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 );
}
void IPM
( const Matrix<Real>& A,
const Matrix<Real>& b,
Real lambda,
Matrix<Real>& x,
const qp::affine::Ctrl<Real>& ctrl )
{
DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const Range<Int> uInd(0,n), vInd(n,2*n), rInd(2*n,2*n+m);
Matrix<Real> Q, c, AHat, G, h;
// Q := | 0 0 0 |
// | 0 0 0 |
// | 0 0 I |
// ==============
Zeros( Q, 2*n+m, 2*n+m );
auto Qrr = Q( rInd, rInd );
FillDiagonal( Qrr, Real(1) );
// c := lambda*[1;1;0]
// ===================
Zeros( c, 2*n+m, 1 );
auto cuv = c( IR(0,2*n), ALL );
Fill( cuv, lambda );
// \hat A := [A, -A, I]
// ====================
Zeros( AHat, m, 2*n+m );
auto AHatu = AHat( IR(0,m), uInd );
auto AHatv = AHat( IR(0,m), vInd );
auto AHatr = AHat( IR(0,m), rInd );
AHatu = A;
AHatv -= A;
FillDiagonal( AHatr, Real(1) );
// G := | -I 0 0 |
// | 0 -I 0 |
// ================
Zeros( G, 2*n, 2*n+m );
FillDiagonal( G, Real(-1) );
// h := 0
// ======
Zeros( h, 2*n, 1 );
// Solve the affine QP
// ===================
Matrix<Real> xHat, y, z, s;
QP( Q, AHat, G, b, c, h, xHat, y, z, s, ctrl );
// x := u - v
// ==========
x = xHat( uInd, ALL );
x -= xHat( vInd, ALL );
}
void LAV
( const AbstractDistMatrix<Real>& A,
const AbstractDistMatrix<Real>& b,
AbstractDistMatrix<Real>& xPre,
const lp::affine::Ctrl<Real>& ctrl )
{
EL_DEBUG_CSE
DistMatrixWriteProxy<Real,Real,MC,MR> xProx( xPre );
auto& x = xProx.Get();
const Int m = A.Height();
const Int n = A.Width();
const Grid& g = A.Grid();
const Range<Int> xInd(0,n), uInd(n,n+m), vInd(n+m,n+2*m);
DistMatrix<Real> c(g), AHat(g), G(g), h(g);
// c := [0;1;1]
// ============
Zeros( c, n+2*m, 1 );
auto cuv = c( IR(n,n+2*m), ALL );
Fill( cuv, Real(1) );
// \hat A := [A, I, -I]
// ====================
Zeros( AHat, m, n+2*m );
auto AHatx = AHat( IR(0,m), xInd );
auto AHatu = AHat( IR(0,m), uInd );
auto AHatv = AHat( IR(0,m), vInd );
AHatx = A;
FillDiagonal( AHatu, Real( 1) );
FillDiagonal( AHatv, Real(-1) );
// G := | 0 -I 0 |
// | 0 0 -I |
// ================
Zeros( G, 2*m, n+2*m );
auto Guv = G( IR(0,2*m), IR(n,n+2*m) );
FillDiagonal( Guv, Real(-1) );
// h := | 0 |
// | 0 |
// ==========
Zeros( h, 2*m, 1 );
// Solve the affine linear program
// ===============================
DistMatrix<Real> xHat(g), y(g), z(g), s(g);
LP( AHat, G, b, c, h, xHat, y, z, s, ctrl );
// Extract x
// =========
x = xHat( xInd, ALL );
}
void LAV
( const SparseMatrix<Real>& A,
const Matrix<Real>& b,
Matrix<Real>& x,
