Int NaturalBisect
( Int nx,
Int ny,
Int nz,
const DistGraph& graph,
Int& nxChild,
Int& nyChild,
Int& nzChild,
DistGraph& child,
DistMap& perm,
bool& onLeft )
{
DEBUG_CSE
const Int numSources = graph.NumSources();
const Int firstLocalSource = graph.FirstLocalSource();
const Int numLocalSources = graph.NumLocalSources();
mpi::Comm comm = graph.Comm();
const Int commSize = mpi::Size( comm );
if( commSize == 1 )
LogicError
("This routine assumes at least two processes are used, "
"otherwise one child will be lost");
Int leftChildSize, rightChildSize, sepSize;
Int nxLeft, nyLeft, nzLeft, nxRight, nyRight, nzRight;
perm.SetComm( comm );
perm.Resize( numSources );
if( nx != 0 && ny != 0 && nz != 0 )
{
if( nx >= ny && nx >= nz )
{
nxLeft = (nx-1)/2;
nyLeft = ny;
nzLeft = nz;
leftChildSize = nxLeft*nyLeft*nzLeft;
nxRight = nx-1-nxLeft;
nyRight = ny;
nzRight = nz;
rightChildSize = nxRight*nyRight*nzRight;
sepSize = ny*nz;
const Int rightOff=leftChildSize,
sepOff=leftChildSize+rightChildSize;
for( Int iLocal=0; iLocal<numLocalSources; ++iLocal )
{
const Int i = iLocal + firstLocalSource;
const Int x = i % nx;
const Int y = (i/nx) % ny;
const Int z = i/(nx*ny);
if( x < nxLeft )
{
const Int xLeft = x;
const Int leftInd = xLeft + y*nxLeft + z*nxLeft*ny;
perm.SetLocal( iLocal, leftInd );
}
else if( x > nxLeft )
{
const Int xRight = x-(nxLeft+1);
const Int rightInd = xRight + y*nxRight + z*nxRight*ny;
perm.SetLocal( iLocal, rightOff+rightInd );
}
else
{
const Int sepInd = y + z*ny;
perm.SetLocal( iLocal, sepOff+sepInd );
}
}
}
else if( ny >= nx && ny >= nz )
{
nxLeft = nx;
nyLeft = (ny-1)/2;
nzLeft = nz;
leftChildSize = nxLeft*nyLeft*nzLeft;
nxRight = nx;
nyRight = ny-1-nyLeft;
nzRight = nz;
rightChildSize = nxRight*nyRight*nzRight;
sepSize = nx*nz;
const Int rightOff=leftChildSize,
sepOff=leftChildSize+rightChildSize;
for( Int iLocal=0; iLocal<numLocalSources; ++iLocal )
{
const Int i = iLocal + firstLocalSource;
const Int x = i % nx;
const Int y = (i/nx) % ny;
const Int z = i/(nx*ny);
if( y < nyLeft )
{
const Int yLeft = y;
const Int leftInd = x + yLeft*nx + z*nx*nyLeft;
perm.SetLocal( iLocal, leftInd );
}
else if( y > nyLeft )
{
const Int yRight = y - (nyLeft+1);
const Int rightInd = x + yRight*nx + z*nx*nyRight;
perm.SetLocal( iLocal, rightOff+rightInd );
}
else
{
const Int sepInd = x + z*nx;
perm.SetLocal( iLocal, sepOff+sepInd );
}
}
}
else
{
nxLeft = nx;
nyLeft = ny;
nzLeft = (nz-1)/2;
leftChildSize = nxLeft*nyLeft*nzLeft;
nxRight = nx;
nyRight = ny;
nzRight = nz-1-nzLeft;
rightChildSize = nxRight*nyRight*nzRight;
sepSize = nx*ny;
const Int rightOff=leftChildSize,
sepOff=leftChildSize+rightChildSize;
for( Int iLocal=0; iLocal<numLocalSources; ++iLocal )
{
const Int i = iLocal + firstLocalSource;
const Int x = i % nx;
const Int y = (i/nx) % ny;
const Int z = i/(nx*ny);
if( z < nzLeft )
{
const Int zLeft = z;
const Int leftInd = x + y*nx + zLeft*nx*ny;
perm.SetLocal( iLocal, leftInd );
}
else if( z > nzLeft )
{
const Int zRight = z - (nzLeft+1);
const Int rightInd = x + y*nx + zRight*nx*ny;
perm.SetLocal( iLocal, rightOff+rightInd );
}
else
{
const Int sepInd = x + y*nx;
perm.SetLocal( iLocal, sepOff+sepInd );
}
}
}
}
else
{
leftChildSize = rightChildSize = sepSize = 0;
nxLeft = nx;
nyLeft = ny;
nzLeft = nz;
nxRight = nx;
nyRight = ny;
nzRight = nz;
}
DEBUG_ONLY(EnsurePermutation( perm ))
BuildChildFromPerm
( graph, perm, leftChildSize, rightChildSize, onLeft, child );
if( onLeft )
{
nxChild = nxLeft;
nyChild = nyLeft;
nzChild = nzLeft;
}
else
{
nxChild = nxRight;
nyChild = nyRight;
nzChild = nzRight;
}
return sepSize;
}
inline void
NestedDissectionRecursion
( const DistGraph& graph,
const DistMap& perm,
DistSeparator& sep,
