alpar@1: /* sorting.mod - how to sort arrays in MathProg */
alpar@1: 
alpar@1: /* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
alpar@1: 
alpar@1: #  Sometimes it is necessary to print parameters or variables in the
alpar@1: #  order of ascending or descending their values. Suppose, for example,
alpar@1: #  that we have the following subscripted parameter:
alpar@1: 
alpar@1: set I := 1..12;
alpar@1: 
alpar@1: param a{i in I} := Uniform(2, 7);
alpar@1: 
alpar@1: #  If we print all its members:
alpar@1: 
alpar@1: printf{i in I} "a[%d] = %g\n", i, a[i];
alpar@1: 
alpar@1: #  the output may look like follows:
alpar@1: #
alpar@1: #  a[1]  = 2.64156
alpar@1: #  a[2]  = 2.04798
alpar@1: #  a[3]  = 2.14843
alpar@1: #  a[4]  = 4.76896
alpar@1: #  a[5]  = 6.09132
alpar@1: #  a[6]  = 3.27780
alpar@1: #  a[7]  = 4.06113
alpar@1: #  a[8]  = 4.05898
alpar@1: #  a[9]  = 6.63120
alpar@1: #  a[10] = 6.50318
alpar@1: #  a[11] = 3.46065
alpar@1: #  a[12] = 4.69845
alpar@1: #
alpar@1: #  However, we would like the parameter members to appear in the order
alpar@1: #  of ascending their values.
alpar@1: #
alpar@1: #  Introduce the following auxiliary parameter:
alpar@1: 
alpar@1: param pos{i in I} :=
alpar@1:       1 + card({j in I: a[j] < a[i] or a[j] = a[i] and j < i});
alpar@1: 
alpar@1: #  where pos[i] = k means that in the sorted list member a[i] would
alpar@1: #  have k-th position, 1 <= k <= |I|. Then introduce another auxiliary
alpar@1: #  parameter:
alpar@1: 
alpar@1: param ind{k in 1..card(I)} := sum{i in I: pos[i] = k} i;
alpar@1: 
alpar@1: #  where ind[k] = i iff pos[k] = i.
alpar@1: #
alpar@1: #  Now, the following statement:
alpar@1: 
alpar@1: printf{k in 1..card(I)} "a[%d] = %g\n", ind[k], a[ind[k]];
alpar@1: 
alpar@1: #  prints the parameter members in the desired order:
alpar@1: #
alpar@1: #  a[2]  = 2.04798
alpar@1: #  a[3]  = 2.14843
alpar@1: #  a[1]  = 2.64156
alpar@1: #  a[6]  = 3.27780
alpar@1: #  a[11] = 3.46065
alpar@1: #  a[8]  = 4.05898
alpar@1: #  a[7]  = 4.06113
alpar@1: #  a[12] = 4.69845
alpar@1: #  a[4]  = 4.76896
alpar@1: #  a[5]  = 6.09132
alpar@1: #  a[10] = 6.50318
alpar@1: #  a[9]  = 6.63120
alpar@1: 
alpar@1: end;