Mercurial > octave
annotate libinterp/corefcn/qz.cc @ 31605:e88a07dec498 stable
maint: Use macros to begin/end C++ namespaces.
* oct-conf-post-public.in.h: Define two macros (OCTAVE_BEGIN_NAMESPACE,
OCTAVE_END_NAMESPACE) that can be used to start/end a namespace.
* mk-opts.pl, build-env.h, build-env.in.cc, __betainc__.cc, __contourc__.cc,
__dsearchn__.cc, __eigs__.cc, __expint__.cc, __ftp__.cc, __gammainc__.cc,
__ichol__.cc, __ilu__.cc, __isprimelarge__.cc, __lin_interpn__.cc,
__magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, auto-shlib.cc,
auto-shlib.h, balance.cc, base-text-renderer.cc, base-text-renderer.h,
besselj.cc, bitfcns.cc, bsxfun.cc, c-file-ptr-stream.cc, c-file-ptr-stream.h,
call-stack.cc, call-stack.h, ccolamd.cc, cellfun.cc, chol.cc, colamd.cc,
colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, data.h, debug.cc,
defaults.cc, defaults.h, defun-int.h, defun.cc, det.cc, dirfns.cc, display.cc,
display.h, dlmread.cc, dmperm.cc, dot.cc, dynamic-ld.cc, dynamic-ld.h, eig.cc,
ellipj.cc, environment.cc, environment.h, error.cc, error.h, errwarn.h,
event-manager.cc, event-manager.h, event-queue.cc, event-queue.h, fcn-info.cc,
fcn-info.h, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc,
ft-text-renderer.cc, ft-text-renderer.h, gcd.cc, getgrent.cc, getpwent.cc,
getrusage.cc, givens.cc, gl-render.cc, gl-render.h, gl2ps-print.cc,
gl2ps-print.h, graphics-toolkit.cc, graphics-toolkit.h, graphics.cc,
graphics.in.h, gsvd.cc, gtk-manager.cc, gtk-manager.h, hash.cc, help.cc,
help.h, hess.cc, hex2num.cc, hook-fcn.cc, hook-fcn.h, input.cc, input.h,
interpreter-private.cc, interpreter-private.h, interpreter.cc, interpreter.h,
inv.cc, jsondecode.cc, jsonencode.cc, kron.cc, latex-text-renderer.cc,
latex-text-renderer.h, load-path.cc, load-path.h, load-save.cc, load-save.h,
lookup.cc, ls-ascii-helper.cc, ls-ascii-helper.h, ls-oct-text.cc, ls-utils.cc,
ls-utils.h, lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mex-private.h,
mex.cc, mgorth.cc, nproc.cc, oct-fstrm.cc, oct-fstrm.h, oct-hdf5-types.cc,
oct-hdf5-types.h, oct-hist.cc, oct-hist.h, oct-iostrm.cc, oct-iostrm.h,
oct-opengl.h, oct-prcstrm.cc, oct-prcstrm.h, oct-procbuf.cc, oct-procbuf.h,
oct-process.cc, oct-process.h, oct-stdstrm.h, oct-stream.cc, oct-stream.h,
oct-strstrm.cc, oct-strstrm.h, oct-tex-lexer.in.ll, oct-tex-parser.yy,
ordqz.cc, ordschur.cc, pager.cc, pager.h, pinv.cc, pow2.cc, pr-flt-fmt.cc,
pr-output.cc, procstream.cc, procstream.h, psi.cc, qr.cc, quad.cc, quadcc.cc,
qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, settings.cc, settings.h,
sighandlers.cc, sighandlers.h, sparse-xdiv.cc, sparse-xdiv.h, sparse-xpow.cc,
sparse-xpow.h, sparse.cc, spparms.cc, sqrtm.cc, stack-frame.cc, stack-frame.h,
stream-euler.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc, sylvester.cc,
symbfact.cc, syminfo.cc, syminfo.h, symrcm.cc, symrec.cc, symrec.h,
symscope.cc, symscope.h, symtab.cc, symtab.h, syscalls.cc, sysdep.cc, sysdep.h,
text-engine.cc, text-engine.h, text-renderer.cc, text-renderer.h, time.cc,
toplev.cc, tril.cc, tsearch.cc, typecast.cc, url-handle-manager.cc,
url-handle-manager.h, urlwrite.cc, utils.cc, utils.h, variables.cc,
variables.h, xdiv.cc, xdiv.h, xnorm.cc, xnorm.h, xpow.cc, xpow.h,
__delaunayn__.cc, __fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc,
__init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audiodevinfo.cc,
audioread.cc, convhulln.cc, fftw.cc, gzip.cc, mk-build-env-features.sh,
mk-builtins.pl, cdef-class.cc, cdef-class.h, cdef-fwd.h, cdef-manager.cc,
cdef-manager.h, cdef-method.cc, cdef-method.h, cdef-object.cc, cdef-object.h,
cdef-package.cc, cdef-package.h, cdef-property.cc, cdef-property.h,
cdef-utils.cc, cdef-utils.h, ov-base.cc, ov-base.h, ov-bool-mat.cc,
ov-builtin.h, ov-cell.cc, ov-class.cc, ov-class.h, ov-classdef.cc,
ov-classdef.h, ov-complex.cc, ov-fcn-handle.cc, ov-fcn-handle.h, ov-fcn.h,
ov-java.cc, ov-java.h, ov-mex-fcn.h, ov-null-mat.cc, ov-oncleanup.cc,
ov-struct.cc, ov-typeinfo.cc, ov-typeinfo.h, ov-usr-fcn.cc, ov-usr-fcn.h,
ov.cc, ov.h, octave.cc, octave.h, mk-ops.sh, op-b-b.cc, op-b-bm.cc,
op-b-sbm.cc, op-bm-b.cc, op-bm-bm.cc, op-bm-sbm.cc, op-cdm-cdm.cc, op-cell.cc,
op-chm.cc, op-class.cc, op-cm-cm.cc, op-cm-cs.cc, op-cm-m.cc, op-cm-s.cc,
op-cm-scm.cc, op-cm-sm.cc, op-cs-cm.cc, op-cs-cs.cc, op-cs-m.cc, op-cs-s.cc,
op-cs-scm.cc, op-cs-sm.cc, op-dm-dm.cc, op-dm-scm.cc, op-dm-sm.cc,
op-dm-template.cc, op-dms-template.cc, op-fcdm-fcdm.cc, op-fcm-fcm.cc,
op-fcm-fcs.cc, op-fcm-fm.cc, op-fcm-fs.cc, op-fcn.cc, op-fcs-fcm.cc,
op-fcs-fcs.cc, op-fcs-fm.cc, op-fcs-fs.cc, op-fdm-fdm.cc, op-fm-fcm.cc,
op-fm-fcs.cc, op-fm-fm.cc, op-fm-fs.cc, op-fs-fcm.cc, op-fs-fcs.cc,
op-fs-fm.cc, op-fs-fs.cc, op-i16-i16.cc, op-i32-i32.cc, op-i64-i64.cc,
op-i8-i8.cc, op-int-concat.cc, op-m-cm.cc, op-m-cs.cc, op-m-m.cc, op-m-s.cc,
op-m-scm.cc, op-m-sm.cc, op-mi.cc, op-pm-pm.cc, op-pm-scm.cc, op-pm-sm.cc,
op-pm-template.cc, op-range.cc, op-s-cm.cc, op-s-cs.cc, op-s-m.cc, op-s-s.cc,
op-s-scm.cc, op-s-sm.cc, op-sbm-b.cc, op-sbm-bm.cc, op-sbm-sbm.cc,
op-scm-cm.cc, op-scm-cs.cc, op-scm-m.cc, op-scm-s.cc, op-scm-scm.cc,
op-scm-sm.cc, op-sm-cm.cc, op-sm-cs.cc, op-sm-m.cc, op-sm-s.cc, op-sm-scm.cc,
op-sm-sm.cc, op-str-m.cc, op-str-s.cc, op-str-str.cc, op-struct.cc,
op-ui16-ui16.cc, op-ui32-ui32.cc, op-ui64-ui64.cc, op-ui8-ui8.cc, ops.h,
anon-fcn-validator.cc, anon-fcn-validator.h, bp-table.cc, bp-table.h,
comment-list.cc, comment-list.h, filepos.h, lex.h, lex.ll, oct-lvalue.cc,
oct-lvalue.h, oct-parse.yy, parse.h, profiler.cc, profiler.h,
pt-anon-scopes.cc, pt-anon-scopes.h, pt-arg-list.cc, pt-arg-list.h,
pt-args-block.cc, pt-args-block.h, pt-array-list.cc, pt-array-list.h,
pt-assign.cc, pt-assign.h, pt-binop.cc, pt-binop.h, pt-bp.cc, pt-bp.h,
pt-cbinop.cc, pt-cbinop.h, pt-cell.cc, pt-cell.h, pt-check.cc, pt-check.h,
pt-classdef.cc, pt-classdef.h, pt-cmd.h, pt-colon.cc, pt-colon.h, pt-const.cc,
pt-const.h, pt-decl.cc, pt-decl.h, pt-eval.cc, pt-eval.h, pt-except.cc,
pt-except.h, pt-exp.cc, pt-exp.h, pt-fcn-handle.cc, pt-fcn-handle.h, pt-id.cc,
pt-id.h, pt-idx.cc, pt-idx.h, pt-jump.h, pt-loop.cc, pt-loop.h, pt-mat.cc,
pt-mat.h, pt-misc.cc, pt-misc.h, pt-pr-code.cc, pt-pr-code.h, pt-select.cc,
pt-select.h, pt-spmd.cc, pt-spmd.h, pt-stmt.cc, pt-stmt.h, pt-tm-const.cc,
pt-tm-const.h, pt-unop.cc, pt-unop.h, pt-vm-eval.cc, pt-walk.cc, pt-walk.h,
pt.cc, pt.h, token.cc, token.h, Range.cc, Range.h, idx-vector.cc, idx-vector.h,
range-fwd.h, CollocWt.cc, CollocWt.h, aepbalance.cc, aepbalance.h, chol.cc,
chol.h, gepbalance.cc, gepbalance.h, gsvd.cc, gsvd.h, hess.cc, hess.h,
lo-mappers.cc, lo-mappers.h, lo-specfun.cc, lo-specfun.h, lu.cc, lu.h,
oct-convn.cc, oct-convn.h, oct-fftw.cc, oct-fftw.h, oct-norm.cc, oct-norm.h,
oct-rand.cc, oct-rand.h, oct-spparms.cc, oct-spparms.h, qr.cc, qr.h, qrp.cc,
qrp.h, randgamma.cc, randgamma.h, randmtzig.cc, randmtzig.h, randpoisson.cc,
randpoisson.h, schur.cc, schur.h, sparse-chol.cc, sparse-chol.h, sparse-lu.cc,
sparse-lu.h, sparse-qr.cc, sparse-qr.h, svd.cc, svd.h, child-list.cc,
child-list.h, dir-ops.cc, dir-ops.h, file-ops.cc, file-ops.h, file-stat.cc,
file-stat.h, lo-sysdep.cc, lo-sysdep.h, lo-sysinfo.cc, lo-sysinfo.h,
mach-info.cc, mach-info.h, oct-env.cc, oct-env.h, oct-group.cc, oct-group.h,
oct-password.cc, oct-password.h, oct-syscalls.cc, oct-syscalls.h, oct-time.cc,
oct-time.h, oct-uname.cc, oct-uname.h, action-container.cc, action-container.h,
base-list.h, cmd-edit.cc, cmd-edit.h, cmd-hist.cc, cmd-hist.h, f77-fcn.h,
file-info.cc, file-info.h, lo-array-errwarn.cc, lo-array-errwarn.h, lo-hash.cc,
lo-hash.h, lo-ieee.h, lo-regexp.cc, lo-regexp.h, lo-utils.cc, lo-utils.h,
oct-base64.cc, oct-base64.h, oct-glob.cc, oct-glob.h, oct-inttypes.h,
oct-mutex.cc, oct-mutex.h, oct-refcount.h, oct-shlib.cc, oct-shlib.h,
oct-sparse.cc, oct-sparse.h, oct-string.h, octave-preserve-stream-state.h,
pathsearch.cc, pathsearch.h, quit.cc, quit.h, unwind-prot.cc, unwind-prot.h,
url-transfer.cc, url-transfer.h : Use new macros to begin/end C++ namespaces.
| author | Rik <rik@octave.org> |
|---|---|
| date | Thu, 01 Dec 2022 14:23:45 -0800 |
| parents | 796f54d4ddbf |
| children | 597f3ee61a48 |
| rev | line source |
|---|---|
|
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 1998-2022 The Octave Project Developers |
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4 // |
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5 // See the file COPYRIGHT.md in the top-level directory of this |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
| 3183 | 25 |
| 26 // Generalized eigenvalue balancing via LAPACK | |
| 3911 | 27 |
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28 // Originally written by A. S. Hodel <scotte@eng.auburn.edu>, but is |
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29 // substantially different with the change to use LAPACK. |
| 3183 | 30 |
| 31 #undef DEBUG | |
| 32 #undef DEBUG_SORT | |
| 33 #undef DEBUG_EIG | |
| 34 | |
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35 #if defined (HAVE_CONFIG_H) |
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36 # include "config.h" |
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37 #endif |
| 3183 | 38 |
| 23430 | 39 #include <cctype> |
| 40 #include <cmath> | |
| 4051 | 41 |
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42 #if defined (DEBUG_EIG) |
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43 # include <iomanip> |
| 23430 | 44 #endif |
| 3183 | 45 |
