Mercurial > octave
annotate libinterp/corefcn/qz.cc @ 20802:8bb38ba1bad6
eliminate return statements after calls to print_usage
* __contourc__.cc, __dispatch__.cc, __dsearchn__.cc, __ichol__.cc,
__lin_interpn__.cc, __qp__.cc, balance.cc, betainc.cc, bsxfun.cc,
colloc.cc, daspk.cc, dasrt.cc, dassl.cc, defaults.cc, det.cc,
dlmread.cc, dot.cc, eig.cc, ellipj.cc, fft.cc, fft2.cc, fftn.cc,
filter.cc, find.cc, gcd.cc, givens.cc, hex2num.cc, inv.cc, lookup.cc,
lu.cc, max.cc, mgorth.cc, ordschur.cc, pinv.cc, profiler.cc, quad.cc,
qz.cc, rcond.cc, schur.cc, str2double.cc:
Eliminate return statements after calls to print_usage.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Fri, 04 Dec 2015 12:03:44 -0500 |
parents | 68e3a747ca02 |
children | 35241c4b696c |
rev | line source |
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3183 | 1 /* |
2 | |
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3 Copyright (C) 1998-2015 A. S. Hodel |
3183 | 4 |
5 This file is part of Octave. | |
6 | |
7 Octave is free software; you can redistribute it and/or modify it | |
8 under the terms of the GNU General Public License as published by the | |
7016 | 9 Free Software Foundation; either version 3 of the License, or (at your |
10 option) any later version. | |
3183 | 11 |
12 Octave is distributed in the hope that it will be useful, but WITHOUT | |
13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
15 for more details. | |
16 | |
17 You should have received a copy of the GNU General Public License | |
7016 | 18 along with Octave; see the file COPYING. If not, see |
19 <http://www.gnu.org/licenses/>. | |
3183 | 20 |
21 */ | |
22 | |
23 // Generalized eigenvalue balancing via LAPACK | |
3911 | 24 |
25 // Author: A. S. Hodel <scotte@eng.auburn.edu> | |
3183 | 26 |
27 #undef DEBUG | |
28 #undef DEBUG_SORT | |
29 #undef DEBUG_EIG | |
30 | |
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31 #ifdef HAVE_CONFIG_H |
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32 #include <config.h> |
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33 #endif |
3183 | 34 |
35 #include <cfloat> | |
4051 | 36 |
3523 | 37 #include <iostream> |
4051 | 38 #include <iomanip> |
3183 | 39 |
40 #include "CmplxQRP.h" | |
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41 #include "CmplxQR.h" |
3183 | 42 #include "dbleQR.h" |
4153 | 43 #include "f77-fcn.h" |
7231 | 44 #include "lo-math.h" |
4153 | 45 #include "quit.h" |
46 | |
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47 #include "defun.h" |
3183 | 48 #include "error.h" |
49 #include "gripes.h" | |
50 #include "oct-obj.h" | |
51 #include "oct-map.h" | |
52 #include "ov.h" | |
53 #include "pager.h" | |
3185 | 54 #if defined (DEBUG) || defined (DEBUG_SORT) |
3183 | 55 #include "pr-output.h" |
56 #endif | |
57 #include "symtab.h" | |
58 #include "utils.h" | |
59 #include "variables.h" | |
60 | |
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61 typedef octave_idx_type (*sort_function) (const octave_idx_type& LSIZE, |
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62 const double& ALPHA, |
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63 const double& BETA, const double& S, |
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64 const double& P); |
3183 | 65 |
66 extern "C" | |
67 { | |
4552 | 68 F77_RET_T |
69 F77_FUNC (dggbal, DGGBAL) (F77_CONST_CHAR_ARG_DECL, | |
10311 | 70 const octave_idx_type& N, double* A, |
71 const octave_idx_type& LDA, double* B, | |
72 const octave_idx_type& LDB, octave_idx_type& ILO, | |
73 octave_idx_type& IHI, double* LSCALE, | |
74 double* RSCALE, double* WORK, | |
75 octave_idx_type& INFO | |
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76 F77_CHAR_ARG_LEN_DECL); |
3183 | 77 |
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78 F77_RET_T |
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79 F77_FUNC (zggbal, ZGGBAL) (F77_CONST_CHAR_ARG_DECL, |
10311 | 80 const octave_idx_type& N, Complex* A, |
81 const octave_idx_type& LDA, Complex* B, | |
82 const octave_idx_type& LDB, octave_idx_type& ILO, | |
83 octave_idx_type& IHI, double* LSCALE, | |
84 double* RSCALE, double* WORK, | |
85 octave_idx_type& INFO | |
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86 F77_CHAR_ARG_LEN_DECL); |
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87 |
4552 | 88 F77_RET_T |
89 F77_FUNC (dggbak, DGGBAK) (F77_CONST_CHAR_ARG_DECL, | |
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90 F77_CONST_CHAR_ARG_DECL, |
10311 | 91 const octave_idx_type& N, |
92 const octave_idx_type& ILO, | |
93 const octave_idx_type& IHI, | |
94 const double* LSCALE, const double* RSCALE, | |
95 octave_idx_type& M, double* V, | |
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96 const octave_idx_type& LDV, octave_idx_type& INFO |
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97 F77_CHAR_ARG_LEN_DECL |
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98 F77_CHAR_ARG_LEN_DECL); |
3183 | 99 |
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100 F77_RET_T |
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101 F77_FUNC (zggbak, ZGGBAK) (F77_CONST_CHAR_ARG_DECL, |
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102 F77_CONST_CHAR_ARG_DECL, |
10311 | 103 const octave_idx_type& N, |
104 const octave_idx_type& ILO, | |
105 const octave_idx_type& IHI, | |
106 const double* LSCALE, const double* RSCALE, | |
107 octave_idx_type& M, Complex* V, | |
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108 const octave_idx_type& LDV, octave_idx_type& INFO |
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109 F77_CHAR_ARG_LEN_DECL |
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110 F77_CHAR_ARG_LEN_DECL); |
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111 |
4552 | 112 F77_RET_T |
113 F77_FUNC (dgghrd, DGGHRD) (F77_CONST_CHAR_ARG_DECL, | |
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114 F77_CONST_CHAR_ARG_DECL, |
10311 | 115 const octave_idx_type& N, |
116 const octave_idx_type& ILO, | |
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117 const octave_idx_type& IHI, double* A, |
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118 const octave_idx_type& LDA, double* B, |
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119 const octave_idx_type& LDB, double* Q, |
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120 const octave_idx_type& LDQ, double* Z, |
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121 const octave_idx_type& LDZ, octave_idx_type& INFO |
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122 F77_CHAR_ARG_LEN_DECL |
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123 F77_CHAR_ARG_LEN_DECL); |
3183 | 124 |
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125 F77_RET_T |
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126 F77_FUNC (zgghrd, ZGGHRD) (F77_CONST_CHAR_ARG_DECL, |
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127 F77_CONST_CHAR_ARG_DECL, |
10311 | 128 const octave_idx_type& N, |
129 const octave_idx_type& ILO, | |
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130 const octave_idx_type& IHI, Complex* A, |
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131 const octave_idx_type& LDA, Complex* B, |
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132 const octave_idx_type& LDB, Complex* Q, |
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133 const octave_idx_type& LDQ, Complex* Z, |
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134 const octave_idx_type& LDZ, octave_idx_type& INFO |
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135 F77_CHAR_ARG_LEN_DECL |
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136 F77_CHAR_ARG_LEN_DECL); |
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137 |
4552 | 138 F77_RET_T |
139 F77_FUNC (dhgeqz, DHGEQZ) (F77_CONST_CHAR_ARG_DECL, | |
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140 F77_CONST_CHAR_ARG_DECL, |
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141 F77_CONST_CHAR_ARG_DECL, |
10311 | 142 const octave_idx_type& N, |
143 const octave_idx_type& ILO, | |
144 const octave_idx_type& IHI, | |
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145 double* A, const octave_idx_type& LDA, double* B, |
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146 const octave_idx_type& LDB, double* ALPHAR, |
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147 double* ALPHAI, double* BETA, double* Q, |
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148 const octave_idx_type& LDQ, double* Z, |
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149 const octave_idx_type& LDZ, double* WORK, |
