예제 #1
0
inline void
RUVB( int offset, const Matrix<R>& H, Matrix<R>& A )
{
#ifndef RELEASE
    CallStackEntry entry("apply_packed_reflectors::RUVB");
    if( offset < 0 || offset > H.Height() )
        throw std::logic_error("Transforms out of bounds");
    if( H.Height() != A.Width() )
        throw std::logic_error
        ("Height of transforms must equal width of target matrix");
#endif
    Matrix<R>
        HTL, HTR,  H00, H01, H02,  HPan, HPanCopy,
        HBL, HBR,  H10, H11, H12,
                   H20, H21, H22;
    Matrix<R> ALeft;

    Matrix<R> SInv, Z;

    LockedPartitionUpDiagonal
    ( H, HTL, HTR,
         HBL, HBR, 0 );
    while( HBR.Height() < H.Height() && HBR.Width() < H.Width() )
    {
        LockedRepartitionUpDiagonal
        ( HTL, /**/ HTR,  H00, H01, /**/ H02,
               /**/       H10, H11, /**/ H12,
         /*************/ /******************/
          HBL, /**/ HBR,  H20, H21, /**/ H22 );

        const int HPanHeight = H01.Height() + H11.Height();
        const int HPanOffset = 
            std::min( H11.Width(), std::max(offset-H00.Width(),0) );
        const int HPanWidth = H11.Width()-HPanOffset;
        LockedView( HPan, H, 0, H00.Width()+HPanOffset, HPanHeight, HPanWidth );

        View( ALeft, A, 0, 0, A.Height(), HPanHeight );

        //--------------------------------------------------------------------//
        HPanCopy = HPan;
        MakeTrapezoidal( RIGHT, UPPER, offset, HPanCopy );
        SetDiagonal( RIGHT, offset, HPanCopy, R(1) );

        Syrk( LOWER, TRANSPOSE, R(1), HPanCopy, SInv );
        HalveMainDiagonal( SInv );

        Gemm( NORMAL, NORMAL, R(1), ALeft, HPanCopy, Z );
        Trsm( RIGHT, LOWER, NORMAL, NON_UNIT, R(1), SInv, Z );
        Gemm( NORMAL, TRANSPOSE, R(-1), Z, HPanCopy, R(1), ALeft );
        //--------------------------------------------------------------------//

        SlideLockedPartitionUpDiagonal
        ( HTL, /**/ HTR,  H00, /**/ H01, H02,
         /*************/ /******************/
               /**/       H10, /**/ H11, H12,
          HBL, /**/ HBR,  H20, /**/ H21, H22 );
    }
}
예제 #2
0
파일: LUN.hpp 프로젝트: jimgoo/Elemental
inline void
TrsmLUNLarge
( UnitOrNonUnit diag,
  F alpha, const DistMatrix<F>& U, DistMatrix<F>& X,
  bool checkIfSingular )
{
#ifndef RELEASE
    PushCallStack("internal::TrsmLUNLarge");
#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);
    DistMatrix<F> XT(g),  X0(g),
                  XB(g),  X1(g),
                          X2(g);

    // Temporary distributions
    DistMatrix<F,MC,  STAR> U01_MC_STAR(g);
    DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
    DistMatrix<F,STAR,MR  > X1_STAR_MR(g);
    DistMatrix<F,STAR,VR  > X1_STAR_VR(g);

    // Start the algorithm
    Scale( alpha, X );
    LockedPartitionUpDiagonal
    ( U, UTL, UTR,
         UBL, UBR, 0 );
    PartitionUp
    ( X, XT,
         XB, 0 );
    while( XT.Height() > 0 )
    {
        LockedRepartitionUpDiagonal
        ( UTL, /**/ UTR,   U00, U01, /**/ U02,
               /**/        U10, U11, /**/ U12,
         /*************/  /******************/
          UBL, /**/ UBR,   U20, U21, /**/ U22 );

        RepartitionUp
        ( XT,  X0,
               X1,
         /**/ /**/
          XB,  X2 );

        U01_MC_STAR.AlignWith( X0 );
        X1_STAR_MR.AlignWith( X0 );
        //--------------------------------------------------------------------//
        U11_STAR_STAR = U11; // U11[* ,* ] <- U11[MC,MR]
        X1_STAR_VR    = X1;  // X1[* ,VR] <- X1[MC,MR]
        
        // X1[* ,VR] := U11^-1[* ,* ] X1[* ,VR]
        LocalTrsm
        ( LEFT, UPPER, NORMAL, diag, F(1), U11_STAR_STAR, X1_STAR_VR,
          checkIfSingular );

        X1_STAR_MR  = X1_STAR_VR; // X1[* ,MR]  <- X1[* ,VR]
        X1          = X1_STAR_MR; // X1[MC,MR] <- X1[* ,MR]
        U01_MC_STAR = U01;        // U01[MC,* ] <- U01[MC,MR]

        // X0[MC,MR] -= U01[MC,* ] X1[* ,MR]
        LocalGemm( NORMAL, NORMAL, F(-1), U01_MC_STAR, X1_STAR_MR, F(1), X0 );
        //--------------------------------------------------------------------//
        U01_MC_STAR.FreeAlignments();
        X1_STAR_MR.FreeAlignments();

        SlideLockedPartitionUpDiagonal
        ( UTL, /**/ UTR,  U00, /**/ U01, U02,
         /*************/ /******************/
               /**/       U10, /**/ U11, U12,
          UBL, /**/ UBR,  U20, /**/ U21, U22 );