const lp::affine::Ctrl<Real>& ctrl )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const Range<Int> xInd(0,n), uInd(n,n+m), vInd(n+m,n+2*m);
SparseMatrix<Real> AHat, G;
Matrix<Real> c, h;
// c := [0;1;1]
// ============
Zeros( c, n+2*m, 1 );
auto cuv = c( IR(n,n+2*m), ALL );
Fill( cuv, Real(1) );
// \hat A := [A, I, -I]
// ====================
Zeros( AHat, m, n+2*m );
const Int numEntriesA = A.NumEntries();
AHat.Reserve( numEntriesA + 2*m );
for( Int e=0; e<numEntriesA; ++e )
AHat.QueueUpdate( A.Row(e), A.Col(e), A.Value(e) );
for( Int i=0; i<m; ++i )
{
AHat.QueueUpdate( i, i+n, Real( 1) );
AHat.QueueUpdate( i, i+n+m, Real(-1) );
}
AHat.ProcessQueues();
// G := | 0 -I 0 |
// | 0 0 -I |
// ================
Zeros( G, 2*m, n+2*m );
G.Reserve( G.Height() );
for( Int i=0; i<2*m; ++i )
G.QueueUpdate( i, i+n, Real(-1) );
G.ProcessQueues();
// h := | 0 |
// | 0 |
// ==========
Zeros( h, 2*m, 1 );
// Solve the affine linear program
// ===============================
Matrix<Real> xHat, y, z, s;
LP( AHat, G, b, c, h, xHat, y, z, s, ctrl );
// Extract x
// =========
x = xHat( xInd, ALL );
}
void LAV
( const Matrix<Real>& A,
const Matrix<Real>& b,
Matrix<Real>& x,
const lp::affine::Ctrl<Real>& ctrl )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const Range<Int> xInd(0,n), uInd(n,n+m), vInd(n+m,n+2*m);
Matrix<Real> c, AHat, G, h;
// c := [0;1;1]
// ============
Zeros( c, n+2*m, 1 );
auto cuv = c( IR(n,n+2*m), ALL );
Fill( cuv, Real(1) );
// \hat A := [A, I, -I]
// ====================
Zeros( AHat, m, n+2*m );
auto AHatx = AHat( IR(0,m), xInd );
auto AHatu = AHat( IR(0,m), uInd );
auto AHatv = AHat( IR(0,m), vInd );
AHatx = A;
FillDiagonal( AHatu, Real( 1) );
FillDiagonal( AHatv, Real(-1) );
// G := | 0 -I 0 |
// | 0 0 -I |
// ================
Zeros( G, 2*m, n+2*m );
auto Guv = G( IR(0,2*m), IR(n,n+2*m) );
FillDiagonal( Guv, Real(-1) );
// h := | 0 |
// | 0 |
// ==========
Zeros( h, 2*m, 1 );
// Solve the affine linear program
// ===============================
Matrix<Real> xHat, y, z, s;
LP( AHat, G, b, c, h, xHat, y, z, s, ctrl );
// Extract x
// ==========
x = xHat( xInd, ALL );
}
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 SparseMatrix<Real>& A,
const Matrix<Real>& b,
Real lambda,
Matrix<Real>& x,
const qp::affine::Ctrl<Real>& ctrl )
{
DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const Range<Int> uInd(0,n), vInd(n,2*n), rInd(2*n,2*n+m);
SparseMatrix<Real> Q, AHat, G;
Matrix<Real> c, h;
// Q := | 0 0 0 |
// | 0 0 0 |
// | 0 0 I |
// ==============
Zeros( Q, 2*n+m, 2*n+m );