10311 | 150 const octave_idx_type& LWORK, |
151 octave_idx_type& INFO | |
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152 F77_CHAR_ARG_LEN_DECL |
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153 F77_CHAR_ARG_LEN_DECL |
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154 F77_CHAR_ARG_LEN_DECL); |
3183 | 155 |
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156 F77_RET_T |
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157 F77_FUNC (zhgeqz, ZHGEQZ) (F77_CONST_CHAR_ARG_DECL, |
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158 F77_CONST_CHAR_ARG_DECL, |
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159 F77_CONST_CHAR_ARG_DECL, |
10311 | 160 const octave_idx_type& N, |
161 const octave_idx_type& ILO, | |
162 const octave_idx_type& IHI, | |
163 Complex* A, const octave_idx_type& LDA, | |
164 Complex* B, const octave_idx_type& LDB, | |
165 Complex* ALPHA, Complex* BETA, Complex* CQ, | |
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166 const octave_idx_type& LDQ, |
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167 Complex* CZ, const octave_idx_type& LDZ, |
10311 | 168 Complex* WORK, const octave_idx_type& LWORK, |
169 double* RWORK, octave_idx_type& INFO | |
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170 F77_CHAR_ARG_LEN_DECL |
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171 F77_CHAR_ARG_LEN_DECL |
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172 F77_CHAR_ARG_LEN_DECL); |
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173 |
4552 | 174 F77_RET_T |
10311 | 175 F77_FUNC (dlag2, DLAG2) (const double* A, const octave_idx_type& LDA, |
176 const double* B, const octave_idx_type& LDB, | |
177 const double& SAFMIN, double& SCALE1, | |
178 double& SCALE2, double& WR1, double& WR2, | |
179 double& WI); | |
3183 | 180 |
181 // Van Dooren's code (netlib.org: toms/590) for reordering | |
182 // GEP. Only processes Z, not Q. | |
4552 | 183 F77_RET_T |
10311 | 184 F77_FUNC (dsubsp, DSUBSP) (const octave_idx_type& NMAX, |
185 const octave_idx_type& N, double* A, | |
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186 double* B, double* Z, sort_function, |
10311 | 187 const double& EPS, octave_idx_type& NDIM, |
188 octave_idx_type& FAIL, octave_idx_type* IND); | |
3183 | 189 |
10311 | 190 // Documentation for DTGEVC incorrectly states that VR, VL are |
3183 | 191 // complex*16; they are declared in DTGEVC as double precision |
10311 | 192 // (probably a cut and paste problem fro ZTGEVC). |
4552 | 193 F77_RET_T |
194 F77_FUNC (dtgevc, DTGEVC) (F77_CONST_CHAR_ARG_DECL, | |
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195 F77_CONST_CHAR_ARG_DECL, |
10311 | 196 octave_idx_type* SELECT, |
197 const octave_idx_type& N, double* A, | |
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198 const octave_idx_type& LDA, double* B, |
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199 const octave_idx_type& LDB, double* VL, |
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200 const octave_idx_type& LDVL, double* VR, |
10311 | 201 const octave_idx_type& LDVR, |
202 const octave_idx_type& MM, octave_idx_type& M, | |
203 double* WORK, octave_idx_type& INFO | |
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204 F77_CHAR_ARG_LEN_DECL |
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205 F77_CHAR_ARG_LEN_DECL); |
3183 | 206 |
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207 F77_RET_T |
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208 F77_FUNC (ztgevc, ZTGEVC) (F77_CONST_CHAR_ARG_DECL, |
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209 F77_CONST_CHAR_ARG_DECL, |
10311 | 210 octave_idx_type* SELECT, |
211 const octave_idx_type& N, const Complex* A, | |
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212 const octave_idx_type& LDA,const Complex* B, |
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213 const octave_idx_type& LDB, Complex* xVL, |
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214 const octave_idx_type& LDVL, Complex* xVR, |
10311 | 215 const octave_idx_type& LDVR, |
216 const octave_idx_type& MM, octave_idx_type& M, | |
217 Complex* CWORK, double* RWORK, | |
218 octave_idx_type& INFO | |
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219 F77_CHAR_ARG_LEN_DECL |
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220 F77_CHAR_ARG_LEN_DECL); |
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221 |
4552 | 222 F77_RET_T |
223 F77_FUNC (xdlamch, XDLAMCH) (F77_CONST_CHAR_ARG_DECL, | |
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224 double& retval |
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225 F77_CHAR_ARG_LEN_DECL); |
3185 | 226 |
4552 | 227 F77_RET_T |
228 F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, | |
10311 | 229 const octave_idx_type&, |
230 const octave_idx_type&, const double*, | |
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231 const octave_idx_type&, double*, double& |
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232 F77_CHAR_ARG_LEN_DECL); |
3183 | 233 } |
234 | |
235 // fcrhp, fin, fout, folhp: | |
236 // routines for ordering of generalized eigenvalues | |
237 // return 1 if test is passed, 0 otherwise | |
238 // fin: |lambda| < 1 | |
239 // fout: |lambda| >= 1 | |
240 // fcrhp: real(lambda) >= 0 | |
241 // folhp: real(lambda) < 0 | |
242 | |
5275 | 243 static octave_idx_type |
244 fcrhp (const octave_idx_type& lsize, const double& alpha, | |
3185 | 245 const double& beta, const double& s, const double&) |
3183 | 246 { |
3185 | 247 if (lsize == 1) |
10311 | 248 return (alpha * beta >= 0 ? 1 : -1); |
3185 | 249 else |
3183 | 250 return (s >= 0 ? 1 : -1); |
251 } | |
3185 | 252 |
5275 | 253 static octave_idx_type |
254 fin (const octave_idx_type& lsize, const double& alpha, | |
3185 | 255 const double& beta, const double&, const double& p) |
3183 | 256 { |
5275 | 257 octave_idx_type retval; |
3183 | 258 |
3185 | 259 if (lsize == 1) |
260 retval = (fabs (alpha) < fabs (beta) ? 1 : -1); | |
261 else | |
262 retval = (fabs (p) < 1 ? 1 : -1); | |
263 | |
264 #ifdef DEBUG | |
3538 | 265 std::cout << "qz: fin: retval=" << retval << std::endl; |
3185 | 266 #endif |
267 | |
3183 | 268 return retval; |
269 } | |
3185 | 270 |
5275 | 271 static octave_idx_type |
272 folhp (const octave_idx_type& lsize, const double& alpha, | |
3185 | 273 const double& beta, const double& s, const double&) |
3183 | 274 { |
3185 | 275 if (lsize == 1) |
10311 | 276 return (alpha * beta < 0 ? 1 : -1); |
3185 | 277 else |
3183 | 278 return (s < 0 ? 1 : -1); |
279 } | |
3185 | 280 |
5275 | 281 static octave_idx_type |
282 fout (const octave_idx_type& lsize, const double& alpha, | |
3185 | 283 const double& beta, const double&, const double& p) |
3183 | 284 { |
3185 | 285 if (lsize == 1) |
286 return (fabs (alpha) >= fabs (beta) ? 1 : -1); | |
287 else | |
288 return (fabs (p) >= 1 ? 1 : -1); | |
3183 | 289 } |
290 | |
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291 |
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292 //FIXME: Matlab does not produce lambda as the first output argument. |
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293 // Compatibility problem? |
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294 DEFUN (qz, args, nargout, |
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295 "-*- texinfo -*-\n\ |
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296 @deftypefn {Built-in Function} {@var{lambda} =} qz (@var{A}, @var{B})\n\ |
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297 @deftypefnx {Built-in Function} {@var{lambda} =} qz (@var{A}, @var{B}, @var{opt})\n\ |
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298 QZ@tie{}decomposition of the generalized eigenvalue problem\n\ |
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299 (@math{A x = s B x}).\n\ |
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300 \n\ |
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301 There are three ways to call this function:\n\ |
3372 | 302 @enumerate\n\ |
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303 @item @code{@var{lambda} = qz (@var{A}, @var{B})}\n\ |
3185 | 304 \n\ |
5016 | 305 Computes the generalized eigenvalues\n\ |
306 @tex\n\ | |
307 $\\lambda$\n\ | |
308 @end tex\n\ | |
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309 @ifnottex\n\ |
5016 | 310 @var{lambda}\n\ |
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311 @end ifnottex\n\ |
5016 | 312 of @math{(A - s B)}.\n\ |
10840 | 313 \n\ |
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314 @item @code{[AA, BB, Q, Z, V, W, @var{lambda}] = qz (@var{A}, @var{B})}\n\ |
3185 | 315 \n\ |
