inline void CholeskyUVar2( DistMatrix<F>& A ) { #ifndef RELEASE CallStackEntry entry("hpd_inverse::CholeskyUVar2"); if( A.Height() != A.Width() ) throw std::logic_error("Nonsquare matrices cannot be triangular"); #endif const Grid& g = A.Grid(); // Matrix views DistMatrix<F> ATL(g), ATR(g), A00(g), A01(g), A02(g), ABL(g), ABR(g), A10(g), A11(g), A12(g), A20(g), A21(g), A22(g); // Temporary distributions DistMatrix<F,STAR,STAR> A11_STAR_STAR(g); DistMatrix<F,VC, STAR> A01_VC_STAR(g); DistMatrix<F,VR, STAR> A01_VR_STAR(g); DistMatrix<F,STAR,VR > A12_STAR_VR(g); DistMatrix<F,STAR,MC > A01Trans_STAR_MC(g); DistMatrix<F,MR, STAR> A01_MR_STAR(g); DistMatrix<F,STAR,MR > A01Adj_STAR_MR(g); DistMatrix<F,STAR,MR > A12_STAR_MR(g); DistMatrix<F,STAR,MC > A12_STAR_MC(g); // Start the algorithm PartitionDownDiagonal ( A, ATL, ATR, ABL, ABR, 0 ); while( ATL.Height() < A.Height() ) { RepartitionDownDiagonal ( ATL, /**/ ATR, A00, /**/ A01, A02, /*************/ /******************/ /**/ A10, /**/ A11, A12, ABL, /**/ ABR, A20, /**/ A21, A22 ); A01_VC_STAR.AlignWith( A00 ); A12_STAR_VR.AlignWith( A02 ); A01Trans_STAR_MC.AlignWith( A00 ); A01_VR_STAR.AlignWith( A00 ); A01Adj_STAR_MR.AlignWith( A00 ); A12_STAR_MR.AlignWith( A02 ); A12_STAR_MC.AlignWith( A22 ); //--------------------------------------------------------------------// A11_STAR_STAR = A11; LocalCholesky( UPPER, A11_STAR_STAR ); A01_VC_STAR = A01; LocalTrsm ( RIGHT, UPPER, NORMAL, NON_UNIT, F(1), A11_STAR_STAR, A01_VC_STAR ); A12_STAR_VR = A12; LocalTrsm ( LEFT, UPPER, ADJOINT, NON_UNIT, F(1), A11_STAR_STAR, A12_STAR_VR ); A01Trans_STAR_MC.TransposeFrom( A01_VC_STAR ); A01_VR_STAR = A01_VC_STAR; A01Adj_STAR_MR.AdjointFrom( A01_VR_STAR ); LocalTrrk ( UPPER, TRANSPOSE, F(1), A01Trans_STAR_MC, A01Adj_STAR_MR, F(1), A00 ); A12_STAR_MR = A12_STAR_VR; LocalGemm ( TRANSPOSE, NORMAL, F(-1), A01Trans_STAR_MC, A12_STAR_MR, F(1), A02 ); A12_STAR_MC = A12_STAR_VR; LocalTrrk ( UPPER, ADJOINT, F(-1), A12_STAR_MC, A12_STAR_MR, F(1), A22 ); LocalTrsm ( RIGHT, UPPER, ADJOINT, NON_UNIT, F(1), A11_STAR_STAR, A01_VC_STAR ); LocalTrsm ( LEFT, UPPER, NORMAL, NON_UNIT, F(-1), A11_STAR_STAR, A12_STAR_VR ); LocalTriangularInverse( UPPER, NON_UNIT, A11_STAR_STAR ); LocalTrtrmm( ADJOINT, UPPER, A11_STAR_STAR ); A11 = A11_STAR_STAR; A01 = A01_VC_STAR; A12 = A12_STAR_VR; //--------------------------------------------------------------------// A01_VC_STAR.FreeAlignments(); A12_STAR_VR.FreeAlignments(); A01Trans_STAR_MC.FreeAlignments(); A01_VR_STAR.FreeAlignments(); A01Adj_STAR_MR.FreeAlignments(); A12_STAR_MR.FreeAlignments(); A12_STAR_MC.FreeAlignments(); SlidePartitionDownDiagonal ( ATL, /**/ ATR, A00, A01, /**/ A02, /**/ A10, A11, /**/ A12, /*************/ /******************/ ABL, /**/ ABR, A20, A21, /**/ A22 ); } }
