Mercurial > octave-antonio
annotate scripts/linear-algebra/qzhess.m @ 19593:446c46af4b42 stable
strip trailing whitespace from most source files
* Makefile.am, NEWS, build-aux/common.mk, configure.ac,
doc/Makefile.am, doc/doxyhtml/Makefile.am,
doc/interpreter/Makefile.am, doc/interpreter/arith.txi,
doc/interpreter/audio.txi, doc/interpreter/basics.txi,
doc/interpreter/bugs.txi, doc/interpreter/container.txi,
doc/interpreter/cp-idx.txi, doc/interpreter/data.txi,
doc/interpreter/debug.txi, doc/interpreter/diagperm.txi,
doc/interpreter/diffeq.txi, doc/interpreter/doccheck/README,
doc/interpreter/doccheck/spellcheck, doc/interpreter/emacs.txi,
doc/interpreter/errors.txi, doc/interpreter/eval.txi,
doc/interpreter/expr.txi, doc/interpreter/external.txi,
doc/interpreter/fn-idx.txi, doc/interpreter/func.txi,
doc/interpreter/geometry.txi, doc/interpreter/geometryimages.m,
doc/interpreter/gpl.txi, doc/interpreter/grammar.txi,
doc/interpreter/gui.txi, doc/interpreter/image.txi,
doc/interpreter/install.txi, doc/interpreter/interp.txi,
doc/interpreter/interpimages.m, doc/interpreter/intro.txi,
doc/interpreter/io.txi, doc/interpreter/java.txi,
doc/interpreter/linalg.txi, doc/interpreter/macros.texi,
doc/interpreter/matrix.txi, doc/interpreter/munge-texi.pl,
doc/interpreter/nonlin.txi, doc/interpreter/numbers.txi,
doc/interpreter/obsolete.txi, doc/interpreter/octave-config.1,
doc/interpreter/octave.texi, doc/interpreter/oop.txi,
doc/interpreter/op-idx.txi, doc/interpreter/optim.txi,
doc/interpreter/package.txi, doc/interpreter/plot.txi,
doc/interpreter/poly.txi, doc/interpreter/preface.txi,
doc/interpreter/quad.txi, doc/interpreter/set.txi,
doc/interpreter/signal.txi, doc/interpreter/sparse.txi,
doc/interpreter/sparseimages.m, doc/interpreter/splineimages.m,
doc/interpreter/stats.txi, doc/interpreter/stmt.txi,
doc/interpreter/strings.txi, doc/interpreter/system.txi,
doc/interpreter/testfun.txi, doc/interpreter/tips.txi,
doc/interpreter/var.txi, doc/interpreter/vectorize.txi,
doc/liboctave/Makefile.am, doc/liboctave/array.texi,
doc/liboctave/bugs.texi, doc/liboctave/cp-idx.texi,
doc/liboctave/dae.texi, doc/liboctave/diffeq.texi,
doc/liboctave/error.texi, doc/liboctave/factor.texi,
doc/liboctave/fn-idx.texi, doc/liboctave/gpl.texi,
doc/liboctave/install.texi, doc/liboctave/intro.texi,
doc/liboctave/liboctave.texi, doc/liboctave/matvec.texi,
doc/liboctave/nleqn.texi, doc/liboctave/nlfunc.texi,
doc/liboctave/ode.texi, doc/liboctave/optim.texi,
doc/liboctave/preface.texi, doc/liboctave/quad.texi,
doc/liboctave/range.texi, doc/refcard/Makefile.am,
doc/refcard/refcard.tex, etc/HACKING, etc/NEWS.1, etc/NEWS.2,
etc/NEWS.3, etc/OLD-ChangeLogs/ChangeLog,
etc/OLD-ChangeLogs/doc-ChangeLog,
etc/OLD-ChangeLogs/scripts-ChangeLog,
etc/OLD-ChangeLogs/src-ChangeLog, etc/OLD-ChangeLogs/test-ChangeLog,
etc/PROJECTS, etc/README.Cygwin, etc/README.MacOS, etc/README.MinGW,
etc/README.gnuplot, etc/gdbinit, etc/icons/Makefile.am,
examples/@polynomial/end.m, examples/@polynomial/subsasgn.m,
examples/Makefile.am, examples/standalonebuiltin.cc,
libgui/Makefile.am, libgui/qterminal/libqterminal/README,
libgui/qterminal/libqterminal/unix/BlockArray.cpp,
