Mercurial > octave-nkf
view scripts/general/interp3.m @ 19631:db92e7e28e1f
strip trailing whitespace from most source files
* NEWS, doc/interpreter/contributors.in, doc/interpreter/func.txi,
doc/interpreter/genpropdoc.m, doc/interpreter/octave_logo.eps,
doc/interpreter/plot.txi, doc/interpreter/stmt.txi,
examples/data/Makefile.am, libinterp/corefcn/data.cc,
libinterp/corefcn/debug.cc, libinterp/corefcn/error.cc,
libinterp/corefcn/file-io.cc, libinterp/corefcn/gl-render.cc,
libinterp/corefcn/graphics.cc, libinterp/corefcn/graphics.in.h,
libinterp/corefcn/load-path.cc, libinterp/corefcn/pr-output.cc,
libinterp/corefcn/pt-jit.cc, libinterp/corefcn/strfind.cc,
libinterp/corefcn/toplev.cc, libinterp/corefcn/toplev.h,
libinterp/corefcn/urlwrite.cc, libinterp/corefcn/variables.cc,
libinterp/octave-value/ov-classdef.cc,
libinterp/octave-value/ov-classdef.h, libinterp/octave.cc,
libinterp/parse-tree/lex.h, libinterp/parse-tree/oct-parse.in.yy,
libinterp/parse-tree/pt-classdef.h, liboctave/system/file-ops.cc,
liboctave/system/oct-env.cc, m4/acinclude.m4,
scripts/deprecated/finite.m, scripts/deprecated/fmod.m,
scripts/deprecated/fnmatch.m, scripts/deprecated/luinc.m,
scripts/deprecated/octave_tmp_file_name.m, scripts/deprecated/syl.m,
scripts/deprecated/usage.m, scripts/general/inputParser.m,
scripts/general/interp1.m, scripts/general/interp2.m,
scripts/general/interp3.m, scripts/general/isequal.m,
scripts/general/private/__isequal__.m, scripts/geometry/voronoi.m,
scripts/image/image.m, scripts/image/imshow.m,
scripts/image/ind2rgb.m, scripts/linear-algebra/bandwidth.m,
scripts/linear-algebra/isbanded.m, scripts/miscellaneous/bzip2.m,
scripts/miscellaneous/cast.m, scripts/miscellaneous/copyfile.m,
scripts/miscellaneous/delete.m, scripts/miscellaneous/fullfile.m,
scripts/miscellaneous/getappdata.m, scripts/miscellaneous/gunzip.m,
scripts/miscellaneous/isappdata.m, scripts/miscellaneous/ls.m,
scripts/miscellaneous/mex.m, scripts/miscellaneous/movefile.m,
scripts/miscellaneous/orderfields.m, scripts/miscellaneous/recycle.m,
scripts/miscellaneous/rmappdata.m, scripts/miscellaneous/setfield.m,
scripts/miscellaneous/symvar.m, scripts/miscellaneous/tar.m,
scripts/miscellaneous/tmpnam.m, scripts/miscellaneous/unpack.m,
scripts/miscellaneous/ver.m, scripts/miscellaneous/what.m,
scripts/miscellaneous/xor.m, scripts/miscellaneous/zip.m,
scripts/optimization/fminbnd.m, scripts/optimization/sqp.m,
scripts/path/private/getsavepath.m, scripts/path/savepath.m,
scripts/pkg/pkg.m, scripts/pkg/private/installed_packages.m,
scripts/plot/draw/plotyy.m, scripts/plot/draw/polar.m,
scripts/plot/draw/private/__quiver__.m,
scripts/plot/draw/private/__scatter__.m,
scripts/plot/draw/private/__stem__.m, scripts/plot/draw/surface.m,
scripts/plot/draw/surfnorm.m, scripts/plot/util/copyobj.m,
scripts/plot/util/hgload.m, scripts/plot/util/hgsave.m,
scripts/plot/util/isprop.m, scripts/plot/util/linkprop.m,
scripts/plot/util/private/__go_draw_axes__.m, scripts/set/setdiff.m,
scripts/set/union.m, scripts/signal/periodogram.m,
scripts/sparse/eigs.m, scripts/sparse/ilu.m, scripts/sparse/qmr.m,
scripts/sparse/sprand.m, scripts/sparse/sprandn.m,
scripts/specfun/beta.m, scripts/specfun/ellipke.m,
scripts/specfun/isprime.m, scripts/statistics/base/lscov.m,
scripts/testfun/__run_test_suite__.m, scripts/testfun/test.m:
Strip trailing whitespace.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Tue, 20 Jan 2015 10:29:54 -0500 |
parents | 0e1f5a750d00 |
children | 5a59c0e1203d |
line wrap: on
line source