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316 Computes QZ@tie{}decomposition, generalized eigenvectors, and generalized\n\ |
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317 eigenvalues of @math{(A - s B)}\n\ |
5016 | 318 @tex\n\ |
319 $$ AV = BV{ \\rm diag }(\\lambda) $$\n\ | |
320 $$ W^T A = { \\rm diag }(\\lambda)W^T B $$\n\ | |
321 $$ AA = Q^T AZ, BB = Q^T BZ $$\n\ | |
322 @end tex\n\ | |
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323 @ifnottex\n\ |
10840 | 324 \n\ |
3372 | 325 @example\n\ |
326 @group\n\ | |
5481 | 327 \n\ |
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328 A * V = B * V * diag (@var{lambda})\n\ |
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329 W' * A = diag (@var{lambda}) * W' * B\n\ |
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330 AA = Q * A * Z, BB = Q * B * Z\n\ |
5481 | 331 \n\ |
3372 | 332 @end group\n\ |
333 @end example\n\ | |
10840 | 334 \n\ |
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335 @end ifnottex\n\ |
5016 | 336 with @var{Q} and @var{Z} orthogonal (unitary)= @var{I}\n\ |
3185 | 337 \n\ |
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338 @item @code{[AA,BB,Z@{, @var{lambda}@}] = qz (@var{A}, @var{B}, @var{opt})}\n\ |
3185 | 339 \n\ |
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340 As in form [2], but allows ordering of generalized eigenpairs for, e.g.,\n\ |
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341 solution of discrete time algebraic Riccati equations. Form 3 is not\n\ |
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342 available for complex matrices, and does not compute the generalized\n\ |
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343 eigenvectors @var{V}, @var{W}, nor the orthogonal matrix @var{Q}.\n\ |
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344 \n\ |
3372 | 345 @table @var\n\ |
346 @item opt\n\ | |
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347 for ordering eigenvalues of the @nospell{GEP} pencil. The leading block of\n\ |
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348 the revised pencil contains all eigenvalues that satisfy:\n\ |
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349 \n\ |
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350 @table @asis\n\ |
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351 @item @qcode{\"N\"}\n\ |
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352 = unordered (default)\n\ |
3183 | 353 \n\ |
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354 @item @qcode{\"S\"}\n\ |
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355 = small: leading block has all |lambda| @leq{} 1\n\ |
3185 | 356 \n\ |
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357 @item @qcode{\"B\"}\n\ |
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358 = big: leading block has all |lambda| @geq{} 1\n\ |
3372 | 359 \n\ |
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360 @item @qcode{\"-\"}\n\ |
5481 | 361 = negative real part: leading block has all eigenvalues\n\ |
362 in the open left half-plane\n\ | |
3372 | 363 \n\ |
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364 @item @qcode{\"+\"}\n\ |
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365 = non-negative real part: leading block has all eigenvalues\n\ |
5481 | 366 in the closed right half-plane\n\ |
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367 @end table\n\ |
3372 | 368 @end table\n\ |
369 @end enumerate\n\ | |
3183 | 370 \n\ |
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371 Note: @code{qz} performs permutation balancing, but not scaling\n\ |
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372 (@pxref{XREFbalance}). The order of output arguments was selected for\n\ |
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373 compatibility with @sc{matlab}.\n\ |
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374 @seealso{eig, balance, lu, chol, hess, qr, qzhess, schur, svd}\n\ |
3372 | 375 @end deftypefn") |
3183 | 376 { |
377 octave_value_list retval; | |
378 int nargin = args.length (); | |
379 | |
3185 | 380 #ifdef DEBUG |
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381 std::cout << "qz: nargin = " << nargin |
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382 << ", nargout = " << nargout << std::endl; |
3185 | 383 #endif |
3183 | 384 |
3185 | 385 if (nargin < 2 || nargin > 3 || nargout > 7) |
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386 print_usage (); |
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387 |
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388 if (nargin == 3 && (nargout < 3 || nargout > 4)) |
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389 error ("qz: invalid number of output arguments for form [3] call"); |
3183 | 390 |
3185 | 391 #ifdef DEBUG |
3538 | 392 std::cout << "qz: determine ordering option" << std::endl; |
3185 | 393 #endif |
3183 | 394 |
10311 | 395 // Determine ordering option. |
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396 volatile char ord_job = 0; |
3183 | 397 static double safmin; |
3185 | 398 |
399 if (nargin == 2) | |
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400 ord_job = 'N'; |
3185 | 401 else |
402 { | |
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403 std::string tmp = args(2).xstring_value ("qz: OPT must be a string"); |
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404 |
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405 if (! tmp.empty ()) |
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406 ord_job = tmp[0]; |
3183 | 407 |
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408 if (! (ord_job == 'N' || ord_job == 'n' |
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409 || ord_job == 'S' || ord_job == 's' |
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410 || ord_job == 'B' || ord_job == 'b' |
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411 || ord_job == '+' || ord_job == '-')) |
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412 { |
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413 error ("qz: invalid order option"); |
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414 return retval; |
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415 } |
3185 | 416 |
417 // overflow constant required by dlag2 | |
4552 | 418 F77_FUNC (xdlamch, XDLAMCH) (F77_CONST_CHAR_ARG2 ("S", 1), |
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419 safmin |
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420 F77_CHAR_ARG_LEN (1)); |
3183 | 421 |
3185 | 422 #ifdef DEBUG_EIG |
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423 std::cout << "qz: initial value of safmin=" |
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424 << setiosflags (std::ios::scientific) |
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425 << safmin << std::endl; |
3185 | 426 #endif |
3183 | 427 |
10311 | 428 // Some machines (e.g., DEC alpha) get safmin = 0; |
429 // for these, use eps instead to avoid problems in dlag2. | |
3185 | 430 if (safmin == 0) |
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431 { |
3185 | 432 #ifdef DEBUG_EIG |
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433 std::cout << "qz: DANGER WILL ROBINSON: safmin is 0!" << std::endl; |
3185 | 434 #endif |
3183 | 435 |
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436 F77_FUNC (xdlamch, XDLAMCH) (F77_CONST_CHAR_ARG2 ("E", 1), |
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437 safmin |
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438 F77_CHAR_ARG_LEN (1)); |
3185 | 439 |
440 #ifdef DEBUG_EIG | |
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441 std::cout << "qz: safmin set to " |
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442 << setiosflags (std::ios::scientific) |
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443 << safmin << std::endl; |
3185 | 444 #endif |
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445 } |
3183 | 446 } |
447 | |
3185 | 448 #ifdef DEBUG |
3538 | 449 std::cout << "qz: check argument 1" << std::endl; |
3185 | 450 #endif |
3183 | 451 |
10311 | 452 // Argument 1: check if it's o.k. dimensioned. |
5275 | 453 octave_idx_type nn = args(0).rows (); |
3185 | 454 |
455 #ifdef DEBUG | |
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456 std::cout << "argument 1 dimensions: (" |
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457 << nn << "," << args(0).columns () << ")" |
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458 << std::endl; |
3185 | 459 #endif |
460 | |
461 int arg_is_empty = empty_arg ("qz", nn, args(0).columns ()); | |
462 | |
