Mercurial > octave-nkf
comparison scripts/special-matrix/gallery.m @ 19627:446c46af4b42 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 | 6dbc866379e2 |
| children | 0e1f5a750d00 |
comparison
equal
deleted
inserted
replaced
| 19488:8dbd55742112 | 19627:446c46af4b42 |
|---|---|
| 1292 ## Must have |s| = norm(x), v = x+s*e_1, and | 1292 ## Must have |s| = norm(x), v = x+s*e_1, and |
| 1293 ## x'y = x'Hx =(x'Hx)' real => arg(s) = arg(x(1)). | 1293 ## x'y = x'Hx =(x'Hx)' real => arg(s) = arg(x(1)). |
| 1294 ## So take s = sign(x(1))*norm(x) (which avoids cancellation). | 1294 ## So take s = sign(x(1))*norm(x) (which avoids cancellation). |
| 1295 ## v'v = (x(1)+s)^2 + x(2)^2 + ... + x(n)^2 | 1295 ## v'v = (x(1)+s)^2 + x(2)^2 + ... + x(n)^2 |
| 1296 ## = 2*norm(x)*(norm(x) + |x(1)|). | 1296 ## = 2*norm(x)*(norm(x) + |x(1)|). |
| 1297 ## | 1297 ## |
| 1298 ## References: | 1298 ## References: |
| 1299 ## G.H. Golub and C.F. Van Loan, Matrix Computations, second edition, | 1299 ## G.H. Golub and C.F. Van Loan, Matrix Computations, second edition, |
| 1300 ## Johns Hopkins University Press, Baltimore, Maryland, 1989. | 1300 ## Johns Hopkins University Press, Baltimore, Maryland, 1989. |
| 1301 ## G.W. Stewart, Introduction to Matrix Computations, Academic Press, | 1301 ## G.W. Stewart, Introduction to Matrix Computations, Academic Press, |
| 1302 ## New York, 1973, | 1302 ## New York, 1973, |
| 1341 "for integerdata matrix."]); | 1341 "for integerdata matrix."]); |
| 1342 endif | 1342 endif |
| 1343 jidx = varargin{end-1}; | 1343 jidx = varargin{end-1}; |
| 1344 svec = [varargin{1:end-1}]; | 1344 svec = [varargin{1:end-1}]; |
| 1345 varargin(end-1) = []; | 1345 varargin(end-1) = []; |
| 1346 else | 1346 else |
| 1347 error (["gallery: J must be an integer in the range [0, 2^32-1] " ... | 1347 error (["gallery: J must be an integer in the range [0, 2^32-1] " ... |
| 1348 "for integerdata matrix"]); | 1348 "for integerdata matrix"]); |
| 1349 endif | 1349 endif |
| 1350 | 1350 |
| 1351 if (! (isnumeric (jidx) && isscalar (jidx) | 1351 if (! (isnumeric (jidx) && isscalar (jidx) |
| 1355 "for integerdata matrix"]); | 1355 "for integerdata matrix"]); |
| 1356 endif | 1356 endif |
| 1357 | 1357 |
| 1358 ## Save and restore random state. Initialization done so that reproducible | 1358 ## Save and restore random state. Initialization done so that reproducible |
| 1359 ## data is available from gallery depending on the jidx and size vector. | 1359 ## data is available from gallery depending on the jidx and size vector. |
| 1360 randstate = rand ("state"); | 1360 randstate = rand ("state"); |
| 1361 unwind_protect | 1361 unwind_protect |
| 1362 rand ("state", svec); | 1362 rand ("state", svec); |
| 1363 A = randi (varargin{:}); | 1363 A = randi (varargin{:}); |
| 1364 unwind_protect_cleanup | 1364 unwind_protect_cleanup |
| 1365 rand ("state", randstate); | 1365 rand ("state", randstate); |
| 1459 ## The determinant and inverse are known explicitly. | 1459 ## The determinant and inverse are known explicitly. |
| 1460 ## If a second output argument is present, d = DET(A) is returned: | 1460 ## If a second output argument is present, d = DET(A) is returned: |
| 1461 ## [A, d] = IPJFACT(N, K); | 1461 ## [A, d] = IPJFACT(N, K); |
| 1462 ## | 1462 ## |
| 1463 ## Suggested by P. R. Graves-Morris. | 1463 ## Suggested by P. R. Graves-Morris. |
| 1464 ## | 1464 ## |
| 1465 ## Reference: | 1465 ## Reference: |
| 1466 ## M.J.C. Gover, The explicit inverse of factorial Hankel matrices, | 1466 ## M.J.C. Gover, The explicit inverse of factorial Hankel matrices, |
