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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 // Author: 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 "quit.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 "f77-fcn.h" |
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40 #include "gripes.h" |
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41 #include "oct-obj.h" |
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42 #include "utils.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_FUNC (dggbal, DGGBAL) (const char* JOB, const int& N, |
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47 double* A, const int& LDA, double* B, |
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48 const int& LDB, int& ILO, int& IHI, |
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49 double* LSCALE, double* RSCALE, |
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50 double* WORK, int& INFO, long); |
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51 |
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52 int F77_FUNC (dggbak, DGGBAK) (const char* JOB, const char* SIDE, |
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53 const int& N, const int& ILO, |
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54 const int& IHI, double* LSCALE, |
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55 double* RSCALE, int& M, double* V, |
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56 const int& LDV, int& INFO, long, long); |
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57 |
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58 int F77_FUNC (zggbal, ZGGBAL) (const char* JOB, const int& N, |
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59 Complex* A, const int& LDA, Complex* B, |
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60 const int& LDB, int& ILO, int& IHI, |
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61 double* LSCALE, double* RSCALE, |
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62 double* WORK, int& INFO, long); |
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63 } |
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64 |
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65 DEFUN_DLD (balance, args, nargout, |
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66 "-*- texinfo -*-\n\ |
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67 @deftypefn {Loadable Function} {@var{aa} =} balance (@var{a}, @var{opt})\n\ |
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68 @deftypefnx {Loadable Function} {[@var{dd}, @var{aa}] =} balance (@var{a}, @var{opt})\n\ |
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69 @deftypefnx {Loadable Function} {[@var{cc}, @var{dd}, @var{aa}, @var{bb}] =} balance (@var{a}, @var{b}, @var{opt})\n\ |
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70 \n\ |
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71 @code{[dd, aa] = balance (a)} returns @code{aa = dd \\ a * dd}.\n\ |
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72 @code{aa} is a matrix whose row and column norms are roughly equal in\n\ |
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73 magnitude, and @code{dd} = @code{p * d}, where @code{p} is a permutation\n\ |
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74 matrix and @code{d} is a diagonal matrix of powers of two. This allows\n\ |
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75 the equilibration to be computed without roundoff. Results of\n\ |
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76 eigenvalue calculation are typically improved by balancing first.\n\ |
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77 \n\ |
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78 @code{[cc, dd, aa, bb] = balance (a, b)} returns @code{aa = cc*a*dd} and\n\ |
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79 @code{bb = cc*b*dd)}, where @code{aa} and @code{bb} have non-zero\n\ |
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80 elements of approximately the same magnitude and @code{cc} and @code{dd}\n\ |
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81 are permuted diagonal matrices as in @code{dd} for the algebraic\n\ |
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82 eigenvalue problem.\n\ |
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83 \n\ |
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84 The eigenvalue balancing option @code{opt} is selected as follows:\n\ |
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85 \n\ |
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86 @table @asis\n\ |
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87 @item @code{\"N\"}, @code{\"n\"}\n\ |
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88 No balancing; arguments copied, transformation(s) set to identity.\n\ |
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89 \n\ |
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90 @item @code{\"P\"}, @code{\"p\"}\n\ |
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91 Permute argument(s) to isolate eigenvalues where possible.\n\ |
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92 \n\ |
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93 @item @code{\"S\"}, @code{\"s\"}\n\ |
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94 Scale to improve accuracy of computed eigenvalues.\n\ |
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95 \n\ |
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96 @item @code{\"B\"}, @code{\"b\"}\n\ |
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97 Permute and scale, in that order. Rows/columns of a (and b)\n\ |
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98 that are isolated by permutation are not scaled. This is the default\n\ |
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99 behavior.\n\ |
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100 @end table\n\ |
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101 \n\ |
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102 Algebraic eigenvalue balancing uses standard @sc{Lapack} routines.\n\ |
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103 \n\ |
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104 Generalized eigenvalue problem balancing uses Ward's algorithm\n\ |
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105 (SIAM Journal on Scientific and Statistical Computing, 1981).\n\ |
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106 @end deftypefn") |
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107 { |
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108 octave_value_list retval; |
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109 |
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110 int nargin = args.length (); |
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111 |
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112 if (nargin < 1 || nargin > 3 || nargout < 0 || nargout > 4) |
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113 { |
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114 print_usage ("balance"); |
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115 return retval; |
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116 } |
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117 |
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118 // determine if it's AEP or GEP |
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119 int AEPcase = nargin == 1 ? 1 : args(1).is_string (); |
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120 std::string bal_job; |
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121 |
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122 // problem dimension |
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123 int nn = args(0).rows (); |
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124 |
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125 int arg_is_empty = empty_arg ("balance", nn, args(0).columns()); |
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126 |
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127 if (arg_is_empty < 0) |
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128 return retval; |
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129 |
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130 if (arg_is_empty > 0) |
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131 return octave_value_list (2, Matrix ()); |