3183 | 463 if (arg_is_empty < 0) |
3185 | 464 { |
465 gripe_empty_arg ("qz: parameter 1", 0); | |
466 return retval; | |
467 } | |
3183 | 468 else if (arg_is_empty > 0) |
3185 | 469 { |
470 gripe_empty_arg ("qz: parameter 1; continuing", 0); | |
471 return octave_value_list (2, Matrix ()); | |
472 } | |
473 else if (args(0).columns () != nn) | |
474 { | |
475 gripe_square_matrix_required ("qz"); | |
476 return retval; | |
477 } | |
3183 | 478 |
10311 | 479 // Argument 1: dimensions look good; get the value. |
3183 | 480 Matrix aa; |
481 ComplexMatrix caa; | |
3185 | 482 |
483 if (args(0).is_complex_type ()) | |
3183 | 484 caa = args(0).complex_matrix_value (); |
3185 | 485 else |
3183 | 486 aa = args(0).matrix_value (); |
3185 | 487 |
488 #ifdef DEBUG | |
3538 | 489 std::cout << "qz: check argument 2" << std::endl; |
3185 | 490 #endif |
3183 | 491 |
10311 | 492 // Extract argument 2 (bb, or cbb if complex). |
3185 | 493 if ((nn != args(1).columns ()) || (nn != args(1).rows ())) |
494 { | |
495 gripe_nonconformant (); | |
496 return retval; | |
497 } | |
498 | |
3183 | 499 Matrix bb; |
500 ComplexMatrix cbb; | |
3185 | 501 |
502 if (args(1).is_complex_type ()) | |
3183 | 503 cbb = args(1).complex_matrix_value (); |
504 else | |
505 bb = args(1).matrix_value (); | |
3185 | 506 |
3183 | 507 // Both matrices loaded, now let's check what kind of arithmetic: |
10311 | 508 // declared volatile to avoid compiler warnings about long jumps, |
509 // vforks. | |
3185 | 510 |
10311 | 511 volatile int complex_case |
3185 | 512 = (args(0).is_complex_type () || args(1).is_complex_type ()); |
10311 | 513 |
3185 | 514 if (nargin == 3 && complex_case) |
515 { | |
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516 error ("qz: cannot re-order complex qz decomposition"); |
3185 | 517 return retval; |
518 } | |
3183 | 519 |
10311 | 520 // First, declare variables used in both the real and complex case. |
3183 | 521 Matrix QQ(nn,nn), ZZ(nn,nn), VR(nn,nn), VL(nn,nn); |
522 RowVector alphar(nn), alphai(nn), betar(nn); | |
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523 ComplexRowVector xalpha(nn), xbeta(nn); |
3185 | 524 ComplexMatrix CQ(nn,nn), CZ(nn,nn), CVR(nn,nn), CVL(nn,nn); |
5275 | 525 octave_idx_type ilo, ihi, info; |
3185 | 526 char compq = (nargout >= 3 ? 'V' : 'N'); |
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527 char compz = ((nargout >= 4 || nargin == 3)? 'V' : 'N'); |
3183 | 528 |
10311 | 529 // Initialize Q, Z to identity if we need either of them. |
3185 | 530 if (compq == 'V' || compz == 'V') |
5275 | 531 for (octave_idx_type ii = 0; ii < nn; ii++) |
532 for (octave_idx_type jj = 0; jj < nn; jj++) | |
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533 { |
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534 OCTAVE_QUIT; |
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535 QQ(ii,jj) = ZZ(ii,jj) = (ii == jj ? 1.0 : 0.0); |
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536 } |
3183 | 537 |
10311 | 538 // Always perform permutation balancing. |
4552 | 539 const char bal_job = 'P'; |
10311 | 540 RowVector lscale (nn), rscale (nn), work (6 * nn), rwork (nn); |
3183 | 541 |
3185 | 542 if (complex_case) |
543 { | |
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544 #ifdef DEBUG |
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545 if (compq == 'V') |
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546 std::cout << "qz: performing balancing; CQ=" << std::endl |
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547 << CQ << std::endl; |
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548 #endif |
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549 if (args(0).is_real_type ()) |
10311 | 550 caa = ComplexMatrix (aa); |
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551 |
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552 if (args(1).is_real_type ()) |
10311 | 553 cbb = ComplexMatrix (bb); |
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554 |
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555 if (compq == 'V') |
10311 | 556 CQ = ComplexMatrix (QQ); |
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557 |
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558 if (compz == 'V') |
10311 | 559 CZ = ComplexMatrix (ZZ); |
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560 |
10311 | 561 F77_XFCN (zggbal, ZGGBAL, |
562 (F77_CONST_CHAR_ARG2 (&bal_job, 1), | |
563 nn, caa.fortran_vec (), nn, cbb.fortran_vec (), | |
564 nn, ilo, ihi, lscale.fortran_vec (), | |
565 rscale.fortran_vec (), work.fortran_vec (), info | |
566 F77_CHAR_ARG_LEN (1))); | |
3185 | 567 } |
3183 | 568 else |
3185 | 569 { |
570 #ifdef DEBUG | |
571 if (compq == 'V') | |
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572 std::cout << "qz: performing balancing; QQ=" << std::endl |
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573 << QQ << std::endl; |
3185 | 574 #endif |
3183 | 575 |
3185 | 576 F77_XFCN (dggbal, DGGBAL, |
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577 (F77_CONST_CHAR_ARG2 (&bal_job, 1), |
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578 nn, aa.fortran_vec (), nn, bb.fortran_vec (), |
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579 nn, ilo, ihi, lscale.fortran_vec (), |
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580 rscale.fortran_vec (), work.fortran_vec (), info |
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581 F77_CHAR_ARG_LEN (1))); |
3185 | 582 } |
3183 | 583 |
584 // Since we just want the balancing matrices, we can use dggbal | |
10311 | 585 // for both the real and complex cases; left first |
3185 | 586 |
10311 | 587 #if 0 |
588 if (compq == 'V') | |
3185 | 589 { |
590 F77_XFCN (dggbak, DGGBAK, | |
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591 (F77_CONST_CHAR_ARG2 (&bal_job, 1), |
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592 F77_CONST_CHAR_ARG2 ("L", 1), |
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593 nn, ilo, ihi, lscale.data (), rscale.data (), |
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594 nn, QQ.fortran_vec (), nn, info |
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595 F77_CHAR_ARG_LEN (1) |
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596 F77_CHAR_ARG_LEN (1))); |
3183 | 597 |
3185 | 598 #ifdef DEBUG |
599 if (compq == 'V') | |
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600 std::cout << "qz: balancing done; QQ=" << std::endl << QQ << std::endl; |
3185 | 601 #endif |
3183 | 602 } |
603 | |
604 // then right | |
3185 | 605 if (compz == 'V') |
606 { | |
4552 | 607 F77_XFCN (dggbak, DGGBAK, |
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608 (F77_CONST_CHAR_ARG2 (&bal_job, 1), |
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609 F77_CONST_CHAR_ARG2 ("R", 1), |
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610 nn, ilo, ihi, lscale.data (), rscale.data (), |
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611 nn, ZZ.fortran_vec (), nn, info |
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612 F77_CHAR_ARG_LEN (1) |
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613 F77_CHAR_ARG_LEN (1))); |
3183 | 614 |
3185 | 615 #ifdef DEBUG |
616 if (compz == 'V') | |
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617 std::cout << "qz: balancing done; ZZ=" << std::endl << ZZ << std::endl; |
3185 | 618 #endif |
10311 | 619 } |
620 #endif | |
3183 | 621 |
622 static char qz_job; | |
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623 qz_job = (nargout < 2 ? 'E' : 'S'); |
3185 | 624 |
3183 | 625 if (complex_case) |
3185 | 626 { |
10311 | 627 // Complex case. |
628 | |
629 // The QR decomposition of cbb. | |
630 ComplexQR cbqr (cbb); | |
631 // The R matrix of QR decomposition for cbb. | |
632 cbb = cbqr.R (); | |
633 // (Q*)caa for following work. | |
634 caa = (cbqr.Q ().hermitian ()) * caa; | |
635 CQ = CQ * cbqr.Q (); | |
636 | |
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637 F77_XFCN (zgghrd, ZGGHRD, |
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638 (F77_CONST_CHAR_ARG2 (&compq, 1), |
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639 F77_CONST_CHAR_ARG2 (&compz, 1), |
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640 nn, ilo, ihi, caa.fortran_vec (), |
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641 nn, cbb.fortran_vec (), nn, CQ.fortran_vec (), nn, |
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642 CZ.fortran_vec (), nn, info |
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643 F77_CHAR_ARG_LEN (1) |
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644 F77_CHAR_ARG_LEN (1))); |
10311 | 645 |
