Mercurial > octave
annotate libinterp/corefcn/balance.cc @ 30564:796f54d4ddbf stable
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2021.
In all .txi and .texi files except gpl.txi and gpl.texi in the
doc/liboctave and doc/interpreter directories, change the copyright
to "Octave Project Developers", the same as used for other source
files. Update copyright notices for 2022 (not done since 2019). For
gpl.txi and gpl.texi, change the copyright notice to be "Free Software
Foundation, Inc." and leave the date at 2007 only because this file
only contains the text of the GPL, not anything created by the Octave
Project Developers.
Add Paul Thomas to contributors.in.
author | John W. Eaton <jwe@octave.org> |
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date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | 7d6709900da7 |
children | e88a07dec498 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 1996-2022 The Octave Project Developers |
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4 // |
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5 // See the file COPYRIGHT.md in the top-level directory of this |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
2928 | 25 |
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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
2928 | 28 #endif |
29 | |
30 #include <string> | |
31 | |
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32 #include "CMatrix.h" |
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33 #include "aepbalance.h" |
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34 #include "dMatrix.h" |
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35 #include "fCMatrix.h" |
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36 #include "fMatrix.h" |
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37 #include "gepbalance.h" |
4153 | 38 #include "quit.h" |
2928 | 39 |
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40 #include "defun.h" |
2928 | 41 #include "error.h" |
3181 | 42 #include "f77-fcn.h" |
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43 #include "errwarn.h" |
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44 #include "ovl.h" |
2928 | 45 #include "utils.h" |
46 | |
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47 OCTAVE_NAMESPACE_BEGIN |
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48 |
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49 DEFUN (balance, args, nargout, |
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50 doc: /* -*- texinfo -*- |
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51 @deftypefn {} {@var{AA} =} balance (@var{A}) |
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52 @deftypefnx {} {@var{AA} =} balance (@var{A}, @var{opt}) |
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53 @deftypefnx {} {[@var{DD}, @var{AA}] =} balance (@var{A}, @var{opt}) |
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54 @deftypefnx {} {[@var{D}, @var{P}, @var{AA}] =} balance (@var{A}, @var{opt}) |
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55 @deftypefnx {} {[@var{CC}, @var{DD}, @var{AA}, @var{BB}] =} balance (@var{A}, @var{B}, @var{opt}) |
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56 |
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57 Balance the matrix @var{A} to reduce numerical errors in future |
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58 calculations. |
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59 |
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60 Compute @code{@var{AA} = @var{DD} \ @var{A} * @var{DD}} in which @var{AA} |
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61 is a matrix whose row and column norms are roughly equal in magnitude, and |
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62 @code{@var{DD} = @var{P} * @var{D}}, in which @var{P} is a permutation |
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63 matrix and @var{D} is a diagonal matrix of powers of two. This allows the |
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64 equilibration to be computed without round-off. Results of eigenvalue |
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65 calculation are typically improved by balancing first. |
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66 |
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67 If two output values are requested, @code{balance} returns |
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68 the diagonal @var{D} and the permutation @var{P} separately as vectors. |
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69 In this case, @code{@var{DD} = eye(n)(:,@var{P}) * diag (@var{D})}, where |
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70 @math{n} is the matrix size. |
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71 |
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72 If four output values are requested, compute @code{@var{AA} = |
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73 @var{CC}*@var{A}*@var{DD}} and @code{@var{BB} = @var{CC}*@var{B}*@var{DD}}, |
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74 in which @var{AA} and @var{BB} have nonzero elements of approximately the |
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75 same magnitude and @var{CC} and @var{DD} are permuted diagonal matrices as |
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76 in @var{DD} for the algebraic eigenvalue problem. |
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77 |
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78 The eigenvalue balancing option @var{opt} may be one of: |
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79 |
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80 @table @asis |
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81 @item @qcode{"noperm"}, @qcode{"S"} |
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82 Scale only; do not permute. |
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83 |
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84 @item @qcode{"noscal"}, @qcode{"P"} |
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85 Permute only; do not scale. |
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86 @end table |
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87 |
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88 Algebraic eigenvalue balancing uses standard @sc{lapack} routines. |
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89 |
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90 Generalized eigenvalue problem balancing uses Ward's algorithm |
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91 (SIAM Journal on Scientific and Statistical Computing, 1981). |
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92 @end deftypefn */) |
2928 | 93 { |
94 int nargin = args.length (); | |
95 | |
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96 if (nargin < 1 || nargin > 3 || nargout < 0) |
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97 print_usage (); |
2928 | 98 |
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99 octave_value_list retval; |
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100 |
3181 | 101 // determine if it's AEP or GEP |
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102 bool AEPcase = nargin == 1 || args(1).is_string (); |
2928 | 103 |
3181 | 104 // problem dimension |
5275 | 105 octave_idx_type nn = args(0).rows (); |
2928 | 106 |
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107 if (nn != args(0).columns ()) |
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108 err_square_matrix_required ("balance", "A"); |
2928 | 109 |
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110 bool isfloat = args(0).is_single_type () |
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111 || (! AEPcase && args(1).is_single_type ()); |
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112 |
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113 bool complex_case = args(0).iscomplex () |
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114 || (! AEPcase && args(1).iscomplex ()); |
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115 |
2928 | 116 // Extract argument 1 parameter for both AEP and GEP. |
117 Matrix aa; | |
118 ComplexMatrix caa; | |
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119 FloatMatrix faa; |
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120 FloatComplexMatrix fcaa; |
3185 | 121 |
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122 if (isfloat) |
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123 { |
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124 if (complex_case) |
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125 fcaa = args(0).float_complex_matrix_value (); |
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126 else |
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127 faa = args(0).float_matrix_value (); |