| 4153 | 46 #include "f77-fcn.h" |
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47 #include "lo-lapack-proto.h" |
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48 #include "qr.h" |
| 4153 | 49 #include "quit.h" |
| 50 | |
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51 #include "defun.h" |
| 3183 | 52 #include "error.h" |
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53 #include "errwarn.h" |
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54 #include "ovl.h" |
| 3185 | 55 #if defined (DEBUG) || defined (DEBUG_SORT) |
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56 # include "pager.h" |
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57 # include "pr-output.h" |
| 3183 | 58 #endif |
| 59 | |
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60 OCTAVE_BEGIN_NAMESPACE(octave) |
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61 |
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62 // FIXME: Matlab does not produce lambda as the first output argument. |
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63 // Compatibility problem? |
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65 DEFUN (qz, args, nargout, |
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66 doc: /* -*- texinfo -*- |
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67 @deftypefn {} {@var{lambda} =} qz (@var{A}, @var{B}) |
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68 @deftypefnx {} {[@var{AA}, @var{BB}, @var{Q}, @var{Z}, @var{V}, @var{W}, @var{lambda}] =} qz (@var{A}, @var{B}) |
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69 @deftypefnx {} {[@var{AA}, @var{BB}, @var{Z}] =} qz (@var{A}, @var{B}, @var{opt}) |
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70 @deftypefnx {} {[@var{AA}, @var{BB}, @var{Z}, @var{lambda}] =} qz (@var{A}, @var{B}, @var{opt}) |
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71 Compute the QZ@tie{}decomposition of a generalized eigenvalue problem. |
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72 |
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73 The generalized eigenvalue problem is defined as |
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74 |
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75 @tex |
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76 $$A x = \lambda B x$$ |
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77 @end tex |
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78 @ifnottex |
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79 |
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80 @math{A x = @var{lambda} B x} |
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81 |
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82 @end ifnottex |
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83 |
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84 There are three calling forms of the function: |
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85 |
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86 @enumerate |
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87 @item @code{@var{lambda} = qz (@var{A}, @var{B})} |
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88 |
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89 Compute the generalized eigenvalues |
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90 @tex |
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91 $\lambda.$ |
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92 @end tex |
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93 @ifnottex |
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94 @var{lambda}. |
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95 @end ifnottex |
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96 |
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97 @item @code{[@var{AA}, @var{BB}, @var{Q}, @var{Z}, @var{V}, @var{W}, @var{lambda}] = qz (@var{A}, @var{B})} |
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98 |
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99 Compute QZ@tie{}decomposition, generalized eigenvectors, and generalized |
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100 eigenvalues. |
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101 @tex |
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102 $$ AA = Q^T AZ, BB = Q^T BZ $$ |
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103 $$ AV = BV{ \rm diag }(\lambda) $$ |
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104 $$ W^T A = { \rm diag }(\lambda)W^T B $$ |
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105 @end tex |
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106 @ifnottex |
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107 |
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108 @example |
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109 @group |
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110 |
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111 @var{AA} = @var{Q} * @var{A} * @var{Z}, @var{BB} = @var{Q} * @var{B} * @var{Z} |
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112 @var{A} * @var{V} = @var{B} * @var{V} * diag (@var{lambda}) |
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113 @var{W}' * @var{A} = diag (@var{lambda}) * @var{W}' * @var{B} |
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114 |
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115 @end group |
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116 @end example |
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117 |
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118 @end ifnottex |
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119 with @var{Q} and @var{Z} orthogonal (unitary for complex case). |
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120 |
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121 @item @code{[@var{AA}, @var{BB}, @var{Z} @{, @var{lambda}@}] = qz (@var{A}, @var{B}, @var{opt})} |
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122 |
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123 As in form 2 above, but allows ordering of generalized eigenpairs for, e.g., |
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124 solution of discrete time algebraic @nospell{Riccati} equations. Form 3 is not |
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125 available for complex matrices, and does not compute the generalized |
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126 eigenvectors @var{V}, @var{W}, nor the orthogonal matrix @var{Q}. |
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127 |
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128 @table @var |
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129 @item opt |
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130 for ordering eigenvalues of the @nospell{GEP} pencil. The leading block of |
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131 the revised pencil contains all eigenvalues that satisfy: |
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132 |
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133 @table @asis |
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134 @item @qcode{"N"} |
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135 unordered (default) |
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136 |
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137 @item @qcode{"S"} |
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138 small: leading block has all |
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139 @tex |
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140 $|\lambda| < 1$ |
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141 @end tex |
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142 @ifnottex |
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143 |@var{lambda}| < 1 |
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144 @end ifnottex |
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145 |
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146 @item @qcode{"B"} |
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147 big: leading block has all |
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148 @tex |
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149 $|\lambda| \geq 1$ |
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150 @end tex |
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151 @ifnottex |
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152 |@var{lambda}| @geq{} 1 |
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153 @end ifnottex |
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154 |
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155 @item @qcode{"-"} |
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156 negative real part: leading block has all eigenvalues in the open left |
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157 half-plane |
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158 |
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159 @item @qcode{"+"} |
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160 non-negative real part: leading block has all eigenvalues in the closed right |
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161 half-plane |
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162 @end table |
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163 @end table |
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164 @end enumerate |
