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1 // f-syl.cc -*- C++ -*- |
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2 /* |
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3 |
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4 Copyright (C) 1993, 1994, 1995 John W. Eaton |
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5 |
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6 This file is part of Octave. |
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7 |
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8 Octave is free software; you can redistribute it and/or modify it |
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9 under the terms of the GNU General Public License as published by the |
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10 Free Software Foundation; either version 2, or (at your option) any |
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11 later version. |
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12 |
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13 Octave is distributed in the hope that it will be useful, but WITHOUT |
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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16 for more details. |
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17 |
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18 You should have received a copy of the GNU General Public License |
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19 along with Octave; see the file COPYING. If not, write to the Free |
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20 Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. |
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21 |
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22 */ |
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23 |
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24 // Written by A. S. Hodel <scotte@eng.auburn.edu> |
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25 |
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26 #ifdef 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 "dMatrix.h" |
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31 #include "CMatrix.h" |
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32 #include "dbleSCHUR.h" |
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33 #include "CmplxSCHUR.h" |
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234
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34 #include "f77-uscore.h" |
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35 |
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36 #include "tree-const.h" |
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37 #include "user-prefs.h" |
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38 #include "gripes.h" |
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39 #include "error.h" |
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40 #include "utils.h" |
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41 #include "help.h" |
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42 #include "defun-dld.h" |
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43 |
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44 extern "C" |
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45 { |
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46 int F77_FCN (dtrsyl) (const char*, const char*, const int&, |
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47 const int&, const int&, const double*, |
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48 const int&, const double*, const int&, |
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49 const double*, const int&, double&, int&, |
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50 long, long); |
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51 |
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52 int F77_FCN (ztrsyl) (const char*, const char*, const int&, |
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53 const int&, const int&, const Complex*, |
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54 const int&, const Complex*, const int&, |
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55 const Complex*, const int&, double&, int&, |
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56 long, long); |
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57 } |
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58 |
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59 DEFUN_DLD_BUILTIN ("syl", Fsyl, Ssyl, 4, 1, |
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60 "X = syl (A, B, C): solve the Sylvester equation A X + X B + C = 0") |
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61 { |
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62 Octave_object retval; |
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63 |
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64 int nargin = args.length (); |
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65 |
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66 if (nargin != 3 || nargout > 1) |
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67 { |
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68 print_usage ("syl"); |
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69 return retval; |
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70 } |
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71 |
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72 tree_constant arg_a = args(0); |
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73 tree_constant arg_b = args(1); |
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74 tree_constant arg_c = args(2); |
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75 |
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76 int a_nr = arg_a.rows (); |
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77 int a_nc = arg_a.columns (); |
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78 |
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79 int b_nr = arg_b.rows (); |
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80 int b_nc = arg_b.columns (); |
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81 |
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82 int c_nr = arg_c.rows (); |
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83 int c_nc = arg_c.columns (); |
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84 |
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85 int arg_a_is_empty = empty_arg ("syl", a_nr, a_nc); |
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86 int arg_b_is_empty = empty_arg ("syl", b_nr, b_nc); |
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87 int arg_c_is_empty = empty_arg ("syl", c_nr, c_nc); |
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88 |
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89 if (arg_a_is_empty > 0 && arg_b_is_empty > 0 && arg_c_is_empty > 0) |
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90 return Matrix (); |
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91 else if (arg_a_is_empty || arg_b_is_empty || arg_c_is_empty) |
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92 return retval; |
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93 |
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94 // Arguments are not empty, so check for correct dimensions. |
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95 |
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96 if (a_nr != a_nc || b_nr != b_nc) |
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97 { |
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98 gripe_square_matrix_required ("syl: first two parameters:"); |
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99 return retval; |
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100 } |
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101 else if (a_nr != c_nr || b_nr != c_nc) |
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102 { |
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103 gripe_nonconformant (); |
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104 return retval; |
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105 } |
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106 |
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107 // Dimensions look o.k., let's solve the problem. |
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108 |
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109 if (arg_a.is_complex_type () |