        SlidePartitionUp
        ( XT,  X0,
         /**/ /**/
               X1,
          XB,  X2 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
예제 #3
0
파일: LUN.hpp 프로젝트: ahmadia/Elemental-1
inline void
TrsmLUNMedium
( UnitOrNonUnit diag, F alpha, const DistMatrix<F>& U, DistMatrix<F>& X,
  bool checkIfSingular )
{
#ifndef RELEASE
    CallStackEntry entry("internal::TrsmLUNMedium");
#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);
    DistMatrix<F> XT(g),  X0(g),
                  XB(g),  X1(g),
                          X2(g);

    // Temporary distributions
    DistMatrix<F,MC,  STAR> U01_MC_STAR(g);
    DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
    DistMatrix<F,MR,  STAR> X1Trans_MR_STAR(g);

    // Start the algorithm
    Scale( alpha, X );
    LockedPartitionUpDiagonal
    ( U, UTL, UTR,
         UBL, UBR, 0 );
    PartitionUp
    ( X, XT,
         XB, 0 );
    while( XT.Height() > 0 )
    {
        LockedRepartitionUpDiagonal
        ( UTL, /**/ UTR,   U00, U01, /**/ U02,
               /**/        U10, U11, /**/ U12,
         /*************/  /******************/
          UBL, /**/ UBR,   U20, U21, /**/ U22 );

        RepartitionUp
        ( XT,  X0,
               X1,
         /**/ /**/
          XB,  X2 );

        U01_MC_STAR.AlignWith( X0 );
        X1Trans_MR_STAR.AlignWith( X0 );
        //--------------------------------------------------------------------//
        U11_STAR_STAR = U11;                 // U11[* ,* ] <- U11[MC,MR]
        X1Trans_MR_STAR.TransposeFrom( X1 ); // X1[* ,MR] <- X1[MC,MR]
        
        // X1[* ,MR] := U11^-1[* ,* ] X1[* ,MR]
        //
        // X1^T[MR,* ] := X1^T[MR,* ] U11^-T[* ,* ]
        LocalTrsm
        ( RIGHT, UPPER, TRANSPOSE, diag, 
          F(1), U11_STAR_STAR, X1Trans_MR_STAR, checkIfSingular );
        X1.TransposeFrom( X1Trans_MR_STAR );

        U01_MC_STAR = U01;  // U01[MC,* ] <- U01[MC,MR]

        // X0[MC,MR] -= U01[MC,* ] X1[* ,MR]
        LocalGemm
        ( NORMAL, TRANSPOSE, F(-1), U01_MC_STAR, X1Trans_MR_STAR, F(1), X0 );
        //--------------------------------------------------------------------//
        U01_MC_STAR.FreeAlignments();
        X1Trans_MR_STAR.FreeAlignments();

        SlideLockedPartitionUpDiagonal
        ( UTL, /**/ UTR,  U00, /**/ U01, U02,
         /*************/ /******************/
               /**/       U10, /**/ U11, U12,
          UBL, /**/ UBR,  U20, /**/ U21, U22 );

        SlidePartitionUp
        ( XT,  X0,
         /**/ /**/
               X1,
          XB,  X2 );
    }
}
예제 #4
0
inline void
internal::TrsvUN
( UnitOrNonUnit diag, 
  const DistMatrix<F,MC,MR>& U, 
        DistMatrix<F,MC,MR>& x )
{
#ifndef RELEASE
    PushCallStack("internal::TrsvUN");
    if( U.Grid() != x.Grid() )
        throw std::logic_error("{U,x} must be distributed over the same grid");
    if( U.Height() != U.Width() )
        throw std::logic_error("U must be square");
    if( x.Width() != 1 && x.Height() != 1 )
        throw std::logic_error("x must be a vector");
    const int xLength = ( x.Width() == 1 ? x.Height() : x.Width() );
    if( U.Width() != xLength )
        throw std::logic_error("Nonconformal TrsvUN");
#endif
    const Grid& g = U.Grid();

    if( x.Width() == 1 )
    {
        // Matrix views 
        DistMatrix<F,MC,MR> 
            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);

        DistMatrix<F,MC,MR> 
            xT(g),  x0(g),
            xB(g),  x1(g),
                    x2(g);

        // Temporary distributions
        DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
        DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
        DistMatrix<F,MR,  STAR> x1_MR_STAR(g);
        DistMatrix<F,MC,  STAR> z0_MC_STAR(g);

        // Start the algorithm
        LockedPartitionUpDiagonal
        ( U, UTL, UTR,
             UBL, UBR, 0 );
        PartitionUp
        ( x, xT,
             xB, 0 );
        while( xT.Height() > 0 )
        {
            LockedRepartitionUpDiagonal
            ( UTL, /**/ UTR,  U00, U01, /**/ U02,
                   /**/       U10, U11, /**/ U12,
             /*************/ /******************/
              UBL, /**/ UBR,  U20, U21, /**/ U22 );

            RepartitionUp
            ( xT,  x0,
                   x1,
             /**/ /**/
              xB,  x2 );

            x1_MR_STAR.AlignWith( U01 );
            z0_MC_STAR.AlignWith( U01 );
            z0_MC_STAR.ResizeTo( x0.Height(), 1 );
            //----------------------------------------------------------------//
            x1_STAR_STAR = x1;
            U11_STAR_STAR = U11;
            Trsv
            ( UPPER, NORMAL, diag,
              U11_STAR_STAR.LockedLocalMatrix(),
              x1_STAR_STAR.LocalMatrix() );
            x1 = x1_STAR_STAR;

            x1_MR_STAR = x1_STAR_STAR;
            Gemv
            ( NORMAL, (F)-1, 
              U01.LockedLocalMatrix(), 
              x1_MR_STAR.LockedLocalMatrix(),
              (F)0, z0_MC_STAR.LocalMatrix() );
            x0.SumScatterUpdate( (F)1, z0_MC_STAR );
            //----------------------------------------------------------------//
            x1_MR_STAR.FreeAlignments();
            z0_MC_STAR.FreeAlignments();

