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1 // f-balance.cc -*- C++ -*- |
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2 /* |
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3 |
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4 Copyright (C) 1993, 1994 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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240
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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 "dbleAEPBAL.h" |
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33 #include "CmplxAEPBAL.h" |
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34 #include "dbleAEPBAL.h" |
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35 #include "CmplxAEPBAL.h" |
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36 #include "dbleGEPBAL.h" |
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37 |
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38 #include "tree-const.h" |
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39 #include "user-prefs.h" |
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49
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40 #include "gripes.h" |
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41 #include "error.h" |
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42 #include "defun-dld.h" |
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43 |
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44 DEFUN_DLD ("balance", Fbalance, Sbalance, 4, 4, |
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45 "AA = balance (A [, OPT]) or [[DD,] AA] = balance (A [, OPT])\n\ |
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46 \n\ |
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47 generalized eigenvalue problem:\n\ |
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48 \n\ |
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49 [cc, dd, aa, bb] = balance (a, b [, opt])\n\ |
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50 \n\ |
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51 where OPT is an optional single character argument as follows: \n\ |
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52 \n\ |
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53 N: no balancing; arguments copied, transformation(s) set to identity\n\ |
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54 P: permute argument(s) to isolate eigenvalues where possible\n\ |
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55 S: scale to improve accuracy of computed eigenvalues\n\ |
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56 B: (default) permute and scale, in that order. Rows/columns\n\ |
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57 of a (and b) that are isolated by permutation are not scaled\n\ |
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58 \n\ |
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59 [DD, AA] = balance (A, OPT) returns aa = dd\a*dd,\n\ |
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60 \n\ |
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61 [CC, DD, AA, BB] = balance (A, B, OPT) returns AA (BB) = CC*A*DD (CC*B*DD)") |
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62 { |
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63 Octave_object 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 < 2 || nargin > 4 || nargout < 0 || nargout > 4) |
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68 { |
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69 print_usage ("balance"); |
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70 return retval; |
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71 } |
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72 |
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73 char *bal_job; |
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74 int my_nargin; // # args w/o optional string arg |
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75 |
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76 // determine if balancing option is listed |
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77 // set my_nargin to the number of matrix inputs |
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78 if (args(nargin-1).const_type () == tree_constant_rep::string_constant) |
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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-2; |
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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-1; |
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87 } |
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88 |
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89 tree_constant arg = args(1).make_numeric (); |
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90 int a_nr = arg.rows (); |
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91 int a_nc = arg.columns (); |
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92 |
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93 // Check argument 1 dimensions. |
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94 |
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95 if (a_nr == 0 || a_nc == 0) |
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96 { |
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97 int flag = user_pref.propagate_empty_matrices; |
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98 if (flag != 0) |
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99 { |
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100 if (flag < 0) |
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101 warning ("balance: argument is empty matrix"); |
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102 |
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103 Matrix m; |
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104 retval.resize (2); |
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105 retval(0) = m; |
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106 retval(1) = m; |
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107 } |
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108 else |
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109 error ("balance: empty matrix is invalid as argument"); |
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110 |
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111 return retval; |
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112 } |
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113 |
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114 if (a_nr != a_nc) |
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115 { |
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116 gripe_square_matrix_required ("balance"); |
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117 return retval; |
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118 } |
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119 |
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120 // Extract argument 1 parameter for both AEP and GEP. |
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121 |
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122 Matrix aa; |
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123 ComplexMatrix caa; |
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124 if (arg.is_complex_type ()) |
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125 { |
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126 if (arg.is_matrix_type ()) |
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127 caa=arg.complex_matrix_value (); |
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128 else |
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129 { |
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130 caa.resize (1, 1); |
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131 caa.elem (0, 0) = arg.complex_value (); |
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132 } |
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133 } |
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134 else |
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135 { |
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136 if (arg.is_matrix_type ()) |
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137 aa = arg.matrix_value (); |
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138 else |
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139 { |
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140 double d = arg.double_value (); |
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141 aa.resize (1, 1); |
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142 aa.elem (0, 0) = d; |
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143 } |
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144 } |
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145 |
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146 // Treat AEP/ GEP cases. |
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147 |
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148 switch (my_nargin) |
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149 { |
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150 case 1: |
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151 |
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152 // Algebraic eigenvalue problem. |
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153 |
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154 retval.resize (nargout ? nargout : 1); |
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155 if (arg.is_complex_type ()) |
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156 { |
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157 ComplexAEPBALANCE result (caa, bal_job); |
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158 |
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159 if (nargout == 0 || nargout == 1) |
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160 retval(0) = result.balanced_matrix (); |
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161 else |
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162 { |
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163 retval(0) = result.balancing_matrix (); |
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164 retval(1) = result.balanced_matrix (); |
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165 } |
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166 } |
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167 else |
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168 { |
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169 AEPBALANCE result (aa, bal_job); |
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170 |
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171 if (nargout == 0 || nargout == 1) |
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172 retval(0) = result.balanced_matrix (); |
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173 else |
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174 { |
