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 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 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) );
}
}
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 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) );
}
}
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 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 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 IPM
( const DistSparseMatrix<Real>& A,
const DistMultiVec<Real>& d,
Real lambda,
DistMultiVec<Real>& x,
const qp::affine::Ctrl<Real>& ctrl )
{
EL_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), b(comm), h(comm);
auto& dLoc = d.LockedMatrix();
auto& cLoc = c.Matrix();
auto& hLoc = h.Matrix();
// Q := | I 0 0 |
// | 0 0 0 |
// | 0 0 0 |
// ==============
Zeros( Q, n+m+1, n+m+1 );
{
// Count the number of local entries in the top-left I
// ---------------------------------------------------
Int numLocalUpdates = 0;
for( Int iLoc=0; iLoc<Q.LocalHeight(); ++iLoc )
if( Q.GlobalRow(iLoc) < n )
++numLocalUpdates;
else
break;
Q.Reserve( numLocalUpdates );
for( Int iLoc=0; iLoc<Q.LocalHeight(); ++iLoc )
if( Q.GlobalRow(iLoc) < n )
Q.QueueLocalUpdate( iLoc, Q.GlobalRow(iLoc), Real(1) );
Q.ProcessLocalQueues();
}
// c := [0;0;lambda]
// =================
Zeros( c, n+m+1, 1 );
for( Int iLoc=0; iLoc<c.LocalHeight(); ++iLoc )
if( c.GlobalRow(iLoc) > n )
cLoc(iLoc) = lambda;
// AHat = []
// =========
Zeros( AHat, 0, n+m+1 );
// b = []
// ======
Zeros( b, 0, 1 );
// G := |-diag(d) A, -d, -I|
// | 0, 0, -I|
// =========================
Zeros( G, 2*m, n+m+1 );
G.Reserve
( A.NumLocalEntries()+d.LocalHeight()+G.LocalHeight(),
A.NumLocalEntries()+d.LocalHeight() );
for( Int e=0; e<A.NumLocalEntries(); ++e )
{
const Int i = A.Row(e);
const Int j = A.Col(e);
const Int iLoc = A.LocalRow(i);
const Real value = -dLoc(iLoc)*A.Value(e);
G.QueueUpdate( i, j, value );
}
for( Int iLoc=0; iLoc<d.LocalHeight(); ++iLoc )
{
const Int i = d.GlobalRow(iLoc);
G.QueueUpdate( i, n, -dLoc(iLoc) );
}
for( Int iLoc=0; iLoc<G.LocalHeight(); ++iLoc )
{
const Int i = G.GlobalRow(iLoc);
if( i < m )
G.QueueLocalUpdate( iLoc, i+n+1, Real(-1) );
else
G.QueueLocalUpdate( iLoc, (i-m)+n+1, Real(-1) );
}
G.ProcessQueues();
// h := [-ones(m,1); zeros(m,1)]
// =============================
Zeros( h, 2*m, 1 );
for( Int iLoc=0; iLoc<h.LocalHeight(); ++iLoc )
if( h.GlobalRow(iLoc) < m )
hLoc(iLoc) = Real(-1);
else
break;
// Solve the affine QP
// ===================
DistMultiVec<Real> y(comm), z(comm), s(comm);
QP( Q, AHat, G, b, c, h, x, y, z, s, ctrl );
}
void RLS
( const DistSparseMatrix<Real>& A,
const DistMultiVec<Real>& b,
Real rho,
DistMultiVec<Real>& x,
const socp::affine::Ctrl<Real>& ctrl )
{
DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
mpi::Comm comm = A.Comm();
DistMultiVec<Int> orders(comm), firstInds(comm);
Zeros( orders, m+n+3, 1 );
Zeros( firstInds, m+n+3, 1 );
{
const Int localHeight = orders.LocalHeight();
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const Int i = orders.GlobalRow(iLoc);
if( i < m+1 )
{
orders.SetLocal( iLoc, 0, m+1 );
firstInds.SetLocal( iLoc, 0, 0 );
}
else
{
orders.SetLocal( iLoc, 0, n+2 );
firstInds.SetLocal( iLoc, 0, m+1 );
}
}
}
// G := | -1 0 0 |
// | 0 0 A |
// | 0 -1 0 |
// | 0 0 -I |
// | 0 0 0 |
DistSparseMatrix<Real> G(comm);
{
Zeros( G, m+n+3, n+2 );
// Count the number of entries of G to reserve
// -------------------------------------------
Int numLocalUpdates = 0;
const Int localHeight = G.LocalHeight();
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const Int i = G.GlobalRow(iLoc);
if( i == 0 || i == m+1 || (i>m+1 && i<m+n+2) )
++numLocalUpdates;
}
const Int numEntriesA = A.NumLocalEntries();
G.Reserve( numLocalUpdates+numEntriesA, numEntriesA );
// Queue the local updates
// -----------------------
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const Int i = G.GlobalRow(iLoc);
if( i == 0 )
G.QueueLocalUpdate( iLoc, 0, -1 );
else if( i == m+1 )
G.QueueLocalUpdate( iLoc, 1, -1 );
else if( i > m+1 && i < m+n+2 )
G.QueueLocalUpdate( iLoc, i-m, -1 );
}
// Queue the remote updates
// ------------------------
for( Int e=0; e<numEntriesA; ++e )
G.QueueUpdate( A.Row(e)+1, A.Col(e)+2, A.Value(e) );
G.ProcessQueues();
}
// h := | 0 |
// | b |
// | 0 |
// | 0 |
// | 1 |
DistMultiVec<Real> h(comm);
Zeros( h, m+n+3, 1 );
auto& bLoc = b.LockedMatrix();
{
const Int bLocalHeight = b.LocalHeight();
h.Reserve( bLocalHeight );
for( Int iLoc=0; iLoc<bLocalHeight; ++iLoc )
h.QueueUpdate( b.GlobalRow(iLoc)+1, 0, bLoc(iLoc) );
h.ProcessQueues();
}
h.Set( END, 0, 1 );
// c := [1; rho; 0]
DistMultiVec<Real> c(comm);
Zeros( c, n+2, 1 );
c.Set( 0, 0, 1 );
c.Set( 1, 0, rho );
DistSparseMatrix<Real> AHat(comm);
Zeros( AHat, 0, n+2 );
DistMultiVec<Real> bHat(comm);
Zeros( bHat, 0, 1 );
DistMultiVec<Real> xHat(comm), y(comm), z(comm), s(comm);
SOCP( AHat, G, bHat, c, h, orders, firstInds, xHat, y, z, s, ctrl );
x = xHat( IR(2,END), ALL );
}
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 );
}
