Mercurial > octave-nkf
annotate doc/interpreter/expr.txi @ 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 | e6a4fa91a2f1 |
| children | 0e1f5a750d00 |
| rev | line source |
|---|---|
|
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1 @c Copyright (C) 1996-2013 John W. Eaton |
| 7018 | 2 @c |
| 3 @c This file is part of Octave. | |
| 4 @c | |
| 5 @c Octave is free software; you can redistribute it and/or modify it | |
| 6 @c under the terms of the GNU General Public License as published by the | |
| 7 @c Free Software Foundation; either version 3 of the License, or (at | |
| 8 @c your option) any later version. | |
|
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9 @c |
| 7018 | 10 @c Octave is distributed in the hope that it will be useful, but WITHOUT |
| 11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 13 @c for more details. | |
|
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14 @c |
| 7018 | 15 @c You should have received a copy of the GNU General Public License |
| 16 @c along with Octave; see the file COPYING. If not, see | |
| 17 @c <http://www.gnu.org/licenses/>. | |
| 3294 | 18 |
| 4167 | 19 @node Expressions |
| 3294 | 20 @chapter Expressions |
| 21 @cindex expressions | |
| 22 | |
| 23 Expressions are the basic building block of statements in Octave. An | |
| 24 expression evaluates to a value, which you can print, test, store in a | |
| 25 variable, pass to a function, or assign a new value to a variable with | |
| 26 an assignment operator. | |
| 27 | |
| 28 An expression can serve as a statement on its own. Most other kinds of | |
| 29 statements contain one or more expressions which specify data to be | |
| 30 operated on. As in other languages, expressions in Octave include | |
| 31 variables, array references, constants, and function calls, as well as | |
| 32 combinations of these with various operators. | |
| 33 | |
| 34 @menu | |
|
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35 * Index Expressions:: |
|
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36 * Calling Functions:: |
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37 * Arithmetic Ops:: |
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38 * Comparison Ops:: |
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39 * Boolean Expressions:: |
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40 * Assignment Ops:: |
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41 * Increment Ops:: |
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42 * Operator Precedence:: |
| 3294 | 43 @end menu |
| 44 | |
| 4167 | 45 @node Index Expressions |
| 3294 | 46 @section Index Expressions |
| 47 | |
| 48 @opindex ( | |
| 49 @opindex ) | |
|
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50 @opindex : |
| 3294 | 51 |
| 52 An @dfn{index expression} allows you to reference or extract selected | |
| 53 elements of a matrix or vector. | |
| 54 | |
| 55 Indices may be scalars, vectors, ranges, or the special operator | |
| 56 @samp{:}, which may be used to select entire rows or columns. | |
| 57 | |
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58 Vectors are indexed using a single index expression. Matrices (2-D) |
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59 and higher multi-dimensional arrays are indexed using either one index |
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60 or @math{N} indices where @math{N} is the dimension of the array. |
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61 When using a single index expression to index 2-D or higher data the |
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62 elements of the array are taken in column-first order (like Fortran). |
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63 |
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64 The output from indexing assumes the dimensions of the index |
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65 expression. For example: |
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66 |
| 5679 | 67 @example |
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68 @group |
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69 a(2) # result is a scalar |
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70 a(1:2) # result is a row vector |
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71 a([1; 2]) # result is a column vector |
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72 @end group |
| 5679 | 73 @end example |
| 74 | |
| 75 As a special case, when a colon is used as a single index, the output | |
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76 is a column vector containing all the elements of the vector or |
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77 matrix. For example: |
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78 |
| 5679 | 79 @example |
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80 @group |
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81 a(:) # result is a column vector |
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82 a(:)' # result is a row vector |
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83 @end group |
| 5679 | 84 @end example |
| 85 | |
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86 The above two code idioms are often used in place of @code{reshape} |
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87 when a simple vector, rather than an arbitrarily sized array, is |
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88 needed. |
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89 |
| 3294 | 90 Given the matrix |
| 91 | |
| 92 @example | |
| 93 a = [1, 2; 3, 4] | |
| 94 @end example | |
| 95 | |
| 96 @noindent | |
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97 all of the following expressions are equivalent and select the first |
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98 row of the matrix. |
| 3294 | 99 |
| 100 @example | |
| 101 @group | |
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102 a(1, [1, 2]) # row 1, columns 1 and 2 |
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103 a(1, 1:2) # row 1, columns in range 1-2 |
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104 a(1, :) # row 1, all columns |
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105 @end group |
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106 @end example |
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107 |
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108 @cindex @code{end}, indexing |
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109 @cindex :end |
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110 |
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111 In index expressions the keyword @code{end} automatically refers to |
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112 the last entry for a particular dimension. This magic index can also |
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113 be used in ranges and typically eliminates the needs to call |
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114 @code{size} or @code{length} to gather array bounds before indexing. |
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115 For example: |
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116 |
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117 @example |
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118 @group |
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119 a = [1, 2, 3, 4]; |
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120 |
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121 a(1:end/2) # first half of a => [1, 2] |
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122 a(end + 1) = 5; # append element |
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123 a(end) = []; # delete element |
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124 a(1:2:end) # odd elements of a => [1, 3] |
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125 a(2:2:end) # even elements of a => [2, 4] |
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126 a(end:-1:1) # reversal of a => [4, 3, 2 , 1] |
| 3294 | 127 @end group |
| 128 @end example | |
| 129 | |
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130 @menu |
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131 * Advanced Indexing:: |
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132 @end menu |
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133 |
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134 @node Advanced Indexing |
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135 @subsection Advanced Indexing |
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136 |
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137 An array with @samp{n} dimensions can be indexed using @samp{m} |
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138 indices. More generally, the set of index tuples determining the |
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139 result is formed by the Cartesian product of the index vectors (or |
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140 ranges or scalars). |
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141 |
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142 For the ordinary and most common case, @w{@code{m == n}}, and each |
