Mercurial > octave
annotate libinterp/corefcn/balance.cc @ 29961:7d6709900da7
eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more
Files affected: __betainc__.cc, __contourc__.cc, __eigs__.cc,
__expint__.cc, __ftp__.cc, __gammainc__.cc, __ichol__.cc, __ilu__.cc,
__magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, balance.cc,
besselj.cc, bsxfun.cc, call-stack.cc, ccolamd.cc, cellfun.cc, chol.cc,
colamd.cc, colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc,
defaults.cc, dirfns.cc, display.cc, dlmread.cc, dmperm.cc, dot.cc,
eig.cc, ellipj.cc, environment.cc, error.cc, event-manager.cc, fft.cc,
fft2.cc, fftn.cc, file-io.cc, find.cc, gcd.cc, getgrent.cc,
getpwent.cc, getrusage.cc, gsvd.cc, hash.cc, help.cc, hess.cc,
hex2num.cc, input.cc, inv.cc, jsondecode.cc, jsonencode.cc,
load-path.cc, load-save.cc, lookup.cc, lsode.cc, lu.cc, max.cc,
mgorth.cc, oct-hist.cc, ordqz.cc, ordschur.cc, pager.cc, pr-output.cc,
psi.cc, qr.cc, quad.cc, quadcc.cc, qz.cc, rand.cc, regexp.cc,
schur.cc, settings.cc, sighandlers.cc, sparse.cc, spparms.cc,
sqrtm.cc, stream-euler.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc,
symbfact.cc, symtab.cc, syscalls.cc, sysdep.cc, time.cc, toplev.cc,
tril.cc, typecast.cc, urlwrite.cc, utils.cc, variables.cc,
__delaunayn__.cc, __fltk_uigetfile__.cc, __glpk__.cc,
__init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audiodevinfo.cc,
audioread.cc, convhulln.cc, fftw.cc, gzip.cc, ov-cell.cc, ov-class.cc,
ov-classdef.cc, ov-fcn-handle.cc, ov-struct.cc, ov-typeinfo.cc,
ov-usr-fcn.cc, octave.cc, lex.ll, oct-parse.yy, profiler.cc,
andpt-eval.cc.
author | John W. Eaton <jwe@octave.org> |
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date | Sat, 14 Aug 2021 22:48:52 -0400 |
parents | 32c3a5805893 |
children | 796f54d4ddbf |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 1996-2021 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. |
221 if (nargin == 2) | |
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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 |