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annotate libinterp/corefcn/mgorth.cc @ 29961:7d6709900da7

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eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more Files affected: __betainc__.cc, __contourc__.cc, __eigs__.cc, __expint__.cc, __ftp__.cc, __gammainc__.cc, __ichol__.cc, __ilu__.cc, __magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, balance.cc, besselj.cc, bsxfun.cc, call-stack.cc, ccolamd.cc, cellfun.cc, chol.cc, colamd.cc, colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, defaults.cc, dirfns.cc, display.cc, dlmread.cc, dmperm.cc, dot.cc, eig.cc, ellipj.cc, environment.cc, error.cc, event-manager.cc, fft.cc, fft2.cc, fftn.cc, file-io.cc, find.cc, gcd.cc, getgrent.cc, getpwent.cc, getrusage.cc, gsvd.cc, hash.cc, help.cc, hess.cc, hex2num.cc, input.cc, inv.cc, jsondecode.cc, jsonencode.cc, load-path.cc, load-save.cc, lookup.cc, lsode.cc, lu.cc, max.cc, mgorth.cc, oct-hist.cc, ordqz.cc, ordschur.cc, pager.cc, pr-output.cc, psi.cc, qr.cc, quad.cc, quadcc.cc, qz.cc, rand.cc, regexp.cc, schur.cc, settings.cc, sighandlers.cc, sparse.cc, spparms.cc, sqrtm.cc, stream-euler.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc, symbfact.cc, symtab.cc, syscalls.cc, sysdep.cc, time.cc, toplev.cc, tril.cc, typecast.cc, urlwrite.cc, utils.cc, variables.cc, __delaunayn__.cc, __fltk_uigetfile__.cc, __glpk__.cc, __init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audiodevinfo.cc, audioread.cc, convhulln.cc, fftw.cc, gzip.cc, ov-cell.cc, ov-class.cc, ov-classdef.cc, ov-fcn-handle.cc, ov-struct.cc, ov-typeinfo.cc, ov-usr-fcn.cc, octave.cc, lex.ll, oct-parse.yy, profiler.cc, andpt-eval.cc.
author John W. Eaton <jwe@octave.org>
date Sat, 14 Aug 2021 22:48:52 -0400
parents 32c3a5805893
children 4f8284dee449
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) 2009-2021 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 h(j) = RowVector (Vcj.hermitian ()) * x;
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47 x -= h(j) * Vcj;
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48 }
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49
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50 h(Vc) = xnorm (x);
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51 if (std::real (h(Vc)) > 0)
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52 x /= h(Vc);
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53 }
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54
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55 DEFUN (mgorth, args, ,
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56 doc: /* -*- texinfo -*-
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57 @deftypefn {} {[@var{y}, @var{h}] =} mgorth (@var{x}, @var{v})
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58 Orthogonalize a given column vector @var{x} with respect to a set of
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59 orthonormal vectors comprising the columns of @var{v} using the modified
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60 Gram-Schmidt method.
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61
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62 On exit, @var{y} is a unit vector such that:
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63
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64 @example
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65 @group
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66 norm (@var{y}) = 1
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67 @var{v}' * @var{y} = 0
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68 @var{x} = [@var{v}, @var{y}]*@var{h}'
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69 @end group
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70 @end example
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71
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72 @end deftypefn */)
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73 {
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74 if (args.length () != 2)
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75 print_usage ();
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76
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77 octave_value arg_x = args(0);
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78 octave_value arg_v = args(1);
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79
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80 if (arg_v.ndims () != 2 || arg_x.ndims () != 2 || arg_x.columns () != 1
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81 || arg_v.rows () != arg_x.rows ())
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82 error ("mgorth: V should be a matrix, and X a column vector with"
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83 " the same number of rows as V.");
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84
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85 if (! arg_x.isnumeric () && ! arg_v.isnumeric ())
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86 error ("mgorth: X and V must be numeric");
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87
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88 octave_value_list retval;
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89
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90 bool iscomplex = (arg_x.iscomplex () || arg_v.iscomplex ());
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91 if (arg_x.is_single_type () || arg_v.is_single_type ())
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92 {
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93 if (iscomplex)
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94 {
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95 FloatComplexColumnVector x
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96 = arg_x.float_complex_column_vector_value ();
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97 FloatComplexMatrix V = arg_v.float_complex_matrix_value ();
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98 FloatComplexRowVector h;
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99 do_mgorth (x, V, h);
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100 retval = ovl (x, h);
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101 }
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102 else
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103 {
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104 FloatColumnVector x = arg_x.float_column_vector_value ();
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105 FloatMatrix V = arg_v.float_matrix_value ();
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106 FloatRowVector h;
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107 do_mgorth (x, V, h);
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108 retval = ovl (x, h);
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109 }
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110 }
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111 else
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112 {
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113 if (iscomplex)
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114 {
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115 ComplexColumnVector x = arg_x.complex_column_vector_value ();
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116 ComplexMatrix V = arg_v.complex_matrix_value ();
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117 ComplexRowVector h;
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118 do_mgorth (x, V, h);
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119 retval = ovl (x, h);
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120 }
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121 else
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122 {
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123 ColumnVector x = arg_x.column_vector_value ();
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124 Matrix V = arg_v.matrix_value ();
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125 RowVector h;
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126 do_mgorth (x, V, h);
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127 retval = ovl (x, h);
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128 }
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129 }
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130
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131 return retval;
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132 }
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133
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134 /*
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135 %!test
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136 %! for ii=1:100
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137 %! assert (abs (mgorth (randn (5, 1), eye (5, 4))), [0 0 0 0 1]', eps);
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138 %! endfor
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139
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140 %!test
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141 %! a = hilb (5);
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142 %! a(:, 1) /= norm (a(:, 1));
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143 %! for ii = 1:5
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144 %! a(:, ii) = mgorth (a(:, ii), a(:, 1:ii-1));
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145 %! endfor
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146 %! assert (a' * a, eye (5), 1e10);
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147 */
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148
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149 OCTAVE_NAMESPACE_END