Mercurial > octave-nkf
view scripts/general/interp1.m @ 17281:bc924baa2c4e
doc: Add new @qcode macro for code samples which are quoted.
Macro handles options ("on") or properties ("position") more elegantly
than @code{"text"}.
* doc/interpreter/macros.texi: Add new @qcode macro.
* doc/interpreter/tips.txi: Add documentation about @qcode macro.
* doc/interpreter/basics.txi, doc/interpreter/container.txi,
doc/interpreter/emacs.txi, doc/interpreter/errors.txi,
doc/interpreter/eval.txi, doc/interpreter/expr.txi,
doc/interpreter/external.txi, doc/interpreter/func.txi,
doc/interpreter/grammar.txi, doc/interpreter/image.txi,
doc/interpreter/install.txi, doc/interpreter/interp.txi,
doc/interpreter/io.txi, doc/interpreter/matrix.txi,
doc/interpreter/numbers.txi, doc/interpreter/oop.txi,
doc/interpreter/package.txi, doc/interpreter/plot.txi,
doc/interpreter/quad.txi, doc/interpreter/sparse.txi,
doc/interpreter/strings.txi, doc/interpreter/system.txi,
doc/interpreter/vectorize.txi, libinterp/corefcn/balance.cc,
libinterp/corefcn/bitfcns.cc, libinterp/corefcn/cellfun.cc,
libinterp/corefcn/conv2.cc, libinterp/corefcn/data.cc,
libinterp/corefcn/debug.cc, libinterp/corefcn/defaults.cc,
libinterp/corefcn/dirfns.cc, libinterp/corefcn/dlmread.cc,
libinterp/corefcn/error.cc, libinterp/corefcn/file-io.cc,
libinterp/corefcn/find.cc, libinterp/corefcn/gammainc.cc,
libinterp/corefcn/graphics.cc, libinterp/corefcn/help.cc,
libinterp/corefcn/hex2num.cc, libinterp/corefcn/input.cc,
libinterp/corefcn/load-path.cc, libinterp/corefcn/load-save.cc,
libinterp/corefcn/ls-oct-ascii.cc, libinterp/corefcn/lu.cc,
libinterp/corefcn/luinc.cc, libinterp/corefcn/matrix_type.cc,
libinterp/corefcn/oct-hist.cc, libinterp/corefcn/pager.cc,
libinterp/corefcn/pr-output.cc, libinterp/corefcn/pt-jit.cc,
libinterp/corefcn/qz.cc, libinterp/corefcn/rand.cc,
libinterp/corefcn/regexp.cc, libinterp/corefcn/schur.cc,
libinterp/corefcn/sighandlers.cc, libinterp/corefcn/sparse.cc,
libinterp/corefcn/spparms.cc, libinterp/corefcn/str2double.cc,
libinterp/corefcn/svd.cc, libinterp/corefcn/symtab.cc,
libinterp/corefcn/syscalls.cc, libinterp/corefcn/toplev.cc,
libinterp/corefcn/tril.cc, libinterp/corefcn/typecast.cc,
libinterp/corefcn/utils.cc, libinterp/corefcn/variables.cc,
libinterp/dldfcn/__init_fltk__.cc, libinterp/dldfcn/chol.cc,
libinterp/dldfcn/colamd.cc, libinterp/dldfcn/fftw.cc, libinterp/dldfcn/qr.cc,
libinterp/dldfcn/symbfact.cc, libinterp/octave-value/ov-base.cc,
libinterp/octave-value/ov-fcn-handle.cc,
libinterp/octave-value/ov-fcn-inline.cc, libinterp/octave-value/ov-java.cc,
libinterp/octave-value/ov-range.cc, libinterp/octave-value/ov-struct.cc,
libinterp/octave-value/ov-usr-fcn.cc, libinterp/parse-tree/oct-parse.in.yy,
libinterp/parse-tree/pt-binop.cc, libinterp/parse-tree/pt-eval.cc,
libinterp/parse-tree/pt-mat.cc, scripts/@ftp/ftp.m,
scripts/deprecated/java_convert_matrix.m, scripts/deprecated/java_debug.m,
scripts/deprecated/java_unsigned_conversion.m, scripts/deprecated/shell_cmd.m,
scripts/general/dblquad.m, scripts/general/display.m,
scripts/general/genvarname.m, scripts/general/idivide.m,
scripts/general/interp1.m, scripts/general/interp2.m,
scripts/general/interp3.m, scripts/general/interpn.m, scripts/general/isa.m,
scripts/general/profexplore.m, scripts/general/profile.m,
scripts/general/quadgk.m, scripts/general/randi.m, scripts/general/structfun.m,
scripts/general/subsindex.m, scripts/general/triplequad.m,
scripts/geometry/griddata.m, scripts/geometry/griddata3.m,
scripts/geometry/griddatan.m, scripts/geometry/voronoi.m, scripts/help/help.m,
scripts/help/lookfor.m, scripts/image/cmpermute.m, scripts/image/colormap.m,
