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annotate libinterp/corefcn/givens.cc @ 23220:092078913d54

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maint: Merge stable to default.
author John W. Eaton <jwe@octave.org>
date Wed, 22 Feb 2017 12:58:07 -0500
parents ef4d915df748 3ac9f9ecfae5
children c3075ae020e1
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1 /*
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2
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3 Copyright (C) 1996-2017 John W. Eaton
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4
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5 This file is part of Octave.
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6
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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7 Octave is free software; you can redistribute it and/or modify it
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8 under the terms of the GNU General Public License as published by
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9 the Free Software Foundation; either version 3 of the License, or
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10 (at your option) any later version.
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11
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12 Octave is distributed in the hope that it will be useful, but
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13 WITHOUT ANY WARRANTY; without even the implied warranty of
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14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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15 GNU General Public License for more details.
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16
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17 You should have received a copy of the GNU General Public License
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18 along with Octave; see the file COPYING. If not, see
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19 <http://www.gnu.org/licenses/>.
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20
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21 */
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22
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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23 // Originally written by A. S. Hodel <scotte@eng.auburn.edu>
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24
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25 #if defined (HAVE_CONFIG_H)
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26 # include "config.h"
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27 #endif
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28
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29 #include "defun.h"
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30 #include "error.h"
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31 #include "ovl.h"
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32
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33 DEFUN (givens, args, nargout,
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34 doc: /* -*- texinfo -*-
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35 @deftypefn {} {@var{G} =} givens (@var{x}, @var{y})
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36 @deftypefnx {} {[@var{c}, @var{s}] =} givens (@var{x}, @var{y})
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37 Compute the Givens rotation matrix @var{G}.
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38
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39 @tex
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40 The Givens matrix is a $2\times 2$ orthogonal matrix
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41 $$
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42 G = \left[\matrix{c & s\cr -s'& c\cr}\right]
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43 $$
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44 such that
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45 $$
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46 G \left[\matrix{x\cr y}\right] = \left[\matrix{\ast\cr 0}\right]
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47 $$
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48 with $x$ and $y$ scalars.
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49 @end tex
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50 @ifnottex
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51 The Givens matrix is a 2 by 2 orthogonal matrix
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52
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53 @code{@var{g} = [@var{c} @var{s}; -@var{s}' @var{c}]}
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54
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55 such that
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56
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57 @code{@var{g} [@var{x}; @var{y}] = [*; 0]}
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58
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59 with @var{x} and @var{y} scalars.
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60 @end ifnottex
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61
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62 If two output arguments are requested, return the factors @var{c} and
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63 @var{s} rather than the Givens rotation matrix.
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64
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65 For example:
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66
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67 @example
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68 @group
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69 givens (1, 1)
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70 @result{} 0.70711 0.70711
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71 -0.70711 0.70711
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72 @end group
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73 @end example
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74 @seealso{planerot}
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75 @end deftypefn */)
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76 {
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77 if (args.length () != 2)
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78 print_usage ();
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79
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80 octave_value_list retval;
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81
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82 if (args(0).is_single_type () || args(1).is_single_type ())
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83 {
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84 if (args(0).is_complex_type () || args(1).is_complex_type ())
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85 {
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86 FloatComplex cx = args(0).float_complex_value ();
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87 FloatComplex cy = args(1).float_complex_value ();
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88
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89 FloatComplexMatrix result = Givens (cx, cy);
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90
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91 switch (nargout)
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92 {
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93 case 0:
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94 case 1:
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95 retval = ovl (result);
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96 break;
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97
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98 case 2:
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99 retval = ovl (result(0, 0), result(0, 1));
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100 break;
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101 }
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102 }
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103 else
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104 {
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105 float x = args(0).float_value ();
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106 float y = args(1).float_value ();
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107
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108 FloatMatrix result = Givens (x, y);
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109
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110 switch (nargout)
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111 {
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112 case 0:
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113 case 1:
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114 retval = ovl (result);
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115 break;
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116
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117 case 2:
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118 retval = ovl (result(0, 0), result(0, 1));
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119 break;
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120 }
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121 }
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122 }
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123 else
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124 {
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125 if (args(0).is_complex_type () || args(1).is_complex_type ())
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126 {
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127 Complex cx = args(0).complex_value ();
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128 Complex cy = args(1).complex_value ();
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129
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130 ComplexMatrix result = Givens (cx, cy);
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131
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132 switch (nargout)
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133 {
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134 case 0:
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135 case 1:
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136 retval = ovl (result);
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137 break;
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138
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139 case 2:
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140 retval = ovl (result(0, 0), result(0, 1));
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141 break;
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142 }
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143 }
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144 else
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145 {
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146 double x = args(0).double_value ();
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147 double y = args(1).double_value ();
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148
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149 Matrix result = Givens (x, y);
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150
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151 switch (nargout)
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152 {
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153 case 0:
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154 case 1:
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José Luis García Pallero <jgpallero@gmail.com>
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155 retval = ovl (result);
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156 break;
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157
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158 case 2:
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159 retval = ovl (result(0, 0), result(0, 1));
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160 break;
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161 }
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162 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
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163 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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164
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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165 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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166 }
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167
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168 /*
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169 %!assert (givens (1,1), [1, 1; -1, 1] / sqrt (2), 2*eps)
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170 %!assert (givens (1,0), eye (2))
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171 %!assert (givens (0,1), [0, 1; -1 0])
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172
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173 %!error givens ()
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174 %!error givens (1)
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175 %!error [a,b,c] = givens (1, 1)
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176 */