CONFIG_H)
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27 # include "config.h"
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28 #endif
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29
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30 #include "oct-norm.h"
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31 #include "defun.h"
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32 #include "error.h"
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33 #include "errwarn.h"
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34
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35 OCTAVE_NAMESPACE_BEGIN
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36
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37 template <typename ColumnVector, typename Matrix, typename RowVector>
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38 static void
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39 do_mgorth (ColumnVector& x, const Matrix& V, RowVector& h)
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40 {
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41 octave_idx_type Vc = V.columns ();
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42 h = RowVector (Vc + 1);
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43 for (octave_idx_type j = 0; j < Vc; j++)
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44 {
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45 ColumnVector Vcj = V.column (j);
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46 RowVector Vcjh = Vcj.hermitian ();
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47 h(j) = Vcjh * x;
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48 x -= h(j) * Vcj;
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49 }
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50
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51 h(Vc) = xnorm (x);
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52 if (std::real (h(Vc)) > 0)
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53 x /= h(Vc);
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54 }
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55
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56 DEFUN (mgorth, args, ,
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57 doc: /* -*- texinfo -*-
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58 @deftypefn {} {[@var{y}, @var{h}] =} mgorth (@var{x}, @var{v})
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59 Orthogonalize a given column vector @var{x} with respect to a set of
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60 orthonormal vectors comprising the columns of @var{v} using the modified
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61 Gram-Schmidt method.
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62
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63 On exit, @var{y} is a unit vector such that:
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64
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65 @example
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66 @group
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67 norm (@var{y}) = 1
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68 @var{v}' * @var{y} = 0
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69 @var{x} = [@var{v}, @var{y}]*@var{h}'
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70 @end group
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71 @end example
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72
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73 @end deftypefn */)
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74 {
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75 if (args.length () != 2)
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76 print_usage ();
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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 error ("mgorth: V should be a matrix, and X a column vector with"
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84 " the same number of rows as V.");
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85
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86 if (! arg_x.isnumeric () && ! arg_v.isnumeric ())
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87 error ("mgorth: X and V must be numeric");
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88
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89 octave_value_list retval;
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90
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91 bool iscomplex = (arg_x.iscomplex () || arg_v.iscomplex ());
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92 if (arg_x.is_single_type () || arg_v.is_single_type ())
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93 {
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94 if (iscomplex)
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95 {
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96 FloatComplexColumnVector x
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97 = arg_x.float_complex_column_vector_value ();
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98 FloatComplexMatrix V = arg_v.float_complex_matrix_value ();
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99 FloatComplexRowVector h;
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100 do_mgorth (x, V, h);
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101 retval = ovl (x, h);
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102 }
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103 else
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104 {
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105 FloatColumnVector x = arg_x.float_column_vector_value ();
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106 FloatMatrix V = arg_v.float_matrix_value ();
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107 FloatRowVector h;
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108 do_mgorth (x, V, h);
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109 retval = ovl (x, h);
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110 }
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111 }
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112 else
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113 {
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114 if (iscomplex)
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115 {
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116 ComplexColumnVector x = arg_x.complex_column_vector_value ();
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117 ComplexMatrix V = arg_v.complex_matrix_value ();
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118 ComplexRowVector h;
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119 do_mgorth (x, V, h);
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120 retval = ovl (x, h);
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121 }
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122 else
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123 {
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124 ColumnVector x = arg_x.column_vector_value ();
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125 Matrix V = arg_v.matrix_value ();
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126 RowVector h;
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127 do_mgorth (x, V, h);
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128 retval = ovl (x, h);
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129 }
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130 }
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131
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132 return retval;
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133 }
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134
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135 /*
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136 %!test
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137 %! for ii=1:100
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138 %! assert (abs (mgorth (randn (5, 1), eye (5, 4))), [0 0 0 0 1]', eps);
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139 %! endfor
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140
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141 %!test
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142 %! a = hilb (5);
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143 %! a(:, 1) /= norm (a(:, 1));
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144 %! for ii = 1:5
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145 %! a(:, ii) = mgorth (a(:, ii), a(:, 1:ii-1));
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146 %! endfor
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147 %! assert (a' * a, eye (5), 1e10);
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148 */
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149
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150 OCTAVE_NAMESPACE_END