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1 /* |
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2 |
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3 Copyright (C) 1996, 1997, 1998, 1999, 2000, 2002, 2003, 2005, 2006, |
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4 2007 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 3 of the License, or (at your |
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11 option) any 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, see |
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20 <http://www.gnu.org/licenses/>. |
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21 |
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22 */ |
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23 |
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24 // Author: A. S. Hodel <scotte@eng.auburn.edu> |
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25 |
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26 #ifdef HAVE_CONFIG_H |
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27 #include <config.h> |
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28 #endif |
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29 |
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30 #include <string> |
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31 |
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32 #include "CmplxAEPBAL.h" |
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33 #include "CmplxAEPBAL.h" |
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34 #include "dbleAEPBAL.h" |
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35 #include "dbleAEPBAL.h" |
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36 #include "quit.h" |
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37 |
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38 #include "defun-dld.h" |
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39 #include "error.h" |
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40 #include "f77-fcn.h" |
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41 #include "gripes.h" |
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42 #include "oct-obj.h" |
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43 #include "utils.h" |
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44 |
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45 extern "C" |
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46 { |
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47 F77_RET_T |
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48 F77_FUNC (dggbal, DGGBAL) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type& N, |
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49 double* A, const octave_idx_type& LDA, double* B, |
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50 const octave_idx_type& LDB, octave_idx_type& ILO, octave_idx_type& IHI, |
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51 double* LSCALE, double* RSCALE, |
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52 double* WORK, octave_idx_type& INFO |
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53 F77_CHAR_ARG_LEN_DECL); |
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54 |
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55 F77_RET_T |
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56 F77_FUNC (dggbak, DGGBAK) (F77_CONST_CHAR_ARG_DECL, |
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57 F77_CONST_CHAR_ARG_DECL, |
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58 const octave_idx_type& N, const octave_idx_type& ILO, |
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59 const octave_idx_type& IHI, const double* LSCALE, |
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60 const double* RSCALE, octave_idx_type& M, double* V, |
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61 const octave_idx_type& LDV, octave_idx_type& INFO |
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62 F77_CHAR_ARG_LEN_DECL |
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63 F77_CHAR_ARG_LEN_DECL); |
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64 |
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65 F77_RET_T |
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66 F77_FUNC (zggbal, ZGGBAL) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type& N, |
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67 Complex* A, const octave_idx_type& LDA, Complex* B, |
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68 const octave_idx_type& LDB, octave_idx_type& ILO, octave_idx_type& IHI, |
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69 double* LSCALE, double* RSCALE, |
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70 double* WORK, octave_idx_type& INFO |
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71 F77_CHAR_ARG_LEN_DECL); |
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72 } |
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73 |
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74 DEFUN_DLD (balance, args, nargout, |
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75 "-*- texinfo -*-\n\ |
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76 @deftypefn {Loadable Function} {@var{aa} =} balance (@var{a}, @var{opt})\n\ |
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77 @deftypefnx {Loadable Function} {[@var{dd}, @var{aa}] =} balance (@var{a}, @var{opt})\n\ |
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78 @deftypefnx {Loadable Function} {[@var{cc}, @var{dd}, @var{aa}, @var{bb}] =} balance (@var{a}, @var{b}, @var{opt})\n\ |
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79 \n\ |
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80 Compute @code{aa = dd \\ a * dd} in which @code{aa} is a matrix whose\n\ |
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81 row and column norms are roughly equal in magnitude, and\n\ |
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82 @code{dd} = @code{p * d}, in which @code{p} is a permutation\n\ |
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83 matrix and @code{d} is a diagonal matrix of powers of two. This allows\n\ |
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84 the equilibration to be computed without roundoff. Results of\n\ |
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85 eigenvalue calculation are typically improved by balancing first.\n\ |
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86 \n\ |
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87 If four output values are requested, compute @code{aa = cc*a*dd} and\n\ |
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88 @code{bb = cc*b*dd)}, in which @code{aa} and @code{bb} have non-zero\n\ |
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89 elements of approximately the same magnitude and @code{cc} and @code{dd}\n\ |
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90 are permuted diagonal matrices as in @code{dd} for the algebraic\n\ |
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91 eigenvalue problem.\n\ |
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92 \n\ |
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93 The eigenvalue balancing option @code{opt} may be one of:\n\ |
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94 \n\ |
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95 @table @asis\n\ |
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96 @item @code{\"N\"}, @code{\"n\"}\n\ |
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97 No balancing; arguments copied, transformation(s) set to identity.\n\ |
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98 \n\ |
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99 @item @code{\"P\"}, @code{\"p\"}\n\ |
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100 Permute argument(s) to isolate eigenvalues where possible.\n\ |
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101 \n\ |
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102 @item @code{\"S\"}, @code{\"s\"}\n\ |
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103 Scale to improve accuracy of computed eigenvalues.\n\ |
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104 \n\ |
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105 @item @code{\"B\"}, @code{\"b\"}\n\ |
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106 Permute and scale, in that order. Rows/columns of a (and b)\n\ |
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107 that are isolated by permutation are not scaled. This is the default\n\ |
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108 behavior.\n\ |
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109 @end table\n\ |
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110 \n\ |