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175 retval(0) = result.balancing_matrix (); |
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176 retval(1) = result.balanced_matrix (); |
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177 } |
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178 } |
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179 break; |
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180 case 2: |
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181 |
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182 // Generalized eigenvalue problem. |
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183 |
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184 { |
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185 retval.resize (nargout ? nargout : 1); |
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186 |
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187 // 1st we have to check argument 2 dimensions and type... |
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188 |
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189 tree_constant brg = args(2).make_numeric (); |
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190 int b_nr = brg.rows (); |
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191 int b_nc = brg.columns (); |
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192 |
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193 // Check argument 2 dimensions -- must match arg 1. |
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194 |
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195 if ((b_nr != b_nc) || (b_nr != a_nr)) |
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196 { |
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197 gripe_nonconformant (); |
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198 return retval; |
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199 } |
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200 |
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201 // Now, extract the second matrix... |
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202 // Extract argument 1 parameter for both AEP and GEP. |
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203 |
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204 Matrix bb; |
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205 ComplexMatrix cbb; |
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206 if (brg.is_complex_type ()) |
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207 { |
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208 if (brg.is_matrix_type ()) |
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209 cbb = brg.complex_matrix_value (); |
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210 else |
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211 { |
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212 cbb.resize (1, 1); |
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213 cbb.elem (0, 0) = brg.complex_value (); |
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214 } |
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215 } |
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216 else |
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217 { |
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218 if (brg.is_matrix_type ()) |
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219 bb = brg.matrix_value (); |
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220 else |
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221 { |
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222 double d = brg.double_value (); |
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223 bb.resize (1, 1); |
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224 bb.elem (0, 0) = d; |
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225 } |
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226 } |
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227 |
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228 // Both matrices loaded, now let's check what kind of arithmetic: |
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229 |
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230 if (arg.is_complex_type () || brg.is_complex_type ()) |
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231 { |
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232 if (arg.is_real_type ()) |
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233 caa = aa; |
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234 else if (brg.is_real_type ()) |
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235 cbb = bb; |
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236 |
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237 // Compute magnitudes of elements for balancing purposes. |
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238 // Surely there's a function I can call someplace! |
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239 |
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240 for (int i = 0; i < a_nr; i++) |
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241 for (int j = 0; j < a_nr; j++) |
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242 { |
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243 aa.elem (i, j) = abs (caa.elem (i, j)); |
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244 bb.elem (i, j) = abs (cbb.elem (i, j)); |
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245 } |
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246 } |
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247 |
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248 GEPBALANCE result (aa, bb, bal_job); |
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249 |
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250 if (arg.is_complex_type () || brg.is_complex_type ()) |
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251 { |
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252 caa = result.left_balancing_matrix () * caa |
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253 * result.right_balancing_matrix (); |
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254 |
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255 cbb = result.left_balancing_matrix () * cbb |
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256 * result.right_balancing_matrix (); |
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257 |
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258 switch (nargout) |
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259 { |
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260 case 0: |
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261 case 1: |
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262 warning ("balance: should use two output arguments"); |
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263 retval(0) = caa; |
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264 break; |
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265 case 2: |
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266 retval(0) = caa; |
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267 retval(1) = cbb; |
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268 break; |
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269 case 4: |
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270 retval(0) = result.left_balancing_matrix (); |
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271 retval(1) = result.right_balancing_matrix (); |
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272 retval(2) = caa; |
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273 retval(3) = cbb; |
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274 break; |
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275 default: |
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276 error ("balance: invalid number of output arguments"); |
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277 break; |
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278 } |
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279 } |
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280 else |
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281 { |
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282 switch (nargout) |
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283 { |
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284 case 0: |
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285 case 1: |
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286 warning ("balance: should use two output arguments"); |
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287 retval(0) = result.balanced_a_matrix (); |
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288 break; |
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289 case 2: |
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290 retval(0) = result.balanced_a_matrix (); |
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291 retval(1) = result.balanced_b_matrix (); |
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292 break; |
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293 case 4: |
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294 retval(0) = result.left_balancing_matrix (); |
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295 retval(1) = result.right_balancing_matrix (); |
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296 retval(2) = result.balanced_a_matrix (); |
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297 retval(3) = result.balanced_b_matrix (); |
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298 break; |
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299 default: |
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300 error ("balance: invalid number of output arguments"); |
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301 break; |
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302 } |
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303 } |
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304 } |
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305 break; |
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306 default: |
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307 error ("balance requires one (AEP) or two (GEP) numeric arguments"); |
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308 break; |
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309 } |
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310 return retval; |
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311 } |
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312 |
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313 /* |
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314 ;;; Local Variables: *** |
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315 ;;; mode: C++ *** |
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316 ;;; page-delimiter: "^/\\*" *** |
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317 ;;; End: *** |
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318 */ |