| 1467 ## Dept. of Mathematics, University of Bradford, 1993. | 1467 ## Dept. of Mathematics, University of Bradford, 1993. |
| 1468 | 1468 |
| 1469 if (nargin < 1 || nargin > 2) | 1469 if (nargin < 1 || nargin > 2) |
| 1860 "for normaldata matrix."]); | 1860 "for normaldata matrix."]); |
| 1861 endif | 1861 endif |
| 1862 jidx = varargin{end-1}; | 1862 jidx = varargin{end-1}; |
| 1863 svec = [varargin{1:end-1}]; | 1863 svec = [varargin{1:end-1}]; |
| 1864 varargin(end-1) = []; | 1864 varargin(end-1) = []; |
| 1865 else | 1865 else |
| 1866 error (["gallery: J must be an integer in the range [0, 2^32-1] " ... | 1866 error (["gallery: J must be an integer in the range [0, 2^32-1] " ... |
| 1867 "for normaldata matrix"]); | 1867 "for normaldata matrix"]); |
| 1868 endif | 1868 endif |
| 1869 | 1869 |
| 1870 if (! (isnumeric (jidx) && isscalar (jidx) | 1870 if (! (isnumeric (jidx) && isscalar (jidx) |
| 1874 "for normaldata matrix"]); | 1874 "for normaldata matrix"]); |
| 1875 endif | 1875 endif |
| 1876 | 1876 |
| 1877 ## Save and restore random state. Initialization done so that reproducible | 1877 ## Save and restore random state. Initialization done so that reproducible |
| 1878 ## data is available from gallery depending on the jidx and size vector. | 1878 ## data is available from gallery depending on the jidx and size vector. |
| 1879 randstate = randn ("state"); | 1879 randstate = randn ("state"); |
| 1880 unwind_protect | 1880 unwind_protect |
| 1881 randn ("state", svec); | 1881 randn ("state", svec); |
| 1882 A = randn (varargin{:}); | 1882 A = randn (varargin{:}); |
| 1883 unwind_protect_cleanup | 1883 unwind_protect_cleanup |
| 1884 randn ("state", randstate); | 1884 randn ("state", randstate); |
| 1979 ## | 1979 ## |
| 1980 ## At the Second SIAM Conference on Linear Algebra, Raleigh, N.C., | 1980 ## At the Second SIAM Conference on Linear Algebra, Raleigh, N.C., |
| 1981 ## 1985, Cleve Moler noted that most of the singular values of | 1981 ## 1985, Cleve Moler noted that most of the singular values of |
| 1982 ## PARTER(N) are very close to PI. An explanation of the phenomenon | 1982 ## PARTER(N) are very close to PI. An explanation of the phenomenon |
| 1983 ## was given by Parter; see also the paper by Tyrtyshnikov. | 1983 ## was given by Parter; see also the paper by Tyrtyshnikov. |
| 1984 ## | 1984 ## |
| 1985 ## References: | 1985 ## References: |
| 1986 ## The MathWorks Newsletter, Volume 1, Issue 1, March 1986, page 2. | 1986 ## The MathWorks Newsletter, Volume 1, Issue 1, March 1986, page 2. |
| 1987 ## S.V. Parter, On the distribution of the singular values of Toeplitz | 1987 ## S.V. Parter, On the distribution of the singular values of Toeplitz |
| 1988 ## matrices, Linear Algebra and Appl., 80 (1986), pp. 115-130. | 1988 ## matrices, Linear Algebra and Appl., 80 (1986), pp. 115-130. |
| 1989 ## E.E. Tyrtyshnikov, Cauchy-Toeplitz matrices and some applications, | 1989 ## E.E. Tyrtyshnikov, Cauchy-Toeplitz matrices and some applications, |
| 2085 ## unitary Hessenberg matrix with positive subdiagonal elements in terms | 2085 ## unitary Hessenberg matrix with positive subdiagonal elements in terms |
| 2086 ## of 2N-1 real parameters (the Schur parametrization). | 2086 ## of 2N-1 real parameters (the Schur parametrization). |
| 2087 ## This M-file handles the real case only and is intended simply as a | 2087 ## This M-file handles the real case only and is intended simply as a |
| 2088 ## convenient way to generate random or non-random orthogonal Hessenberg | 2088 ## convenient way to generate random or non-random orthogonal Hessenberg |
| 2089 ## matrices. | 2089 ## matrices. |
