octave-nkf: scripts/general/gradient.m annotate

annotate scripts/general/gradient.m @ 9015:06cebb6c5dde

Fix calculation of gradient for dims>2. Vector arguments are interpreted as coordinate now. Tests added.

author	Kai Habel <kai.habel@gmx.de>
date	Wed, 25 Mar 2009 14:33:44 -0400
parents	eb63fbe60fab
children	1bf0ce0930be

rev	line source
8920 eb63fbe60fab update copyright notices John W. Eaton <jwe@octave.org> parents: 8601 diff changeset	1 ## Copyright (C) 2000, 2006, 2007, 2008, 2009 Kai Habel
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	2 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	3 ## This file is part of Octave.
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	4 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	6 ## under the terms of the GNU General Public License as published by
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7001 diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7001 diff changeset	8 ## your option) any later version.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	9 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	13 ## General Public License for more details.
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	14 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	15 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7001 diff changeset	16 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7001 diff changeset	17 ## <http://www.gnu.org/licenses/>.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	18
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	19 ## -- texinfo --
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	20 ## @deftypefn {Function File} {@var{dx} =} gradient (@var{m})
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	21 ## @deftypefnx {Function File} {[@var{dx}, @var{dy}, @var{dz}, @dots{}] =} gradient (@var{m})
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	22 ## @deftypefnx {Function File} {[@dots{}] =} gradient (@var{m}, @var{s})
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	23 ## @deftypefnx {Function File} {[@dots{}] =} gradient (@var{m}, @var{x}, @var{y}, @var{z}, @dots{})
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	24 ## @deftypefnx {Function File} {[@dots{}] =} gradient (@var{f}, @var{x0})
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	25 ## @deftypefnx {Function File} {[@dots{}] =} gradient (@var{f}, @var{x0}, @var{s})
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	26 ## @deftypefnx {Function File} {[@dots{}] =} gradient (@var{f}, @var{x0}, @var{x}, @var{y}, @dots{})
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	27 ##
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	28 ## Calculate the gradient of sampled data, or of a function. If @var{m}
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	29 ## is a vector, calculate the one dimensional gradient of @var{m}. If
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	30 ## @var{m} is a matrix the gradient is calculated for each dimension.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	31 ##
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	32 ## @code{[@var{dx}, @var{dy}] = gradient (@var{m})} calculates the one
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	33 ## dimensional gradient for @var{x} and @var{y} direction if @var{m} is a
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	34 ## matrix. Additional return arguments can be use for multi-dimensional
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	35 ## matrices.
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	36 ##
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	37 ## A constant spacing between two points can be provided by the
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	38 ## @var{s} parameter. If @var{s} is a scalar, it is assumed to be the spacing
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	39 ## for all dimensions.
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	40 ## Otherwise, separate values of the spacing can be supplied by
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	41 ## the @var{x}, @dots{} arguments. Scalar values specify an equidistant spacing.
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	42 ## Vector values for the @var{x}, @dots{} arguments specify the coordinate for that
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	43 ## dimension. The length must match their respective dimension of @var{m}.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	44 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	45 ## At boundary points a linear extrapolation is applied. Interior points
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	46 ## are calculated with the first approximation of the numerical gradient
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	47 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	48 ## @example
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	49 ## y'(i) = 1/(x(i+1)-x(i-1)) * (y(i-1)-y(i+1)).
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	50 ## @end example
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	51 ##
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	52 ## If the first argument @var{f} is a function handle, the gradient of the
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	53 ## function at the points in @var{x0} is approximated using central
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	54 ## difference. For example, @code{gradient (@@cos, 0)} approximates the
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	55 ## gradient of the cosine function in the point @math{x0 = 0}. As with
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	56 ## sampled data, the spacing values between the points from which the
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	57 ## gradient is estimated can be set via the @var{s} or @var{dx},
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	58 ## @var{dy}, @dots{} arguments. By default a spacing of 1 is used.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	59 ## @end deftypefn
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	60
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	61 ## Author: Kai Habel <kai.habel@gmx.de>
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	62 ## Modified: David Bateman <dbateman@free.fr> Added NDArray support
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	63
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	64 function varargout = gradient (m, varargin)
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	65
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	66 if (nargin < 1)
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	67 print_usage ()
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	68 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	69
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	70 nargout_with_ans = max(1,nargout);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	71 if (ismatrix (m))
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	72 [varargout{1:nargout_with_ans}] = matrix_gradient (m, varargin{:});
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	73 elseif (isa (m, "function_handle"))
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	74 [varargout{1:nargout_with_ans}] = handle_gradient (m, varargin{:});
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	75 elseif (ischar(m))
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	76 [varargout{1:nargout_with_ans}] = handle_gradient (str2func (m), varargin{:});
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	77 else
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	78 error ("gradient: first input must be an array or a function");
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	79 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	80