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132 |
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133 if (nn != args(0).columns()) |
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134 { |
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135 gripe_square_matrix_required ("balance"); |
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136 return retval; |
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137 } |
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138 |
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139 // Extract argument 1 parameter for both AEP and GEP. |
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140 Matrix aa; |
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141 ComplexMatrix caa; |
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142 |
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143 if (args(0).is_complex_type ()) |
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144 caa = args(0).complex_matrix_value (); |
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145 else |
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146 aa = args(0).matrix_value (); |
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147 |
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148 if (error_state) |
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149 return retval; |
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150 |
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151 // Treat AEP/GEP cases. |
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152 if (AEPcase) |
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153 { |
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154 // Algebraic eigenvalue problem. |
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155 |
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156 if (nargin == 1) |
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157 bal_job = "B"; |
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158 else if (args(1).is_string ()) |
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159 bal_job = args(1).string_value (); |
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160 else |
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161 { |
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162 error ("balance: AEP argument 2 must be a string"); |
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163 return retval; |
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164 } |
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165 |
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166 // balance the AEP |
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167 if (args(0).is_complex_type ()) |
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168 { |
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169 ComplexAEPBALANCE result (caa, 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(1) = result.balanced_matrix (); |
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176 retval(0) = result.balancing_matrix (); |
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177 } |
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178 } |
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179 else |
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180 { |
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181 AEPBALANCE result (aa, bal_job); |
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182 |
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183 if (nargout == 0 || nargout == 1) |
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184 retval(0) = result.balanced_matrix (); |
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185 else |
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186 { |
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187 retval(1) = result.balanced_matrix (); |
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188 retval(0) = result.balancing_matrix (); |
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189 } |
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190 } |
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191 } |
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192 else |
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193 { |
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194 // Generalized eigenvalue problem. |
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195 if (nargin == 2) |
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196 bal_job = "B"; |
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197 else if (args(2).is_string ()) |
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198 bal_job = args(2).string_value (); |
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199 else |
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200 { |
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201 error ("balance: GEP argument 3 must be a string"); |
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202 return retval; |
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203 } |
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204 |
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205 if ((nn != args(1).columns ()) || (nn != args(1).rows ())) |
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206 { |
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207 gripe_nonconformant (); |
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208 return retval; |
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209 } |
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210 |
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211 Matrix bb; |
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212 ComplexMatrix cbb; |
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213 |
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214 if (args(1).is_complex_type ()) |
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215 cbb = args(1).complex_matrix_value (); |
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216 else |
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217 bb = args(1).matrix_value (); |
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218 |
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219 if (error_state) |
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220 return retval; |
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221 |
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222 // Both matrices loaded, now let's check what kind of arithmetic: |
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223 // first, declare variables used in both the real and complex case |
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224 |
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225 int ilo, ihi, info; |
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226 RowVector lscale(nn), rscale(nn), work(6*nn); |
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227 char job = bal_job[0]; |
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228 |
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229 static int complex_case |
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230 = (args(0).is_complex_type () || args(1).is_complex_type ()); |
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231 |
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232 // now balance |
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233 if (complex_case) |
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234 { |
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235 if (args(0).is_real_type ()) |
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236 caa = ComplexMatrix (aa); |
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237 |
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238 if (args(1).is_real_type ()) |
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239 cbb = ComplexMatrix (bb); |
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240 |
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241 F77_XFCN (zggbal, ZGGBAL, |
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242 (&job, nn, caa.fortran_vec(), nn, |
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243 cbb.fortran_vec(), nn, ilo, ihi, |
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244 lscale.fortran_vec(), rscale.fortran_vec(), |
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245 work.fortran_vec(), info, 1L)); |
