Re: [Help-glpk] Multidimesional Arrays in GLPK/L

[Andrew Makhorin]

>How to work with cost matrices that have more than two dimwnsions?

In glpk/l there are three ways to initialize a parameter with more than
two dimensions.

Let, for example, there be a three-dimensional parameter declared as
follows:

   sets  A = (a1, a2, a3),
         B = (b1, b2, b3, b4, b5),
         C = (c1, c2, c3, c4);

   parameter
         p[A, B, C];

The first way is to assign a value to each (non-zero) parameter member
separately, for example:

   p[#a1,#b1,#c1] := 1;
   p[#a1,#b2,#c1] := 2;
   p[#a3,#b4,#c2] := 6;
   /* etc. */

The second way is to use the data clause, for example:

   p[i,j,k] := data
               (  i in A, j in B, k in C:
                  a1      b1      c1      1
                  a1      b2      c1      2
                  a3      b4      c2      6
                  /* etc. */
               );

And the third way is to use the table clause, for example:

   p[#a1,j,k] := table(k in C, j in B:
                      b1  b2  b3  b4  b5:
                  c1  1   2   3   .   4
                  c2  .   .   5   6   .
                  c3  7   .   .   .   8
                  c4  .   .   9   .  10 );

   p[#a2,j,k] := table(k in C, j in B:
                      b1  b2  b3  b4  b5:
                  c1  10  9   8   .   7
                  c2  6   5   .   .   .
                  c3  .   .   4   .   3
                  c4  2   .   .   1   . );

   p[#a3,j,k] := table(k in C, j in B:
                      b1  b2  b3  b4  b5:
                  c1  .   .   5   .   8
                  c2  1   .   .   6   9
                  c3  2   4   .   .   .
                  c4  3   .   .   7   10 );

In any case you can use the display statement, for example:

   display p;

to see what you get.

Being initialized a multidimensional parameter can be used in model
expressions, in particular, to define an objective function row, for
example:

   obj := sum((i,j,k), p[i,j,k] * x[i,j,k]);

where x is a three-dimensional model variable.