            SlideLockedPartitionUpDiagonal
            ( UTL, /**/ UTR,  U00, /**/ U01, U02,
             /*************/ /******************/
                   /**/       U10, /**/ U11, U12,
              UBL, /**/ UBR,  U20, /**/ U21, U22 );

            SlidePartitionUp
            ( xT,  x0,
             /**/ /**/
                   x1,
              xB,  x2 );
        }
    }
    else
    {
        // Matrix views 
        DistMatrix<F,MC,MR> 
            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);

        DistMatrix<F,MC,MR> 
            xL(g), xR(g),
            x0(g), x1(g), x2(g);

        // Temporary distributions
        DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
        DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
        DistMatrix<F,STAR,MR  > x1_STAR_MR(g);
        DistMatrix<F,STAR,MC  > z0_STAR_MC(g);
        DistMatrix<F,MR,  MC  > z0_MR_MC(g);
        DistMatrix<F,MC,  MR  > z0(g);

        // Start the algorithm
        LockedPartitionUpDiagonal
        ( U, UTL, UTR,
             UBL, UBR, 0 );
        PartitionLeft( x,  xL, xR, 0 );
        while( xL.Width() > 0 )
        {
            LockedRepartitionUpDiagonal
            ( UTL, /**/ UTR,  U00, U01, /**/ U02,
                   /**/       U10, U11, /**/ U12,
             /*************/ /******************/
              UBL, /**/ UBR,  U20, U21, /**/ U22 );

            RepartitionLeft
            ( xL,     /**/ xR,
              x0, x1, /**/ x2 );

            x1_STAR_MR.AlignWith( U01 );
            z0_STAR_MC.AlignWith( U01 );
            z0.AlignWith( x0 );
            z0_STAR_MC.ResizeTo( 1, x0.Width() );
            //----------------------------------------------------------------//
            x1_STAR_STAR = x1;
            U11_STAR_STAR = U11;
            Trsv
            ( UPPER, NORMAL, diag,
              U11_STAR_STAR.LockedLocalMatrix(),
              x1_STAR_STAR.LocalMatrix() );
            x1 = x1_STAR_STAR;

            x1_STAR_MR = x1_STAR_STAR;
            Gemv
            ( NORMAL, (F)-1, 
              U01.LockedLocalMatrix(), 
              x1_STAR_MR.LockedLocalMatrix(),
              (F)0, z0_STAR_MC.LocalMatrix() );
            z0_MR_MC.SumScatterFrom( z0_STAR_MC );
            z0 = z0_MR_MC;
            Axpy( (F)1, z0, x0 );
            //----------------------------------------------------------------//
            x1_STAR_MR.FreeAlignments();
            z0_STAR_MC.FreeAlignments();
            z0.FreeAlignments(); 

            SlideLockedPartitionUpDiagonal
            ( UTL, /**/ UTR,  U00, /**/ U01, U02,
             /*************/ /******************/
                   /**/       U10, /**/ U11, U12,
              UBL, /**/ UBR,  U20, /**/ U21, U22 );

            SlidePartitionLeft
            ( xL, /**/ xR,
              x0, /**/ x1, x2 );
        }
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
예제 #5
0
파일: LUHB.hpp 프로젝트: certik/Elemental
inline void
ApplyPackedReflectorsLUHB
( int offset, 
  const DistMatrix<R>& H,
        DistMatrix<R>& A )
{
#ifndef RELEASE
    PushCallStack("internal::ApplyPackedReflectorsLUHB");
    if( H.Grid() != A.Grid() )
        throw std::logic_error("{H,A} must be distributed over the same grid");
    if( offset < 0 || offset > H.Width() )
        throw std::logic_error("Transforms out of bounds");
    if( H.Width() != A.Height() )
        throw std::logic_error
        ("Width of transforms must equal height of target matrix");
#endif
    const Grid& g = H.Grid();

    DistMatrix<R>
        HTL(g), HTR(g),  H00(g), H01(g), H02(g),  HPan(g), HPanCopy(g),
        HBL(g), HBR(g),  H10(g), H11(g), H12(g),
                         H20(g), H21(g), H22(g);
    DistMatrix<R> ABottom(g);

    DistMatrix<R,STAR,VR  > HPan_STAR_VR(g);
    DistMatrix<R,STAR,MC  > HPan_STAR_MC(g);
    DistMatrix<R,STAR,STAR> SInv_STAR_STAR(g);
    DistMatrix<R,STAR,MR  > Z_STAR_MR(g);
    DistMatrix<R,STAR,VR  > Z_STAR_VR(g);

    LockedPartitionUpDiagonal
    ( H, HTL, HTR,
         HBL, HBR, 0 );
    while( HBR.Height() < H.Height() && HBR.Width() < H.Width() )
    {
        LockedRepartitionUpDiagonal
        ( HTL, /**/ HTR,  H00, H01, /**/ H02,
               /**/       H10, H11, /**/ H12,
         /*************/ /******************/
          HBL, /**/ HBR,  H20, H21, /**/ H22 );
    
        const int HPanWidth = H11.Width() + H12.Width();
        const int HPanHeight = 
            std::min( H11.Height(), std::max(HPanWidth-offset,0) );
        const int leftover = A.Height()-HPanWidth;
        HPan.LockedView( H, H00.Height(), H00.Width(), HPanHeight, HPanWidth );