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646 ComplexRowVector cwork (1 * nn); |
10311 | 647 |
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648 F77_XFCN (zhgeqz, ZHGEQZ, |
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649 (F77_CONST_CHAR_ARG2 (&qz_job, 1), |
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650 F77_CONST_CHAR_ARG2 (&compq, 1), |
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651 F77_CONST_CHAR_ARG2 (&compz, 1), |
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652 nn, ilo, ihi, |
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653 caa.fortran_vec (), nn, |
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654 cbb.fortran_vec (),nn, |
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655 xalpha.fortran_vec (), xbeta.fortran_vec (), |
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656 CQ.fortran_vec (), nn, |
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657 CZ.fortran_vec (), nn, |
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658 cwork.fortran_vec (), nn, rwork.fortran_vec (), info |
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659 F77_CHAR_ARG_LEN (1) |
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660 F77_CHAR_ARG_LEN (1) |
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661 F77_CHAR_ARG_LEN (1))); |
3185 | 662 |
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663 if (compq == 'V') |
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664 { |
10311 | 665 // Left eigenvector. |
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666 F77_XFCN (zggbak, ZGGBAK, |
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667 (F77_CONST_CHAR_ARG2 (&bal_job, 1), |
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668 F77_CONST_CHAR_ARG2 ("L", 1), |
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669 nn, ilo, ihi, lscale.data (), rscale.data (), |
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670 nn, CQ.fortran_vec (), nn, info |
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671 F77_CHAR_ARG_LEN (1) |
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672 F77_CHAR_ARG_LEN (1))); |
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673 } |
3185 | 674 |
10311 | 675 // Right eigenvector. |
3185 | 676 if (compz == 'V') |
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677 { |
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678 F77_XFCN (zggbak, ZGGBAK, |
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679 (F77_CONST_CHAR_ARG2 (&bal_job, 1), |
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680 F77_CONST_CHAR_ARG2 ("R", 1), |
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681 nn, ilo, ihi, lscale.data (), rscale.data (), |
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682 nn, CZ.fortran_vec (), nn, info |
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683 F77_CHAR_ARG_LEN (1) |
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684 F77_CHAR_ARG_LEN (1))); |
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685 } |
3185 | 686 |
687 } | |
10311 | 688 else |
3185 | 689 { |
690 #ifdef DEBUG | |
3538 | 691 std::cout << "qz: peforming qr decomposition of bb" << std::endl; |
3185 | 692 #endif |
3183 | 693 |
10311 | 694 // Compute the QR factorization of bb. |
3185 | 695 QR bqr (bb); |
696 | |
697 #ifdef DEBUG | |
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698 std::cout << "qz: qr (bb) done; now peforming qz decomposition" |
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699 << std::endl; |
3185 | 700 #endif |
3183 | 701 |
3185 | 702 bb = bqr.R (); |
703 | |
704 #ifdef DEBUG | |
3538 | 705 std::cout << "qz: extracted bb" << std::endl; |
3185 | 706 #endif |
3183 | 707 |
10311 | 708 aa = (bqr.Q ()).transpose () * aa; |
3185 | 709 |
710 #ifdef DEBUG | |
3538 | 711 std::cout << "qz: updated aa " << std::endl; |
712 std::cout << "bqr.Q () = " << std::endl << bqr.Q () << std::endl; | |
3183 | 713 |
3185 | 714 if (compq == 'V') |
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715 std::cout << "QQ =" << QQ << std::endl; |
3185 | 716 #endif |
3183 | 717 |
3185 | 718 if (compq == 'V') |
10311 | 719 QQ = QQ * bqr.Q (); |
3183 | 720 |
3185 | 721 #ifdef DEBUG |
3538 | 722 std::cout << "qz: precursors done..." << std::endl; |
3185 | 723 #endif |
3183 | 724 |
3185 | 725 #ifdef DEBUG |
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726 std::cout << "qz: compq = " << compq << ", compz = " << compz |
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727 << std::endl; |
3185 | 728 #endif |
3183 | 729 |
10311 | 730 // Reduce to generalized hessenberg form. |
3185 | 731 F77_XFCN (dgghrd, DGGHRD, |
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732 (F77_CONST_CHAR_ARG2 (&compq, 1), |
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733 F77_CONST_CHAR_ARG2 (&compz, 1), |
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734 nn, ilo, ihi, aa.fortran_vec (), |
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735 nn, bb.fortran_vec (), nn, QQ.fortran_vec (), nn, |
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736 ZZ.fortran_vec (), nn, info |
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737 F77_CHAR_ARG_LEN (1) |
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738 F77_CHAR_ARG_LEN (1))); |
3183 | 739 |
10311 | 740 // Check if just computing generalized eigenvalues or if we're |
741 // actually computing the decomposition. | |
3183 | 742 |
10311 | 743 // Reduce to generalized Schur form. |
3185 | 744 F77_XFCN (dhgeqz, DHGEQZ, |
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745 (F77_CONST_CHAR_ARG2 (&qz_job, 1), |
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746 F77_CONST_CHAR_ARG2 (&compq, 1), |
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747 F77_CONST_CHAR_ARG2 (&compz, 1), |
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748 nn, ilo, ihi, aa.fortran_vec (), nn, bb.fortran_vec (), |
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749 nn, alphar.fortran_vec (), alphai.fortran_vec (), |
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750 betar.fortran_vec (), QQ.fortran_vec (), nn, |
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751 ZZ.fortran_vec (), nn, work.fortran_vec (), nn, info |
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752 F77_CHAR_ARG_LEN (1) |
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753 F77_CHAR_ARG_LEN (1) |
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754 F77_CHAR_ARG_LEN (1))); |
10311 | 755 |
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756 if (compq == 'V') |
10311 | 757 { |
758 F77_XFCN (dggbak, DGGBAK, | |
759 (F77_CONST_CHAR_ARG2 (&bal_job, 1), | |
760 F77_CONST_CHAR_ARG2 ("L", 1), | |
761 nn, ilo, ihi, lscale.data (), rscale.data (), | |
762 nn, QQ.fortran_vec (), nn, info | |
763 F77_CHAR_ARG_LEN (1) | |
764 F77_CHAR_ARG_LEN (1))); | |
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765 |
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766 #ifdef DEBUG |
10311 | 767 if (compq == 'V') |
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768 std::cout << "qz: balancing done; QQ=" << std::endl |
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769 << QQ << std::endl; |
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770 #endif |
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771 } |
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772 |
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773 // then right |
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774 if (compz == 'V') |
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775 { |
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776 F77_XFCN (dggbak, DGGBAK, |
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777 (F77_CONST_CHAR_ARG2 (&bal_job, 1), |
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778 F77_CONST_CHAR_ARG2 ("R", 1), |
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779 nn, ilo, ihi, lscale.data (), rscale.data (), |
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780 nn, ZZ.fortran_vec (), nn, info |
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781 F77_CHAR_ARG_LEN (1) |
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782 F77_CHAR_ARG_LEN (1))); |
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783 |
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784 #ifdef DEBUG |
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785 if (compz == 'V') |
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786 std::cout << "qz: balancing done; ZZ=" << std::endl |
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787 << ZZ << std::endl; |
