X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Foptim-1.2.0%2Fnmsmax.m;fp=octave_packages%2Foptim-1.2.0%2Fnmsmax.m;h=b221a967832fe9026f5273a660bbea828304533a;hp=0000000000000000000000000000000000000000;hb=c880e8788dfc484bf23ce13fa2787f2c6bca4863;hpb=1705066eceaaea976f010f669ce8e972f3734b05 diff --git a/octave_packages/optim-1.2.0/nmsmax.m b/octave_packages/optim-1.2.0/nmsmax.m new file mode 100644 index 0000000..b221a96 --- /dev/null +++ b/octave_packages/optim-1.2.0/nmsmax.m @@ -0,0 +1,213 @@ +%% Copyright (C) 2002 N.J.Higham +%% Copyright (C) 2003 Andy Adler +%% +%% This program 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. +%% +%% This program 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 +%% this program; if not, see . + +%%NMSMAX Nelder-Mead simplex method for direct search optimization. +%% [x, fmax, nf] = NMSMAX(FUN, x0, STOPIT, SAVIT) attempts to +%% maximize the function FUN, using the starting vector x0. +%% The Nelder-Mead direct search method is used. +%% Output arguments: +%% x = vector yielding largest function value found, +%% fmax = function value at x, +%% nf = number of function evaluations. +%% The iteration is terminated when either +%% - the relative size of the simplex is <= STOPIT(1) +%% (default 1e-3), +%% - STOPIT(2) function evaluations have been performed +%% (default inf, i.e., no limit), or +%% - a function value equals or exceeds STOPIT(3) +%% (default inf, i.e., no test on function values). +%% The form of the initial simplex is determined by STOPIT(4): +%% STOPIT(4) = 0: regular simplex (sides of equal length, the default) +%% STOPIT(4) = 1: right-angled simplex. +%% Progress of the iteration is not shown if STOPIT(5) = 0 (default 1). +%% STOPIT(6) indicates the direction (ie. minimization or +%% maximization.) Default is 1, maximization. +%% set STOPIT(6)=-1 for minimization +%% If a non-empty fourth parameter string SAVIT is present, then +%% `SAVE SAVIT x fmax nf' is executed after each inner iteration. +%% NB: x0 can be a matrix. In the output argument, in SAVIT saves, +%% and in function calls, x has the same shape as x0. +%% NMSMAX(fun, x0, STOPIT, SAVIT, P1, P2,...) allows additional +%% arguments to be passed to fun, via feval(fun,x,P1,P2,...). +%% References: +%% N. J. Higham, Optimization by direct search in matrix computations, +%% SIAM J. Matrix Anal. Appl, 14(2): 317-333, 1993. +%% C. T. Kelley, Iterative Methods for Optimization, Society for Industrial +%% and Applied Mathematics, Philadelphia, PA, 1999. + +% From Matrix Toolbox +% Copyright (C) 2002 N.J.Higham +% www.maths.man.ac.uk/~higham/mctoolbox +% Modifications for octave by A.Adler 2003 + +function [x, fmax, nf] = nmsmax(fun, x, stopit, savit, varargin) + +x0 = x(:); % Work with column vector internally. +n = length(x0); + +% Set up convergence parameters etc. +if (nargin < 3 || isempty(stopit)) + stopit(1) = 1e-3; +end +tol = stopit(1); % Tolerance for cgce test based on relative size of simplex. +if length(stopit) == 1, stopit(2) = inf; end % Max no. of f-evaluations. +if length(stopit) == 2, stopit(3) = inf; end % Default target for f-values. +if length(stopit) == 3, stopit(4) = 0; end % Default initial simplex. +if length(stopit) == 4, stopit(5) = 1; end % Default: show progress. +trace = stopit(5); +if length(stopit) == 5, stopit(6) = 1; end % Default: maximize +dirn= stopit(6); +if nargin < 4, savit = []; end % File name for snapshots. + +V = [zeros(n,1) eye(n)]; +f = zeros(n+1,1); +V(:,1) = x0; +f(1) = dirn*feval(fun,x,varargin{:}); +fmax_old = f(1); + +if trace, fprintf('f(x0) = %9.4e\n', f(1)), end + +k = 0; m = 0; + +% Set up initial simplex. +scale = max(norm(x0,inf),1); +if stopit(4) == 0 + % Regular simplex - all edges have same length. + % Generated from construction given in reference [18, pp. 80-81] of [1]. + alpha = scale / (n*sqrt(2)) * [ sqrt(n+1)-1+n sqrt(n+1)-1 ]; + V(:,2:n+1) = (x0 + alpha(2)*ones(n,1)) * ones(1,n); + for j=2:n+1 + V(j-1,j) = x0(j-1) + alpha(1); + x(:) = V(:,j); + f(j) = dirn*feval(fun,x,varargin{:}); + end +else + % Right-angled simplex based on co-ordinate axes. + alpha = scale*ones(n+1,1); + for j=2:n+1 + V(:,j) = x0 + alpha(j)*V(:,j); + x(:) = V(:,j); + f(j) = dirn*feval(fun,x,varargin{:}); + end +end +nf = n+1; +how = 'initial '; + +[temp,j] = sort(f); +j = j(n+1:-1:1); +f = f(j); V = V(:,j); + +alpha = 1; beta = 1/2; gamma = 2; + +while 1 %%%%%% Outer (and only) loop. +k = k+1; + + fmax = f(1); + if fmax > fmax_old + if ~isempty(savit) + x(:) = V(:,1); eval(['save ' savit ' x fmax nf']) + end + end + if trace + fprintf('Iter. %2.0f,', k) + fprintf([' how = ' how ' ']); + fprintf('nf = %3.0f, f = %9.4e (%2.1f%%)\n', nf, fmax, ... + 100*(fmax-fmax_old)/(abs(fmax_old)+eps)) + end + fmax_old = fmax; + + %%% Three stopping tests from MDSMAX.M + + % Stopping Test 1 - f reached target value? + if fmax >= stopit(3) + msg = ['Exceeded target...quitting\n']; + break % Quit. + end + + % Stopping Test 2 - too many f-evals? + if nf >= stopit(2) + msg = ['Max no. of function evaluations exceeded...quitting\n']; + break % Quit. + end + + % Stopping Test 3 - converged? This is test (4.3) in [1]. + v1 = V(:,1); + size_simplex = norm(V(:,2:n+1)-v1(:,ones(1,n)),1) / max(1, norm(v1,1)); + if size_simplex <= tol + msg = sprintf('Simplex size %9.4e <= %9.4e...quitting\n', ... + size_simplex, tol); + break % Quit. + end + + % One step of the Nelder-Mead simplex algorithm + % NJH: Altered function calls and changed CNT to NF. + % Changed each `fr < f(1)' type test to `>' for maximization + % and re-ordered function values after sort. + + vbar = (sum(V(:,1:n)')/n)'; % Mean value + vr = (1 + alpha)*vbar - alpha*V(:,n+1); + x(:) = vr; + fr = dirn*feval(fun,x,varargin{:}); + nf = nf + 1; + vk = vr; fk = fr; how = 'reflect, '; + if fr > f(n) + if fr > f(1) + ve = gamma*vr + (1-gamma)*vbar; + x(:) = ve; + fe = dirn*feval(fun,x,varargin{:}); + nf = nf + 1; + if fe > f(1) + vk = ve; fk = fe; + how = 'expand, '; + end + end + else + vt = V(:,n+1); ft = f(n+1); + if fr > ft + vt = vr; ft = fr; + end + vc = beta*vt + (1-beta)*vbar; + x(:) = vc; + fc = dirn*feval(fun,x,varargin{:}); + nf = nf + 1; + if fc > f(n) + vk = vc; fk = fc; + how = 'contract,'; + else + for j = 2:n + V(:,j) = (V(:,1) + V(:,j))/2; + x(:) = V(:,j); + f(j) = dirn*feval(fun,x,varargin{:}); + end + nf = nf + n-1; + vk = (V(:,1) + V(:,n+1))/2; + x(:) = vk; + fk = dirn*feval(fun,x,varargin{:}); + nf = nf + 1; + how = 'shrink, '; + end + end + V(:,n+1) = vk; + f(n+1) = fk; + [temp,j] = sort(f); + j = j(n+1:-1:1); + f = f(j); V = V(:,j); + +end %%%%%% End of outer (and only) loop. + +% Finished. +if trace, fprintf(msg), end +x(:) = V(:,1);