\$title Test for various permutations (PERM1,SEQ=556) \$ontext Contributor: Michael Bussieck \$offtext * part 1 set i / i1*i3 /; * Set i consists of i1 i2 i3. Since sets can be reordered, we need a second index * to represent a permutation set perm1(i,i) / i1.i2, i2.i1, i3.i3 /; * This set represents in cycle notation: (1 2)(3) * Using the factorial we can compute the number of all possible * permutations of i: 3! = 3*2*1 = 6 \$eval pmax fact(card(i)) set p permutation index /p1*p%pmax%/; * For this small set i we can write them all down set table pall(p,i,i) i1 i2 i3 p1.i1 1 p1.i2 1 p1.i3 1 p2.i1 1 p2.i2 1 p2.i3 1 p3.i1 1 p3.i2 1 p3.i3 1 p4.i1 1 p4.i2 1 p4.i3 1 p5.i1 1 p5.i2 1 p5.i3 1 p6.i1 1 p6.i2 1 p6.i3 1 ; * There is also special GAMS syntax to produce the set pall from the set p and i set pall2(p,i,i); option pall2 > i; * The order of the permutation depends on how we generate them, but will still * compare pall and pall2 alias (i,ii); set error01(p,i,i); error01(p,i,ii) = pall(p,i,ii) xor pall(p,i,ii); abort\$card(error01) 'permutation pall and pall2 differ', error01; * This syntax is not limited to one dimensional sets i, we can do the same with * multidimensional sets: set j / j1*j2 /, k / k1*k5 / jk(j,k) / j1.k3, j1.k5, j2.k1 /; * jk is a three element set, so we will have 3! = 3*2*1 = 6 permutations * so we can use the p index to represent all permutations set pjkall(p,j,k,j,k); option pjkall > jk; execute_unload 'jk', pjkall; execute_load 'jk', pjkall; * pikall will have j1.k3 -> j1.k3, j1.k5 -> j1.k5, j2.k1 -> j2.k1 * j1.k3 -> j1.k3, j1.k5 -> j2.k1, j2.k1 -> j1.k5 * j1.k3 -> j1.k5, j1.k5 -> j1.k3, j2.k1 -> j2.k1 * ... * We can use our pall set to verify this set ijk(i,j,k) / #i:#jk /; set pjkall2(p,j,k,j,k); loop(pall(p,i,ii), pjkall2(p,jk,j,k)\$ijk(i,jk) = sum(ijk(ii,j,k),1)); set error02(p,j,k,j,k); error02(p,jk,j,k) = pjkall(p,jk,j,k) xor pjkall2(p,jk,j,k); abort\$card(error02) 'permutation pjkall and pjkall2 differ', error02; * We can permute set elements using a second index as seen above, but we can * also permute numerical data in a GAMS parameter. Parameter a(i) /i1 1, i2 2, i3 3/; * Here we do not need to have another index we can just represent the * permutations in the following way Table paall(p,i) i1 i2 i3 p1 1 2 3 p2 1 3 2 p3 2 1 3 p4 2 3 1 p5 3 1 2 p6 3 2 1 ; Parameter paall2(p,i); option paall2 > a; set error03(p,i); error03(p,i) = paall(p,i) <> paall2(p,i); abort\$card(error03) 'paall and paall2 differ', error03, paall, paall2; * Note that we can also compute the data permutation from the set permuatation Parameter paall3(p,i); paall3(p,i) = sum(pall(p,i,ii), a(ii)); set error04(p,i); error04(p,i) = paall(p,i) <> paall3(p,i); abort\$card(error04) 'paall and paall3 differ', error03, paall, paall3; * Again data permutations can be also done for multi dimensional parameters Parameter b(j,k) /j1.k3 1, j1.k5 2, j2.k1 3/; Table pball(p,j,k) j1.k3 j1.k5 j2.k1 p1 1 2 3 p2 1 3 2 p3 2 1 3 p4 2 3 1 p5 3 1 2 p6 3 2 1 ; Parameter pball2(p,j,k); option pball2 > b; execute_unload 'jk', pball2; execute_load 'jk', pball2; set error05(p,j,k); error05(p,jk) = pball(p,jk) <> pball2(p,jk); abort\$card(error05) 'pball and pball2 differ', error05, pball, pball2; * With the data permutation there is one particularity. If the data contain * a number twice, for example Parameter c(i) /i1 1, i2 1, i3 3/; * The GAMS permutation does not fold the permutations that result in the * same data record. So we have again 6 permutations where p1=p3, p2=p4 and p5=p6 Table pcall(p,i) i1 i2 i3 p1 1 1 3 p2 1 3 1 p3 1 1 3 p4 1 3 1 p5 3 1 1 p6 3 1 1 ; Parameter pcall2(p,i); option pcall2 > c; set error06(p,i); error06(p,i) = pcall(p,i) <> pcall2(p,i); abort\$card(error06) 'pcall and pcall2 differ', error06, pcall, pcall2;