--- /dev/null
+## Copyright (C) 2007-2012 David Bateman
+##
+## 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{vi} =} interpn (@var{x1}, @var{x2}, @dots{}, @var{v}, @var{y1}, @var{y2}, @dots{})
+## @deftypefnx {Function File} {@var{vi} =} interpn (@var{v}, @var{y1}, @var{y2}, @dots{})
+## @deftypefnx {Function File} {@var{vi} =} interpn (@var{v}, @var{m})
+## @deftypefnx {Function File} {@var{vi} =} interpn (@var{v})
+## @deftypefnx {Function File} {@var{vi} =} interpn (@dots{}, @var{method})
+## @deftypefnx {Function File} {@var{vi} =} interpn (@dots{}, @var{method}, @var{extrapval})
+##
+## Perform @var{n}-dimensional interpolation, where @var{n} is at least two.
+## Each element of the @var{n}-dimensional array @var{v} represents a value
+## at a location given by the parameters @var{x1}, @var{x2}, @dots{}, @var{xn}.
+## The parameters @var{x1}, @var{x2}, @dots{}, @var{xn} are either
+## @var{n}-dimensional arrays of the same size as the array @var{v} in
+## the 'ndgrid' format or vectors. The parameters @var{y1}, etc. respect a
+## similar format to @var{x1}, etc., and they represent the points at which
+## the array @var{vi} is interpolated.
+##
+## If @var{x1}, @dots{}, @var{xn} are omitted, they are assumed to be
+## @code{x1 = 1 : size (@var{v}, 1)}, etc. If @var{m} is specified, then
+## the interpolation adds a point half way between each of the interpolation
+## points. This process is performed @var{m} times. If only @var{v} is
+## specified, then @var{m} is assumed to be @code{1}.
+##
+## Method is one of:
+##
+## @table @asis
+## @item 'nearest'
+## Return the nearest neighbor.
+##
+## @item 'linear'
+## Linear interpolation from nearest neighbors.
+##
+## @item 'cubic'
+## Cubic interpolation from four nearest neighbors (not implemented yet).
+##
+## @item 'spline'
+## Cubic spline interpolation---smooth first and second derivatives
+## throughout the curve.
+## @end table
+##
+## The default method is 'linear'.
+##
+## If @var{extrapval} is the scalar value, use it to replace the values
+## beyond the endpoints with that number. If @var{extrapval} is missing,
+## assume NA.
+## @seealso{interp1, interp2, spline, ndgrid}
+## @end deftypefn
+
+function vi = interpn (varargin)
+
+ method = "linear";
+ extrapval = NA;
+ nargs = nargin;
+
+ if (nargin < 1 || ! isnumeric (varargin{1}))
+ print_usage ();
+ endif
+
+ if (ischar (varargin{end}))
+ method = varargin{end};
+ nargs = nargs - 1;
+ elseif (nargs > 1 && ischar (varargin{end - 1}))
+ if (! isnumeric (varargin{end}) || ! isscalar (varargin{end}))
+ error ("interpn: extrapal is expected to be a numeric scalar");
+ endif
+ method = varargin{end - 1};
+ extrapval = varargin{end};
+ nargs = nargs - 2;
+ endif
+
+ if (nargs < 3)
+ v = varargin{1};
+ m = 1;
+ if (nargs == 2)
+ if (ischar (varargin{2}))
+ method = varargin{2};
+ elseif (isnumeric (m) && isscalar (m) && fix (m) == m)