Q.Reserve( m );
for( Int e=0; e<m; ++e )
Q.QueueUpdate( 2*n+e, 2*n+e, Real(1) );
Q.ProcessQueues();
// c := lambda*[1;1;0]
// ===================
Zeros( c, 2*n+m, 1 );
auto cuv = c( IR(0,2*n), ALL );
Fill( cuv, lambda );
// \hat A := [A, -A, I]
// ====================
const Int numEntriesA = A.NumEntries();
Zeros( AHat, m, 2*n+m );
AHat.Reserve( 2*numEntriesA+m );
for( Int e=0; e<numEntriesA; ++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 e=0; e<m; ++e )
AHat.QueueUpdate( e, e+2*n, Real(1) );
AHat.ProcessQueues();
// G := | -I 0 0 |
// | 0 -I 0 |
// ================
Zeros( G, 2*n, 2*n+m );
G.Reserve( 2*m );
for( Int e=0; e<2*m; ++e )
G.QueueUpdate( e, e, Real(-1) );
G.ProcessQueues();
// h := 0
// ======
Zeros( h, 2*n, 1 );
// Solve the affine QP
// ===================
Matrix<Real> xHat, y, z, s;
QP( Q, AHat, G, b, c, h, xHat, y, z, s, ctrl );
// x := u - v
// ==========
x = xHat( uInd, ALL );
x -= xHat( vInd, ALL );
}
void IPM
( const AbstractDistMatrix<Real>& APre,
const AbstractDistMatrix<Real>& b,
Real lambda,
AbstractDistMatrix<Real>& xPre,
const qp::affine::Ctrl<Real>& ctrl )
{
EL_DEBUG_CSE
DistMatrixReadProxy<Real,Real,MC,MR> AProx( APre );
const auto& A = AProx.GetLocked();
DistMatrixWriteProxy<Real,Real,MC,MR> xProx( xPre );
auto& x = xProx.Get();
const Int m = A.Height();
const Int n = A.Width();
const Grid& g = A.Grid();
const Range<Int> uInd(0,n), vInd(n,2*n), rInd(2*n,2*n+m);
DistMatrix<Real> Q(g), c(g), AHat(g), G(g), h(g);
// Q := | 0 0 0 |
// | 0 0 0 |
// | 0 0 I |
// ==============
Zeros( Q, 2*n+m, 2*n+m );
auto Qrr = Q( rInd, rInd );
FillDiagonal( Qrr, Real(1) );
// c := lambda*[1;1;0]
// ===================
Zeros( c, 2*n+m, 1 );
auto cuv = c( IR(0,2*n), ALL );
Fill( cuv, lambda );
// \hat A := [A, -A, I]
// ====================
Zeros( AHat, m, 2*n+m );
auto AHatu = AHat( IR(0,m), uInd );
auto AHatv = AHat( IR(0,m), vInd );
auto AHatr = AHat( IR(0,m), rInd );
AHatu = A;
AHatv -= A;
FillDiagonal( AHatr, Real(1) );
// G := | -I 0 0 |
// | 0 -I 0 |
// ================
Zeros( G, 2*n, 2*n+m );
FillDiagonal( G, Real(-1) );
// h := 0
// ======
Zeros( h, 2*n, 1 );
// Solve the affine QP
// ===================
DistMatrix<Real> xHat(g), y(g), z(g), s(g);
QP( Q, AHat, G, b, c, h, xHat, y, z, s, ctrl );
// x := u - v
// ==========
x = xHat( uInd, ALL );
x -= xHat( vInd, ALL );
}
void RLS
( const Matrix<Real>& A,
const Matrix<Real>& b,
Real rho,
Matrix<Real>& x,
const socp::affine::Ctrl<Real>& ctrl )
{
DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
