Mercurial > octave-nkf
view scripts/testfun/speed.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 | 817da22e58ed |
children | 4197fc428c7d |
line wrap: on
line source
## Copyright (C) 2000-2013 Paul Kienzle ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {} speed (@var{f}, @var{init}, @var{max_n}, @var{f2}, @var{tol}) ## @deftypefnx {Function File} {[@var{order}, @var{n}, @var{T_f}, @var{T_f2}] =} speed (@dots{}) ## ## Determine the execution time of an expression (@var{f}) for various input ## values (@var{n}). The @var{n} are log-spaced from 1 to @var{max_n}. For ## each @var{n}, an initialization expression (@var{init}) is computed to ## create any data needed for the test. If a second expression (@var{f2}) is ## given then the execution times of the two expressions are compared. When ## called without output arguments the results are printed to stdout and ## displayed graphically. ## ## @table @code ## @item @var{f} ## The code expression to evaluate. ## ## @item @var{max_n} ## The maximum test length to run. The default value is 100. Alternatively, ## use @code{[min_n, max_n]} or specify the @var{n} exactly with ## @code{[n1, n2, @dots{}, nk]}. ## ## @item @var{init} ## Initialization expression for function argument values. Use @var{k} ## for the test number and @var{n} for the size of the test. This should ## compute values for all variables used by @var{f}. Note that @var{init} will ## be evaluated first for @math{k = 0}, so things which are constant throughout ## the test series can be computed once. The default value is ## @code{@var{x} = randn (@var{n}, 1)}. ## ## @item @var{f2} ## An alternative expression to evaluate, so that the speed of two ## expressions can be directly compared. The default is @code{[]}. ## ## @item @var{tol} ## Tolerance used to compare the results of expression @var{f} and expression ## @var{f2}. If @var{tol} is positive, the tolerance is an absolute one. ## If @var{tol} is negative, the tolerance is a relative one. The default is ## @code{eps}. If @var{tol} is @code{Inf}, then no comparison will be made. ## ## @item @var{order} ## The time complexity of the expression @math{O(a*n^p)}. This ## is a structure with fields @code{a} and @code{p}. ## ## @item @var{n} ## The values @var{n} for which the expression was calculated @strong{AND} ## the execution time was greater than zero. ## ## @item @var{T_f} ## The nonzero execution times recorded for the expression @var{f} in seconds. ## ## @item @var{T_f2} ## The nonzero execution times recorded for the expression @var{f2} in seconds. ## If required, the mean time ratio is simply @code{mean (T_f ./ T_f2)}. ## ## @end table ## ## The slope of the execution time graph shows the approximate ## power of the asymptotic running time @math{O(n^p)}. This ## power is plotted for the region over which it is approximated ## (the latter half of the graph). The estimated power is not ## very accurate, but should be sufficient to determine the ## general order of an algorithm. It should indicate if, for ## example, the implementation is unexpectedly @math{O(n^2)} ## rather than @math{O(n)} because it extends a vector each ## time through the loop rather than pre-allocating storage. ## In the current version of Octave, the following is not the ## expected @math{O(n)}. ## ## @example ## speed ("for i = 1:n, y@{i@} = x(i); endfor", "", [1000, 10000]) ## @end example ## ## @noindent ## But it is if you preallocate the cell array @code{y}: ## ## @example ## @group ## speed ("for i = 1:n, y@{i@} = x(i); endfor", ... ## "x = rand (n, 1); y = cell (size (x));", [1000, 10000]) ## @end group ## @end example ## ## An attempt is made to approximate the cost of individual ## operations, but it is wildly inaccurate. You can improve the ## stability somewhat by doing more work for each @code{n}. For ## example: ## ## @example ## speed ("airy(x)", "x = rand (n, 10)", [10000, 100000]) ## @end example ## ## When comparing two different expressions (@var{f}, @var{f2}), the slope ## of the line on the speedup ratio graph should be larger than 1 if the new ## expression is faster. Better algorithms have a shallow slope. Generally, ## vectorizing an algorithm will not change the slope of the execution ## time graph, but will shift it relative to the original. For ## example: ## ## @example ## @group ## speed ("sum (x)", "", [10000, 100000], ... ## "v = 0; for i = 1:length (x), v += x(i); endfor") ## @end group ## @end example ## ## The following is a more complex example. If there was an