Mercurial > octave
view scripts/general/interp1.m @ 19593:446c46af4b42 stable
strip trailing whitespace from most source files
* Makefile.am, NEWS, build-aux/common.mk, configure.ac,
doc/Makefile.am, doc/doxyhtml/Makefile.am,
doc/interpreter/Makefile.am, doc/interpreter/arith.txi,
doc/interpreter/audio.txi, doc/interpreter/basics.txi,
doc/interpreter/bugs.txi, doc/interpreter/container.txi,
doc/interpreter/cp-idx.txi, doc/interpreter/data.txi,
doc/interpreter/debug.txi, doc/interpreter/diagperm.txi,
doc/interpreter/diffeq.txi, doc/interpreter/doccheck/README,
doc/interpreter/doccheck/spellcheck, doc/interpreter/emacs.txi,
doc/interpreter/errors.txi, doc/interpreter/eval.txi,
doc/interpreter/expr.txi, doc/interpreter/external.txi,
doc/interpreter/fn-idx.txi, doc/interpreter/func.txi,
doc/interpreter/geometry.txi, doc/interpreter/geometryimages.m,
doc/interpreter/gpl.txi, doc/interpreter/grammar.txi,
doc/interpreter/gui.txi, doc/interpreter/image.txi,
doc/interpreter/install.txi, doc/interpreter/interp.txi,
doc/interpreter/interpimages.m, doc/interpreter/intro.txi,
doc/interpreter/io.txi, doc/interpreter/java.txi,
doc/interpreter/linalg.txi, doc/interpreter/macros.texi,
doc/interpreter/matrix.txi, doc/interpreter/munge-texi.pl,
doc/interpreter/nonlin.txi, doc/interpreter/numbers.txi,
doc/interpreter/obsolete.txi, doc/interpreter/octave-config.1,
doc/interpreter/octave.texi, doc/interpreter/oop.txi,
doc/interpreter/op-idx.txi, doc/interpreter/optim.txi,
doc/interpreter/package.txi, doc/interpreter/plot.txi,
doc/interpreter/poly.txi, doc/interpreter/preface.txi,
doc/interpreter/quad.txi, doc/interpreter/set.txi,
doc/interpreter/signal.txi, doc/interpreter/sparse.txi,
doc/interpreter/sparseimages.m, doc/interpreter/splineimages.m,
doc/interpreter/stats.txi, doc/interpreter/stmt.txi,
doc/interpreter/strings.txi, doc/interpreter/system.txi,
doc/interpreter/testfun.txi, doc/interpreter/tips.txi,
doc/interpreter/var.txi, doc/interpreter/vectorize.txi,
doc/liboctave/Makefile.am, doc/liboctave/array.texi,
doc/liboctave/bugs.texi, doc/liboctave/cp-idx.texi,
doc/liboctave/dae.texi, doc/liboctave/diffeq.texi,
doc/liboctave/error.texi, doc/liboctave/factor.texi,
doc/liboctave/fn-idx.texi, doc/liboctave/gpl.texi,
doc/liboctave/install.texi, doc/liboctave/intro.texi,
doc/liboctave/liboctave.texi, doc/liboctave/matvec.texi,
doc/liboctave/nleqn.texi, doc/liboctave/nlfunc.texi,
doc/liboctave/ode.texi, doc/liboctave/optim.texi,
doc/liboctave/preface.texi, doc/liboctave/quad.texi,
doc/liboctave/range.texi, doc/refcard/Makefile.am,
doc/refcard/refcard.tex, etc/HACKING, etc/NEWS.1, etc/NEWS.2,
etc/NEWS.3, etc/OLD-ChangeLogs/ChangeLog,
etc/OLD-ChangeLogs/doc-ChangeLog,
etc/OLD-ChangeLogs/scripts-ChangeLog,
etc/OLD-ChangeLogs/src-ChangeLog, etc/OLD-ChangeLogs/test-ChangeLog,
etc/PROJECTS, etc/README.Cygwin, etc/README.MacOS, etc/README.MinGW,
etc/README.gnuplot, etc/gdbinit, etc/icons/Makefile.am,
examples/@polynomial/end.m, examples/@polynomial/subsasgn.m,
examples/Makefile.am, examples/standalonebuiltin.cc,
libgui/Makefile.am, libgui/qterminal/libqterminal/README,
libgui/qterminal/libqterminal/unix/BlockArray.cpp,
libgui/qterminal/libqterminal/unix/BlockArray.h,
libgui/qterminal/libqterminal/unix/Character.h,
libgui/qterminal/libqterminal/unix/CharacterColor.h,
libgui/qterminal/libqterminal/unix/Emulation.cpp,
libgui/qterminal/libqterminal/unix/Emulation.h,
libgui/qterminal/libqterminal/unix/Filter.cpp,
libgui/qterminal/libqterminal/unix/Filter.h,
libgui/qterminal/libqterminal/unix/History.cpp,
libgui/qterminal/libqterminal/unix/History.h,
libgui/qterminal/libqterminal/unix/KeyboardTranslator.cpp,
libgui/qterminal/libqterminal/unix/KeyboardTranslator.h,
libgui/qterminal/libqterminal/unix/LineFont.h,
libgui/qterminal/libqterminal/unix/QUnixTerminalImpl.cpp,
libgui/qterminal/libqterminal/unix/QUnixTerminalImpl.h,