Matrix<Int> orders, firstInds;
Zeros( orders, m+n+3, 1 );
Zeros( firstInds, m+n+3, 1 );
for( Int i=0; i<m+1; ++i )
{
orders.Set( i, 0, m+1 );
firstInds.Set( i, 0, 0 );
}
for( Int i=0; i<n+2; ++i )
{
orders.Set( i+m+1, 0, n+2 );
firstInds.Set( i+m+1, 0, m+1 );
}
// G := | -1 0 0 |
// | 0 0 A |
// | 0 -1 0 |
// | 0 0 -I |
// | 0 0 0 |
Matrix<Real> G;
{
Zeros( G, m+n+3, n+2 );
G.Set( 0, 0, -1 );
auto GA = G( IR(1,m+1), IR(2,n+2) );
GA = A;
G.Set( m+1, 1, -1 );
auto GI = G( IR(m+2,m+n+2), IR(2,n+2) );
Identity( GI, n, n );
GI *= -1;
}
// h := | 0 |
// | b |
// | 0 |
// | 0 |
// | 1 |
Matrix<Real> h;
Zeros( h, m+n+3, 1 );
auto hb = h( IR(1,m+1), ALL );
hb = b;
h.Set( END, 0, 1 );
// c := [1; rho; 0]
Matrix<Real> c;
Zeros( c, n+2, 1 );
c.Set( 0, 0, 1 );
c.Set( 1, 0, rho );
Matrix<Real> AHat, bHat;
Zeros( AHat, 0, n+2 );
Zeros( bHat, 0, 1 );
Matrix<Real> xHat, y, z, s;
SOCP( AHat, G, bHat, c, h, orders, firstInds, xHat, y, z, s, ctrl );
x = xHat( IR(2,END), ALL );
}
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 RLS
( const SparseMatrix<Real>& A,
const Matrix<Real>& b,
Real rho,
Matrix<Real>& x,
const socp::affine::Ctrl<Real>& ctrl )
{
DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
Matrix<Int> orders, firstInds;
Zeros( orders, m+n+3, 1 );
Zeros( firstInds, m+n+3, 1 );
for( Int i=0; i<m+1; ++i )
{
orders.Set( i, 0, m+1 );
firstInds.Set( i, 0, 0 );
}
for( Int i=0; i<n+2; ++i )
{
orders.Set( i+m+1, 0, n+2 );
firstInds.Set( i+m+1, 0, m+1 );
}
// G := | -1 0 0 |
// | 0 0 A |
// | 0 -1 0 |
// | 0 0 -I |
// | 0 0 0 |
SparseMatrix<Real> G;
{
const Int numEntriesA = A.NumEntries();
Zeros( G, m+n+3, n+2 );
G.Reserve( numEntriesA+n+2 );
G.QueueUpdate( 0, 0, -1 );
for( Int e=0; e<numEntriesA; ++e )
G.QueueUpdate( A.Row(e)+1, A.Col(e)+2, A.Value(e) );
G.QueueUpdate( m+1, 1, -1 );
for( Int j=0; j<n; ++j )
G.QueueUpdate( j+m+2, j+2, -1 );
G.ProcessQueues();
}
// h := | 0 |
// | b |
// | 0 |
// | 0 |
// | 1 |
Matrix<Real> h;
Zeros( h, m+n+3, 1 );
auto hb = h( IR(1,m+1), ALL );
hb = b;
h.Set( END, 0, 1 );
// c := [1; rho; 0]
Matrix<Real> c;
Zeros( c, n+2, 1 );
c.Set( 0, 0, 1 );
c.Set( 1, 0, rho );
SparseMatrix<Real> AHat;
Zeros( AHat, 0, n+2 );
Matrix<Real> bHat;
Zeros( bHat, 0, 1 );
Matrix<Real> xHat, y, z, s;
SOCP( AHat, G, bHat, c, h, orders, firstInds, xHat, y, z, s, ctrl );
x = xHat( IR(2,END), ALL );
}
void RLS
( const ElementalMatrix<Real>& APre,
const ElementalMatrix<Real>& bPre,
Real rho,
ElementalMatrix<Real>& xPre,