original version ## of @code{xcorr} using for loops and a second version using an FFT, then ## one could compare the run speed for various lags as follows, or for a fixed ## lag with varying vector lengths as follows: ## ## @example ## @group ## speed ("xcorr (x, n)", "x = rand (128, 1);", 100, ## "xcorr_orig (x, n)", -100*eps) ## speed ("xcorr (x, 15)", "x = rand (20+n, 1);", 100, ## "xcorr_orig (x, n)", -100*eps) ## @end group ## @end example ## ## Assuming one of the two versions is in xcorr_orig, this ## would compare their speed and their output values. Note that the ## FFT version is not exact, so one must specify an acceptable tolerance on ## the comparison @code{100*eps}. In this case, the comparison should be ## computed relatively, as @code{abs ((@var{x} - @var{y}) ./ @var{y})} rather ## than absolutely as @code{abs (@var{x} - @var{y})}. ## ## Type @kbd{example ("speed")} to see some real examples or ## @kbd{demo ("speed")} to run them. ## @end deftypefn ## FIXME: consider two dimensional speedup surfaces for functions like kron. function [__order, __test_n, __tnew, __torig] = speed (__f1, __init, __max_n = 100, __f2 = "", __tol = eps) if (nargin < 1 || nargin > 6) print_usage (); endif if (nargin < 2 || isempty (__init)) __init = "x = randn (n, 1)"; endif if (isempty (__max_n)) __max_n = 100; endif __numtests = 15; ## Let user specify range of n. if (isscalar (__max_n)) __min_n = 1; assert (__max_n > __min_n); __test_n = logspace (0, log10 (__max_n), __numtests); elseif (length (__max_n) == 2) [__min_n, __max_n] = deal (__max_n(1), __max_n(2)); assert (__min_n >= 1); assert (__max_n > __min_n); __test_n = logspace (log10 (__min_n), log10 (__max_n), __numtests); else assert (all (__max_n > 0)); __test_n = __max_n; endif ## Force n to be an integer. __test_n = unique (round (__test_n)); assert (__test_n >= 1); __torig = __tnew = zeros (size (__test_n)); ## Print and plot the data if no output is requested. do_display = (nargout == 0); if (do_display) disp (["testing " __f1 "\ninit: " __init]); endif ## Add semicolon closure to all code fragments in case user has not done so. __init(end+1) = ";"; __f1(end+1) = ";"; if (! isempty (__f2)) __f2(end+1) = ";"; endif ## Make sure the functions are freshly loaded by evaluating them at ## test_n(1); first have to initialize the args though. n = 1; k = 0; eval (__init); eval (__f1); if (! isempty (__f2)) eval (__f2); endif ## Run the tests. for k = 1:length (__test_n) n = __test_n(k); eval (__init); if (do_display) printf ("n%i = %i ", k, n); fflush (stdout); endif eval (["__t = time();" __f1 "__v1=ans; __t = time()-__t;"]); if (__t < 0.25) eval (["__t2 = time();" __f1 "__t2 = time()-__t2;"]); eval (["__t3 = time();" __f1 "__t3 = time()-__t3;"]); __t = min ([__t, __t2, __t3]); endif __tnew(k) = __t; if (! isempty (__f2)) eval (["__t = time();" __f2 "__v2=ans; __t = time()-__t;"]); if (__t < 0.25) eval (["__t2 = time();" __f2 "__t2 = time()-__t2;"]); eval (["__t3 = time();" __f2 "__t3 = time()-__t3;"]); __t = min ([__t, __t2, __t3]); endif __torig(k) = __t; if (! isinf(__tol)) assert (__v1, __v2, __tol); endif endif endfor ## Drop times of zero. if (isempty (__f2)) zidx = (__tnew < 100*eps); __test_n(zidx) = []; __tnew(zidx) = []; else zidx = (__tnew < 100*eps | __torig < 100*eps); __test_n(zidx) = []; __tnew(zidx) = []; __torig(zidx) = []; endif if (isempty (__test_n)) error (["speed: All running times were zero.\n", "error: speed: Choose larger MAX_N or do more work per function evaluation"]); endif ## Approximate time complexity and return it if requested. tailidx = ceil (length (__test_n)/2):length (__test_n); p = polyfit (log (__test_n(tailidx)), log (__tnew(tailidx)), 1); if (nargout > 0) __order.p = p(1); __order.a = exp (p(2)); endif if (do_display) figure; ## Strip semicolon added to code fragments before displaying __init(end) = ""; __f1(end) = ""; if (! isempty (__f2)) __f2(end) = ""; endif endif if (do_display && isempty (__f2)) loglog (__test_n, __tnew*1000, "*-g;execution time;"); xlabel ("test length"); ylabel ("best execution time (ms)"); title ({__f1, ["init: " __init]}); elseif (do_display) subplot (1, 2, 1); semilogx (__test_n, __torig./__tnew, ["-*r;" strrep(__f1, ";", ".") " / " strrep(__f2, ";", ".") ";"], __test_n, __tnew./__torig, ["-*g;", strrep(__f2, ";", ".") " / " strrep(__f1, ";", ".") ";"]); title ("Speedup Ratio"); xlabel ("test length"); ylabel ("speedup ratio"); subplot (1, 2, 2); loglog (__test_n, __tnew*1000, ["*-g;" strrep(__f1,";",".") ";"], __test_n, __torig*1000, ["*-r;" strrep(__f2,";",".") ";"]); title ({"Execution Times", ["init: " __init]}); xlabel ("test length"); ylabel ("best execution time (ms)"); ratio = mean (__torig ./ __tnew); printf ("\n\nMean runtime ratio = %.3g for '%s' vs '%s'\n", ratio, __f2, __f1); endif if (do_display) ## Plot time complexity approximation (using milliseconds). figure; # Open second plot window order = round (10*p(1))/10; if (order >= 0.1) order = sprintf ("O(n^%g)", order); else order = "O(1)"; endif v = polyval (p, log (__test_n(tailidx))); loglog (__test_n(tailidx), exp (v) * 1000, sprintf ("b;%s;", order)); title ({"Time Complexity", __f1}); xlabel ("test length"); ## Get base time to 1 digit of accuracy. dt = exp (p(2)); dt = floor (dt/10^floor (log10 (dt)))*10^floor (log10 (dt)); if (log10 (dt) >= -0.5) time = sprintf ("%g s", dt); elseif (log10 (dt) >= -3.5) time = sprintf ("%g ms", dt*1e3); elseif (log10 (dt) >= -6.5) time = sprintf ("%g us", dt*1e6); else time = sprintf ("%g ns", dt*1e9); endif ## Display nicely formatted complexity. printf ("\nFor %s:\n", __f1); printf (" asymptotic power: %s\n", order); printf (" approximate time per operation: %s\n", time); endif endfunction %% FIXME: Demos with declared functions do not work. See bug #31815. %% A workaround has been hacked by not declaring the functions %% but using eval to create them in the proper context. %% Unfortunately, we can't remove them from the user's workspace %% because of another bug (#34497). %!demo %! fstr_build_orig = cstrcat ( %! "function x = build_orig (n)\n", %! " ## extend the target vector on the fly\n", %! " for i=0:n-1, x([1:100]+i*100) = 1:100; endfor\n", %! "endfunction"); %! fstr_build = cstrcat ( %! "function x = build (n)\n", %! " ## preallocate the target vector\n", %! " x = zeros (1, n*100);\n", %! " for i=0:n-1, x([1:100]+i*100) = 1:100; endfor\n", %! "endfunction"); %! %! disp ("-----------------------"); %! disp (fstr_build_orig); %! disp ("-----------------------"); %! disp (fstr_build); %! disp ("-----------------------"); %! %! ## Eval functions strings to create them in the current context %! eval (fstr_build_orig); %! eval (fstr_build); %! %! disp ("Preallocated vector test.\nThis takes a little while..."); %! speed ("build (n)", "", 1000, "build_orig (n)"); %! clear -f build build_orig %! disp ("-----------------------"); %! disp ("Note how much faster it is to pre-allocate a vector."); %! disp ("Notice the peak speedup ratio."); %!demo %! fstr_build_orig = cstrcat ( %! "function x = build_orig (n)\n", %! " for i=0:n-1, x([1:100]+i*100) = 1:100; endfor\n", %! "endfunction"); %! fstr_build = cstrcat ( %! "function x = build (n)\n", %! " idx = [1:100]';\n", %! " x = idx(:,ones(1,n));\n", %! " x = reshape (x, 1, n*100);\n", %! "endfunction"); %! %! disp ("-----------------------"); %! disp (fstr_build_orig); %! disp ("-----------------------"); %! disp (fstr_build); %! disp ("-----------------------"); %! %! ## Eval functions strings to create them in the current context %! eval (fstr_build_orig); %! eval (fstr_build); %! %! disp ("Vectorized test.\nThis takes a little while..."); %! speed ("build (n)", "", 1000, "build_orig (n)"); %! clear -f build build_orig %! disp ("-----------------------"); %! disp ("This time, the for loop is done away with entirely."); %! disp ("Notice how much bigger the speedup is than in example 1."); ## FIXME: Tests are known to fail on operating systems with low resolution ## timers such as MinGW. Therefore, tests are made xtests so that false ## failures are not reported. However, it might be better to either ## force the tests to do more work, or use %!testif to check the OS. %!xtest %! [order, n, T_f1, T_f2] = speed ("airy (x)", "x = rand (n, 10)", [100, 1000]); %! assert (isstruct (order)); %! assert (size (order), [1, 1]); %! assert (fieldnames (order), {"p"; "a"}); %! assert (isnumeric (n)); %! assert (length (n) > 10); %! assert (isnumeric (T_f1)); %! assert (size (T_f1), size (n)); %! assert (isnumeric (T_f2)); %! assert (length (T_f2) > 10); %!xtest %! [order, n, T_f1, T_f2] = speed ("sum (x)", "", [100, 1000], "v = 0; for i = 1:length (x), v += x(i); endfor"); %! assert (isstruct (order)); %! assert (size (order), [1, 1]); %! assert (fieldnames (order), {"p"; "a"}); %! assert (isnumeric (n)); %! assert (length (n) > 10); %! assert (isnumeric (T_f1)); %! assert (size (T_f1), size (n)); %! assert (isnumeric (T_f2)); %! assert (length (T_f2) > 10); %% Test input validation %!error speed () %!error speed (1, 2, 3, 4, 5, 6, 7)