        ABottom.View( A, leftover, 0, HPanWidth, A.Width() );

        HPan_STAR_MC.AlignWith( ABottom );
        Z_STAR_MR.AlignWith( ABottom );
        Z_STAR_VR.AlignWith( ABottom );
        Zeros( HPanHeight, ABottom.Width(), Z_STAR_MR );
        Zeros( HPanHeight, HPanHeight, SInv_STAR_STAR );
        //--------------------------------------------------------------------//
        HPanCopy = HPan;
        MakeTrapezoidal( LEFT, UPPER, offset, HPanCopy );
        SetDiagonalToOne( LEFT, offset, HPanCopy );

        HPan_STAR_VR = HPanCopy;
        Syrk
        ( UPPER, NORMAL,
          R(1), HPan_STAR_VR.LockedLocalMatrix(),
          R(0), SInv_STAR_STAR.LocalMatrix() );
        SInv_STAR_STAR.SumOverGrid();
        HalveMainDiagonal( SInv_STAR_STAR );

        HPan_STAR_MC = HPan_STAR_VR;
        LocalGemm
        ( NORMAL, NORMAL, R(1), HPan_STAR_MC, ABottom, R(0), Z_STAR_MR );
        Z_STAR_VR.SumScatterFrom( Z_STAR_MR );

        LocalTrsm
        ( LEFT, UPPER, NORMAL, NON_UNIT, R(1), SInv_STAR_STAR, Z_STAR_VR );

        Z_STAR_MR = Z_STAR_VR;
        LocalGemm
        ( TRANSPOSE, NORMAL, R(-1), HPan_STAR_MC, Z_STAR_MR, R(1), ABottom );
        //--------------------------------------------------------------------//
        HPan_STAR_MC.FreeAlignments();
        Z_STAR_MR.FreeAlignments();
        Z_STAR_VR.FreeAlignments();

        SlideLockedPartitionUpDiagonal
        ( HTL, /**/ HTR,  H00, /**/ H01, H02,
         /*************/ /******************/
               /**/       H10, /**/ H11, H12,
          HBL, /**/ HBR,  H20, /**/ H21, H22 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
예제 #6
0
파일: LUHB.hpp 프로젝트: certik/Elemental
inline void
ApplyPackedReflectorsLUHB
( int offset, const Matrix<R>& H, Matrix<R>& A )
{
#ifndef RELEASE
    PushCallStack("internal::ApplyPackedReflectorsLUHB");
    if( offset < 0 || offset > H.Width() )
        throw std::logic_error("Transforms out of bounds");
    if( H.Width() != A.Height() )
        throw std::logic_error
        ("Width of transforms must equal height of target matrix");
#endif
    Matrix<R>
        HTL, HTR,  H00, H01, H02,  HPan, HPanCopy,
        HBL, HBR,  H10, H11, H12,
                   H20, H21, H22;
    Matrix<R> ABottom;

    Matrix<R> SInv, Z;

    LockedPartitionUpDiagonal
    ( H, HTL, HTR,
         HBL, HBR, 0 );
    while( HBR.Height() < H.Height() && HBR.Width() < H.Width() )
    {
        LockedRepartitionUpDiagonal
        ( HTL, /**/ HTR,  H00, H01, /**/ H02,
               /**/       H10, H11, /**/ H12,
         /*************/ /******************/
          HBL, /**/ HBR,  H20, H21, /**/ H22 );
    
        const int HPanWidth = H11.Width() + H12.Width();
        const int HPanHeight = 
            std::min( H11.Height(), std::max(HPanWidth-offset,0) );
        const int leftover = A.Height()-HPanWidth;
        HPan.LockedView( H, H00.Height(), H00.Width(), HPanHeight, HPanWidth );

        ABottom.View( A, leftover, 0, HPanWidth, A.Width() );

        Zeros( HPanHeight, ABottom.Width(), Z );
        Zeros( HPanHeight, HPanHeight, SInv );
        //--------------------------------------------------------------------//
        HPanCopy = HPan;
        MakeTrapezoidal( LEFT, UPPER, offset, HPanCopy );
        SetDiagonalToOne( LEFT, offset, HPanCopy );

        Syrk( UPPER, NORMAL, R(1), HPanCopy, R(0), SInv );
        HalveMainDiagonal( SInv );

        Gemm( NORMAL, NORMAL, R(1), HPanCopy, ABottom, R(0), Z );
        Trsm( LEFT, UPPER, NORMAL, NON_UNIT, R(1), SInv, Z );
        Gemm( TRANSPOSE, NORMAL, R(-1), HPanCopy, Z, R(1), ABottom );
        //--------------------------------------------------------------------//

        SlideLockedPartitionUpDiagonal
        ( HTL, /**/ HTR,  H00, /**/ H01, H02,
         /*************/ /******************/
               /**/       H10, /**/ H11, H12,
          HBL, /**/ HBR,  H20, /**/ H21, H22 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
예제 #7
0
파일: RLN.hpp 프로젝트: mcg1969/Elemental
inline void
TrsmRLN
( UnitOrNonUnit diag, F alpha, const DistMatrix<F>& L, DistMatrix<F>& X,
  bool checkIfSingular )
{
#ifndef RELEASE
    PushCallStack("internal::TrsmRLN");
#endif
    const Grid& g = L.Grid();

    // Matrix views
    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);

    DistMatrix<F> XL(g), XR(g),
                  X0(g), X1(g), X2(g);

