# nested k for loops for a parameter k

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Minoo Zarsav on 23 Aug 2020
Edited: Jan on 23 Aug 2020
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.
Stephen Cobeldick on 23 Aug 2020

Jan on 23 Aug 2020
Edited: Jan on 23 Aug 2020
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.

madhan ravi on 23 Aug 2020
Minoo Zarsav on 23 Aug 2020
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.