function R = SteepestDescent2(F,GF,x0,alphak, tol,kmax)
% Minimization of a function of several variables: Steepest Descent.
% version with constant step (learning rate) alphak.
% input  :
%       
%       F  :   handle to the objective function 
%       GF  :  handle to the gradient of the objective function 
%       x0  :  column vector – initial approximation of the solution
%       alphak: constant step (learning rate)
%       tol:   tolerance
%       kmax:  maximum number of iterations
%
% output :
%
%       R   : Matrix of the sequence of approximated
%             solutions (by columns)
%
xcurr = x0; R = x0;
% initialize xprec
 xprev = 10*x0*tol; k=1;
 B = -GF(xprev);
while(norm(xprev-xcurr)/norm(xprev)>=tol+eps && norm(B)>=tol+eps && k<kmax)
    k = k+1;
    xprev = xcurr;
    B = -GF(xprev);
    c = alphak*B;
    xcurr = xprev + c ;
    R = [R xcurr];
end
if nargout==0
   w=sprintf('Number of iterations : %d\n ',k);
   disp(w)
   w=sprintf('Estimated error :%f\n',norm(c));disp(w)
   w=sprintf('Solution : [%f , %f]',xcurr); disp(w) 
 end
end