libgui/qterminal/libqterminal/unix/Screen.cpp,
libgui/qterminal/libqterminal/unix/Screen.h,
libgui/qterminal/libqterminal/unix/ScreenWindow.cpp,
libgui/qterminal/libqterminal/unix/ScreenWindow.h,
libgui/qterminal/libqterminal/unix/TerminalCharacterDecoder.cpp,
libgui/qterminal/libqterminal/unix/TerminalCharacterDecoder.h,
libgui/qterminal/libqterminal/unix/Vt102Emulation.h,
libgui/qterminal/libqterminal/win32/QWinTerminalImpl.cpp,
libgui/qterminal/qterminal/main.cpp,
libgui/src/m-editor/file-editor-tab.cc, libgui/src/octave-gui.cc,
libgui/src/octave-qt-link.cc, libinterp/corefcn/data.cc,
libinterp/corefcn/defun-int.h, libinterp/corefcn/det.cc,
libinterp/corefcn/gl2ps-renderer.cc, libinterp/corefcn/graphics.cc,
libinterp/corefcn/graphics.in.h, libinterp/corefcn/ls-mat5.cc,
libinterp/corefcn/lu.cc, libinterp/corefcn/oct-tex-parser.yy,
libinterp/corefcn/oct-tex-symbols.in, libinterp/corefcn/quadcc.cc,
libinterp/corefcn/zfstream.cc, libinterp/dldfcn/__eigs__.cc,
libinterp/dldfcn/__voronoi__.cc, libinterp/gendoc.pl,
libinterp/genprops.awk, libinterp/mk-errno-list, libinterp/mk-pkg-add,
libinterp/mkbuiltins, libinterp/mkdefs, libinterp/mkdocs,
libinterp/mkops, libinterp/octave-value/ov-java.cc,
libinterp/parse-tree/lex.ll, libinterp/parse-tree/oct-parse.in.yy,
libinterp/parse-tree/octave.gperf, liboctave/Makefile.am,
liboctave/array/Array.cc, liboctave/array/module.mk,
liboctave/cruft/daspk/datv.f, liboctave/cruft/daspk/dcnst0.f,
liboctave/cruft/daspk/dcnstr.f, liboctave/cruft/daspk/ddasic.f,
liboctave/cruft/daspk/ddasid.f, liboctave/cruft/daspk/ddasik.f,
liboctave/cruft/daspk/ddaspk.f, liboctave/cruft/daspk/ddstp.f,
liboctave/cruft/daspk/ddwnrm.f, liboctave/cruft/daspk/dfnrmd.f,
liboctave/cruft/daspk/dfnrmk.f, liboctave/cruft/daspk/dhels.f,
liboctave/cruft/daspk/dheqr.f, liboctave/cruft/daspk/dinvwt.f,
liboctave/cruft/daspk/dlinsd.f, liboctave/cruft/daspk/dlinsk.f,
liboctave/cruft/daspk/dmatd.f, liboctave/cruft/daspk/dnedd.f,
liboctave/cruft/daspk/dnedk.f, liboctave/cruft/daspk/dnsd.f,
liboctave/cruft/daspk/dnsid.f, liboctave/cruft/daspk/dnsik.f,
liboctave/cruft/daspk/dnsk.f, liboctave/cruft/daspk/dorth.f,
liboctave/cruft/daspk/dslvd.f, liboctave/cruft/daspk/dslvk.f,
liboctave/cruft/daspk/dspigm.f, liboctave/cruft/daspk/dyypnw.f,
liboctave/cruft/dasrt/ddasrt.f, liboctave/cruft/dasrt/drchek.f,
liboctave/cruft/dassl/ddaslv.f, liboctave/cruft/dassl/ddassl.f,
liboctave/cruft/misc/blaswrap.c, liboctave/cruft/misc/module.mk,
liboctave/cruft/odepack/cfode.f, liboctave/cruft/odepack/dlsode.f,
liboctave/cruft/odepack/ewset.f, liboctave/cruft/odepack/intdy.f,
liboctave/cruft/odepack/prepj.f, liboctave/cruft/odepack/sintdy.f,
liboctave/cruft/odepack/slsode.f, liboctave/cruft/odepack/solsy.f,
liboctave/cruft/odepack/ssolsy.f, liboctave/cruft/odepack/stode.f,
liboctave/cruft/odepack/vnorm.f, liboctave/cruft/ranlib/Basegen.doc,
liboctave/cruft/ranlib/README, liboctave/cruft/ranlib/genbet.f,
liboctave/cruft/ranlib/genexp.f, liboctave/cruft/ranlib/gennch.f,
liboctave/cruft/ranlib/gennf.f, liboctave/cruft/ranlib/gennor.f,
liboctave/cruft/ranlib/getsd.f, liboctave/cruft/ranlib/initgn.f,
liboctave/cruft/ranlib/phrtsd.f, liboctave/cruft/ranlib/randlib.fdoc,
liboctave/cruft/ranlib/setsd.f, liboctave/cruft/ranlib/tstgmn.for,
liboctave/cruft/ranlib/tstmid.for, liboctave/cruft/slatec-fn/atanh.f,
liboctave/cruft/slatec-fn/datanh.f,
liboctave/cruft/slatec-fn/xgmainc.f,
liboctave/cruft/slatec-fn/xsgmainc.f, liboctave/numeric/module.mk,
liboctave/operators/mk-ops.awk, liboctave/operators/mx-ops,
liboctave/operators/sparse-mk-ops.awk,
liboctave/operators/sparse-mx-ops, liboctave/operators/vx-ops,
liboctave/util/module.mk, run-octave.in, scripts/@ftp/ftp.m,
scripts/audio/wavread.m, scripts/deprecated/java_convert_matrix.m,
scripts/deprecated/java_debug.m, scripts/deprecated/java_invoke.m,
scripts/deprecated/java_new.m,
scripts/deprecated/java_unsigned_conversion.m,
