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bfgsmin.m

## Copyright (C) 2006  Michael Creel   <michael.creel@uab.es>
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; if not, write to the Free Software
## Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA

## bfgsmin: bfgs or limited memory bfgs minimization of function
##
## Usage: [x, obj_value, convergence, iters] = bfgsmin(f, args, control)
##
## The function must be of the form
## [value, return_2,..., return_m] = f(arg_1, arg_2,..., arg_n)
## By default, minimization is w.r.t. arg_1, but it can be done
## w.r.t. any argument that is a vector. Numeric derivatives are
## used unless analytic derivatives are supplied. See bfgsmin_example.m
## for methods.
##
## Arguments:
## * f: name of function to minimize (string)
## * args: a cell array that holds all arguments of the function
##    The argument with respect to which minimization is done
##    MUST be a vector
## * control: an optional cell array of 1-8 elements. If a cell
##   array shorter than 8 elements is provided, the trailing elements
##   are provided with default values.
##    * elem 1: maximum iterations  (positive integer, or -1 or Inf for unlimited (default))
##    * elem 2: verbosity
##          0 = no screen output (default)
##          1 = only final results
##          2 = summary every iteration
##          3 = detailed information
##    * elem 3: convergence criterion
##          1 = strict (function, gradient and param change) (default)
##          0 = weak - only function convergence required
##    * elem 4: arg in f_args with respect to which minimization is done (default is first)
##    * elem 5: (optional) Memory limit for lbfgs. If it's a positive integer
##          then lbfgs will be use. Otherwise ordinary bfgs is used
##    * elem 6: function change tolerance, default 1e-12
##    * elem 7: parameter change tolerance, default 1e-6
##    * elem 8: gradient tolerance, default 1e-5
##
## Returns:
## * x: the minimizer
## * obj_value: the value of f() at x
## * convergence: 1 if normal conv, other values if not
## * iters: number of iterations performed
##
## Example: see bfgsmin_example.m

function [parameter, obj, convergence, iters] = bfgsmin(f, f_args, control)

      # check number and types of arguments
      if ((nargin < 2) || (nargin > 3))
            usage("bfgsmin: you must supply 2 or 3 arguments");
      endif
      if (!ischar(f)) usage("bfgsmin: first argument must be string holding objective function name"); endif
      if (!iscell(f_args)) usage("bfgsmin: second argument must cell array of function arguments"); endif
      if (nargin > 2)
            if (!iscell(control))
                  usage("bfgsmin: 3rd argument must be a cell array of 1-8 elements");
            endif
            if (length(control) > 8)
                  usage("bfgsmin: 3rd argument must be a cell array of 1-8 elements");
            endif
      else control = {};
      endif

      # provide defaults for missing controls
      if (length(control) == 0) control{1} = -1; endif # limit on iterations
      if (length(control) == 1) control{2} = 0; endif # level of verbosity
      if (length(control) == 2) control{3} = 1; endif # strong (function, gradient and parameter change) convergence required?
      if (length(control) == 3) control{4} = 1; endif # argument with respect to which minimization is done
      if (length(control) == 4) control{5} = 0; endif # memory for lbfgs: 0 uses ordinary bfgs
      if (length(control) == 5) control{6} = 1e-10; endif # tolerance for function convergence
      if (length(control) == 6) control{7} = 1e-6; endif # tolerance for parameter convergence
      if (length(control) == 7) control{8} = 1e-5; endif # tolerance for gradient convergence

      # validity checks on all controls
      tmp = control{1};
      if (((tmp !=Inf) && (tmp != -1)) && (tmp > 0 && (mod(tmp,1) != 0)))
            usage("bfgsmin: 1st element of 3rd argument (iteration limit) must be Inf or positive integer");
      endif
      tmp = control{2};
      if ((tmp < 0) || (tmp > 3) || (mod(tmp,1) != 0))
            usage("bfgsmin: 2nd element of 3rd argument (verbosity level) must be 0, 1, 2, or 3");
      endif
      tmp = control{3};
      if ((tmp != 0) && (tmp != 1))
            usage("bfgsmin: 3rd element of 3rd argument (strong/weak convergence) must be 0 (weak) or 1 (strong)");
      endif
      tmp = control{4};
      if ((tmp < 1) || (tmp > length(f_args)) || (mod(tmp,1) != 0))
            usage("bfgsmin: 4th element of 3rd argument (arg with respect to which minimization is done) must be an integer that indicates one of the elements of f_args");
      endif
      tmp = control{5};
      if ((tmp < 0) || (mod(tmp,1) != 0))
            usage("bfgsmin: 5th element of 3rd argument (memory for lbfgs must be zero (regular bfgs) or a positive integer");
      endif
      tmp = control{6};
      if (tmp < 0)
            usage("bfgsmin: 6th element of 3rd argument (tolerance for function convergence) must be a positive real number");
      endif
      tmp = control{7};
      if (tmp < 0)
            usage("bfgsmin: 7th element of 3rd argument (tolerance for parameter convergence) must be a positive real number");
      endif
      tmp = control{8};
      if (tmp < 0)
            usage("bfgsmin: 8th element of 3rd argument (tolerance for gradient convergence) must be a positive real number");
      endif

      # check that the parameter we minimize w.r.t. is a vector
      minarg = control{4};
      theta = f_args{minarg};
      theta = theta(:);
      if (!isvector(theta)) usage("bfgsmin: minimization must be done with respect to a vector of parameters"); endif
      f_args{minarg} = theta;

      # now go ahead and do the minimization
      [parameter, obj, convergence, iters] = __bfgsmin(f, f_args, control);
endfunction

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