const socp::affine::Ctrl<Real>& ctrl )
{
DEBUG_CSE
DistMatrixReadProxy<Real,Real,MC,MR>
AProx( APre ),
bProx( bPre );
DistMatrixWriteProxy<Real,Real,MC,MR>
xProx( xPre );
auto& A = AProx.GetLocked();
auto& b = bProx.GetLocked();
auto& x = xProx.Get();
const Int m = A.Height();
const Int n = A.Width();
const Grid& g = A.Grid();
DistMatrix<Int,VC,STAR> orders(g), firstInds(g);
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 |
DistMatrix<Real> G(g);
{
Zeros( G, m+n+3, n+2 );
G.Set( 0, 0, -1 );
auto GA = G( IR(1,m+1), IR(2,n+2) );
GA = A;
G.Set( m+1, 1, -1 );
auto GI = G( IR(m+2,m+n+2), IR(2,n+2) );
Identity( GI, n, n );
GI *= -1;
}
// h := | 0 |
// | b |
// | 0 |
// | 0 |
// | 1 |
DistMatrix<Real> h(g);
Zeros( h, m+n+3, 1 );
auto hb = h( IR(1,m+1), ALL );
hb = b;
h.Set( END, 0, 1 );
// c := [1; rho; 0]
DistMatrix<Real> c(g);
Zeros( c, n+2, 1 );
c.Set( 0, 0, 1 );
c.Set( 1, 0, rho );
DistMatrix<Real> AHat(g), bHat(g);
Zeros( AHat, 0, n+2 );
Zeros( bHat, 0, 1 );
DistMatrix<Real> xHat(g), y(g), z(g), s(g);
SOCP( AHat, G, bHat, c, h, orders, firstInds, xHat, y, z, s, ctrl );
x = xHat( IR(2,END), ALL );
}
Int ADMM
( const AbstractDistMatrix<Real>& APre,
const AbstractDistMatrix<Real>& bPre,
const AbstractDistMatrix<Real>& cPre,
AbstractDistMatrix<Real>& zPre,
const ADMMCtrl<Real>& ctrl )
{
EL_DEBUG_CSE
DistMatrixReadProxy<Real,Real,MC,MR>
AProx( APre ),
bProx( bPre ),
cProx( cPre );
DistMatrixWriteProxy<Real,Real,MC,MR>
zProx( zPre );
auto& A = AProx.GetLocked();
auto& b = bProx.GetLocked();
auto& c = cProx.GetLocked();
auto& z = zProx.Get();
// Cache a custom partially-pivoted LU factorization of
// | rho*I A^H | = | B11 B12 |
// | A 0 | | B21 B22 |
// by (justifiably) avoiding pivoting in the first n steps of
// the factorization, so that
// [I,rho*I] = lu(rho*I).
// The factorization would then proceed with
// B21 := B21 U11^{-1} = A (rho*I)^{-1} = A/rho
// B12 := L11^{-1} B12 = I A^H = A^H.
// The Schur complement would then be
// B22 := B22 - B21 B12 = 0 - (A*A^H)/rho.
// We then factor said matrix with LU with partial pivoting and
// swap the necessary rows of B21 in order to implicitly commute
// the row pivots with the Gauss transforms in the manner standard
// for GEPP. Unless A A' is singular, pivoting should not be needed,
// as Cholesky factorization of the negative matrix should be valid.
//
// The result is the factorization
// | I 0 | | rho*I A^H | = | I 0 | | rho*I U12 |,
// | 0 P22 | | A 0 | | L21 L22 | | 0 U22 |
// where [L22,U22] are stored within B22.