scripts/deprecated/javafields.m, scripts/deprecated/javamethods.m,
scripts/deprecated/shell_cmd.m, scripts/general/accumarray.m,
scripts/general/display.m, scripts/general/fieldnames.m,
scripts/general/interp1.m, scripts/general/interp2.m,
scripts/general/interp3.m, scripts/general/isa.m,
scripts/general/methods.m, scripts/general/sortrows.m,
scripts/geometry/convhull.m, scripts/geometry/delaunay.m,
scripts/geometry/delaunay3.m, scripts/geometry/delaunayn.m,
scripts/geometry/griddata.m, scripts/geometry/griddatan.m,
scripts/geometry/voronoi.m, scripts/geometry/voronoin.m,
scripts/gui/guihandles.m, scripts/gui/inputdlg.m,
scripts/gui/listdlg.m, scripts/gui/msgbox.m, scripts/gui/questdlg.m,
scripts/gui/uigetfile.m, scripts/gui/waitbar.m, scripts/gui/warndlg.m,
scripts/help/doc.m, scripts/help/help.m, scripts/help/type.m,
scripts/image/bone.m, scripts/image/cmpermute.m,
scripts/image/cmunique.m, scripts/image/colorcube.m,
scripts/image/colormap.m, scripts/image/contrast.m,
scripts/image/gray2ind.m, scripts/image/image.m,
scripts/image/imshow.m, scripts/image/ind2gray.m, scripts/image/jet.m,
scripts/image/rgb2ntsc.m, scripts/image/spinmap.m,
scripts/io/importdata.m, scripts/io/strread.m, scripts/io/textread.m,
scripts/io/textscan.m, scripts/java/java_get.m,
scripts/java/java_set.m, scripts/java/javaaddpath.m,
scripts/java/javaclasspath.m, scripts/java/javamem.m,
scripts/linear-algebra/linsolve.m, scripts/linear-algebra/qzhess.m,
scripts/miscellaneous/debug.m, scripts/miscellaneous/desktop.m,
scripts/miscellaneous/dir.m, scripts/miscellaneous/dos.m,
scripts/miscellaneous/edit.m, scripts/miscellaneous/fact.m,
scripts/miscellaneous/getappdata.m, scripts/miscellaneous/inputname.m,
scripts/miscellaneous/license.m, scripts/miscellaneous/ls_command.m,
scripts/miscellaneous/run.m, scripts/miscellaneous/setfield.m,
scripts/miscellaneous/unix.m, scripts/miscellaneous/ver.m,
scripts/mk-pkg-add, scripts/mkdoc.pl,
scripts/optimization/fminsearch.m, scripts/optimization/optimset.m,
scripts/optimization/sqp.m, scripts/pkg/pkg.m,
scripts/pkg/private/create_pkgadddel.m,
scripts/pkg/private/fix_depends.m, scripts/pkg/private/install.m,
scripts/plot/appearance/axis.m, scripts/plot/appearance/box.m,
scripts/plot/appearance/clabel.m, scripts/plot/appearance/daspect.m,
scripts/plot/appearance/datetick.m, scripts/plot/appearance/grid.m,
scripts/plot/appearance/legend.m, scripts/plot/appearance/orient.m,
scripts/plot/appearance/shading.m, scripts/plot/appearance/text.m,
scripts/plot/appearance/title.m, scripts/plot/appearance/xlabel.m,
scripts/plot/appearance/ylabel.m, scripts/plot/appearance/zlabel.m,
scripts/plot/draw/area.m, scripts/plot/draw/bar.m,
scripts/plot/draw/barh.m, scripts/plot/draw/colorbar.m,
scripts/plot/draw/contour.m, scripts/plot/draw/contour3.m,
scripts/plot/draw/contourf.m, scripts/plot/draw/ellipsoid.m,
scripts/plot/draw/errorbar.m, scripts/plot/draw/ezcontour.m,
scripts/plot/draw/ezcontourf.m, scripts/plot/draw/ezmesh.m,
scripts/plot/draw/ezpolar.m, scripts/plot/draw/fill.m,
scripts/plot/draw/fplot.m, scripts/plot/draw/hist.m,
scripts/plot/draw/meshc.m, scripts/plot/draw/meshz.m,
scripts/plot/draw/pareto.m, scripts/plot/draw/patch.m,
scripts/plot/draw/peaks.m, scripts/plot/draw/pie.m,
scripts/plot/draw/pie3.m, scripts/plot/draw/plot.m,
scripts/plot/draw/plotyy.m, scripts/plot/draw/private/__bar__.m,
scripts/plot/draw/private/__contour__.m,
scripts/plot/draw/private/__errplot__.m,
scripts/plot/draw/private/__ezplot__.m,
scripts/plot/draw/private/__patch__.m,
scripts/plot/draw/private/__stem__.m, scripts/plot/draw/rectangle.m,
scripts/plot/draw/ribbon.m, scripts/plot/draw/rose.m,
scripts/plot/draw/scatter.m, scripts/plot/draw/scatter3.m,
scripts/plot/draw/semilogx.m, scripts/plot/draw/shrinkfaces.m,
scripts/plot/draw/sombrero.m, scripts/plot/draw/sphere.m,
scripts/plot/draw/stairs.m, scripts/plot/draw/stem.m,
