matrix-functions: matrixcomp/nmsmax.m annotate

annotate matrixcomp/nmsmax.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
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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] = nmsmax(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 %NMSMAX Nelder-Mead simplex 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] = NMSMAX(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 Nelder-Mead direct search method 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 % NMSMAX(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 % References:
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	29 % 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	30 % 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	31 % C. T. Kelley, Iterative Methods for Optimization, Society for Industrial
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	32 % and Applied Mathematics, Philadelphia, PA, 1999.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	33
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	34 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	35 n = length(x0);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	36
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	37 % 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	38 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	39 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	40 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	41 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	42 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	43 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	44 trace = stopit(5);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	45 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	46
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	47 V = [zeros(n,1) eye(n)];
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	48 f = zeros(n+1,1);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	49 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	50 fmax_old = f(1);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	51
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	52 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	53
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	54 k = 0; m = 0;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	55
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	56 % Set up initial simplex.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	57 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	58 if stopit(4) == 0
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	59 % 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	60 % 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	61 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	62 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	63 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	64 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	65 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	66 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	67 else
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	68 % 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	69 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	70 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	71 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	72 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	73 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	74 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	75 nf = n+1;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	76 how = 'initial ';
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	77
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	78 [temp,j] = sort(f);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	79 j = j(n+1:-1:1);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	80 f = f(j); V = V(:,j);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	81
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	82 alpha = 1; beta = 1/2; gamma = 2;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	83
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	84 while 1 %%%%%% Outer (and only) loop.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	85 k = k+1;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	86
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	87 fmax = f(1);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	88 if fmax > fmax_old
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	89 if ~isempty(savit)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	90 x(:) = V(:,1); eval(['save ' savit ' x fmax nf'])
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	91 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	92 if trace
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	93 fprintf('Iter. %2.0f,', k)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	94 fprintf([' how = ' how ' ']);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	95 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	96 100*(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	97 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	98 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	99 fmax_old = fmax;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	100
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	101 %%% Three stopping tests from MDSMAX.M
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	102
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	103 % 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	104 if fmax >= stopit(3)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	105 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	106 break % Quit.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	107 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	108
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	109 % 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	110 if nf >= stopit(2)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	111 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	112 break % Quit.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	113 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	114
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	115 % 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	116 v1 = V(:,1);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	117 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	118 if size_simplex <= tol
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	119 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	120 size_simplex, tol);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	121 break % Quit.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	122 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	123
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	124 % One step of the Nelder-Mead simplex algorithm
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	125 % NJH: Altered function calls and changed CNT to NF.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	126 % Changed each `fr < f(1)' type test to `>' for maximization
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	127 % and re-ordered function values after sort.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	128
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	129 vbar = (sum(V(:,1:n)')/n)'; % Mean value
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	130 vr = (1 + alpha)vbar - alphaV(:,n+1); x(:) = vr; fr = feval(fun,x,varargin{:});
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	131 nf = nf + 1;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	132 vk = vr; fk = fr; how = 'reflect, ';
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	133 if fr > f(n)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	134 if fr > f(1)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	135 ve = gammavr + (1-gamma)vbar; x(:) = ve; fe = feval(fun,x,varargin{:});
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	136 nf = nf + 1;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	137 if fe > f(1)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	138 vk = ve; fk = fe;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	139 how = 'expand, ';
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	140 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	141 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	142 else
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	143 vt = V(:,n+1); ft = f(n+1);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	144 if fr > ft
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	145 vt = vr; ft = fr;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	146 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	147 vc = betavt + (1-beta)vbar; x(:) = vc; fc = feval(fun,x,varargin{:});
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	148 nf = nf + 1;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	149 if fc > f(n)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	150 vk = vc; fk = fc;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	151 how = 'contract,';
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	152 else
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	153 for j = 2:n
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	154 V(:,j) = (V(:,1) + V(:,j))/2;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	155 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	156 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	157 nf = nf + n-1;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	158 vk = (V(:,1) + V(:,n+1))/2; x(:) = vk; fk = feval(fun,x,varargin{:});
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	159 nf = nf + 1;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	160 how = 'shrink, ';
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	161 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	162 end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	163 V(:,n+1) = vk;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	164 f(n+1) = fk;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	165 [temp,j] = sort(f);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	166 j = j(n+1:-1:1);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	167 f = f(j); V = V(:,j);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	168
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	169 end %%%%%% End of outer (and only) loop.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	170
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	171 % Finished.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done. Antonio Pino Robles <data.script93@gmail.com> parents: diff changeset	172 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	173 x(:) = V(:,1);

Mercurial > matrix-functions

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