/* sorting.mod - how to sort arrays in MathProg */

 /* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */

 #  Sometimes it is necessary to print parameters or variables in the

 #  order of ascending or descending their values. Suppose, for example,

 #  that we have the following subscripted parameter:

 set I := 1..12;

 param a{i in I} := Uniform(2, 7);

 #  If we print all its members:

 printf{i in I} "a[%d] = %g\n", i, a[i];

 #  the output may look like follows:

 #

 #  a[1]  = 2.64156

 #  a[2]  = 2.04798

 #  a[3]  = 2.14843

 #  a[4]  = 4.76896

 #  a[5]  = 6.09132

 #  a[6]  = 3.27780

 #  a[7]  = 4.06113

 #  a[8]  = 4.05898

 #  a[9]  = 6.63120

 #  a[10] = 6.50318

 #  a[11] = 3.46065

 #  a[12] = 4.69845

 #

 #  However, we would like the parameter members to appear in the order

 #  of ascending their values.

 #

 #  Introduce the following auxiliary parameter:

 param pos{i in I} :=

       1 + card({j in I: a[j] < a[i] or a[j] = a[i] and j < i});

 #  where pos[i] = k means that in the sorted list member a[i] would

 #  have k-th position, 1 <= k <= |I|. Then introduce another auxiliary

 #  parameter:

 param ind{k in 1..card(I)} := sum{i in I: pos[i] = k} i;

 #  where ind[k] = i iff pos[k] = i.

 #

 #  Now, the following statement:

 printf{k in 1..card(I)} "a[%d] = %g\n", ind[k], a[ind[k]];

 #  prints the parameter members in the desired order:

 #

 #  a[2]  = 2.04798

 #  a[3]  = 2.14843

 #  a[1]  = 2.64156

 #  a[6]  = 3.27780

 #  a[11] = 3.46065

 #  a[8]  = 4.05898

 #  a[7]  = 4.06113

 #  a[12] = 4.69845

 #  a[4]  = 4.76896

 #  a[5]  = 6.09132

 #  a[10] = 6.50318

 #  a[9]  = 6.63120

 end;