    // Temporary distributions
    DistMatrix<F,MR,  STAR> L10Trans_MR_STAR(g);
    DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
    DistMatrix<F,STAR,MC  > X1Trans_STAR_MC(g);
    DistMatrix<F,VC,  STAR> X1_VC_STAR(g);

    // Start the algorithm
    Scale( alpha, X );
    LockedPartitionUpDiagonal
    ( L, LTL, LTR,
         LBL, LBR, 0 );
    PartitionLeft( X, XL, XR, 0 );
    while( XL.Width() > 0 )
    {
        LockedRepartitionUpDiagonal
        ( LTL, /**/ LTR,  L00, L01, /**/ L02,
               /**/       L10, L11, /**/ L12,
         /*************/ /******************/
          LBL, /**/ LBR,  L20, L21, /**/ L22 );
 
        RepartitionLeft
        ( XL,     /**/ XR,
          X0, X1, /**/ X2 );

        X1Trans_STAR_MC.AlignWith( X0 );
        L10Trans_MR_STAR.AlignWith( X0 );
        //--------------------------------------------------------------------//
        L11_STAR_STAR = L11;
        X1_VC_STAR = X1;
        LocalTrsm
        ( RIGHT, LOWER, NORMAL, diag, F(1), L11_STAR_STAR, X1_VC_STAR,
          checkIfSingular );

        // X0[MC,MR] -= X1[MC,* ]   L10[*,MR]
        //            = X1^T[* ,MC] L10^T[MR,* ]
        X1Trans_STAR_MC.TransposeFrom( X1_VC_STAR );
        X1.TransposeFrom( X1Trans_STAR_MC );
        L10Trans_MR_STAR.TransposeFrom( L10 );
        LocalGemm
        ( TRANSPOSE, TRANSPOSE, 
          F(-1), X1Trans_STAR_MC, L10Trans_MR_STAR, F(1), X0 );
        //--------------------------------------------------------------------//
        X1Trans_STAR_MC.FreeAlignments();
        L10Trans_MR_STAR.FreeAlignments();

        SlideLockedPartitionUpDiagonal
        ( LTL, /**/ LTR,  L00, /**/ L01, L02,
         /*************/ /******************/
               /**/       L10, /**/ L11, L12,
          LBL, /**/ LBR,  L20, /**/ L21, L22 );

        SlidePartitionLeft
        ( XL, /**/ XR,
          X0, /**/ X1, X2 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
예제 #8
0
파일: LLT.hpp 프로젝트: mcg1969/Elemental
inline void
TrsmLLTLarge
( Orientation orientation, UnitOrNonUnit diag,
  F alpha, const DistMatrix<F>& L, DistMatrix<F>& X,
  bool checkIfSingular )
{
#ifndef RELEASE
    PushCallStack("internal::TrsmLLTLarge");
    if( orientation == NORMAL )
        throw std::logic_error("TrsmLLT expects a (Conjugate)Transpose option");
#endif
    const Grid& g = L.Grid();

    // Matrix views
    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);
    DistMatrix<F> XT(g),  X0(g),
                  XB(g),  X1(g),
                          X2(g);

    // Temporary distributions
    DistMatrix<F,STAR,MC  > L10_STAR_MC(g);
    DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
    DistMatrix<F,STAR,MR  > X1_STAR_MR(g);
    DistMatrix<F,STAR,VR  > X1_STAR_VR(g);

    // Start the algorithm
    Scale( alpha, X );
    LockedPartitionUpDiagonal
    ( L, LTL, LTR,
         LBL, LBR, 0 );
    PartitionUp
    ( X, XT,
         XB, 0 );
    while( XT.Height() > 0 )
    {
        LockedRepartitionUpDiagonal
        ( LTL, /**/ LTR,  L00, L01, /**/ L02,
               /**/       L10, L11, /**/ L12,
         /*************/ /******************/
          LBL, /**/ LBR,  L20, L21, /**/ L22 );

        RepartitionUp
        ( XT,  X0,
               X1,
         /**/ /**/
          XB,  X2 ); 

        L10_STAR_MC.AlignWith( X0 );
        X1_STAR_MR.AlignWith( X0 );
        //--------------------------------------------------------------------//
        L11_STAR_STAR = L11; // L11[* ,* ] <- L11[MC,MR]
        X1_STAR_VR    = X1;  // X1[* ,VR] <- X1[MC,MR]

        // X1[* ,VR] := L11^-[T/H][* ,* ] X1[* ,VR]
        LocalTrsm
        ( LEFT, LOWER, orientation, diag, F(1), L11_STAR_STAR, X1_STAR_VR,
          checkIfSingular );

        X1_STAR_MR  = X1_STAR_VR; // X1[* ,MR] <- X1[* ,VR]
        X1          = X1_STAR_MR; // X1[MC,MR] <- X1[* ,MR]
        L10_STAR_MC = L10;        // L10[* ,MC] <- L10[MC,MR]

        // X0[MC,MR] -= (L10[* ,MC])^(T/H) X1[* ,MR]
        //            = L10^[T/H][MC,* ] X1[* ,MR]
        LocalGemm
        ( orientation, NORMAL, F(-1), L10_STAR_MC, X1_STAR_MR, F(1), X0 );
        //--------------------------------------------------------------------//
        L10_STAR_MC.FreeAlignments();
        X1_STAR_MR.FreeAlignments();

        SlideLockedPartitionUpDiagonal
        ( LTL, /**/ LTR,  L00, /**/ L01, L02,
         /*************/ /******************/
               /**/       L10, /**/ L11, L12,
          LBL, /**/ LBR,  L20, /**/ L21, L22 );

