annotate libinterp/corefcn/givens.cc @ 33617:ec2635a02328 bytecode-interpreter tip

maint: Merge default to bytecode-interpreter.
author Markus Mützel <markus.muetzel@gmx.de>
date Tue, 21 May 2024 18:29:03 +0200
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1 ////////////////////////////////////////////////////////////////////////
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2 //
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3 // Copyright (C) 1996-2024 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 // Originally written by A. S. Hodel <scotte@eng.auburn.edu>
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27
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28 #if defined (HAVE_CONFIG_H)
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29 # include "config.h"
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30 #endif
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31
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32 #include "defun.h"
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33 #include "error.h"
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34 #include "ovl.h"
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35
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36 OCTAVE_BEGIN_NAMESPACE(octave)
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37
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38 DEFUN (givens, args, nargout,
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39 doc: /* -*- texinfo -*-
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40 @deftypefn {} {@var{G} =} givens (@var{x}, @var{y})
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41 @deftypefnx {} {[@var{c}, @var{s}] =} givens (@var{x}, @var{y})
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42 Compute the Givens rotation matrix @var{G}.
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43
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44 @tex
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45 The Givens matrix is a $2\times 2$ orthogonal matrix
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46 $$
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47 G = \left[\matrix{c & s\cr -s'& c\cr}\right]
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48 $$
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49 such that
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50 $$
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51 G \left[\matrix{x\cr y}\right] = \left[\matrix{\ast\cr 0}\right]
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52 $$
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53 with $x$ and $y$ scalars.
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54 @end tex
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55 @ifnottex
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56 The Givens matrix is a 2-by-2 orthogonal matrix
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57
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58 @example
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59 @group
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60 @var{G} = [ @var{c} , @var{s}
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61 -@var{s}', @var{c}]
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62 @end group
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63 @end example
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64
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65 @noindent
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66 such that
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67
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68 @example
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69 @var{G} * [@var{x}; @var{y}] = [*; 0]
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70 @end example
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71
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72 @noindent
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73 with @var{x} and @var{y} scalars.
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74 @end ifnottex
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75
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76 If two output arguments are requested, return the factors @var{c} and @var{s}
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77 rather than the Givens rotation matrix.
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78
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79 For example:
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80
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81 @example
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82 @group
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83 givens (1, 1)
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84 @result{} 0.70711 0.70711
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85 -0.70711 0.70711
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86 @end group
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87 @end example
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88
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89 Note: The Givens matrix represents a counterclockwise rotation of a 2-D
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90 plane and can be used to introduce zeros into a matrix prior to complete
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91 factorization.
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92 @seealso{planerot, qr}
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93 @end deftypefn */)
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94 {
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95 if (args.length () != 2)
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96 print_usage ();
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97
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98 octave_value_list retval;
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99
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100 if (args(0).is_single_type () || args(1).is_single_type ())
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101 {
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102 if (args(0).iscomplex () || args(1).iscomplex ())
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103 {
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104 FloatComplex cx = args(0).float_complex_value ();
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105 FloatComplex cy = args(1).float_complex_value ();
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106
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107 FloatComplexMatrix result = Givens (cx, cy);
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108
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109 switch (nargout)
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110 {
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111 case 0:
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112 case 1:
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113 retval = ovl (result);
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114 break;
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115
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116 case 2:
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117 retval = ovl (result(0, 0), result(0, 1));
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118 break;
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119 }
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120 }
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121 else
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122 {
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123 float x = args(0).float_value ();
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124 float y = args(1).float_value ();
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125
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126 FloatMatrix result = Givens (x, y);
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127
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128 switch (nargout)
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129 {
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130 case 0:
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131 case 1:
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132 retval = ovl (result);
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133 break;
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134
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135 case 2:
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136 retval = ovl (result(0, 0), result(0, 1));
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137 break;
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138 }
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139 }
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140 }
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141 else
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142 {
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143 if (args(0).iscomplex () || args(1).iscomplex ())
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144 {
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145 Complex cx = args(0).complex_value ();
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146 Complex cy = args(1).complex_value ();
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147
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148 ComplexMatrix result = Givens (cx, cy);
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149
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150 switch (nargout)
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151 {
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152 case 0:
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153 case 1:
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154 retval = ovl (result);
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155 break;
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82be108cc558 First attempt at single precision tyeps
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156
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157 case 2:
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158 retval = ovl (result(0, 0), result(0, 1));
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159 break;
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160 }
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161 }
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162 else
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163 {
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164 double x = args(0).double_value ();
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165 double y = args(1).double_value ();
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166
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167 Matrix result = Givens (x, y);
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168
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169 switch (nargout)
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170 {
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171 case 0:
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172 case 1:
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173 retval = ovl (result);
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174 break;
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175
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176 case 2:
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177 retval = ovl (result(0, 0), result(0, 1));
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178 break;
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179 }
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180 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
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181 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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182
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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183 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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184 }
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185
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186 /*
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187 %!assert (givens (1,1), [1, 1; -1, 1] / sqrt (2), 2*eps)
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188 %!assert (givens (1,0), eye (2))
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189 %!assert (givens (0,1), [0, 1; -1 0])
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190
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191 %!error givens ()
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192 %!error givens (1)
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193 %!error [a,b,c] = givens (1, 1)
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194 */
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195
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196 OCTAVE_END_NAMESPACE(octave)