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246 |
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247 if (f77_exception_encountered) |
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248 { |
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249 error ("unrecoverable error in balance GEP"); |
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250 return retval; |
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251 } |
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252 } |
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253 else |
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254 { |
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255 // real matrices case |
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256 |
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257 F77_XFCN (dggbal, DGGBAL, |
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258 (&job, nn, aa.fortran_vec(), nn, bb.fortran_vec(), |
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259 nn, ilo, ihi, lscale.fortran_vec(), |
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260 rscale.fortran_vec(), work.fortran_vec(), info, 1L)); |
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261 |
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262 if (f77_exception_encountered) |
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263 { |
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264 error ("unrecoverable error in balance GEP"); |
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265 return retval; |
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266 } |
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267 } |
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268 |
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269 // Since we just want the balancing matrices, we can use dggbal |
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270 // for both the real and complex cases. |
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271 |
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272 Matrix Pl(nn,nn), Pr(nn,nn); |
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273 |
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274 for (int ii = 0; ii < nn; ii++) |
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275 for (int jj = 0; jj < nn; jj++) |
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276 { |
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277 OCTAVE_QUIT; |
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278 |
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279 Pl(ii,jj) = Pr(ii,jj) = (ii == jj ? 1.0 : 0.0); |
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280 } |
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281 |
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282 // left first |
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283 F77_XFCN (dggbak, DGGBAK, |
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284 (&job, "L", nn, ilo, ihi, lscale.fortran_vec(), |
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285 rscale.fortran_vec(), nn, Pl.fortran_vec(), |
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286 nn, info, 1L, 1L)); |
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287 |
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288 if (f77_exception_encountered) |
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289 { |
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290 error ("unrecoverable error in balance GEP(L)"); |
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291 return retval; |
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292 } |
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293 |
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294 // then right |
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295 F77_XFCN (dggbak, DGGBAK, |
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296 (&job, "R", nn, ilo, ihi, lscale.fortran_vec(), |
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297 rscale.fortran_vec(), nn, Pr.fortran_vec(), |
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298 nn, info, 1L, 1L)); |
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299 |
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300 if (f77_exception_encountered) |
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301 { |
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302 error ("unrecoverable error in balance GEP(R)"); |
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303 return retval; |
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304 } |
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305 |
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306 switch (nargout) |
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307 { |
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308 case 0: |
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309 case 1: |
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310 warning ("balance: used GEP, should have two output arguments"); |
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311 if (complex_case) |
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312 retval(0) = caa; |
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313 else |
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314 retval(0) = aa; |
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315 break; |
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316 |
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317 case 2: |
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318 if (complex_case) |
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319 { |
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320 retval(1) = cbb; |
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321 retval(0) = caa; |
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322 } |
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323 else |
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324 { |
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325 retval(1) = bb; |
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326 retval(0) = aa; |
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327 } |
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328 break; |
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329 |
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330 case 4: |
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331 if (complex_case) |
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332 { |
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333 retval(3) = cbb; |
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334 retval(2) = caa; |
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335 } |
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336 else |
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337 { |
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338 retval(3) = bb; |
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339 retval(2) = aa; |
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340 } |
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341 retval(1) = Pr; |
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342 retval(0) = Pl.transpose (); // so that aa_bal = cc*aa*dd, etc. |
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343 break; |
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344 |
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345 default: |
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346 error ("balance: invalid number of output arguments"); |
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347 break; |
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348 } |
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349 } |
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350 |
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351 return retval; |
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352 } |
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353 |
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354 /* |
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355 ;;; Local Variables: *** |
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356 ;;; mode: C++ *** |
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357 ;;; End: *** |
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358 */ |