DistNodeInfo& node,
Int off,
const BisectCtrl& ctrl )
{
DEBUG_ONLY(CSE cse("ldl::NestedDissectionRecursion"))
mpi::Comm comm = graph.Comm();
const int commSize = mpi::Size(comm);
mpi::Dup( comm, sep.comm );
mpi::Dup( comm, node.comm );
if( commSize > 1 )
{
const Int numLocalSources = graph.NumLocalSources();
const Int firstLocalSource = graph.FirstLocalSource();
const Int* offsetBuf = graph.LockedOffsetBuffer();
const Int* targetBuf = graph.LockedTargetBuffer();
// Partition the graph and construct the inverse map
DistGraph child;
bool childIsOnLeft;
DistMap map;
const Int sepSize = Bisect( graph, child, map, childIsOnLeft, ctrl );
const Int numSources = graph.NumSources();
const Int childSize = child.NumSources();
const Int leftChildSize =
( childIsOnLeft ? childSize : numSources-sepSize-childSize );
DistMap invMap;
InvertMap( map, invMap );
// Mostly fill this node of the DistSeparatorTree
// (we will finish computing the separator indices at the end)
sep.off = off + (numSources-sepSize);
sep.inds.resize( sepSize );
for( Int s=0; s<sepSize; ++s )
sep.inds[s] = s + (numSources-sepSize);
invMap.Translate( sep.inds );
// Fill in this node of the DistNode
node.size = sepSize;
node.off = sep.off;
set<Int> localLowerStruct;
for( Int s=0; s<sepSize; ++s )
{
const Int source = sep.inds[s];
if( source >= firstLocalSource &&
source < firstLocalSource+numLocalSources )
{
const Int localSource = source - firstLocalSource;
const Int edgeOff = offsetBuf[localSource];
const Int numConn = offsetBuf[localSource+1] - edgeOff;
for( Int t=0; t<numConn; ++t )
{
const Int target = targetBuf[edgeOff+t];
if( target >= numSources )
localLowerStruct.insert( off+target );
}
}
}
const int numLocalConnected = localLowerStruct.size();
vector<int> localConnectedSizes( commSize );
mpi::AllGather
( &numLocalConnected, 1, localConnectedSizes.data(), 1, comm );
vector<Int> localConnectedVec;
CopySTL( localLowerStruct, localConnectedVec );
vector<int> localConnectedOffs;
const int sumOfLocalConnectedSizes =
Scan( localConnectedSizes, localConnectedOffs );
vector<Int> localConnections( sumOfLocalConnectedSizes );
mpi::AllGather
( localConnectedVec.data(), numLocalConnected,
localConnections.data(),
localConnectedSizes.data(), localConnectedOffs.data(), comm );
set<Int> lowerStruct
( localConnections.begin(), localConnections.end() );
CopySTL( lowerStruct, node.origLowerStruct );
// Finish computing the separator indices
perm.Translate( sep.inds );
// Construct map from child indices to the original ordering
DistMap newPerm( child.NumSources(), child.Comm() );
const Int localChildSize = child.NumLocalSources();
const Int firstLocalChildSource = child.FirstLocalSource();
auto& newPermLoc = newPerm.Map();
if( childIsOnLeft )
for( Int s=0; s<localChildSize; ++s )
newPermLoc[s] = s+firstLocalChildSource;
else
for( Int s=0; s<localChildSize; ++s )
newPermLoc[s] = s+firstLocalChildSource+leftChildSize;
invMap.Extend( newPerm );
perm.Extend( newPerm );
// Recurse
const Int childOff = ( childIsOnLeft ? off : off+leftChildSize );
sep.child = new DistSeparator(&sep);
node.child = new DistNodeInfo(&node);
node.child->onLeft = childIsOnLeft;
NestedDissectionRecursion
( child, newPerm, *sep.child, *node.child, childOff, ctrl );
}
else
{
Graph seqGraph( graph );
sep.duplicate = new Separator(&sep);
node.duplicate = new NodeInfo(&node);
NestedDissectionRecursion
( seqGraph, perm.Map(), *sep.duplicate, *node.duplicate, off, ctrl );
// Pull information up from the duplicates
sep.off = sep.duplicate->off;
sep.inds = sep.duplicate->inds;
node.size = node.duplicate->size;
node.off = node.duplicate->off;
node.origLowerStruct = node.duplicate->origLowerStruct;
}
}