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

annotate scripts/general/gradient.m @ 8920:eb63fbe60fab

update copyright notices

author	John W. Eaton <jwe@octave.org>
date	Sat, 07 Mar 2009 10:41:27 -0500
parents	b297b86f4ad9
children	06cebb6c5dde

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 --
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	20 ## @deftypefn {Function File} {@var{x} =} gradient (@var{m})
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	21 ## @deftypefnx {Function File} {[@var{x}, @var{y}, @dots{}] =} gradient (@var{m})
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})
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	23 ## @deftypefnx {Function File} {[@dots{}] =} gradient (@var{m}, @var{dx}, @var{dy}, @dots{})
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})
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	26 ## @deftypefnx {Function File} {[@dots{}] =} gradient (@var{f}, @var{x0}, @var{dx}, @var{dy}, @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
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	30 ## @var{m} is a matrix the gradient is calculated for each row.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	31 ##
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	32 ## @code{[@var{x}, @var{y}] = gradient (@var{m})} calculates the one
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	33 ## dimensional gradient for each direction if @var{m} 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 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	37 ## Spacing values between two points can be provided by the
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	38 ## @var{dx}, @var{dy} or @var{h} parameters. If @var{h} is supplied it
7001 8b0cfeb06365 [project @ 2007-10-10 18:02:59 by jwe] jwe parents: 5838 diff changeset	39 ## is assumed to be the spacing in all directions. Otherwise, separate
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	40 ## values of the spacing can be supplied by the @var{dx}, etc variables.
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	41 ## A scalar value specifies an equidistant spacing, while a vector value
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	42 ## can be used to specify a variable spacing. The length must match
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	43 ## 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
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	49 ## y'(i) = 1/(x(i+1)-x(i-1)) *(y(i-1)-y(i+1)).
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))
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	86 ## make a column vector.
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);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	93 if (nargin > 2 && nargin != nd + 1)
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	94 print_usage ()
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	95 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	96
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	97 d = cell (1, nd);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	98 if (nargin == 1)
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7650 diff changeset	99 for i = 1:nd
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	100 d{i} = ones (sz(i), 1);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	101 endfor
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	102 elseif (nargin == 2)
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	103 if (isscalar (varargin{1}))
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	104 for i = 1:nd
376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	105 d{i} = varargin{1} * ones (sz(i), 1);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	106 endfor
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	107 else
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	108 for i = 1:nd
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	109 d{i} = varargin{1};
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	110 endfor
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	111 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	112 else
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7650 diff changeset	113 for i = 1:nd
7120 a2174fb073d4 [project @ 2007-11-07 21:26:43 by jwe] jwe parents: 7017 diff changeset	114 if (isscalar (varargin{i}))
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7650 diff changeset	115 ## Why the hell did Matlab decide to swap these two values?
7120 a2174fb073d4 [project @ 2007-11-07 21:26:43 by jwe] jwe parents: 7017 diff changeset	116 if (i == 1)
a2174fb073d4 [project @ 2007-11-07 21:26:43 by jwe] jwe parents: 7017 diff changeset	117 d{2} = varargin{1} * ones (sz(2), 1);
a2174fb073d4 [project @ 2007-11-07 21:26:43 by jwe] jwe parents: 7017 diff changeset	118 elseif (i == 2)
a2174fb073d4 [project @ 2007-11-07 21:26:43 by jwe] jwe parents: 7017 diff changeset	119 d{1} = varargin{2} * ones (sz(1), 1);
a2174fb073d4 [project @ 2007-11-07 21:26:43 by jwe] jwe parents: 7017 diff changeset	120 else
a2174fb073d4 [project @ 2007-11-07 21:26:43 by jwe] jwe parents: 7017 diff changeset	121 d{i} = varargin{i} * ones (sz(i), 1);
a2174fb073d4 [project @ 2007-11-07 21:26:43 by jwe] jwe parents: 7017 diff changeset	122 endif
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	123 else
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7650 diff changeset	124 ## Why the hell did Matlab decide to swap these two values?
7120 a2174fb073d4 [project @ 2007-11-07 21:26:43 by jwe] jwe parents: 7017 diff changeset	125 if (i == 1)
a2174fb073d4 [project @ 2007-11-07 21:26:43 by jwe] jwe parents: 7017 diff changeset	126 d{2} = varargin{1};
a2174fb073d4 [project @ 2007-11-07 21:26:43 by jwe] jwe parents: 7017 diff changeset	127 elseif (i == 2)
a2174fb073d4 [project @ 2007-11-07 21:26:43 by jwe] jwe parents: 7017 diff changeset	128 d{1} = varargin{2};
a2174fb073d4 [project @ 2007-11-07 21:26:43 by jwe] jwe parents: 7017 diff changeset	129 else
a2174fb073d4 [project @ 2007-11-07 21:26:43 by jwe] jwe parents: 7017 diff changeset	130 d{i} = varargin{i};
a2174fb073d4 [project @ 2007-11-07 21:26:43 by jwe] jwe parents: 7017 diff changeset	131 endif
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	132 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	133 endfor
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	134 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	135
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	136 for i = 1:max (2, min (nd, nargout))
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	137 mr = sz(i);
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	138 mc = prod ([sz(1:i-1), sz(i+1:nd)]);
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	139 Y = zeros (size (m), class (m));
