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 RowMaxNorms( const DistMultiVec<F>& A, DistMultiVec<Base<F>>& norms )
{
DEBUG_CSE
norms.SetComm( A.Comm() );
norms.Resize( A.Height(), 1 );
RowMaxNorms( A.LockedMatrix(), norms.Matrix() );
}
void Mehrotra
( const DistSparseMatrix<Real>& A,
const DistMultiVec<Real>& b,
const DistMultiVec<Real>& c,
const DistMultiVec<Int>& orders,
const DistMultiVec<Int>& firstInds,
DistMultiVec<Real>& x,
DistMultiVec<Real>& y,
DistMultiVec<Real>& z,
const MehrotraCtrl<Real>& ctrl )
{
EL_DEBUG_CSE
const Int n = c.Height();
mpi::Comm comm = c.Comm();
DistSparseMatrix<Real> G(comm);
Identity( G, n, n );
G *= -1;
DistMultiVec<Real> h(comm);
Zeros( h, n, 1 );
MehrotraCtrl<Real> affineCtrl = ctrl;
affineCtrl.primalInit = false;
affineCtrl.dualInit = false;
DistMultiVec<Real> s(comm);
socp::affine::Mehrotra(A,G,b,c,h,orders,firstInds,x,y,z,s,affineCtrl);
}
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 );
}
void SOCApply
( const DistMultiVec<Real>& x,
DistMultiVec<Real>& y,
const DistMultiVec<Int>& orders,
const DistMultiVec<Int>& firstInds, Int cutoff )
{
DEBUG_ONLY(CSE cse("SOCApply"))
// TODO?: Optimize
DistMultiVec<Real> z(x.Comm());
SOCApply( x, y, z, orders, firstInds, cutoff );
y = z;
}
Real ComplementRatio
( const DistMultiVec<Real>& s,
const DistMultiVec<Real>& z )
{
DEBUG_CSE
const Int localHeight = s.LocalHeight();
const Real* sBuf = s.LockedMatrix().LockedBuffer();
const Real* zBuf = z.LockedMatrix().LockedBuffer();
Real maxLocProd = 0;
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
maxLocProd = Max( sBuf[iLoc]*zBuf[iLoc], maxLocProd );
const Real maxProd = mpi::AllReduce( maxLocProd, mpi::MAX, s.Comm() );
Real minLocProd = maxProd;
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
minLocProd = Min( sBuf[iLoc]*zBuf[iLoc], minLocProd );
const Real minProd = mpi::AllReduce( minLocProd, mpi::MIN, s.Comm() );
return maxProd/minProd;
}
Int Degree( const DistMultiVec<Int>& firstInds )
{
DEBUG_CSE
Int localDegree = 0;
const Int localHeight = firstInds.LocalHeight();
auto& firstIndsLoc = firstInds.LockedMatrix();
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const Int i = firstInds.GlobalRow(iLoc);
if( i == firstIndsLoc(iLoc) )
++localDegree;
}
return mpi::AllReduce( localDegree, firstInds.Comm() );
}
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() );
}
void NesterovTodd
( const DistMultiVec<Real>& s,
const DistMultiVec<Real>& z,
DistMultiVec<Real>& w )
{
DEBUG_CSE
w.SetComm( s.Comm() );
w.Resize( s.Height(), 1 );
const Real* sBuf = s.LockedMatrix().LockedBuffer();
const Real* zBuf = z.LockedMatrix().LockedBuffer();
Real* wBuf = w.Matrix().Buffer();
const Int localHeight = w.LocalHeight();
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
wBuf[iLoc] = Sqrt(sBuf[iLoc]/zBuf[iLoc]);
}
Real MaxStep
( const DistMultiVec<Real>& s,
const DistMultiVec<Real>& ds,
Real upperBound )
{
EL_DEBUG_CSE
const Int kLocal = s.LocalHeight();
const Real* sBuf = s.LockedMatrix().LockedBuffer();
const Real* dsBuf = ds.LockedMatrix().LockedBuffer();
Real alpha = upperBound;
for( Int iLoc=0; iLoc<kLocal; ++iLoc )
{
const Real si = sBuf[iLoc];
const Real dsi = dsBuf[iLoc];
if( dsi < Real(0) )
alpha = Min(alpha,-si/dsi);
}
return mpi::AllReduce( alpha, mpi::MIN, s.Comm() );
}
void Inverse
( const DistMultiVec<Real>& x,
DistMultiVec<Real>& xInv,
const DistMultiVec<Int>& orders,
const DistMultiVec<Int>& firstInds,
Int cutoff )
{
DEBUG_CSE
DistMultiVec<Real> dInv(x.Comm());
soc::Dets( x, dInv, orders, firstInds, cutoff );
cone::Broadcast( dInv, orders, firstInds );
auto entryInv = [=]( Real alpha ) { return Real(1)/alpha; };
EntrywiseMap( dInv, function<Real(Real)>(entryInv) );
auto Rx = x;
soc::Reflect( Rx, orders, firstInds );
Hadamard( dInv, Rx, xInv );
}
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) );
}
}