scripts/plot/draw/stemleaf.m, scripts/plot/draw/surf.m,
scripts/plot/draw/surface.m, scripts/plot/draw/surfc.m,
scripts/plot/draw/surfl.m, scripts/plot/draw/surfnorm.m,
scripts/plot/draw/tetramesh.m, scripts/plot/draw/trimesh.m,
scripts/plot/draw/triplot.m, scripts/plot/draw/trisurf.m,
scripts/plot/util/__gnuplot_drawnow__.m,
scripts/plot/util/__plt_get_axis_arg__.m, scripts/plot/util/axes.m,
scripts/plot/util/clf.m, scripts/plot/util/copyobj.m,
scripts/plot/util/figure.m, scripts/plot/util/gcbo.m,
scripts/plot/util/graphics_toolkit.m, scripts/plot/util/hggroup.m,
scripts/plot/util/meshgrid.m, scripts/plot/util/newplot.m,
scripts/plot/util/print.m,
scripts/plot/util/private/__add_default_menu__.m,
scripts/plot/util/private/__fltk_print__.m,
scripts/plot/util/private/__gnuplot_print__.m,
scripts/plot/util/private/__print_parse_opts__.m,
scripts/plot/util/refreshdata.m, scripts/plot/util/subplot.m,
scripts/polynomial/conv.m, scripts/polynomial/poly.m,
scripts/polynomial/polyeig.m, scripts/polynomial/polyfit.m,
scripts/polynomial/polyval.m,
scripts/polynomial/private/__splinefit__.m,
scripts/polynomial/spline.m, scripts/prefs/prefdir.m,
scripts/prefs/preferences.m, scripts/prefs/private/prefsfile.m,
scripts/prefs/rmpref.m, scripts/signal/freqz.m,
scripts/signal/module.mk, scripts/sparse/eigs.m, scripts/sparse/pcg.m,
scripts/sparse/private/__sprand_impl__.m, scripts/sparse/sprand.m,
scripts/sparse/sprandn.m, scripts/sparse/spy.m, scripts/sparse/svds.m,
scripts/specfun/expint.m, scripts/specfun/factor.m,
scripts/special-matrix/gallery.m, scripts/special-matrix/hankel.m,
scripts/special-matrix/toeplitz.m, scripts/startup/inputrc,
scripts/statistics/base/kurtosis.m, scripts/statistics/base/moment.m,
scripts/statistics/base/qqplot.m, scripts/statistics/base/var.m,
scripts/statistics/distributions/betarnd.m,
scripts/statistics/distributions/binoinv.m,
scripts/statistics/distributions/binopdf.m,
scripts/statistics/distributions/binornd.m,
scripts/statistics/distributions/cauchy_rnd.m,
scripts/statistics/distributions/chi2rnd.m,
scripts/statistics/distributions/discrete_pdf.m,
scripts/statistics/distributions/discrete_rnd.m,
scripts/statistics/distributions/empirical_rnd.m,
scripts/statistics/distributions/exprnd.m,
scripts/statistics/distributions/frnd.m,
scripts/statistics/distributions/gamrnd.m,
scripts/statistics/distributions/geornd.m,
scripts/statistics/distributions/hygernd.m,
scripts/statistics/distributions/kolmogorov_smirnov_cdf.m,
scripts/statistics/distributions/laplace_cdf.m,
scripts/statistics/distributions/laplace_pdf.m,
scripts/statistics/distributions/logistic_cdf.m,
scripts/statistics/distributions/logistic_pdf.m,
scripts/statistics/distributions/lognrnd.m,
scripts/statistics/distributions/nbincdf.m,
scripts/statistics/distributions/nbininv.m,
scripts/statistics/distributions/nbinpdf.m,
scripts/statistics/distributions/nbinrnd.m,
scripts/statistics/distributions/normrnd.m,
scripts/statistics/distributions/poissinv.m,
scripts/statistics/distributions/poissrnd.m,
scripts/statistics/distributions/tinv.m,
scripts/statistics/distributions/trnd.m,
scripts/statistics/distributions/unidcdf.m,
scripts/statistics/distributions/unidpdf.m,
scripts/statistics/distributions/unidrnd.m,
scripts/statistics/distributions/unifrnd.m,
scripts/statistics/distributions/wblrnd.m,
scripts/statistics/models/module.mk,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/strings/base2dec.m, scripts/strings/deblank.m,
scripts/strings/dec2base.m, scripts/strings/dec2bin.m,
scripts/strings/dec2hex.m, scripts/strings/mat2str.m,
scripts/strings/ostrsplit.m, scripts/strings/regexptranslate.m,
scripts/strings/str2num.m, scripts/strings/strcat.m,
scripts/strings/strjoin.m, scripts/strings/strsplit.m,
scripts/strings/strtok.m, scripts/strings/strtrim.m,
scripts/strings/strtrunc.m, scripts/strings/substr.m,
