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Use Octave coding conventions in all m-file %!test blocks
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Use Octave coding conventions in all m-file %!test blocks
author | Rik <octave@nomad.inbox5.com> |
---|---|
date | Mon, 13 Feb 2012 07:29:44 -0800 |
parents | 72c96de7a403 |
children | 5d3a684236b0 |
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## Copyright (C) 2000-2012 Kai Habel ## ## 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{dx} =} gradient (@var{m}) ## @deftypefnx {Function File} {[@var{dx}, @var{dy}, @var{dz}, @dots{}] =} gradient (@var{m}) ## @deftypefnx {Function File} {[@dots{}] =} gradient (@var{m}, @var{s}) ## @deftypefnx {Function File} {[@dots{}] =} gradient (@var{m}, @var{x}, @var{y}, @var{z}, @dots{}) ## @deftypefnx {Function File} {[@dots{}] =} gradient (@var{f}, @var{x0}) ## @deftypefnx {Function File} {[@dots{}] =} gradient (@var{f}, @var{x0}, @var{s}) ## @deftypefnx {Function File} {[@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 ## Author: Kai Habel <kai.habel@gmx.de> ## Modified: David Bateman <dbateman@free.fr> Added NDArray support function varargout = gradient (m, varargin) if (nargin < 1) print_usage (); endif nargout_with_ans = max(1,nargout); if (ismatrix (m)) [varargout{1:nargout_with_ans}] = matrix_gradient (m, varargin{:}); elseif (isa (m, "function_handle")) [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 = (size (m, 2) == 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 (); 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)