        SlidePartitionUp
        ( XT,  X0,
         /**/ /**/
               X1,
          XB,  X2 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
예제 #9
0
파일: RUN.hpp 프로젝트: ahmadia/Elemental-1
inline void
TrmmRUNC
( UnitOrNonUnit diag,
  T alpha, const DistMatrix<T>& U,
                 DistMatrix<T>& X )
{
#ifndef RELEASE
    CallStackEntry entry("internal::TrmmRUNC");
    if( U.Grid() != X.Grid() )
        throw std::logic_error
        ("U and X must be distributed over the same grid");
    if( U.Height() != U.Width() || X.Width() != U.Height() )
    {
        std::ostringstream msg;
        msg << "Nonconformal TrmmRUNC: \n"
            << "  U ~ " << U.Height() << " x " << U.Width() << "\n"
            << "  X ~ " << X.Height() << " x " << X.Width() << "\n";
        throw std::logic_error( msg.str().c_str() );
    }
#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);

    DistMatrix<T> XL(g), XR(g),
                  X0(g), X1(g), X2(g);

    // Temporary distributions
    DistMatrix<T,MR,  STAR> U12Trans_MR_STAR(g);
    DistMatrix<T,STAR,STAR> U11_STAR_STAR(g);
    DistMatrix<T,VC,  STAR> X1_VC_STAR(g);
    DistMatrix<T,MC,  STAR> X1_MC_STAR(g);
    
    // Start the algorithm
    Scale( alpha, X );
    LockedPartitionUpDiagonal
    ( U, UTL, UTR,
         UBL, UBR, 0 );
    PartitionLeft( X, XL, XR, 0 );
    while( XL.Width() > 0 )
    {
        LockedRepartitionUpDiagonal
        ( UTL, /**/ UTR,  U00, U01, /**/ U02,
               /**/       U10, U11, /**/ U12, 
         /*************/ /******************/
          UBL, /**/ UBR,  U20, U21, /**/ U22 );

        RepartitionLeft
        ( XL,     /**/ XR,
          X0, X1, /**/ X2 ); 

        X1_MC_STAR.AlignWith( X2 );
        U12Trans_MR_STAR.AlignWith( X2 );
        X1_VC_STAR.AlignWith( X1 );
        //--------------------------------------------------------------------//
        X1_MC_STAR = X1;
        U12Trans_MR_STAR.TransposeFrom( U12 );
        LocalGemm
        ( NORMAL, TRANSPOSE, T(1), X1_MC_STAR, U12Trans_MR_STAR, T(1), X2 );

        U11_STAR_STAR = U11;
        X1_VC_STAR = X1_MC_STAR;
        LocalTrmm
        ( RIGHT, UPPER, NORMAL, diag, T(1), U11_STAR_STAR, X1_VC_STAR );
        X1 = X1_VC_STAR;
        //--------------------------------------------------------------------//
        X1_MC_STAR.FreeAlignments();
        U12Trans_MR_STAR.FreeAlignments();
        X1_VC_STAR.FreeAlignments();

        SlideLockedPartitionUpDiagonal
        ( UTL, /**/ UTR,  U00, /**/ U01, U02,
         /*************/ /******************/
               /**/       U10, /**/ U11, U12,
          UBL, /**/ UBR,  U20, /**/ U21, U22 );

        SlidePartitionLeft
        ( XL, /**/ XR,
          X0, /**/ X1, X2 );
    }
}
예제 #10
0
inline void
internal::TrsvLT
( Orientation orientation,
  UnitOrNonUnit diag, 
  const DistMatrix<F,MC,MR>& L, 
        DistMatrix<F,MC,MR>& x )
{
#ifndef RELEASE
    PushCallStack("internal::TrsvLT");
    if( L.Grid() != x.Grid() )
        throw std::logic_error("{L,x} must be distributed over the same grid");
    if( orientation == NORMAL )
        throw std::logic_error("TrsvLT expects a (conjugate-)transpose option");
    if( L.Height() != L.Width() )
        throw std::logic_error("L must be square");
    if( x.Width() != 1 && x.Height() != 1 )
        throw std::logic_error("x must be a vector");
    const int xLength = ( x.Width() == 1 ? x.Height() : x.Width() );
    if( L.Width() != xLength )
        throw std::logic_error("Nonconformal TrsvLT");
#endif
    const Grid& g = L.Grid();

    if( x.Width() == 1 )
    {
        // Matrix views 
        DistMatrix<F,MC,MR> 
            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);

        DistMatrix<F,MC,MR> 
            xT(g),  x0(g),
            xB(g),  x1(g),
                    x2(g);

        // Temporary distributions
        DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
        DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
        DistMatrix<F,MC,  STAR> x1_MC_STAR(g);
        DistMatrix<F,MR,  STAR> z0_MR_STAR(g);
        DistMatrix<F,MR,  MC  > z0_MR_MC(g);
        DistMatrix<F,MC,  MR  > z0(g);

        // Start the algorithm
        LockedPartitionUpDiagonal
        ( L, LTL, LTR,
             LBL, LBR, 0 );
        PartitionUp
        ( x, xT,
             xB, 0 );
        while( xT.Height() > 0 )
        {
            LockedRepartitionUpDiagonal
            ( LTL, /**/ LTR,  L00, L01, /**/ L02,
                   /**/       L10, L11, /**/ L12,
             /*************/ /******************/
              LBL, /**/ LBR,  L20, L21, /**/ L22 );