scripts/testfun/__run_test_suite__.m, scripts/testfun/speed.m,
scripts/testfun/test.m, scripts/time/asctime.m,
scripts/time/datenum.m, scripts/time/datevec.m,
scripts/time/weekday.m, src/Makefile.am, test/Makefile.am,
test/build-bc-overload-tests.sh, test/build-sparse-tests.sh,
test/jit.tst, test/line-continue.tst: Strip trailing whitespace.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Tue, 20 Jan 2015 08:26:57 -0500 |
parents | ef649fe230f5 |
children | 0e1f5a750d00 |
line wrap: on
line source
## Copyright (C) 2000-2013 Paul Kienzle ## Copyright (C) 2009 VZLU Prague ## ## 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} {@var{yi} =} interp1 (@var{x}, @var{y}, @var{xi}) ## @deftypefnx {Function File} {@var{yi} =} interp1 (@var{y}, @var{xi}) ## @deftypefnx {Function File} {@var{yi} =} interp1 (@dots{}, @var{method}) ## @deftypefnx {Function File} {@var{yi} =} interp1 (@dots{}, @var{extrap}) ## @deftypefnx {Function File} {@var{yi} =} interp1 (@dots{}, "left") ## @deftypefnx {Function File} {@var{yi} =} interp1 (@dots{}, "right") ## @deftypefnx {Function File} {@var{pp} =} interp1 (@dots{}, "pp") ## ## One-dimensional interpolation. ## ## Interpolate input data to determine the value of @var{yi} at the points ## @var{xi}. If not specified, @var{x} is taken to be the indices of @var{y}. ## If @var{y} is a matrix or an N-dimensional array, the interpolation is ## performed on each column of @var{y}. ## ## Method is one of: ## ## @table @asis ## @item @qcode{"nearest"} ## Return the nearest neighbor ## ## @item @qcode{"linear"} ## Linear interpolation from nearest neighbors ## ## @item @qcode{"pchip"} ## Piecewise cubic Hermite interpolating polynomial ## ## @item @qcode{"cubic"} ## Cubic interpolation (same as @code{pchip}) ## ## @item @qcode{"spline"} ## Cubic spline interpolation---smooth first and second derivatives ## throughout the curve ## @end table ## ## Adding '*' to the start of any method above forces @code{interp1} ## to assume that @var{x} is uniformly spaced, and only @code{@var{x}(1)} ## and @code{@var{x}(2)} are referenced. This is usually faster, ## and is never slower. The default method is @qcode{"linear"}. ## ## If @var{extrap} is the string @qcode{"extrap"}, then extrapolate values ## beyond the endpoints using the current @var{method}. If @var{extrap} is a ## number, then replace values beyond the endpoints with that number. When ## unspecified, @var{extrap} defaults to NA. ## ## If the string argument @qcode{"pp"} is specified, then @var{xi} should not ## be supplied and @code{interp1} returns a piecewise polynomial object. This ## object can later be used with @code{ppval} to evaluate the interpolation. ## There is an equivalence, such that @code{ppval (interp1 (@var{x}, ## @var{y}, @var{method}, @qcode{"pp"}), @var{xi}) == interp1 (@var{x}, @var{y}, ## @var{xi}, @var{method}, @qcode{"extrap"})}. ## ## Duplicate points in @var{x} specify a discontinuous interpolant. There ## may be at most 2 consecutive points with the same value. ## If @var{x} is increasing, the default discontinuous interpolant is ## right-continuous. If @var{x} is decreasing, the default discontinuous ## interpolant is left-continuous. ## The continuity condition of the interpolant may be specified by using ## the options, @qcode{"left"} or @qcode{"right"}, to select a left-continuous ## or right-continuous interpolant, respectively. ## Discontinuous interpolation is only allowed for @qcode{"nearest"} and ## @qcode{"linear"} methods; in all other cases, the @var{x}-values must be ## unique. ## ## An example of the use of @code{interp1} is ## ## @example ## @group ## xf = [0:0.05:10]; ## yf = sin (2*pi*xf/5); ## xp = [0:10]; ## yp = sin (2*pi*xp/5); ## lin = interp1 (xp, yp, xf); ## spl = interp1 (xp, yp, xf, "spline"); ## cub = interp1 (xp, yp, xf, "cubic"); ## near = interp1 (xp, yp, xf, "nearest"); ## plot (xf, yf, "r", xf, lin, "g", xf, spl, "b", ## xf, cub, "c", xf, near, "m", xp, yp, "r*"); ## legend ("original", "linear", "spline", "cubic", "nearest"); ## @end group ## @end example ## ## @seealso{interpft, interp2, interp3, interpn} ## @end deftypefn ## Author: Paul Kienzle ## Date: 2000-03-25 ## added 'nearest' as suggested by Kai Habel ## 2000-07-17 Paul Kienzle ## added '*' methods and matrix y ## check for proper table lengths ## 2002-01-23 Paul Kienzle ## fixed extrapolation function yi = interp1 (x, y, varargin) if (nargin < 2 || nargin > 6) print_usage (); endif method = "linear"; extrap = NA; xi = []; ispp = false; firstnumeric = true; rightcontinuous = NaN; if (nargin > 2) for i = 1:length (varargin) arg = varargin{i}; if (ischar (arg)) arg = tolower (arg); if (strcmp ("extrap", arg)) extrap = "extrap"; elseif (strcmp ("pp", arg)) ispp = true; elseif (strcmp (arg, "right") || strcmp (arg, "-right")) rightcontinuous = true; elseif (strcmp (arg, "left") || strcmp (arg, "-left")) rightcontinuous = false; else method = arg; endif else if (firstnumeric) xi = arg; firstnumeric = false; else extrap = arg; endif endif endfor endif if (isempty (xi) && firstnumeric && ! ispp) xi = y; y = x; if (isvector (y)) x = 1:numel (y); else x = 1:rows (y); endif endif ## reshape matrices for convenience x = x(:); nx = rows (x); szx = size (xi); if (isvector (y)) y = y(:); endif szy = size (y); y = y(:,:); [ny, nc] = size (y); xi = xi(:); ## determine sizes if (nx < 2 || ny < 2) error ("interp1: table too short"); endif ## check whether x is sorted; sort if not. if (! issorted (x, "either")) [x, p] = sort (x); y = y(p,:); endif if (isnan (rightcontinuous)) ## If not specified, set the continuity condition if (x(end) < x(1)) rightcontinuous = false; else rightcontinuous = true; endif endif if ((rightcontinuous && (x(end) < x(1))) || (! rightcontinuous && (x(end) > x(1)))) ## Switch between left-continuous and right-continuous x = flipud (x); y = flipud (y); endif starmethod = method(1) == "*"; if (starmethod) dx = x(2) - x(1); else jumps = x(1:end-1) == x(2:end); have_jumps = any (jumps); if (have_jumps) if (strcmp (method, "linear") || strcmp (method, ("nearest"))) if (any (jumps(1:nx-2) & jumps(2:nx-1))) warning ("interp1: multiple discontinuities at the same X value"); endif else error ("interp1: discontinuities not supported for method '%s'", method); endif endif endif ## Proceed with interpolating by all methods. switch (method) case "nearest" pp = mkpp ([x(1); (x(1:nx-1)+x(2:nx))/2; x(nx)], shiftdim (y, 1), szy(2:end)); pp.orient = "first"; if (ispp) yi = pp; else yi = ppval (pp, reshape (xi, szx)); endif case "*nearest" pp = mkpp ([x(1), x(1)+[0.5:(nx-1)]*dx, x(nx)], shiftdim (y, 1), szy(2:end)); pp.orient = "first"; if (ispp) yi = pp; else yi = ppval (pp, reshape (xi, szx)); endif case "linear" xx = x; nxx = nx; yy = y; dy = diff (yy); if (have_jumps) ## Omit zero-size intervals. xx(jumps) = []; nxx = rows (xx); yy(jumps, :) = []; dy(jumps, :) = []; endif dx = diff (xx); dx = repmat (dx, [1 size(dy)(2:end)]); coefs = [(dy./dx).', yy(1:nxx-1, :).']; pp = mkpp (xx, coefs, szy(2:end)); pp.orient = "first"; if (ispp) yi = pp; else yi = ppval (pp, reshape (xi, szx)); endif case "*linear" dy = diff (y); coefs = [(dy/dx).'(:), y(1:nx-1, :).'