Operations on 3d array without using for loop

I am trying to write the following code without for loops

gf_k = gf(0:3,2);  % gf is a Galois-field matlab function
gf_a = gf(a, 2); %  gf is a Galois-field matlab function
for i = 1 : l
    for j = 1 : h
        for k = 0 : 3
            c = gf_k.x(k+1) + gf_a.x(i,j); % As both gf_k and gf_a are GF(4) variables, Value of c is between any of 0,1,2,3
            D(i,j,k+1) = B(i,j,k+1) + A(i,j,c+1); 
        end
    end
end

I tried using sub2ind but I couldn't get right.

[Bruno Luong]

"I am trying to write the following code without for loops"

Why people obcessing with removing loops. This is insane.

Furthermore such statement of function calling in general cannot be vectorized when inside the loops

c = func1(k) + func2(a(i,j))

[SHRAVAN GARLAPATI]

@Bruno - Thanks for your quick reply.

Removing loops can give me upto 4x time savings. Instead of 4 hours, sim takes 1 hour. Saves lot of time for multiple runs.

I updated the code. I removed func1 and func2. Replaced them with the computation I need. I moved them out of the for-loops. Please take a look at the code again and see if we can remove loops now.

[William Rose]

Well said, @Bruno Luong!

[SHRAVAN GARLAPATI]

@William Rose and @Bruno Luong - Please take another look. I updated the code without func1 and func2. Removing for loops definetly improves speed. I had another 4-d for loop, I vectorized it and saw 4x speed-up. Hoping to do same for this 3-d for loop. But stuck.

[Bruno Luong]

This line of code is perhaps wrong

c = gf_k.x(k+1) + gf_a.x(i,j);

it adds two double and not GF(4) elements.

Answer 1

[Bruno Luong]

I don't have communication tbx, so I code this blindly

l = 300;
h = 400;
a = randi([0,3], l, h);
gf_k = gf(0:3,2);
gf_a = gf(a, 2);
A = rand(l,h,4);
B = rand(l,h,4);

% Addition table of GF(4)
[X,Y] = ndgrid(0:3);
GF4_addTable = (gf(X,2) + gf(Y,2));
GF4_addTable = GF4_addTable.x;
%GF4_addTable = [...
%    0 1 2 3;
%    1 0 3 2;
%    2 3 0 1;
%    3 2 1 0 ];
tic
gf_k_x = gf_k.x;
gf_a_x = gf_a.x;
gf_k_x = reshape(gf_k_x, [1 1 4]);
ilin = 1 + gf_a_x + 4*gf_k_x;
c = GF4_addTable(ilin); % gf_k_x + gf_a_x; in GF4
D = B + A((1:l)'+l*((0:h-1)+h*double(c)));
toc

Elapsed time is 0.023939 seconds.

[SHRAVAN GARLAPATI]

@Bruno Luong - The code you provided works. Thanks. I see a speed-up around 3.5x. In my code, I already reduced the 3-for loops to 2-for loops. So, speed-up of 3.5x is w.r.t 2-for loops. w.r.t 3-for loops, I think the speedup your code provides is around 10x. I have the following questions:

ilin = 1 + gf_a_x + 4*gf_k_x;

gf_a_x is of dim(l,h) and gf_k_x is of dim(1,1,4). How can we add these two?

A((1:l)'+l*((0:h-1)+h*double(c)));

Is there a Matlab documentation page to understand this? Looks like you are using linear indexing. Is this correct?

[Bruno Luong]

"gf_a_x is of dim(l,h) and gf_k_x is of dim(1,1,4). How can we add these two?"

via auto expansion https://blogs.mathworks.com/loren/2016/10/24/matlab-arithmetic-expands-in-r2016b/

A((1:l)'+l*((0:h-1)+h*double(c)));

... Looks like you are using linear indexing. Is this correct?

Correct. It does the work like sub2ind but with auto-expansion capability and without the overhead of verification for overflow that I don't need.