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143 index corresponds to its respective dimension. If @w{@code{m < n}} |
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144 and every index is less than the size of the array in the |
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145 @math{i^{th}} dimension, @code{m(i) < n(i)}, then the index expression |
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146 is padded with trailing singleton dimensions (@code{[ones (m-n, 1)]}). |
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147 If @w{@code{m < n}} but one of the indices @code{m(i)} is outside the |
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148 size of the current array, then the last @w{@code{n-m+1}} dimensions |
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149 are folded into a single dimension with an extent equal to the product |
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150 of extents of the original dimensions. This is easiest to understand |
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151 with an example. |
| 3294 | 152 |
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153 @example |
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154 a = reshape (1:8, 2, 2, 2) # Create 3-D array |
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155 a = |
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156 |
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157 ans(:,:,1) = |
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158 |
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159 1 3 |
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160 2 4 |
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161 |
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162 ans(:,:,2) = |
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163 |
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164 5 7 |
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165 6 8 |
| 9159 | 166 |
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167 a(2,1,2); # Case (m == n): ans = 6 |
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168 a(2,1); # Case (m < n), idx within array: |
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169 # equivalent to a(2,1,1), ans = 2 |
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170 a(2,4); # Case (m < n), idx outside array: |
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171 # Dimension 2 & 3 folded into new dimension of size 2x2 = 4 |
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172 # Select 2nd row, 4th element of [2, 4, 6, 8], ans = 8 |
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173 @end example |
| 3294 | 174 |
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175 One advanced use of indexing is to create arrays filled with a single |
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176 value. This can be done by using an index of ones on a scalar value. |
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177 The result is an object with the dimensions of the index expression |
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178 and every element equal to the original scalar. For example, the |
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179 following statements |
| 3294 | 180 |
| 181 @example | |
| 182 @group | |
| 183 a = 13; | |
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184 a(ones (1, 4)) |
| 3294 | 185 @end group |
| 186 @end example | |
| 187 | |
| 188 @noindent | |
| 189 produce a vector whose four elements are all equal to 13. | |
| 190 | |
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191 Similarly, by indexing a scalar with two vectors of ones it is |
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192 possible to create a matrix. The following statements |
| 3294 | 193 |
| 194 @example | |
| 195 @group | |
| 196 a = 13; | |
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197 a(ones (1, 2), ones (1, 3)) |
| 3294 | 198 @end group |
| 199 @end example | |
| 200 | |
| 201 @noindent | |
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202 create a 2x3 matrix with all elements equal to 13. |
| 3294 | 203 |
| 9159 | 204 The last example could also be written as |
| 205 | |
| 206 @example | |
| 207 @group | |
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208 13(ones (2, 3)) |
| 9159 | 209 @end group |
| 210 @end example | |
| 211 | |
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212 It is more efficient to use indexing rather than the code construction |
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213 @code{scalar * ones (N, M, @dots{})} because it avoids the unnecessary |
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214 multiplication operation. Moreover, multiplication may not be |
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215 defined for the object to be replicated whereas indexing an array is |
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216 always defined. The following code shows how to create a 2x3 cell |
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217 array from a base unit which is not itself a scalar. |
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218 |
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219 @example |
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220 @group |
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221 @{"Hello"@}(ones (2, 3)) |
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222 @end group |
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223 @end example |
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224 |
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225 It should be, noted that @code{ones (1, n)} (a row vector of ones) |
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226 results in a range (with zero increment). A range is stored |
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227 internally as a starting value, increment, end value, and total number |
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228 of values; hence, it is more efficient for storage than a vector or |
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229 matrix of ones whenever the number of elements is greater than 4. In |
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230 particular, when @samp{r} is a row vector, the expressions |
| 9159 | 231 |
| 232 @example | |
| 233 r(ones (1, n), :) | |
| 234 @end example | |
| 235 | |
| 236 @example | |
| 237 r(ones (n, 1), :) | |
| 238 @end example | |
| 239 | |
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240 @noindent |
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241 will produce identical results, but the first one will be |
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242 significantly faster, at least for @samp{r} and @samp{n} large enough. |
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243 In the first case the index is held in compressed form as a range |
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244 which allows Octave to choose a more efficient algorithm to handle the |
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245 expression. |
| 9159 | 246 |
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247 A general recommendation, for a user unaware of these subtleties, is |
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248 to use the function @code{repmat} for replicating smaller arrays into |
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249 bigger ones. |
| 3294 | 250 |
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251 A second use of indexing is to speed up code. Indexing is a fast |
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252 operation and judicious use of it can reduce the requirement for |
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253 looping over individual array elements which is a slow operation. |
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254 |
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255 Consider the following example which creates a 10-element row vector |
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256 @math{a} containing the values |
| 6642 | 257 @tex |
| 258 $a_i = \sqrt{i}$. | |
| 259 @end tex | |
| 260 @ifnottex | |
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261 a(i) = sqrt (i). |
| 6642 | 262 @end ifnottex |
| 263 | |
| 264 @example | |
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265 @group |
| 6642 | 266 for i = 1:10 |
| 267 a(i) = sqrt (i); | |
| 268 endfor | |
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269 @end group |
| 6642 | 270 @end example |
| 271 | |
| 272 @noindent | |
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273 It is quite inefficient to create a vector using a loop like this. In |
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274 this case, it would have been much more efficient to use the |
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275 expression |
| 3294 | 276 |
| 277 @example | |
| 278 a = sqrt (1:10); | |
| 279 @end example | |
| 280 | |
| 281 @noindent | |
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282 which avoids the loop entirely. |
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283 |