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788 #endif |
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789 } |
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790 |
3185 | 791 } |
3183 | 792 |
10311 | 793 // Order the QZ decomposition? |
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794 if (! (ord_job == 'N' || ord_job == 'n')) |
3183 | 795 { |
3185 | 796 if (complex_case) |
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797 { |
10311 | 798 // Probably not needed, but better be safe. |
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799 error ("qz: cannot re-order complex qz decomposition"); |
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800 return retval; |
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801 } |
3185 | 802 else |
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803 { |
3185 | 804 #ifdef DEBUG_SORT |
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805 std::cout << "qz: ordering eigenvalues: ord_job = " |
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806 << ord_job << std::endl; |
3185 | 807 #endif |
3183 | 808 |
10311 | 809 // Declared static to avoid vfork/long jump compiler complaints. |
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810 static sort_function sort_test; |
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811 sort_test = 0; |
3183 | 812 |
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813 switch (ord_job) |
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814 { |
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815 case 'S': |
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816 case 's': |
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817 sort_test = &fin; |
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818 break; |
3183 | 819 |
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820 case 'B': |
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821 case 'b': |
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822 sort_test = &fout; |
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823 break; |
3183 | 824 |
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825 case '+': |
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826 sort_test = &fcrhp; |
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827 break; |
3183 | 828 |
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829 case '-': |
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830 sort_test = &folhp; |
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831 break; |
3185 | 832 |
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833 default: |
10311 | 834 // Invalid order option (should never happen, since we |
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835 // checked the options at the top). |
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836 panic_impossible (); |
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837 break; |
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838 } |
3183 | 839 |
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840 octave_idx_type ndim, fail; |
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841 double inf_norm; |
3185 | 842 |
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843 F77_XFCN (xdlange, XDLANGE, |
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844 (F77_CONST_CHAR_ARG2 ("I", 1), |
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845 nn, nn, aa.data (), nn, work.fortran_vec (), inf_norm |
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846 F77_CHAR_ARG_LEN (1))); |
3185 | 847 |
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848 double eps = std::numeric_limits<double>::epsilon () * inf_norm * nn; |
3185 | 849 |
850 #ifdef DEBUG_SORT | |
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851 std::cout << "qz: calling dsubsp: aa=" << std::endl; |
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852 octave_print_internal (std::cout, aa, 0); |
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853 std::cout << std::endl << "bb=" << std::endl; |
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854 octave_print_internal (std::cout, bb, 0); |
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855 if (compz == 'V') |
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856 { |
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857 std::cout << std::endl << "ZZ=" << std::endl; |
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858 octave_print_internal (std::cout, ZZ, 0); |
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859 } |
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860 std::cout << std::endl; |
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861 std::cout << "alphar = " << std::endl; |
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862 octave_print_internal (std::cout, (Matrix) alphar, 0); |
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863 std::cout << std::endl << "alphai = " << std::endl; |
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864 octave_print_internal (std::cout, (Matrix) alphai, 0); |
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865 std::cout << std::endl << "beta = " << std::endl; |
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866 octave_print_internal (std::cout, (Matrix) betar, 0); |
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867 std::cout << std::endl; |
3185 | 868 #endif |
869 | |
11570
57632dea2446
attempt better backward compatibility for Array constructors
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870 Array<octave_idx_type> ind (dim_vector (nn, 1)); |
3550 | 871 |
10154
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872 F77_XFCN (dsubsp, DSUBSP, |
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873 (nn, nn, aa.fortran_vec (), bb.fortran_vec (), |
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874 ZZ.fortran_vec (), sort_test, eps, ndim, fail, |
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875 ind.fortran_vec ())); |
3185 | 876 |
877 #ifdef DEBUG | |
10154
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878 std::cout << "qz: back from dsubsp: aa=" << std::endl; |
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879 octave_print_internal (std::cout, aa, 0); |
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880 std::cout << std::endl << "bb=" << std::endl; |
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881 octave_print_internal (std::cout, bb, 0); |
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882 if (compz == 'V') |
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883 { |
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884 std::cout << std::endl << "ZZ=" << std::endl; |
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885 octave_print_internal (std::cout, ZZ, 0); |
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886 } |
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887 std::cout << std::endl; |
3185 | 888 #endif |
889 | |
10311 | 890 // Manually update alphar, alphai, betar. |
10154
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891 static int jj; |
3185 | 892 |
10311 | 893 jj = 0; |
10154
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894 while (jj < nn) |
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895 { |
3185 | 896 #ifdef DEBUG_EIG |
10154
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897 std::cout << "computing gen eig #" << jj << std::endl; |
3185 | 898 #endif |
899 | |
10311 | 900 // Number of zeros in this block. |
901 static int zcnt; | |
3185 | 902 |
10154
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903 if (jj == (nn-1)) |
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904 zcnt = 1; |
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905 else if (aa(jj+1,jj) == 0) |
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|
906 zcnt = 1; |
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|
907 else zcnt = 2; |
3185 | 908 |
10311 | 909 if (zcnt == 1) |
10154
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910 { |
10311 | 911 // Real zero. |
3185 | 912 #ifdef DEBUG_EIG |
10154
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|
913 std::cout << " single gen eig:" << std::endl; |
17787
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Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
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|
914 std::cout << " alphar(" << jj << ") = " << aa(jj,jj) |
175b392e91fe
Use GNU style coding conventions for code in libinterp/
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|
915 << std::endl; |
18678
6113e0c6920b
maint: Clean up extra spaces before/after parentheses.
