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annotate libinterp/corefcn/mgorth.cc @ 19822:2f4406e9dad6

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maint: Periodic merge of gui-release to default.
author John W. Eaton <jwe@octave.org>
date Fri, 23 Jan 2015 16:40:25 -0500
parents 175b392e91fe
children 4197fc428c7d
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) 2009-2013 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.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 (mgorth, args, nargout,
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52 "-*- texinfo -*-\n\
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53 @deftypefn {Built-in 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 set of\n\
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55 orthonormal vectors comprising the columns of @var{v}\n\
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56 using the modified Gram-Schmidt method.\n\
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57 On exit, @var{y} is a unit vector such that:\n\
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58 \n\
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59 @example\n\
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60 @group\n\
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61 norm (@var{y}) = 1\n\
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62 @var{v}' * @var{y} = 0\n\
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63 @var{x} = [@var{v}, @var{y}]*@var{h}'\n\
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64 @end group\n\
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65 @end example\n\
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66 \n\
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67 @end deftypefn")
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68 {
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69 octave_value_list retval;
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70
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71 int nargin = args.length ();
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72
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73 if (nargin != 2 || nargout > 2)
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74 {
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75 print_usage ();
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76 return retval;
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77 }
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78
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79 octave_value arg_x = args(0);
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80 octave_value arg_v = args(1);
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81
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82 if (arg_v.ndims () != 2 || arg_x.ndims () != 2 || arg_x.columns () != 1
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83 || arg_v.rows () != arg_x.rows ())
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84 {
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85 error ("mgorth: V should be a matrix, and X a column vector with"
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86 " the same number of rows as V.");
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87 return retval;
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88 }
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89
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90 if (! arg_x.is_numeric_type () && ! arg_v.is_numeric_type ())
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91 {
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92 error ("mgorth: X and V must be numeric");
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93 }
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94
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95 bool iscomplex = (arg_x.is_complex_type () || arg_v.is_complex_type ());
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96 if (arg_x.is_single_type () || arg_v.is_single_type ())
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97 {
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98 if (iscomplex)
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99 {
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100 FloatComplexColumnVector x
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101 = arg_x.float_complex_column_vector_value ();
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102 FloatComplexMatrix V = arg_v.float_complex_matrix_value ();
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103 FloatComplexRowVector h;
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104 do_mgorth (x, V, h);
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105 retval(1) = h;
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106 retval(0) = x;
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107 }
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108 else
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109 {
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110 FloatColumnVector x = arg_x.float_column_vector_value ();
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111 FloatMatrix V = arg_v.float_matrix_value ();
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112 FloatRowVector h;
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113 do_mgorth (x, V, h);
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114 retval(1) = h;
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115 retval(0) = x;
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116 }
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117 }
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118 else
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119 {
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120 if (iscomplex)
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121 {
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122 ComplexColumnVector x = arg_x.complex_column_vector_value ();
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123 ComplexMatrix V = arg_v.complex_matrix_value ();
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124 ComplexRowVector h;
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125 do_mgorth (x, V, h);
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126 retval(1) = h;
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127 retval(0) = x;
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128 }
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129 else
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130 {
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131 ColumnVector x = arg_x.column_vector_value ();
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132 Matrix V = arg_v.matrix_value ();
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133 RowVector h;
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134 do_mgorth (x, V, h);
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135 retval(1) = h;
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136 retval(0) = x;
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137 }
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138 }
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139
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140 return retval;
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141 }
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142
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143 /*
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144 %!test
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145 %! for ii=1:100
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146 %! assert (abs (mgorth (randn (5, 1), eye (5, 4))), [0 0 0 0 1]', eps);
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147 %! endfor
12509
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148
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149 %!test
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150 %! a = hilb (5);
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151 %! a(:, 1) /= norm (a(:, 1));
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152 %! for ii = 1:5
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153 %! a(:, ii) = mgorth (a(:, ii), a(:, 1:ii-1));
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154 %! endfor
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155 %! assert (a' * a, eye (5), 1e10);
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156 */