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165 |
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166 Note: @code{qz} performs permutation balancing, but not scaling |
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167 (@pxref{XREFbalance,,@code{balance}}), which may be lead to less accurate |
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168 results than @code{eig}. The order of output arguments was selected for |
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169 compatibility with @sc{matlab}. |
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170 @seealso{eig, gsvd, balance, chol, hess, lu, qr, qzhess, schur} |
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171 @end deftypefn */) |
| 3183 | 172 { |
| 23430 | 173 int nargin = args.length (); |
| 3183 | 174 |
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175 #if defined (DEBUG) |
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176 octave_stdout << "qz: nargin = " << nargin |
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177 << ", nargout = " << nargout << std::endl; |
| 3185 | 178 #endif |
| 3183 | 179 |
| 3185 | 180 if (nargin < 2 || nargin > 3 || nargout > 7) |
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181 print_usage (); |
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182 |
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183 if (nargin == 3 && (nargout < 3 || nargout > 4)) |
| 23430 | 184 error ("qz: invalid number of output arguments for form 3 call"); |
| 3183 | 185 |
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186 #if defined (DEBUG) |
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187 octave_stdout << "qz: determine ordering option" << std::endl; |
| 3185 | 188 #endif |
| 3183 | 189 |
| 10311 | 190 // Determine ordering option. |
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191 |
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192 char ord_job = 'N'; |
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193 double safmin = 0.0; |
| 3185 | 194 |
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195 if (nargin == 3) |
| 3185 | 196 { |
| 23430 | 197 std::string opt = args(2).xstring_value ("qz: OPT must be a string"); |
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198 |
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199 if (opt.empty ()) |
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200 error ("qz: OPT must be a non-empty string"); |
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201 |
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202 ord_job = std::toupper (opt[0]); |
| 3183 | 203 |
| 23430 | 204 std::string valid_opts = "NSB+-"; |
| 205 | |
| 206 if (valid_opts.find_first_of (ord_job) == std::string::npos) | |
| 207 error ("qz: invalid order option '%c'", ord_job); | |
| 3185 | 208 |
| 209 // overflow constant required by dlag2 | |
| 4552 | 210 F77_FUNC (xdlamch, XDLAMCH) (F77_CONST_CHAR_ARG2 ("S", 1), |
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211 safmin |
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212 F77_CHAR_ARG_LEN (1)); |
| 3183 | 213 |
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214 #if defined (DEBUG_EIG) |
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215 octave_stdout << "qz: initial value of safmin=" |
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216 << setiosflags (std::ios::scientific) |
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217 << safmin << std::endl; |
| 3185 | 218 #endif |
| 3183 | 219 |
| 10311 | 220 // Some machines (e.g., DEC alpha) get safmin = 0; |
| 221 // for these, use eps instead to avoid problems in dlag2. | |
| 3185 | 222 if (safmin == 0) |
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223 { |
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224 #if defined (DEBUG_EIG) |
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225 octave_stdout << "qz: DANGER WILL ROBINSON: safmin is 0!" |
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226 << std::endl; |
| 3185 | 227 #endif |
| 3183 | 228 |
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229 F77_FUNC (xdlamch, XDLAMCH) (F77_CONST_CHAR_ARG2 ("E", 1), |
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230 safmin |
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231 F77_CHAR_ARG_LEN (1)); |
| 3185 | 232 |
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233 #if defined (DEBUG_EIG) |
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234 octave_stdout << "qz: safmin set to " |
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235 << setiosflags (std::ios::scientific) |
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236 << safmin << std::endl; |
| 3185 | 237 #endif |
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238 } |
| 3183 | 239 } |
| 240 | |
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241 #if defined (DEBUG) |
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242 octave_stdout << "qz: check matrix A" << std::endl; |
| 3185 | 243 #endif |
| 244 | |
| 23430 | 245 // Matrix A: check dimensions. |
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246 F77_INT nn = to_f77_int (args(0).rows ()); |
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247 F77_INT nc = to_f77_int (args(0).columns ()); |
| 20892 | 248 |
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249 #if defined (DEBUG) |
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250 octave_stdout << "Matrix A dimensions: (" << nn << ',' << nc << ')' |
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251 << std::endl; |
| 3185 | 252 #endif |
| 253 | |
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254 if (args(0).isempty ()) |
| 3185 | 255 { |
| 23430 | 256 warn_empty_arg ("qz: A"); |
| 3185 | 257 return octave_value_list (2, Matrix ()); |
| 258 } | |
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259 else if (nc != nn) |
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260 err_square_matrix_required ("qz", "A"); |
| 3183 | 261 |
| 23430 | 262 // Matrix A: get value. |
| 3183 | 263 Matrix aa; |
| 264 ComplexMatrix caa; | |
| 3185 | 265 |
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266 if (args(0).iscomplex ()) |
| 3183 | 267 caa = args(0).complex_matrix_value (); |
| 3185 | 268 else |
| 3183 | 269 aa = args(0).matrix_value (); |
| 3185 | 270 |
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271 #if defined (DEBUG) |
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272 octave_stdout << "qz: check matrix B" << std::endl; |
| 3185 | 273 #endif |
| 3183 | 274 |
| 10311 | 275 // Extract argument 2 (bb, or cbb if complex). |
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276 F77_INT b_nr = to_f77_int (args(1).rows ()); |
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277 F77_INT b_nc = to_f77_int (args(1).columns ()); |
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278 |
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279 if (nn != b_nc || nn != b_nr) |
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280 ::err_nonconformant (); |
| 3185 | 281 |
| 3183 | 282 Matrix bb; |
| 283 ComplexMatrix cbb; | |
| 3185 | 284 |
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285 if (args(1).iscomplex ()) |
| 3183 | 286 cbb = args(1).complex_matrix_value (); |
| 287 else | |
| 288 bb = args(1).matrix_value (); | |
| 3185 | 289 |
| 23430 | 290 // Both matrices loaded, now check whether to calculate complex or real val. |
| 3185 | 291 |
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292 bool complex_case = (args(0).iscomplex () || args(1).iscomplex ()); |
| 10311 | 293 |
| 3185 | 294 if (nargin == 3 && complex_case) |
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295 error ("qz: cannot re-order complex qz decomposition"); |
| 3183 | 296 |
| 23430 | 297 // First, declare variables used in both the real and complex cases. |
| 298 // FIXME: There are a lot of excess variables declared. | |
| 299 // Probably a better way to handle this. | |
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300 Matrix QQ (nn, nn), ZZ (nn, nn), VR (nn, nn), VL (nn, nn); |
| 23430 | 301 RowVector alphar (nn), alphai (nn), betar (nn); |
| 302 ComplexRowVector xalpha (nn), xbeta (nn); | |
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303 ComplexMatrix CQ (nn, nn), CZ (nn, nn), CVR (nn, nn), CVL (nn, nn); |
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304 F77_INT ilo, ihi, info; |
| 23430 | 305 char comp_q = (nargout >= 3 ? 'V' : 'N'); |
| 306 char comp_z = ((nargout >= 4 || nargin == 3)? 'V' : 'N'); | |
| 3183 | 307 |
| 23430 | 308 // Initialize Q, Z to identity matrix if either is needed |
| 309 if (comp_q == 'V' || comp_z == 'V') | |
| 310 { | |
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311 double *QQptr = QQ.fortran_vec (); |
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312 double *ZZptr = ZZ.fortran_vec (); |
| 23430 | 313 std::fill_n (QQptr, QQ.numel (), 0.0); |
| 314 std::fill_n (ZZptr, ZZ.numel (), 0.0); | |
| 315 for (F77_INT i = 0; i < nn; i++) | |
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316 { |
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317 QQ(i, i) = 1.0; |
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318 ZZ(i, i) = 1.0; |
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319 } |
| 23430 | 320 } |
| 3183 | 321 |
| 10311 | 322 // Always perform permutation balancing. |