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284 In cases where a loop cannot be avoided, or a number of values must be |
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285 combined to form a larger matrix, it is generally faster to set the |
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286 size of the matrix first (pre-allocate storage), and then insert |
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287 elements using indexing commands. For example, given a matrix |
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288 @code{a}, |
| 3294 | 289 |
| 290 @example | |
| 291 @group | |
| 292 [nr, nc] = size (a); | |
| 293 x = zeros (nr, n * nc); | |
| 294 for i = 1:n | |
| 3602 | 295 x(:,(i-1)*nc+1:i*nc) = a; |
| 3294 | 296 endfor |
| 297 @end group | |
| 298 @end example | |
| 299 | |
| 300 @noindent | |
| 301 is considerably faster than | |
| 302 | |
| 303 @example | |
| 304 @group | |
| 305 x = a; | |
| 306 for i = 1:n-1 | |
| 307 x = [x, a]; | |
| 308 endfor | |
| 309 @end group | |
| 310 @end example | |
| 311 | |
| 312 @noindent | |
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313 because Octave does not have to repeatedly resize the intermediate |
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314 result. |
| 3294 | 315 |
| 6549 | 316 @DOCSTRING(sub2ind) |
| 317 | |
| 318 @DOCSTRING(ind2sub) | |
| 319 | |
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320 @DOCSTRING(isindex) |
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321 |
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322 @DOCSTRING(allow_noninteger_range_as_index) |
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323 |
| 4167 | 324 @node Calling Functions |
| 3294 | 325 @section Calling Functions |
| 326 | |
| 327 A @dfn{function} is a name for a particular calculation. Because it has | |
| 328 a name, you can ask for it by name at any point in the program. For | |
| 329 example, the function @code{sqrt} computes the square root of a number. | |
| 330 | |
| 331 A fixed set of functions are @dfn{built-in}, which means they are | |
| 332 available in every Octave program. The @code{sqrt} function is one of | |
| 333 these. In addition, you can define your own functions. | |
| 334 @xref{Functions and Scripts}, for information about how to do this. | |
| 335 | |
| 336 @cindex arguments in function call | |
| 337 The way to use a function is with a @dfn{function call} expression, | |
| 338 which consists of the function name followed by a list of | |
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339 @dfn{arguments} in parentheses. The arguments are expressions which give |
| 3294 | 340 the raw materials for the calculation that the function will do. When |
| 341 there is more than one argument, they are separated by commas. If there | |
| 342 are no arguments, you can omit the parentheses, but it is a good idea to | |
| 343 include them anyway, to clearly indicate that a function call was | |
| 344 intended. Here are some examples: | |
| 345 | |
| 346 @example | |
| 347 @group | |
| 348 sqrt (x^2 + y^2) # @r{One argument} | |
| 349 ones (n, m) # @r{Two arguments} | |
| 350 rand () # @r{No arguments} | |
| 351 @end group | |
| 352 @end example | |
| 353 | |
| 354 Each function expects a particular number of arguments. For example, the | |
| 355 @code{sqrt} function must be called with a single argument, the number | |
| 356 to take the square root of: | |
| 357 | |
| 358 @example | |
| 359 sqrt (@var{argument}) | |
| 360 @end example | |
| 361 | |
| 362 Some of the built-in functions take a variable number of arguments, | |
| 363 depending on the particular usage, and their behavior is different | |
| 364 depending on the number of arguments supplied. | |
| 365 | |
| 366 Like every other expression, the function call has a value, which is | |
| 367 computed by the function based on the arguments you give it. In this | |
| 368 example, the value of @code{sqrt (@var{argument})} is the square root of | |
| 369 the argument. A function can also have side effects, such as assigning | |
| 370 the values of certain variables or doing input or output operations. | |
| 371 | |
| 372 Unlike most languages, functions in Octave may return multiple values. | |
| 373 For example, the following statement | |
| 374 | |
| 375 @example | |
| 376 [u, s, v] = svd (a) | |
| 377 @end example | |
| 378 | |
| 379 @noindent | |
| 380 computes the singular value decomposition of the matrix @code{a} and | |
| 381 assigns the three result matrices to @code{u}, @code{s}, and @code{v}. | |
| 382 | |
| 383 The left side of a multiple assignment expression is itself a list of | |
| 384 expressions, and is allowed to be a list of variable names or index | |
| 385 expressions. See also @ref{Index Expressions}, and @ref{Assignment Ops}. | |
| 386 | |
| 387 @menu | |
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388 * Call by Value:: |
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389 * Recursion:: |
| 3294 | 390 @end menu |
| 391 | |
| 4167 | 392 @node Call by Value |
| 3294 | 393 @subsection Call by Value |
| 394 | |
| 395 In Octave, unlike Fortran, function arguments are passed by value, which | |
| 396 means that each argument in a function call is evaluated and assigned to | |
| 397 a temporary location in memory before being passed to the function. | |
| 398 There is currently no way to specify that a function parameter should be | |
| 399 passed by reference instead of by value. This means that it is | |
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400 impossible to directly alter the value of a function parameter in the |
| 3294 | 401 calling function. It can only change the local copy within the function |
| 402 body. For example, the function | |
| 403 | |
| 404 @example | |
| 405 @group | |
| 406 function f (x, n) | |
| 407 while (n-- > 0) | |
| 408 disp (x); | |
| 409 endwhile | |
| 410 endfunction | |
| 411 @end group | |
| 412 @end example | |
| 413 | |
| 414 @noindent | |
| 415 displays the value of the first argument @var{n} times. In this | |
| 416 function, the variable @var{n} is used as a temporary variable without | |
| 417 having to worry that its value might also change in the calling | |
| 418 function. Call by value is also useful because it is always possible to | |
| 419 pass constants for any function parameter without first having to | |
| 420 determine that the function will not attempt to modify the parameter. | |
| 421 | |
| 422 The caller may use a variable as the expression for the argument, but | |
| 423 the called function does not know this: it only knows what value the | |
| 424 argument had. For example, given a function called as | |
| 425 | |
| 426 @example | |
| 427 @group | |
| 428 foo = "bar"; | |
| 429 fcn (foo) | |
| 430 @end group | |
| 431 @end example | |
| 432 | |
| 433 @noindent | |
| 434 you should not think of the argument as being ``the variable | |
| 435 @code{foo}.'' Instead, think of the argument as the string value, | |
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436 @qcode{"bar"}. |
| 3294 | 437 |
| 438 Even though Octave uses pass-by-value semantics for function arguments, | |
| 439 values are not copied unnecessarily. For example, | |
| 440 | |
| 441 @example | |
| 442 @group | |
| 443 x = rand (1000); | |
| 444 f (x); | |
| 445 @end group | |
| 446 @end example | |
| 447 | |
| 448 @noindent | |
| 449 does not actually force two 1000 by 1000 element matrices to exist | |
| 450 @emph{unless} the function @code{f} modifies the value of its | |
| 451 argument. Then Octave must create a copy to avoid changing the | |
| 452 value outside the scope of the function @code{f}, or attempting (and | |
| 453 probably failing!) to modify the value of a constant or the value of a | |
| 454 temporary result. | |
| 455 | |
| 4167 | 456 @node Recursion |
| 3294 | 457 @subsection Recursion |
| 458 @cindex factorial function | |
| 459 | |
| 6939 | 460 With some restrictions@footnote{Some of Octave's functions are |
| 3294 | 461 implemented in terms of functions that cannot be called recursively. |
| 462 For example, the ODE solver @code{lsode} is ultimately implemented in a | |
| 463 Fortran subroutine that cannot be called recursively, so @code{lsode} | |
| 464 should not be called either directly or indirectly from within the | |
| 465 user-supplied function that @code{lsode} requires. Doing so will result | |
| 6642 | 466 in an error.}, recursive function calls are allowed. A |
| 3294 | 467 @dfn{recursive function} is one which calls itself, either directly or |
| 468 indirectly. For example, here is an inefficient@footnote{It would be | |
| 469 much better to use @code{prod (1:n)}, or @code{gamma (n+1)} instead, | |
| 470 after first checking to ensure that the value @code{n} is actually a | |
| 471 positive integer.} way to compute the factorial of a given integer: | |
| 472 | |
| 473 @example | |
| 474 @group | |
| 475 function retval = fact (n) | |
| 476 if (n > 0) | |
| 477 retval = n * fact (n-1); | |
| 478 else | |
| 479 retval = 1; | |
| 480 endif | |
| 481 endfunction | |
| 482 @end group | |
| 483 @end example | |
| 484 | |
| 485 This function is recursive because it calls itself directly. It | |
| 486 eventually terminates because each time it calls itself, it uses an | |
