function [M_2h] = downscale(M)
% This function takes a staggered grid and creates a downscaled grid
% ====================================================
% Boundaries are zero for all meshes but the first one
% ====================================================

s = size(M); rows = s(1) ; cols = s(2);
new_rows = (rows - 1)/2 + 1;
new_cols = (cols - 1)/2 + 1;

R = calc_error(M);

M_2h = zeros([new_rows,new_cols]);

%===========================================
% Transfer the F error (Full Weighting)
mask_F = [.25 0 .25 ; 0 0 0;  .25 0 .25];
tmp_residual_F = conv2(R,mask_F,'same');
for i=2:2: new_rows-1
    for j=2:2: new_cols -1
        M_2h(i,j) = tmp_residual_F(2*i-1,2*j-1);
    end
end


%============================================
% Transfer the G error (Full Weighting)
mask_G = [ 
    1/16 0 1/8 0 1/16 
    0    0  0  0  0 
    1/8  0 1/4 0 1/8 
     0   0  0  0  0
    1/16 0 1/8 0 1/16 ];

tmp_residual_G = conv2(R,mask_G,'same');
for i=3:2: new_rows-2
    for j=3:2: new_cols -2
        i1 = 1 + (i - 1)*2 ; j1 = 1 + (j-1)*2;
        M_2h(i,j) = tmp_residual_G(i1,j1);
    end
end