wolffd@0: function [x, options, flog, pointlog] = conjgrad(f, x, options, gradf, ...
wolffd@0:                                     varargin)
wolffd@0: %CONJGRAD Conjugate gradients optimization.
wolffd@0: %
wolffd@0: %	Description
wolffd@0: %	[X, OPTIONS, FLOG, POINTLOG] = CONJGRAD(F, X, OPTIONS, GRADF) uses a
wolffd@0: %	conjugate gradients algorithm to find the minimum of the function
wolffd@0: %	F(X) whose gradient is given by GRADF(X).  Here X is a row vector and
wolffd@0: %	F returns a scalar value.  The point at which F has a local minimum
wolffd@0: %	is returned as X.  The function value at that point is returned in
wolffd@0: %	OPTIONS(8).  A log of the function values after each cycle is
wolffd@0: %	(optionally) returned in FLOG, and a log of the points visited is
wolffd@0: %	(optionally) returned in POINTLOG.
wolffd@0: %
wolffd@0: %	CONJGRAD(F, X, OPTIONS, GRADF, P1, P2, ...) allows  additional
wolffd@0: %	arguments to be passed to F() and GRADF().
wolffd@0: %
wolffd@0: %	The optional parameters have the following interpretations.
wolffd@0: %
wolffd@0: %	OPTIONS(1) is set to 1 to display error values; also logs error
wolffd@0: %	values in the return argument ERRLOG, and the points visited in the
wolffd@0: %	return argument POINTSLOG.  If OPTIONS(1) is set to 0, then only
wolffd@0: %	warning messages are displayed.  If OPTIONS(1) is -1, then nothing is
wolffd@0: %	displayed.
wolffd@0: %
wolffd@0: %	OPTIONS(2) is a measure of the absolute precision required for the
wolffd@0: %	value of X at the solution.  If the absolute difference between the
wolffd@0: %	values of X between two successive steps is less than OPTIONS(2),
wolffd@0: %	then this condition is satisfied.
wolffd@0: %
wolffd@0: %	OPTIONS(3) is a measure of the precision required of the objective
wolffd@0: %	function at the solution.  If the absolute difference between the
wolffd@0: %	objective function values between two successive steps is less than
wolffd@0: %	OPTIONS(3), then this condition is satisfied. Both this and the
wolffd@0: %	previous condition must be satisfied for termination.
wolffd@0: %
wolffd@0: %	OPTIONS(9) is set to 1 to check the user defined gradient function.
wolffd@0: %
wolffd@0: %	OPTIONS(10) returns the total number of function evaluations
wolffd@0: %	(including those in any line searches).
wolffd@0: %
wolffd@0: %	OPTIONS(11) returns the total number of gradient evaluations.
wolffd@0: %
wolffd@0: %	OPTIONS(14) is the maximum number of iterations; default 100.
wolffd@0: %
wolffd@0: %	OPTIONS(15) is the precision in parameter space of the line search;
wolffd@0: %	default 1E-4.
wolffd@0: %
wolffd@0: %	See also
wolffd@0: %	GRADDESC, LINEMIN, MINBRACK, QUASINEW, SCG
wolffd@0: %
wolffd@0: 
wolffd@0: %	Copyright (c) Ian T Nabney (1996-2001)
wolffd@0: 
wolffd@0: %  Set up the options.
