function [M] = V_cycle(M,n1,n2)
%========================================================
% Solve the cauchy schwartz equations using a V-cycle
  
% This is a recursive algorithm based on cycles in which a fine grid equation
% is solved on a coarse grid.
% (n1,n2) - are the number of sweeps to preform in the algorithm before and after the recrusion
%=====================================================================
%=====================================================================
for k = 1:1    
    s = size(M) ; rows = s(1) ; cols = s(2);
    n = rows-1;
    h = 1/n;
    
    %=====================================================================
    % n1 sweeps of Relaxation giving an approximation U_tild returning
    % the residual
    %===================================================================== 
    for i = 1:n1
        M = relax_F(M,n);
        M = relax_G(M,n);
    end
    
    %Give some estimation to the distance from the solution
    %In previous work this was preformed by |%R_h = F - laplacian(U_h);
    %                                       |%norma = norm(R_h(:),2)*h; % need to multiply by h to compare the convergence in the V-cycle
    %=====================================================================
    % Coarse to fine residual transfer with full-weighting
    %=====================================================================
    
    % Calculate the residual to solve over the coarser grid and: 
    % Trasfer the F,G with full weighting and the U,V boundaries are zero
    M_2h = downscale(M); 
    
    
    %=====================================================================
    % Solve for the residual on the coarse grid
    %=====================================================================
    new_rows = (rows-1)/2 + 1;
    new_cols = (cols-1)/2 + 1;
    
    
    if (new_rows <=5) 
         new_rows;
         M_2h = solve_direct(M_2h);
    else
        M_2h = V_cycle(M_2h,n1,n2);
    end
    
    %=====================================================================
    % Interpolate back to the fine grid and correct the former approx
    %=====================================================================
    M_new = upscale(M_2h); % The U,V for the error interpolated to the fine grid (boundaries are zeroed)
    
    M = M + M_new;
    %eval_error(M)
   
    %=====================================================================
    % Additional n2 relaxation sweeps
    %=====================================================================
    
    for i = 1:n2
        M = relax_F(M,n);
        M = relax_G(M,n);
    end
    
    %=====================================================================
    
end

%Give some estimation to the distance from the solution
    %In previous work this was preformed by |%R_h = F - laplacian(U_h);
    %                                       |%norma = norm(R_h(:),2)*h; % need to multiply by h to compare the convergence in the V-cycle