| 487 argument that is one less than was used for the previous call. Once the | |
| 488 argument is no longer greater than zero, it does not call itself, and | |
| 489 the recursion ends. | |
| 490 | |
| 491 The built-in variable @code{max_recursion_depth} specifies a limit to | |
| 492 the recursion depth and prevents Octave from recursing infinitely. | |
| 493 | |
| 3371 | 494 @DOCSTRING(max_recursion_depth) |
| 3294 | 495 |
| 4167 | 496 @node Arithmetic Ops |
| 3294 | 497 @section Arithmetic Operators |
| 498 @cindex arithmetic operators | |
| 499 @cindex operators, arithmetic | |
| 500 @cindex addition | |
| 501 @cindex subtraction | |
| 502 @cindex multiplication | |
| 503 @cindex matrix multiplication | |
| 504 @cindex division | |
| 505 @cindex quotient | |
| 506 @cindex negation | |
| 507 @cindex unary minus | |
| 508 @cindex exponentiation | |
| 509 @cindex transpose | |
| 510 @cindex Hermitian operator | |
| 511 @cindex transpose, complex-conjugate | |
| 512 @cindex complex-conjugate transpose | |
| 513 | |
| 514 The following arithmetic operators are available, and work on scalars | |
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515 and matrices. The element-by-element operators and functions broadcast |
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516 (@pxref{Broadcasting}). |
| 3294 | 517 |
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518 @table @asis |
| 3294 | 519 @item @var{x} + @var{y} |
| 520 @opindex + | |
| 521 Addition. If both operands are matrices, the number of rows and columns | |
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522 must both agree, or they must be broadcastable to the same shape. |
| 3294 | 523 |
| 524 @item @var{x} .+ @var{y} | |
| 525 @opindex .+ | |
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526 Element-by-element addition. This operator is equivalent to @code{+}. |
| 3294 | 527 |
| 528 @item @var{x} - @var{y} | |
| 529 @opindex - | |
| 530 Subtraction. If both operands are matrices, the number of rows and | |
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531 columns of both must agree, or they must be broadcastable to the same |
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532 shape. |
| 3294 | 533 |
| 534 @item @var{x} .- @var{y} | |
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535 Element-by-element subtraction. This operator is equivalent to @code{-}. |
| 3294 | 536 |
| 537 @item @var{x} * @var{y} | |
| 538 @opindex * | |
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539 Matrix multiplication. The number of columns of @var{x} must agree with |
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540 the number of rows of @var{y}, or they must be broadcastable to the same |
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541 shape. |
| 3294 | 542 |
| 543 @item @var{x} .* @var{y} | |
| 544 @opindex .* | |
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545 Element-by-element multiplication. If both operands are matrices, the |
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546 number of rows and columns must both agree, or they must be |
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547 broadcastable to the same shape. |
| 3294 | 548 |
| 549 @item @var{x} / @var{y} | |
| 550 @opindex / | |
| 551 Right division. This is conceptually equivalent to the expression | |
| 552 | |
| 553 @example | |
| 554 (inverse (y') * x')' | |
| 555 @end example | |
| 556 | |
| 557 @noindent | |
| 558 but it is computed without forming the inverse of @var{y'}. | |
| 559 | |
| 560 If the system is not square, or if the coefficient matrix is singular, | |
| 561 a minimum norm solution is computed. | |
| 562 | |
| 563 @item @var{x} ./ @var{y} | |
| 564 @opindex ./ | |
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565 Element-by-element right division. |
| 3294 | 566 |
| 567 @item @var{x} \ @var{y} | |
| 568 @opindex \ | |
| 569 Left division. This is conceptually equivalent to the expression | |
| 570 | |
| 571 @example | |
| 572 inverse (x) * y | |
| 573 @end example | |
| 574 | |
| 575 @noindent | |
| 576 but it is computed without forming the inverse of @var{x}. | |
| 577 | |
| 578 If the system is not square, or if the coefficient matrix is singular, | |
| 579 a minimum norm solution is computed. | |
| 580 | |
| 581 @item @var{x} .\ @var{y} | |
| 582 @opindex .\ | |
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583 Element-by-element left division. Each element of @var{y} is divided |
| 3294 | 584 by each corresponding element of @var{x}. |
| 585 | |
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586 @item @var{x} ^ @var{y} |
| 3294 | 587 @itemx @var{x} ** @var{y} |
| 588 @opindex ** | |
| 589 @opindex ^ | |
| 590 Power operator. If @var{x} and @var{y} are both scalars, this operator | |
| 591 returns @var{x} raised to the power @var{y}. If @var{x} is a scalar and | |
| 592 @var{y} is a square matrix, the result is computed using an eigenvalue | |
| 7001 | 593 expansion. If @var{x} is a square matrix, the result is computed by |
| 3294 | 594 repeated multiplication if @var{y} is an integer, and by an eigenvalue |
| 595 expansion if @var{y} is not an integer. An error results if both | |
| 596 @var{x} and @var{y} are matrices. | |
| 597 | |
| 598 The implementation of this operator needs to be improved. | |
| 599 | |
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600 @item @var{x} .^ @var{y} |
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601 @itemx @var{x} .** @var{y} |
| 3294 | 602 @opindex .** |
| 603 @opindex .^ | |
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604 Element-by-element power operator. If both operands are matrices, the |
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605 number of rows and columns must both agree, or they must be |
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606 broadcastable to the same shape. If several complex results are |
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607 possible, the one with smallest non-negative argument (angle) is taken. |
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608 This rule may return a complex root even when a real root is also possible. |
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609 Use @code{realpow}, @code{realsqrt}, @code{cbrt}, or @code{nthroot} if a |
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610 real result is preferred. |
| 3294 | 611 |
| 612 @item -@var{x} | |
| 613 @opindex - | |
| 614 Negation. | |
| 615 | |
| 616 @item +@var{x} | |
| 617 @opindex + | |
| 618 Unary plus. This operator has no effect on the operand. | |
| 619 | |
| 620 @item @var{x}' | |
| 621 @opindex ' | |
| 622 Complex conjugate transpose. For real arguments, this operator is the | |
| 623 same as the transpose operator. For complex arguments, this operator is | |
| 624 equivalent to the expression | |
| 625 | |
| 626 @example | |
| 627 conj (x.') | |
| 628 @end example | |
| 629 | |
| 630 @item @var{x}.' | |
| 631 @opindex .' | |
| 632 Transpose. | |
| 633 @end table | |
| 634 | |
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635 Note that because Octave's element-by-element operators begin with a |
| 3294 | 636 @samp{.}, there is a possible ambiguity for statements like |
| 637 | |
| 638 @example | |
| 639 1./m | |
| 640 @end example | |
| 641 | |
| 642 @noindent | |
| 643 because the period could be interpreted either as part of the constant | |
| 644 or as part of the operator. To resolve this conflict, Octave treats the | |
| 645 expression as if you had typed | |
| 646 | |
| 647 @example | |
| 648 (1) ./ m | |
| 649 @end example | |
| 650 | |
| 651 @noindent | |
| 652 and not | |
| 653 | |
| 654 @example | |
| 655 (1.) / m | |
| 656 @end example | |
| 657 | |
| 658 @noindent | |
| 659 Although this is inconsistent with the normal behavior of Octave's | |
| 660 lexer, which usually prefers to break the input into tokens by | |
| 661 preferring the longest possible match at any given point, it is more | |
| 662 useful in this case. | |
| 663 | |
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664 @opindex ' |
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665 @DOCSTRING(ctranspose) |
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666 |
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667 @opindex .\ |
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668 @DOCSTRING(ldivide) |
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669 |
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670 @opindex - |
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671 @DOCSTRING(minus) |
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672 |
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673 @opindex \ |
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674 @DOCSTRING(mldivide) |
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675 |
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676 @opindex ** |
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677 @opindex ^ |
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678 @DOCSTRING(mpower) |
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679 |
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680 @opindex / |
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681 @DOCSTRING(mrdivide) |
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682 |
