How to convert dependent equation to independent for parallel computing (parfor)

I am trying to run my code using 'parfor' but getting error due to dependent term. How to resolve that.

The code similar to below. I am getting error for third loop expression

image(: , : , i) = image(: , : , i) + image(: , : , i -1);

parfor ix = 1:nx
    % expression to calculate image_c and image_d
    
    for i = 1:nt
        image(:,:,i) = image_c(:,:,i) +image_d(:,:,i);
    end
    
    for i=2:nt
        image(:,:,i) = image(:,:,i) +image(:,:,i-1);
    end
end

Answer 1

[Walter Roberson]

You cannot do that in parallel.

What you can do is roughly

total = zeros(size(image));
parfor i = 1 : nt
    total = total + image(:,:,i);
end

MATLAB recognizes total as being a "reduction variable" and will take care of doing the relevant additions and locking.

[Abhishek Saini]

Thanks Walter for your answer!

I apologise not to mention it befor. Actually I have the loop where the initail image value is not zeros. It is calculated from the previous loop. The code is like that.

parfor ix = 1:nx
    % expression to calculate image_c and image_d
    
    for i = 1:nt
        image(:,:,i) = image_c(:,:,i) +image_d(:,:,i);
    end
    
    for i=2:nt
        image(:,:,i) = image(:,:,i) +image(:,:,i-1);
    end
end

[Walter Roberson]

what is the output ? I do not see any output variable indexed by the parfor variable .

[Abhishek Saini]

Here is original code

data = zeros(size(nt,nx));
snapshot_i = zeros(nz+npad,nx+2*npad,nt);
image = zeros(nz+npad,nx+2*npad);

for ixs = 1 :64 
    rw = ricker(f,nz+2*npad,dt,dt*ixs,0);
    rw = rw(1:nz+npad,:);
    [data, snapshot_s] = fm2d(V,rw,dx,nt,dt,npad);         
    [data_const, snapshot_c] = fm2d(Vc,rw,dx,nt,dt,npad);   
    data_refl = data - data_const;
    [~,snapshot_d] = bm2d(Vc,data_refl',dx,dt,npad );
    
    for i = 1:nt
        snapshot_i(:,:,i) = snapshot_c(:,:,i) .* snapshot_d(:,:,i);
    end
    
    for i = 2:nt        
        snapshot_i(:,:,i) = snapshot_i(:,:,i) + snapshot_i(:,:,i-1);
    end
    image = image + snapshot_i(:,:,i); 
end

[Walter Roberson]

why bother to take a cumulative sum of snapshot_i but then only extract the last layer? Why not just sum(snapshot_i,3) ?

[Walter Roberson]

Also it looks like

snapshot_i = snapshot_c .* snapshot_d;

with no loop needed ?