| 4552 | 323 const char bal_job = 'P'; |
| 10311 | 324 RowVector lscale (nn), rscale (nn), work (6 * nn), rwork (nn); |
| 3183 | 325 |
| 3185 | 326 if (complex_case) |
| 327 { | |
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328 #if defined (DEBUG) |
| 23430 | 329 if (comp_q == 'V') |
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330 octave_stdout << "qz: performing balancing; CQ =\n" << CQ << std::endl; |
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331 #endif |
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332 if (args(0).isreal ()) |
| 10311 | 333 caa = ComplexMatrix (aa); |
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334 |
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335 if (args(1).isreal ()) |
| 10311 | 336 cbb = ComplexMatrix (bb); |
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337 |
| 23430 | 338 if (comp_q == 'V') |
| 10311 | 339 CQ = ComplexMatrix (QQ); |
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340 |
| 23430 | 341 if (comp_z == 'V') |
| 10311 | 342 CZ = ComplexMatrix (ZZ); |
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343 |
| 10311 | 344 F77_XFCN (zggbal, ZGGBAL, |
| 345 (F77_CONST_CHAR_ARG2 (&bal_job, 1), | |
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346 nn, F77_DBLE_CMPLX_ARG (caa.fortran_vec ()), nn, |
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347 F77_DBLE_CMPLX_ARG (cbb.fortran_vec ()), |
| 10311 | 348 nn, ilo, ihi, lscale.fortran_vec (), |
| 349 rscale.fortran_vec (), work.fortran_vec (), info | |
| 350 F77_CHAR_ARG_LEN (1))); | |
| 3185 | 351 } |
| 3183 | 352 else |
| 3185 | 353 { |
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354 #if defined (DEBUG) |
| 23430 | 355 if (comp_q == 'V') |
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356 octave_stdout << "qz: performing balancing; QQ =\n" << QQ << std::endl; |
| 3185 | 357 #endif |
| 3183 | 358 |
| 3185 | 359 F77_XFCN (dggbal, DGGBAL, |
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360 (F77_CONST_CHAR_ARG2 (&bal_job, 1), |
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361 nn, aa.fortran_vec (), nn, bb.fortran_vec (), |
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362 nn, ilo, ihi, lscale.fortran_vec (), |
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363 rscale.fortran_vec (), work.fortran_vec (), info |
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364 F77_CHAR_ARG_LEN (1))); |
| 3185 | 365 } |
| 3183 | 366 |
| 23430 | 367 // Only permutation balance above is done. Skip scaling balance. |
| 368 | |
| 369 #if 0 | |
| 3183 | 370 // Since we just want the balancing matrices, we can use dggbal |
| 10311 | 371 // for both the real and complex cases; left first |
| 3185 | 372 |
| 23430 | 373 if (comp_q == 'V') |
| 3185 | 374 { |
| 375 F77_XFCN (dggbak, DGGBAK, | |
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376 (F77_CONST_CHAR_ARG2 (&bal_job, 1), |
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377 F77_CONST_CHAR_ARG2 ("L", 1), |
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378 nn, ilo, ihi, lscale.data (), rscale.data (), |
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379 nn, QQ.fortran_vec (), nn, info |
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380 F77_CHAR_ARG_LEN (1) |
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381 F77_CHAR_ARG_LEN (1))); |
| 3183 | 382 |
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383 #if defined (DEBUG) |
| 23430 | 384 if (comp_q == 'V') |
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385 octave_stdout << "qz: balancing done; QQ =\n" << QQ << std::endl; |
| 3185 | 386 #endif |
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387 } |
| 3183 | 388 |
| 389 // then right | |
| 23430 | 390 if (comp_z == 'V') |
| 3185 | 391 { |
| 4552 | 392 F77_XFCN (dggbak, DGGBAK, |
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393 (F77_CONST_CHAR_ARG2 (&bal_job, 1), |
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394 F77_CONST_CHAR_ARG2 ("R", 1), |
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395 nn, ilo, ihi, lscale.data (), rscale.data (), |
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396 nn, ZZ.fortran_vec (), nn, info |
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397 F77_CHAR_ARG_LEN (1) |
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398 F77_CHAR_ARG_LEN (1))); |
| 3183 | 399 |
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400 #if defined (DEBUG) |
| 23430 | 401 if (comp_z == 'V') |
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402 octave_stdout << "qz: balancing done; ZZ=\n" << ZZ << std::endl; |
| 3185 | 403 #endif |
| 10311 | 404 } |
| 405 #endif | |
| 3183 | 406 |
| 23430 | 407 char qz_job = (nargout < 2 ? 'E' : 'S'); |
| 3185 | 408 |
| 3183 | 409 if (complex_case) |
| 3185 | 410 { |
| 10311 | 411 // Complex case. |
| 412 | |
| 413 // The QR decomposition of cbb. | |
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414 math::qr<ComplexMatrix> cbqr (cbb); |
| 10311 | 415 // The R matrix of QR decomposition for cbb. |
| 416 cbb = cbqr.R (); | |
| 417 // (Q*)caa for following work. | |
| 418 caa = (cbqr.Q ().hermitian ()) * caa; | |
| 419 CQ = CQ * cbqr.Q (); | |
| 420 | |
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421 F77_XFCN (zgghrd, ZGGHRD, |
| 23430 | 422 (F77_CONST_CHAR_ARG2 (&comp_q, 1), |
| 423 F77_CONST_CHAR_ARG2 (&comp_z, 1), | |
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424 nn, ilo, ihi, F77_DBLE_CMPLX_ARG (caa.fortran_vec ()), |
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425 nn, F77_DBLE_CMPLX_ARG (cbb.fortran_vec ()), nn, |
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426 F77_DBLE_CMPLX_ARG (CQ.fortran_vec ()), nn, |
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427 F77_DBLE_CMPLX_ARG (CZ.fortran_vec ()), nn, info |
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428 F77_CHAR_ARG_LEN (1) |
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429 F77_CHAR_ARG_LEN (1))); |
| 10311 | 430 |
| 23430 | 431 ComplexRowVector cwork (nn); |
| 10311 | 432 |
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433 F77_XFCN (zhgeqz, ZHGEQZ, |
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434 (F77_CONST_CHAR_ARG2 (&qz_job, 1), |
| 23430 | 435 F77_CONST_CHAR_ARG2 (&comp_q, 1), |
| 436 F77_CONST_CHAR_ARG2 (&comp_z, 1), | |
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437 nn, ilo, ihi, |
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438 F77_DBLE_CMPLX_ARG (caa.fortran_vec ()), nn, |
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439 F77_DBLE_CMPLX_ARG (cbb.fortran_vec ()), nn, |
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440 F77_DBLE_CMPLX_ARG (xalpha.fortran_vec ()), |
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441 F77_DBLE_CMPLX_ARG (xbeta.fortran_vec ()), |
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442 F77_DBLE_CMPLX_ARG (CQ.fortran_vec ()), nn, |
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443 F77_DBLE_CMPLX_ARG (CZ.fortran_vec ()), nn, |
| 23430 | 444 F77_DBLE_CMPLX_ARG (cwork.fortran_vec ()), nn, |
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445 rwork.fortran_vec (), info |
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446 F77_CHAR_ARG_LEN (1) |
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447 F77_CHAR_ARG_LEN (1) |
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448 F77_CHAR_ARG_LEN (1))); |
| 3185 | 449 |
| 23430 | 450 if (comp_q == 'V') |
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451 { |
| 10311 | 452 // Left eigenvector. |
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453 F77_XFCN (zggbak, ZGGBAK, |
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454 (F77_CONST_CHAR_ARG2 (&bal_job, 1), |
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455 F77_CONST_CHAR_ARG2 ("L", 1), |
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456 nn, ilo, ihi, lscale.data (), rscale.data (), |
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457 nn, F77_DBLE_CMPLX_ARG (CQ.fortran_vec ()), nn, info |
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458 F77_CHAR_ARG_LEN (1) |
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459 F77_CHAR_ARG_LEN (1))); |
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460 } |
| 3185 | 461 |
| 23430 | 462 if (comp_z == 'V') |
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463 { |
| 23430 | 464 // Right eigenvector. |
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465 F77_XFCN (zggbak, ZGGBAK, |
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466 (F77_CONST_CHAR_ARG2 (&bal_job, 1), |
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467 F77_CONST_CHAR_ARG2 ("R", 1), |
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468 nn, ilo, ihi, lscale.data (), rscale.data (), |
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469 nn, F77_DBLE_CMPLX_ARG (CZ.fortran_vec ()), nn, info |
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470 F77_CHAR_ARG_LEN (1) |
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471 F77_CHAR_ARG_LEN (1))); |
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472 } |
| 3185 | 473 |
| 474 } | |
| 10311 | 475 else |
| 3185 | 476 { |
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477 #if defined (DEBUG) |
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478 octave_stdout << "qz: performing qr decomposition of bb" << std::endl; |
| 3185 | 479 #endif |
| 3183 | 480 |