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111 Algebraic eigenvalue balancing uses standard @sc{Lapack} routines.\n\ |
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112 \n\ |
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113 Generalized eigenvalue problem balancing uses Ward's algorithm\n\ |
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114 (SIAM Journal on Scientific and Statistical Computing, 1981).\n\ |
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115 @end deftypefn") |
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116 { |
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117 octave_value_list retval; |
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118 |
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119 int nargin = args.length (); |
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120 |
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121 if (nargin < 1 || nargin > 3 || nargout < 0 || nargout > 4) |
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122 { |
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123 print_usage (); |
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124 return retval; |
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125 } |
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126 |
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127 // determine if it's AEP or GEP |
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128 int AEPcase = nargin == 1 ? 1 : args(1).is_string (); |
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129 std::string bal_job; |
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130 |
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131 // problem dimension |
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132 octave_idx_type nn = args(0).rows (); |
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133 |
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134 octave_idx_type arg_is_empty = empty_arg ("balance", nn, args(0).columns()); |
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135 |
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136 if (arg_is_empty < 0) |
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137 return retval; |
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138 |
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139 if (arg_is_empty > 0) |
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140 return octave_value_list (2, Matrix ()); |
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141 |
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142 if (nn != args(0).columns()) |
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143 { |
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144 gripe_square_matrix_required ("balance"); |
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145 return retval; |
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146 } |
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147 |
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148 // Extract argument 1 parameter for both AEP and GEP. |
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149 Matrix aa; |
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150 ComplexMatrix caa; |
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151 |
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152 if (args(0).is_complex_type ()) |
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153 caa = args(0).complex_matrix_value (); |
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154 else |
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155 aa = args(0).matrix_value (); |
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156 |
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157 if (error_state) |
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158 return retval; |
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159 |
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160 // Treat AEP/GEP cases. |
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161 if (AEPcase) |
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162 { |
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163 // Algebraic eigenvalue problem. |
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164 |
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165 if (nargin == 1) |
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166 bal_job = "B"; |
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167 else if (args(1).is_string ()) |
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168 bal_job = args(1).string_value (); |
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169 else |
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170 { |
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171 error ("balance: AEP argument 2 must be a string"); |
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172 return retval; |
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173 } |
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174 |
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175 // balance the AEP |
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176 if (args(0).is_complex_type ()) |
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177 { |
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178 ComplexAEPBALANCE result (caa, bal_job); |
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179 |
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180 if (nargout == 0 || nargout == 1) |
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181 retval(0) = result.balanced_matrix (); |
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182 else |
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183 { |
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184 retval(1) = result.balanced_matrix (); |
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185 retval(0) = result.balancing_matrix (); |
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186 } |
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187 } |
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188 else |
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189 { |
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190 AEPBALANCE result (aa, bal_job); |
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191 |
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192 if (nargout == 0 || nargout == 1) |
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193 retval(0) = result.balanced_matrix (); |
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194 else |
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195 { |
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196 retval(1) = result.balanced_matrix (); |
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197 retval(0) = result.balancing_matrix (); |
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198 } |
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199 } |
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200 } |
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201 else |
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202 { |
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203 // Generalized eigenvalue problem. |
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204 if (nargin == 2) |
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205 bal_job = "B"; |
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206 else if (args(2).is_string ()) |
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207 bal_job = args(2).string_value (); |
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208 else |
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209 { |
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210 error ("balance: GEP argument 3 must be a string"); |
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211 return retval; |
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212 } |
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213 |
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214 if ((nn != args(1).columns ()) || (nn != args(1).rows ())) |
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215 { |
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216 gripe_nonconformant (); |
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217 return retval; |
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218 } |
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219 |
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220 Matrix bb; |
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221 ComplexMatrix cbb; |
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222 |
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223 if (args(1).is_complex_type ()) |
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224 cbb = args(1).complex_matrix_value (); |
