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view scripts/general/interpn.m @ 30564:796f54d4ddbf stable
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2021.
In all .txi and .texi files except gpl.txi and gpl.texi in the
doc/liboctave and doc/interpreter directories, change the copyright
to "Octave Project Developers", the same as used for other source
files. Update copyright notices for 2022 (not done since 2019). For
gpl.txi and gpl.texi, change the copyright notice to be "Free Software
Foundation, Inc." and leave the date at 2007 only because this file
only contains the text of the GPL, not anything created by the Octave
Project Developers.
Add Paul Thomas to contributors.in.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | 01de0045b2e3 |
children | 92cda11fb171 |
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######################################################################## ## ## Copyright (C) 2007-2022 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## 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 ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {@var{vi} =} interpn (@var{x1}, @var{x2}, @dots{}, @var{v}, @var{y1}, @var{y2}, @dots{}) ## @deftypefnx {} {@var{vi} =} interpn (@var{v}, @var{y1}, @var{y2}, @dots{}) ## @deftypefnx {} {@var{vi} =} interpn (@var{v}, @var{m}) ## @deftypefnx {} {@var{vi} =} interpn (@var{v}) ## @deftypefnx {} {@var{vi} =} interpn (@dots{}, @var{method}) ## @deftypefnx {} {@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 @qcode{"ndgrid"} format or vectors. ## ## The parameters @var{y1}, @var{y2}, @dots{}, @var{yn} represent the points at ## which the array @var{vi} is interpolated. They can be vectors of the same ## length and orientation in which case they are interpreted as coordinates of ## scattered points. If they are vectors of differing orientation or length, ## they are used to form a grid in @qcode{"ndgrid"} format. They can also be ## @var{n}-dimensional arrays of equal size. ## ## 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}. ## ## The interpolation @var{method} is one of: ## ## @table @asis ## @item @qcode{"nearest"} ## Return the nearest neighbor. ## ## @item @qcode{"linear"} (default) ## Linear interpolation from nearest neighbors. ## ## @item @qcode{"pchip"} ## Piecewise cubic Hermite interpolating polynomial---shape-preserving ## interpolation with smooth first derivative (not implemented yet). ## ## @item @qcode{"cubic"} ## Cubic interpolation (same as @qcode{"pchip"} [not implemented yet]). ## ## @item @qcode{"spline"} ## Cubic spline interpolation---smooth first and second derivatives ## throughout the curve. ## @end table ## ## The default method is @qcode{"linear"}. ## ## @var{extrapval} is a scalar number. It replaces values beyond the endpoints ## with @var{extrapval}. Note that if @var{extrapval} is used, @var{method} ## must be specified as well. If @var{extrapval} is omitted and the ## @var{method} is @qcode{"spline"}, then the extrapolated values of the ## @qcode{"spline"} are used. Otherwise the default @var{extrapval} value for ## any other @var{method} is @code{NA}. ## @seealso{interp1, interp2, interp3, spline, ndgrid} ## @end deftypefn function vi = interpn (varargin) if (nargin < 1 || ! isnumeric (varargin{1})) print_usage (); endif method = "linear"; extrapval = []; nargs = nargin; ## Find and validate EXTRAPVAL and/or METHOD inputs if (nargs > 1 && ischar (varargin{end-1})) if (! isnumeric (varargin{end}) || ! isscalar (varargin{end})) error ("interpn: EXTRAPVAL must be a numeric scalar"); endif extrapval = varargin{end}; method = varargin{end-1}; nargs -= 2; elseif (ischar (varargin{end})) method = varargin{end}; nargs -= 1; endif if (method(1) == "*") warning ("interpn: ignoring unsupported '*' flag to METHOD"); method(1) = []; endif method = validatestring (method, {"nearest", "linear", "pchip", "cubic", "spline"}, "interpn"); if (nargs <= 2) ## Calling form interpn (V, ...) v = varargin{1}; m = 1; if (nargs == 2) m = varargin{2}; if (! (isnumeric (m) && isscalar (m) && m == fix (m))) 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)) ## Calling form interpn (V, Y1, Y2, ...) 