bool
DynamicPersistenceTrails<D,CT,OT,E,Cmp,CCmp>::
transpose(iterator i, const DimensionFunctor& dimension, Visitor visitor)
{
#if LOGGING
typename Traits::OutputMap outmap(order());
#endif
Count(cTransposition);
typedef typename Element::Trail::iterator TrailIterator;
visitor.transpose(i);
iterator i_prev = i++;
if (dimension(i_prev) != dimension(i))
{
swap(i_prev, i);
rLog(rlTranspositions, "Different dimension");
Count(cTranspositionDiffDim);
return false;
}
bool si = i_prev->sign(), sii = i->sign();
if (si && sii)
{
rLog(rlTranspositions, "Trail prev: %s", i_prev->trail.tostring(outmap).c_str());
// Case 1
if (trail_remove_if_contains(i_prev, index(i)))
rLog(rlTranspositions, "Case 1, U[i,i+1] = 1");
iterator k = iterator_to(i_prev->pair);
iterator l = iterator_to(i->pair);
// rLog(rlTranspositions, "(i_prev, k), (i, l): (%s, %s), (%s, %s)",
// outmap(i_prev).c_str(), outmap(k).c_str(),
// outmap(i).c_str(), outmap(l).c_str());
// Explicit treatment of unpaired simplex
if (l == i)
{
swap(i_prev, i);
rLog(rlTranspositions, "Case 1.2 --- unpaired");
rLog(rlTranspositions, "%s", outmap(i_prev).c_str());
Count(cTranspositionCase12);
return false;
} else if (k == i_prev)
{
if (!(l->cycle.contains(index(i_prev))))
{
// Case 1.2
swap(i_prev, i);
rLog(rlTranspositions, "Case 1.2 --- unpaired");
rLog(rlTranspositions, outmap(i_prev).c_str());
Count(cTranspositionCase12);
return false;
} else
{
// Case 1.2 --- special version (plain swap, but pairing switches)
swap(i_prev, i);
pairing_switch(i_prev, i);
visitor.switched(i, Case12);
rLog(rlTranspositions, "Case 1.2 --- unpaired (pairing switch)");
rLog(rlTranspositions, outmap(i_prev).c_str());
Count(cTranspositionCase12s);
return true;
}
}
rLog(rlTranspositions, "l cycle: %s", l->cycle.tostring(outmap).c_str());
if (!(l->cycle.contains(index(i_prev))))
{
// Case 1.2
rLog(rlTranspositions, "k is in l: %d", (bool) l->trail.contains(index(k))); // if true, a special update would be needed to maintain lazy decomposition
swap(i_prev, i);
rLog(rlTranspositions, "Case 1.2");
Count(cTranspositionCase12);
return false;
} else
{
// Case 1.1
if (std::not2(order_comparison())(index(k),index(l)))
{
// Case 1.1.1
swap(i_prev, i);
cycle_add(l, k->cycle); // Add column k to l
trail_add(k, l->trail); // Add row l to k
rLog(rlTranspositions, "Case 1.1.1");
Count(cTranspositionCase111);
return false;
} else
{
// Case 1.1.2
swap(i_prev, i);
cycle_add(k, l->cycle); // Add column l to k
trail_add(l, k->trail); // Add row k to l
pairing_switch(i_prev, i);
visitor.switched(i, Case112);
rLog(rlTranspositions, "Case 1.1.2");
Count(cTranspositionCase112);
return true;
}
}
} else if (!si && !sii)
{
// Case 2
if (!(i_prev->trail.contains(index(i))))
{
// Case 2.2
swap(i_prev, i);
rLog(rlTranspositions, "Case 2.2");
Count(cTranspositionCase22);
return false;
} else
{
// Case 2.1
iterator low_i = iterator_to(i_prev->pair);
iterator low_ii = iterator_to(i->pair);
trail_add(i_prev, i->trail); // Add row i to i_prev
cycle_add(i, i_prev->cycle); // Add column i_prev to i
swap(i_prev, i);
if (std::not2(order_comparison())(index(low_ii), index(low_i)))
{
// Case 2.1.2