| 10311 | 481 // Compute the QR factorization of bb. |
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482 math::qr<Matrix> bqr (bb); |
| 3185 | 483 |
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484 #if defined (DEBUG) |
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485 octave_stdout << "qz: qr (bb) done; now performing qz decomposition" |
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486 << std::endl; |
| 3185 | 487 #endif |
| 3183 | 488 |
| 3185 | 489 bb = bqr.R (); |
| 490 | |
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491 #if defined (DEBUG) |
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492 octave_stdout << "qz: extracted bb" << std::endl; |
| 3185 | 493 #endif |
| 3183 | 494 |
| 10311 | 495 aa = (bqr.Q ()).transpose () * aa; |
| 3185 | 496 |
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497 #if defined (DEBUG) |
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498 octave_stdout << "qz: updated aa " << std::endl; |
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499 octave_stdout << "bqr.Q () =\n" << bqr.Q () << std::endl; |
| 3183 | 500 |
| 23430 | 501 if (comp_q == 'V') |
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502 octave_stdout << "QQ =" << QQ << std::endl; |
| 3185 | 503 #endif |
| 3183 | 504 |
| 23430 | 505 if (comp_q == 'V') |
| 10311 | 506 QQ = QQ * bqr.Q (); |
| 3183 | 507 |
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508 #if defined (DEBUG) |
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509 octave_stdout << "qz: precursors done..." << std::endl; |
| 3185 | 510 #endif |
| 3183 | 511 |
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512 #if defined (DEBUG) |
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513 octave_stdout << "qz: comp_q = " << comp_q << ", comp_z = " << comp_z |
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514 << std::endl; |
| 3185 | 515 #endif |
| 3183 | 516 |
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517 // Reduce to generalized Hessenberg form. |
| 3185 | 518 F77_XFCN (dgghrd, DGGHRD, |
| 23430 | 519 (F77_CONST_CHAR_ARG2 (&comp_q, 1), |
| 520 F77_CONST_CHAR_ARG2 (&comp_z, 1), | |
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521 nn, ilo, ihi, aa.fortran_vec (), |
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522 nn, bb.fortran_vec (), nn, QQ.fortran_vec (), nn, |
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523 ZZ.fortran_vec (), nn, info |
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524 F77_CHAR_ARG_LEN (1) |
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525 F77_CHAR_ARG_LEN (1))); |
| 3183 | 526 |
| 23430 | 527 // Check if just computing generalized eigenvalues, |
| 528 // or if we're actually computing the decomposition. | |
| 3183 | 529 |
| 10311 | 530 // Reduce to generalized Schur form. |
| 3185 | 531 F77_XFCN (dhgeqz, DHGEQZ, |
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532 (F77_CONST_CHAR_ARG2 (&qz_job, 1), |
| 23430 | 533 F77_CONST_CHAR_ARG2 (&comp_q, 1), |
| 534 F77_CONST_CHAR_ARG2 (&comp_z, 1), | |
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535 nn, ilo, ihi, aa.fortran_vec (), nn, bb.fortran_vec (), |
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536 nn, alphar.fortran_vec (), alphai.fortran_vec (), |
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537 betar.fortran_vec (), QQ.fortran_vec (), nn, |
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538 ZZ.fortran_vec (), nn, work.fortran_vec (), nn, info |
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539 F77_CHAR_ARG_LEN (1) |
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540 F77_CHAR_ARG_LEN (1) |
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541 F77_CHAR_ARG_LEN (1))); |
| 10311 | 542 |
| 23430 | 543 if (comp_q == 'V') |
| 10311 | 544 { |
| 545 F77_XFCN (dggbak, DGGBAK, | |
| 546 (F77_CONST_CHAR_ARG2 (&bal_job, 1), | |
| 547 F77_CONST_CHAR_ARG2 ("L", 1), | |
| 548 nn, ilo, ihi, lscale.data (), rscale.data (), | |
| 549 nn, QQ.fortran_vec (), nn, info | |
| 550 F77_CHAR_ARG_LEN (1) | |
| 551 F77_CHAR_ARG_LEN (1))); | |
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552 |
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553 #if defined (DEBUG) |
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555 octave_stdout << "qz: balancing done; QQ=\n" << QQ << std::endl; |
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556 #endif |
|
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557 } |
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558 |
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559 // then right |
| 23430 | 560 if (comp_z == 'V') |
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561 { |
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562 F77_XFCN (dggbak, DGGBAK, |
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563 (F77_CONST_CHAR_ARG2 (&bal_job, 1), |
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564 F77_CONST_CHAR_ARG2 ("R", 1), |
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565 nn, ilo, ihi, lscale.data (), rscale.data (), |
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566 nn, ZZ.fortran_vec (), nn, info |
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567 F77_CHAR_ARG_LEN (1) |
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568 F77_CHAR_ARG_LEN (1))); |
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569 |
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570 #if defined (DEBUG) |
| 23430 | 571 if (comp_z == 'V') |
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572 octave_stdout << "qz: balancing done; ZZ=\n" << ZZ << std::endl; |
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573 #endif |
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574 } |
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575 |
| 3185 | 576 } |
| 3183 | 577 |
| 10311 | 578 // Order the QZ decomposition? |
| 23430 | 579 if (ord_job != 'N') |
| 3183 | 580 { |
| 3185 | 581 if (complex_case) |
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582 // Probably not needed, but better be safe. |
| 23430 | 583 error ("qz: cannot re-order complex QZ decomposition"); |
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584 |
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585 #if defined (DEBUG_SORT) |
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586 octave_stdout << "qz: ordering eigenvalues: ord_job = " |
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587 << ord_job << std::endl; |
| 3185 | 588 #endif |
| 3183 | 589 |
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590 Array<F77_LOGICAL> select (dim_vector (nn, 1)); |
| 3183 | 591 |
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592 for (int j = 0; j < nn; j++) |
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593 { |
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594 switch (ord_job) |
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595 { |
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596 case 'S': |
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597 select(j) = alphar(j)*alphar(j) + alphai(j)*alphai(j) < betar(j)*betar(j); |
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598 break; |
| 3183 | 599 |
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600 case 'B': |
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601 select(j) = alphar(j)*alphar(j) + alphai(j)*alphai(j) >= betar(j)*betar(j); |
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602 break; |
| 3183 | 603 |
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604 case '+': |
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605 select(j) = alphar(j) * betar(j) >= 0; |
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606 break; |
| 3183 | 607 |
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608 case '-': |
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609 select(j) = alphar(j) * betar(j) < 0; |
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610 break; |
| 3185 | 611 |
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612 default: |
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613 // Invalid order option |
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614 // (should never happen since options were checked at the top). |
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615 panic_impossible (); |
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616 break; |
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617 } |
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618 } |
| 3183 | 619 |
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620 F77_LOGICAL wantq = 0, wantz = (comp_z == 'V'); |
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621 F77_INT ijob = 0, mm, lrwork3 = 4*nn+16, liwork = nn; |
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622 F77_DBLE pl, pr; |
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623 RowVector rwork3(lrwork3); |
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624 Array<F77_INT> iwork (dim_vector (liwork, 1)); |
| 3185 | 625 |
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626 F77_XFCN (dtgsen, DTGSEN, |
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627 (ijob, wantq, wantz, |
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628 select.fortran_vec (), nn, |
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629 aa.fortran_vec (), nn, |
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630 bb.fortran_vec (), nn, |
