function pk = findDirction(gk,n,Hk,delta)
%FINDDIRCTION search dirction of modified Newton's method.CMSC 764 HW1.
%   pk = findDirction(gk,n,Hk,delta) finds the search direction pk in 
%   Newton's method for given gradient gk, dimension n and hessian Hk.
%   When the hessian is not s.p.d,we modify by Hk <- Hk + delta*I.
%   Here the solving of equations is done by Cholesky factorization.
%
%   See also NEWTONMIN,FINDDELTALM

%  Dianne P. O'Leary oleary@cs.umd.edu 
%  Geping Liu geping@math.umd.edu 
%  09-21-06
  
if (delta ~= 0)
    for i = 1 : n
        Hk(i,i) = Hk(i,i) + delta;
    end
end
    
R = chol(Hk);
    
y = R' \ (- gk);
pk = R \ y ;