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683 @opindex * |
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684 @DOCSTRING(mtimes) |
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685 |
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686 @opindex + |
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687 @DOCSTRING(plus) |
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688 |
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689 @opindex .** |
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690 @opindex .^ |
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691 @DOCSTRING(power) |
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692 |
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693 @opindex ./ |
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694 @DOCSTRING(rdivide) |
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695 |
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696 @opindex .* |
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697 @DOCSTRING(times) |
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698 |
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699 @opindex .' |
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700 @DOCSTRING(transpose) |
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701 |
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702 @opindex - |
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703 @DOCSTRING(uminus) |
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704 |
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705 @opindex + |
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706 @DOCSTRING(uplus) |
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707 |
| 4167 | 708 @node Comparison Ops |
| 3294 | 709 @section Comparison Operators |
| 710 @cindex comparison expressions | |
| 711 @cindex expressions, comparison | |
| 712 @cindex relational operators | |
| 713 @cindex operators, relational | |
| 714 @cindex less than operator | |
| 715 @cindex greater than operator | |
| 716 @cindex equality operator | |
| 717 @cindex tests for equality | |
| 718 @cindex equality, tests for | |
| 719 | |
| 720 @dfn{Comparison operators} compare numeric values for relationships | |
| 721 such as equality. They are written using | |
| 722 @emph{relational operators}. | |
| 723 | |
| 724 All of Octave's comparison operators return a value of 1 if the | |
| 725 comparison is true, or 0 if it is false. For matrix values, they all | |
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726 work on an element-by-element basis. Broadcasting rules apply. |
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727 @xref{Broadcasting}. For example: |
| 3294 | 728 |
| 729 @example | |
| 730 @group | |
| 731 [1, 2; 3, 4] == [1, 3; 2, 4] | |
| 732 @result{} 1 0 | |
| 733 0 1 | |
| 734 @end group | |
| 735 @end example | |
| 736 | |
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737 According to broadcasting rules, if one operand is a scalar and the |
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738 other is a matrix, the scalar is compared to each element of the matrix |
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739 in turn, and the result is the same size as the matrix. |
| 3294 | 740 |
| 741 @table @code | |
| 742 @item @var{x} < @var{y} | |
| 743 @opindex < | |
| 744 True if @var{x} is less than @var{y}. | |
| 745 | |
| 746 @item @var{x} <= @var{y} | |
| 747 @opindex <= | |
| 748 True if @var{x} is less than or equal to @var{y}. | |
| 749 | |
| 750 @item @var{x} == @var{y} | |
| 751 @opindex == | |
| 752 True if @var{x} is equal to @var{y}. | |
| 753 | |
| 754 @item @var{x} >= @var{y} | |
| 755 @opindex >= | |
| 756 True if @var{x} is greater than or equal to @var{y}. | |
| 757 | |
| 758 @item @var{x} > @var{y} | |
| 759 @opindex > | |
| 760 True if @var{x} is greater than @var{y}. | |
| 761 | |
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762 @item @var{x} != @var{y} |
| 3294 | 763 @itemx @var{x} ~= @var{y} |
| 764 @opindex != | |
| 765 @opindex ~= | |
| 766 True if @var{x} is not equal to @var{y}. | |
| 767 @end table | |
| 768 | |
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769 For complex numbers, the following ordering is defined: |
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770 @var{z1} < @var{z2} |
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771 if and only if |
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772 |
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773 @example |
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774 @group |
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775 abs (@var{z1}) < abs (@var{z2}) |
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776 || (abs (@var{z1}) == abs (@var{z2}) && arg (@var{z1}) < arg (@var{z2})) |
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777 @end group |
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778 @end example |
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779 |
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780 This is consistent with the ordering used by @dfn{max}, @dfn{min} and |
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781 @dfn{sort}, but is not consistent with @sc{matlab}, which only compares the real |
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782 parts. |
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783 |
| 3294 | 784 String comparisons may also be performed with the @code{strcmp} |
| 785 function, not with the comparison operators listed above. | |
| 786 @xref{Strings}. | |
| 787 | |
|
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788 @opindex == |
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789 @DOCSTRING(eq) |
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790 |
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791 @opindex >= |
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792 @DOCSTRING(ge) |
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793 |
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794 @opindex > |
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795 @DOCSTRING(gt) |
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796 |
| 6550 | 797 @DOCSTRING(isequal) |
| 798 | |
|
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799 @DOCSTRING(isequaln) |
| 6550 | 800 |
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801 @opindex <= |
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802 @DOCSTRING(le) |
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803 |
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804 @opindex < |
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805 @DOCSTRING(lt) |
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806 |
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807 @opindex != |
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808 @opindex ~= |
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809 @DOCSTRING(ne) |
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810 |
| 4167 | 811 @node Boolean Expressions |
| 3294 | 812 @section Boolean Expressions |
| 813 @cindex expressions, boolean | |
| 814 @cindex boolean expressions | |
| 815 @cindex expressions, logical | |
| 816 @cindex logical expressions | |
| 817 @cindex operators, boolean | |
| 818 @cindex boolean operators | |
| 819 @cindex logical operators | |
| 820 @cindex operators, logical | |
| 821 @cindex and operator | |
| 822 @cindex or operator | |
| 823 @cindex not operator | |
| 824 | |
| 825 @menu | |
|
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826 * Element-by-element Boolean Operators:: |
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827 * Short-circuit Boolean Operators:: |
| 3294 | 828 @end menu |
| 829 | |
| 4167 | 830 @node Element-by-element Boolean Operators |
| 3294 | 831 @subsection Element-by-element Boolean Operators |
| 832 @cindex element-by-element evaluation | |
| 833 | |
| 834 An @dfn{element-by-element boolean expression} is a combination of | |
| 835 comparison expressions using the boolean | |
| 836 operators ``or'' (@samp{|}), ``and'' (@samp{&}), and ``not'' (@samp{!}), | |
| 837 along with parentheses to control nesting. The truth of the boolean | |
| 838 expression is computed by combining the truth values of the | |
| 839 corresponding elements of the component expressions. A value is | |
| 840 considered to be false if it is zero, and true otherwise. | |
| 841 | |
| 842 Element-by-element boolean expressions can be used wherever comparison | |
| 843 expressions can be used. They can be used in @code{if} and @code{while} | |
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844 statements. However, a matrix value used as the condition in an |
| 3294 | 845 @code{if} or @code{while} statement is only true if @emph{all} of its |
| 846 elements are nonzero. | |
| 847 | |
| 848 Like comparison operations, each element of an element-by-element | |
| 849 boolean expression also has a numeric value (1 if true, 0 if false) that | |
| 850 comes into play if the result of the boolean expression is stored in a | |
| 851 variable, or used in arithmetic. | |
| 852 | |
| 853 Here are descriptions of the three element-by-element boolean operators. | |
| 854 | |
| 855 @table @code | |