wolffd@0: if length(options) < 18
wolffd@0:   error('Options vector too short')
wolffd@0: end
wolffd@0: 
wolffd@0: if(options(14))
wolffd@0:   niters = options(14);
wolffd@0: else
wolffd@0:   niters = 100;
wolffd@0: end
wolffd@0: 
wolffd@0: % Set up options for line search
wolffd@0: line_options = foptions;
wolffd@0: % Need a precise line search for success
wolffd@0: if options(15) > 0
wolffd@0:   line_options(2) = options(15);
wolffd@0: else
wolffd@0:   line_options(2) = 1e-4;
wolffd@0: end
wolffd@0: 
wolffd@0: display = options(1);
wolffd@0: 
wolffd@0: % Next two lines allow conjgrad to work with expression strings
wolffd@0: f = fcnchk(f, length(varargin));
wolffd@0: gradf = fcnchk(gradf, length(varargin));
wolffd@0: 
wolffd@0: %  Check gradients
wolffd@0: if (options(9))
wolffd@0:   feval('gradchek', x, f, gradf, varargin{:});
wolffd@0: end
wolffd@0: 
wolffd@0: options(10) = 0;
wolffd@0: options(11) = 0;
wolffd@0: nparams = length(x);
wolffd@0: fnew = feval(f, x, varargin{:});
wolffd@0: options(10) = options(10) + 1;
wolffd@0: gradnew = feval(gradf, x, varargin{:});
wolffd@0: options(11) = options(11) + 1;
wolffd@0: d = -gradnew;		% Initial search direction
wolffd@0: br_min = 0;
wolffd@0: br_max = 1.0;	% Initial value for maximum distance to search along
wolffd@0: tol = sqrt(eps);
wolffd@0: 
wolffd@0: j = 1;
wolffd@0: if nargout >= 3
wolffd@0:   flog(j, :) = fnew;
wolffd@0:   if nargout == 4
wolffd@0:     pointlog(j, :) = x;
wolffd@0:   end
wolffd@0: end
wolffd@0: 
wolffd@0: while (j <= niters)
wolffd@0: 
wolffd@0:   xold = x;
wolffd@0:   fold = fnew;
wolffd@0:   gradold = gradnew;
wolffd@0: 
wolffd@0:   gg = gradold*gradold';
wolffd@0:   if (gg == 0.0)
wolffd@0:     % If the gradient is zero then we are done.
wolffd@0:     options(8) = fnew;
wolffd@0:     return;
wolffd@0:   end
wolffd@0: 
wolffd@0:   % This shouldn't occur, but rest of code depends on d being downhill
wolffd@0:   if (gradnew*d' > 0)
wolffd@0:     d = -d;
wolffd@0:     if options(1) >= 0
wolffd@0:       warning('search direction uphill in conjgrad');
wolffd@0:     end
wolffd@0:   end
wolffd@0: 
wolffd@0:   line_sd = d./norm(d);
wolffd@0:   [lmin, line_options] = feval('linemin', f, xold, line_sd, fold, ...
wolffd@0:     line_options, varargin{:});
wolffd@0:   options(10) = options(10) + line_options(10);
wolffd@0:   options(11) = options(11) + line_options(11);
wolffd@0:   % Set x and fnew to be the actual search point we have found
wolffd@0:   x = xold + lmin * line_sd;
wolffd@0:   fnew = line_options(8);
wolffd@0: 
wolffd@0:   % Check for termination
wolffd@0:   if (max(abs(x - xold)) < options(2) & max(abs(fnew - fold)) < options(3))
wolffd@0:     options(8) = fnew;
wolffd@0:     return;
wolffd@0:   end
wolffd@0: 
wolffd@0:   gradnew = feval(gradf, x, varargin{:});
wolffd@0:   options(11) = options(11) + 1;
wolffd@0: 
wolffd@0:   % Use Polak-Ribiere formula to update search direction
wolffd@0:   gamma = ((gradnew - gradold)*(gradnew)')/gg;
wolffd@0:   d = (d .* gamma) - gradnew;
wolffd@0: 
wolffd@0:   if (display > 0)
wolffd@0:     fprintf(1, 'Cycle %4d  Function %11.6f\n', j, line_options(8));
wolffd@0:   end
wolffd@0: 
wolffd@0:   j = j + 1;
wolffd@0:   if nargout >= 3
wolffd@0:     flog(j, :) = fnew;
wolffd@0:     if nargout == 4
wolffd@0:       pointlog(j, :) = x;
wolffd@0:     end
wolffd@0:   end
wolffd@0: end
wolffd@0: 
wolffd@0: % If we get here, then we haven't terminated in the given number of 
wolffd@0: % iterations.
wolffd@0: 
wolffd@0: options(8) = fold;
wolffd@0: if (options(1) >= 0)
wolffd@0:   disp(maxitmess);
wolffd@0: end