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    filename: initbox.m
    path of file: ./repos/informME/third_party/global_optim
    
    the code of the file until where you have to start completion: %
% Permission was provided by the author, Arnold Neumaier, to 
% modify and distribute this MATLAB code with the informME 
% package. Contact the original author directly for use outside 
% this package. 
%
% Author's website:
% http://www.mat.univie.ac.at/~neum/
%
% Author's source websites:
% http://www.mat.univie.ac.at/~neum/software/mcs/
% http://www.mat.univie.ac.at/~neum/software/minq/
% http://www.mat.univie.ac.at/~neum/software/ls/
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% initbox.m %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% function [ipar,level,ichild,f,isplit,p,xbest,fbest]=initbox(x0,f0,l,
% L,istar,u,v,prt)
% generates the boxes in the initialization procedure
% For each coordinate i we compute the quadratic interpolant to any
% three consecutive (x0(i,j),f0(j,i)). xl and xu are the minimum and
% maximum of the quadratic interpolant, respectively. If x0(i,istar(i)) 
% belongs to two boxes, the one containing the minimizer of the 
% quadratic model in coordinate i is taken as the current box for the
% next coordinate. All boxes generated in the initialization procedure
% get the level of their parent box increased by one.
%
% Input:
% x0(1:n,1:max(L))   coordinates used in the initialization list
% f0(1:max(L),1:n)  function values appertaining to the initialization
%             list; f0(j,i) = function value at x = (x0(1,istar(1)),...,
%             x0(i-1,istar(i-1)),x0(i,j),x0(i+1,l(i+1)),...,x0(n,l(n)))
% l(1:n)      pointer to the initial point x^0 = (x0(1,l(1)),...,
%             x0(n,l(n)) of the initialization list
% L(1:n)      the init. list contains L(i) values for coordinate i
% istar(1:n)  pointer to the final best point x^* of the init. list
%             x^* = (x0(1,istar(1)),...,x0(n,istar(n))) 
% [u,v]       initial box
% Output:
% ipar        vector containing the labels of the parents of the newly
%             created boxes
% level       vector containing their levels
% ichild      the absolute values of this vector specify which
    
function [ipar,level,ichild,f,isplit,p,xbest,fbest]=initbox(x0,f0,l,
% L,istar,u,v,prt)
% generates the boxes in the initialization procedure
% For each coordinate i we compute the quadratic interpolant to any
% three consecutive (x0(i,j),f0(j,i)). xl and xu are the minimum and
% maximum of the quadratic interpolant, respectively. If x0(i,istar(i)) 
% belongs to two boxes, the one containing the minimizer of the 
% quadratic model in coordinate i is taken as the current box for the
% next coordinate. All boxes generated in the initialization procedure
% get the level of their parent box increased by one.
%
% Input:
% x0(1:n,1:max(L))   coordinates used in the initialization list
% f0(1:max(L),1:n)  function values appertaining to the initialization
%             list; f0(j,i) = function value at x = (x0(1,istar(1)),...,
%             x0(i-1,istar(i-1)),x0(i,j),x0(i+1,l(i+1)),...,x0(n,l(n)))
% l(1:n)      pointer to the initial point x^0 = (x0(1,l(1)),...,
%             x0(n,l(n)) of the initialization list
% L(1:n)      the init. list contains L(i) values for coordinate i
% istar(1:n)  pointer to the final best point x^* of the init. list
%             x^* = (x0(1,istar(1)),...,x0(n,istar(n))) 
% [u,v]       initial box
% Output:
% ipar        vector containing the labels of the parents of the newly
%             created boxes
% level       vector containing their levels
% ichild      the absolute values of this vector specify which child 
%             they are; ichild(j) < 0 for the boxes generated in the 
%             initialization procedure
% f(1:2,:)    f(1,j) contains the base vertex function value of box j
% isplit      vector containing the splitting indices of the boxes that
%             have already been split
% p(1:n)      ranking of variability; the ith component has the p(i)th 
%             highest estimated variability 
% xbest       best vertex after the initialization procedure
% fbest       best function value after the initialization procedure
% prt	      print level
%
% Uses the following functions/m-files:
% genbox.m
% polint.m
% quadmin.m
% quadpol.m 
% split1.m
% updtoptl.m 

function [ipar,level,ichild,f,isplit,p,xbest,fbest]=initbox(x0,f0,l,L,istar,u,v,prt)
global nboxes nglob xglob
% nboxes      counter for boxes not in the base list
% nglob       number of global minimizers of a test function in [u,v]
% xglob(1:n,1:nglob) x(:,i), i=1:nglob, are the global minimizers of a 
% test function in [u,v]
n = length(u);
% parameter values appertaining to box 1
ipar(1) = 0;
level(1) = 1;  
ichild(1) = 1;
f(1,1) = f0(l(1),1);
par = 1;
if prt > 1,
  iopt = 1:nglob;
end