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; }