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128 } |
3185 | 129 else |
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130 { |
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131 if (complex_case) |
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132 caa = args(0).complex_matrix_value (); |
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133 else |
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134 aa = args(0).matrix_value (); |
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135 } |
3185 | 136 |
2928 | 137 // Treat AEP/GEP cases. |
3185 | 138 if (AEPcase) |
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139 { |
3185 | 140 // Algebraic eigenvalue problem. |
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141 bool noperm = false; |
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142 bool noscal = false; |
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143 if (nargin > 1) |
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144 { |
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145 std::string a1s = args(1).string_value (); |
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146 noperm = a1s == "noperm" || a1s == "S"; |
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147 noscal = a1s == "noscal" || a1s == "P"; |
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148 } |
3185 | 149 |
150 // balance the AEP | |
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151 if (isfloat) |
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152 { |
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153 if (complex_case) |
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154 { |
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155 math::aepbalance<FloatComplexMatrix> result (fcaa, noperm, noscal); |
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157 if (nargout == 0 || nargout == 1) |
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158 retval = ovl (result.balanced_matrix ()); |
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159 else if (nargout == 2) |
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160 retval = ovl (result.balancing_matrix (), |
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161 result.balanced_matrix ()); |
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162 else |
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163 retval = ovl (result.scaling_vector (), |
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164 result.permuting_vector (), |
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165 result.balanced_matrix ()); |
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166 } |
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167 else |
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168 { |
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169 math::aepbalance<FloatMatrix> result (faa, noperm, noscal); |
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170 |
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171 if (nargout == 0 || nargout == 1) |
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172 retval = ovl (result.balanced_matrix ()); |
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173 else if (nargout == 2) |
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174 retval = ovl (result.balancing_matrix (), |
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175 result.balanced_matrix ()); |
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176 else |
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177 retval = ovl (result.scaling_vector (), |
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178 result.permuting_vector (), |
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179 result.balanced_matrix ()); |
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180 } |
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181 } |
3181 | 182 else |
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183 { |
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184 if (complex_case) |
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185 { |
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186 math::aepbalance<ComplexMatrix> result (caa, noperm, noscal); |
3185 | 187 |
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188 if (nargout == 0 || nargout == 1) |
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189 retval = ovl (result.balanced_matrix ()); |
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190 else if (nargout == 2) |
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191 retval = ovl (result.balancing_matrix (), |
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192 result.balanced_matrix ()); |
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193 else |
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194 retval = ovl (result.scaling_vector (), |
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195 result.permuting_vector (), |
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196 result.balanced_matrix ()); |
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197 } |
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198 else |
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199 { |
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200 math::aepbalance<Matrix> result (aa, noperm, noscal); |
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201 |
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202 if (nargout == 0 || nargout == 1) |
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203 retval = ovl (result.balanced_matrix ()); |
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204 else if (nargout == 2) |
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205 retval = ovl (result.balancing_matrix (), |
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206 result.balanced_matrix ()); |
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207 else |
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208 retval = ovl (result.scaling_vector (), |
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209 result.permuting_vector (), |
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210 result.balanced_matrix ()); |
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211 } |
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212 } |
3181 | 213 } |
214 else | |
215 { | |
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216 std::string bal_job; |
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217 if (nargout == 1) |
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218 warning ("balance: used GEP, should have two output arguments"); |
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219 |
3185 | 220 // Generalized eigenvalue problem. |
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222 bal_job = 'B'; |
3185 | 223 else |
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224 bal_job = args(2).xstring_value ("balance: OPT argument must be a string"); |
3185 | 225 |
226 if ((nn != args(1).columns ()) || (nn != args(1).rows ())) | |
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227 ::err_nonconformant (); |
3185 | 228 |
229 Matrix bb; | |
230 ComplexMatrix cbb; | |
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231 FloatMatrix fbb; |
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232 FloatComplexMatrix fcbb; |
3185 | 233 |
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234 if (isfloat) |
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235 { |
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236 if (complex_case) |
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237 fcbb = args(1).float_complex_matrix_value (); |
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238 else |
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239 fbb = args(1).float_matrix_value (); |
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240 } |
3185 | 241 else |
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242 { |
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243 if (complex_case) |
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244 cbb = args(1).complex_matrix_value (); |
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245 else |
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246 bb = args(1).matrix_value (); |
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247 } |
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249 // balance the GEP |
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250 if (isfloat) |
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251 { |
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252 if (complex_case) |
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253 { |
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254 math::gepbalance<FloatComplexMatrix> result (fcaa, fcbb, bal_job); |
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255 |
