inline void TwoSidedTrsmLVar5 ( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& L ) { #ifndef RELEASE CallStackEntry entry("internal::TwoSidedTrsmLVar5"); if( A.Height() != A.Width() ) LogicError("A must be square"); if( L.Height() != L.Width() ) LogicError("Triangular matrices must be square"); if( A.Height() != L.Height() ) LogicError("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,STAR,STAR> A11_STAR_STAR(g); DistMatrix<F,MC, STAR> A21_MC_STAR(g); DistMatrix<F,VC, STAR> A21_VC_STAR(g); DistMatrix<F,VR, STAR> A21_VR_STAR(g); DistMatrix<F,STAR,MR > A21Adj_STAR_MR(g); DistMatrix<F,STAR,STAR> L11_STAR_STAR(g); DistMatrix<F,MC, STAR> L21_MC_STAR(g); DistMatrix<F,VC, STAR> L21_VC_STAR(g); DistMatrix<F,VR, STAR> L21_VR_STAR(g); DistMatrix<F,STAR,MR > L21Adj_STAR_MR(g); DistMatrix<F,VC, STAR> Y21_VC_STAR(g); DistMatrix<F> Y21(g); 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 ); A21_MC_STAR.AlignWith( A22 ); A21_VC_STAR.AlignWith( A22 ); A21_VR_STAR.AlignWith( A22 ); A21Adj_STAR_MR.AlignWith( A22 ); L21_MC_STAR.AlignWith( A22 ); L21_VC_STAR.AlignWith( A22 ); L21_VR_STAR.AlignWith( A22 ); L21Adj_STAR_MR.AlignWith( A22 ); Y21.AlignWith( A21 ); Y21_VC_STAR.AlignWith( A22 ); //--------------------------------------------------------------------// // A11 := inv(L11) A11 inv(L11)' L11_STAR_STAR = L11; A11_STAR_STAR = A11; LocalTwoSidedTrsm( LOWER, diag, A11_STAR_STAR, L11_STAR_STAR ); A11 = A11_STAR_STAR; // Y21 := L21 A11 L21_VC_STAR = L21; Zeros( Y21_VC_STAR, A21.Height(), A21.Width() ); Hemm ( RIGHT, LOWER, F(1), A11_STAR_STAR.Matrix(), L21_VC_STAR.Matrix(), F(0), Y21_VC_STAR.Matrix() ); Y21 = Y21_VC_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; // A21 := A21 - 1/2 Y21 Axpy( F(-1)/F(2), Y21, A21 ); // A22 := A22 - (L21 A21' + A21 L21') A21_MC_STAR = A21; L21_MC_STAR = L21; A21_VC_STAR = A21_MC_STAR; A21_VR_STAR = A21_VC_STAR; L21_VR_STAR = L21_VC_STAR; A21Adj_STAR_MR.AdjointFrom( A21_VR_STAR ); L21Adj_STAR_MR.AdjointFrom( L21_VR_STAR ); LocalTrr2k ( LOWER, F(-1), L21_MC_STAR, A21Adj_STAR_MR, A21_MC_STAR, L21Adj_STAR_MR, F(1), A22 ); // A21 := A21 - 1/2 Y21 Axpy( F(-1)/F(2), Y21, A21 ); // A21 := inv(L22) A21 // // This is the bottleneck because A21 only has blocksize columns Trsm( LEFT, LOWER, NORMAL, diag, F(1), L22, A21 ); //--------------------------------------------------------------------// 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 ); } }
inline void HPDInverseLVar2( DistMatrix<F>& A ) { #ifndef RELEASE PushCallStack("internal::HPDInverseLVar2"); 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,STAR,VR > A10_STAR_VR(g); DistMatrix<F,VC, STAR> A21_VC_STAR(g); DistMatrix<F,STAR,MC > A10_STAR_MC(g); DistMatrix<F,STAR,MR > A10_STAR_MR(g); DistMatrix<F,STAR,MC > A21Trans_STAR_MC(g); DistMatrix<F,VR, STAR> A21_VR_STAR(g); DistMatrix<F,STAR,MR > A21Adj_STAR_MR(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 ); A10_STAR_VR.AlignWith( A00 ); A21_VC_STAR.AlignWith( A20 ); A10_STAR_MC.AlignWith( A00 ); A10_STAR_MR.AlignWith( A00 ); A21Trans_STAR_MC.AlignWith( A20 ); A21_VR_STAR.AlignWith( A22 ); A21Adj_STAR_MR.AlignWith( A22 ); //--------------------------------------------------------------------// A11_STAR_STAR = A11; LocalCholesky( LOWER, A11_STAR_STAR ); A10_STAR_VR = A10; LocalTrsm ( LEFT, LOWER, NORMAL, NON_UNIT, F(1), A11_STAR_STAR, A10_STAR_VR ); A21_VC_STAR = A21; LocalTrsm ( RIGHT, LOWER, ADJOINT, NON_UNIT, F(1), A11_STAR_STAR, A21_VC_STAR ); A10_STAR_MC = A10_STAR_VR; A10_STAR_MR = A10_STAR_VR; LocalTrrk ( LOWER, ADJOINT, F(1), A10_STAR_MC, A10_STAR_MR, F(1), A00 ); A21Trans_STAR_MC.TransposeFrom( A21_VC_STAR ); LocalGemm ( TRANSPOSE, NORMAL, F(-1), A21Trans_STAR_MC, A10_STAR_MR, F(1), A20 ); A21_VR_STAR = A21_VC_STAR; A21Adj_STAR_MR.AdjointFrom( A21_VR_STAR ); LocalTrrk ( LOWER, TRANSPOSE, F(-1), A21Trans_STAR_MC, A21Adj_STAR_MR, F(1), A22 ); LocalTrsm ( LEFT, LOWER, ADJOINT, NON_UNIT, F(1), A11_STAR_STAR, A10_STAR_VR ); LocalTrsm ( RIGHT, LOWER, NORMAL, NON_UNIT, F(-1), A11_STAR_STAR, A21_VC_STAR ); LocalTriangularInverse( LOWER, NON_UNIT, A11_STAR_STAR ); LocalTrtrmm( ADJOINT, LOWER, A11_STAR_STAR ); A11 = A11_STAR_STAR; A10 = A10_STAR_VR; A21 = A21_VC_STAR; //--------------------------------------------------------------------// A10_STAR_VR.FreeAlignments(); A21_VC_STAR.FreeAlignments(); A10_STAR_MC.FreeAlignments(); A10_STAR_MR.FreeAlignments(); A21Trans_STAR_MC.FreeAlignments(); A21_VR_STAR.FreeAlignments(); A21Adj_STAR_MR.FreeAlignments(); SlidePartitionDownDiagonal ( ATL, /**/ ATR, A00, A01, /**/ A02, /**/ A10, A11, /**/ A12, /*************/ /******************/ ABL, /**/ ABR, A20, A21, /**/ A22 ); } #ifndef RELEASE PopCallStack(); #endif }
inline void internal::CholeskyLVar3( DistMatrix<F,MC,MR>& A ) { #ifndef RELEASE PushCallStack("internal::CholeskyLVar3"); if( A.Height() != A.Width() ) throw std::logic_error ("Can only compute Cholesky factor of square matrices"); #endif const Grid& g = A.Grid(); // Matrix views DistMatrix<F,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 matrices DistMatrix<F,STAR,STAR> A11_STAR_STAR(g); DistMatrix<F,VC, STAR> A21_VC_STAR(g); DistMatrix<F,VR, STAR> A21_VR_STAR(g); DistMatrix<F,STAR,MC > A21Trans_STAR_MC(g); DistMatrix<F,STAR,MR > A21Adj_STAR_MR(g); // Start the algorithm PartitionDownDiagonal ( A, ATL, ATR, ABL, ABR, 0 ); while( ABR.Height() > 0 ) { RepartitionDownDiagonal ( ATL, /**/ ATR, A00, /**/ A01, A02, /*************/ /******************/ /**/ A10, /**/ A11, A12, ABL, /**/ ABR, A20, /**/ A21, A22 ); A21_VR_STAR.AlignWith( A22 ); A21_VC_STAR.AlignWith( A22 ); A21Trans_STAR_MC.AlignWith( A22 ); A21Adj_STAR_MR.AlignWith( A22 ); //--------------------------------------------------------------------// A11_STAR_STAR = A11; internal::LocalCholesky( LOWER, A11_STAR_STAR ); A11 = A11_STAR_STAR; A21_VC_STAR = A21; internal::LocalTrsm ( RIGHT, LOWER, ADJOINT, NON_UNIT, (F)1, A11_STAR_STAR, A21_VC_STAR ); A21_VR_STAR = A21_VC_STAR; A21Trans_STAR_MC.TransposeFrom( A21_VC_STAR ); A21Adj_STAR_MR.AdjointFrom( A21_VR_STAR ); // (A21^T[* ,MC])^T A21^H[* ,MR] = A21[MC,* ] A21^H[* ,MR] // = (A21 A21^H)[MC,MR] internal::LocalTrrk ( LOWER, TRANSPOSE, (F)-1, A21Trans_STAR_MC, A21Adj_STAR_MR, (F)1, A22 ); A21.TransposeFrom( A21Trans_STAR_MC ); //--------------------------------------------------------------------// A21_VR_STAR.FreeAlignments(); A21_VC_STAR.FreeAlignments(); A21Trans_STAR_MC.FreeAlignments(); A21Adj_STAR_MR.FreeAlignments(); SlidePartitionDownDiagonal ( ATL, /**/ ATR, A00, A01, /**/ A02, /**/ A10, A11, /**/ A12, /*************/ /******************/ ABL, /**/ ABR, A20, A21, /**/ A22 ); } #ifndef RELEASE PopCallStack(); #endif }