How do I create multiple for loops depending on the array size?

I would like to iterate over multiple for-loops, but the amount of for-loops depends on the size of a vector. Is there a good way to do this, without using a lot of if-statements?

arr = [a1 a2 ... an]

for a1=1:...
   for a2=1:...
       ...
           for an=1:...
               %do something
           end
    end
end

for for examle if the vector arr has "n" entries I would like to have "n" for loops.

Answer 1

[Jan]

As in the answers you find in Stephen's links: Use an index vector instead of a list of for loops. Replace:

arr = [a1 a2 ... an]
for i1 = 1:a1
  for i2 = 1:a2
     ...
         for in = 1:an
             %do something with [i1, i2, ... in]
         end
  end
end

By:

% Loops from 1 to a(n):
n   = length(arr)
ini = ones(1, n);
fin = [a1 a2 ... an];

v     = ini;
iterN = prod(find - ini + 1);  % Number of iterations
for iter = 1:iterN
   % Do something with v
   ...
   % Increase index vector:
   for k = 1:n   % Or n:-1:1, as you want to
      if v(k) < fin(k)
        v(k)  = v(k) + 1;
        break;           % Stop "for k" loop
      end
      v(k) = ini(k);     % Reset this index
   end
end

Answer 2

[Stephen23]

A recursive function is the obvious solution, although this depends on whether you count recursive functions as being "a good way to do this", as they are famously fickle beasts, and are not always easy to debug. Often the best solution is to use indexing, as Jan Simon explained in this answer. Recursive functions, indexing and other solutions have been discussed before:

https://www.mathworks.com/matlabcentral/answers/386638-how-to-loop-through-an-unknown-number-of-matrix-dimensions

https://www.mathworks.com/matlabcentral/answers/333926-recursive-function-for-replacing-multiple-for-loops

https://www.mathworks.com/matlabcentral/answers/374159-varying-number-of-nested-loops

https://www.mathworks.com/matlabcentral/answers/39881-create-a-variable-number-of-nested-for-loops-select-elements-in-matrix-with-variables-dimensions

Answer 3

[Walter Roberson]

https://www.mathworks.com/matlabcentral/answers/357969-using-recursive-function-to-calculate-all-possible-peptide-combinations#answer_282766