how to efficiently vectorize nested for loops

Hi everyone,

I am practicing vectorize programing and i faced a code that became a challenge for me,

this is the code in normal mode which runs correctly:

for t = 1:N
A(t,:) = a;    B(t,:) = b;    C(t,:) = c;
S = 0;
            for i=1:2
              for j=1:2
                  for k=1:2
                      M =((-1) ^ i).*((-1) ^ j).*((-1) ^ k);
                      R = sqrt((a(i))^2+(b(j))^2+(c(k))^2);    
                      N = atan( (a(i) * b(j))  /  (c(k) * R) );
                    S = S + R*sin(N/M);
                    end
                end
            end
end

here A,B and C are (N*2) data arrays.

first i dont know the general strategy when having more than 2 for loops.

and how can i rewrite the terms M and R and N for this example how can i write this code in effective way.

Thank you

Answer 1

[Walter Roberson]

[aG, bG, cG] = ndgrid(a, b, c);
[iG, jG, kG] = ndgrid(1:size(a,2), 1:size(b,2), 1:size(c,2));
M = (-1).^(iG + jG + kG);
R = sqrt(aG.^2 + bG.^2 + cG.^2);
N = atan2(aG .* bG, cG .* R);
RS = R .* sin(N .* M);         %with M being -1 or +1, multiplication is faster than division
S = sum(RS(:));

However, please check your equations to see whether atan2(y,x) makes sense instead of atan(y./x). The difference would be in the quadrant, which would affect the sign of the sin().

[M.R]

this works for me. thank you. and also i enjoyed the brevity of the code.