inline void internal::HermitianTridiagU( DistMatrix<R,MC,MR>& A ) { #ifndef RELEASE PushCallStack("internal::HermitianTridiagU"); if( A.Height() != A.Width() ) throw std::logic_error( "A must be square." ); #endif const Grid& g = A.Grid(); if( g.InGrid() ) { // Matrix views DistMatrix<R,MC,MR> ATL(g), ATR(g), A00(g), A01(g), A02(g), ABL(g), ABR(g), A10(g), A11(g), A12(g), A20(g), A21(g), A22(g); // Temporary distributions DistMatrix<R,MC, MR > WPan(g); DistMatrix<R,STAR,STAR> A11_STAR_STAR(g); DistMatrix<R,MC, STAR> APan_MC_STAR(g), A01_MC_STAR(g), A11_MC_STAR(g); DistMatrix<R,MR, STAR> APan_MR_STAR(g), A01_MR_STAR(g), A11_MR_STAR(g); DistMatrix<R,MC, STAR> WPan_MC_STAR(g), W01_MC_STAR(g), W11_MC_STAR(g); DistMatrix<R,MR, STAR> WPan_MR_STAR(g), W01_MR_STAR(g), W11_MR_STAR(g); PartitionUpDiagonal ( A, ATL, ATR, ABL, ABR, 0 ); while( ABR.Height() < A.Height() ) { RepartitionUpDiagonal ( ATL, /**/ ATR, A00, A01, /**/ A02, /**/ A10, A11, /**/ A12, /*************/ /******************/ ABL, /**/ ABR, A20, A21, /**/ A22 ); if( A00.Height() > 0 ) { WPan.AlignWith( A01 ); APan_MC_STAR.AlignWith( A00 ); WPan_MC_STAR.AlignWith( A00 ); APan_MR_STAR.AlignWith( A00 ); WPan_MR_STAR.AlignWith( A00 ); //------------------------------------------------------------// WPan.ResizeTo( ATL.Height(), A11.Width() ); APan_MC_STAR.ResizeTo( ATL.Height(), A11.Width() ); WPan_MC_STAR.ResizeTo( ATL.Height(), A11.Width() ); APan_MR_STAR.ResizeTo( ATL.Height(), A11.Width() ); WPan_MR_STAR.ResizeTo( ATL.Height(), A11.Width() ); internal::HermitianPanelTridiagU ( ATL, WPan, APan_MC_STAR, APan_MR_STAR, WPan_MC_STAR, WPan_MR_STAR ); PartitionUp ( APan_MC_STAR, A01_MC_STAR, A11_MC_STAR, A11.Height() ); PartitionUp ( APan_MR_STAR, A01_MR_STAR, A11_MR_STAR, A11.Height() ); PartitionUp ( WPan_MC_STAR, W01_MC_STAR, W11_MC_STAR, A11.Height() ); PartitionUp ( WPan_MR_STAR, W01_MR_STAR, W11_MR_STAR, A11.Height() ); internal::LocalTrr2k ( UPPER, TRANSPOSE, TRANSPOSE, (R)-1, A01_MC_STAR, W01_MR_STAR, W01_MC_STAR, A01_MR_STAR, (R)1, A00 ); //------------------------------------------------------------// WPan_MR_STAR.FreeAlignments(); APan_MR_STAR.FreeAlignments(); WPan_MC_STAR.FreeAlignments(); APan_MC_STAR.FreeAlignments(); WPan.FreeAlignments(); } else { A11_STAR_STAR = A11; HermitianTridiag( UPPER, A11_STAR_STAR.LocalMatrix() ); A11 = A11_STAR_STAR; } SlidePartitionUpDiagonal ( ATL, /**/ ATR, A00, /**/ A01, A02, /*************/ /******************/ /**/ A10, /**/ A11, A12, ABL, /**/ ABR, A20, /**/ A21, A22 ); } } #ifndef RELEASE PopCallStack(); #endif }
inline void TwoSidedTrmmUVar5 ( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& U ) { #ifndef RELEASE PushCallStack("internal::TwoSidedTrmmUVar5"); if( A.Height() != A.Width() ) throw std::logic_error("A must be square"); if( U.Height() != U.Width() ) throw std::logic_error("Triangular matrices must be square"); if( A.Height() != U.Height() ) throw std::logic_error("A and U must be the same size"); #endif const Grid& g = A.Grid(); // Matrix views DistMatrix<F> ATL(g), ATR(g), A00(g), A01(g), A02(g), ABL(g), ABR(g), A10(g), A11(g), A12(g), A20(g), A21(g), A22(g); DistMatrix<F> UTL(g), UTR(g), U00(g), U01(g), U02(g), UBL(g), UBR(g), U10(g), U11(g), U12(g), U20(g), U21(g), U22(g); // Temporary distributions