| 856 @item @var{boolean1} & @var{boolean2} | |
| 857 @opindex & | |
| 858 Elements of the result are true if both corresponding elements of | |
| 859 @var{boolean1} and @var{boolean2} are true. | |
| 860 | |
| 861 @item @var{boolean1} | @var{boolean2} | |
| 862 @opindex | | |
| 863 Elements of the result are true if either of the corresponding elements | |
| 864 of @var{boolean1} or @var{boolean2} is true. | |
| 865 | |
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866 @item ! @var{boolean} |
| 3294 | 867 @itemx ~ @var{boolean} |
| 868 @opindex ~ | |
| 869 @opindex ! | |
| 870 Each element of the result is true if the corresponding element of | |
| 871 @var{boolean} is false. | |
| 872 @end table | |
| 873 | |
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874 These operators work on an element-by-element basis. For example, the |
|
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875 expression |
| 3294 | 876 |
| 877 @example | |
| 878 [1, 0; 0, 1] & [1, 0; 2, 3] | |
| 879 @end example | |
| 880 | |
| 881 @noindent | |
| 882 returns a two by two identity matrix. | |
| 883 | |
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884 For the binary operators, broadcasting rules apply. @xref{Broadcasting}. |
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885 In particular, if one of the operands is a scalar and the other a |
| 3294 | 886 matrix, the operator is applied to the scalar and each element of the |
| 887 matrix. | |
| 888 | |
| 889 For the binary element-by-element boolean operators, both subexpressions | |
| 890 @var{boolean1} and @var{boolean2} are evaluated before computing the | |
| 891 result. This can make a difference when the expressions have side | |
| 892 effects. For example, in the expression | |
| 893 | |
| 894 @example | |
| 895 a & b++ | |
| 896 @end example | |
| 897 | |
| 898 @noindent | |
| 899 the value of the variable @var{b} is incremented even if the variable | |
| 900 @var{a} is zero. | |
| 901 | |
| 902 This behavior is necessary for the boolean operators to work as | |
| 903 described for matrix-valued operands. | |
| 904 | |
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905 @opindex & |
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906 @DOCSTRING(and) |
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907 |
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908 @opindex ~ |
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909 @opindex ! |
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910 @DOCSTRING(not) |
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911 |
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912 @opindex | |
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913 @DOCSTRING(or) |
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914 |
| 4167 | 915 @node Short-circuit Boolean Operators |
| 3294 | 916 @subsection Short-circuit Boolean Operators |
| 917 @cindex short-circuit evaluation | |
| 918 | |
| 919 Combined with the implicit conversion to scalar values in @code{if} and | |
| 920 @code{while} conditions, Octave's element-by-element boolean operators | |
| 921 are often sufficient for performing most logical operations. However, | |
| 922 it is sometimes desirable to stop evaluating a boolean expression as | |
| 923 soon as the overall truth value can be determined. Octave's | |
| 924 @dfn{short-circuit} boolean operators work this way. | |
| 925 | |
| 926 @table @code | |
| 927 @item @var{boolean1} && @var{boolean2} | |
| 928 @opindex && | |
| 929 The expression @var{boolean1} is evaluated and converted to a scalar | |
| 6632 | 930 using the equivalent of the operation @code{all (@var{boolean1}(:))}. |
| 3294 | 931 If it is false, the result of the overall expression is 0. If it is |
| 932 true, the expression @var{boolean2} is evaluated and converted to a | |
| 6632 | 933 scalar using the equivalent of the operation @code{all |
| 934 (@var{boolean1}(:))}. If it is true, the result of the overall expression | |
| 3294 | 935 is 1. Otherwise, the result of the overall expression is 0. |
| 936 | |
| 6632 | 937 @strong{Warning:} there is one exception to the rule of evaluating |
| 938 @code{all (@var{boolean1}(:))}, which is when @code{boolean1} is the | |
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939 empty matrix. The truth value of an empty matrix is always @code{false} |
| 6632 | 940 so @code{[] && true} evaluates to @code{false} even though |
| 941 @code{all ([])} is @code{true}. | |
| 942 | |
| 3294 | 943 @item @var{boolean1} || @var{boolean2} |
| 944 @opindex || | |
| 945 The expression @var{boolean1} is evaluated and converted to a scalar | |
| 6632 | 946 using the equivalent of the operation @code{all (@var{boolean1}(:))}. |
| 3294 | 947 If it is true, the result of the overall expression is 1. If it is |
| 948 false, the expression @var{boolean2} is evaluated and converted to a | |
| 6632 | 949 scalar using the equivalent of the operation @code{all |
| 950 (@var{boolean1}(:))}. If it is true, the result of the overall expression | |
| 3294 | 951 is 1. Otherwise, the result of the overall expression is 0. |
| 6632 | 952 |
| 953 @strong{Warning:} the truth value of an empty matrix is always @code{false}, | |
| 954 see the previous list item for details. | |
| 3294 | 955 @end table |
| 956 | |
| 957 The fact that both operands may not be evaluated before determining the | |
| 958 overall truth value of the expression can be important. For example, in | |
| 959 the expression | |
| 960 | |
| 961 @example | |
| 962 a && b++ | |
| 963 @end example | |
| 964 | |
| 965 @noindent | |
| 966 the value of the variable @var{b} is only incremented if the variable | |
| 967 @var{a} is nonzero. | |
| 968 | |
| 969 This can be used to write somewhat more concise code. For example, it | |
| 970 is possible write | |
| 971 | |
| 972 @example | |
| 973 @group | |
| 974 function f (a, b, c) | |
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975 if (nargin > 2 && ischar (c)) |
| 3294 | 976 @dots{} |
| 977 @end group | |
| 978 @end example | |
| 979 | |
| 980 @noindent | |
| 981 instead of having to use two @code{if} statements to avoid attempting to | |
| 982 evaluate an argument that doesn't exist. For example, without the | |
| 983 short-circuit feature, it would be necessary to write | |
| 984 | |
| 985 @example | |
| 986 @group | |
| 987 function f (a, b, c) | |
| 988 if (nargin > 2) | |
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989 if (ischar (c)) |
| 3294 | 990 @dots{} |
| 991 @end group | |
| 992 @end example | |
| 993 | |
| 6632 | 994 @noindent |
| 3294 | 995 Writing |
| 996 | |
| 997 @example | |
| 998 @group | |
| 999 function f (a, b, c) | |
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1000 if (nargin > 2 & ischar (c)) |
| 3294 | 1001 @dots{} |
| 1002 @end group | |
| 1003 @end example | |
| 1004 | |
| 1005 @noindent | |
| 1006 would result in an error if @code{f} were called with one or two | |
| 1007 arguments because Octave would be forced to try to evaluate both of the | |
| 1008 operands for the operator @samp{&}. | |
| 1009 | |
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1010 @sc{matlab} has special behavior that allows the operators @samp{&} and |
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1011 @samp{|} to short-circuit when used in the truth expression for @code{if} and |
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1012 @code{while} statements. The Octave parser may be instructed to behave in the |
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1013 same manner, but its use is strongly discouraged. |
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1014 |
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1015 @DOCSTRING(do_braindead_shortcircuit_evaluation) |
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1016 |
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1017 Finally, the ternary operator (?:) is not supported in Octave. If |
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1018 short-circuiting is not important, it can be replaced by the @code{ifelse} |
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1019 function. |
| 10308 | 1020 |
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1021 @DOCSTRING(merge) |
| 10308 | 1022 |
| 4167 | 1023 @node Assignment Ops |
| 3294 | 1024 @section Assignment Expressions |
| 1025 @cindex assignment expressions | |
| 1026 @cindex assignment operators | |
| 1027 @cindex operators, assignment | |
| 1028 @cindex expressions, assignment | |
| 1029 | |
| 1030 @opindex = | |
| 1031 | |
| 1032 An @dfn{assignment} is an expression that stores a new value into a | |
| 1033 variable. For example, the following expression assigns the value 1 to | |
| 1034 the variable @code{z}: | |
| 1035 | |
| 1036 @example | |
| 1037 z = 1 | |
| 1038 @end example | |
| 1039 | |
| 6632 | 1040 @noindent |
| 3294 | 1041 After this expression is executed, the variable @code{z} has the value 1. |
| 1042 Whatever old value @code{z} had before the assignment is forgotten. | |
| 1043 The @samp{=} sign is called an @dfn{assignment operator}. | |
| 1044 | |
| 1045 Assignments can store string values also. For example, the following | |
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1046 expression would store the value @qcode{"this food is good"} in the |
