get_maxstep

 Computes the maximal step length at point 'x' in direction 'dir'
 to be still in the inner area of barriered constraints
 At the moment, the only supported constraints in a barrier are
 box constraints. For others it is necessary to change this func.

 Function has to be initiated from the outer loop level (where constraints
 are not composed to the augmented Lagrangian yet). To init call:
 get_maxstep(x,[],barind,gx,dgx);
 where 'barind' is a list of indicies of the constraints in the barrier,
 gx, dgx are function and gradient values of inequality constraints

 After the initialization it is possible to use the function in
 the inner loop: rMaxStep=get_maxstep(x,dir);
 The step length is limited to maximal length 1.0.

 If the function is not initializated or no restrictions are given,
 returns 1.0 always.

0001 function [rRelLength] = get_maxstep(obj,x,dir,varargin)
0002 % Computes the maximal step length at point 'x' in direction 'dir'
0003 % to be still in the inner area of barriered constraints
0004 % At the moment, the only supported constraints in a barrier are
0005 % box constraints. For others it is necessary to change this func.
0006 %
0007 % Function has to be initiated from the outer loop level (where constraints
0008 % are not composed to the augmented Lagrangian yet). To init call:
0009 % get_maxstep(x,[],barind,gx,dgx);
0010 % where 'barind' is a list of indicies of the constraints in the barrier,
0011 % gx, dgx are function and gradient values of inequality constraints
0012 %
0013 % After the initialization it is possible to use the function in
0014 % the inner loop: rMaxStep=get_maxstep(x,dir);
0015 % The step length is limited to maximal length 1.0.
0016 %
0017 % If the function is not initializated or no restrictions are given,
0018 % returns 1.0 always.
0019 %
0020 
0021 %
0022 % last update: 10/08/2009
0023 %
0024 
0025   error('not adjusted for PenLab yet.');
0026   % all considered barriered constraints are of the form: +/-1*x_i + c_j<=0
0027   % the j-th constraint is: xsgn(j) * x(xidx(j)) + constants(j) <=0
0028   persistent no_bconst;  % number of these (barriered) constraints
0029   persistent constants;  % constants c_j, j=1:no_constr
0030   persistent xidx;       % there is x(xidx(j)) in the j-th constraint
0031   persistent xsgn;       %   ... with sign xsgn(j)
0032 
0033   % distance from the boundary?
0034   bound_margin = 0.95;
0035 
0036   % initialization
0037   if (size(varargin,2) > 0)
0038     rRelLength=1.0;  % doesn't really matter
0039     if (size(varargin,2) ~= 3)
0040       pen_out(5,Inf,'Error@get_maxstep.m: Inconsistant call, user error?');
0041       return;
0042     end
0043     barind=varargin{1};
0044     gx=varargin{2};
0045     dgx=varargin{3};
0046 
0047     no_bconst=length(barind);
0048     if (no_bconst~=0)
0049       [xidx,col_ignore,xsgn]=find(dgx(:,barind));
0050       % in each column there should be exactly one entry +1 or -1
0051       % in the row appropriate to the index of 'x'
0052       % sorted column-wise
0053       constants=gx(barind)-xsgn.*x(xidx);
0054     else
0055       constants=[];
0056       xidx=[];
0057       xsgn=[];
0058     end
0059     return;
0060   end
0061 
0062   % normal usage - no restriction/not init
0063   if (isempty(no_bconst) || no_bconst==0)
0064     rRelLength = 1.0;
0065     return;
0066   end
0067 
0068   % normal usage - restrictions apply
0069   sdir=xsgn.*dir(xidx);
0070   idx=find(sdir > 0);
0071   rRelLength=min([-bound_margin*(constants(idx) + xsgn(idx).*x(xidx(idx)))./sdir(idx); 1.0]);
0072   %rRelLength=min(1.0, rRelLength);
0073 
0074   return;
0075