inline void TwoSidedTrsmUVar1 ( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& U ) { #ifndef RELEASE CallStackEntry entry("internal::TwoSidedTrsmUVar1"); if( A.Height() != A.Width() ) LogicError("A must be square"); if( U.Height() != U.Width() ) LogicError("Triangular matrices must be square"); if( A.Height() != U.Height() ) LogicError("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,VC, STAR> A01_VC_STAR(g); DistMatrix<F,STAR,STAR> U11_STAR_STAR(g); DistMatrix<F,MC, STAR> U01_MC_STAR(g); DistMatrix<F,VC, STAR> U01_VC_STAR(g); DistMatrix<F,VR, STAR> U01_VR_STAR(g); DistMatrix<F,STAR,MR > U01Adj_STAR_MR(g); DistMatrix<F,STAR,STAR> X11_STAR_STAR(g); DistMatrix<F,MR, MC > Z01_MR_MC(g); DistMatrix<F,MC, STAR> Z01_MC_STAR(g); DistMatrix<F,MR, STAR> Z01_MR_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_VC_STAR.AlignWith( A01 ); U01_MC_STAR.AlignWith( A00 ); U01_VR_STAR.AlignWith( A00 ); U01_VC_STAR.AlignWith( A00 ); U01Adj_STAR_MR.AlignWith( A00 ); Y01.AlignWith( A01 ); Z01_MR_MC.AlignWith( A01 ); Z01_MC_STAR.AlignWith( A00 ); Z01_MR_STAR.AlignWith( A00 ); //--------------------------------------------------------------------// // Y01 := A00 U01 U01_MC_STAR = U01; U01_VR_STAR = U01_MC_STAR; U01Adj_STAR_MR.AdjointFrom( U01_VR_STAR ); Zeros( Z01_MC_STAR, A01.Height(), A01.Width() ); Zeros( Z01_MR_STAR, A01.Height(), A01.Width() ); LocalSymmetricAccumulateLU ( ADJOINT, F(1), A00, U01_MC_STAR, U01Adj_STAR_MR, Z01_MC_STAR, Z01_MR_STAR ); Z01_MR_MC.SumScatterFrom( Z01_MR_STAR ); Y01 = Z01_MR_MC; Y01.SumScatterUpdate( F(1), Z01_MC_STAR ); // A01 := inv(U00)' A01 // // This is the bottleneck because A01 only has blocksize columns Trsm( LEFT, UPPER, ADJOINT, diag, F(1), U00, A01 ); // A01 := A01 - 1/2 Y01 Axpy( F(-1)/F(2), Y01, A01 ); // A11 := A11 - (U01' A01 + A01' U01) A01_VC_STAR = A01; U01_VC_STAR = U01_MC_STAR; Zeros( X11_STAR_STAR, A11.Height(), A11.Width() ); Her2k ( UPPER, ADJOINT, F(-1), A01_VC_STAR.Matrix(), U01_VC_STAR.Matrix(), F(0), X11_STAR_STAR.Matrix() ); A11.SumScatterUpdate( F(1), X11_STAR_STAR ); // A11 := inv(U11)' A11 inv(U11) A11_STAR_STAR = A11; U11_STAR_STAR = U11; LocalTwoSidedTrsm( UPPER, diag, A11_STAR_STAR, U11_STAR_STAR ); A11 = A11_STAR_STAR; // A01 := A01 - 1/2 Y01 Axpy( F(-1)/F(2), Y01, A01 ); // A01 := A01 inv(U11) A01_VC_STAR = A01; LocalTrsm ( RIGHT, UPPER, NORMAL, diag, F(1), U11_STAR_STAR, A01_VC_STAR ); A01 = A01_VC_STAR; //--------------------------------------------------------------------// 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 ); } }
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 UVar3( UnitOrNonUnit diag, DistMatrix<F>& U ) { #ifndef RELEASE CallStackEntry entry("triangular_inverse::UVar3"); if( U.Height() != U.Width() ) LogicError("Nonsquare matrices cannot be triangular"); #endif const Grid& g = U.Grid(); // Matrix views 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,VC, STAR> U01_VC_STAR(g); DistMatrix<F,STAR,STAR> U11_STAR_STAR(g); DistMatrix<F,STAR,VR > U12_STAR_VR(g); DistMatrix<F,STAR,MC > U01Trans_STAR_MC(g); DistMatrix<F,MR, STAR> U12Trans_MR_STAR(g); // Start the algorithm PartitionUpDiagonal ( U, UTL, UTR, UBL, UBR, 0 ); while( UBR.Height() < U.Height() ) { RepartitionUpDiagonal ( UTL, /**/ UTR, U00, U01, /**/ U02, /**/ U10, U11, /**/ U12, /*************/ /******************/ UBL, /**/ UBR, U20, U21, /**/ U22 ); U01Trans_STAR_MC.AlignWith( U02 ); U12Trans_MR_STAR.AlignWith( U02 ); //--------------------------------------------------------------------// U01_VC_STAR = U01; U11_STAR_STAR = U11; LocalTrsm ( RIGHT, UPPER, NORMAL, diag, F(-1), U11_STAR_STAR, U01_VC_STAR ); // We transpose before the communication to avoid cache-thrashing // in the unpacking stage. U12Trans_MR_STAR.TransposeFrom( U12 ); U01Trans_STAR_MC.TransposeFrom( U01_VC_STAR ); LocalGemm ( TRANSPOSE, TRANSPOSE, F(1), U01Trans_STAR_MC, U12Trans_MR_STAR, F(1), U02 ); U01.TransposeFrom( U01Trans_STAR_MC ); U12_STAR_VR.TransposeFrom( U12Trans_MR_STAR ); LocalTrsm ( LEFT, UPPER, NORMAL, diag, F(1), U11_STAR_STAR, U12_STAR_VR ); LocalTriangularInverse( UPPER, diag, U11_STAR_STAR ); U11 = U11_STAR_STAR; U12 = U12_STAR_VR; //--------------------------------------------------------------------// SlidePartitionUpDiagonal ( UTL, /**/ UTR, U00, /**/ U01, U02, /*************/ /******************/ /**/ U10, /**/ U11, U12, UBL, /**/ UBR, U20, /**/ U21, U22 ); } }
inline void TrtrmmUVar1( Orientation orientation, DistMatrix<T>& U ) { #ifndef RELEASE PushCallStack("internal::TrtrmmUVar1"); if( U.Height() != U.Width() ) throw std::logic_error("U must be square"); #endif const Grid& g = U.Grid(); // Matrix views DistMatrix<T> 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<T,MC, STAR> U01_MC_STAR(g); DistMatrix<T,VC, STAR> U01_VC_STAR(g); DistMatrix<T,VR, STAR> U01_VR_STAR(g); DistMatrix<T,STAR,MR > U01AdjOrTrans_STAR_MR(g); DistMatrix<T,STAR,STAR> U11_STAR_STAR(g); U01_MC_STAR.AlignWith( U ); U01_VC_STAR.AlignWith( U ); U01_VR_STAR.AlignWith( U ); U01AdjOrTrans_STAR_MR.AlignWith( U ); PartitionDownDiagonal ( U, UTL, UTR, UBL, UBR, 0 ); while( UTL.Height() < U.Height() && UTL.Width() < U.Height() ) { RepartitionDownDiagonal ( UTL, /**/ UTR, U00, /**/ U01, U02, /*************/ /******************/ /**/ U10, /**/ U11, U12, UBL, /**/ UBR, U20, /**/ U21, U22 ); //--------------------------------------------------------------------// U01_MC_STAR = U01; U01_VC_STAR = U01_MC_STAR; U01_VR_STAR = U01_VC_STAR; if( orientation == ADJOINT ) U01AdjOrTrans_STAR_MR.AdjointFrom( U01_VR_STAR ); else U01AdjOrTrans_STAR_MR.TransposeFrom( U01_VR_STAR ); LocalTrrk( UPPER, T(1), U01_MC_STAR, U01AdjOrTrans_STAR_MR, T(1), U00 ); U11_STAR_STAR = U11; LocalTrmm ( RIGHT, UPPER, orientation, NON_UNIT, T(1), U11_STAR_STAR, U01_VC_STAR ); U01 = U01_VC_STAR; LocalTrtrmm( orientation, UPPER, U11_STAR_STAR ); U11 = U11_STAR_STAR; //--------------------------------------------------------------------// SlidePartitionDownDiagonal ( UTL, /**/ UTR, U00, U01, /**/ U02, /**/ U10, U11, /**/ U12, /*************/ /******************/ UBL, /**/ UBR, U20, U21, /**/ U22 ); } #ifndef RELEASE PopCallStack(); #endif }