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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 2, or (at your option) any |
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10 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, write to the Free |
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19 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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20 |
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21 */ |
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22 |
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23 // Written by A. S. Hodel <scotte@eng.auburn.edu> |
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24 |
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25 #ifdef 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 <string> |
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30 |
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31 #include "CmplxAEPBAL.h" |
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32 #include "CmplxAEPBAL.h" |
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33 #include "dbleAEPBAL.h" |
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34 #include "dbleAEPBAL.h" |
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35 #include "dbleGEPBAL.h" |
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36 |
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37 #include "defun-dld.h" |
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38 #include "error.h" |
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39 #include "gripes.h" |
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40 #include "oct-obj.h" |
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41 #include "utils.h" |
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42 |
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43 DEFUN_DLD (balance, args, nargout, |
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44 "AA = balance (A [, OPT]) or [[DD,] AA] = balance (A [, OPT])\n\ |
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45 \n\ |
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46 generalized eigenvalue problem:\n\ |
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47 \n\ |
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48 [cc, dd, aa, bb] = balance (a, b [, opt])\n\ |
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49 \n\ |
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50 where OPT is an optional single character argument as follows: \n\ |
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51 \n\ |
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52 N: no balancing; arguments copied, transformation(s) set to identity\n\ |
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53 P: permute argument(s) to isolate eigenvalues where possible\n\ |
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54 S: scale to improve accuracy of computed eigenvalues\n\ |
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55 B: (default) permute and scale, in that order. Rows/columns\n\ |
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56 of a (and b) that are isolated by permutation are not scaled\n\ |
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57 \n\ |
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58 [DD, AA] = balance (A, OPT) returns aa = inv(dd)*a*dd,\n\ |
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59 \n\ |
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60 [CC, DD, AA, BB] = balance (A, B, OPT) returns AA (BB) = CC*A*DD (CC*B*DD)") |
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61 { |
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62 octave_value_list 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 < 1 || nargin > 3 || nargout < 0 || nargout > 4) |
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67 { |
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68 print_usage ("balance"); |
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69 return retval; |
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70 } |
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71 |
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72 string bal_job; |
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73 int my_nargin; // # args w/o optional string arg |
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74 |
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75 // Determine if balancing option is listed. Set my_nargin to the |
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76 // number of matrix inputs. |
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77 |
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78 if (args(nargin-1).is_string ()) |
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79 { |
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80 bal_job = args(nargin-1).string_value (); |
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81 my_nargin = nargin-1; |
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82 } |
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83 else |
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84 { |
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85 bal_job = "B"; |
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86 my_nargin = nargin; |
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87 } |
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88 |
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89 octave_value arg_a = args(0); |
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90 |
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91 int a_nr = arg_a.rows (); |
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92 int a_nc = arg_a.columns (); |
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93 |
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94 // Check argument 1 dimensions. |
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95 |
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96 int arg_is_empty = empty_arg ("balance", a_nr, a_nc); |
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97 |
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98 if (arg_is_empty < 0) |
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99 return retval; |
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100 if (arg_is_empty > 0) |
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101 return octave_value_list (2, Matrix ()); |
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102 |
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103 if (a_nr != a_nc) |
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104 { |
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105 gripe_square_matrix_required ("balance"); |
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106 return retval; |
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107 } |
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108 |
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109 // Extract argument 1 parameter for both AEP and GEP. |
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110 |
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111 Matrix aa; |
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112 ComplexMatrix caa; |
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113 if (arg_a.is_complex_type ()) |
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114 caa = arg_a.complex_matrix_value (); |
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115 else |
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116 aa = arg_a.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 // Treat AEP/GEP cases. |
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122 |
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123 switch (my_nargin) |
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124 { |
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125 case 1: |
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126 |
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127 // Algebraic eigenvalue problem. |
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128 |
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129 if (arg_a.is_complex_type ()) |
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130 { |
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131 ComplexAEPBALANCE result (caa, bal_job); |
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132 |
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133 if (nargout == 0 || nargout == 1) |
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134 retval(0) = result.balanced_matrix (); |
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135 else |
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136 { |
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137 retval(1) = result.balanced_matrix (); |
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138 retval(0) = result.balancing_matrix (); |
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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 AEPBALANCE result (aa, bal_job); |
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144 |
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145 if (nargout == 0 || nargout == 1) |
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146 retval(0) = result.balanced_matrix (); |
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147 else |
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148 { |
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149 retval(1) = result.balanced_matrix (); |
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150 retval(0) = result.balancing_matrix (); |
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151 } |
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152 } |
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153 break; |
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154 |
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155 case 2: |
