matrix-functions: matrixcomp/mdsmax.m annotate

annotate matrixcomp/mdsmax.m @ 0:8f23314345f4 draft

Create local repository for matrix toolboxes. Step #0 done.

author	Antonio Pino Robles <data.script93@gmail.com>
date	Wed, 06 May 2015 14:56:53 +0200
parents
children

rev	line source
0 8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	1 function [x, fmax, nf] = mdsmax(fun, x, stopit, savit, varargin)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	2 %MDSMAX Multidirectional search method for direct search optimization.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	3 % [x, fmax, nf] = MDSMAX(FUN, x0, STOPIT, SAVIT) attempts to
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	4 % maximize the function FUN, using the starting vector x0.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	5 % The method of multidirectional search is used.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	6 % Output arguments:
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	7 % x = vector yielding largest function value found,
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	8 % fmax = function value at x,
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	9 % nf = number of function evaluations.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	10 % The iteration is terminated when either
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	11 % - the relative size of the simplex is <= STOPIT(1)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	12 % (default 1e-3),
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	13 % - STOPIT(2) function evaluations have been performed
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	14 % (default inf, i.e., no limit), or
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	15 % - a function value equals or exceeds STOPIT(3)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	16 % (default inf, i.e., no test on function values).
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	17 % The form of the initial simplex is determined by STOPIT(4):
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	18 % STOPIT(4) = 0: regular simplex (sides of equal length, the default),
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	19 % STOPIT(4) = 1: right-angled simplex.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	20 % Progress of the iteration is not shown if STOPIT(5) = 0 (default 1).
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	21 % If a non-empty fourth parameter string SAVIT is present, then
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	22 % `SAVE SAVIT x fmax nf' is executed after each inner iteration.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	23 % NB: x0 can be a matrix. In the output argument, in SAVIT saves,
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	24 % and in function calls, x has the same shape as x0.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	25 % MDSMAX(fun, x0, STOPIT, SAVIT, P1, P2,...) allows additional
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	26 % arguments to be passed to fun, via feval(fun,x,P1,P2,...).
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	27
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	28 % This implementation uses 2n^2 elements of storage (two simplices), where x0
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	29 % is an n-vector. It is based on the algorithm statement in [2, sec.3],
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	30 % modified so as to halve the storage (with a slight loss in readability).
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	31
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	32 % References:
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	33 % [1] V. J. Torczon, Multi-directional search: A direct search algorithm for
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	34 % parallel machines, Ph.D. Thesis, Rice University, Houston, Texas, 1989.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	35 % [2] V. J. Torczon, On the convergence of the multidirectional search
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	36 % algorithm, SIAM J. Optimization, 1 (1991), pp. 123-145.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	37 % [3] N. J. Higham, Optimization by direct search in matrix computations,
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	38 % SIAM J. Matrix Anal. Appl, 14(2): 317-333, 1993.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	39 % [4] N. J. Higham, Accuracy and Stability of Numerical Algorithms,
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	40 % Second edition, Society for Industrial and Applied Mathematics,
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	41 % Philadelphia, PA, 2002; sec. 20.5.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	42
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	43 x0 = x(:); % Work with column vector internally.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	44 n = length(x0);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	45
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	46 mu = 2; % Expansion factor.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	47 theta = 0.5; % Contraction factor.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	48
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	49 % Set up convergence parameters etc.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	50 if nargin < 3 \| isempty(stopit), stopit(1) = 1e-3; end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	51 tol = stopit(1); % Tolerance for cgce test based on relative size of simplex.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	52 if length(stopit) == 1, stopit(2) = inf; end % Max no. of f-evaluations.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	53 if length(stopit) == 2, stopit(3) = inf; end % Default target for f-values.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	54 if length(stopit) == 3, stopit(4) = 0; end % Default initial simplex.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	55 if length(stopit) == 4, stopit(5) = 1; end % Default: show progress.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	56 trace = stopit(5);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	57 if nargin < 4, savit = []; end % File name for snapshots.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	58
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	59 V = [zeros(n,1) eye(n)]; T = V;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	60 f = zeros(n+1,1); ft = f;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	61 V(:,1) = x0; f(1) = feval(fun,x,varargin{:});
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	62 fmax_old = f(1);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	63
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	64 if trace, fprintf('f(x0) = %9.4e\n', f(1)), end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	65
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	66 k = 0; m = 0;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	67
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	68 % Set up initial simplex.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	69 scale = max(norm(x0,inf),1);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	70 if stopit(4) == 0
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	71 % Regular simplex - all edges have same length.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	72 % Generated from construction given in reference [18, pp. 80-81] of [1].
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	73 alpha = scale / (nsqrt(2)) [ sqrt(n+1)-1+n sqrt(n+1)-1 ];
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	74 V(:,2:n+1) = (x0 + alpha(2)ones(n,1)) ones(1,n);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	75 for j=2:n+1