libgui/qterminal/libqterminal/unix/BlockArray.h,
libgui/qterminal/libqterminal/unix/Character.h,
libgui/qterminal/libqterminal/unix/CharacterColor.h,
libgui/qterminal/libqterminal/unix/Emulation.cpp,
libgui/qterminal/libqterminal/unix/Emulation.h,
libgui/qterminal/libqterminal/unix/Filter.cpp,
libgui/qterminal/libqterminal/unix/Filter.h,
libgui/qterminal/libqterminal/unix/History.cpp,
libgui/qterminal/libqterminal/unix/History.h,
libgui/qterminal/libqterminal/unix/KeyboardTranslator.cpp,
libgui/qterminal/libqterminal/unix/KeyboardTranslator.h,
libgui/qterminal/libqterminal/unix/LineFont.h,
libgui/qterminal/libqterminal/unix/QUnixTerminalImpl.cpp,
libgui/qterminal/libqterminal/unix/QUnixTerminalImpl.h,
libgui/qterminal/libqterminal/unix/Screen.cpp,
libgui/qterminal/libqterminal/unix/Screen.h,
libgui/qterminal/libqterminal/unix/ScreenWindow.cpp,
libgui/qterminal/libqterminal/unix/ScreenWindow.h,
libgui/qterminal/libqterminal/unix/TerminalCharacterDecoder.cpp,
libgui/qterminal/libqterminal/unix/TerminalCharacterDecoder.h,
libgui/qterminal/libqterminal/unix/Vt102Emulation.h,
libgui/qterminal/libqterminal/win32/QWinTerminalImpl.cpp,
libgui/qterminal/qterminal/main.cpp,
libgui/src/m-editor/file-editor-tab.cc, libgui/src/octave-gui.cc,
libgui/src/octave-qt-link.cc, libinterp/corefcn/data.cc,
libinterp/corefcn/defun-int.h, libinterp/corefcn/det.cc,
libinterp/corefcn/gl2ps-renderer.cc, libinterp/corefcn/graphics.cc,
libinterp/corefcn/graphics.in.h, libinterp/corefcn/ls-mat5.cc,
libinterp/corefcn/lu.cc, libinterp/corefcn/oct-tex-parser.yy,
libinterp/corefcn/oct-tex-symbols.in, libinterp/corefcn/quadcc.cc,
libinterp/corefcn/zfstream.cc, libinterp/dldfcn/__eigs__.cc,
libinterp/dldfcn/__voronoi__.cc, libinterp/gendoc.pl,
libinterp/genprops.awk, libinterp/mk-errno-list, libinterp/mk-pkg-add,
libinterp/mkbuiltins, libinterp/mkdefs, libinterp/mkdocs,
libinterp/mkops, libinterp/octave-value/ov-java.cc,
libinterp/parse-tree/lex.ll, libinterp/parse-tree/oct-parse.in.yy,
libinterp/parse-tree/octave.gperf, liboctave/Makefile.am,
liboctave/array/Array.cc, liboctave/array/module.mk,
liboctave/cruft/daspk/datv.f, liboctave/cruft/daspk/dcnst0.f,
liboctave/cruft/daspk/dcnstr.f, liboctave/cruft/daspk/ddasic.f,
liboctave/cruft/daspk/ddasid.f, liboctave/cruft/daspk/ddasik.f,
liboctave/cruft/daspk/ddaspk.f, liboctave/cruft/daspk/ddstp.f,
liboctave/cruft/daspk/ddwnrm.f, liboctave/cruft/daspk/dfnrmd.f,
liboctave/cruft/daspk/dfnrmk.f, liboctave/cruft/daspk/dhels.f,
liboctave/cruft/daspk/dheqr.f, liboctave/cruft/daspk/dinvwt.f,
liboctave/cruft/daspk/dlinsd.f, liboctave/cruft/daspk/dlinsk.f,
liboctave/cruft/daspk/dmatd.f, liboctave/cruft/daspk/dnedd.f,
liboctave/cruft/daspk/dnedk.f, liboctave/cruft/daspk/dnsd.f,
liboctave/cruft/daspk/dnsid.f, liboctave/cruft/daspk/dnsik.f,
liboctave/cruft/daspk/dnsk.f, liboctave/cruft/daspk/dorth.f,
liboctave/cruft/daspk/dslvd.f, liboctave/cruft/daspk/dslvk.f,
liboctave/cruft/daspk/dspigm.f, liboctave/cruft/daspk/dyypnw.f,
liboctave/cruft/dasrt/ddasrt.f, liboctave/cruft/dasrt/drchek.f,
liboctave/cruft/dassl/ddaslv.f, liboctave/cruft/dassl/ddassl.f,
liboctave/cruft/misc/blaswrap.c, liboctave/cruft/misc/module.mk,
