inline void LVar2( DistMatrix<F>& A ) { #ifndef RELEASE CallStackEntry entry("cholesky::LVar2"); if( A.Height() != A.Width() ) LogicError("Can only compute Cholesky factor of square matrices"); #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,MR, STAR> A10Adj_MR_STAR(g); DistMatrix<F,STAR,STAR> A11_STAR_STAR(g); DistMatrix<F,VC, STAR> A21_VC_STAR(g); DistMatrix<F,MC, STAR> X11_MC_STAR(g); DistMatrix<F,MC, STAR> X21_MC_STAR(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 ); A10Adj_MR_STAR.AlignWith( A10 ); X11_MC_STAR.AlignWith( A10 ); X21_MC_STAR.AlignWith( A20 ); //--------------------------------------------------------------------// A10Adj_MR_STAR.AdjointFrom( A10 ); LocalGemm( NORMAL, NORMAL, F(1), A10, A10Adj_MR_STAR, X11_MC_STAR ); A11.SumScatterUpdate( F(-1), X11_MC_STAR ); A11_STAR_STAR = A11; LocalCholesky( LOWER, A11_STAR_STAR ); A11 = A11_STAR_STAR; LocalGemm( NORMAL, NORMAL, F(1), A20, A10Adj_MR_STAR, X21_MC_STAR ); A21.SumScatterUpdate( F(-1), X21_MC_STAR ); A21_VC_STAR = A21; LocalTrsm ( RIGHT, LOWER, ADJOINT, NON_UNIT, F(1), A11_STAR_STAR, A21_VC_STAR ); A21 = A21_VC_STAR; //--------------------------------------------------------------------// SlidePartitionDownDiagonal ( ATL, /**/ ATR, A00, A01, /**/ A02, /**/ A10, A11, /**/ A12, /*************/ /******************/ ABL, /**/ ABR, A20, A21, /**/ A22 ); } }
inline void TwoSidedTrsmLVar2 ( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& L ) { #ifndef RELEASE PushCallStack("internal::TwoSidedTrsmLVar2"); if( A.Height() != A.Width() ) throw std::logic_error("A must be square"); if( L.Height() != L.Width() ) throw std::logic_error("Triangular matrices must be square"); if( A.Height() != L.Height() ) throw std::logic_error("A and L 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> LTL(g), LTR(g), L00(g), L01(g), L02(g), LBL(g), LBR(g), L10(g), L11(g), L12(g), L20(g), L21(g), L22(g); // Temporary distributions DistMatrix<F,MR, STAR> A10Adj_MR_STAR(g); DistMatrix<F,STAR,VR > A10_STAR_VR(g); DistMatrix<F,STAR,STAR> A11_STAR_STAR(g); DistMatrix<F,VC, STAR> A21_VC_STAR(g); DistMatrix<F,MR, STAR> F10Adj_MR_STAR(g); DistMatrix<F,MR, STAR> L10Adj_MR_STAR(g); DistMatrix<F,VC, STAR> L10Adj_VC_STAR(g); DistMatrix<F,STAR,MC > L10_STAR_MC(g); DistMatrix<F,STAR,STAR> L11_STAR_STAR(g); DistMatrix<F,MC, STAR> X11_MC_STAR(g); DistMatrix<F,MC, STAR> X21_MC_STAR(g); DistMatrix<F,MC, STAR> Y10Adj_MC_STAR(g); DistMatrix<F,MR, MC > Y10Adj_MR_MC(g); DistMatrix<F> X11(g); DistMatrix<F> Y10Adj(g); Matrix<F> Y10Local; PartitionDownDiagonal ( A, ATL, ATR, ABL, ABR, 0 ); LockedPartitionDownDiagonal ( L, LTL, LTR, LBL, LBR, 0 ); while( ATL.Height() < A.Height() ) { RepartitionDownDiagonal ( ATL, /**/ ATR, A00, /**/ A01, A02, /*************/ /******************/ /**/ A10, /**/ A11, A12, ABL, /**/ ABR, A20, /**/ A21, A22 ); LockedRepartitionDownDiagonal ( LTL, /**/ LTR, L00, /**/ L01, L02, /*************/ /******************/ /**/ L10, /**/ L11, L12, LBL, /**/ LBR, L20, /**/ L21, L22 ); A10Adj_MR_STAR.AlignWith( L10 ); F10Adj_MR_STAR.AlignWith( A00 ); L10Adj_MR_STAR.AlignWith( A00 ); L10Adj_VC_STAR.AlignWith( A00 ); L10_STAR_MC.AlignWith( A00 ); X11.AlignWith( A11 ); X11_MC_STAR.AlignWith( L10 ); X21_MC_STAR.AlignWith( A20 ); Y10Adj_MC_STAR.AlignWith( A00 ); Y10Adj_MR_MC.AlignWith( A10 ); //--------------------------------------------------------------------// // Y10 := L10 A00 L10Adj_MR_STAR.AdjointFrom( L10 ); L10Adj_VC_STAR = L10Adj_MR_STAR; L10_STAR_MC.AdjointFrom( L10Adj_VC_STAR ); Y10Adj_MC_STAR.ResizeTo( A10.Width(), A10.Height() ); F10Adj_MR_STAR.ResizeTo( A10.Width(), A10.Height() ); Zero( Y10Adj_MC_STAR ); Zero( F10Adj_MR_STAR ); LocalSymmetricAccumulateRL ( ADJOINT, F(1), A00, L10_STAR_MC, L10Adj_MR_STAR, Y10Adj_MC_STAR, F10Adj_MR_STAR ); Y10Adj.SumScatterFrom( Y10Adj_MC_STAR ); Y10Adj_MR_MC = Y10Adj; Y10Adj_MR_MC.SumScatterUpdate( F(1), F10Adj_MR_STAR ); Adjoint( Y10Adj_MR_MC.LockedLocalMatrix(), Y10Local ); // X11 := A10 L10' X11_MC_STAR.ResizeTo( A11.Height(), A11.Width() ); LocalGemm ( NORMAL, NORMAL, F(1), A10, L10Adj_MR_STAR, F(0), X11_MC_STAR ); // A10 := A10 - Y10 Axpy( F(-1), Y10Local, A10.LocalMatrix() ); A10Adj_MR_STAR.AdjointFrom( A10 ); // A11 := A11 - (X11 + L10 A10') = A11 - (A10 L10' + L10 A10') LocalGemm ( NORMAL, NORMAL, F(1), L10, A10Adj_MR_STAR, F(1), X11_MC_STAR ); X11.SumScatterFrom( X11_MC_STAR ); MakeTrapezoidal( LEFT, LOWER, 0, X11 ); Axpy( F(-1), X11, A11 ); // A10 := inv(L11) A10 L11_STAR_STAR = L11; A10_STAR_VR.AdjointFrom( A10Adj_MR_STAR ); LocalTrsm ( LEFT, LOWER, NORMAL, diag, F(1), L11_STAR_STAR, A10_STAR_VR ); A10 = A10_STAR_VR; // A11 := inv(L11) A11 inv(L11)' A11_STAR_STAR = A11; LocalTwoSidedTrsm( LOWER, diag, A11_STAR_STAR, L11_STAR_STAR ); A11 = A11_STAR_STAR; // A21 := A21 - A20 L10' X21_MC_STAR.ResizeTo( A21.Height(), A21.Width() ); LocalGemm ( NORMAL, NORMAL, F(1), A20, L10Adj_MR_STAR, F(0), X21_MC_STAR ); A21.SumScatterUpdate( F(-1), X21_MC_STAR ); // A21 := A21 inv(L11)' A21_VC_STAR = A21; LocalTrsm ( RIGHT, LOWER, ADJOINT, diag, F(1), L11_STAR_STAR, A21_VC_STAR ); A21 = A21_VC_STAR; //--------------------------------------------------------------------// A10Adj_MR_STAR.FreeAlignments(); F10Adj_MR_STAR.FreeAlignments(); L10Adj_MR_STAR.FreeAlignments(); L10Adj_VC_STAR.FreeAlignments(); L10_STAR_MC.FreeAlignments(); X11.FreeAlignments(); X11_MC_STAR.FreeAlignments(); X21_MC_STAR.FreeAlignments(); Y10Adj_MC_STAR.FreeAlignments(); Y10Adj_MR_MC.FreeAlignments(); SlidePartitionDownDiagonal ( ATL, /**/ ATR, A00, A01, /**/ A02, /**/ A10, A11, /**/ A12, /*************/ /******************/ ABL, /**/ ABR, A20, A21, /**/ A22 ); SlideLockedPartitionDownDiagonal ( LTL, /**/ LTR, L00, L01, /**/ L02, /**/ L10, L11, /**/ L12, /**********************************/ LBL, /**/ LBR, L20, L21, /**/ L22 ); } #ifndef RELEASE PopCallStack(); #endif }