nested k for loops for a parameter k

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.

[Stephen23]

https://www.mathworks.com/matlabcentral/answers/345551-function-with-varying-number-of-for-loops

https://www.mathworks.com/matlabcentral/answers/381505-creating-a-variable-number-of-nested-for-loops

etc., easy to find by searching this forum (the search field is in the top right of the page).

Answer 1

[Jan]

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.

Answer 2

[madhan ravi]

https://www.mathworks.com/help/matlab/math/parameterizing-functions.html

[Minoo Zarsav]

Thanks alot for your answer but this is not what I meant. I need to write pice of code like this

for v1=1:2
    for v2=1:2
        for u3=1:2
            for u4=1:2
                for w1=1:2
                    for w2=1:2
                        for u5=1:2
                            for u6=1:2
                                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;
                            end
                        end
                    end
                end
            end
        end
    end
end

This is when we know k= 6. but now I want to write it for the general case. It is not a nested function. I just need to write k for loops to define a multi-dimensional array.