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1 /* |
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2 |
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3 Copyright (C) 1996, 1997 John W. Eaton |
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4 |
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5 This file is part of Octave. |
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6 |
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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 the |
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9 Free Software Foundation; either version 3 of the License, or (at your |
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10 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 WITHOUT |
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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15 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 |
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23 #ifdef HAVE_CONFIG_H |
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24 #include <config.h> |
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25 #endif |
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26 |
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27 #include "CmplxHESS.h" |
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28 #include "dbleHESS.h" |
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29 |
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30 #include "defun-dld.h" |
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31 #include "error.h" |
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32 #include "gripes.h" |
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33 #include "oct-obj.h" |
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34 #include "utils.h" |
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35 |
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36 DEFUN_DLD (hess, args, nargout, |
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37 "-*- texinfo -*-\n\ |
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38 @deftypefn {Loadable Function} {@var{h} =} hess (@var{a})\n\ |
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39 @deftypefnx {Loadable Function} {[@var{p}, @var{h}] =} hess (@var{a})\n\ |
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40 @cindex Hessenberg decomposition\n\ |
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41 Compute the Hessenberg decomposition of the matrix @var{a}.\n\ |
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42 \n\ |
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43 The Hessenberg decomposition is usually used as the first step in an\n\ |
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44 eigenvalue computation, but has other applications as well (see Golub,\n\ |
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45 Nash, and Van Loan, IEEE Transactions on Automatic Control, 1979). The\n\ |
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46 Hessenberg decomposition is\n\ |
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47 @iftex\n\ |
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48 @tex\n\ |
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49 $$\n\ |
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50 A = PHP^T\n\ |
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51 $$\n\ |
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52 where $P$ is a square unitary matrix ($P^HP = I$), and $H$\n\ |
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53 is upper Hessenberg ($H_{i,j} = 0, \\forall i \\ge j+1$).\n\ |
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54 @end tex\n\ |
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55 @end iftex\n\ |
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56 @ifinfo\n\ |
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57 @code{p * h * p' = a} where @code{p} is a square unitary matrix\n\ |
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58 (@code{p' * p = I}, using complex-conjugate transposition) and @code{h}\n\ |
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59 is upper Hessenberg (@code{i >= j+1 => h (i, j) = 0}).\n\ |
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60 @end ifinfo\n\ |
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61 @end deftypefn") |
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62 { |
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63 octave_value_list retval; |
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64 |
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65 int nargin = args.length (); |
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66 |
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67 if (nargin != 1 || nargout > 2) |
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68 { |
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69 print_usage (); |
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70 return retval; |
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71 } |
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72 |
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73 octave_value arg = args(0); |
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74 |
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75 octave_idx_type nr = arg.rows (); |
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76 octave_idx_type nc = arg.columns (); |
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77 |
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78 int arg_is_empty = empty_arg ("hess", nr, nc); |
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79 |
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80 if (arg_is_empty < 0) |
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81 return retval; |
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82 else if (arg_is_empty > 0) |
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83 return octave_value_list (2, Matrix ()); |
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84 |
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85 if (nr != nc) |
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86 { |
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87 gripe_square_matrix_required ("hess"); |
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88 return retval; |
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89 } |
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90 |
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91 if (arg.is_real_type ()) |
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92 { |
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93 Matrix tmp = arg.matrix_value (); |
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94 |
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95 if (! error_state) |
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96 { |
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97 HESS result (tmp); |
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98 |
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99 if (nargout == 0 || nargout == 1) |
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100 { |
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101 retval.resize (1); |
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102 retval(0) = result.hess_matrix (); |
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103 } |
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104 else |
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105 { |
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106 retval.resize (2); |
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107 retval(0) = result.unitary_hess_matrix (); |
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108 retval(1) = result.hess_matrix (); |
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109 } |
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110 } |
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111 } |
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112 else if (arg.is_complex_type ()) |
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113 { |
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114 ComplexMatrix ctmp = arg.complex_matrix_value (); |
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115 |
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116 if (! error_state) |
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117 { |
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118 ComplexHESS result (ctmp); |
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119 |
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120 if (nargout == 0 || nargout == 1) |
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121 { |
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122 retval.resize (1); |
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123 retval(0) = result.hess_matrix (); |
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124 } |
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125 else |
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126 { |
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127 retval.resize (2); |
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128 retval(0) = result.unitary_hess_matrix (); |
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129 retval(1) = result.hess_matrix (); |
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130 } |
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131 } |
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132 } |
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133 else |
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134 { |
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135 gripe_wrong_type_arg ("hess", arg); |
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136 } |
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137 |
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138 return retval; |
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139 } |
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140 |
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141 /* |
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142 ;;; Local Variables: *** |
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143 ;;; mode: C++ *** |
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144 ;;; End: *** |
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145 */ |