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256 switch (nargout) |
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257 { |
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258 case 4: |
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259 retval(3) = result.balanced_matrix2 (); |
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260 OCTAVE_FALLTHROUGH; |
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261 |
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262 case 3: |
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263 retval(2) = result.balanced_matrix (); |
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264 retval(1) = result.balancing_matrix2 (); |
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265 retval(0) = result.balancing_matrix (); |
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266 break; |
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267 |
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268 case 2: |
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269 retval(1) = result.balancing_matrix2 (); |
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270 OCTAVE_FALLTHROUGH; |
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271 |
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272 case 1: |
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273 retval(0) = result.balancing_matrix (); |
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274 break; |
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275 |
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276 default: |
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277 error ("balance: invalid number of output arguments"); |
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278 break; |
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279 } |
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280 } |
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281 else |
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282 { |
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283 math::gepbalance<FloatMatrix> result (faa, fbb, bal_job); |
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284 |
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285 switch (nargout) |
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286 { |
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287 case 4: |
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288 retval(3) = result.balanced_matrix2 (); |
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289 OCTAVE_FALLTHROUGH; |
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290 |
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291 case 3: |
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292 retval(2) = result.balanced_matrix (); |
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293 retval(1) = result.balancing_matrix2 (); |
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294 retval(0) = result.balancing_matrix (); |
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295 break; |
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296 |
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297 case 2: |
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298 retval(1) = result.balancing_matrix2 (); |
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299 OCTAVE_FALLTHROUGH; |
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300 |
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301 case 1: |
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302 retval(0) = result.balancing_matrix (); |
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303 break; |
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304 |
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305 default: |
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306 error ("balance: invalid number of output arguments"); |
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307 break; |
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308 } |
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309 } |
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310 } |
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311 else |
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312 { |
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313 if (complex_case) |
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314 { |
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315 math::gepbalance<ComplexMatrix> result (caa, cbb, bal_job); |
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316 |
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317 switch (nargout) |
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318 { |
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319 case 4: |
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320 retval(3) = result.balanced_matrix2 (); |
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321 OCTAVE_FALLTHROUGH; |
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322 |
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323 case 3: |
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324 retval(2) = result.balanced_matrix (); |
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325 retval(1) = result.balancing_matrix2 (); |
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326 retval(0) = result.balancing_matrix (); |
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327 break; |
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328 |
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329 case 2: |
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330 retval(1) = result.balancing_matrix2 (); |
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331 OCTAVE_FALLTHROUGH; |
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332 |
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333 case 1: |
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334 retval(0) = result.balancing_matrix (); |
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335 break; |
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336 |
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337 default: |
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338 error ("balance: invalid number of output arguments"); |
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339 break; |
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340 } |
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341 } |
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342 else |
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343 { |
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344 math::gepbalance<Matrix> result (aa, bb, bal_job); |
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345 |
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346 switch (nargout) |
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347 { |
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348 case 4: |
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349 retval(3) = result.balanced_matrix2 (); |
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350 OCTAVE_FALLTHROUGH; |
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351 |
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352 case 3: |
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353 retval(2) = result.balanced_matrix (); |
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354 retval(1) = result.balancing_matrix2 (); |
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355 retval(0) = result.balancing_matrix (); |
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356 break; |
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357 |
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358 case 2: |
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359 retval(1) = result.balancing_matrix2 (); |
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360 OCTAVE_FALLTHROUGH; |
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361 |
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362 case 1: |
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363 retval(0) = result.balancing_matrix (); |
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364 break; |
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365 |
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366 default: |
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367 error ("balance: invalid number of output arguments"); |
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368 break; |
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369 } |
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370 } |
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371 } |
2928 | 372 } |
3185 | 373 |
2928 | 374 return retval; |
375 } | |
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376 |
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377 OCTAVE_NAMESPACE_END |