comparison toolboxes/FullBNT-1.0.7/netlab3.3/conjgrad.m @ 0:e9a9cd732c1e tip

first hg version after svn

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