MATLAB: Nested k for loops for a parameter k

nested for loopsnested loops

How can I make k nested for loops when k is a parameter?!
I try to write a function with some parameter and I need to write k for loops when I don't know k and give it just as input.

Best Answer

Start with simplyfying your code: Replace the 2 innermost loops:
s = 0;
for u1=1:2
   for u2=1:2
      s = s + t1(u1,v1,w1)*t2(u2,v2,w2)*x1(u1,u2,u3,u4,u5,u6);
   end
end
y1(v1,v2,u3,u4,w1,w2,u5,u6) = s;
by
y1(v1,v2,u3,u4,w1,w2,u5,u6) = ...
    sum(t1(:, v1, w1) .* t2(:, v2, w2).' .* x1(:, :, u3,u4,u5,u6), 'all');
This is remarkably slower. What a pity.
A further simplification for the whole code:
y = zeros(2,2,2,2,2,2,2,2);  % Preallocation!!!   
for v1 = 1:2
   for v2 = 1:2
      for w1 = 1:2
         for w2 = 1:2
            y1(v1, v2, :, :, w1, w2, :, :) = ...
               sum(t1(:, v1, w1) * t2(:, v2, w2).' .* x1, [1, 2]);
         end
      end
   end
end
Now you have 4 loops only. It is possible to remove them also using some reshape commands, but tedious. Alternatively you can use this approach:
fcn = @(v) sum(t1(:, v(1), v(2)) * t2(:, v(3), v(4)).' .* x1, [1, 2]);
C   = NestedLoops([1,1,1,1], [2,2,2,2], fcn);
M   = reshape(cell2mat(C), [2,2,2,2,2,2,2,2]);
M   = permute(M, [1,4,3,5,2,6,7,8]);
function Result = NestedLoops(ini, fin, fcn)
nv     = fin - ini + 1;
nvProd = prod(nv);
Result = cell([nv, 1]);  % Avoid creation of {nv x nv} cell matrix
iR = 0;
n  = numel(ini);
v  = ini(:).';           % Current index vector as row
for k = 1:nvProd
   % Call the function with the index vector as first input:
   iR         = iR + 1;
   Result{iR} = fcn(v);
   
   % Increase index vector:
   for iv = 1:n
      if v(iv) < fin(iv)
        v(iv) = v(iv) + 1;
        break;           % Stop "for k" loop
      end
      v(iv) = ini(iv);   % Reset this index
   end
end
Well, I admit that this is not nice. Most of all it is not trivial to expand it to more dimensions and the permutation needed to join the output cell is ugly.
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