cycle_add(i_prev, i->cycle); // Add column i to i_prev (after transposition)
trail_add(i, i_prev->trail); // Add row i to i_prev
pairing_switch(i_prev, i);
visitor.switched(i, Case212);
rLog(rlTranspositions, "Case 2.1.2");
Count(cTranspositionCase212);
return true;
}
// Case 2.1.1
rLog(rlTranspositions, "Case 2.1.1");
Count(cTranspositionCase211);
return false;
}
} else if (!si && sii)
{
// Case 3
if (!(i_prev->trail.contains(index(i))))
{
// Case 3.2
swap(i_prev, i);
rLog(rlTranspositions, "Case 3.2");
Count(cTranspositionCase32);
return false;
} else
{
// Case 3.1
trail_add(i_prev, i->trail); // Add row i to i_prev
cycle_add(i, i_prev->cycle); // Add column i_prev to i
swap(i_prev, i);
cycle_add(i_prev, i->cycle); // Add column i_prev to i (after transposition)
trail_add(i, i_prev->trail); // Add row i to i_prev
pairing_switch(i_prev, i);
visitor.switched(i, Case31);
rLog(rlTranspositions, "Case 3.1");
Count(cTranspositionCase31);
return true;
}
} else if (si && !sii)
{
// Case 4
if (trail_remove_if_contains(i_prev, index(i)))
rLog(rlTranspositions, "Case 4, U[i,i+1] = 1");
swap(i_prev, i);
rLog(rlTranspositions, "Case 4");
Count(cTranspositionCase4);
return false;
}
return false; // to avoid compiler complaints; we should never reach this point
}
void
StaticPersistence<D, CT, OT, E, Cmp>::
pair_simplices(iterator bg, iterator end, bool store_negative, const Visitor& visitor)
{
#if LOGGING
typename ContainerTraits::OutputMap outmap(order_);
#endif
// FIXME: need sane output for logging
rLog(rlPersistence, "Entered: pair_simplices");
for (iterator j = bg; j != end; ++j)
{
visitor.init(j);
rLog(rlPersistence, "Simplex %s", outmap(j).c_str());
Cycle z;
swap_cycle(j, z);
rLog(rlPersistence, " has boundary: %s", z.tostring(outmap).c_str());
// Sparsify the cycle by removing the negative elements
if (!store_negative)
{
typename OrderElement::Cycle zz;
BOOST_FOREACH(OrderIndex i, z)
if (i->sign()) // positive
zz.push_back(i);
z.swap(zz);
}
// --------------------------
CountNum(cPersistencePairBoundaries, z.size());
#ifdef COUNTERS
Count(cPersistencePair);
#endif // COUNTERS
while(!z.empty())
{
OrderIndex i = z.top(ocmp_); // take the youngest element with respect to the OrderComparison
rLog(rlPersistence, " %s: %s", outmap(i).c_str(), outmap(i->pair).c_str());
// TODO: is this even a meaningful assert?
AssertMsg(!ocmp_(i, index(j)),
"Simplices in the cycle must precede current simplex: (%s in cycle of %s)",
outmap(i).c_str(), outmap(j).c_str());
// i is not paired, so we pair j with i
if (iterator_to(i->pair) == iterator_to(i))
{
rLog(rlPersistence, " Pairing %s and %s with cycle %s",
outmap(i).c_str(), outmap(j).c_str(),
z.tostring(outmap).c_str());
set_pair(i, j);
swap_cycle(j, z);
set_pair(j, i);
CountNum(cPersistencePairCycleLength, j->cycle.size());
CountBy (cPersistencePairCycleLength, j->cycle.size());
break;
}
// update element
z.add(i->pair->cycle, ocmp_);
visitor.update(j, iterator_to(i));
rLog(rlPersistence, " new cycle: %s", z.tostring(outmap).c_str());
}
// if z was empty, so is (already) j->cycle, so nothing to do
visitor.finished(j);
rLog(rlPersistence, "Finished with %s: %s",
outmap(j).c_str(), outmap(j->pair).c_str());
}