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225 else |
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226 bb = args(1).matrix_value (); |
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227 |
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228 if (error_state) |
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229 return retval; |
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230 |
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231 // Both matrices loaded, now let's check what kind of arithmetic: |
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232 // first, declare variables used in both the real and complex case |
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233 |
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234 octave_idx_type ilo, ihi, info; |
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235 RowVector lscale(nn), rscale(nn), work(6*nn); |
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236 char job = bal_job[0]; |
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237 |
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238 static octave_idx_type complex_case |
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239 = (args(0).is_complex_type () || args(1).is_complex_type ()); |
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240 |
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241 // now balance |
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242 if (complex_case) |
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243 { |
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244 if (args(0).is_real_type ()) |
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245 caa = ComplexMatrix (aa); |
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246 |
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247 if (args(1).is_real_type ()) |
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248 cbb = ComplexMatrix (bb); |
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249 |
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250 F77_XFCN (zggbal, ZGGBAL, |
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251 (F77_CONST_CHAR_ARG2 (&job, 1), |
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252 nn, caa.fortran_vec (), nn, cbb.fortran_vec (), |
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253 nn, ilo, ihi, lscale.fortran_vec (), |
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254 rscale.fortran_vec (), work.fortran_vec (), info |
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255 F77_CHAR_ARG_LEN (1))); |
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256 } |
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257 else |
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258 { |
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259 // real matrices case |
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260 |
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261 F77_XFCN (dggbal, DGGBAL, |
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262 (F77_CONST_CHAR_ARG2 (&job, 1), |
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263 nn, aa.fortran_vec (), nn, bb.fortran_vec (), |
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264 nn, ilo, ihi, lscale.fortran_vec (), |
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265 rscale.fortran_vec (), work.fortran_vec (), info |
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266 F77_CHAR_ARG_LEN (1))); |
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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 (octave_idx_type ii = 0; ii < nn; ii++) |
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275 for (octave_idx_type 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 (F77_CONST_CHAR_ARG2 (&job, 1), |
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285 F77_CONST_CHAR_ARG2 ("L", 1), |
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286 nn, ilo, ihi, lscale.data (), rscale.data (), |
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287 nn, Pl.fortran_vec (), nn, info |
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288 F77_CHAR_ARG_LEN (1) |
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289 F77_CHAR_ARG_LEN (1))); |
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290 |
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291 // then right |
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292 F77_XFCN (dggbak, DGGBAK, |
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293 (F77_CONST_CHAR_ARG2 (&job, 1), |
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294 F77_CONST_CHAR_ARG2 ("R", 1), |
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295 nn, ilo, ihi, lscale.data (), rscale.data (), |
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296 nn, Pr.fortran_vec (), nn, info |
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297 F77_CHAR_ARG_LEN (1) |
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298 F77_CHAR_ARG_LEN (1))); |
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299 |
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300 switch (nargout) |
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301 { |
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302 case 0: |
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303 case 1: |
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304 warning ("balance: used GEP, should have two output arguments"); |
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305 if (complex_case) |
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306 retval(0) = caa; |
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307 else |
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308 retval(0) = aa; |
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309 break; |
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310 |
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311 case 2: |
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312 if (complex_case) |
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313 { |
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314 retval(1) = cbb; |
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315 retval(0) = caa; |
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316 } |
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317 else |
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318 { |
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319 retval(1) = bb; |
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320 retval(0) = aa; |
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321 } |
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322 break; |
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323 |
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324 case 4: |
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325 if (complex_case) |
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326 { |
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327 retval(3) = cbb; |
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328 retval(2) = caa; |
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329 } |
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330 else |
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331 { |
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332 retval(3) = bb; |
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333 retval(2) = aa; |
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334 } |
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335 retval(1) = Pr; |
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336 retval(0) = Pl.transpose (); // so that aa_bal = cc*aa*dd, etc. |
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337 break; |
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338 |
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339 default: |
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340 error ("balance: invalid number of output arguments"); |
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341 break; |
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342 } |
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343 } |
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344 |
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345 return retval; |
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346 } |
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347 |
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348 /* |
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349 ;;; Local Variables: *** |
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350 ;;; mode: C++ *** |
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351 ;;; End: *** |
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352 */ |
