How to convert an M-dimensional array to an N-dimensional array?

So you just want to reformat your matrices while no data is changed. As I hinted in my comment the simplest is to use 1D array mid step for converting from M to N dimensions.

The other answers here are on the same track but are lacking the whole math ... they have just examples up to some small dimension without universal equation so here it is:

To convert between A[A0][A1]...[A(M-1)] and X[A0*A1*...*A(M-1)] where A0,A1,...A(M-1) are the dimension sizes of your container (resolution) simply do this:

// M-D -> 1D
x = a0
   +a1*A0
   +a2*A0*A1
   ...
   +a(M-1)*A0*A1*...*A(M-2);

// 1D -> M-D   
q=x;
a0 = q%A0; q/=A0;
a1 = q%A1; q/=A1;
a2 = q%A2; q/=A2;
...
a(M-1) = q%A(M-1); q/=A(M-1);

where a0,a1,...a(M-1) and x are the indexes in the arrays.

You actually do not need to convert the M-D array into 1D and then back to N-D its enough to just convert the indexes so:

for (a0=0;a0<A0;a0++)
 for (a1=0;a1<A1;a1++)
  ...
   for (a(M-1)=0;a(M-1)<A(M-1);a(M-1)++)
      {
      // M-D -> 1D
      x = a0
         +a1*A0
         +a2*A0*A1
         ...
         +a(M-1)*A0*A1*...*A(M-2);
      // 1D -> N-D   
      q=x;
      b0 = q%B0; q/=B0;
      b1 = q%B1; q/=B1;
      b2 = q%B2; q/=B2;
      ...
      b(N-1) = q%B(N-1); q/=B(N-1);
      // copy A -> B
      B[b0][b1]...[b(N-1)] = A[A0][A1]...[A(M-1)];
      }

Do not forget that the sizes must be:

A0*A1*...*A(M-1) <= B0*B1*...*B(N-1)

otherwise you will access array out of its bounds as the data in A will not fit into B.

In case you got dynamic dimensionality you can use:

• dynamicaly nested for loop nested_for