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view scripts/general/gradient.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> |
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date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | 7854d5752dd2 |
children |
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######################################################################## ## ## Copyright (C) 2000-2022 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{dx} =} gradient (@var{m}) ## @deftypefnx {} {[@var{dx}, @var{dy}, @var{dz}, @dots{}] =} gradient (@var{m}) ## @deftypefnx {} {[@dots{}] =} gradient (@var{m}, @var{s}) ## @deftypefnx {} {[@dots{}] =} gradient (@var{m}, @var{x}, @var{y}, @var{z}, @dots{}) ## @deftypefnx {} {[@dots{}] =} gradient (@var{f}, @var{x0}) ## @deftypefnx {} {[@dots{}] =} gradient (@var{f}, @var{x0}, @var{s}) ## @deftypefnx {} {[@dots{}] =} gradient (@var{f}, @var{x0}, @var{x}, @var{y}, @dots{}) ## ## Calculate the gradient of sampled data or a function. ## ## If @var{m} is a vector, calculate the one-dimensional gradient of @var{m}. ## If @var{m} is a matrix the gradient is calculated for each dimension. ## ## @code{[@var{dx}, @var{dy}] = gradient (@var{m})} calculates the ## one-dimensional gradient for @var{x} and @var{y} direction if @var{m} is a ## matrix. Additional return arguments can be use for multi-dimensional ## matrices. ## ## A constant spacing between two points can be provided by the @var{s} ## parameter. If @var{s} is a scalar, it is assumed to be the spacing for all ## dimensions. Otherwise, separate values of the spacing can be supplied by ## the @var{x}, @dots{} arguments. Scalar values specify an equidistant ## spacing. Vector values for the @var{x}, @dots{} arguments specify the ## coordinate for that dimension. The length must match their respective ## dimension of @var{m}. ## ## At boundary points a linear extrapolation is applied. Interior points ## are calculated with the first approximation of the numerical gradient ## ## @example ## y'(i) = 1/(x(i+1)-x(i-1)) * (y(i-1)-y(i+1)). ## @end example ## ## If the first argument @var{f} is a function handle, the gradient of the ## function at the points in @var{x0} is approximated using central difference. ## For example, @code{gradient (@@cos, 0)} approximates the gradient of the ## cosine function in the point @math{x0 = 0}. As with sampled data, the ## spacing values between the points from which the gradient is estimated can ## be set via the @var{s} or @var{dx}, @var{dy}, @dots{} arguments. By default ## a spacing of 1 is used. ## @seealso{diff, del2} ## @end deftypefn function varargout = gradient (m, varargin) if (nargin < 1) print_usage (); endif nargout_with_ans = max (1,nargout); if (isnumeric (m)) [varargout{1:nargout_with_ans}] = matrix_gradient (m, varargin{:}); elseif (is_function_handle (m)) [varargout{1:nargout_with_ans}] = handle_gradient (m, varargin{:}); elseif (ischar (m)) [varargout{1:nargout_with_ans}] = handle_gradient (str2func (m), ... varargin{:}); else error ("gradient: first input must be an array or a function"); endif endfunction function varargout = matrix_gradient (m, varargin) transposed = false; if (isvector (m)) ## make a row vector. transposed = (columns (m) == 1); m = m(:).'; endif nd = ndims (m); sz = size (m); if (length (sz) > 1) tmp = sz(1); sz(1) = sz(2); sz(2) = tmp; endif if (nargin > 2 && nargin != nd + 1) print_usage ("gradient"); endif ## cell d stores a spacing vector for each dimension d = cell (1, nd); if (nargin == 1) ## no spacing given - assume 1.0 for all dimensions for i = 1:nd d{i} = ones (sz(i) - 1, 1); endfor elseif (nargin == 2) if (isscalar (varargin{1})) ## single scalar value for all dimensions for i = 1:nd d{i} = varargin{1} * ones (sz(i) - 1, 1); endfor else ## vector for one-dimensional derivative d{1} = diff (varargin{1}(:)); endif else ## have spacing value for each dimension if (length (varargin) != nd) error ("gradient: dimensions and number of spacing values do not match"); endif for i = 1:nd if (isscalar (varargin{i})) d{i} = varargin{i} * ones (sz(i) - 1, 1); else d{i} = diff (varargin{i}(:)); endif endfor endif m = shiftdim (m, 1); for i = 1:min (nd, nargout) mr = rows (m); mc = numel (m) / mr; Y = zeros (size (m), class (m)); if (mr > 1) ## Top and bottom boundary. Y(1,:) = diff (m(1:2, :)) / d{i}(1); Y(mr,:) = diff (m(mr-1:mr, :) / d{i}(mr - 1)); endif if (mr > 2) ## Interior points. Y(2:mr-1,:) = ((m(3:mr,:) - m(1:mr-2,:)) ./ kron (d{i}(1:mr-2) + d{i}(2:mr-1), ones (1, mc))); endif ## turn multi-dimensional matrix in a way, that gradient ## along x-direction is calculated first then y, z, ... if (i == 1) varargout{i} = shiftdim (Y, nd - 1); m = shiftdim (m, nd - 1); elseif (i == 2) varargout{i} = Y; m = shiftdim (m, 2); else varargout{i} = shiftdim (Y, nd - i + 1); m = shiftdim (m, 1); endif endfor if (transposed) varargout{1} = varargout{1}.'; endif endfunction function varargout = handle_gradient (f, p0, varargin) ## Input checking p0_size = size (p0); if (numel (p0_size) != 2) error ("gradient: the second input argument should either be a vector or a matrix"); endif if (any (p0_size == 1)) p0 = p0(:); dim = 1; num_points = numel (p0); else num_points = p0_size (1); dim = p0_size (2); endif if (length (varargin) == 0) delta = 1; elseif (length (varargin) == 1 || length (varargin) == dim) try delta = [varargin{:}]; catch error ("gradient: spacing parameters must be scalars or a vector"); end_try_catch else error ("gradient: incorrect number of spacing parameters"); endif if (isscalar (delta)) delta = repmat (delta, 1, dim); elseif (! isvector (delta)) error ("gradient: spacing values must be scalars or a vector"); endif ## Calculate the gradient p0 = mat2cell (p0, num_points, ones (1, dim)); varargout = cell (1, dim); for d = 1:dim s = delta(d); df_dx = (f (p0{1:d-1}, p0{d}+s, p0{d+1:end}) - f (p0{1:d-1}, p0{d}-s, p0{d+1:end})) ./ (2*s); if (dim == 1) varargout{d} = reshape (df_dx, p0_size); else varargout{d} = df_dx; endif endfor endfunction %!test %! data = [1, 2, 4, 2]; %! dx = gradient (data); %! dx2 = gradient (data, 0.25); %! dx3 = gradient (data, [0.25, 0.5, 1, 3]); %! assert (dx, [1, 3/2, 0, -2]); %! assert (dx2, [4, 6, 0, -8]); %! assert (dx3, [4, 4, 0, -1]); %! assert (size_equal (data, dx)); %!test %! [Y,X,Z,U] = ndgrid (2:2:8,1:5,4:4:12,3:5:30); %! [dX,dY,dZ,dU] = gradient (X); %! assert (all (dX(:) == 1)); %! assert (all (dY(:) == 0)); %! assert (all (dZ(:) == 0)); %! assert (all (dU(:) == 0)); %! [dX,dY,dZ,dU] = gradient (Y); %! assert (all (dX(:) == 0)); %! assert (all (dY(:) == 2)); %! assert (all (dZ(:) == 0)); %! assert (all (dU(:) == 0)); %! [dX,dY,dZ,dU] = gradient (Z); %! assert (all (dX(:) == 0)); %! assert (all (dY(:) == 0)); %! assert (all (dZ(:) == 4)); %! assert (all (dU(:) == 0)); %! [dX,dY,dZ,dU] = gradient (U); %! assert (all (dX(:) == 0)); %! assert (all (dY(:) == 0)); %! assert (all (dZ(:) == 0)); %! assert (all (dU(:) == 5)); %! assert (size_equal (dX, dY, dZ, dU, X, Y, Z, U)); %! [dX,dY,dZ,dU] = gradient (U, 5.0); %! assert (all (dU(:) == 1)); %! [dX,dY,dZ,dU] = gradient (U, 1.0, 2.0, 3.0, 2.5); %! assert (all (dU(:) == 2)); %!test %! [Y,X,Z,U] = ndgrid (2:2:8,1:5,4:4:12,3:5:30); %! [dX,dY,dZ,dU] = gradient (X+j*X); %! assert (all (dX(:) == 1+1j)); %! assert (all (dY(:) == 0)); %! assert (all (dZ(:) == 0)); %! assert (all (dU(:) == 0)); %! [dX,dY,dZ,dU] = gradient (Y-j*Y); %! assert (all (dX(:) == 0)); %! assert (all (dY(:) == 2-j*2)); %! assert (all (dZ(:) == 0)); %! assert (all (dU(:) == 0)); %! [dX,dY,dZ,dU] = gradient (Z+j*1); %! assert (all (dX(:) == 0)); %! assert (all (dY(:) == 0)); %! assert (all (dZ(:) == 4)); %! assert (all (dU(:) == 0)); %! [dX,dY,dZ,dU] = gradient (U-j*1); %! assert (all (dX(:) == 0)); %! assert (all (dY(:) == 0)); %! assert (all (dZ(:) == 0)); %! assert (all (dU(:) == 5)); %! assert (size_equal (dX, dY, dZ, dU, X, Y, Z, U)); %! [dX,dY,dZ,dU] = gradient (U, 5.0); %! assert (all (dU(:) == 1)); %! [dX,dY,dZ,dU] = gradient (U, 1.0, 2.0, 3.0, 2.5); %! assert (all (dU(:) == 2)); %!test %! x = 0:10; %! f = @cos; %! df_dx = @(x) -sin (x); %! assert (gradient (f, x), df_dx (x), 0.2); %! assert (gradient (f, x, 0.5), df_dx (x), 0.1); %!test %! xy = reshape (1:10, 5, 2); %! f = @(x,y) sin (x) .* cos (y); %! df_dx = @(x, y) cos (x) .* cos (y); %! df_dy = @(x, y) -sin (x) .* sin (y); %! [dx, dy] = gradient (f, xy); %! assert (dx, df_dx (xy (:, 1), xy (:, 2)), 0.1); %! assert (dy, df_dy (xy (:, 1), xy (:, 2)), 0.1);