scripts/image/image.m, scripts/image/imagesc.m, scripts/image/imfinfo.m,
scripts/image/imformats.m, scripts/image/imread.m, scripts/image/imshow.m,
scripts/image/imwrite.m, scripts/image/ind2gray.m, scripts/image/lines.m,
scripts/image/rgb2ind.m, scripts/image/spinmap.m, scripts/io/dlmwrite.m,
scripts/io/strread.m, scripts/io/textread.m, scripts/io/textscan.m,
scripts/java/javaclasspath.m, scripts/java/usejava.m,
scripts/miscellaneous/bzip2.m, scripts/miscellaneous/computer.m,
scripts/miscellaneous/copyfile.m, scripts/miscellaneous/debug.m,
scripts/miscellaneous/dos.m, scripts/miscellaneous/edit.m,
scripts/miscellaneous/gzip.m, scripts/miscellaneous/license.m,
scripts/miscellaneous/mkoctfile.m, scripts/miscellaneous/movefile.m,
scripts/miscellaneous/parseparams.m, scripts/miscellaneous/unix.m,
scripts/optimization/fminbnd.m, scripts/optimization/fminsearch.m,
scripts/optimization/fminunc.m, scripts/optimization/fsolve.m,
scripts/optimization/fzero.m, scripts/optimization/glpk.m,
scripts/optimization/lsqnonneg.m, scripts/optimization/optimset.m,
scripts/optimization/pqpnonneg.m, scripts/pkg/pkg.m, scripts/plot/allchild.m,
scripts/plot/ancestor.m, scripts/plot/area.m, scripts/plot/axis.m,
scripts/plot/bar.m, scripts/plot/barh.m, scripts/plot/box.m,
scripts/plot/caxis.m, scripts/plot/cla.m, scripts/plot/clabel.m,
scripts/plot/clf.m, scripts/plot/close.m, scripts/plot/colorbar.m,
scripts/plot/daspect.m, scripts/plot/ezmesh.m, scripts/plot/ezmeshc.m,
scripts/plot/ezsurf.m, scripts/plot/ezsurfc.m, scripts/plot/findall.m,
scripts/plot/findobj.m, scripts/plot/gcbo.m, scripts/plot/gcf.m,
scripts/plot/gco.m, scripts/plot/grid.m, scripts/plot/guihandles.m,
scripts/plot/hdl2struct.m, scripts/plot/hidden.m, scripts/plot/hold.m,
scripts/plot/isonormals.m, scripts/plot/isosurface.m, scripts/plot/legend.m,
scripts/plot/mesh.m, scripts/plot/meshc.m, scripts/plot/meshz.m,
scripts/plot/newplot.m, scripts/plot/orient.m, scripts/plot/pareto.m,
scripts/plot/patch.m, scripts/plot/pbaspect.m, scripts/plot/pcolor.m,
scripts/plot/plot.m, scripts/plot/print.m,
scripts/plot/private/__add_default_menu__.m, scripts/plot/quiver.m,
scripts/plot/quiver3.m, scripts/plot/refreshdata.m, scripts/plot/saveas.m,
scripts/plot/scatter.m, scripts/plot/scatter3.m, scripts/plot/shading.m,
scripts/plot/shrinkfaces.m, scripts/plot/slice.m, scripts/plot/stem.m,
scripts/plot/stem3.m, scripts/plot/struct2hdl.m, scripts/plot/subplot.m,
scripts/plot/surf.m, scripts/plot/surfc.m, scripts/plot/surfl.m,
scripts/plot/tetramesh.m, scripts/plot/uigetfile.m, scripts/plot/uimenu.m,
scripts/plot/uiputfile.m, scripts/plot/waterfall.m, scripts/plot/whitebg.m,
scripts/plot/xlim.m, scripts/plot/ylim.m, scripts/plot/zlim.m,
scripts/polynomial/conv.m, scripts/polynomial/polyout.m,
scripts/polynomial/splinefit.m, scripts/set/ismember.m, scripts/set/powerset.m,
scripts/set/setdiff.m, scripts/set/union.m, scripts/set/unique.m,
scripts/signal/detrend.m, scripts/signal/filter2.m, scripts/signal/freqz.m,
scripts/signal/periodogram.m, scripts/signal/spectral_adf.m,
scripts/signal/spectral_xdf.m, scripts/sparse/eigs.m, scripts/sparse/svds.m,
scripts/specfun/legendre.m, scripts/special-matrix/gallery.m,
scripts/statistics/base/mean.m, scripts/statistics/base/moment.m,
scripts/statistics/tests/cor_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test_2.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/sign_test.m,
scripts/statistics/tests/t_test.m, scripts/statistics/tests/t_test_2.m,
scripts/statistics/tests/t_test_regression.m,
scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m,
