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 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 StackedRuizEquil
( DistSparseMatrix<Field>& A,
DistSparseMatrix<Field>& B,
DistMultiVec<Base<Field>>& dRowA,
DistMultiVec<Base<Field>>& dRowB,
DistMultiVec<Base<Field>>& dCol,
bool progress )
{
EL_DEBUG_CSE
typedef Base<Field> Real;
const Int mA = A.Height();
const Int mB = B.Height();
const Int n = A.Width();
mpi::Comm comm = A.Comm();
dRowA.SetComm( comm );
dRowB.SetComm( comm );
dCol.SetComm( comm );
Ones( dRowA, mA, 1 );
Ones( dRowB, mB, 1 );
Ones( dCol, n, 1 );
// TODO(poulson): Expose to control structure
// For, simply hard-code a small number of iterations
const Int maxIter = 4;
DistMultiVec<Real> scales(comm), maxAbsValsB(comm);
auto& scalesLoc = scales.Matrix();
auto& maxAbsValsBLoc = maxAbsValsB.Matrix();
const Int localHeight = scalesLoc.Height();
const Int indent = PushIndent();
for( Int iter=0; iter<maxIter; ++iter )
{
// Rescale the columns
// -------------------
ColumnMaxNorms( A, scales );
ColumnMaxNorms( B, maxAbsValsB );
for( Int jLoc=0; jLoc<localHeight; ++jLoc )
scalesLoc(jLoc) = Max(scalesLoc(jLoc),maxAbsValsBLoc(jLoc));
EntrywiseMap( scales, MakeFunction(DampScaling<Real>) );
DiagonalScale( LEFT, NORMAL, scales, dCol );
DiagonalSolve( RIGHT, NORMAL, scales, A );
DiagonalSolve( RIGHT, NORMAL, scales, B );
// Rescale the rows
// ----------------
RowMaxNorms( A, scales );
EntrywiseMap( scales, MakeFunction(DampScaling<Real>) );
DiagonalScale( LEFT, NORMAL, scales, dRowA );
DiagonalSolve( LEFT, NORMAL, scales, A );
RowMaxNorms( B, scales );
EntrywiseMap( scales, MakeFunction(DampScaling<Real>) );
DiagonalScale( LEFT, NORMAL, scales, dRowB );
DiagonalSolve( LEFT, NORMAL, scales, B );
}
SetIndent( indent );
}
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() );
}
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 SymmetricRuizEquil
( DistSparseMatrix<Field>& A,
DistMultiVec<Base<Field>>& d,
Int maxIter, bool progress )
{
EL_DEBUG_CSE
typedef Base<Field> Real;
const Int n = A.Height();
const Grid& grid = A.Grid();
d.SetGrid( grid );
Ones( d, n, 1 );
DistMultiVec<Real> scales(grid);
const Int indent = PushIndent();
for( Int iter=0; iter<maxIter; ++iter )
{
// Rescale the columns (and rows)
// ------------------------------
ColumnMaxNorms( A, scales );
EntrywiseMap( scales, MakeFunction(DampScaling<Real>) );
EntrywiseMap( scales, MakeFunction(SquareRootScaling<Real>) );
DiagonalScale( LEFT, NORMAL, scales, d );
SymmetricDiagonalSolve( scales, A );
}
SetIndent( indent );
}
void SymmetricRuizEquil
( DistSparseMatrix<F>& A,
DistMultiVec<Base<F>>& d,
Int maxIter, bool progress )
{
DEBUG_CSE
typedef Base<F> Real;
const Int n = A.Height();
mpi::Comm comm = A.Comm();
d.SetComm( comm );
Ones( d, n, 1 );
DistMultiVec<Real> scales(comm);
const Int indent = PushIndent();
for( Int iter=0; iter<maxIter; ++iter )
{
// Rescale the columns (and rows)
// ------------------------------
ColumnMaxNorms( A, scales );
EntrywiseMap( scales, function<Real(Real)>(DampScaling<Real>) );
EntrywiseMap( scales, function<Real(Real)>(SquareRootScaling<Real>) );
DiagonalScale( LEFT, NORMAL, scales, d );
SymmetricDiagonalSolve( scales, A );
}
SetIndent( indent );
}
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");
)
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 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;
}
}
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;
}
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;
}
void RowMaxNorms( const DistSparseMatrix<F>& A, DistMultiVec<Base<F>>& norms )
{
DEBUG_CSE