## Copyright (C) 2007-2013 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} =} interp3 (@var{x}, @var{y}, @var{z}, @var{v}, @var{xi}, @var{yi}, @var{zi}) ## @deftypefnx {Function File} {@var{vi} =} interp3 (@var{v}, @var{xi}, @var{yi}, @var{zi}) ## @deftypefnx {Function File} {@var{vi} =} interp3 (@var{v}, @var{n}) ## @deftypefnx {Function File} {@var{vi} =} interp3 (@var{v}) ## @deftypefnx {Function File} {@var{vi} =} interp3 (@dots{}, @var{method}) ## @deftypefnx {Function File} {@var{vi} =} interp3 (@dots{}, @var{method}, @var{extrapval}) ## ## Three-dimensional interpolation. ## ## Interpolate reference data @var{x}, @var{y}, @var{z}, @var{v} to determine ## @var{vi} at the coordinates @var{xi}, @var{yi}, @var{zi}. The reference ## data @var{x}, @var{y}, @var{z} can be matrices, as returned by ## @code{meshgrid}, in which case the sizes of ## @var{x}, @var{y}, @var{z}, and @var{v} must be equal. If @var{x}, @var{y}, ## @var{z} are vectors describing a cubic grid then ## @code{length (@var{x}) == columns (@var{v})}, ## @code{length (@var{y}) == rows (@var{v})}, ## and @code{length (@var{z}) == size (@var{v}, 3)}. In either case the input ## data must be strictly monotonic. ## ## If called without @var{x}, @var{y}, @var{z}, and just a single reference ## data matrix @var{v}, the 3-D region ## @code{@var{x} = 1:columns (@var{v}), @var{y} = 1:rows (@var{v}), ## @var{z} = 1:size (@var{v}, 3)} is assumed. ## This saves memory if the grid is regular and the distance between points is ## not important. ## ## If called with a single reference data matrix @var{v} and a refinement ## value @var{n}, then perform interpolation over a 3-D grid where each original ## interval has been recursively subdivided @var{n} times. This results in ## @code{2^@var{n}-1} additional points for every interval in the original ## grid. If @var{n} is omitted a value of 1 is used. As an example, the ## interval [0,1] with @code{@var{n}==2} results in a refined interval with ## points at [0, 1/4, 1/2, 3/4, 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 ## ## If @var{extrapval} is a number, then replace values beyond the endpoints ## with that number. When unspecified, @var{extrapval} defaults to @code{NA}. ## Note that if @var{extrapval} is used, @var{method} must be specified as well. ## @seealso{interp1, interp2, interpn, meshgrid} ## @end deftypefn ## FIXME: Need to validate N argument (maybe change interpn). ## FIXME: Need to add support for 'pchip' method (maybe change interpn). ## FIXME: Need to add support for "extrap" string value (maybe change interpn). function vi = interp3 (varargin) method = "linear"; extrapval = NA; nargs = nargin; if (nargin < 1 || ! isnumeric (varargin{1})) print_usage (); endif if (ischar (varargin{end})) method = varargin{end}; nargs--; elseif (nargs > 1 && ischar (varargin{end-1})) ## FIXME: No support for "extrap" string if (! isnumeric (varargin{end}) || ! isscalar (varargin{end})) error ("interp3: EXTRAPVAL must be a numeric scalar"); endif extrapval = varargin{end}; method = varargin{end-1}; nargs -= 2; endif if (method(1) == "*") warning ("interp3: ignoring unsupported '*' flag to METHOD"); method(1) = []; endif if (nargs < 3) ## Calling form interp3 (v) OR interp3 (v, n) v = varargin{1}; if (ndims (v) != 3) error ("interp3: V must be a 3-D array of values"); endif n = varargin(2:nargs); v = permute (v, [2, 1, 3]); vi = ipermute (interpn (v, n{:}, method, extrapval), [2, 1, 3]); elseif (nargs == 4 && ! isvector (varargin{1})) ## Calling form interp3 (v, xi, yi, zi) v = varargin{1}; if (ndims (v) != 3) error ("interp3: V must be a 3-D array of values"); endif xi = varargin(2:4); if (any (! cellfun (@isvector, xi))) ## Meshgridded values rather than vectors if (! size_equal (xi{:})) error ("interp3: XI, YI, and ZI dimensions must be equal"); endif for i = 1 : 3 xi{i} = permute (xi{i}, [2, 1, 3]); endfor endif v = permute (v, [2, 1, 3]); vi = ipermute (interpn (v, xi{:}, method, extrapval), [2, 1, 3]); elseif (nargs == 7) ## Calling form interp3 (x, y, z, v, xi, yi, zi) v = varargin{4}; if (ndims (v) != 3) error ("interp3: V must be a 3-D array of values"); endif x = varargin(1:3); if (any (! cellfun (@isvector, x))) ## Meshgridded values rather than vectors if (! size_equal (x{:}, v)) error ("interp3: X, Y, Z, and V dimensions must be equal"); endif for i = 1 : 3 x{i} = permute (x{i}, [2, 1, 3]); endfor endif xi = varargin(5:7); if (any (! cellfun (@isvector, xi))) ## Meshgridded values rather than vectors if (! size_equal (xi{:})) error ("interp3: XI, YI, and ZI dimensions must be equal"); endif for i = 1 : 3 xi{i} = permute (xi{i}, [2, 1, 3]); endfor endif v = permute (v, [2, 1, 3]); vi = ipermute (interpn (x{:}, v, xi{:}, method, extrapval), [2, 1, 3]); else error ("interp3: wrong number or incorrectly formatted input arguments"); endif endfunction %% FIXME: Need some demo blocks here to show off the function like interp2.m. %!test # basic test %! x = y = z = -1:1; y = y + 2; %! f = @(x,y,z) x.^2 - y - z.^2; %! [xx, yy, zz] = meshgrid (x, y, z); %! v = f (xx,yy,zz); %! xi = yi = zi = -1:0.5:1; yi = yi + 2.1; %! [xxi, yyi, zzi] = meshgrid (xi, yi, zi); %! vi = interp3 (x, y, z, v, xxi, yyi, zzi); %! [xxi, yyi, zzi] = ndgrid (yi, xi, zi); %! vi2 = interpn (y, x, z, v, xxi, yyi, zzi); %! assert (vi, vi2, 10*eps); %!test # meshgridded xi, yi, zi %! x = z = 1:2; y = 1:3; %! v = ones ([3,2,2]); v(:,2,1) = [7;5;4]; v(:,1,2) = [2;3;5]; %! xi = zi = .6:1.6; yi = 1; %! [xxi3, yyi3, zzi3] = meshgrid (xi, yi, zi); %! [xxi, yyi, zzi] = ndgrid (yi, xi, zi); %! vi = interp3 (x, y, z, v, xxi3, yyi3, zzi3, "nearest"); %! vi2 = interpn (y, x, z, v, xxi, yyi, zzi, "nearest"); %! assert (vi, vi2); %!test # vector xi, yi, zi %! x = z = 1:2; y = 1:3; %! v = ones ([3,2,2]); v(:,2,1) = [7;5;4]; v(:,1,2) = [2;3;5]; %! xi = zi = .6:1.6; yi = 1; %! vi = interp3 (x, y, z, v, xi, yi, zi, "nearest"); %! vi2 = interpn (y, x, z, v, yi, xi, zi,"nearest"); %! assert (vi, vi2); %!test # vector xi+1 with extrap value %! x = z = 1:2; y = 1:3; %! v = ones ([3,2,2]); v(:,2,1) = [7;5;4]; v(:,1,2) = [2;3;5]; %! xi = zi = .6:1.6; yi = 1; %! vi = interp3 (x, y, z, v, xi+1, yi, zi, "nearest", 3); %! vi2 = interpn (y, x, z, v, yi, xi+1, zi, "nearest", 3); %! assert (vi, vi2); %!test # input value matrix--no x,y,z %! x = z = 1:2; y = 1:3; %! v = ones ([3,2,2]); v(:,2,1) = [7;5;4]; v(:,1,2) = [2;3;5]; %! xi = zi = .6:1.6; yi = 1; %! vi = interp3 (v, xi, yi, zi, "nearest"); %! vi2 = interpn (v, yi, xi, zi,"nearest"); %! assert (vi, vi2); %!test # input value matrix--no x,y,z, with extrap value %! x = z = 1:2; y = 1:3; %! v = ones ([3,2,2]); v(:,2,1) = [7;5;4]; v(:,1,2) = [2;3;5]; %! xi = zi = .6:1.6; yi = 1; %! vi = interp3 (v, xi, yi, zi, "nearest", 3); %! vi2 = interpn (v, yi, xi, zi, "nearest", 3); %! assert (vi, vi2); %!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 (interp3 (z), zout, tol) %!assert (interp3 (z, "linear"), zout, tol) %!assert (interp3 (z, "spline"), zout, tol) %% Test input validation %!error interp3 () %!error interp3 ({1}) %!error <EXTRAPVAL must be a numeric scalar> interp3 (1,2,3,4,1,2,3,"linear", {1}) %!error <EXTRAPVAL must be a numeric scalar> interp3 (1,2,3,4,1,2,3,"linear", ones (2,2)) %!warning <ignoring unsupported '\*' flag> interp3 (rand (3,3,3), 1, "*linear"); %!error <V must be a 3-D array> interp3 (rand (2,2)) %!error <V must be a 3-D array> interp3 (rand (2,2), 1,1,1) %!error <XI, YI, and ZI dimensions must be equal> interp3 (rand (2,2,2), 1,1, ones (2,2)) %!error <V must be a 3-D array> interp3 (1:2, 1:2, 1:2, rand (2,2), 1,1,1) %!error <X, Y, Z, and V dimensions must be equal> interp3 (ones(1,2,2), ones(2,2,2), ones(2,2,2), rand (2,2,2), 1,1,1) %!error <XI, YI, and ZI dimensions must be equal> interp3 (1:2, 1:2, 1:2, rand (2,2,2), 1,1, ones (2,2))