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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 |
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36 #include "defun-dld.h" |
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37 #include "error.h" |
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38 #include "f77-fcn.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 extern "C" |
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44 { |
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45 int F77_FCN (dggbal, DGGBAL) (const char* JOB, const int& N, |
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46 double* A, const int& LDA, double* B, |
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47 const int& LDB, int& ILO, int& IHI, |
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48 double* LSCALE, double* RSCALE, |
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49 double* WORK, int& INFO, long); |
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50 |
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51 int F77_FCN (dggbak, DGGBAK) (const char* JOB, const char* SIDE, |
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52 const int& N, const int& ILO, |
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53 const int& IHI, double* LSCALE, |
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54 double* RSCALE, int& M, double* V, |
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55 const int& LDV, int& INFO, long, long); |
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56 |
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57 int F77_FCN (zggbal, ZGGBAL) (const char* JOB, const int& N, |
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58 Complex* A, const int& LDA, Complex* B, |
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59 const int& LDB, int& ILO, int& IHI, |
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60 double* LSCALE, double* RSCALE, |
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61 double* WORK, int& INFO, long); |
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62 } |
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63 |
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64 DEFUN_DLD (balance, args, nargout, |
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65 "-*- texinfo -*- |
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66 @deftypefn {Loadable Function} {@var{aa} =} balance (@var{a}, @var{opt})\n\ |
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67 @deftypefnx {Loadable Function} {[@var{dd}, @var{aa}] =} balance (@var{a}, @var{opt})\n\ |
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68 @deftypefnx {Loadable Function} {[@var{cc}, @var{dd}, @var{aa}, @var{bb}] =} balance (@var{a}, @var{b}, @var{opt})\n\ |
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69 \n\ |
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70 @code{[dd, aa] = balance (a)} returns @code{aa = dd \\ a * dd}.\n\ |
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71 @code{aa} is a matrix whose row and column norms are roughly equal in\n\ |
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72 magnitude, and @code{dd} = @code{p * d}, where @code{p} is a permutation\n\ |
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73 matrix and @code{d} is a diagonal matrix of powers of two. This allows\n\ |
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74 the equilibration to be computed without roundoff. Results of\n\ |
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75 eigenvalue calculation are typically improved by balancing first.\n\ |
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76 \n\ |
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77 @code{[cc, dd, aa, bb] = balance (a, b)} returns @code{aa = cc*a*dd} and\n\ |
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78 @code{bb = cc*b*dd)}, where @code{aa} and @code{bb} have non-zero\n\ |
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79 elements of approximately the same magnitude and @code{cc} and @code{dd}\n\ |
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80 are permuted diagonal matrices as in @code{dd} for the algebraic\n\ |
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81 eigenvalue problem.\n\ |
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82 \n\ |
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83 The eigenvalue balancing option @code{opt} is selected as follows:\n\ |
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84 \n\ |
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85 @table @asis\n\ |
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86 @item @code{\"N\"}, @code{\"n\"}\n\ |
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87 No balancing; arguments copied, transformation(s) set to identity.\n\ |
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88 \n\ |
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89 @item @code{\"P\"}, @code{\"p\"}\n\ |
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90 Permute argument(s) to isolate eigenvalues where possible.\n\ |
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91 \n\ |
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92 @item @code{\"S\"}, @code{\"s\"}\n\ |
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93 Scale to improve accuracy of computed eigenvalues.\n\ |
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94 \n\ |
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95 @item @code{\"B\"}, @code{\"b\"}\n\ |
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96 Permute and scale, in that order. Rows/columns of a (and b)\n\ |
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97 that are isolated by permutation are not scaled. This is the default\n\ |
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98 behavior.\n\ |
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99 @end table\n\ |
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100 \n\ |
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101 Algebraic eigenvalue balancing uses standard @sc{Lapack} routines.\n\ |
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102 \n\ |
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103 Generalized eigenvalue problem balancing uses Ward's algorithm\n\ |
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104 (SIAM Journal on Scientific and Statistical Computing, 1981).\n\ |
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105 @end deftypefn") |
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106 { |
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107 octave_value_list retval; |
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108 |
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109 int nargin = args.length (); |
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110 |
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111 if (nargin < 1 || nargin > 3 || nargout < 0 || nargout > 4) |
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112 { |
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113 print_usage ("balance"); |
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114 return retval; |
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115 } |
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116 |
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117 // determine if it's AEP or GEP |
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118 int AEPcase = nargin == 1 ? 1 : args(1).is_string (); |
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119 std::string bal_job; |
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120 |
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121 // problem dimension |
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122 int nn = args(0).rows (); |
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123 |
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124 int arg_is_empty = empty_arg ("balance", nn, args(0).columns()); |
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125 |
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126 if (arg_is_empty < 0) |
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127 return retval; |
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128 |
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129 if (arg_is_empty > 0) |
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130 return octave_value_list (2, Matrix ()); |