typedef Base<F> Real;
const Int localHeight = A.LocalHeight();
const F* valBuf = A.LockedValueBuffer();
const Int* offsetBuf = A.LockedOffsetBuffer();
norms.SetComm( A.Comm() );
norms.Resize( A.Height(), 1 );
auto& normsLoc = norms.Matrix();
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
Real rowMax = 0;
const Int offset = offsetBuf[iLoc];
const Int numConn = offsetBuf[iLoc+1] - offset;
for( Int e=offset; e<offset+numConn; ++e )
rowMax = Max(rowMax,Abs(valBuf[e]));
normsLoc(iLoc) = rowMax;
}
}
void Apply
( 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("soc::Apply"))
soc::Dots( x, y, z, orders, firstInds );
auto xRoots = x;
auto yRoots = y;
cone::Broadcast( xRoots, orders, firstInds );
cone::Broadcast( yRoots, orders, firstInds );
const Int firstLocalRow = x.FirstLocalRow();
const Int localHeight = x.LocalHeight();
const Real* xBuf = x.LockedMatrix().LockedBuffer();
const Real* xRootBuf = xRoots.LockedMatrix().LockedBuffer();
const Real* yBuf = y.LockedMatrix().LockedBuffer();
const Real* yRootBuf = yRoots.LockedMatrix().LockedBuffer();
Real* zBuf = z.Matrix().Buffer();
const Int* firstIndBuf = firstInds.LockedMatrix().LockedBuffer();
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const Int i = iLoc + firstLocalRow;
const Int firstInd = firstIndBuf[iLoc];
if( i != firstInd )
zBuf[iLoc] += xRootBuf[iLoc]*yBuf[iLoc] + yRootBuf[iLoc]*xBuf[iLoc];
}
}
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 RuizEquil
( DistSparseMatrix<Field>& A,
DistMultiVec<Base<Field>>& dRow,
DistMultiVec<Base<Field>>& dCol,
bool progress )
{
EL_DEBUG_CSE
typedef Base<Field> Real;
const Int m = A.Height();
const Int n = A.Width();
mpi::Comm comm = A.Comm();
dRow.SetComm( comm );
dCol.SetComm( comm );
Ones( dRow, m, 1 );
Ones( dCol, n, 1 );
// TODO(poulson): Expose to control structure
// For, simply hard-code a small number of iterations
const Int maxIter = 4;
DistMultiVec<Real> scales(comm);
const Int indent = PushIndent();
for( Int iter=0; iter<maxIter; ++iter )
{
// Rescale the columns
// -------------------
ColumnMaxNorms( A, scales );
EntrywiseMap( scales, MakeFunction(DampScaling<Real>) );
DiagonalScale( LEFT, NORMAL, scales, dCol );
DiagonalSolve( RIGHT, NORMAL, scales, A );
// Rescale the rows
// ----------------
RowMaxNorms( A, scales );
EntrywiseMap( scales, MakeFunction(DampScaling<Real>) );
DiagonalScale( LEFT, NORMAL, scales, dRow );
DiagonalSolve( LEFT, NORMAL, scales, A );
}
SetIndent( indent );
}
void RowTwoNorms( const DistSparseMatrix<F>& A, DistMultiVec<Base<F>>& norms )
{
DEBUG_CSE
typedef Base<F> Real;
const Int localHeight = A.LocalHeight();
const F* valBuf = A.LockedValueBuffer();
const Int* offsetBuf = A.LockedOffsetBuffer();
norms.SetComm( A.Comm() );
norms.Resize( A.Height(), 1 );
auto& normLoc = norms.Matrix();
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
Real scale = 0;
Real scaledSquare = 1;
const Int offset = offsetBuf[iLoc];
const Int numConn = offsetBuf[iLoc+1] - offset;
for( Int e=offset; e<offset+numConn; ++e )
UpdateScaledSquare( valBuf[e], scale, scaledSquare );
normLoc(iLoc) = scale*Sqrt(scaledSquare);
}
}
void GetMappedDiagonal
( const DistSparseMatrix<T>& A,
DistMultiVec<S>& d,
function<S(const T&)> func,
Int offset )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const T* valBuf = A.LockedValueBuffer();
const Int* colBuf = A.LockedTargetBuffer();
if( m != n )
LogicError("DistSparseMatrix GetMappedDiagonal assumes square matrix");
if( offset != 0 )
LogicError("DistSparseMatrix GetMappedDiagonal assumes offset=0");
d.SetGrid( A.Grid() );
d.Resize( El::DiagonalLength(m,n,offset), 1 );