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156 { |
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157 // Generalized eigenvalue problem. |
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158 |
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159 // 1st we have to check argument 2 dimensions and type... |
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160 |
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161 octave_value arg_b = args(1); |
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162 |
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163 int b_nr = arg_b.rows (); |
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164 int b_nc = arg_b.columns (); |
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165 |
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166 // Check argument 2 dimensions -- must match arg 1. |
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167 |
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168 if (b_nr != b_nc || b_nr != a_nr) |
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169 { |
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170 gripe_nonconformant (); |
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171 return retval; |
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172 } |
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173 |
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174 // Now, extract the second matrix... |
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175 // Extract argument 1 parameter for both AEP and GEP. |
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176 |
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177 Matrix bb; |
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178 ComplexMatrix cbb; |
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179 if (arg_b.is_complex_type ()) |
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180 cbb = arg_b.complex_matrix_value (); |
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181 else |
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182 bb = arg_b.matrix_value (); |
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183 |
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184 if (error_state) |
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185 return retval; |
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186 |
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187 // Both matrices loaded, now let's check what kind of arithmetic: |
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188 |
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189 if (arg_a.is_complex_type () || arg_b.is_complex_type ()) |
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190 { |
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191 if (arg_a.is_real_type ()) |
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192 caa = aa; |
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193 |
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194 if (arg_b.is_real_type ()) |
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195 cbb = bb; |
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196 |
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197 // Compute magnitudes of elements for balancing purposes. |
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198 // Surely there's a function I can call someplace! |
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199 |
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200 for (int i = 0; i < a_nr; i++) |
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201 for (int j = 0; j < a_nc; j++) |
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202 { |
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203 aa (i, j) = abs (caa (i, j)); |
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204 bb (i, j) = abs (cbb (i, j)); |
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205 } |
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206 } |
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207 |
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208 GEPBALANCE result (aa, bb, bal_job); |
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209 |
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210 if (arg_a.is_complex_type () || arg_b.is_complex_type ()) |
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211 { |
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212 caa = result.left_balancing_matrix () * caa |
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213 * result.right_balancing_matrix (); |
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214 |
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215 cbb = result.left_balancing_matrix () * cbb |
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216 * result.right_balancing_matrix (); |
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217 |
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218 switch (nargout) |
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219 { |
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220 case 0: |
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221 case 1: |
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222 warning ("balance: should use two output arguments"); |
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223 retval(0) = caa; |
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224 break; |
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225 |
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226 case 2: |
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227 retval(1) = cbb; |
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228 retval(0) = caa; |
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229 break; |
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230 |
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231 case 4: |
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232 retval(3) = cbb; |
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233 retval(2) = caa; |
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234 retval(1) = result.right_balancing_matrix (); |
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235 retval(0) = result.left_balancing_matrix (); |
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236 break; |
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237 |
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238 default: |
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239 error ("balance: invalid number of output arguments"); |
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240 break; |
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241 } |
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242 } |
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243 else |
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244 { |
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245 switch (nargout) |
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246 { |
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247 case 0: |
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248 case 1: |
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249 warning ("balance: should use two output arguments"); |
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250 retval(0) = result.balanced_a_matrix (); |
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251 break; |
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252 |
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253 case 2: |
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254 retval(1) = result.balanced_b_matrix (); |
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255 retval(0) = result.balanced_a_matrix (); |
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256 break; |
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257 |
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258 case 4: |
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259 retval(3) = result.balanced_b_matrix (); |
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260 retval(2) = result.balanced_a_matrix (); |
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261 retval(1) = result.right_balancing_matrix (); |
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262 retval(0) = result.left_balancing_matrix (); |
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263 break; |
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264 |
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265 default: |
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266 error ("balance: invalid number of output arguments"); |
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267 break; |
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268 } |
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269 } |
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270 } |
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271 break; |
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272 |
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273 default: |
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274 error ("balance requires one (AEP) or two (GEP) numeric arguments"); |
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275 break; |
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276 } |
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277 |
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278 return retval; |
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279 } |
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280 |
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281 /* |
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282 ;;; Local Variables: *** |
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283 ;;; mode: C++ *** |
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284 ;;; End: *** |
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285 */ |