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	76 V(j-1,j) = x0(j-1) + alpha(1);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	77 x(:) = V(:,j); f(j) = feval(fun,x,varargin{:});
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	78 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	79 else
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	80 % Right-angled simplex based on co-ordinate axes.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	81 alpha = scale*ones(n+1,1);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	82 for j=2:n+1
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	83 V(:,j) = x0 + alpha(j)*V(:,j);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	84 x(:) = V(:,j); f(j) = feval(fun,x,varargin{:});
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	85 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	86 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	87 nf = n+1;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	88 size = 0; % Integer that keeps track of expansions/contractions.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	89 flag_break = 0; % Flag which becomes true when ready to quit outer loop.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	90
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	91 while 1 %%%%%% Outer loop.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	92 k = k+1;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	93
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	94 % Find a new best vertex x and function value fmax = f(x).
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	95 [fmax,j] = max(f);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	96 V(:,[1 j]) = V(:,[j 1]); v1 = V(:,1);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	97 if ~isempty(savit), x(:) = v1; eval(['save ' savit ' x fmax nf']), end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	98 f([1 j]) = f([j 1]);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	99 if trace
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	100 fprintf('Iter. %2.0f, inner = %2.0f, size = %2.0f, ', k, m, size)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	101 fprintf('nf = %3.0f, f = %9.4e (%2.1f%%)\n', nf, fmax, ...
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	102 100*(fmax-fmax_old)/(abs(fmax_old)+eps))
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	103 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	104 fmax_old = fmax;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	105
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	106 % Stopping Test 1 - f reached target value?
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	107 if fmax >= stopit(3)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	108 msg = ['Exceeded target...quitting\n'];
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	109 break % Quit.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	110 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	111
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	112 m = 0;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	113 while 1 %%% Inner repeat loop.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	114 m = m+1;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	115
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	116 % Stopping Test 2 - too many f-evals?
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	117 if nf >= stopit(2)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	118 msg = ['Max no. of function evaluations exceeded...quitting\n'];
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	119 flag_break = 1; break % Quit.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	120 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	121
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	122 % Stopping Test 3 - converged? This is test (4.3) in [1].
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	123 size_simplex = norm(V(:,2:n+1)- v1(:,ones(1,n)),1) / max(1, norm(v1,1));
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	124 if size_simplex <= tol
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	125 msg = sprintf('Simplex size %9.4e <= %9.4e...quitting\n', ...
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	126 size_simplex, tol);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	127 flag_break = 1; break % Quit.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	128 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	129
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	130 for j=2:n+1 % ---Rotation (reflection) step.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	131 T(:,j) = 2*v1 - V(:,j);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	132 x(:) = T(:,j); ft(j) = feval(fun,x,varargin{:});
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	133 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	134 nf = nf + n;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	135
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	136 replaced = ( max(ft(2:n+1)) > fmax );
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	137
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	138 if replaced
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	139 for j=2:n+1 % ---Expansion step.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	140 V(:,j) = (1-mu)v1 + muT(:,j);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	141 x(:) = V(:,j); f(j) = feval(fun,x,varargin{:});
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	142 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	143 nf = nf + n;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	144 % Accept expansion or rotation?
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	145 if max(ft(2:n+1)) > max(f(2:n+1))
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	146 V(:,2:n+1) = T(:,2:n+1); f(2:n+1) = ft(2:n+1); % Accept rotation.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	147 else
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	148 size = size + 1; % Accept expansion (f and V already set).
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	149 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	150 else
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	151 for j=2:n+1 % ---Contraction step.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	152 V(:,j) = (1+theta)v1 - thetaT(:,j);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	153 x(:) = V(:,j); f(j) = feval(fun,x,varargin{:});
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	154 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	155 nf = nf + n;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	156 replaced = ( max(f(2:n+1)) > fmax );
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	157 % Accept contraction (f and V already set).
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	158 size = size - 1;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	159 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	160
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	161 if replaced, break, end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	162 if trace & rem(m,10) == 0, fprintf(' ...inner = %2.0f...\n',m), end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	163 end %%% Of inner repeat loop.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	164
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	165 if flag_break, break, end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	166 end %%%%%% Of outer loop.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	167
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	168 % Finished.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	169 if trace, fprintf(msg), end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	170 x(:) = v1;

Mercurial > matrix-functions

annotate matrixcomp/mdsmax.m @ 0:8f23314345f4 draft