Ah! Thanks for pointing that out. I did not notice that before.
I still don't understand how it all works, but I translated your Excel formulas into SAS/IML and reproduced your computations. The program is below. Maybe it will be useful for you.
Notice that I transposed the definition of the column marginal (blue) and I interlaced the even and odd columns of your 3D matrices because I think that is what the IPF and MARG calls expect. However, I am not an expert on using those calls, so I might have made some mistakes. I am also not sure how to properly update the 3D matrix. I used the REPEAT and SHAPE functions to get the dimensions to work out, but the code might break if you change from this 3x2x4 example.
Anyway, HTH.
proc iml;
/* 3 x 2 x 4 example */
dim={3 2 4 };
A = {1 2 1,
5 4 2,
3 5 5,
5 5 5,
6 2 2,
3 8 7,
1 7 2,
2 7 6};
start RowMarginal(dim, A);
call marg(locmar, m, dim, A, {2,3});
return( shape(m,dim[3],dim[2]) );
finish;
start ColMarginal(dim, A);
call marg(locmar, m, dim, A, {1,2});
return( shape(m,dim[2],dim[1]) );
finish;
start SliceMarginal(dim, A);
call marg(locmar, m, dim, A, {1,3});
return( shape(m,dim[3],dim[1]) );
finish;
/* define target marginals */
RowTarg = {9 11,
17 13,
19 16,
7 8};
ColTarg = {22 20 10,
13 20 15};
SliceTarg = {7 9 4,
8 12 10,
15 12 8,
5 7 3};
B = A;
do iter = 1 to 4;
print iter;
/* row adjustment */
RowFactor = RowTarg / RowMarginal(dim, B);
B = B # shape(RowFactor, dim[2]*dim[3]);
print B[F=5.2];
/* col adjustment */
ColFactor = ColTarg / ColMarginal(dim, B);
B = B # shape(repeat(ColFactor, dim[3]), 0, dim[1]);
print B[F=5.2];
/* slice adjustment */
SliceFactor = SliceTarg / SliceMarginal(dim, B);
B = B # shape(repeat(SliceFactor, 1, dim[2]), 0, dim[1]);
print B[F=5.2];
end;