(:)]; pp = mkpp (x, coefs, szy(2:end)); pp.orient = "first"; if (ispp) yi = pp; else yi = ppval (pp, reshape (xi, szx)); endif case {"pchip", "*pchip", "cubic", "*cubic"} if (nx == 2 || starmethod) x = linspace (x(1), x(nx), ny); endif if (ispp) y = shiftdim (reshape (y, szy), 1); yi = pchip (x, y); yi.orient = "first"; else y = shiftdim (y, 1); yi = pchip (x, y, reshape (xi, szx)); if (! isvector (y)) yi = shiftdim (yi, 1); endif endif case {"spline", "*spline"} if (nx == 2 || starmethod) x = linspace (x(1), x(nx), ny); endif if (ispp) y = shiftdim (reshape (y, szy), 1); yi = spline (x, y); yi.orient = "first"; else y = shiftdim (y, 1); yi = spline (x, y, reshape (xi, szx)); if (! isvector (y)) yi = shiftdim (yi, 1); endif endif otherwise error ("interp1: invalid method '%s'", method); endswitch if (! ispp && ! ischar (extrap)) ## determine which values are out of range and set them to extrap, ## unless extrap == "extrap". minx = min (x(1), x(nx)); maxx = max (x(1), x(nx)); xi = reshape (xi, szx); outliers = xi < minx | ! (xi <= maxx); # this even catches NaNs if (size_equal (outliers, yi)) yi(outliers) = extrap; yi = reshape (yi, szx); elseif (! isvector (yi)) yi(outliers, :) = extrap; else yi(outliers.') = extrap; endif endif endfunction %!demo %! clf; %! xf = 0:0.05:10; yf = sin (2*pi*xf/5); %! xp = 0:10; yp = sin (2*pi*xp/5); %! lin = interp1 (xp,yp,xf, "linear"); %! spl = interp1 (xp,yp,xf, "spline"); %! cub = interp1 (xp,yp,xf, "pchip"); %! near= interp1 (xp,yp,xf, "nearest"); %! plot (xf,yf,"r",xf,near,"g",xf,lin,"b",xf,cub,"c",xf,spl,"m",xp,yp,"r*"); %! legend ("original", "nearest", "linear", "pchip", "spline"); %! %-------------------------------------------------------- %! % confirm that interpolated function matches the original %!demo %! clf; %! xf = 0:0.05:10; yf = sin (2*pi*xf/5); %! xp = 0:10; yp = sin (2*pi*xp/5); %! lin = interp1 (xp,yp,xf, "*linear"); %! spl = interp1 (xp,yp,xf, "*spline"); %! cub = interp1 (xp,yp,xf, "*cubic"); %! near= interp1 (xp,yp,xf, "*nearest"); %! plot (xf,yf,"r",xf,near,"g",xf,lin,"b",xf,cub,"c",xf,spl,"m",xp,yp,"r*"); %! legend ("*original", "*nearest", "*linear", "*cubic", "*spline"); %! %-------------------------------------------------------- %! % confirm that interpolated function matches the original %!demo %! clf; %! t = 0 : 0.3 : pi; dt = t(2)-t(1); %! n = length (t); k = 100; dti = dt*n/k; %! ti = t(1) + [0 : k-1]*dti; %! y = sin (4*t + 0.3) .* cos (3*t - 0.1); %! ddyc = diff (diff (interp1 (t,y,ti, "cubic")) ./dti)./dti; %! ddys = diff (diff (interp1 (t,y,ti, "spline"))./dti)./dti; %! ddyp = diff (diff (interp1 (t,y,ti, "pchip")) ./dti)./dti; %! plot (ti(2:end-1),ddyc,'g+', ti(2:end-1),ddys,'b*', ti(2:end-1),ddyp,'c^'); %! legend ("cubic", "spline", "pchip"); %! title ("Second derivative of interpolated 'sin (4*t + 0.3) .* cos (3*t - 0.1)'"); %!demo %! clf; %! xf = 0:0.05:10; yf = sin (2*pi*xf/5) - (xf >= 5); %! xp = [0:.5:4.5,4.99,5:.5:10]; yp = sin (2*pi*xp/5) - (xp >= 5); %! lin = interp1 (xp,yp,xf, "linear"); %! near= interp1 (xp,yp,xf, "nearest"); %! plot (xf,yf,"r", xf,near,"g", xf,lin,"b", xp,yp,"r*"); %! legend ("original", "nearest", "linear"); %! %-------------------------------------------------------- %! % confirm that interpolated function matches the original %!demo %! clf; %! x = 0:0.5:3; %! x1 = [3 2 2 1]; %! x2 = [1 2 2 3]; %! y1 = [1 1 0 0]; %! y2 = [0 0 1 1]; %! h = plot (x, interp1 (x1, y1, x), 'b', x1, y1, 'sb'); %! hold on %! g = plot (x, interp1 (x2, y2, x), 'r', x2, y2, '*r'); %! axis ([0.5 3.5 -0.5 1.5]) %! legend ([h(1), g(1)], {'left-continuous', 'right-continuous'}, ... %! 'location', 'northwest') %! legend boxoff %! %-------------------------------------------------------- %! % red curve is left-continuous and blue is right-continuous at x = 2 ##FIXME: add test for n-d arguments here ## For each type of interpolated test, confirm that the interpolated ## value at the knots match the values at the knots. Points away ## from the knots are requested, but only "nearest" and "linear" ## confirm they are the correct values. %!shared xp, yp, xi, style %! xp = 0:2:10; %! yp = sin (2*pi*xp/5); %! xi = [-1, 0, 2.2, 4, 6.6, 10, 11]; ## The following BLOCK/ENDBLOCK section is repeated for each style ## nearest, linear, cubic, spline, pchip ## The test for ppval of cubic has looser tolerance, but otherwise ## the tests are identical. ## Note that the block checks style and *style; if you add more tests ## be sure to add them to both sections of each block. One test, ## style vs. *style, occurs only in the first section. ## There is an ENDBLOCKTEST after the final block %!test style = "nearest"; ## BLOCK %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!error interp1 (1,1,1, style) %!assert (interp1 (xp,[yp',yp'],xi,style), %! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) %!test style = ["*",style]; %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!error interp1 (1,1,1, style) ## ENDBLOCK %!test style = "linear"; ## BLOCK %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!error interp1 (1,1,1, style) %!assert (interp1 (xp,[yp',yp'],xi,style), %! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) %!test style = ['*',style]; %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!assert (interp1 ([1 2 2 3], [1 2 3 4], 2), 3); %!assert (interp1 ([3 2 2 1], [4 3 2 1], 2), 2); %!error interp1 (1,1,1, style) ## ENDBLOCK %!test style = "cubic"; ## BLOCK %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),100*eps) %!error interp1 (1,1,1, style) %!assert (interp1 (xp,[yp',yp'],xi,style), %! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) %!test style = ["*",style]; %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),100*eps) %!error interp1 (1,1,1, style) ## ENDBLOCK %!test style = "pchip"; ## BLOCK %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!error interp1 (1,1,1, style) %!assert (interp1 (xp,[yp',yp'],xi,style), %! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) %!test style = ["*",style]; %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!error interp1 (1,1,1, style) ## ENDBLOCK %!test style = "spline"; ## BLOCK %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!error interp1 (1,1,1, style) %!assert (interp1 (xp,[yp',yp'],xi,style), %! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) %!test style = ["*",style]; %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!error interp1 (1,1,1, style) ## ENDBLOCK ## ENDBLOCKTEST ## test extrapolation (linear) %!assert (interp1 ([1:5],[3:2:11],[0,6],"linear","extrap"), [1, 13], eps) %!assert (interp1 (xp, yp, [-1, max(xp)+1],"linear",5), [5, 5]) %!assert (interp1 ([0,1],[1,0],[0.1,0.9;0.2,1.1]), [0.9 0.1; 0.8 NA], eps) %!assert (interp1 ([0,1],[1,0],[0.1,0.9;0.2,1]), [0.9 0.1; 0.8 0], eps) ## Basic sanity checks %!assert (interp1 (1:2,1:2,1.4,"nearest"), 1) %!assert (interp1 (1:2,1:2,1.4,"linear"), 1.4) %!assert (interp1 (1:4,1:4,1.4,"cubic"), 1.4) %!assert (interp1 (1:2,1:2,1.1,"spline"), 1.1) %!assert (interp1 (1:3,1:3,1.4,"spline"), 1.4) %!assert (interp1 (1:2:4,1:2:4,1.4,"*nearest"), 1) %!assert (interp1 (1:2:4,1:2:4,[0,1,1.4,3,4],"*linear"), [NA,1,1.4,3,NA]) %!assert (interp1 (1:2:8,1:2:8,1.4,"*cubic"), 1.4) %!assert (interp1 (1:2,1:2,1.3, "*spline"), 1.3) %!assert (interp1 (1:2:6,1:2:6,1.4,"*spline"), 1.4) %!assert (interp1 ([3,2,1],[3,2,2],2.5), 2.5) %!assert (interp1 ([4,4,3,2,0],[0,1,4,2,1],[1.5,4,4.5], "linear"), [1.75,1,NA]) %!assert (interp1 (0:4, 2.5), 1.5) ## Left and Right discontinuities %!assert (interp1 ([1,2,2,3,4],[0,1,4,2,1],[-1,1.5,2,2.5,3.5], "linear", "extrap", "right"), [-2,0.5,4,3,1.5]) %!assert (interp1 ([1,2,2,3,4],[0,1,4,2,1],[-1,1.5,2,2.5,3.5], "linear", "extrap", "left"), [-2,0.5,1,3,1.5]) %% Test input validation %!error interp1 () %!error interp1 (1,2,3,4,5,6,7) %!error <table too short> interp1 (1,1,1, "linear") %!error <table too short> interp1 (1,1,1, "*nearest") %!error <table too short> interp1 (1,1,1, "*linear") %!warning <multiple discontinuities> interp1 ([1 1 1 2], [1 2 3 4], 1); %!error <discontinuities not supported> interp1 ([1 1],[1 2],1, "pchip") %!error <discontinuities not supported> interp1 ([1 1],[1 2],1, "cubic") %!error <discontinuities not supported> interp1 ([1 1],[1 2],1, "spline") %!error <invalid method> interp1 (1:2,1:2,1, "bogus")