DistMatrix<F,STAR,STAR> A11_STAR_STAR(g); DistMatrix<F,MC, STAR> A01_MC_STAR(g); DistMatrix<F,MR, STAR> A01_MR_STAR(g); DistMatrix<F,VC, STAR> A01_VC_STAR(g); DistMatrix<F,STAR,STAR> U11_STAR_STAR(g); DistMatrix<F,MC, STAR> U01_MC_STAR(g); DistMatrix<F,MR, STAR> U01_MR_STAR(g); DistMatrix<F,VC, STAR> U01_VC_STAR(g); DistMatrix<F,VC, STAR> Y01_VC_STAR(g); DistMatrix<F> Y01(g); PartitionDownDiagonal ( A, ATL, ATR, ABL, ABR, 0 ); LockedPartitionDownDiagonal ( U, UTL, UTR, UBL, UBR, 0 ); while( ATL.Height() < A.Height() ) { RepartitionDownDiagonal ( ATL, /**/ ATR, A00, /**/ A01, A02, /*************/ /******************/ /**/ A10, /**/ A11, A12, ABL, /**/ ABR, A20, /**/ A21, A22 ); LockedRepartitionDownDiagonal ( UTL, /**/ UTR, U00, /**/ U01, U02, /*************/ /******************/ /**/ U10, /**/ U11, U12, UBL, /**/ UBR, U20, /**/ U21, U22 ); A01_MC_STAR.AlignWith( A00 ); A01_MR_STAR.AlignWith( A00 ); A01_VC_STAR.AlignWith( A00 ); U01_MC_STAR.AlignWith( A00 ); U01_MR_STAR.AlignWith( A00 ); U01_VC_STAR.AlignWith( A00 ); Y01.AlignWith( A01 ); Y01_VC_STAR.AlignWith( A01 ); //--------------------------------------------------------------------// // Y01 := U01 A11 A11_STAR_STAR = A11; U01_VC_STAR = U01; Y01_VC_STAR.ResizeTo( A01.Height(), A01.Width() ); Hemm ( RIGHT, UPPER, F(1), A11_STAR_STAR.LocalMatrix(), U01_VC_STAR.LocalMatrix(), F(0), Y01_VC_STAR.LocalMatrix() ); Y01 = Y01_VC_STAR; // A01 := U00 A01 Trmm( LEFT, UPPER, NORMAL, diag, F(1), U00, A01 ); // A01 := A01 + 1/2 Y01 Axpy( F(1)/F(2), Y01, A01 ); // A00 := A00 + (U01 A01' + A01 U01') A01_MC_STAR = A01; U01_MC_STAR = U01; A01_VC_STAR = A01_MC_STAR; A01_MR_STAR = A01_VC_STAR; U01_MR_STAR = U01_MC_STAR; LocalTrr2k ( UPPER, ADJOINT, ADJOINT, F(1), U01_MC_STAR, A01_MR_STAR, A01_MC_STAR, U01_MR_STAR, F(1), A00 ); // A01 := A01 + 1/2 Y01 Axpy( F(1)/F(2), Y01_VC_STAR, A01_VC_STAR ); // A01 := A01 U11' U11_STAR_STAR = U11; LocalTrmm ( RIGHT, UPPER, ADJOINT, diag, F(1), U11_STAR_STAR, A01_VC_STAR ); A01 = A01_VC_STAR; // A11 := U11 A11 U11' LocalTwoSidedTrmm( UPPER, diag, A11_STAR_STAR, U11_STAR_STAR ); A11 = A11_STAR_STAR; //--------------------------------------------------------------------// A01_MC_STAR.FreeAlignments(); A01_MR_STAR.FreeAlignments(); A01_VC_STAR.FreeAlignments(); U01_MC_STAR.FreeAlignments(); U01_MR_STAR.FreeAlignments(); U01_VC_STAR.FreeAlignments(); Y01.FreeAlignments(); Y01_VC_STAR.FreeAlignments(); SlidePartitionDownDiagonal ( ATL, /**/ ATR, A00, A01, /**/ A02, /**/ A10, A11, /**/ A12, /*************/ /******************/ ABL, /**/ ABR, A20, A21, /**/ A22 ); SlideLockedPartitionDownDiagonal ( UTL, /**/ UTR, U00, U01, /**/ U02, /**/ U10, U11, /**/ U12, /*************/ /******************/ UBL, /**/ UBR, U20, U21, /**/ U22 ); } #ifndef RELEASE PopCallStack(); #endif }