| 3294 | 1047 variable @code{message}: |
| 1048 | |
| 1049 @example | |
| 1050 @group | |
| 1051 thing = "food" | |
| 1052 predicate = "good" | |
| 1053 message = [ "this " , thing , " is " , predicate ] | |
| 1054 @end group | |
| 1055 @end example | |
| 1056 | |
| 1057 @noindent | |
| 1058 (This also illustrates concatenation of strings.) | |
| 1059 | |
| 1060 @cindex side effect | |
| 1061 Most operators (addition, concatenation, and so on) have no effect | |
| 1062 except to compute a value. If you ignore the value, you might as well | |
| 1063 not use the operator. An assignment operator is different. It does | |
| 1064 produce a value, but even if you ignore the value, the assignment still | |
| 1065 makes itself felt through the alteration of the variable. We call this | |
| 1066 a @dfn{side effect}. | |
| 1067 | |
| 1068 @cindex lvalue | |
| 1069 The left-hand operand of an assignment need not be a variable | |
| 1070 (@pxref{Variables}). It can also be an element of a matrix | |
| 1071 (@pxref{Index Expressions}) or a list of return values | |
| 1072 (@pxref{Calling Functions}). These are all called @dfn{lvalues}, which | |
| 1073 means they can appear on the left-hand side of an assignment operator. | |
| 1074 The right-hand operand may be any expression. It produces the new value | |
| 1075 which the assignment stores in the specified variable, matrix element, | |
| 1076 or list of return values. | |
| 1077 | |
| 1078 It is important to note that variables do @emph{not} have permanent types. | |
| 1079 The type of a variable is simply the type of whatever value it happens | |
| 1080 to hold at the moment. In the following program fragment, the variable | |
| 1081 @code{foo} has a numeric value at first, and a string value later on: | |
| 1082 | |
| 1083 @example | |
| 1084 @group | |
| 1085 octave:13> foo = 1 | |
| 1086 foo = 1 | |
| 1087 octave:13> foo = "bar" | |
| 1088 foo = bar | |
| 1089 @end group | |
| 1090 @end example | |
| 1091 | |
| 1092 @noindent | |
| 1093 When the second assignment gives @code{foo} a string value, the fact that | |
| 1094 it previously had a numeric value is forgotten. | |
| 1095 | |
| 1096 Assignment of a scalar to an indexed matrix sets all of the elements | |
| 1097 that are referenced by the indices to the scalar value. For example, if | |
| 1098 @code{a} is a matrix with at least two columns, | |
| 1099 | |
| 1100 @example | |
| 1101 @group | |
| 1102 a(:, 2) = 5 | |
| 1103 @end group | |
| 1104 @end example | |
| 1105 | |
| 1106 @noindent | |
| 1107 sets all the elements in the second column of @code{a} to 5. | |
| 1108 | |
| 1109 Assigning an empty matrix @samp{[]} works in most cases to allow you to | |
| 1110 delete rows or columns of matrices and vectors. @xref{Empty Matrices}. | |
| 1111 For example, given a 4 by 5 matrix @var{A}, the assignment | |
| 1112 | |
| 1113 @example | |
| 1114 A (3, :) = [] | |
| 1115 @end example | |
| 1116 | |
| 1117 @noindent | |
| 1118 deletes the third row of @var{A}, and the assignment | |
| 1119 | |
| 1120 @example | |
| 1121 A (:, 1:2:5) = [] | |
| 1122 @end example | |
| 1123 | |
| 1124 @noindent | |
| 6672 | 1125 deletes the first, third, and fifth columns. |
| 3294 | 1126 |
| 1127 An assignment is an expression, so it has a value. Thus, @code{z = 1} | |
| 1128 as an expression has the value 1. One consequence of this is that you | |
| 1129 can write multiple assignments together: | |
| 1130 | |
| 1131 @example | |
| 1132 x = y = z = 0 | |
| 1133 @end example | |
| 1134 | |
| 1135 @noindent | |
| 1136 stores the value 0 in all three variables. It does this because the | |
| 1137 value of @code{z = 0}, which is 0, is stored into @code{y}, and then | |
| 1138 the value of @code{y = z = 0}, which is 0, is stored into @code{x}. | |
| 1139 | |
| 1140 This is also true of assignments to lists of values, so the following is | |
| 1141 a valid expression | |
| 1142 | |
| 1143 @example | |
| 1144 [a, b, c] = [u, s, v] = svd (a) | |
| 1145 @end example | |
| 1146 | |
| 1147 @noindent | |
| 1148 that is exactly equivalent to | |
| 1149 | |
| 1150 @example | |
| 1151 @group | |
| 1152 [u, s, v] = svd (a) | |
| 1153 a = u | |
| 1154 b = s | |
| 1155 c = v | |
| 1156 @end group | |
| 1157 @end example | |
| 1158 | |
| 1159 In expressions like this, the number of values in each part of the | |
| 1160 expression need not match. For example, the expression | |
| 1161 | |
| 1162 @example | |
| 1163 [a, b] = [u, s, v] = svd (a) | |
| 1164 @end example | |
| 1165 | |
| 1166 @noindent | |
|
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1167 is equivalent to |
| 3294 | 1168 |
| 1169 @example | |
| 1170 @group | |
| 1171 [u, s, v] = svd (a) | |
| 1172 a = u | |
| 1173 b = s | |
| 1174 @end group | |
| 1175 @end example | |
| 1176 | |
| 6632 | 1177 @noindent |
| 1178 The number of values on the left side of the expression can, however, | |
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1179 not exceed the number of values on the right side. For example, the |
| 6632 | 1180 following will produce an error. |
| 1181 | |
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1182 @example |
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1183 @group |
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1184 [a, b, c, d] = [u, s, v] = svd (a); |
| 7031 | 1185 @print{} error: element number 4 undefined in return list |
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1186 @end group |
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1187 @end example |
| 6632 | 1188 |
|
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1189 The symbol @code{~} may be used as a placeholder in the list of lvalues, |
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1190 indicating that the corresponding return value should be ignored and not stored |
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1191 anywhere: |
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1192 |
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1193 @example |
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1194 @group |
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1195 [~, s, v] = svd (a); |
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1196 @end group |
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1197 @end example |
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1198 |
| 10228 | 1199 This is cleaner and more memory efficient than using a dummy variable. |
| 1200 The @code{nargout} value for the right-hand side expression is not affected. | |
|
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1201 If the assignment is used as an expression, the return value is a |
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1202 comma-separated list with the ignored values dropped. |
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1203 |
| 6642 | 1204 @opindex += |
| 1205 A very common programming pattern is to increment an existing variable | |
| 1206 with a given value, like this | |
| 1207 | |
| 1208 @example | |
| 1209 a = a + 2; | |
| 1210 @end example | |
| 1211 | |
| 1212 @noindent | |
| 1213 This can be written in a clearer and more condensed form using the | |
| 1214 @code{+=} operator | |
| 1215 | |
| 1216 @example | |
| 1217 a += 2; | |
| 1218 @end example | |
| 1219 | |
| 1220 @noindent | |
| 1221 @opindex -= | |
| 1222 @opindex *= | |
| 1223 @opindex /= | |
| 1224 Similar operators also exist for subtraction (@code{-=}), | |
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1225 multiplication (@code{*=}), and division (@code{/=}). An expression |
| 6642 | 1226 of the form |
| 1227 | |
| 1228 @example | |
| 1229 @var{expr1} @var{op}= @var{expr2} | |
| 1230 @end example | |
| 1231 | |
| 1232 @noindent | |
| 1233 is evaluated as | |
| 1234 | |
| 1235 @example | |
| 1236 @var{expr1} = (@var{expr1}) @var{op} (@var{expr2}) | |
| 1237 @end example | |
| 1238 | |
| 1239 @noindent | |
|
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1240 where @var{op} can be either @code{+}, @code{-}, @code{*}, or @code{/}, |
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1241 as long as @var{expr2} is a simple expression with no side effects. If |
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1242 @var{expr2} also contains an assignment operator, then this expression |
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1243 is evaluated as |
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1244 |
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1245 @example |
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1246 @var{temp} = @var{expr2} |
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1247 @var{expr1} = (@var{expr1}) @var{op} @var{temp} |
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1248 @end example |
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1249 |
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1250 @noindent |
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1251 where @var{temp} is a placeholder temporary value storing the computed |
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1252 result of evaluating @var{expr2}. So, the expression |
| 6642 | 1253 |
| 1254 @example | |
| 1255 a *= b+1 | |
| 1256 @end example | |
| 1257 | |
| 1258 @noindent | |
| 1259 is evaluated as | |