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631 alphar.fortran_vec (), |
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632 alphai.fortran_vec (), |
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633 betar.fortran_vec (), |
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634 nullptr, nn, |
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635 ZZ.fortran_vec (), nn, |
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636 mm, |
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637 pl, pr, |
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638 nullptr, |
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639 rwork3.fortran_vec (), lrwork3, |
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640 iwork.fortran_vec (), liwork, |
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641 info)); |
| 3185 | 642 |
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643 #if defined (DEBUG_SORT) |
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644 octave_stdout << "qz: back from dtgsen: aa =\n"; |
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645 octave_print_internal (octave_stdout, aa); |
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646 octave_stdout << "\nbb =\n"; |
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647 octave_print_internal (octave_stdout, bb); |
| 23430 | 648 if (comp_z == 'V') |
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649 { |
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650 octave_stdout << "\nZZ =\n"; |
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651 octave_print_internal (octave_stdout, ZZ); |
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652 } |
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653 octave_stdout << "\nqz: info=" << info; |
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654 octave_stdout << "\nalphar =\n"; |
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655 octave_print_internal (octave_stdout, Matrix (alphar)); |
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656 octave_stdout << "\nalphai =\n"; |
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657 octave_print_internal (octave_stdout, Matrix (alphai)); |
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658 octave_stdout << "\nbeta =\n"; |
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659 octave_print_internal (octave_stdout, Matrix (betar)); |
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660 octave_stdout << std::endl; |
| 3185 | 661 #endif |
| 3183 | 662 } |
| 3185 | 663 |
| 23430 | 664 // Compute the generalized eigenvalues as well? |
| 3183 | 665 ComplexColumnVector gev; |
| 3185 | 666 |
| 667 if (nargout < 2 || nargout == 7 || (nargin == 3 && nargout == 4)) | |
| 3183 | 668 { |
| 3185 | 669 if (complex_case) |
|
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670 { |
| 23430 | 671 ComplexColumnVector tmp (nn); |
|
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672 |
| 23430 | 673 for (F77_INT i = 0; i < nn; i++) |
| 674 tmp(i) = xalpha(i) / xbeta(i); | |
| 10311 | 675 |
| 676 gev = tmp; | |
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677 } |
| 3185 | 678 else |
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679 { |
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680 #if defined (DEBUG) |
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681 octave_stdout << "qz: computing generalized eigenvalues" << std::endl; |
| 3185 | 682 #endif |
| 3183 | 683 |
| 10311 | 684 // Return finite generalized eigenvalues. |
| 23430 | 685 ComplexColumnVector tmp (nn); |
| 3185 | 686 |
| 23430 | 687 for (F77_INT i = 0; i < nn; i++) |
|
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688 { |
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689 if (betar(i) != 0) |
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690 tmp(i) = Complex (alphar(i), alphai(i)) / betar(i); |
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691 else |
|
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692 tmp(i) = numeric_limits<double>::Inf (); |
|
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693 } |
| 10311 | 694 |
|
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695 gev = tmp; |
|
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696 } |
| 3183 | 697 } |
| 698 | |
| 10311 | 699 // Right, left eigenvector matrices. |
| 3185 | 700 if (nargout >= 5) |
| 3183 | 701 { |
| 10311 | 702 // Which side to compute? |
| 703 char side = (nargout == 5 ? 'R' : 'B'); | |
| 704 // Compute all of them and backtransform | |
| 23430 | 705 char howmany = 'B'; |
| 10311 | 706 // Dummy pointer; select is not used. |
|
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707 F77_INT *select = nullptr; |
| 3185 | 708 |
| 709 if (complex_case) | |
|
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710 { |
| 10311 | 711 CVL = CQ; |
| 712 CVR = CZ; | |
| 713 ComplexRowVector cwork2 (2 * nn); | |
| 714 RowVector rwork2 (8 * nn); | |
|
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715 F77_INT m; |
|
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|
716 |
| 10311 | 717 F77_XFCN (ztgevc, ZTGEVC, |
| 718 (F77_CONST_CHAR_ARG2 (&side, 1), | |
| 23430 | 719 F77_CONST_CHAR_ARG2 (&howmany, 1), |
|
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|
720 select, nn, F77_DBLE_CMPLX_ARG (caa.fortran_vec ()), nn, |
|
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|
721 F77_DBLE_CMPLX_ARG (cbb.fortran_vec ()), |
|
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|
722 nn, F77_DBLE_CMPLX_ARG (CVL.fortran_vec ()), nn, |
|
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|
723 F77_DBLE_CMPLX_ARG (CVR.fortran_vec ()), nn, nn, |
| 23430 | 724 m, F77_DBLE_CMPLX_ARG (cwork2.fortran_vec ()), |
| 725 rwork2.fortran_vec (), info | |
| 10311 | 726 F77_CHAR_ARG_LEN (1) |
|
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|
727 F77_CHAR_ARG_LEN (1))); |
|
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|
728 } |
| 3185 | 729 else |
|
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730 { |
|
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731 #if defined (DEBUG) |
|
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|
732 octave_stdout << "qz: computing generalized eigenvectors" << std::endl; |
| 3185 | 733 #endif |
| 734 | |
|
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735 VL = QQ; |
|
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736 VR = ZZ; |
|
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|
737 F77_INT m; |
| 10311 | 738 |
|
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|
739 F77_XFCN (dtgevc, DTGEVC, |
|
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|
740 (F77_CONST_CHAR_ARG2 (&side, 1), |
| 23430 | 741 F77_CONST_CHAR_ARG2 (&howmany, 1), |
|
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|
742 select, nn, aa.fortran_vec (), nn, bb.fortran_vec (), |
|
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|
743 nn, VL.fortran_vec (), nn, VR.fortran_vec (), nn, nn, |
|
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744 m, work.fortran_vec (), info |
|
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|
745 F77_CHAR_ARG_LEN (1) |
|
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|
746 F77_CHAR_ARG_LEN (1))); |
| 3185 | 747 |
| 10311 | 748 // Now construct the complex form of VV, WW. |
| 23430 | 749 F77_INT j = 0; |
| 3185 | 750 |
| 23430 | 751 while (j < nn) |
|
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752 { |
|
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|
753 octave_quit (); |
| 4153 | 754 |
| 10311 | 755 // See if real or complex eigenvalue. |
| 756 | |
| 757 // Column increment; assume complex eigenvalue. | |
| 758 int cinc = 2; | |
| 3185 | 759 |
| 23430 | 760 if (j == (nn-1)) |
| 10311 | 761 // Single column. |
| 762 cinc = 1; | |
|
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|
763 else if (aa(j+1, j) == 0) |
|
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|
764 cinc = 1; |
| 3185 | 765 |
| 10311 | 766 // Now copy the eigenvector (s) to CVR, CVL. |
|
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|
767 if (cinc == 1) |
|
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|
768 { |
| 23430 | 769 for (F77_INT i = 0; i < nn; i++) |
|
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|
770 CVR(i, j) = VR(i, j); |
| 3185 | 771 |
|
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|
772 if (side == 'B') |
| 23430 | 773 for (F77_INT i = 0; i < nn; i++) |
|
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|
774 CVL(i, j) = VL(i, j); |
|
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|
775 } |
|
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|
776 else |
|
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|
777 { |
| 10311 | 778 // Double column; complex vector. |
| 3185 | 779 |
| 23430 | 780 for (F77_INT i = 0; i < nn; i++) |
|
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|
781 { |
|
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|
782 CVR(i, j) = Complex (VR(i, j), VR(i, j+1)); |
|
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|
783 CVR(i, j+1) = Complex (VR(i, j), -VR(i, j+1)); |
|
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|
784 } |
| 3183 | 785 |
|
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|
786 if (side == 'B') |
| 23430 | 787 for (F77_INT i = 0; i < nn; i++) |
|
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|
788 { |
|
