X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fm%2Fgeneral%2Finterp1.m;fp=octave_packages%2Fm%2Fgeneral%2Finterp1.m;h=56cce53cec5c9ff4b3b9cf88ceb7990199a71bed;hp=0000000000000000000000000000000000000000;hb=1c0469ada9531828709108a4882a751d2816994a;hpb=63de9f36673d49121015e3695f2c336ea92bc278

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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.  Interpolate @var{y}, defined at the
+## points @var{x}, at the points @var{xi}.  The sample points @var{x}
+## must be monotonic.  If not specified, @var{x} is taken to be the
+## indices of @var{y}.  If @var{y} is an array, treat the columns
+## of @var{y} separately.
+##
+## Method is one of:
+##
+## @table @asis
+## @item 'nearest'
+## Return the nearest neighbor.
+##
+## @item 'linear'
+## Linear interpolation from nearest neighbors
+##
+## @item 'pchip'
+## Piecewise cubic Hermite interpolating polynomial
+##
+## @item 'cubic'
+## Cubic interpolation (same as @code{pchip})
+##
+## @item '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 'linear'.
+##
+## If @var{extrap} is the string '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 '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}, 'pp'), @var{xi}) == interp1 (@var{x}, @var{y},
+## @var{xi}, @var{method}, 'extrap')}.
+##
+## Duplicate points in @var{x} specify a discontinuous interpolant.  There
+## should be at most 2 consecutive points with the same value.
+## The discontinuous interpolant is right-continuous if @var{x} is increasing,
+## left-continuous if it is decreasing.
+## Discontinuities are (currently) only allowed for "nearest" and "linear"
+## methods; in all other cases, @var{x} must be strictly monotonic.
+##
+## 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;
+
+  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;
+        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;
+    x = 1:numel(y);
+  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
+
+  starmethod = method(1) == "*";
+
+  if (starmethod)
+    dx = x(2) - x(1);
+  else
+    jumps = x(1:nx-1) == x(2:nx);
+    have_jumps = any (jumps);
+    if (have_jumps)
+      if (any (strcmp (method, {"nearest", "linear"})))
+        if (any (jumps(1:nx-2) & jumps(2:nx-1)))
+          warning ("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);
+    else
+      y = shiftdim (y, 1);
+      yi = pchip (x, y, reshape (xi, szx));
+    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);
+    else
+      y = shiftdim (y, 1);
+      yi = spline (x, y, reshape (xi, szx));
+    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))
+        if (strcmp (method, "pchip") || strcmp (method, "*pchip")
+          ||strcmp (method, "cubic") || strcmp (method, "*cubic")
+          ||strcmp (method, "spline") || strcmp (method, "*spline"))
+          yi(:, outliers) = extrap;
+          yi = shiftdim(yi, 1);
+        else
+          yi(outliers, :) = extrap;
+        endif
+      else
+        yi(outliers.') = extrap;
+      endif
+    endif
+  else
+    yi.orient = "first";
+  endif
+
+endfunction
+
+%!demo
+%! 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
+%! 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
+%! 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
+%! 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
+
+##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
+## before 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);
+%!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]);
+
+%!error interp1
+%!error interp1(1:2,1:2,1,"bogus")
+
+%!assert (interp1(1:2,1:2,1.4,"nearest"),1);
+%!error interp1(1,1,1, "linear");
+%!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);
+
+%!error interp1(1,1,1, "*nearest");
+%!assert (interp1(1:2:4,1:2:4,1.4,"*nearest"),1);
+%!error interp1(1,1,1, "*linear");
+%!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)