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	140
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	141 if (mr > 1)
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7650 diff changeset	142 ## Top and bottom boundary.
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	143 Y(1,:) = diff (m(1:2,:)) / d{i}(1);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	144 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	145 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	146
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	147 if (mr > 2)
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7650 diff changeset	148 ## Interior points.
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	149 Y(2:mr-1,:) = ((m(3:mr,:) - m(1:mr-2,:))
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	150 ./ 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	151 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	152 varargout{i} = ipermute (Y, [i:nd,1:i-1]);
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	153 m = permute (m, [2:nd,1]);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	154 endfor
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	155
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7650 diff changeset	156 ## Why the hell did Matlab decide to swap these two values?
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	157 tmp = varargout{1};
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	158 varargout{1} = varargout{2};
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	159 varargout{2} = tmp;
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	160
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	161 if (transposed)
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	162 varargout{1} = varargout{1}.';
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	163 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	164 endfunction
8601 b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	165
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	166 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	167 ## Input checking
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	168 p0_size = size (p0);
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 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	171 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	172 endif
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 (any (p0_size == 1))
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	175 p0 = p0 (:);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	176 dim = 1;
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	177 num_points = numel (p0);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	178 else
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	179 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	180 dim = p0_size (2);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	181 endif
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	182
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	183 if (length (varargin) == 0)
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	184 delta = 1;
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	185 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	186 try
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	187 delta = [varargin{:}];
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	188 catch
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	189 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	190 end_try_catch
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	191 else
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	192 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	193 endif
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	194
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	195 if (isscalar (delta))
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	196 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	197 elseif (!isvector (delta))
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	198 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	199 endif
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	200
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	201 ## Calculate the gradient
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	202 p0 = mat2cell (p0, num_points, ones (1, dim));
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	203 varargout = cell (1,dim);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	204 for d = 1:dim
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	205 s = delta (d);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	206 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	207 - 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	208 if (dim == 1)
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	209 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	210 else
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	211 varargout{d} = df_dx;
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	212 endif
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	213 endfor
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	214 endfunction
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	215
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	216 %!test
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	217 %! 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	218 %! dx = gradient (data);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	219 %! assert (dx, [1, 3/2, 0, -2]);
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	220
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	221 %!test
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	222 %! x = 0:10;
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	223 %! f = @cos;
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	224 %! 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	225 %! 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	226 %! 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	227
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	228 %!test
b297b86f4ad9 gradient.m: Add support for computing the gradient of a function handle sh@sh-t400 parents: 8507 diff changeset	229 %! 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	230 %! 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	231 %! 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	232 %! 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	233 %! [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	234 %! 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	235 %! 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	236

Mercurial > octave-antonio

annotate scripts/general/gradient.m @ 8920:eb63fbe60fab