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131 |
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132 if (nn != args(0).columns()) |
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133 { |
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134 gripe_square_matrix_required ("balance"); |
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135 return retval; |
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136 } |
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137 |
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138 // Extract argument 1 parameter for both AEP and GEP. |
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139 Matrix aa; |
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140 ComplexMatrix caa; |
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141 |
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142 if (args(0).is_complex_type ()) |
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143 caa = args(0).complex_matrix_value (); |
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144 else |
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145 aa = args(0).matrix_value (); |
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146 |
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147 if (error_state) |
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148 return retval; |
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149 |
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150 // Treat AEP/GEP cases. |
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151 if (AEPcase) |
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152 { |
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153 // Algebraic eigenvalue problem. |
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154 |
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155 if (nargin == 1) |
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156 bal_job = "B"; |
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157 else if (args(1).is_string ()) |
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158 bal_job = args(1).string_value (); |
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159 else |
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160 { |
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161 error ("balance: AEP argument 2 must be a string"); |
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162 return retval; |
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163 } |
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164 |
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165 // balance the AEP |
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166 if (args(0).is_complex_type ()) |
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167 { |
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168 ComplexAEPBALANCE result (caa, bal_job); |
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169 |
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170 if (nargout == 0 || nargout == 1) |
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171 retval(0) = result.balanced_matrix (); |
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172 else |
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173 { |
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174 retval(1) = result.balanced_matrix (); |
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175 retval(0) = result.balancing_matrix (); |
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176 } |
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177 } |
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178 else |
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179 { |
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180 AEPBALANCE result (aa, bal_job); |
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181 |
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182 if (nargout == 0 || nargout == 1) |
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183 retval(0) = result.balanced_matrix (); |
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184 else |
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185 { |
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186 retval(1) = result.balanced_matrix (); |
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187 retval(0) = result.balancing_matrix (); |
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188 } |
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189 } |
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190 } |
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191 else |
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192 { |
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193 // Generalized eigenvalue problem. |
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194 if (nargin == 2) |
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195 bal_job = "B"; |
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196 else if (args(2).is_string ()) |
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197 bal_job = args(2).string_value (); |
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198 else |
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199 { |
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200 error ("balance: GEP argument 3 must be a string"); |
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201 return retval; |
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202 } |
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203 |
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204 if ((nn != args(1).columns ()) || (nn != args(1).rows ())) |
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205 { |
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206 gripe_nonconformant (); |
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207 return retval; |
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208 } |
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209 |
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210 Matrix bb; |
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211 ComplexMatrix cbb; |
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212 |
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213 if (args(1).is_complex_type ()) |
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214 cbb = args(1).complex_matrix_value (); |
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215 else |
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216 bb = args(1).matrix_value (); |
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217 |
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218 if (error_state) |
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219 return retval; |
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220 |
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221 // Both matrices loaded, now let's check what kind of arithmetic: |
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222 // first, declare variables used in both the real and complex case |
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223 |
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224 int ilo, ihi, info; |
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225 RowVector lscale(nn), rscale(nn), work(6*nn); |
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226 char job = bal_job[0]; |
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227 |
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228 static int complex_case |
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229 = (args(0).is_complex_type () || args(1).is_complex_type ()); |
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230 |
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231 // now balance |
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232 if (complex_case) |
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233 { |
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234 if (args(0).is_real_type ()) |
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235 caa = aa; |
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236 |
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237 if (args(1).is_real_type ()) |
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238 cbb = bb; |
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239 |
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240 F77_XFCN (zggbal, ZGGBAL, |
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241 (&job, nn, caa.fortran_vec(), nn, |