scripts/statistics/tests/welch_test.m,
scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m,
scripts/statistics/tests/z_test_2.m, scripts/strings/base2dec.m,
scripts/strings/index.m, scripts/strings/isstrprop.m,
scripts/strings/mat2str.m, scripts/strings/regexptranslate.m,
scripts/strings/rindex.m, scripts/strings/str2num.m, scripts/strings/strcat.m,
scripts/strings/strjust.m, scripts/strings/strmatch.m,
scripts/strings/validatestring.m, scripts/testfun/demo.m,
scripts/testfun/example.m, scripts/testfun/test.m, scripts/time/addtodate.m,
scripts/time/asctime.m, scripts/time/datestr.m, scripts/time/datetick.m,
scripts/time/weekday.m, scripts/ui/errordlg.m, scripts/ui/helpdlg.m,
scripts/ui/inputdlg.m, scripts/ui/listdlg.m, scripts/ui/msgbox.m,
scripts/ui/questdlg.m, scripts/ui/warndlg.m: Use new @qcode macro.
author | Rik <rik@octave.org> |
---|---|
date | Mon, 19 Aug 2013 20:46:38 -0700 |
parents | c3c1ebfaa7dc |
children | 09543e9c8f40 |
line wrap: on
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## Copyright (C) 2000-2012 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{pp} =} interp1 (@dots{}, "pp") ## ## One-dimensional interpolation. Interpolates 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 ## ## Appending '*' to the start of the above method 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. If @var{extrap} is a number, replace values beyond ## the endpoints with that number. If @var{extrap} is missing, assume NA. ## ## If the string argument @qcode{"pp"} is specified, then @var{xi} should not be ## supplied and @code{interp1} returns the piecewise polynomial that ## 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} ## @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 = []; 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 (any (strcmp ({"right", "-right"}, arg))) rightcontinuous = true; elseif (any (strcmp ({"left", "-left"}, arg))) 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 (isempty (rightcontinuous)) ## If not specified, set the continuity condition if (x(end) < x(1)) rightcontinuous = false; else rightcontinuous = true; end 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); end 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 (any (strcmp (method, {"nearest", "linear"}))) if (any (jumps(1:nx-2) & jumps(2:nx-1))) error ("interp1: extra points in discontinuities"); 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" dy = diff (y); dx = diff (x); dx = repmat (dx, [1 size(dy)(2:end)]); coefs = [(dy./dx).'(:), y(1:nx-1, :).'(:)]; xx = x; if (have_jumps) ## Omit zero-size intervals. coefs(jumps, :) = []; xx(jumps) = []; endif 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) if (! 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)); outliers = xi < minx | ! (xi <= maxx); # this catches even 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 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'); %! xlim ([1 3]) %! legend ([h(1), g(1)], {'left-continous', 'right-continuous'}, ... %! 'location', 'east') %! legend boxoff %! %-------------------------------------------------------- %! % red curve is left-continuos 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 linear extrapolation %!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 (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 ([1,2,2,3,4],[0,1,4,2,1],[-1,1.5,2,2.5,3.5], "linear", "extrap"), [-2,0.5,4,3,1.5]) %!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) %!error interp1 () %!error interp1 (1,1,1, "linear") %!error interp1 (1,1,1, "*nearest") %!error interp1 (1,1,1, "*linear") %!error interp1 (1:2,1:2,1, "bogus")