+ m = varargin{2};
+ else
+ print_usage ();
+ endif
+ endif
+ sz = size (v);
+ nd = ndims (v);
+ x = cell (1, nd);
+ y = cell (1, nd);
+ for i = 1 : nd;
+ x{i} = 1 : sz(i);
+ y{i} = 1 : (1 / (2 ^ m)) : sz(i);
+ endfor
+ y{1} = y{1}.';
+ [y{:}] = ndgrid (y{:});
+ elseif (! isvector (varargin{1}) && nargs == (ndims (varargin{1}) + 1))
+ v = varargin{1};
+ sz = size (v);
+ nd = ndims (v);
+ x = cell (1, nd);
+ y = varargin (2 : nargs);
+ for i = 1 : nd;
+ x{i} = 1 : sz(i);
+ endfor
+ elseif (rem (nargs, 2) == 1 && nargs ==
+ (2 * ndims (varargin{ceil (nargs / 2)})) + 1)
+ nv = ceil (nargs / 2);
+ v = varargin{nv};
+ sz = size (v);
+ nd = ndims (v);
+ x = varargin (1 : (nv - 1));
+ y = varargin ((nv + 1) : nargs);
+ else
+ error ("interpn: wrong number or incorrectly formatted input arguments");
+ endif
+
+ if (any (! cellfun ("isvector", x)))
+ for i = 2 : nd
+ if (! size_equal (x{1}, x{i}) || ! size_equal (x{i}, v))
+ error ("interpn: dimensional mismatch");
+ endif
+ idx (1 : nd) = {1};
+ idx (i) = ":";
+ x{i} = x{i}(idx{:})(:);
+ endfor
+ idx (1 : nd) = {1};
+ idx (1) = ":";
+ x{1} = x{1}(idx{:})(:);
+ endif
+
+ method = tolower (method);
+
+ all_vectors = all (cellfun ("isvector", y));
+ different_lengths = numel (unique (cellfun ("numel", y))) > 1;
+ if (all_vectors && different_lengths)
+ [foobar(1:numel(y)).y] = ndgrid (y{:});
+ y = {foobar.y};
+ endif
+
+ if (strcmp (method, "linear"))
+ vi = __lin_interpn__ (x{:}, v, y{:});
+ vi (isna (vi)) = extrapval;
+ elseif (strcmp (method, "nearest"))
+ yshape = size (y{1});
+ yidx = cell (1, nd);
+ for i = 1 : nd
+ y{i} = y{i}(:);
+ yidx{i} = lookup (x{i}, y{i}, "lr");
+ endfor
+ idx = cell (1,nd);
+ for i = 1 : nd
+ idx{i} = yidx{i} + (y{i} - x{i}(yidx{i})(:) >= x{i}(yidx{i} + 1)(:) - y{i});
+ endfor
+ vi = v (sub2ind (sz, idx{:}));
+ idx = zeros (prod (yshape), 1);
+ for i = 1 : nd
+ idx |= y{i} < min (x{i}(:)) | y{i} > max (x{i}(:));
+ endfor
+ vi(idx) = extrapval;
+ vi = reshape (vi, yshape);
+ elseif (strcmp (method, "spline"))
+ if (any (! cellfun ("isvector", y)))
+ for i = 2 : nd
+ if (! size_equal (y{1}, y{i}))
+ error ("interpn: dimensional mismatch");
+ endif
+ idx (1 : nd) = {1};
+ idx (i) = ":";
+ y{i} = y{i}(idx{:});
+ endfor
+ idx (1 : nd) = {1};
+ idx (1) = ":";
+ y{1} = y{1}(idx{:});
+ endif
+
+ vi = __splinen__ (x, v, y, extrapval, "interpn");
+
+ if (size_equal (y{:}))
+ ly = length (y{1});
+ idx = cell (1, ly);
+ q = cell (1, nd);
+ for i = 1 : ly
+ q(:) = i;
+ idx {i} = q;
+ endfor
+ vi = vi (cellfun (@(x) sub2ind (size(vi), x{:}), idx));
+ vi = reshape (vi, size(y{1}));
+ endif
+ elseif (strcmp (method, "cubic"))
+ error ("interpn: cubic interpolation not yet implemented");
+ else
+ error ("interpn: unrecognized interpolation METHOD");
+ endif
+
+endfunction
+
+%!demo
+%! A=[13,-1,12;5,4,3;1,6,2];
+%! x=[0,1,4]; y=[10,11,12];
+%! xi=linspace(min(x),max(x),17);