liboctave/cruft/odepack/cfode.f, liboctave/cruft/odepack/dlsode.f,
liboctave/cruft/odepack/ewset.f, liboctave/cruft/odepack/intdy.f,
liboctave/cruft/odepack/prepj.f, liboctave/cruft/odepack/sintdy.f,
liboctave/cruft/odepack/slsode.f, liboctave/cruft/odepack/solsy.f,
liboctave/cruft/odepack/ssolsy.f, liboctave/cruft/odepack/stode.f,
liboctave/cruft/odepack/vnorm.f, liboctave/cruft/ranlib/Basegen.doc,
liboctave/cruft/ranlib/README, liboctave/cruft/ranlib/genbet.f,
liboctave/cruft/ranlib/genexp.f, liboctave/cruft/ranlib/gennch.f,
liboctave/cruft/ranlib/gennf.f, liboctave/cruft/ranlib/gennor.f,
liboctave/cruft/ranlib/getsd.f, liboctave/cruft/ranlib/initgn.f,
liboctave/cruft/ranlib/phrtsd.f, liboctave/cruft/ranlib/randlib.fdoc,
liboctave/cruft/ranlib/setsd.f, liboctave/cruft/ranlib/tstgmn.for,
liboctave/cruft/ranlib/tstmid.for, liboctave/cruft/slatec-fn/atanh.f,
liboctave/cruft/slatec-fn/datanh.f,
liboctave/cruft/slatec-fn/xgmainc.f,
liboctave/cruft/slatec-fn/xsgmainc.f, liboctave/numeric/module.mk,
liboctave/operators/mk-ops.awk, liboctave/operators/mx-ops,
liboctave/operators/sparse-mk-ops.awk,
liboctave/operators/sparse-mx-ops, liboctave/operators/vx-ops,
liboctave/util/module.mk, run-octave.in, scripts/@ftp/ftp.m,
scripts/audio/wavread.m, scripts/deprecated/java_convert_matrix.m,
scripts/deprecated/java_debug.m, scripts/deprecated/java_invoke.m,
scripts/deprecated/java_new.m,
scripts/deprecated/java_unsigned_conversion.m,
scripts/deprecated/javafields.m, scripts/deprecated/javamethods.m,
scripts/deprecated/shell_cmd.m, scripts/general/accumarray.m,
scripts/general/display.m, scripts/general/fieldnames.m,
scripts/general/interp1.m, scripts/general/interp2.m,
scripts/general/interp3.m, scripts/general/isa.m,
scripts/general/methods.m, scripts/general/sortrows.m,
scripts/geometry/convhull.m, scripts/geometry/delaunay.m,
scripts/geometry/delaunay3.m, scripts/geometry/delaunayn.m,
scripts/geometry/griddata.m, scripts/geometry/griddatan.m,
scripts/geometry/voronoi.m, scripts/geometry/voronoin.m,
scripts/gui/guihandles.m, scripts/gui/inputdlg.m,
scripts/gui/listdlg.m, scripts/gui/msgbox.m, scripts/gui/questdlg.m,
scripts/gui/uigetfile.m, scripts/gui/waitbar.m, scripts/gui/warndlg.m,
scripts/help/doc.m, scripts/help/help.m, scripts/help/type.m,
scripts/image/bone.m, scripts/image/cmpermute.m,
scripts/image/cmunique.m, scripts/image/colorcube.m,
scripts/image/colormap.m, scripts/image/contrast.m,
scripts/image/gray2ind.m, scripts/image/image.m,
scripts/image/imshow.m, scripts/image/ind2gray.m, scripts/image/jet.m,
scripts/image/rgb2ntsc.m, scripts/image/spinmap.m,
scripts/io/importdata.m, scripts/io/strread.m, scripts/io/textread.m,
scripts/io/textscan.m, scripts/java/java_get.m,
scripts/java/java_set.m, scripts/java/javaaddpath.m,
scripts/java/javaclasspath.m, scripts/java/javamem.m,
scripts/linear-algebra/linsolve.m, scripts/linear-algebra/qzhess.m,
scripts/miscellaneous/debug.m, scripts/miscellaneous/desktop.m,
scripts/miscellaneous/dir.m, scripts/miscellaneous/dos.m,
scripts/miscellaneous/edit.m, scripts/miscellaneous/fact.m,
scripts/miscellaneous/getappdata.m, scripts/miscellaneous/inputname.m,
