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 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();
const Grid& grid = A.Grid();
DistSparseMatrix<Real> G(grid);
Identity( G, n, n );
G *= -1;
DistMultiVec<Real> h(grid);
Zeros( h, n, 1 );
MehrotraCtrl<Real> affineCtrl = ctrl;
affineCtrl.primalInit = false;
affineCtrl.dualInit = false;
DistMultiVec<Real> s(grid);
socp::affine::Mehrotra(A,G,b,c,h,orders,firstInds,x,y,z,s,affineCtrl);
}
void LAV
( const DistSparseMatrix<Real>& A,
const DistMultiVec<Real>& b,
DistMultiVec<Real>& x,
const lp::affine::Ctrl<Real>& ctrl )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const Grid& grid = A.Grid();
DistSparseMatrix<Real> AHat(grid), G(grid);
DistMultiVec<Real> c(grid), h(grid);
// c := [0;1;1]
// ============
Zeros( c, n+2*m, 1 );
for( Int iLoc=0; iLoc<c.LocalHeight(); ++iLoc )
if( c.GlobalRow(iLoc) >= n )
c.SetLocal( iLoc, 0, Real(1) );
// \hat A := [A, I, -I]
// ====================
Zeros( AHat, m, n+2*m );
const Int numLocalEntriesA = A.NumLocalEntries();
AHat.Reserve( numLocalEntriesA + 2*AHat.LocalHeight() );
for( Int e=0; e<numLocalEntriesA; ++e )
AHat.QueueUpdate( A.Row(e), A.Col(e), A.Value(e) );
for( Int iLoc=0; iLoc<AHat.LocalHeight(); ++iLoc )
{
const Int i = AHat.GlobalRow(iLoc);
AHat.QueueLocalUpdate( iLoc, i+n, Real( 1) );
AHat.QueueLocalUpdate( iLoc, i+n+m, Real(-1) );
}
AHat.ProcessLocalQueues();
// G := | 0 -I 0 |
// | 0 0 -I |
// ================
Zeros( G, 2*m, n+2*m );
G.Reserve( G.LocalHeight() );
for( Int iLoc=0; iLoc<G.LocalHeight(); ++iLoc )
G.QueueLocalUpdate( iLoc, G.GlobalRow(iLoc)+n, Real(-1) );
G.ProcessLocalQueues();
// h := | 0 |
// | 0 |
// ==========
Zeros( h, 2*m, 1 );
// Solve the affine QP
// ===================
DistMultiVec<Real> xHat(grid), y(grid), z(grid), s(grid);
LP( AHat, G, b, c, h, xHat, y, z, s, ctrl );
// Extract x
// =========
x = xHat( IR(0,n), ALL );
}
DistSparseMatrix<Ring>::DistSparseMatrix( const DistSparseMatrix<Ring>& A )
{
EL_DEBUG_CSE
distGraph_.numSources_ = -1;
distGraph_.numTargets_ = -1;
distGraph_.grid_ = &A.Grid();
if( &A != this )
*this = A;
EL_DEBUG_ONLY(
else
LogicError("Tried to construct DistMultiVec via itself");
)
}
void KKT
( const DistSparseMatrix<Real>& A,
const DistSparseMatrix<Real>& G,
const DistMultiVec<Real>& s,
const DistMultiVec<Real>& z,
DistSparseMatrix<Real>& J,
bool onlyLower )
{
EL_DEBUG_CSE
const Int n = A.Width();
DistSparseMatrix<Real> Q(A.Grid());
Q.Resize( n, n );
qp::affine::KKT( Q, A, G, s, z, J, onlyLower );
}
void StaticKKT
( const DistSparseMatrix<Real>& A,
const DistSparseMatrix<Real>& G,
Real gamma,
Real delta,
Real beta,
DistSparseMatrix<Real>& J,
bool onlyLower )
{
EL_DEBUG_CSE
const Int n = A.Width();
DistSparseMatrix<Real> Q(A.Grid());
Q.Resize( n, n );
qp::affine::StaticKKT( Q, A, G, gamma, delta, beta, J, onlyLower );
}
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 EN
( const DistSparseMatrix<Real>& A,
const DistMultiVec<Real>& b,
Real lambda1,
Real lambda2,
DistMultiVec<Real>& x,
const qp::affine::Ctrl<Real>& ctrl )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const Grid& grid = A.Grid();
DistSparseMatrix<Real> Q(grid), AHat(grid), G(grid);
DistMultiVec<Real> c(grid), h(grid);
// Q := | 2*lambda_2 0 0 |
// | 0 2*lambda_2 0 |
// | 0 0 2 |
// ================================
Zeros( Q, 2*n+m, 2*n+m );
Q.Reserve( Q.LocalHeight() );
for( Int iLoc=0; iLoc<Q.LocalHeight(); ++iLoc )
{
const Int i = Q.GlobalRow(iLoc);
if( i < 2*n )
Q.QueueLocalUpdate( iLoc, i, 2*lambda2 );
else
Q.QueueLocalUpdate( iLoc, i, Real(2) );
}
Q.ProcessLocalQueues();
// c := lambda_1*[1;1;0]
// =====================
Zeros( c, 2*n+m, 1 );
for( Int iLoc=0; iLoc<c.LocalHeight(); ++iLoc )
if( c.GlobalRow(iLoc) < 2*n )
c.SetLocal( iLoc, 0, lambda1 );
// \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(grid), y(grid), z(grid), s(grid);
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 );
for( Int iLoc=0; iLoc<xHat.LocalHeight(); ++iLoc )
{
const Int i = xHat.GlobalRow(iLoc);
if( i < n )
x.QueueUpdate( i, 0, xHat.GetLocal(iLoc,0) );
else if( i < 2*n )
x.QueueUpdate( i-n, 0, -xHat.GetLocal(iLoc,0) );
else
break;
}
x.ProcessQueues();
}
