$title 'Check handling of singleton sets' (SINGLE01,SEQ=639)

$onText
This test checks that the singleton sets can be used as expected
when strictSingleton=0

Contributor: Lutz Westermann, January 2014
$offText

set i /i1*i3/
    j /j1*j3/
    k /k1*k3/
    l /l1*l3/;

singleton set si(i)    /i2/
              sid      /#si/
              sk(k)    /k2/
              sl(l)    /l2/
              sij(i,j) /i2.j2/
              sjk(j,k) /j2.k2/
              skl(k,l) /k2.l2/ ;

parameter pi(i)
          psi(sid)
          pii(i,i)
          psii(sid,sid)
          pij(i,j)
          pijk(i,j,k)
          pijkl(i,j,k,l);

alias (i,a);
alias(si,sai);
alias (sid,sad);
pi(i)          =      ord(i);
psi(sid)       = pi(si);
pij(i,j)       = 10  *ord(i)+    ord(j);
pii(i,a)       = 10  *ord(i)+    ord(a);
psii(sid,sad)  = pii(si,sai);
pijk(i,j,k)    = 100 *ord(i)+10 *ord(j)+   ord(k);
pijkl(i,j,k,l) = 1000*ord(i)+100*ord(j)+10*ord(k)+ord(l);

scalar w,x,y,z;

w = psi(sid);
x = pi(si);
y = sum(si,pi(si));
abort$(x<>y) 'Unexpected difference',x,y;
abort$(w<>y) 'Unexpected difference',w,y;
loop(i,
  si(i)=yes;
  x = pi(si);
  y = sum(si,pi(si));
);
abort$(x<>y) 'Unexpected difference',x,y;

option strictSingleton = 0;
z = 0;
while(z<=2,
  si(i)=yes;
  x = pi(si);
  y = sum(si,pi(si));
  z = z+1;
);
abort$(x<>y) 'Unexpected difference',x,y;
for(z=1 to 2,
  si(i)=yes;
  x = pi(si);
  y = sum(si,pi(si));
);
abort$(x<>y) 'Unexpected difference',x,y;
z = 0;
repeat(
  si(i)=yes;
  x = pi(si);
  y = sum(si,pi(si));
  z = z+1;
until(z>2));
abort$(x<>y) 'Unexpected difference',x,y;

x = pij(sij);
y = sum(sij,pij(sij));
abort$(x<>y) 'Unexpected difference',x,y;
loop((i,j),
  sij(i,j)=yes;
  x = pij(sij);
  y = sum(sij,pij(sij));
);
abort$(x<>y) 'Unexpected difference',x,y;

loop(k,
  x = pijkl(sij,k-pi(si),sl);
  y = sum((sij,sl), pijkl(sij,k-sum(si,pi(si)),sl));
);
abort$(x<>y) 'Unexpected difference',x,y;
loop((i,j,k),
  sij(i,j)=yes;
  sl(l)   =yes;
  x = pijkl(sij,k-pi(si),sl);
  y = sum((sij,sl), pijkl(sij,k-sum(si,pi(si)),sl));
);
abort$(x<>y) 'Unexpected difference',x,y;

loop(k,
  x = sum(l,pijk(sij,k-pi(si)));
  y = sum(l,sum(sij, pijk(sij,k-sum(si,pi(si)))));
);
abort$(x<>y) 'Unexpected difference',x,y;
loop((i,j,k),
  sij(i,j)=yes;
  si(i)   =yes;
  x = sum(l,pijk(sij,k-pi(si)));
  y = sum(l,sum(sij, pijk(sij,k-sum(si,pi(si)))));
);
abort$(x<>y) 'Unexpected difference',x,y;

x = pijk(sij,sk);
y = sum((sij,sk),pijk(sij,sk));
abort$(x<>y) 'Unexpected difference',x,y;
loop((i,j,k),
  sij(i,j)=yes;
  sk(k)   =yes;
  x = pijk(sij,sk);
  y = sum((sij,sk),pijk(sij,sk));
);
abort$(x<>y) 'Unexpected difference',x,y;
loop((i,j),
  sij(i,j)=yes;
  x = pijk(sij,sk);
  y = sum((sij,sk),pijk(sij,sk));
);
abort$(x<>y) 'Unexpected difference',x,y;
loop(k,
  sk(k)=yes;
  x = pijk(sij,sk);
  y = sum((sij,sk),pijk(sij,sk));
);
abort$(x<>y) 'Unexpected difference',x,y;

x = pijkl(si,sjk,sl);
y = sum((si,sjk,sl),pijkl(si,sjk,sl));
abort$(x<>y) 'Unexpected difference',x,y;
loop((i,j,k,l),
  si(i)   =yes;
  sjk(j,k)=yes;
  sl(l)   =yes;
  x = pijkl(si,sjk,sl);
  y = sum((si,sjk,sl),pijkl(si,sjk,sl));
);
loop((j,k,l),
  sjk(j,k)=yes;
  sl(l)   =yes;
  x = pijkl(si,sjk,sl);
  y = sum((si,sjk,sl),pijkl(si,sjk,sl));
);
loop((i,l),
  si(i)   =yes;
  sl(l)   =yes;
  x = pijkl(si,sjk,sl);
  y = sum((si,sjk,sl),pijkl(si,sjk,sl));
);
loop((i,j,k),
  si(i)   =yes;
  sjk(j,k)=yes;
  x = pijkl(si,sjk,sl);
  y = sum((si,sjk,sl),pijkl(si,sjk,sl));
);
abort$(x<>y) 'Unexpected difference',x,y;