inline void internal::HermitianTridiagU ( DistMatrix<Complex<R>,MC, MR >& A, DistMatrix<Complex<R>,STAR,STAR>& t ) { #ifndef RELEASE PushCallStack("internal::HermitianTridiagU"); if( A.Grid() != t.Grid() ) throw std::logic_error("{A,t} must be distributed over the same grid"); if( A.Height() != A.Width() ) throw std::logic_error("A must be square"); if( t.Viewing() ) throw std::logic_error("t must not be a view"); #endif typedef Complex<R> C; const Grid& g = A.Grid(); DistMatrix<C,MD,STAR> tDiag(g); tDiag.AlignWithDiagonal( A, 1 ); tDiag.ResizeTo( A.Height()-1, 1 ); if( g.InGrid() ) { // Matrix views DistMatrix<C,MC,MR> ATL(g), ATR(g), A00(g), A01(g), A02(g), ABL(g), ABR(g), A10(g), A11(g), A12(g), A20(g), A21(g), A22(g); DistMatrix<C,MD,STAR> tT(g), t0(g), tB(g), t1(g), t2(g); // Temporary distributions DistMatrix<C,MC, MR > WPan(g); DistMatrix<C,STAR,STAR> t1_STAR_STAR(g); DistMatrix<C,STAR,STAR> A11_STAR_STAR(g); DistMatrix<C,MC, STAR> APan_MC_STAR(g), A01_MC_STAR(g), A11_MC_STAR(g); DistMatrix<C,MR, STAR> APan_MR_STAR(g), A01_MR_STAR(g), A11_MR_STAR(g); DistMatrix<C,MC, STAR> WPan_MC_STAR(g), W01_MC_STAR(g), W11_MC_STAR(g); DistMatrix<C,MR, STAR> WPan_MR_STAR(g), W01_MR_STAR(g), W11_MR_STAR(g); PartitionUpDiagonal ( A, ATL, ATR, ABL, ABR, 0 ); PartitionUp ( tDiag, tT, tB, 0 ); while( ABR.Height() < A.Height() ) { RepartitionUpDiagonal ( ATL, /**/ ATR, A00, A01, /**/ A02, /**/ A10, A11, /**/ A12, /*************/ /******************/ ABL, /**/ ABR, A20, A21, /**/ A22 ); RepartitionUp ( tT, t0, t1, /**/ /**/ tB, t2 ); if( A00.Height() > 0 ) { WPan.AlignWith( A01 ); APan_MC_STAR.AlignWith( A00 ); WPan_MC_STAR.AlignWith( A00 ); APan_MR_STAR.AlignWith( A00 ); WPan_MR_STAR.AlignWith( A00 ); //------------------------------------------------------------// WPan.ResizeTo( ATL.Height(), A11.Width() ); APan_MC_STAR.ResizeTo( ATL.Height(), A11.Width() ); WPan_MC_STAR.ResizeTo( ATL.Height(), A11.Width() ); APan_MR_STAR.ResizeTo( ATL.Height(), A11.Width() ); WPan_MR_STAR.ResizeTo( ATL.Height(), A11.Width() ); internal::HermitianPanelTridiagU ( ATL, WPan, t1, APan_MC_STAR, APan_MR_STAR, WPan_MC_STAR, WPan_MR_STAR ); PartitionUp ( APan_MC_STAR, A01_MC_STAR, A11_MC_STAR, A11.Height() ); PartitionUp ( APan_MR_STAR, A01_MR_STAR, A11_MR_STAR, A11.Height() ); PartitionUp ( WPan_MC_STAR, W01_MC_STAR, W11_MC_STAR, A11.Height() ); PartitionUp ( WPan_MR_STAR, W01_MR_STAR, W11_MR_STAR, A11.Height() ); internal::LocalTrr2k ( UPPER, ADJOINT, ADJOINT, (C)-1, A01_MC_STAR, W01_MR_STAR, W01_MC_STAR, A01_MR_STAR, (C)1, A00 ); //------------------------------------------------------------// WPan_MR_STAR.FreeAlignments(); APan_MR_STAR.FreeAlignments(); WPan_MC_STAR.FreeAlignments(); APan_MC_STAR.FreeAlignments(); WPan.FreeAlignments(); } else { A11_STAR_STAR = A11; t1_STAR_STAR.ResizeTo( t1.Height(), 1 ); HermitianTridiag ( UPPER, A11_STAR_STAR.LocalMatrix(), t1_STAR_STAR.LocalMatrix() ); A11 = A11_STAR_STAR; t1 = t1_STAR_STAR; } SlidePartitionUp ( tT, t0, /**/ /**/ t1, tB, t2 ); SlidePartitionUpDiagonal ( ATL, /**/ ATR, A00, /**/ A01, A02, /*************/ /******************/ /**/ A10, /**/ A11, A12, ABL, /**/ ABR, A20, /**/ A21, A22 ); } } // Redistribute from matrix-diagonal form to fully replicated t = tDiag; #ifndef RELEASE PopCallStack(); #endif }