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242 cbb.fortran_vec(), nn, ilo, ihi, |
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243 lscale.fortran_vec(), rscale.fortran_vec(), |
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244 work.fortran_vec(), info, 1L)); |
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245 |
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246 if (f77_exception_encountered) |
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247 { |
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248 error ("unrecoverable error in balance GEP"); |
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249 return retval; |
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250 } |
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251 } |
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252 else |
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253 { |
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254 // real matrices case |
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255 |
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256 F77_XFCN (dggbal, DGGBAL, |
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257 (&job, nn, aa.fortran_vec(), nn, bb.fortran_vec(), |
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258 nn, ilo, ihi, lscale.fortran_vec(), |
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259 rscale.fortran_vec(), work.fortran_vec(), info, 1L)); |
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260 |
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261 if (f77_exception_encountered) |
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262 { |
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263 error ("unrecoverable error in balance GEP"); |
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264 return retval; |
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265 } |
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266 } |
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267 |
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268 // Since we just want the balancing matrices, we can use dggbal |
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269 // for both the real and complex cases. |
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270 |
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271 Matrix Pl(nn,nn), Pr(nn,nn); |
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272 |
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273 for (int ii = 0; ii < nn; ii++) |
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274 for (int jj = 0; jj < nn; jj++) |
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275 Pl(ii,jj) = Pr(ii,jj) = (ii == jj ? 1.0 : 0.0); |
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276 |
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277 // left first |
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278 F77_XFCN (dggbak, DGGBAK, |
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279 (&job, "L", nn, ilo, ihi, lscale.fortran_vec(), |
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280 rscale.fortran_vec(), nn, Pl.fortran_vec(), |
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281 nn, info, 1L, 1L)); |
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282 |
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283 if (f77_exception_encountered) |
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284 { |
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285 error ("unrecoverable error in balance GEP(L)"); |
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286 return retval; |
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287 } |
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288 |
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289 // then right |
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290 F77_XFCN (dggbak, DGGBAK, |
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291 (&job, "R", nn, ilo, ihi, lscale.fortran_vec(), |
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292 rscale.fortran_vec(), nn, Pr.fortran_vec(), |
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293 nn, info, 1L, 1L)); |
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294 |
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295 if (f77_exception_encountered) |
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296 { |
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297 error ("unrecoverable error in balance GEP(R)"); |
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298 return retval; |
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299 } |
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300 |
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301 switch (nargout) |
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302 { |
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303 case 0: |
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304 case 1: |
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305 warning ("balance: used GEP, should have two output arguments"); |
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306 if (complex_case) |
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307 retval(0) = caa; |
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308 else |
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309 retval(0) = aa; |
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310 break; |
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311 |
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312 case 2: |
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313 if (complex_case) |
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314 { |
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315 retval(1) = cbb; |
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316 retval(0) = caa; |
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317 } |
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318 else |
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319 { |
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320 retval(1) = bb; |
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321 retval(0) = aa; |
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322 } |
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323 break; |
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324 |
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325 case 4: |
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326 if (complex_case) |
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327 { |
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328 retval(3) = cbb; |
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329 retval(2) = caa; |
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330 } |
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331 else |
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332 { |
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333 retval(3) = bb; |
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334 retval(2) = aa; |
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335 } |
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336 retval(1) = Pr; |
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337 retval(0) = Pl.transpose (); // so that aa_bal = cc*aa*dd, etc. |
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338 break; |
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339 |
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340 default: |
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341 error ("balance: invalid number of output arguments"); |
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342 break; |
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343 } |
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344 } |
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345 |
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346 return retval; |
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347 } |
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348 |
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349 /* |
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350 ;;; Local Variables: *** |
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351 ;;; mode: C++ *** |
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352 ;;; End: *** |
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353 */ |