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	81 endfunction
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	82
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	83 function varargout = matrix_gradient (m, varargin)
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	84 transposed = false;
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	85 if (isvector (m))
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	86 ## make a row vector.
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	87 transposed = (size (m, 2) == 1);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	88 m = m(:)';
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	89 endif
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	90
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	91 nd = ndims (m);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	92 sz = size (m);
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	93 if (length(sz) > 1)
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	94 tmp = sz(1); sz(1) = sz(2); sz(2) = tmp;
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	95 endif
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	96
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	97 if (nargin > 2 && nargin != nd + 1)
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	98 print_usage ()
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	99 endif
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	100
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	101 ## cell d stores a spacing vector for each dimension
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	102 d = cell (1, nd);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	103 if (nargin == 1)
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	104 ## no spacing given - assume 1.0 for all dimensions
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7650 diff changeset	105 for i = 1:nd
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	106 d{i} = ones (sz(i) - 1, 1);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	107 endfor
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	108 elseif (nargin == 2)
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	109 if (isscalar (varargin{1}))
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	110 ## single scalar value for all dimensions
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	111 for i = 1:nd
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	112 d{i} = varargin{1} * ones (sz(i) - 1, 1);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	113 endfor
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	114 else
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	115 ## vector for one-dimensional derivative
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	116 d{1} = diff (varargin{1}(:));
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	117 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	118 else
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	119 ## have spacing value for each dimension
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	120 if (length(varargin) != nd)
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	121 error ("dimensions and number of spacing values do not match.");
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	122 end
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7650 diff changeset	123 for i = 1:nd
7120 a2174fb073d4 [project @ 2007-11-07 21:26:43 by jwe] jwe parents: 7017 diff changeset	124 if (isscalar (varargin{i}))
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	125 d{i} = varargin{i} * ones (sz(i) - 1, 1);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	126 else
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	127 d{i} = diff (varargin{i}(:));
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	128 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	129 endfor
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	130 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	131
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	132 m = shiftdim (m, 1);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	133 for i = 1:min (nd, nargout)
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	134 mr = rows (m);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	135 mc = numel (m) / mr;
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	136 Y = zeros (size (m), class (m));
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	137
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	138 if (mr > 1)
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7650 diff changeset	139 ## Top and bottom boundary.
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	140 Y(1,:) = diff (m(1:2, :)) / d{i}(1);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	141 Y(mr,:) = diff (m(mr-1:mr, :) / d{i}(mr - 1));
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	142 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	143
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	144 if (mr > 2)
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7650 diff changeset	145 ## Interior points.
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	146 Y(2:mr-1,:) = ((m(3:mr,:) - m(1:mr-2,:))
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	147 ./ kron (d{i}(1:mr-2) + d{i}(2:mr-1), ones (1, mc)));
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	148 endif
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	149
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	150 ## turn multi-dimensional matrix in a way, that gradient
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	151 ## along x-direction is calculated first then y, z, ...
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	152
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	153 if (i == 1)
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	154 varargout{i} = shiftdim (Y, nd - 1);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	155 m = shiftdim (m, nd - 1);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	156 elseif (i == 2)
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	157 varargout{i} = Y;
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	158 m = shiftdim (m, 2);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	159 else
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	160 varargout{i} = shiftdim (Y, nd - i + 1);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	161 m = shiftdim (m, 1);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	162 endif
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	163 endfor
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	164
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	165 if (transposed)
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	166 varargout{1} = varargout{1}.';
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	167 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	168 endfunction
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	169
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	170 function varargout = handle_gradient (f, p0, varargin)
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	171 ## Input checking
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	172 p0_size = size (p0);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	173
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	174 if (numel (p0_size) != 2)
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	175 error ("gradient: the second input argument should either be a vector or a matrix");
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	176 endif
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	177
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	178 if (any (p0_size == 1))
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	179 p0 = p0 (:);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	180 dim = 1;
