void EntrywiseMap
( const DistMultiVec<S>& A,
DistMultiVec<T>& B,
function<T(S)> func )
{
DEBUG_CSE
B.SetComm( A.Comm() );
B.Resize( A.Height(), A.Width() );
EntrywiseMap( A.LockedMatrix(), B.Matrix(), func );
}
Int NumOutside( const DistMultiVec<Real>& A )
{
EL_DEBUG_CSE
const Int localHeight = A.LocalHeight();
const Int width = A.Width();
const Real* ABuf = A.LockedMatrix().LockedBuffer();
const Int ALDim = A.LockedMatrix().LDim();
Int numLocalNonPos = 0;
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
for( Int j=0; j<width; ++j )
if( ABuf[iLoc+j*ALDim] <= Real(0) )
++numLocalNonPos;
return mpi::AllReduce( numLocalNonPos, A.Comm() );
}
inline void
DistNodalMultiVec<F>::Pull
( const DistMap& inverseMap, const DistSymmInfo& info,
const DistMultiVec<F>& X )
{
DEBUG_ONLY(CallStackEntry cse("DistNodalMultiVec::Pull"))
height_ = X.Height();
width_ = X.Width();
// Traverse our part of the elimination tree to see how many indices we need
int numRecvInds=0;
const int numLocal = info.localNodes.size();
for( int s=0; s<numLocal; ++s )
numRecvInds += info.localNodes[s].size;
const int numDist = info.distNodes.size();
for( int s=1; s<numDist; ++s )
numRecvInds += info.distNodes[s].multiVecMeta.localSize;
// Fill the set of indices that we need to map to the original ordering
int off=0;
std::vector<int> mappedInds( numRecvInds );
for( int s=0; s<numLocal; ++s )
{
const SymmNodeInfo& nodeInfo = info.localNodes[s];
for( int t=0; t<nodeInfo.size; ++t )
mappedInds[off++] = nodeInfo.off+t;
}
for( int s=1; s<numDist; ++s )
{
const DistSymmNodeInfo& nodeInfo = info.distNodes[s];
const Grid& grid = *nodeInfo.grid;
const int gridSize = grid.Size();
const int gridRank = grid.VCRank();
const int alignment = 0;
const int shift = Shift( gridRank, alignment, gridSize );
for( int t=shift; t<nodeInfo.size; t+=gridSize )
mappedInds[off++] = nodeInfo.off+t;
}
DEBUG_ONLY(
if( off != numRecvInds )
LogicError("mappedInds was filled incorrectly");
)
void QP
( const DistSparseMatrix<Real>& A,
const DistMultiVec<Real>& B,
DistMultiVec<Real>& X,
const qp::direct::Ctrl<Real>& ctrl )
{
DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const Int k = B.Width();
mpi::Comm comm = A.Comm();
DistSparseMatrix<Real> Q(comm), AHat(comm);
DistMultiVec<Real> bHat(comm), c(comm);
Herk( LOWER, ADJOINT, Real(1), A, Q );
MakeHermitian( LOWER, Q );
Zeros( AHat, 0, n );
Zeros( bHat, 0, 1 );
Zeros( X, n, k );
DistMultiVec<Real> q(comm), y(comm), z(comm);
auto& qLoc = q.Matrix();
auto& XLoc = X.Matrix();
auto& BLoc = B.LockedMatrix();
for( Int j=0; j<k; ++j )
{
auto xLoc = XLoc( ALL, IR(j) );
auto bLoc = BLoc( ALL, IR(j) );
Zeros( c, n, 1 );
Zeros( q, m, 1 );
qLoc = bLoc;
Multiply( ADJOINT, Real(-1), A, q, Real(0), c );
Zeros( q, n, 1 );
qLoc = xLoc;
El::QP( Q, AHat, bHat, c, q, y, z, ctrl );
xLoc = qLoc;
}
}
void Tikhonov
( Orientation orientation,
const DistSparseMatrix<F>& A,
const DistMultiVec<F>& B,
const DistSparseMatrix<F>& G,
DistMultiVec<F>& X,
const LeastSquaresCtrl<Base<F>>& ctrl )
{
DEBUG_CSE
mpi::Comm comm = A.Comm();
// Explicitly form W := op(A)
// ==========================
DistSparseMatrix<F> W(comm);
if( orientation == NORMAL )
W = A;
else if( orientation == TRANSPOSE )
Transpose( A, W );
else
Adjoint( A, W );
const Int m = W.Height();
const Int n = W.Width();
const Int numRHS = B.Width();
// Embed into a higher-dimensional problem via appending regularization
// ====================================================================
DistSparseMatrix<F> WEmb(comm);
if( m >= n )
VCat( W, G, WEmb );
else
HCat( W, G, WEmb );
DistMultiVec<F> BEmb(comm);
Zeros( BEmb, WEmb.Height(), numRHS );
if( m >= n )
{
// BEmb := [B; 0]
// --------------
const Int mLocB = B.LocalHeight();
BEmb.Reserve( mLocB*numRHS );
for( Int iLoc=0; iLoc<mLocB; ++iLoc )
{
const Int i = B.GlobalRow(iLoc);
for( Int j=0; j<numRHS; ++j )
BEmb.QueueUpdate( i, j, B.GetLocal(iLoc,j) );
}
BEmb.ProcessQueues();
}
else
BEmb = B;
// Solve the higher-dimensional problem
// ====================================
DistMultiVec<F> XEmb(comm);
LeastSquares( NORMAL, WEmb, BEmb, XEmb, ctrl );
// Extract the solution
// ====================
if( m >= n )
X = XEmb;
else
GetSubmatrix( XEmb, IR(0,n), IR(0,numRHS), X );
}