const Int m = A.Height();
const Int n = A.Width();
const Grid& grid = A.Grid();
DistMatrix<Real> U12(grid), L21(grid), B22(grid), bPiv(grid);
U12.Align( 0, n%U12.RowStride() );
L21.Align( n%L21.ColStride(), 0 );
B22.Align( n%B22.ColStride(), n%B22.RowStride() );
Adjoint( A, U12 );
L21 = A;
L21 *= 1/ctrl.rho;
Herk( LOWER, NORMAL, -1/ctrl.rho, A, B22 );
MakeHermitian( LOWER, B22 );
DistPermutation P2(grid);
LU( B22, P2 );
P2.PermuteRows( L21 );
bPiv = b;
P2.PermuteRows( bPiv );
// Possibly form the inverse of L22 U22
DistMatrix<Real> X22(grid);
if( ctrl.inv )
{
X22 = B22;
MakeTrapezoidal( LOWER, X22 );
FillDiagonal( X22, Real(1) );
TriangularInverse( LOWER, UNIT, X22 );
Trsm( LEFT, UPPER, NORMAL, NON_UNIT, Real(1), B22, X22 );
}
Int numIter=0;
DistMatrix<Real> g(grid), xTmp(grid), y(grid), t(grid);
Zeros( g, m+n, 1 );
PartitionDown( g, xTmp, y, n );
DistMatrix<Real> x(grid), u(grid), zOld(grid), xHat(grid);
Zeros( z, n, 1 );
Zeros( u, n, 1 );
Zeros( t, n, 1 );
while( numIter < ctrl.maxIter )
{
zOld = z;
// Find x from
// | rho*I A^H | | x | = | rho*(z-u)-c |
// | A 0 | | y | | b |
// via our cached custom factorization:
//
// |x| = inv(U) inv(L) P' |rho*(z-u)-c|
// |y| |b |
// = |rho*I U12|^{-1} |I 0 | |I 0 | |rho*(z-u)-c|
// = |0 U22| |L21 L22| |0 P22'| |b |
// = " " |rho*(z-u)-c|
// | P22' b |
xTmp = z;
xTmp -= u;
xTmp *= ctrl.rho;
xTmp -= c;
y = bPiv;
Gemv( NORMAL, Real(-1), L21, xTmp, Real(1), y );
if( ctrl.inv )
{
Gemv( NORMAL, Real(1), X22, y, t );
y = t;
}
else
{
Trsv( LOWER, NORMAL, UNIT, B22, y );
Trsv( UPPER, NORMAL, NON_UNIT, B22, y );
}
Gemv( NORMAL, Real(-1), U12, y, Real(1), xTmp );
xTmp *= 1/ctrl.rho;
// xHat := alpha*x + (1-alpha)*zOld
xHat = xTmp;
xHat *= ctrl.alpha;
Axpy( 1-ctrl.alpha, zOld, xHat );
// z := pos(xHat+u)
z = xHat;
z += u;
LowerClip( z, Real(0) );
// u := u + (xHat-z)
u += xHat;
u -= z;
const Real objective = Dot( c, xTmp );
// rNorm := || x - z ||_2
t = xTmp;
t -= z;
const Real rNorm = FrobeniusNorm( t );
// sNorm := |rho| || z - zOld ||_2
t = z;
t -= zOld;
const Real sNorm = Abs(ctrl.rho)*FrobeniusNorm( t );
const Real epsPri = Sqrt(Real(n))*ctrl.absTol +
ctrl.relTol*Max(FrobeniusNorm(xTmp),FrobeniusNorm(z));
const Real epsDual = Sqrt(Real(n))*ctrl.absTol +
ctrl.relTol*Abs(ctrl.rho)*FrobeniusNorm(u);
if( ctrl.print )
{
t = xTmp;
LowerClip( t, Real(0) );
t -= xTmp;
const Real clipDist = FrobeniusNorm( t );
if( grid.Rank() == 0 )
cout << numIter << ": "
<< "||x-z||_2=" << rNorm << ", "
<< "epsPri=" << epsPri << ", "
<< "|rho| ||z-zOld||_2=" << sNorm << ", "
<< "epsDual=" << epsDual << ", "
<< "||x-Pos(x)||_2=" << clipDist << ", "
<< "c'x=" << objective << endl;
}
if( rNorm < epsPri && sNorm < epsDual )
break;
++numIter;
}
if( ctrl.maxIter == numIter && grid.Rank() == 0 )
cout << "ADMM failed to converge" << endl;
x = xTmp;
return numIter;
}
