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ptycho/+engines/+ML/cgmin1.m

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+function [x, p] = cgmin1(func,x,itmax,ftol,xtol,varargin)
+% conjugate-gradient optimization routine
+% NOTE: linesearch subroutines do not use the gradient
+%
+% [x] = cgmin1(func,x,itmax,ftol,xtol,varargin)
+%
+%     func = string name of objective function which returns both the
+%            objective function value and the gradient
+%        x = input as initial starting point and output as final point
+%    itmax = maximum number of iterations (empty for default = 50)
+%     ftol = relative function tolerance (empty for default = 1e-3)
+%     xtol = absolute solution tolerance (empty for default = 1e-3)
+% varargin = extra variables required by objective function
+%
+% DISCLAIMER: This code is not intended for distribution. I have many
+% versions of this code and am constantly revising it. I believe this
+% version is working properly. However, I will not vouch for the code.
+% Anyone using the code for thesis research has a responsibility to go
+% through the code line-by-line and read relevant references to understand
+% the code completely. In my opinion, you have two options if you want to
+% publish results obtained with the code: (i) go through the code line-by-
+% line and read relevent references to understand how the code works and make
+% sure it is working properly for your application, or (ii) I can sit down
+% with you an go through this code and the additional code that you have
+% written to go along with it and make sure it is working properly. Option
+% (i) is preferred, and I ask that you do NOT acknowledge me in print (first,
+% it would be more appropriate for you to reference "Numerical Recipes",
+% and second, I prefer not to be named in a paper with which I do not have
+% detailed knowledge). If you decide to go with option (ii), I would expect
+% to learn the details of your research and be included in the author list.
+%
+% Sam Thurman, May 9, 2005
+
+import utils.*
+
+if isempty(itmax), itmax = 50; end
+if isempty(ftol), ftol = 1e-3; end
+if isempty(xtol), xtol = 1e-3; end
+% loop
+flg = 0; % use steepest descent for first iteration
+step = 0; % to guess at initial steplength
+for it = 1:itmax
+   % function evaluation
+   [f,grad,p] = feval(func,x,varargin{:});
+%    disp(f)
+   % check for feasibility
+   if isinf(f), error('encountered an infeasible solution'), end
+   if norm(grad(:))==0, return, end % done if gradient is zero (unlikely)
+   % pick search direction
+   if (flg==1) & (rem(it,25)~=0) % linesearch found a minimum -> use cg equations
+       gg = g(:)'*g(:);
+%        dgg = grad(:)'*grad(:); % this statement for Fletcher-Reeves
+       dgg = (grad(:)+g(:))'*grad(:);  % this statement for Polak-Ribiere
+       ga = dgg/gg;
+       g = -grad;
+       h = g+ga*h;
+       dx = h/norm(h(:));
+       df = grad(:)'*dx(:);
+   end
+   if (flg==0) | (rem(it,25)==0) | (df>0) % revert to steepest decent
+       g = -grad;
+       h = g;
+       dx = h/norm(h(:));
+       df = grad(:)'*dx(:);
+   end
+   % initial steplength guess
+   if step == 0
+       step = max(0.001,min([1,2*abs(f/(grad(:)'*dx(:)))])); % same as fminusub.m (line 124) in optim toolbox
+   else % oterwise use previous steplength
+        step = step/10;
+   end
+   % linesearch
+   [x,fvalue,step,flg] = engines.ML.linesearch(func,x,f,df,dx,step,varargin{:});
+   % test for convergence
+   if (2*abs(f-fvalue)<=ftol*(abs(f)+abs(fvalue)+ftol)) & (step*norm(dx(:))<=xtol) & (it~=1) % normal return
+       return
+   end
+end
+verbose(3, 'Maximum number of iterations exceeded.')
+return
+end
+