Rik <rik@octave.org>
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17787
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|
916 std::cout << " betar(" << jj << ") = " << bb(jj,jj) |
17787
175b392e91fe
Use GNU style coding conventions for code in libinterp/
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|
917 << std::endl; |
10154
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918 std::cout << " alphai(" << jj << ") = 0" << std::endl; |
3185 | 919 #endif |
920 | |
10154
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|
921 alphar(jj) = aa(jj,jj); |
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|
922 alphai(jj) = 0; |
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|
923 betar(jj) = bb(jj,jj); |
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|
924 } |
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|
925 else |
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|
926 { |
10311 | 927 // Complex conjugate pair. |
3185 | 928 #ifdef DEBUG_EIG |
10154
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|
929 std::cout << "qz: calling dlag2:" << std::endl; |
40dfc0c99116
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|
930 std::cout << "safmin=" |
17787
175b392e91fe
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|
931 << setiosflags (std::ios::scientific) |
175b392e91fe
Use GNU style coding conventions for code in libinterp/
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|
932 << safmin << std::endl; |
3185 | 933 |
10154
40dfc0c99116
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|
934 for (int idr = jj; idr <= jj+1; idr++) |
40dfc0c99116
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|
935 { |
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|
936 for (int idc = jj; idc <= jj+1; idc++) |
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|
937 { |
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|
938 std::cout << "aa(" << idr << "," << idc << ")=" |
17787
175b392e91fe
Use GNU style coding conventions for code in libinterp/
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|
939 << aa(idr,idc) << std::endl; |
10154
40dfc0c99116
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|
940 std::cout << "bb(" << idr << "," << idc << ")=" |
17787
175b392e91fe
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|
941 << bb(idr,idc) << std::endl; |
10154
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|
942 } |
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|
943 } |
3185 | 944 #endif |
945 | |
17787
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changeset
|
946 // FIXME: probably should be using |
10154
40dfc0c99116
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|
947 // fortran_vec instead of &aa(jj,jj) here. |
4566 | 948 |
10154
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|
949 double scale1, scale2, wr1, wr2, wi; |
10311 | 950 const double *aa_ptr = aa.data () + jj * nn + jj; |
951 const double *bb_ptr = bb.data () + jj * nn + jj; | |
10154
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|
952 F77_XFCN (dlag2, DLAG2, |
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|
953 (aa_ptr, nn, bb_ptr, nn, safmin, |
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|
954 scale1, scale2, wr1, wr2, wi)); |
3185 | 955 |
956 #ifdef DEBUG_EIG | |
10154
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|
957 std::cout << "dlag2 returns: scale1=" << scale1 |
17787
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|
958 << "\tscale2=" << scale2 << std::endl |
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|
959 << "\twr1=" << wr1 << "\twr2=" << wr2 |
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changeset
|
960 << "\twi=" << wi << std::endl; |
3185 | 961 #endif |
962 | |
10311 | 963 // Just to be safe, check if it's a real pair. |
10154
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|
964 if (wi == 0) |
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|
965 { |
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|
966 alphar(jj) = wr1; |
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|
967 alphai(jj) = 0; |
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|
968 betar(jj) = scale1; |
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|
969 alphar(jj+1) = wr2; |
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970 alphai(jj+1) = 0; |
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|
971 betar(jj+1) = scale2; |
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|
972 } |
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|
973 else |
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|
974 { |
10311 | 975 alphar(jj) = alphar(jj+1) = wr1; |
10154
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|
976 alphai(jj) = -(alphai(jj+1) = wi); |
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|
977 betar(jj) = betar(jj+1) = scale1; |
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978 } |
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|
979 } |
3185 | 980 |
10311 | 981 // Advance past this block. |
10154
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|
982 jj += zcnt; |
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|
983 } |
3185 | 984 |
985 #ifdef DEBUG_SORT | |
10154
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|
986 std::cout << "qz: back from dsubsp: aa=" << std::endl; |
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|
987 octave_print_internal (std::cout, aa, 0); |
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988 std::cout << std::endl << "bb=" << std::endl; |
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|
989 octave_print_internal (std::cout, bb, 0); |
3185 | 990 |
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991 if (compz == 'V') |
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992 { |
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993 std::cout << std::endl << "ZZ=" << std::endl; |
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|
994 octave_print_internal (std::cout, ZZ, 0); |
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|
995 } |
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|
996 std::cout << std::endl << "qz: ndim=" << ndim << std::endl |
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997 << "fail=" << fail << std::endl; |
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998 std::cout << "alphar = " << std::endl; |
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999 octave_print_internal (std::cout, (Matrix) alphar, 0); |
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1000 std::cout << std::endl << "alphai = " << std::endl; |
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1001 octave_print_internal (std::cout, (Matrix) alphai, 0); |
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1002 std::cout << std::endl << "beta = " << std::endl; |
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1003 octave_print_internal (std::cout, (Matrix) betar, 0); |
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1004 std::cout << std::endl; |
3185 | 1005 #endif |
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1006 } |
3183 | 1007 } |
3185 | 1008 |
10311 | 1009 // Compute generalized eigenvalues? |
3183 | 1010 ComplexColumnVector gev; |
3185 | 1011 |
1012 if (nargout < 2 || nargout == 7 || (nargin == 3 && nargout == 4)) | |
3183 | 1013 { |
3185 | 1014 if (complex_case) |
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1015 { |
10311 | 1016 int cnt = 0; |
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1017 |
10311 | 1018 for (int ii = 0; ii < nn; ii++) |
1019 cnt++; | |
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1020 |
10311 | 1021 ComplexColumnVector tmp (cnt); |
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1022 |
10311 | 1023 cnt = 0; |
1024 for (int ii = 0; ii < nn; ii++) | |
1025 tmp(cnt++) = xalpha(ii) / xbeta(ii); | |
1026 | |
1027 gev = tmp; | |
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1028 } |
3185 | 1029 else |
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1030 { |
3185 | 1031 #ifdef DEBUG |
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1032 std::cout << "qz: computing generalized eigenvalues" << std::endl; |
3185 | 1033 #endif |
3183 | 1034 |
10311 | 1035 // Return finite generalized eigenvalues. |
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1036 int cnt = 0; |
3185 | 1037 |
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1038 for (int ii = 0; ii < nn; ii++) |
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1039 if (betar(ii) != 0) |
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1040 cnt++; |
3185 | 1041 |
10311 | 1042 ComplexColumnVector tmp (cnt); |
3185 | 1043 |
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1044 cnt = 0; |
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1045 for (int ii = 0; ii < nn; ii++) |
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1046 if (betar(ii) != 0) |
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1047 tmp(cnt++) = Complex(alphar(ii), alphai(ii))/betar(ii); |
10311 | 1048 |
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1049 gev = tmp; |
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1050 } |
3183 | 1051 } |
1052 | |
10311 | 1053 // Right, left eigenvector matrices. |
3185 | 1054 if (nargout >= 5) |
3183 | 1055 { |
10311 | 1056 // Which side to compute? |
1057 char side = (nargout == 5 ? 'R' : 'B'); | |
1058 // Compute all of them and backtransform | |
1059 char howmny = 'B'; | |
1060 // Dummy pointer; select is not used. | |
1061 octave_idx_type *select = 0; | |
3185 | 1062 |
1063 if (complex_case) | |
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1064 { |
10311 | 1065 CVL = CQ; |
1066 CVR = CZ; | |
1067 ComplexRowVector cwork2 (2 * nn); | |
1068 RowVector rwork2 (8 * nn); | |
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1069 octave_idx_type m; |
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1070 |
10311 | 1071 F77_XFCN (ztgevc, ZTGEVC, |
1072 (F77_CONST_CHAR_ARG2 (&side, 1), | |
1073 F77_CONST_CHAR_ARG2 (&howmny, 1), | |
1074 select, nn, caa.fortran_vec (), nn, cbb.fortran_vec (), | |
1075 nn, CVL.fortran_vec (), nn, CVR.fortran_vec (), nn, nn, | |
1076 m, cwork2.fortran_vec (), rwork2.fortran_vec (), info | |
1077 F77_CHAR_ARG_LEN (1) | |
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1078 F77_CHAR_ARG_LEN (1))); |
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1079 } |
3185 | 1080 else |
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1081 { |
3185 | 1082 #ifdef DEBUG |
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1083 std::cout << "qz: computing generalized eigenvectors" << std::endl; |
3185 | 1084 #endif |
1085 | |
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1086 VL = QQ; |
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1087 VR = ZZ; |
10311 | 1088 octave_idx_type m; |
1089 | |
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1090 F77_XFCN (dtgevc, DTGEVC, |
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1091 (F77_CONST_CHAR_ARG2 (&side, 1), |
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1092 F77_CONST_CHAR_ARG2 (&howmny, 1), |
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1093 select, nn, aa.fortran_vec (), nn, bb.fortran_vec (), |
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1094 nn, VL.fortran_vec (), nn, VR.fortran_vec (), nn, nn, |
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1095 m, work.fortran_vec (), info |
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1096 F77_CHAR_ARG_LEN (1) |
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1097 F77_CHAR_ARG_LEN (1))); |
3185 | 1098 |
10311 | 1099 // Now construct the complex form of VV, WW. |
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1100 int jj = 0; |
3185 | 1101 |
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1102 while (jj < nn) |
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1103 { |
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1104 OCTAVE_QUIT; |
4153 | 1105 |
10311 | 1106 // See if real or complex eigenvalue. |
1107 | |
1108 // Column increment; assume complex eigenvalue. | |
1109 int cinc = 2; | |
3185 | 1110 |
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1111 if (jj == (nn-1)) |
10311 | 1112 // Single column. |
1113 cinc = 1; | |
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1114 else if (aa(jj+1,jj) == 0) |
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1115 cinc = 1; |
3185 | 1116 |
10311 | 1117 // Now copy the eigenvector (s) to CVR, CVL. |
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1118 if (cinc == 1) |
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1119 { |
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1120 for (int ii = 0; ii < nn; ii++) |
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1121 CVR(ii,jj) = VR(ii,jj); |
3185 | 1122 |
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1123 if (side == 'B') |
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1124 for (int ii = 0; ii < nn; ii++) |
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1125 CVL(ii,jj) = VL(ii,jj); |
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1126 } |
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1127 else |
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1128 { |
10311 | 1129 // Double column; complex vector. |
3185 | 1130 |
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1131 for (int ii = 0; ii < nn; ii++) |
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1132 { |
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1133 CVR(ii,jj) = Complex (VR(ii,jj), VR(ii,jj+1)); |
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1134 CVR(ii,jj+1) = Complex (VR(ii,jj), -VR(ii,jj+1)); |
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1135 } |
3183 | 1136 |
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1137 if (side == 'B') |
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1138 for (int ii = 0; ii < nn; ii++) |
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1139 { |
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1140 CVL(ii,jj) = Complex (VL(ii,jj), VL(ii,jj+1)); |
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1141 CVL(ii,jj+1) = Complex (VL(ii,jj), -VL(ii,jj+1)); |
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1142 } |
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1143 } |
3185 | 1144 |
10311 | 1145 // Advance to next eigenvectors (if any). |
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1146 jj += cinc; |
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1147 } |
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1148 } |
3183 | 1149 } |
3185 | 1150 |
1151 switch (nargout) | |
1152 { | |
1153 case 7: | |
1154 retval(6) = gev; | |
1155 | |
10311 | 1156 case 6: |
1157 // Return eigenvectors. | |
3185 | 1158 retval(5) = CVL; |
1159 | |
10311 | 1160 case 5: |
1161 // Return eigenvectors. | |
3185 | 1162 retval(4) = CVR; |
1163 | |
1164 case 4: | |
1165 if (nargin == 3) | |
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1166 { |
3185 | 1167 #ifdef DEBUG |
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1168 std::cout << "qz: sort: retval(3) = gev = " << std::endl; |
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1169 octave_print_internal (std::cout, gev); |
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1170 std::cout << std::endl; |
3185 | 1171 #endif |
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1172 retval(3) = gev; |
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1173 } |
3185 | 1174 else |
10311 | 1175 { |
1176 if (complex_case) | |
1177 retval(3) = CZ; | |
1178 else | |
1179 retval(3) = ZZ; | |
1180 } | |
3185 | 1181 |
1182 case 3: | |
1183 if (nargin == 3) | |
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1184 { |
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1185 if (complex_case) |
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1186 retval(2) = CZ; |
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1187 else |
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1188 retval(2) = ZZ; |
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1189 } |
3185 | 1190 else |
10311 | 1191 { |
1192 if (complex_case) | |
1193 retval(2) = CQ.hermitian (); | |
1194 else | |
1195 retval(2) = QQ.transpose (); | |
1196 } | |
1197 | |
3185 | 1198 case 2: |
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1199 { |
10311 | 1200 if (complex_case) |
1201 { | |
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1202 #ifdef DEBUG |
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1203 std::cout << "qz: retval(1) = cbb = " << std::endl; |
10311 | 1204 octave_print_internal (std::cout, cbb, 0); |
1205 std::cout << std::endl << "qz: retval(0) = caa = " <<std::endl; | |
1206 octave_print_internal (std::cout, caa, 0); | |
1207 std::cout << std::endl; | |
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1208 #endif |
10311 | 1209 retval(1) = cbb; |
1210 retval(0) = caa; | |
1211 } | |
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1212 else |
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1213 { |
3185 | 1214 #ifdef DEBUG |
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1215 std::cout << "qz: retval(1) = bb = " << std::endl; |
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1216 octave_print_internal (std::cout, bb, 0); |
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1217 std::cout << std::endl << "qz: retval(0) = aa = " <<std::endl; |
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1218 octave_print_internal (std::cout, aa, 0); |
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1219 std::cout << std::endl; |
3185 | 1220 #endif |
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Use GNU style coding conventions for code in libinterp/
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1221 retval(1) = bb; |
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Use GNU style coding conventions for code in libinterp/
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1222 retval(0) = aa; |
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Use GNU style coding conventions for code in libinterp/
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1223 } |
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1224 } |
10311 | 1225 break; |
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1226 |
3185 | 1227 |
1228 case 1: | |
1229 case 0: | |
1230 #ifdef DEBUG | |
3538 | 1231 std::cout << "qz: retval(0) = gev = " << gev << std::endl; |
3185 | 1232 #endif |
1233 retval(0) = gev; | |
1234 break; | |
1235 | |
1236 default: | |
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1237 error ("qz: too many return arguments"); |
3185 | 1238 break; |
3183 | 1239 } |
1240 | |
3185 | 1241 #ifdef DEBUG |
3538 | 1242 std::cout << "qz: exiting (at long last)" << std::endl; |
3185 | 1243 #endif |
3183 | 1244 |
1245 return retval; | |
1246 } | |
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1247 |
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1248 /* |
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1249 %!shared a, b, c |
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1250 %! a = [1 2; 0 3]; |
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1251 %! b = [1 0; 0 0]; |
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1252 %! c = [0 1; 0 0]; |
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1253 %!assert (qz (a,b), 1) |
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1254 %!assert (isempty (qz (a,c))) |
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1255 |
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1256 ## Exaple 7.7.3 in Golub & Van Loan |
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1257 %!test |
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1258 %! a = [ 10 1 2; |
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1259 %! 1 2 -1; |
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1260 %! 1 1 2]; |
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1261 %! b = reshape (1:9,3,3); |
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1262 %! [aa, bb, q, z, v, w, lambda] = qz (a, b); |
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1263 %! sz = length (lambda); |
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1264 %! observed = (b * v * diag ([lambda;0])) (:, 1:sz); |
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1265 %! assert ((a*v)(:, 1:sz), observed, norm (observed) * 1e-14); |
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1266 %! observed = (diag ([lambda;0]) * w' * b) (1:sz, :); |
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1267 %! assert ((w'*a)(1:sz, :) , observed, norm (observed) * 1e-13); |
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1268 %! assert (q * a * z, aa, norm (aa) * 1e-14); |
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1269 %! assert (q * b * z, bb, norm (bb) * 1e-14); |
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1270 |
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1271 %!test |
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1272 %! A = [0, 0, -1, 0; 1, 0, 0, 0; -1, 0, -2, -1; 0, -1, 1, 0]; |
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1273 %! B = [0, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]; |
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1274 %! [AA, BB, Q, Z1] = qz (A, B); |
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1275 %! [AA, BB, Z2] = qz (A, B, '-'); |
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1276 %! assert (Z1, Z2); |
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1277 */ |