            RepartitionUp
            ( xT,  x0,
                   x1,
             /**/ /**/
              xB,  x2 );

            x1_MC_STAR.AlignWith( L10 );
            z0_MR_STAR.AlignWith( L10 );
            z0_MR_STAR.ResizeTo( x0.Height(), 1 );
            z0.AlignWith( x0 );
            //----------------------------------------------------------------//
            x1_STAR_STAR = x1;
            L11_STAR_STAR = L11;
            Trsv
            ( LOWER, orientation, diag,
              L11_STAR_STAR.LockedLocalMatrix(),
              x1_STAR_STAR.LocalMatrix() );
            x1 = x1_STAR_STAR;

            x1_MC_STAR = x1_STAR_STAR;
            Gemv
            ( orientation, (F)-1, 
              L10.LockedLocalMatrix(), 
              x1_MC_STAR.LockedLocalMatrix(),
              (F)0, z0_MR_STAR.LocalMatrix() );
            z0_MR_MC.SumScatterFrom( z0_MR_STAR );
            z0 = z0_MR_MC;
            Axpy( (F)1, z0, x0 );
            //----------------------------------------------------------------//
            x1_MC_STAR.FreeAlignments();
            z0_MR_STAR.FreeAlignments();
            z0.FreeAlignments();

            SlideLockedPartitionUpDiagonal
            ( LTL, /**/ LTR,  L00, /**/ L01, L02,
             /*************/ /******************/
                   /**/       L10, /**/ L11, L12,
              LBL, /**/ LBR,  L20, /**/ L21, L22 );

            SlidePartitionUp
            ( xT,  x0,
             /**/ /**/
                   x1,
              xB,  x2 );
        }
    }
    else
    {
        // Matrix views 
        DistMatrix<F,MC,MR> 
            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);

        DistMatrix<F,MC,MR> 
            xL(g), xR(g),
            x0(g), x1(g), x2(g);

        // Temporary distributions
        DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
        DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
        DistMatrix<F,STAR,MC  > x1_STAR_MC(g);
        DistMatrix<F,STAR,MR  > z0_STAR_MR(g);

        // Start the algorithm
        LockedPartitionUpDiagonal
        ( L, LTL, LTR,
             LBL, LBR, 0 );
        PartitionLeft( x,  xL, xR, 0 );
        while( xL.Width() > 0 )
        {
            LockedRepartitionUpDiagonal
            ( LTL, /**/ LTR,  L00, L01, /**/ L02,
                   /**/       L10, L11, /**/ L12,
             /*************/ /******************/
              LBL, /**/ LBR,  L20, L21, /**/ L22 );

            RepartitionLeft
            ( xL,     /**/ xR,
              x0, x1, /**/ x2 );

            x1_STAR_MC.AlignWith( L10 );
            z0_STAR_MR.AlignWith( L10 );
            //----------------------------------------------------------------//
            x1_STAR_STAR = x1;
            L11_STAR_STAR = L11;
            Trsv
            ( LOWER, orientation, diag,
              L11_STAR_STAR.LockedLocalMatrix(),
              x1_STAR_STAR.LocalMatrix() );
            x1 = x1_STAR_STAR;

            x1_STAR_MC = x1_STAR_STAR;
            Gemv
            ( orientation, (F)-1, 
              L10.LockedLocalMatrix(), 
              x1_STAR_MC.LockedLocalMatrix(),
              (F)0, z0_STAR_MR.LocalMatrix() );
            x0.SumScatterUpdate( (F)1, z0_STAR_MR );
            //----------------------------------------------------------------//
            x1_STAR_MC.FreeAlignments();
            z0_STAR_MR.FreeAlignments();

            SlideLockedPartitionUpDiagonal
            ( LTL, /**/ LTR,  L00, /**/ L01, L02,
             /*************/ /******************/
                   /**/       L10, /**/ L11, L12,
              LBL, /**/ LBR,  L20, /**/ L21, L22 );

            SlidePartitionLeft
            ( xL, /**/ xR,
              x0, /**/ x1, x2 );
        }
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
예제 #11
0
파일: RUT.hpp 프로젝트: jimgoo/Elemental
inline void
TrsmRUT
( Orientation orientation, UnitOrNonUnit diag,
  F alpha, const DistMatrix<F>& U, DistMatrix<F>& X,
  bool checkIfSingular )
{
#ifndef RELEASE
    PushCallStack("internal::TrsmRUT");
    if( orientation == NORMAL )
        throw std::logic_error("TrsmRUT expects a (Conjugate)Transpose option");
#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);

    DistMatrix<F> XL(g), XR(g),
                  X0(g), X1(g), X2(g);

    // Temporary distributions
    DistMatrix<F,VR,  STAR> U01_VR_STAR(g);
    DistMatrix<F,STAR,MR  > U01AdjOrTrans_STAR_MR(g);
    DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
    DistMatrix<F,VC,  STAR> X1_VC_STAR(g);
    DistMatrix<F,STAR,MC  > X1Trans_STAR_MC(g);
    
    // Start the algorithm
    Scale( alpha, X );
    LockedPartitionUpDiagonal
    ( U, UTL, UTR,
         UBL, UBR, 0 );
    PartitionLeft( X, XL, XR, 0 );
    while( XL.Width() > 0 )
    {
        LockedRepartitionUpDiagonal
        ( UTL, /**/ UTR,  U00, U01, /**/ U02,
               /**/       U10, U11, /**/ U12,
         /*************/ /******************/
          UBL, /**/ UBR,  U20, U21, /**/ U22 );

        RepartitionLeft
        ( XL,     /**/ XR,
          X0, X1, /**/ X2 );

