Hi everyone! Currently, I am trying to reduce the dimension of some parameters by means of a “projection” (I am not sure if project is the right word in this case). According to the example below, I need to reduce the 2-dimensional matrix (a) into the vector vec(k). Hence, vec(k) should equal [1,2,3,1,3,4,1,4,3]. The set g(i,j,k) defines the mapping rule (tuple), but I cannot figure out how to use it to get vec(k). I tried with conditionals, but I cannot make it work. I appreciate any help. Thanks!

I believe night_dog was on the right track. Here’s my version of her code, with the crucial change being the one to the definition of the set g.

Set i /i1*i3 /;
Set j /j1*j3 /;
Set k /k1*k9/;
Set g(k,i,j) /#k:(#i.#j)/;
Table a(i,j) 'original matrix'
j1 j2 j3
i1 1 2 3
i2 11 12 13
i3 21 22 23;
Parameters
vec(k) 'suggestion of abhosekar'
v2(k) 'original intent of night_dog?'
chk(k)
;
vec(k) = sum{(i,j)$[(ord(i) - 1)*card(j) + ord(j) = ord(k)] , a(i,j)};
v2(k) = sum{g(k,i,j), a(i,j)};
chk(k) = vec(k) - v2(k);
execute_unload 'dachshund';
abort$[card(chk)] 'vec - v2 is nonzero', chk;

The idea to construct a mapping g(k,i,j) between indices k and tuples (i,j) and then use a sum to convert i-j-tuples to indices k (or vice versa) is a very useful idiom in GAMS. I like it because the expression

v2(k) = sum{g(k,i,j), a(i,j)};

is terse and easy to understand. To see what it does, we can just look at the map g in Studio or elsewhere. In this case g is simple, but even if the mapping gets very complicated, we need only change the data in g. The code to compute v2 remains unchanged.

give the identical results and have the same space and time requirements in a running GAMS job. AFAIK they both produce identical internal representations of this statement.