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	181 num_points = numel (p0);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	182 else
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	183 num_points = p0_size (1);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	184 dim = p0_size (2);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	185 endif
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	186
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	187 if (length (varargin) == 0)
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	188 delta = 1;
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	189 elseif (length (varargin) == 1 \|\| length (varargin) == dim)
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	190 try
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	191 delta = [varargin{:}];
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	192 catch
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	193 error ("gradient: spacing parameters must be scalars or a vector");
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	194 end_try_catch
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	195 else
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	196 error ("gradient: incorrect number of spacing parameters");
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	197 endif
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	198
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	199 if (isscalar (delta))
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	200 delta = repmat (delta, 1, dim);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	201 elseif (!isvector (delta))
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	202 error ("gradient: spacing values must be scalars or a vector");
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	203 endif
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	204
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	205 ## Calculate the gradient
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	206 p0 = mat2cell (p0, num_points, ones (1, dim));
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	207 varargout = cell (1, dim);
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	208 for d = 1:dim
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	209 s = delta (d);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	210 df_dx = (f (p0{1:d-1}, p0{d}+s, p0{d+1:end})
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	211 - f (p0{1:d-1}, p0{d}-s, p0{d+1:end})) ./ (2*s);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	212 if (dim == 1)
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	213 varargout{d} = reshape (df_dx, p0_size);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	214 else
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	215 varargout{d} = df_dx;
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	216 endif
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	217 endfor
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	218 endfunction
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	219
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	220 %!test
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	221 %! data = [1, 2, 4, 2];
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	222 %! dx = gradient (data);
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	223 %! dx2 = gradient (data, 0.25);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	224 %! dx3 = gradient (data, [0.25, 0.5, 1, 3]);
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	225 %! assert (dx, [1, 3/2, 0, -2]);
9015 06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	226 %! assert (dx2, [4, 6, 0, -8]);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	227 %! assert (dx3, [4, 4, 0, -1]);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	228 %! assert (size_equal(data, dx));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	229
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	230 %!test
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	231 %! [Y,X,Z,U] = ndgrid (2:2:8,1:5,4:4:12,3:5:30);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	232 %! [dX,dY,dZ,dU] = gradient (X);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	233 %! assert (all(dX(:)==1));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	234 %! assert (all(dY(:)==0));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	235 %! assert (all(dZ(:)==0));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	236 %! assert (all(dU(:)==0));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	237 %! [dX,dY,dZ,dU] = gradient (Y);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	238 %! assert (all(dX(:)==0));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	239 %! assert (all(dY(:)==2));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	240 %! assert (all(dZ(:)==0));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	241 %! assert (all(dU(:)==0));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	242 %! [dX,dY,dZ,dU] = gradient (Z);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	243 %! assert (all(dX(:)==0));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	244 %! assert (all(dY(:)==0));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	245 %! assert (all(dZ(:)==4));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	246 %! assert (all(dU(:)==0));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	247 %! [dX,dY,dZ,dU] = gradient (U);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	248 %! assert (all(dX(:)==0));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	249 %! assert (all(dY(:)==0));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	250 %! assert (all(dZ(:)==0));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	251 %! assert (all(dU(:)==5));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	252 %! assert (size_equal(dX, dY, dZ, dU, X, Y, Z, U));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	253 %! [dX,dY,dZ,dU] = gradient (U, 5.0);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	254 %! assert (all(dU(:)==1));
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	255 %! [dX,dY,dZ,dU] = gradient (U, 1.0, 2.0, 3.0, 2.5);
06cebb6c5dde Fix calculation of gradient for dims>2. Vector arguments are interpreted as Kai Habel <kai.habel@gmx.de> parents: 8920 diff changeset	256 %! assert (all(dU(:)==2));
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	257
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	258 %!test
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	259 %! x = 0:10;
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	260 %! f = @cos;
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	261 %! df_dx = @(x) -sin (x);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	262 %! assert (gradient (f, x), df_dx (x), 0.2);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	263 %! assert (gradient (f, x, 0.5), df_dx (x), 0.1);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	264
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	265 %!test
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	266 %! xy = reshape (1:10, 5, 2);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	267 %! f = @(x,y) sin (x) .* cos (y);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	268 %! df_dx = @(x, y) cos (x) .* cos (y);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	269 %! df_dy = @(x, y) -sin (x) .* sin (y);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	270 %! [dx, dy] = gradient (f, xy);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	271 %! assert (dx, df_dx (xy (:, 1), xy (:, 2)), 0.1)
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	272 %! assert (dy, df_dy (xy (:, 1), xy (:, 2)), 0.1)
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	273

Mercurial > octave-nkf

annotate scripts/general/gradient.m @ 9015:06cebb6c5dde