x = pijkl(si,'j1',skl);
y = sum((si,skl),pijkl(si,'j1',skl));
abort$(x<>y) 'Unexpected difference',x,y;
loop((i,k,l),
  si(i)   =yes;
  skl(k,l)=yes;
  x = pijkl(si,'j1',skl);
  y = sum((si,skl),pijkl(si,'j1',skl));
);
abort$(x<>y) 'Unexpected difference',x,y;

x = sum(j,pijkl(si,j,skl));
y = sum(j,sum((si,skl),pijkl(si,j,skl)));
abort$(x<>y) 'Unexpected difference',x,y;
loop((i,k,l),
  si(i)   =yes;
  skl(k,l)=yes;
  x = sum(j,pijkl(si,j,skl));
  y = sum(j,sum((si,skl),pijkl(si,j,skl)));
);
abort$(x<>y) 'Unexpected difference',x,y;

x = pijkl(sij,skl);
y = sum((sij,skl),pijkl(sij,skl));
abort$(x<>y) 'Unexpected difference',x,y;
loop((i,j,k,l),
  sij(i,j)=yes;
  skl(k,l)=yes;
  x = pijkl(sij,skl);
  y = sum((sij,skl),pijkl(sij,skl));
);
abort$(x<>y) 'Unexpected difference',x,y;
loop((i,j),
  sij(i,j)=yes;
  x = pijkl(sij,skl);
  y = sum((sij,skl),pijkl(sij,skl));
);
abort$(x<>y) 'Unexpected difference',x,y;
loop((k,l),
  skl(k,l)=yes;
  x = pijkl(sij,skl);
  y = sum((sij,skl),pijkl(sij,skl));
);
abort$(x<>y) 'Unexpected difference',x,y;

loop(i,
  x = pijkl(i-pi(si),sjk,sl);
  y = sum((sjk,sl), pijkl(i-sum(si,pi(si)),sjk,sl));
);
abort$(x<>y) 'Unexpected difference',x,y;
loop((i,j,k,l),
  si(i)=yes;
  sjk(j,k)=yes;
  sl(l)=yes;
  x = pijkl(i-pi(si),sjk,sl);
  y = sum((sjk,sl), pijkl(i-sum(si,pi(si)),sjk,sl));
);
abort$(x<>y) 'Unexpected difference',x,y;

loop(i,
  x = pijkl(i-pi(si),sjk,sl);
  y = sum((sjk), pijkl(i-sum(si,pi(si)),sjk,'l2'));
);
abort$(x<>y) 'Unexpected difference',x,y;
loop((i,j,k),
  si(i)=yes;
  sjk(j,k)=yes;
  x = pijkl(i-pi(si),sjk,sl);
  y = sum((sjk), pijkl(i-sum(si,pi(si)),sjk,'l2'));
);
abort$(x<>y) 'Unexpected difference',x,y;

x = pi(sai);
y = sum(sai,pi(sai));
abort$(x<>y) 'Unexpected difference',x,y;
loop(i,
  sai(i)=yes;
  x = pi(sai);
  y = sum(sai,pi(sai));
);
abort$(x<>y) 'Unexpected difference',x,y;

si('i2') = yes;
w = psii(sid,sad);
x = pii(si,sai);
y = sum((si,sai),pii(si,sai));
abort$(w<>y) 'Unexpected difference',w,y;
abort$(x<>y) 'Unexpected difference',x,y;
loop(i,
  si(i)=yes;
  sai(i)=yes;
  x = pii(si,sai);
  y = sum((si,sai),pii(si,sai));
);
abort$(x<>y) 'Unexpected difference',x,y;

si('i2') = yes;
w = psii(sid,sid);
x = pii(si,si);
y = sum((si),pii(si,si));
abort$(w<>y) 'Unexpected difference',w,y;
abort$(x<>y) 'Unexpected difference',x,y;
loop(i,
  si(i)=yes;
  x = pii(si,si);
  y = sum((si),pii(si,si));
);
abort$(x<>y) 'Unexpected difference',x,y;

alias(sjk,sajk);
loop(i,
  x = pijkl(i-pi(si),sajk,sl);
  y = sum((sajk,sl), pijkl(i-sum(si,pi(si)),sajk,sl));
);
abort$(x<>y) 'Unexpected difference',x,y;
loop((i,j,k),
  si(i)    =yes;
  sajk(j,k)=yes;
  sl(l)    =yes;
  x = pijkl(i-pi(si),sajk,sl);
  y = sum((sajk,sl), pijkl(i-sum(si,pi(si)),sajk,sl));
);
abort$(x<>y) 'Unexpected difference',x,y;

set u / 1*10 /;
singleton set su(u) /5/;

x = su.val;
y = sum(su,su.val);
abort$(x<>y) 'Unexpected difference',x,y;

x = 0; y = 0;
loop(u,
  su(u) = yes;
  x = x + su.val;
  y = y + sum(su,su.val);
);
abort$(x<>y) 'Unexpected difference',x,y;