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) ## Calling form interpn (X1, X2, ..., V, Y1, Y2, ...) 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 = 1 : nd if (! size_equal (x{i}, v)) error ("interpn: incorrect dimensions for input X%d", i); endif idx(1 : nd) = {1}; idx(i) = ":"; x{i} = x{i}(idx{:})(:); endfor endif all_vectors = all (cellfun ("isvector", y)); same_size = size_equal (y{:}); if (all_vectors && ! same_size) [y{:}] = ndgrid (y{:}); endif if (strcmp (method, "linear")) vi = __lin_interpn__ (x{:}, v, y{:}); if (isempty (extrapval)) extrapval = NA; endif vi(isna (vi)) = extrapval; elseif (strcmp (method, "nearest")) ## FIXME: This seems overly complicated. Is there a way to simplify ## all the code after the call to lookup (which should be fast)? ## Could Qhull be used for quick nearest neighbor calculation? yshape = size (y{1}); yidx = cell (1, nd); ## Find rough nearest index using lookup function [O(log2 (N)]. for i = 1 : nd y{i} = y{i}(:); yidx{i} = lookup (x{i}, y{i}, "lr"); endfor ## Single comparison to next largest index to see which is closer. 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{:})); ## Apply EXTRAPVAL to points outside original volume. idx = false (prod (yshape), 1); for i = 1 : nd idx |= y{i} < min (x{i}(:)) | y{i} > max (x{i}(:)); endfor if (isempty (extrapval)) extrapval = NA; endif vi(idx) = extrapval; vi = reshape (vi, yshape); elseif (strcmp (method, "spline")) if (any (! cellfun ("isvector", y))) ysz = size (y{1}); for i = 1 : nd if (any (size (y{i}) != ysz)) error ("interpn: incorrect dimensions for input Y%d", i); endif idx(1 : nd) = {1}; idx(i) = ":"; y{i} = y{i}(idx{:}); endfor 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, "pchip")) error ("interpn: pchip interpolation not yet implemented"); elseif (strcmp (method, "cubic")) error ("interpn: cubic interpolation not yet implemented"); endif endfunction %!demo %! clf; %! colormap ("default"); %! 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 %! clf; %! colormap ("default"); %! 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 # FIXME: Uncomment when support for "cubic" has been added %! clf; %! colormap ("default"); %! 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 %! clf; %! colormap ("default"); %! 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 %! clf; %! colormap ("default"); %! 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); %!test %! 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); %! endfor %! tol = 10*eps; %! assert (interpn (z), zout, tol); %! assert (interpn (z, "linear"), zout, tol); %! assert (interpn (z, "spline"), zout, tol); ## Test input validation %!error <Invalid call> interpn () %!error <Invalid call> interpn ("foobar") %!error <EXTRAPVAL must be a numeric scalar> interpn (1, "linear", {1}) %!error <EXTRAPVAL must be a numeric scalar> interpn (1, "linear", [1, 2]) %!warning <ignoring unsupported '\*' flag> interpn (rand (3,3), 1, "*linear"); %!error <'foobar' does not match any of> interpn (1, "foobar") %!error <wrong number or incorrectly formatted input arguments> %! interpn (1, 2, 3, 4); %!error <incorrect dimensions for input X1> %! interpn ([1,2], ones (2,2), magic (3), [1,2], [1,2]) %!error <incorrect dimensions for input X2> %! interpn (ones (3,3), ones (2,2), magic (3), [1,2], [1,2]) %!error <incorrect dimensions for input Y2> %! interpn ([1,2], [1,2], magic (3), [1,2], ones (2,2), "spline") %!error <pchip interpolation not yet implemented> interpn ([1,2], "pchip") %!error <cubic interpolation not yet implemented> interpn ([1,2], "cubic")