| 2090 ## | 2090 ## |
| 2091 ## Reference: | 2091 ## Reference: |
| 2092 ## W.B. Gragg, The QR algorithm for unitary Hessenberg matrices, | 2092 ## W.B. Gragg, The QR algorithm for unitary Hessenberg matrices, |
| 2093 ## J. Comp. Appl. Math., 16 (1986), pp. 1-8. | 2093 ## J. Comp. Appl. Math., 16 (1986), pp. 1-8. |
| 2094 | 2094 |
| 2095 if (nargin != 1) | 2095 if (nargin != 1) |
| 2581 "for uniformdata matrix."]); | 2581 "for uniformdata matrix."]); |
| 2582 endif | 2582 endif |
| 2583 jidx = varargin{end-1}; | 2583 jidx = varargin{end-1}; |
| 2584 svec = [varargin{1:end-1}]; | 2584 svec = [varargin{1:end-1}]; |
| 2585 varargin(end-1) = []; | 2585 varargin(end-1) = []; |
| 2586 else | 2586 else |
| 2587 error (["gallery: J must be an integer in the range [0, 2^32-1] " ... | 2587 error (["gallery: J must be an integer in the range [0, 2^32-1] " ... |
| 2588 "for uniformdata matrix"]); | 2588 "for uniformdata matrix"]); |
| 2589 endif | 2589 endif |
| 2590 | 2590 |
| 2591 if (! (isnumeric (jidx) && isscalar (jidx) | 2591 if (! (isnumeric (jidx) && isscalar (jidx) |
| 2595 "for uniformdata matrix"]); | 2595 "for uniformdata matrix"]); |
| 2596 endif | 2596 endif |
| 2597 | 2597 |
| 2598 ## Save and restore random state. Initialization done so that reproducible | 2598 ## Save and restore random state. Initialization done so that reproducible |
| 2599 ## data is available from gallery depending on the jidx and size vector. | 2599 ## data is available from gallery depending on the jidx and size vector. |
| 2600 randstate = rand ("state"); | 2600 randstate = rand ("state"); |
| 2601 unwind_protect | 2601 unwind_protect |
| 2602 rand ("state", svec); | 2602 rand ("state", svec); |
| 2603 A = rand (varargin{:}); | 2603 A = rand (varargin{:}); |
| 2604 unwind_protect_cleanup | 2604 unwind_protect_cleanup |
| 2605 rand ("state", randstate); | 2605 rand ("state", randstate); |
| 2711 | 2711 |
| 2712 rho = 100 * rand (nx, ny); | 2712 rho = 100 * rand (nx, ny); |
| 2713 | 2713 |
| 2714 for j = 1:ny | 2714 for j = 1:ny |
| 2715 for i = 1:nx | 2715 for i = 1:nx |
| 2716 ## | 2716 ## |
| 2717 ## For the element (I,J), determine the indices of the 8 nodes. | 2717 ## For the element (I,J), determine the indices of the 8 nodes. |
| 2718 ## | 2718 ## |
| 2719 nn(1) = 3*j*nx + 2*i + 2*j + 1; | 2719 nn(1) = 3*j*nx + 2*i + 2*j + 1; |
| 2720 nn(2) = nn(1) - 1; | 2720 nn(2) = nn(1) - 1; |
| 2721 nn(3) = nn(2) - 1; | 2721 nn(3) = nn(2) - 1; |
| 2722 nn(4) = (3*j - 1) * nx + 2*j + i - 1; | 2722 nn(4) = (3*j - 1) * nx + 2*j + i - 1; |
| 2723 nn(5) = 3 * (j-1) * nx + 2*i + 2*j - 3; | 2723 nn(5) = 3 * (j-1) * nx + 2*i + 2*j - 3; |
| 2813 ## | 2813 ## |
| 2814 ## Called by RANDSVD. | 2814 ## Called by RANDSVD. |
| 2815 ## This is a `standard' reduction. Cf. reduction to bidiagonal form | 2815 ## This is a `standard' reduction. Cf. reduction to bidiagonal form |
| 2816 ## prior to computing the SVD. This code is a little wasteful in that | 2816 ## prior to computing the SVD. This code is a little wasteful in that |
| 2817 ## it computes certain elements which are immediately set to zero! | 2817 ## it computes certain elements which are immediately set to zero! |
| 2818 ## | 2818 ## |
| 2819 ## Reference: | 2819 ## Reference: |
| 2820 ## G.H. Golub and C.F. Van Loan, Matrix Computations, second edition, | 2820 ## G.H. Golub and C.F. Van Loan, Matrix Computations, second edition, |
| 2821 ## Johns Hopkins University Press, Baltimore, Maryland, 1989. | 2821 ## Johns Hopkins University Press, Baltimore, Maryland, 1989. |
| 2822 ## Section 5.4.3. | 2822 ## Section 5.4.3. |
| 2823 | 2823 |