scripts/miscellaneous/license.m, scripts/miscellaneous/ls_command.m,
scripts/miscellaneous/run.m, scripts/miscellaneous/setfield.m,
scripts/miscellaneous/unix.m, scripts/miscellaneous/ver.m,
scripts/mk-pkg-add, scripts/mkdoc.pl,
scripts/optimization/fminsearch.m, scripts/optimization/optimset.m,
scripts/optimization/sqp.m, scripts/pkg/pkg.m,
scripts/pkg/private/create_pkgadddel.m,
scripts/pkg/private/fix_depends.m, scripts/pkg/private/install.m,
scripts/plot/appearance/axis.m, scripts/plot/appearance/box.m,
scripts/plot/appearance/clabel.m, scripts/plot/appearance/daspect.m,
scripts/plot/appearance/datetick.m, scripts/plot/appearance/grid.m,
scripts/plot/appearance/legend.m, scripts/plot/appearance/orient.m,
scripts/plot/appearance/shading.m, scripts/plot/appearance/text.m,
scripts/plot/appearance/title.m, scripts/plot/appearance/xlabel.m,
scripts/plot/appearance/ylabel.m, scripts/plot/appearance/zlabel.m,
scripts/plot/draw/area.m, scripts/plot/draw/bar.m,
scripts/plot/draw/barh.m, scripts/plot/draw/colorbar.m,
scripts/plot/draw/contour.m, scripts/plot/draw/contour3.m,
scripts/plot/draw/contourf.m, scripts/plot/draw/ellipsoid.m,
scripts/plot/draw/errorbar.m, scripts/plot/draw/ezcontour.m,
scripts/plot/draw/ezcontourf.m, scripts/plot/draw/ezmesh.m,
scripts/plot/draw/ezpolar.m, scripts/plot/draw/fill.m,
scripts/plot/draw/fplot.m, scripts/plot/draw/hist.m,
scripts/plot/draw/meshc.m, scripts/plot/draw/meshz.m,
scripts/plot/draw/pareto.m, scripts/plot/draw/patch.m,
scripts/plot/draw/peaks.m, scripts/plot/draw/pie.m,
scripts/plot/draw/pie3.m, scripts/plot/draw/plot.m,
scripts/plot/draw/plotyy.m, scripts/plot/draw/private/__bar__.m,
scripts/plot/draw/private/__contour__.m,
scripts/plot/draw/private/__errplot__.m,
scripts/plot/draw/private/__ezplot__.m,
scripts/plot/draw/private/__patch__.m,
scripts/plot/draw/private/__stem__.m, scripts/plot/draw/rectangle.m,
scripts/plot/draw/ribbon.m, scripts/plot/draw/rose.m,
scripts/plot/draw/scatter.m, scripts/plot/draw/scatter3.m,
scripts/plot/draw/semilogx.m, scripts/plot/draw/shrinkfaces.m,
scripts/plot/draw/sombrero.m, scripts/plot/draw/sphere.m,
scripts/plot/draw/stairs.m, scripts/plot/draw/stem.m,
scripts/plot/draw/stemleaf.m, scripts/plot/draw/surf.m,
scripts/plot/draw/surface.m, scripts/plot/draw/surfc.m,
scripts/plot/draw/surfl.m, scripts/plot/draw/surfnorm.m,
scripts/plot/draw/tetramesh.m, scripts/plot/draw/trimesh.m,
scripts/plot/draw/triplot.m, scripts/plot/draw/trisurf.m,
scripts/plot/util/__gnuplot_drawnow__.m,
scripts/plot/util/__plt_get_axis_arg__.m, scripts/plot/util/axes.m,
scripts/plot/util/clf.m, scripts/plot/util/copyobj.m,
scripts/plot/util/figure.m, scripts/plot/util/gcbo.m,
scripts/plot/util/graphics_toolkit.m, scripts/plot/util/hggroup.m,
scripts/plot/util/meshgrid.m, scripts/plot/util/newplot.m,
scripts/plot/util/print.m,
scripts/plot/util/private/__add_default_menu__.m,
scripts/plot/util/private/__fltk_print__.m,
scripts/plot/util/private/__gnuplot_print__.m,
scripts/plot/util/private/__print_parse_opts__.m,
scripts/plot/util/refreshdata.m, scripts/plot/util/subplot.m,
scripts/polynomial/conv.m, scripts/polynomial/poly.m,
scripts/polynomial/polyeig.m, scripts/polynomial/polyfit.m,
scripts/polynomial/polyval.m,
scripts/polynomial/private/__splinefit__.m,
scripts/polynomial/spline.m, scripts/prefs/prefdir.m,
scripts/prefs/preferences.m, scripts/prefs/private/prefsfile.m,
scripts/prefs/rmpref.m, scripts/signal/freqz.m,
scripts/signal/module.mk, scripts/sparse/eigs.m, scripts/sparse/pcg.m,
scripts/sparse/private/__sprand_impl__.m, scripts/sparse/sprand.m,
scripts/sparse/sprandn.m, scripts/sparse/spy.m, scripts/sparse/svds.m,
scripts/specfun/expint.m, scripts/specfun/factor.m,
scripts/special-matrix/gallery.m, scripts/special-matrix/hankel.m,
scripts/special-matrix/toeplitz.m, scripts/startup/inputrc,
scripts/statistics/base/kurtosis.m, scripts/statistics/base/moment.m,
scripts/statistics/base/qqplot.m, scripts/statistics/base/var.m,
scripts/statistics/distributions/betarnd.m,
scripts/statistics/distributions/binoinv.m,
scripts/statistics/distributions/binopdf.m,
scripts/statistics/distributions/binornd.m,
scripts/statistics/distributions/cauchy_rnd.m,
scripts/statistics/distributions/chi2rnd.m,
scripts/statistics/distributions/discrete_pdf.m,
scripts/statistics/distributions/discrete_rnd.m,
scripts/statistics/distributions/empirical_rnd.m,
scripts/statistics/distributions/exprnd.m,
scripts/statistics/distributions/frnd.m,
scripts/statistics/distributions/gamrnd.m,
scripts/statistics/distributions/geornd.m,
scripts/statistics/distributions/hygernd.m,
scripts/statistics/distributions/kolmogorov_smirnov_cdf.m,
scripts/statistics/distributions/laplace_cdf.m,
scripts/statistics/distributions/laplace_pdf.m,
scripts/statistics/distributions/logistic_cdf.m,
scripts/statistics/distributions/logistic_pdf.m,
scripts/statistics/distributions/lognrnd.m,
scripts/statistics/distributions/nbincdf.m,
scripts/statistics/distributions/nbininv.m,
scripts/statistics/distributions/nbinpdf.m,
scripts/statistics/distributions/nbinrnd.m,
scripts/statistics/distributions/normrnd.m,
scripts/statistics/distributions/poissinv.m,
scripts/statistics/distributions/poissrnd.m,
scripts/statistics/distributions/tinv.m,
scripts/statistics/distributions/trnd.m,
scripts/statistics/distributions/unidcdf.m,
scripts/statistics/distributions/unidpdf.m,
scripts/statistics/distributions/unidrnd.m,
scripts/statistics/distributions/unifrnd.m,
scripts/statistics/distributions/wblrnd.m,
scripts/statistics/models/module.mk,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/strings/base2dec.m, scripts/strings/deblank.m,
scripts/strings/dec2base.m, scripts/strings/dec2bin.m,
scripts/strings/dec2hex.m, scripts/strings/mat2str.m,
scripts/strings/ostrsplit.m, scripts/strings/regexptranslate.m,
scripts/strings/str2num.m, scripts/strings/strcat.m,
scripts/strings/strjoin.m, scripts/strings/strsplit.m,
scripts/strings/strtok.m, scripts/strings/strtrim.m,
scripts/strings/strtrunc.m, scripts/strings/substr.m,
scripts/testfun/__run_test_suite__.m, scripts/testfun/speed.m,
scripts/testfun/test.m, scripts/time/asctime.m,
scripts/time/datenum.m, scripts/time/datevec.m,
scripts/time/weekday.m, src/Makefile.am, test/Makefile.am,
test/build-bc-overload-tests.sh, test/build-sparse-tests.sh,
test/jit.tst, test/line-continue.tst: Strip trailing whitespace.
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Tue, 20 Jan 2015 08:26:57 -0500 |
| parents | d63878346099 |
| children | 0e1f5a750d00 |
| rev | line source |
|---|---|
|
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|
1 ## Copyright (C) 1993-2013 John W. Eaton |
| 2313 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 2313 | 9 ## |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 245 | 18 |
| 3372 | 19 ## -*- texinfo -*- |
|
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20 ## @deftypefn {Function File} {[@var{aa}, @var{bb}, @var{q}, @var{z}] =} qzhess (@var{A}, @var{B}) |
| 3372 | 21 ## Compute the Hessenberg-triangular decomposition of the matrix pencil |
|
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22 ## @code{(@var{A}, @var{B})}, returning |
|
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23 ## @code{@var{aa} = @var{q} * @var{A} * @var{z}}, |
|
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24 ## @code{@var{bb} = @var{q} * @var{B} * @var{z}}, with @var{q} and @var{z} |
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25 ## orthogonal. For example: |
| 3426 | 26 ## |
| 3372 | 27 ## @example |
| 28 ## @group | |
| 29 ## [aa, bb, q, z] = qzhess ([1, 2; 3, 4], [5, 6; 7, 8]) | |
| 30 ## @result{} aa = [ -3.02244, -4.41741; 0.92998, 0.69749 ] | |
| 31 ## @result{} bb = [ -8.60233, -9.99730; 0.00000, -0.23250 ] | |
| 32 ## @result{} q = [ -0.58124, -0.81373; -0.81373, 0.58124 ] | |
| 33 ## @result{} z = [ 1, 0; 0, 1 ] | |
| 34 ## @end group | |
| 35 ## @end example | |
| 3426 | 36 ## |
| 3372 | 37 ## The Hessenberg-triangular decomposition is the first step in |
|
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38 ## Moler and Stewart's QZ@tie{}decomposition algorithm. |
| 3426 | 39 ## |
|
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40 ## Algorithm taken from Golub and Van Loan, |
|
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41 ## @cite{Matrix Computations, 2nd edition}. |
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42 ## |
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43 ## @seealso{lu, chol, hess, qr, qz, schur, svd} |
| 3372 | 44 ## @end deftypefn |
| 29 | 45 |
| 2312 | 46 ## Author: A. S. Hodel <scotte@eng.auburn.edu> |
| 47 ## Created: August 1993 | |
| 48 ## Adapted-By: jwe | |
| 29 | 49 |
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50 function [aa, bb, q, z] = qzhess (A, B) |
| 72 | 51 |
| 54 | 52 if (nargin != 2) |
| 6046 | 53 print_usage (); |
| 54 | 54 endif |
| 55 | |
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56 [na, ma] = size (A); |
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57 [nb, mb] = size (B); |
| 54 | 58 if (na != ma || na != nb || nb != mb) |
| 59 error ("qzhess: incompatible dimensions"); | |
| 60 endif | |
| 61 | |
| 2303 | 62 ## Reduce to hessenberg-triangular form. |
| 29 | 63 |
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64 [q, bb] = qr (B); |
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65 aa = q' * A; |
| 54 | 66 q = q'; |
| 67 z = eye (na); | |
| 68 for j = 1:(na-2) | |
| 69 for i = na:-1:(j+2) | |
| 70 | |
| 2303 | 71 ## disp (["zero out aa(", num2str(i), ",", num2str(j), ")"]) |
| 54 | 72 |
| 73 rot = givens (aa (i-1, j), aa (i, j)); | |
| 74 aa ((i-1):i, :) = rot *aa ((i-1):i, :); | |
| 75 bb ((i-1):i, :) = rot *bb ((i-1):i, :); | |
| 76 q ((i-1):i, :) = rot *q ((i-1):i, :); | |
| 77 | |
| 2303 | 78 ## disp (["now zero out bb(", num2str(i), ",", num2str(i-1), ")"]) |
| 54 | 79 |
| 80 rot = givens (bb (i, i), bb (i, i-1))'; | |
| 81 bb (:, (i-1):i) = bb (:, (i-1):i) * rot'; | |
| 82 aa (:, (i-1):i) = aa (:, (i-1):i) * rot'; | |
| 83 z (:, (i-1):i) = z (:, (i-1):i) * rot'; | |
| 84 | |
| 85 endfor | |
| 29 | 86 endfor |
| 87 | |
| 54 | 88 bb (2, 1) = 0.0; |
| 89 for i = 3:na | |
| 90 bb (i, 1:(i-1)) = zeros (1, i-1); | |
| 91 aa (i, 1:(i-2)) = zeros (1, i-2); | |
| 92 endfor | |
| 93 | |
| 29 | 94 endfunction |
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95 |
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96 |
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97 %!test |
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98 %! a = [1 2 1 3; |
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99 %! 2 5 3 2; |
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100 %! 5 5 1 0; |
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101 %! 4 0 3 2]; |
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102 %! b = [0 4 2 1; |
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103 %! 2 3 1 1; |
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104 %! 1 0 2 1; |
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105 %! 2 5 3 2]; |
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106 %! mask = [0 0 0 0; |
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107 %! 0 0 0 0; |
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108 %! 1 0 0 0; |
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109 %! 1 1 0 0]; |
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110 %! [aa, bb, q, z] = qzhess (a, b); |
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111 %! assert (inv (q) - q', zeros (4), 2e-8); |
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112 %! assert (inv (z) - z', zeros (4), 2e-8); |
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113 %! assert (q * a * z, aa, 2e-8); |
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114 %! assert (aa .* mask, zeros (4), 2e-8); |
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115 %! assert (q * b * z, bb, 2e-8); |
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116 %! assert (bb .* mask, zeros (4), 2e-8); |
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117 |
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118 %!test |
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119 %! a = [1 2 3 4 5; |
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120 %! 3 2 3 1 0; |
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121 %! 4 3 2 1 1; |
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122 %! 0 1 0 1 0; |
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123 %! 3 2 1 0 5]; |
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124 %! b = [5 0 4 0 1; |
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125 %! 1 1 1 2 5; |
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126 %! 0 3 2 1 0; |
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127 %! 4 3 0 3 5; |
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128 %! 2 1 2 1 3]; |
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129 %! mask = [0 0 0 0 0; |
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130 %! 0 0 0 0 0; |
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131 %! 1 0 0 0 0; |
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132 %! 1 1 0 0 0; |
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133 %! 1 1 1 0 0]; |
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134 %! [aa, bb, q, z] = qzhess (a, b); |
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135 %! assert (inv (q) - q', zeros (5), 2e-8); |
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136 %! assert (inv (z) - z', zeros (5), 2e-8); |
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137 %! assert (q * a * z, aa, 2e-8); |
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138 %! assert (aa .* mask, zeros (5), 2e-8); |
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139 %! assert (q * b * z, bb, 2e-8); |
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140 %! assert (bb .* mask, zeros (5), 2e-8); |
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141 |
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142 %!error qzhess ([0]) |
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143 %!error qzhess () |
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144 |