+%! yi=linspace(min(y),max(y),26)';
+%! mesh(xi,yi,interpn(x,y,A.',xi,yi,"linear").');
+%! [x,y] = meshgrid(x,y);
+%! hold on; plot3(x(:),y(:),A(:),"b*"); hold off;
+
+%!demo
+%! A=[13,-1,12;5,4,3;1,6,2];
+%! x=[0,1,4]; y=[10,11,12];
+%! xi=linspace(min(x),max(x),17);
+%! yi=linspace(min(y),max(y),26)';
+%! mesh(xi,yi,interpn(x,y,A.',xi,yi,"nearest").');
+%! [x,y] = meshgrid(x,y);
+%! hold on; plot3(x(:),y(:),A(:),"b*"); hold off;
+
+%!#demo
+%! A=[13,-1,12;5,4,3;1,6,2];
+%! x=[0,1,2]; y=[10,11,12];
+%! xi=linspace(min(x),max(x),17);
+%! yi=linspace(min(y),max(y),26)';
+%! mesh(xi,yi,interpn(x,y,A.',xi,yi,"cubic").');
+%! [x,y] = meshgrid(x,y);
+%! hold on; plot3(x(:),y(:),A(:),"b*"); hold off;
+
+%!demo
+%! A=[13,-1,12;5,4,3;1,6,2];
+%! x=[0,1,2]; y=[10,11,12];
+%! xi=linspace(min(x),max(x),17);
+%! yi=linspace(min(y),max(y),26)';
+%! mesh(xi,yi,interpn(x,y,A.',xi,yi,"spline").');
+%! [x,y] = meshgrid(x,y);
+%! hold on; plot3(x(:),y(:),A(:),"b*"); hold off;
+
+
+%!demo
+%! x = y = z = -1:1;
+%! f = @(x,y,z) x.^2 - y - z.^2;
+%! [xx, yy, zz] = meshgrid (x, y, z);
+%! v = f (xx,yy,zz);
+%! xi = yi = zi = -1:0.1:1;
+%! [xxi, yyi, zzi] = ndgrid (xi, yi, zi);
+%! vi = interpn(x, y, z, v, xxi, yyi, zzi, 'spline');
+%! mesh (yi, zi, squeeze (vi(1,:,:)));
+
+
+%!test
+%! [x,y,z] = ndgrid(0:2);
+%! f = x+y+z;
+%! assert (interpn(x,y,z,f,[.5 1.5],[.5 1.5],[.5 1.5]), [1.5, 4.5])
+%! assert (interpn(x,y,z,f,[.51 1.51],[.51 1.51],[.51 1.51],'nearest'), [3, 6])
+%! assert (interpn(x,y,z,f,[.5 1.5],[.5 1.5],[.5 1.5],'spline'), [1.5, 4.5])
+%! assert (interpn(x,y,z,f,x,y,z), f)
+%! assert (interpn(x,y,z,f,x,y,z,'nearest'), f)
+%! assert (interpn(x,y,z,f,x,y,z,'spline'), f)
+
+%!test
+%! [x, y, z] = ndgrid (0:2, 1:4, 2:6);
+%! f = x + y + z;
+%! xi = [0.5 1.0 1.5];
+%! yi = [1.5 2.0 2.5 3.5];
+%! zi = [2.5 3.5 4.0 5.0 5.5];
+%! fi = interpn (x, y, z, f, xi, yi, zi);
+%! [xi, yi, zi] = ndgrid (xi, yi, zi);
+%! assert (fi, xi + yi + zi)
+
+%!test
+%! xi = 0:2;
+%! yi = 1:4;
+%! zi = 2:6;
+%! [x, y, z] = ndgrid (xi, yi, zi);
+%! f = x + y + z;
+%! fi = interpn (x, y, z, f, xi, yi, zi, "nearest");
+%! assert (fi, x + y + z)
+
+%!test
+%! [x,y,z] = ndgrid(0:2);
+%! f = x.^2+y.^2+z.^2;
+%! assert (interpn(x,y,-z,f,1.5,1.5,-1.5), 7.5)
+
+%!test % for Matlab-compatible rounding for 'nearest'
+%! X = meshgrid (1:4);
+%! assert (interpn (X, 2.5, 2.5, 'nearest'), 3);
+
+%!shared z, zout, tol
+%! z = zeros (3, 3, 3);
+%! zout = zeros (5, 5, 5);
+%! z(:,:,1) = [1 3 5; 3 5 7; 5 7 9];
+%! z(:,:,2) = z(:,:,1) + 2;
+%! z(:,:,3) = z(:,:,2) + 2;
+%! for n = 1:5
+%! zout(:,:,n) = [1 2 3 4 5;
+%! 2 3 4 5 6;
+%! 3 4 5 6 7;
+%! 4 5 6 7 8;
+%! 5 6 7 8 9] + (n-1);
+%! end
+%! tol = 10 * eps;
+%!assert (interpn (z), zout, tol)
+%!assert (interpn (z, "linear"), zout, tol)
+%!assert (interpn (z, "spline"), zout, tol)
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff