void PushPairInto
( DistMultiVec<Real>& s,
DistMultiVec<Real>& z,
const DistMultiVec<Real>& w,
const DistMultiVec<Int>& orders,
const DistMultiVec<Int>& firstInds,
Real wMaxNormLimit, Int cutoff )
{
DEBUG_ONLY(CSE cse("soc::PushPairInto"))
DistMultiVec<Real> sLower(s.Comm()), zLower(z.Comm());
soc::LowerNorms( s, sLower, orders, firstInds, cutoff );
soc::LowerNorms( z, zLower, orders, firstInds, cutoff );
const int localHeight = s.LocalHeight();
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const Int i = s.GlobalRow(iLoc);
const Real w0 = w.GetLocal(iLoc,0);
if( i == firstInds.GetLocal(iLoc,0) && w0 > wMaxNormLimit )
{
// TODO: Switch to a non-adhoc modification
s.UpdateLocal( iLoc, 0, Real(1)/wMaxNormLimit );
z.UpdateLocal( iLoc, 0, Real(1)/wMaxNormLimit );
}
}
}
void SOCSquareRoot
( const DistMultiVec<Real>& x,
DistMultiVec<Real>& xRoot,
const DistMultiVec<Int>& orders,
const DistMultiVec<Int>& firstInds, Int cutoff )
{
DEBUG_ONLY(CSE cse("SOCSquareRoot"))
DistMultiVec<Real> d(x.Comm());
SOCDets( x, d, orders, firstInds );
ConeBroadcast( d, orders, firstInds );
auto roots = x;
ConeBroadcast( roots, orders, firstInds );
const Int localHeight = x.LocalHeight();
xRoot.SetComm( x.Comm() );
Zeros( xRoot, x.Height(), 1 );
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const Int i = x.GlobalRow(iLoc);
const Real x0 = roots.GetLocal(iLoc,0);
const Real det = d.GetLocal(iLoc,0);
const Real eta0 = Sqrt(x0+Sqrt(det))/Sqrt(Real(2));
if( i == firstInds.GetLocal(iLoc,0) )
xRoot.SetLocal( iLoc, 0, eta0 );
else
xRoot.SetLocal( iLoc, 0, x.GetLocal(iLoc,0)/(2*eta0) );
}
}
void PushInto
( DistMultiVec<Real>& x,
const DistMultiVec<Int>& orders,
const DistMultiVec<Int>& firstInds,
Real minDist, Int cutoff )
{
DEBUG_ONLY(CSE cse("soc::PushInto"))
DistMultiVec<Real> d(x.Comm());
soc::LowerNorms( x, d, orders, firstInds, cutoff );
const int localHeight = x.LocalHeight();
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const Int i = x.GlobalRow(iLoc);
const Real x0 = x.GetLocal(iLoc,0);
const Real lowerNorm = d.GetLocal(iLoc,0);
if( i == firstInds.GetLocal(iLoc,0) && x0-lowerNorm < minDist )
x.UpdateLocal( iLoc, 0, minDist - (x0-lowerNorm) );
}
}
void SOCApply
( const DistMultiVec<Real>& x,
const DistMultiVec<Real>& y,
DistMultiVec<Real>& z,
const DistMultiVec<Int>& orders,
const DistMultiVec<Int>& firstInds, Int cutoff )
{
DEBUG_ONLY(CSE cse("SOCApply"))
SOCDots( x, y, z, orders, firstInds );
auto xRoots = x;
auto yRoots = y;
ConeBroadcast( xRoots, orders, firstInds );
ConeBroadcast( yRoots, orders, firstInds );
const Int localHeight = x.LocalHeight();
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const Int i = x.GlobalRow(iLoc);
const Int firstInd = firstInds.GetLocal(iLoc,0);
if( i != firstInd )
z.UpdateLocal
( iLoc, 0, xRoots.GetLocal(iLoc,0)*y.GetLocal(iLoc,0) +
yRoots.GetLocal(iLoc,0)*x.GetLocal(iLoc,0) );
}
}
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 );
}