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Rik <rik@octave.org>
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|
789 CVL(i, j) = Complex (VL(i, j), VL(i, j+1)); |
|
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changeset
|
790 CVL(i, j+1) = Complex (VL(i, j), -VL(i, j+1)); |
|
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|
791 } |
|
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|
792 } |
| 3185 | 793 |
| 10311 | 794 // Advance to next eigenvectors (if any). |
| 23430 | 795 j += cinc; |
|
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|
796 } |
|
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|
797 } |
| 3183 | 798 } |
| 3185 | 799 |
| 23430 | 800 octave_value_list retval (nargout); |
| 801 | |
| 3185 | 802 switch (nargout) |
| 803 { | |
| 804 case 7: | |
| 805 retval(6) = gev; | |
|
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|
806 OCTAVE_FALLTHROUGH; |
| 3185 | 807 |
| 10311 | 808 case 6: |
| 23430 | 809 // Return left eigenvectors. |
| 3185 | 810 retval(5) = CVL; |
|
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|
811 OCTAVE_FALLTHROUGH; |
| 3185 | 812 |
| 10311 | 813 case 5: |
| 23430 | 814 // Return right eigenvectors. |
| 3185 | 815 retval(4) = CVR; |
|
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|
816 OCTAVE_FALLTHROUGH; |
| 3185 | 817 |
| 818 case 4: | |
| 819 if (nargin == 3) | |
|
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|
820 { |
|
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|
821 #if defined (DEBUG) |
|
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|
822 octave_stdout << "qz: sort: retval(3) = gev =\n"; |
|
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|
823 octave_print_internal (octave_stdout, ComplexMatrix (gev)); |
|
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|
824 octave_stdout << std::endl; |
| 3185 | 825 #endif |
|
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|
826 retval(3) = gev; |
|
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|
827 } |
| 3185 | 828 else |
| 10311 | 829 { |
| 830 if (complex_case) | |
| 831 retval(3) = CZ; | |
| 832 else | |
| 833 retval(3) = ZZ; | |
| 834 } | |
|
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|
835 OCTAVE_FALLTHROUGH; |
| 3185 | 836 |
| 837 case 3: | |
| 838 if (nargin == 3) | |
|
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|
839 { |
|
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|
840 if (complex_case) |
|
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|
841 retval(2) = CZ; |
|
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|
842 else |
|
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|
843 retval(2) = ZZ; |
|
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|
844 } |
| 3185 | 845 else |
| 10311 | 846 { |
| 847 if (complex_case) | |
| 848 retval(2) = CQ.hermitian (); | |
| 849 else | |
| 850 retval(2) = QQ.transpose (); | |
| 851 } | |
|
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|
852 OCTAVE_FALLTHROUGH; |
| 10311 | 853 |
| 3185 | 854 case 2: |
|
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|
855 { |
| 10311 | 856 if (complex_case) |
| 857 { | |
|
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858 #if defined (DEBUG) |
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859 octave_stdout << "qz: retval(1) = cbb =\n"; |
|
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|
860 octave_print_internal (octave_stdout, cbb); |
|
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861 octave_stdout << "\nqz: retval(0) = caa =\n"; |
|
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862 octave_print_internal (octave_stdout, caa); |
|
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863 octave_stdout << std::endl; |
|
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|
864 #endif |
| 10311 | 865 retval(1) = cbb; |
| 866 retval(0) = caa; | |
| 867 } | |
|
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868 else |
|
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869 { |
|
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870 #if defined (DEBUG) |
|
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871 octave_stdout << "qz: retval(1) = bb =\n"; |
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872 octave_print_internal (octave_stdout, bb); |
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873 octave_stdout << "\nqz: retval(0) = aa =\n"; |
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874 octave_print_internal (octave_stdout, aa); |
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875 octave_stdout << std::endl; |
| 3185 | 876 #endif |
|
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877 retval(1) = bb; |
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878 retval(0) = aa; |
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175b392e91fe
Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents:
17744
diff
changeset
|
879 } |
|
11586
12df7854fa7c
strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents:
11570
diff
changeset
|
880 } |
| 10311 | 881 break; |
|
10307
4e4270ab70d6
support complex case in qz
Jyh-miin Lin <jyhmiinlin@gmail.com>
parents:
10155
diff
changeset
|
882 |
| 3185 | 883 case 1: |
| 884 case 0: | |
|
21724
aba2e6293dd8
use "#if ..." consistently instead of "#ifdef" and "#ifndef"
John W. Eaton <jwe@octave.org>
parents:
21562
diff
changeset
|
885 #if defined (DEBUG) |
|
26001
acb4689aa5f2
* qz.cc: Use octave_stdout instead of std::cout for debugging messages.
John W. Eaton <jwe@octave.org>
parents:
25734
diff
changeset
|
886 octave_stdout << "qz: retval(0) = gev = " << gev << std::endl; |
| 3185 | 887 #endif |
| 888 retval(0) = gev; | |
| 889 break; | |
| 890 | |
| 891 default: | |
|
11553
01f703952eff
Improve docstrings for functions in DLD-FUNCTIONS directory.
Rik <octave@nomad.inbox5.com>
parents:
11523
diff
changeset
|
892 error ("qz: too many return arguments"); |
| 3185 | 893 break; |
|
25103
078b795c5219
maint: style check C++ ahead of 4.4 release.
Rik <rik@octave.org>
parents:
25054
diff
changeset
|
894 } |
| 3183 | 895 |
|
21724
aba2e6293dd8
use "#if ..." consistently instead of "#ifdef" and "#ifndef"
John W. Eaton <jwe@octave.org>
parents:
21562
diff
changeset
|
896 #if defined (DEBUG) |
|
26001
acb4689aa5f2
* qz.cc: Use octave_stdout instead of std::cout for debugging messages.
John W. Eaton <jwe@octave.org>
parents:
25734
diff
changeset
|
897 octave_stdout << "qz: exiting (at long last)" << std::endl; |
| 3185 | 898 #endif |
| 3183 | 899 |
| 900 return retval; | |
| 901 } | |
|
13074
0b789a03bde1
codesprint: Add 3 tests for qz.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12642
diff
changeset
|
902 |
|
0b789a03bde1
codesprint: Add 3 tests for qz.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12642
diff
changeset
|
903 /* |
|
29556
d75aa2bf4915
qz.cc: return correct number of eigenvalues (bug #60357).
Rik <rik@octave.org>
parents:
29358
diff
changeset
|
904 %!test |
|
d75aa2bf4915
qz.cc: return correct number of eigenvalues (bug #60357).
Rik <rik@octave.org>
parents:
29358
diff
changeset
|
905 %! A = [1 2; 0 3]; |
|
d75aa2bf4915
qz.cc: return correct number of eigenvalues (bug #60357).
Rik <rik@octave.org>
parents:
29358
diff
changeset
|
906 %! B = [1 0; 0 0]; |
|
d75aa2bf4915
qz.cc: return correct number of eigenvalues (bug #60357).
Rik <rik@octave.org>
parents:
29358
diff
changeset
|
907 %! C = [0 1; 0 0]; |
|
d75aa2bf4915
qz.cc: return correct number of eigenvalues (bug #60357).
Rik <rik@octave.org>
parents:
29358
diff
changeset
|
908 %! assert (qz (A,B), [1; Inf]); |
|
d75aa2bf4915
qz.cc: return correct number of eigenvalues (bug #60357).
Rik <rik@octave.org>
parents:
29358
diff
changeset
|
909 %! assert (qz (A,C), [Inf; Inf]); |
|
13074
0b789a03bde1
codesprint: Add 3 tests for qz.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12642
diff
changeset
|
910 |
| 23430 | 911 ## Example 7.7.3 in Golub & Van Loan |
|
13074
0b789a03bde1
codesprint: Add 3 tests for qz.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12642
diff
changeset
|
912 %!test |
|
0b789a03bde1
codesprint: Add 3 tests for qz.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12642
diff
changeset
|
913 %! a = [ 10 1 2; |
|
0b789a03bde1
codesprint: Add 3 tests for qz.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12642
diff
changeset
|
914 %! 1 2 -1; |
|
29556
d75aa2bf4915
qz.cc: return correct number of eigenvalues (bug #60357).
Rik <rik@octave.org>
parents:
29358
diff
changeset
|
915 %! 1 1 2 ]; |
|
d75aa2bf4915
qz.cc: return correct number of eigenvalues (bug #60357).
Rik <rik@octave.org>
parents:
29358
diff
changeset
|
916 %! b = reshape (1:9, 3,3); |
|
13074
0b789a03bde1
codesprint: Add 3 tests for qz.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12642
diff
changeset
|
917 %! [aa, bb, q, z, v, w, lambda] = qz (a, b); |
|
13088
4ffea87ad71b
codesprint: Fix tolerance for qz.cc tests.
Ben Abbott <bpabbott@mac.com>
parents:
13074
diff
changeset
|
918 %! assert (q * a * z, aa, norm (aa) * 1e-14); |
|
4ffea87ad71b
codesprint: Fix tolerance for qz.cc tests.
Ben Abbott <bpabbott@mac.com>
parents:
13074
diff
changeset
|
919 %! assert (q * b * z, bb, norm (bb) * 1e-14); |
|
29557
50aa945836c3
qz.cc: Let test pass with LAPACK 3.9.1 and earlier versions (bug #60357).
Markus Mützel <markus.muetzel@gmx.de>
parents:
29556
diff
changeset
|
920 %! is_finite = abs (lambda) < 1 / eps (max (a(:))); |
|
50aa945836c3
qz.cc: Let test pass with LAPACK 3.9.1 and earlier versions (bug #60357).
