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 );
}
Int ZeroNorm( const DistSparseMatrix<T>& A, Base<T> tol )
{
DEBUG_ONLY(CSE cse("ZeroNorm"))
Int numNonzeros = 0;
const Int numLocalEntries = A.NumLocalEntries();
for( Int k=0; k<numLocalEntries; ++k )
if( Abs(A.Value(k)) > tol )
++numNonzeros;
return mpi::AllReduce( numNonzeros, A.Comm() );
}
Base<Field>
MinAbsNonzero( const DistSparseMatrix<Field>& A, Base<Field> upperBound )
{
EL_DEBUG_CSE
typedef Base<Field> Real;
const Int numEntries = A.NumLocalEntries();
Real minLocAbs = upperBound;
for( Int e=0; e<numEntries; ++e )
{
const Real absVal = Abs(A.Value(e));
if( absVal > Real(0) )
minLocAbs = Min(minLocAbs,absVal);
}
return mpi::AllReduce( minLocAbs, mpi::MIN, A.Comm() );
}
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 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 );
}