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110 || arg_b.is_complex_type () |
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111 || arg_c.is_complex_type ()) |
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112 { |
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113 |
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114 // Do everything in complex arithmetic; |
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115 |
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116 ComplexMatrix ca = arg_a.complex_matrix_value (); |
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117 |
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118 if (error_state) |
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119 return retval; |
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120 |
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121 ComplexMatrix cb = arg_b.complex_matrix_value (); |
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122 |
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123 if (error_state) |
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124 return retval; |
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125 |
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126 ComplexMatrix cc = arg_c.complex_matrix_value (); |
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127 |
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128 if (error_state) |
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129 return retval; |
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130 |
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131 // Compute Schur decompositions |
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132 |
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133 ComplexSCHUR as (ca, "U"); |
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134 ComplexSCHUR bs (cb, "U"); |
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135 |
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136 // Transform cc to new coordinates. |
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137 |
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138 ComplexMatrix ua = as.unitary_matrix (); |
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139 ComplexMatrix sch_a = as.schur_matrix (); |
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140 ComplexMatrix ub = bs.unitary_matrix (); |
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141 ComplexMatrix sch_b = bs.schur_matrix (); |
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142 |
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143 ComplexMatrix cx = ua.hermitian () * cc * ub; |
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144 |
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145 // Solve the sylvester equation, back-transform, and return the solution. |
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146 |
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147 double scale; |
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148 int info; |
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149 |
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150 F77_FCN (ztrsyl) ("N", "N", 1, a_nr, b_nr, |
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151 sch_a.fortran_vec (), a_nr, |
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152 sch_b.fortran_vec (), b_nr, |
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153 cx.fortran_vec (), a_nr, scale, info, |
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154 1L, 1L); |
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155 |
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156 cx = -ua * cx * ub.hermitian (); |
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157 |
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158 retval = cx; |
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159 } |
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160 else |
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161 { |
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162 |
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163 // Do everything in real arithmetic; |
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164 |
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165 Matrix ca = arg_a.matrix_value (); |
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166 |
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167 if (error_state) |
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168 return retval; |
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169 |
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170 Matrix cb = arg_b.matrix_value (); |
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171 |
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172 if (error_state) |
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173 return retval; |
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174 |
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175 Matrix cc = arg_c.matrix_value (); |
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176 |
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177 if (error_state) |
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178 return retval; |
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179 |
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180 // Compute Schur decompositions. |
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181 |
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182 SCHUR as (ca, "U"); |
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183 SCHUR bs (cb, "U"); |
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184 |
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185 // Transform cc to new coordinates. |
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186 |
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187 Matrix ua = as.unitary_matrix (); |
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188 Matrix sch_a = as.schur_matrix (); |
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189 Matrix ub = bs.unitary_matrix (); |
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190 Matrix sch_b = bs.schur_matrix (); |
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191 |
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192 Matrix cx = ua.transpose () * cc * ub; |
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193 |
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194 // Solve the sylvester equation, back-transform, and return the solution. |
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195 |
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196 double scale; |
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197 int info; |
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198 |
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199 F77_FCN (dtrsyl) ("N", "N", 1, a_nr, b_nr, |
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200 sch_a.fortran_vec (), a_nr, |
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201 sch_b.fortran_vec (), b_nr, |
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202 cx.fortran_vec (), a_nr, scale, info, |
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203 1L, 1L); |
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204 |
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205 if (info) |
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206 error ("syl: trouble in dtrsyl info = %d", info); |
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207 |
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208 cx = -ua*cx*ub.transpose (); |
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209 |
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210 retval = cx; |
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211 } |
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212 |
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213 return retval; |
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214 } |
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215 |
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216 /* |
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217 ;;; Local Variables: *** |
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218 ;;; mode: C++ *** |
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219 ;;; page-delimiter: "^/\\*" *** |
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220 ;;; End: *** |
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221 */ |
