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view scripts/general/gradient.m @ 27918:b442ec6dda5c
use centralized file for copyright info for individual contributors
* COPYRIGHT.md: New file.
* In most other files, use "Copyright (C) YYYY-YYYY The Octave Project
Developers" instead of tracking individual names in separate source
files. The motivation is to reduce the effort required to update the
notices each year.
Until now, the Octave source files contained copyright notices that
list individual contributors. I adopted these file-scope copyright
notices because that is what everyone was doing 30 years ago in the
days before distributed version control systems. But now, with many
contributors and modern version control systems, having these
file-scope copyright notices causes trouble when we update copyright
years or refactor code.
Over time, the file-scope copyright notices may become outdated as new
contributions are made or code is moved from one file to
another. Sometimes people contribute significant patches but do not
add a line claiming copyright. Other times, people add a copyright
notice for their contribution but then a later refactoring moves part
or all of their contribution to another file and the notice is not
moved with the code. As a practical matter, moving such notices is
difficult -- determining what parts are due to a particular
contributor requires a time-consuming search through the project
history. Even managing the yearly update of copyright years is
problematic. We have some contributors who are no longer
living. Should we update the copyright dates for their contributions
when we release new versions? Probably not, but we do still want to
claim copyright for the project as a whole.
To minimize the difficulty of maintaining the copyright notices, I
would like to change Octave's sources to use what is described here:
https://softwarefreedom.org/resources/2012/ManagingCopyrightInformation.html
in the section "Maintaining centralized copyright notices":
The centralized notice approach consolidates all copyright
notices in a single location, usually a top-level file.
This file should contain all of the copyright notices
provided project contributors, unless the contribution was
clearly insignificant. It may also credit -- without a copyright
notice -- anyone who helped with the project but did not
contribute code or other copyrighted material.
This approach captures less information about contributions
within individual files, recognizing that the DVCS is better
equipped to record those details. As we mentioned before, it
does have one disadvantage as compared to the file-scope
approach: if a single file is separated from the distribution,
the recipient won't see the contributors' copyright notices.
But this can be easily remedied by including a single
copyright notice in each file's header, pointing to the
top-level file:
Copyright YYYY-YYYY The Octave Project Developers
See the COPYRIGHT file at the top-level directory
of this distribution or at https://octave.org/COPYRIGHT.html.
followed by the usual GPL copyright statement.
For more background, see the discussion here:
https://lists.gnu.org/archive/html/octave-maintainers/2020-01/msg00009.html
Most files in the following directories have been skipped intentinally
in this changeset:
doc
libgui/qterminal
liboctave/external
m4
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Mon, 06 Jan 2020 15:38:17 -0500 |
parents | f2bb4f2093b9 |
children | 1891570abac8 |
line wrap: on
line source
## Copyright (C) 2000-2019 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this distribution ## or <https://octave.org/COPYRIGHT.html/>. ## ## ## 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 ## 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 (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);