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update Octave Project Developers copyright for the new year
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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
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Add Paul Thomas to contributors.in.
author | John W. Eaton <jwe@octave.org> |
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date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | 7854d5752dd2 |
children |
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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} =} interp3 (@var{x}, @var{y}, @var{z}, @var{v}, @var{xi}, @var{yi}, @var{zi}) ## @deftypefnx {} {@var{vi} =} interp3 (@var{v}, @var{xi}, @var{yi}, @var{zi}) ## @deftypefnx {} {@var{vi} =} interp3 (@var{v}, @var{n}) ## @deftypefnx {} {@var{vi} =} interp3 (@var{v}) ## @deftypefnx {} {@var{vi} =} interp3 (@dots{}, @var{method}) ## @deftypefnx {} {@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{"cubic"} ## Piecewise cubic Hermite interpolating polynomial---shape-preserving ## interpolation with smooth first derivative (not implemented yet). ## ## @item @qcode{"spline"} ## Cubic spline interpolation---smooth first and second derivatives ## throughout the curve. ## @end table ## ## @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 @qcode{"NA"}. ## @seealso{interp1, interp2, interpn, meshgrid} ## @end deftypefn ## FIXME: Need to add support for 'cubic' method (maybe change interpn). function vi = interp3 (varargin) narginchk (1,9); method = "linear"; extrapval = []; nargs = nargin; if (! isnumeric (varargin{1})) print_usage (); endif if (nargs > 1 && ischar (varargin{end-1})) 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; elseif (ischar (varargin{end})) method = varargin{end}; nargs -= 1; endif if (method(1) == "*") warning ("interp3: ignoring unsupported '*' flag to METHOD"); method(1) = []; endif method = validatestring (method, {"nearest", "linear", "cubic", "spline"}); 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]); if (isempty (extrapval)) vi = interpn (v, n{:}, method); else vi = interpn (v, n{:}, method, extrapval); endif 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]); if (isempty (extrapval)) vi = interpn (v, xi{:}, method); else vi = interpn (v, xi{:}, method, extrapval); endif 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]); if (isempty (extrapval)) vi = interpn (x{:}, v, xi{:}, method); else vi = interpn (x{:}, v, xi{:}, method, extrapval); endif else error ("interp3: wrong number or incorrectly formatted input arguments"); endif if (! isvector (vi)) vi = ipermute (vi, [2, 1, 3]); 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); %!test # extrapolation %! X = [0,0.5,1]; Y=X; Z=X; %! V = zeros (3,3,3); %! V(:,:,1) = [1 3 5; 3 5 7; 5 7 9]; %! V(:,:,2) = V(:,:,1) + 2; %! V(:,:,3) = V(:,:,2) + 2; %! tol = 10 * eps; %! x = y = z = [-0.1,0,0.1]; %! assert (interp3 (X,Y,Z,V,x,y,z,"spline"), [-0.2, 1.0, 2.2], tol); %! assert (interp3 (X,Y,Z,V,x,y,z,"linear"), [NA, 1.0, 2.2], tol); %! assert (interp3 (X,Y,Z,V,x,y,z,"spline", 0), [0, 1.0, 2.2], tol); %! assert (interp3 (X,Y,Z,V,x,y,z,"linear", 0), [0, 1.0, 2.2], tol); %!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); %! endfor %! tol = 10 * eps; %! %!assert (interp3 (z), zout, tol) %!assert (interp3 (z, "linear"), zout, tol) %!assert (interp3 (z, "spline"), zout, tol) %!test <*57450> %! [x, y, z] = meshgrid (1:10); %! v = x; %! xi = yi = zi = linspace (1, 10, 20).'; %! vi = interp3 (x, y, z, v, xi, yi, zi); %! assert (size (vi), [20, 1]); ## Test input validation %!error <not enough input arguments> interp3 () %!error <Invalid call> 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 (ones (2,2)) %!error <V must be a 3-D array> interp3 (ones (2,2), 1,1,1) %!error <XI, YI, and ZI dimensions must be equal> interp3 (ones (2,2,2), 1,1, ones (2,2)) %!error <V must be a 3-D array> interp3 (1:2, 1:2, 1:2, ones (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), ones (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)) %!error <wrong number .* input arguments> interp3 (1:2, 1:2, 1:2)