Markus Mützel <markus.muetzel@gmx.de>
parents:
29556
diff
changeset
|
921 %! observed = (b * v * diag (lambda))(:,is_finite); |
|
50aa945836c3
qz.cc: Let test pass with LAPACK 3.9.1 and earlier versions (bug #60357).
Markus Mützel <markus.muetzel@gmx.de>
parents:
29556
diff
changeset
|
922 %! assert (observed, (a*v)(:,is_finite), norm (observed) * 1e-14); |
|
50aa945836c3
qz.cc: Let test pass with LAPACK 3.9.1 and earlier versions (bug #60357).
Markus Mützel <markus.muetzel@gmx.de>
parents:
29556
diff
changeset
|
923 %! observed = (diag (lambda) * w' * b)(is_finite,:); |
|
50aa945836c3
qz.cc: Let test pass with LAPACK 3.9.1 and earlier versions (bug #60357).
Markus Mützel <markus.muetzel@gmx.de>
parents:
29556
diff
changeset
|
924 %! assert (observed, (w'*a)(is_finite,:), norm (observed) * 1e-13); |
|
13074
0b789a03bde1
codesprint: Add 3 tests for qz.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12642
diff
changeset
|
925 |
|
14876
54a386f2ac4e
correcly compute Z for 3-output call to qz (bug #36728)
John W. Eaton <jwe@octave.org>
parents:
14844
diff
changeset
|
926 %!test |
|
54a386f2ac4e
correcly compute Z for 3-output call to qz (bug #36728)
John W. Eaton <jwe@octave.org>
parents:
14844
diff
changeset
|
927 %! A = [0, 0, -1, 0; 1, 0, 0, 0; -1, 0, -2, -1; 0, -1, 1, 0]; |
|
54a386f2ac4e
correcly compute Z for 3-output call to qz (bug #36728)
John W. Eaton <jwe@octave.org>
parents:
14844
diff
changeset
|
928 %! B = [0, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]; |
|
54a386f2ac4e
correcly compute Z for 3-output call to qz (bug #36728)
John W. Eaton <jwe@octave.org>
parents:
14844
diff
changeset
|
929 %! [AA, BB, Q, Z1] = qz (A, B); |
| 23430 | 930 %! [AA, BB, Z2] = qz (A, B, "-"); |
|
14876
54a386f2ac4e
correcly compute Z for 3-output call to qz (bug #36728)
John W. Eaton <jwe@octave.org>
parents:
14844
diff
changeset
|
931 %! assert (Z1, Z2); |
|
25570
da2b38b7a077
Use LAPACK DTGSEN subrouting for ordered-qz computation (bug #53761)
Sébastien Villemot <sebastien@debian.org>
parents:
25106
diff
changeset
|
932 |
|
da2b38b7a077
Use LAPACK DTGSEN subrouting for ordered-qz computation (bug #53761)
Sébastien Villemot <sebastien@debian.org>
parents:
25106
diff
changeset
|
933 %!test |
|
da2b38b7a077
Use LAPACK DTGSEN subrouting for ordered-qz computation (bug #53761)
Sébastien Villemot <sebastien@debian.org>
parents:
25106
diff
changeset
|
934 %! A = [ -1.03428 0.24929 0.43205 -0.12860; |
|
da2b38b7a077
Use LAPACK DTGSEN subrouting for ordered-qz computation (bug #53761)
Sébastien Villemot <sebastien@debian.org>
parents:
25106
diff
changeset
|
935 %! 1.16228 0.27870 2.12954 0.69250; |
|
da2b38b7a077
Use LAPACK DTGSEN subrouting for ordered-qz computation (bug #53761)
Sébastien Villemot <sebastien@debian.org>
parents:
25106
diff
changeset
|
936 %! -0.51524 -0.34939 -0.77820 2.13721; |
|
da2b38b7a077
Use LAPACK DTGSEN subrouting for ordered-qz computation (bug #53761)
Sébastien Villemot <sebastien@debian.org>
parents:
25106
diff
changeset
|
937 %! -1.32941 2.11870 0.72005 1.00835 ]; |
|
da2b38b7a077
Use LAPACK DTGSEN subrouting for ordered-qz computation (bug #53761)
Sébastien Villemot <sebastien@debian.org>
parents:
25106
diff
changeset
|
938 %! B = [ 1.407302 -0.632956 -0.360628 0.068534; |
|
da2b38b7a077
Use LAPACK DTGSEN subrouting for ordered-qz computation (bug #53761)
Sébastien Villemot <sebastien@debian.org>
parents:
25106
diff
changeset
|
939 %! 0.149898 0.298248 0.991777 0.023652; |
|
da2b38b7a077
Use LAPACK DTGSEN subrouting for ordered-qz computation (bug #53761)
Sébastien Villemot <sebastien@debian.org>
parents:
25106
diff
changeset
|
940 %! 0.169281 -0.405205 -1.775834 1.511730; |
|
da2b38b7a077
Use LAPACK DTGSEN subrouting for ordered-qz computation (bug #53761)
Sébastien Villemot <sebastien@debian.org>
parents:
25106
diff
changeset
|
941 %! 0.717770 1.291390 -1.766607 -0.531352 ]; |
|
da2b38b7a077
Use LAPACK DTGSEN subrouting for ordered-qz computation (bug #53761)
Sébastien Villemot <sebastien@debian.org>
parents:
25106
diff
changeset
|
942 %! [AA, BB, Z, lambda] = qz (A, B, "+"); |
|
29556
d75aa2bf4915
qz.cc: return correct number of eigenvalues (bug #60357).
Rik <rik@octave.org>
parents:
29358
diff
changeset
|
943 %! assert (all (real (lambda(1:3)) >= 0)); |
|
d75aa2bf4915
qz.cc: return correct number of eigenvalues (bug #60357).
Rik <rik@octave.org>
parents:
29358
diff
changeset
|
944 %! assert (real (lambda(4) < 0)); |
|
25570
da2b38b7a077
Use LAPACK DTGSEN subrouting for ordered-qz computation (bug #53761)
Sébastien Villemot <sebastien@debian.org>
parents:
25106
diff
changeset
|
945 %! [AA, BB, Z, lambda] = qz (A, B, "-"); |
|
29556
d75aa2bf4915
qz.cc: return correct number of eigenvalues (bug #60357).
Rik <rik@octave.org>
parents:
29358
diff
changeset
|
946 %! assert (real (lambda(1) < 0)); |
|
d75aa2bf4915
qz.cc: return correct number of eigenvalues (bug #60357).
Rik <rik@octave.org>
parents:
29358
diff
changeset
|
947 %! assert (all (real (lambda(2:4)) >= 0)); |
|
25570
da2b38b7a077
Use LAPACK DTGSEN subrouting for ordered-qz computation (bug #53761)
Sébastien Villemot <sebastien@debian.org>
parents:
25106
diff
changeset
|
948 %! [AA, BB, Z, lambda] = qz (A, B, "B"); |
|
29556
d75aa2bf4915
qz.cc: return correct number of eigenvalues (bug #60357).
Rik <rik@octave.org>
parents:
29358
diff
changeset
|
949 %! assert (all (abs (lambda(1:3)) >= 1)); |
|
d75aa2bf4915
qz.cc: return correct number of eigenvalues (bug #60357).
Rik <rik@octave.org>
parents:
29358
diff
changeset
|
950 %! assert (abs (lambda(4) < 1)); |
|
25570
da2b38b7a077
Use LAPACK DTGSEN subrouting for ordered-qz computation (bug #53761)
Sébastien Villemot <sebastien@debian.org>
parents:
25106
diff
changeset
|
951 %! [AA, BB, Z, lambda] = qz (A, B, "S"); |
|
29556
d75aa2bf4915
qz.cc: return correct number of eigenvalues (bug #60357).
Rik <rik@octave.org>
parents:
29358
diff
changeset
|
952 %! assert (abs (lambda(1) < 1)); |
|
d75aa2bf4915
qz.cc: return correct number of eigenvalues (bug #60357).
Rik <rik@octave.org>
parents:
29358
diff
changeset
|
953 %! assert (all (abs (lambda(2:4)) >= 1)); |
|
13074
0b789a03bde1
codesprint: Add 3 tests for qz.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12642
diff
changeset
|
954 */ |
|
29958
32c3a5805893
move DEFUN and DEFMETHOD functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents:
29558
diff
changeset
|
955 |
|
31605
e88a07dec498
maint: Use macros to begin/end C++ namespaces.
Rik <rik@octave.org>
parents:
30564
diff
changeset
|
956 OCTAVE_END_NAMESPACE(octave) |