Mercurial > octave
annotate libinterp/corefcn/mgorth.cc @ 31706:597f3ee61a48 stable
update Octave Project Developers copyright for the new year
author | John W. Eaton <jwe@octave.org> |
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date | Fri, 06 Jan 2023 13:11:27 -0500 |
parents | e88a07dec498 |
children | 2e484f9f1f18 |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 2009-2023 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_BEGIN_NAMESPACE(octave) |
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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_END_NAMESPACE(octave) |