| 1260 | |
| 1261 @example | |
| 1262 a = a * (b+1) | |
| 1263 @end example | |
| 1264 | |
| 1265 @noindent | |
| 1266 and @emph{not} | |
| 1267 | |
| 1268 @example | |
| 1269 a = a * b + 1 | |
| 1270 @end example | |
| 1271 | |
| 3294 | 1272 You can use an assignment anywhere an expression is called for. For |
| 1273 example, it is valid to write @code{x != (y = 1)} to set @code{y} to 1 | |
| 1274 and then test whether @code{x} equals 1. But this style tends to make | |
| 1275 programs hard to read. Except in a one-shot program, you should rewrite | |
| 1276 it to get rid of such nesting of assignments. This is never very hard. | |
| 1277 | |
| 1278 @cindex increment operator | |
| 1279 @cindex decrement operator | |
| 1280 @cindex operators, increment | |
| 1281 @cindex operators, decrement | |
| 1282 | |
| 4167 | 1283 @node Increment Ops |
| 3294 | 1284 @section Increment Operators |
| 1285 | |
| 1286 @emph{Increment operators} increase or decrease the value of a variable | |
| 1287 by 1. The operator to increment a variable is written as @samp{++}. It | |
| 1288 may be used to increment a variable either before or after taking its | |
| 1289 value. | |
| 1290 | |
| 1291 For example, to pre-increment the variable @var{x}, you would write | |
| 1292 @code{++@var{x}}. This would add one to @var{x} and then return the new | |
| 1293 value of @var{x} as the result of the expression. It is exactly the | |
| 1294 same as the expression @code{@var{x} = @var{x} + 1}. | |
| 1295 | |
| 1296 To post-increment a variable @var{x}, you would write @code{@var{x}++}. | |
| 1297 This adds one to the variable @var{x}, but returns the value that | |
| 1298 @var{x} had prior to incrementing it. For example, if @var{x} is equal | |
| 1299 to 2, the result of the expression @code{@var{x}++} is 2, and the new | |
| 1300 value of @var{x} is 3. | |
| 1301 | |
| 1302 For matrix and vector arguments, the increment and decrement operators | |
| 1303 work on each element of the operand. | |
| 1304 | |
| 1305 Here is a list of all the increment and decrement expressions. | |
| 1306 | |
| 1307 @table @code | |
| 1308 @item ++@var{x} | |
| 1309 @opindex ++ | |
| 1310 This expression increments the variable @var{x}. The value of the | |
| 1311 expression is the @emph{new} value of @var{x}. It is equivalent to the | |
| 1312 expression @code{@var{x} = @var{x} + 1}. | |
| 1313 | |
| 1314 @item --@var{x} | |
| 1315 @opindex @code{--} | |
| 1316 This expression decrements the variable @var{x}. The value of the | |
| 1317 expression is the @emph{new} value of @var{x}. It is equivalent to the | |
| 1318 expression @code{@var{x} = @var{x} - 1}. | |
| 1319 | |
| 1320 @item @var{x}++ | |
| 1321 @opindex ++ | |
| 1322 This expression causes the variable @var{x} to be incremented. The | |
| 1323 value of the expression is the @emph{old} value of @var{x}. | |
| 1324 | |
| 1325 @item @var{x}-- | |
| 1326 @opindex @code{--} | |
| 1327 This expression causes the variable @var{x} to be decremented. The | |
| 1328 value of the expression is the @emph{old} value of @var{x}. | |
| 1329 @end table | |
| 1330 | |
| 4167 | 1331 @node Operator Precedence |
| 3294 | 1332 @section Operator Precedence |
| 1333 @cindex operator precedence | |
| 1334 | |
| 1335 @dfn{Operator precedence} determines how operators are grouped, when | |
| 1336 different operators appear close by in one expression. For example, | |
| 1337 @samp{*} has higher precedence than @samp{+}. Thus, the expression | |
| 1338 @code{a + b * c} means to multiply @code{b} and @code{c}, and then add | |
| 1339 @code{a} to the product (i.e., @code{a + (b * c)}). | |
| 1340 | |
| 1341 You can overrule the precedence of the operators by using parentheses. | |
| 1342 You can think of the precedence rules as saying where the parentheses | |
| 1343 are assumed if you do not write parentheses yourself. In fact, it is | |
| 1344 wise to use parentheses whenever you have an unusual combination of | |
| 1345 operators, because other people who read the program may not remember | |
| 1346 what the precedence is in this case. You might forget as well, and then | |
| 1347 you too could make a mistake. Explicit parentheses will help prevent | |
| 1348 any such mistake. | |
| 1349 | |
| 1350 When operators of equal precedence are used together, the leftmost | |
|
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1351 operator groups first, except for the assignment operators, which group |
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1352 in the opposite order. Thus, the expression @code{a - b + c} groups as |
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1353 @code{(a - b) + c}, but the expression @code{a = b = c} groups as |
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1354 @code{a = (b = c)}. |
| 3294 | 1355 |
| 1356 The precedence of prefix unary operators is important when another | |
| 1357 operator follows the operand. For example, @code{-x^2} means | |
| 1358 @code{-(x^2)}, because @samp{-} has lower precedence than @samp{^}. | |
| 1359 | |
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1360 Here is a table of the operators in Octave, in order of decreasing |
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1361 precedence. Unless noted, all operators group left to right. |
| 3294 | 1362 |
| 1363 @table @code | |
|
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1364 @item function call and array indexing, cell array indexing, and structure element indexing |
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1365 @samp{()} @samp{@{@}} @samp{.} |
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1366 |
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1367 @item postfix increment, and postfix decrement |
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1368 @samp{++} @samp{--} |
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1369 |
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1370 These operators group right to left. |
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1371 |
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1372 @item transpose and exponentiation |
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1373 @samp{'} @samp{.'} @samp{^} @samp{**} @samp{.^} @samp{.**} |
| 3294 | 1374 |
|
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1375 @item unary plus, unary minus, prefix increment, prefix decrement, and logical "not" |
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1376 @samp{+} @samp{-} @samp{++} @samp{--} @samp{~} @samp{!} |
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1377 |
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1378 @item multiply and divide |
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1379 @samp{*} @samp{/} @samp{\} @samp{.\} @samp{.*} @samp{./} |
| 3294 | 1380 |
|
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1381 @item add, subtract |
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1382 @samp{+} @samp{-} |
| 3294 | 1383 |
|
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1384 @item colon |
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1385 @samp{:} |
| 3294 | 1386 |
| 1387 @item relational | |
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1388 @samp{<} @samp{<=} @samp{==} @samp{>=} @samp{>} @samp{!=} |
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1389 @samp{~=} |
| 3294 | 1390 |
|
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1391 @item element-wise "and" |
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1392 @samp{&} |
| 3294 | 1393 |
|
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1394 @item element-wise "or" |
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1395 @samp{|} |
| 3294 | 1396 |
|
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1397 @item logical "and" |
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002948ae5bc0
fix precedence level of transpose operators (bug #32533)
John W. Eaton <jwe@octave.org>
parents:
12601
diff
changeset
|
1398 @samp{&&} |
| 3294 | 1399 |
|
12627
002948ae5bc0
fix precedence level of transpose operators (bug #32533)
John W. Eaton <jwe@octave.org>
parents:
12601
diff
changeset
|
1400 @item logical "or" |
|
002948ae5bc0
fix precedence level of transpose operators (bug #32533)
John W. Eaton <jwe@octave.org>
parents:
12601
diff
changeset
|
1401 @samp{||} |
| 3294 | 1402 |
|
12627
002948ae5bc0
fix precedence level of transpose operators (bug #32533)
John W. Eaton <jwe@octave.org>
parents:
12601
diff
changeset
|
1403 @item assignment |
|
002948ae5bc0
fix precedence level of transpose operators (bug #32533)
John W. Eaton <jwe@octave.org>
parents:
12601
diff
changeset
|
1404 @samp{=} @samp{+=} @samp{-=} @samp{*=} @samp{/=} @samp{\=} |
|
002948ae5bc0
fix precedence level of transpose operators (bug #32533)
John W. Eaton <jwe@octave.org>
parents:
12601
diff
changeset
|
1405 @samp{^=} @samp{.*=} @samp{./=} @samp{.\=} @samp{.^=} @samp{|=} |
|
002948ae5bc0
fix precedence level of transpose operators (bug #32533)
John W. Eaton <jwe@octave.org>
parents:
12601
diff
changeset
|
1406 @samp{&=} |
| 3294 | 1407 |
|
12627
002948ae5bc0
fix precedence level of transpose operators (bug #32533)
John W. Eaton <jwe@octave.org>
parents:
12601
diff
changeset
|
1408 These operators group right to left. |
| 3294 | 1409 @end table |