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/* 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;
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