Fill( d, S(1) );
S* dBuf = d.Matrix().Buffer();
const Int dLocalHeight = d.LocalHeight();
for( Int iLoc=0; iLoc<dLocalHeight; ++iLoc )
{
const Int i = d.GlobalRow(iLoc);
const Int thisOff = A.RowOffset(iLoc);
const Int nextOff = A.RowOffset(iLoc+1);
auto it = std::lower_bound( colBuf+thisOff, colBuf+nextOff, i );
if( *it == i )
{
const Int e = it-colBuf;
dBuf[iLoc] = func(valBuf[e]);
}
else
dBuf[iLoc] = func(0);
}
}
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]);
}
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) );
}
}
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 Round( DistMultiVec<T>& A )
{ Round( A.Matrix() ); }
void EntrywiseMap( DistMultiVec<T>& A, function<T(T)> func )
{ EntrywiseMap( A.Matrix(), func ); }
void SafeScale
( Base<Field> numerator, Base<Field> denominator, DistMultiVec<Field>& A )
{
EL_DEBUG_CSE
SafeScale( numerator, denominator, A.Matrix() );
}
void IPM
( const DistSparseMatrix<Real>& A,
const DistMultiVec<Real>& b,
Real lambda,
DistMultiVec<Real>& x,
const qp::affine::Ctrl<Real>& ctrl )
{
DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
mpi::Comm comm = A.Comm();
DistSparseMatrix<Real> Q(comm), AHat(comm), G(comm);
DistMultiVec<Real> c(comm), h(comm);
// Q := | 0 0 0 |
// | 0 0 0 |
// | 0 0 I |
// ==============
Zeros( Q, 2*n+m, 2*n+m );
{
Int numLocalUpdates = 0;
for( Int iLoc=0; iLoc<Q.LocalHeight(); ++iLoc )
if( Q.GlobalRow(iLoc) >= 2*n )
++numLocalUpdates;
Q.Reserve( numLocalUpdates );
for( Int iLoc=0; iLoc<Q.LocalHeight(); ++iLoc )
if( Q.GlobalRow(iLoc) >= 2*n )
Q.QueueLocalUpdate( iLoc, Q.GlobalRow(iLoc), Real(1) );
Q.ProcessLocalQueues();
}
// c := lambda*[1;1;0]
// ===================
Zeros( c, 2*n+m, 1 );
auto& cLoc = c.Matrix();
for( Int iLoc=0; iLoc<c.LocalHeight(); ++iLoc )
if( c.GlobalRow(iLoc) < 2*n )
cLoc(iLoc) = lambda;
// \hat A := [A, -A, I]
// ====================
// NOTE: Since A and \hat A are the same height and each distributed within
// columns, it is possible to form \hat A from A without communication
const Int numLocalEntriesA = A.NumLocalEntries();
Zeros( AHat, m, 2*n+m );
AHat.Reserve( 2*numLocalEntriesA+AHat.LocalHeight() );
for( Int e=0; e<numLocalEntriesA; ++e )
{
AHat.QueueUpdate( A.Row(e), A.Col(e), A.Value(e) );
AHat.QueueUpdate( A.Row(e), A.Col(e)+n, -A.Value(e) );
}
for( Int iLoc=0; iLoc<AHat.LocalHeight(); ++iLoc )
{
const Int i = AHat.GlobalRow(iLoc);
AHat.QueueLocalUpdate( iLoc, i+2*n, Real(1) );
}
AHat.ProcessLocalQueues();
// G := | -I 0 0 |
// | 0 -I 0 |
// ================
Zeros( G, 2*n, 2*n+m );
G.Reserve( G.LocalHeight() );
for( Int iLoc=0; iLoc<G.LocalHeight(); ++iLoc )
{
const Int i = G.GlobalRow(iLoc);
G.QueueLocalUpdate( iLoc, i, Real(-1) );
}
G.ProcessLocalQueues();
// h := 0
// ======
Zeros( h, 2*n, 1 );
// Solve the affine QP
// ===================
DistMultiVec<Real> xHat(comm), y(comm), z(comm), s(comm);
QP( Q, AHat, G, b, c, h, xHat, y, z, s, ctrl );
// x := u - v
// ==========
Zeros( x, n, 1 );
Int numRemoteUpdates = 0;
for( Int iLoc=0; iLoc<xHat.LocalHeight(); ++iLoc )
if( xHat.GlobalRow(iLoc) < 2*n )
++numRemoteUpdates;
else
break;
x.Reserve( numRemoteUpdates );
auto& xHatLoc = xHat.LockedMatrix();
for( Int iLoc=0; iLoc<xHat.LocalHeight(); ++iLoc )
{
const Int i = xHat.GlobalRow(iLoc);
if( i < n )
x.QueueUpdate( i, 0, xHatLoc(iLoc) );
else if( i < 2*n )
x.QueueUpdate( i-n, 0, -xHatLoc(iLoc) );
else
break;
}
x.ProcessQueues();
}
void Ones( DistMultiVec<T>& A, Int m, Int n )
{
EL_DEBUG_CSE
A.Resize( m, n );
Fill( A, T(1) );
}
void Fill( DistMultiVec<T>& A, T alpha )
{
EL_DEBUG_CSE
Fill( A.Matrix(), alpha );
}