        X1_VC_STAR.AlignWith( X0 );
        X1Trans_STAR_MC.AlignWith( X0 );
        U01_VR_STAR.AlignWith( X0 );
        U01AdjOrTrans_STAR_MR.AlignWith( X0 );
        //--------------------------------------------------------------------//
        U11_STAR_STAR = U11;
        X1_VC_STAR = X1; 

        LocalTrsm
        ( RIGHT, UPPER, orientation, diag, 
          F(1), U11_STAR_STAR, X1_VC_STAR, checkIfSingular );

        X1Trans_STAR_MC.TransposeFrom( X1_VC_STAR );
        X1.TransposeFrom( X1Trans_STAR_MC );
        U01_VR_STAR = U01;
        if( orientation == ADJOINT )
            U01AdjOrTrans_STAR_MR.AdjointFrom( U01_VR_STAR );
        else
            U01AdjOrTrans_STAR_MR.TransposeFrom( U01_VR_STAR );

        // X0[MC,MR] -= X1[MC,* ] (U01[MR,* ])^(T/H)
        //            = X1^T[* ,MC] (U01^(T/H))[* ,MR]
        LocalGemm
        ( TRANSPOSE, NORMAL, 
          F(-1), X1Trans_STAR_MC, U01AdjOrTrans_STAR_MR, F(1), X0 );
        //--------------------------------------------------------------------//
        X1_VC_STAR.FreeAlignments();
        X1Trans_STAR_MC.FreeAlignments();
        U01_VR_STAR.FreeAlignments();
        U01AdjOrTrans_STAR_MR.FreeAlignments();

        SlideLockedPartitionUpDiagonal
        ( UTL, /**/ UTR,  U00, /**/ U01, U02,
         /*************/ /******************/
               /**/       U10, /**/ U11, U12, 
          UBL, /**/ UBR,  U20, /**/ U21, U22 );

        SlidePartitionLeft
        ( XL, /**/     XR,
          X0, /**/ X1, X2 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
예제 #12
0
파일: RLVB.hpp 프로젝트: mcg1969/Elemental
inline void
RLVB
( Conjugation conjugation, int offset, 
  const DistMatrix<Complex<R> >& H,
  const DistMatrix<Complex<R>,MD,STAR>& t,
        DistMatrix<Complex<R> >& A )
{
#ifndef RELEASE
    PushCallStack("apply_packed_reflectors::RLVB");
    if( H.Grid() != t.Grid() || t.Grid() != A.Grid() )
        throw std::logic_error
        ("{H,t,A} must be distributed over the same grid");
    if( offset > 0 || offset < -H.Height() )
        throw std::logic_error("Transforms out of bounds");
    if( H.Height() != A.Width() )
        throw std::logic_error
        ("Height of transforms must equal width of target matrix");
    if( t.Height() != H.DiagonalLength( offset ) )
        throw std::logic_error("t must be the same length as H's offset diag");
    if( !t.AlignedWithDiagonal( H, offset ) )
        throw std::logic_error("t must be aligned with H's 'offset' diagonal");
#endif
    typedef Complex<R> C;
    const Grid& g = H.Grid();

    DistMatrix<C>
        HTL(g), HTR(g),  H00(g), H01(g), H02(g),  HPan(g), HPanCopy(g),
        HBL(g), HBR(g),  H10(g), H11(g), H12(g),
                         H20(g), H21(g), H22(g);
    DistMatrix<C> ARight(g);
    DistMatrix<C,MD,STAR>
        tT(g),  t0(g),
        tB(g),  t1(g),
                t2(g);
    
    DistMatrix<C,VC,  STAR> HPan_VC_STAR(g);
    DistMatrix<C,MR,  STAR> HPan_MR_STAR(g);
    DistMatrix<C,STAR,STAR> t1_STAR_STAR(g);
    DistMatrix<C,STAR,STAR> SInv_STAR_STAR(g);
    DistMatrix<C,STAR,MC  > ZAdj_STAR_MC(g);
    DistMatrix<C,STAR,VC  > ZAdj_STAR_VC(g);

    LockedPartitionUpDiagonal
    ( H, HTL, HTR,
         HBL, HBR, 0 );
    LockedPartitionUp
    ( t, tT,
         tB, 0 );
    while( HBR.Height() < H.Height() && HBR.Width() < H.Width() )
    {
        LockedRepartitionUpDiagonal
        ( HTL, /**/ HTR,  H00, H01, /**/ H02,
               /**/       H10, H11, /**/ H12,
         /*************/ /******************/
          HBL, /**/ HBR,  H20, H21, /**/ H22 );

        const int HPanHeight = H11.Height() + H21.Height();
        const int HPanWidth = 
            std::min( H11.Width(), std::max(HPanHeight+offset,0) );
        const int leftover = A.Width()-HPanHeight;
        LockedView( HPan, H, H00.Height(), H00.Width(), HPanHeight, HPanWidth );

        LockedRepartitionUp
        ( tT,  t0,
               t1,
         /**/ /**/
          tB,  t2, HPanWidth );

        View( ARight, A, 0, leftover, A.Height(), HPanHeight );

        HPan_MR_STAR.AlignWith( ARight );
        ZAdj_STAR_MC.AlignWith( ARight );
        ZAdj_STAR_VC.AlignWith( ARight );
        Zeros( HPan.Width(), ARight.Height(), ZAdj_STAR_MC );
        Zeros( HPan.Width(), HPan.Width(), SInv_STAR_STAR );
        //--------------------------------------------------------------------//
        HPanCopy = HPan;
        MakeTrapezoidal( LEFT, LOWER, offset, HPanCopy );
        SetDiagonal( LEFT, offset, HPanCopy, C(1) );

        HPan_VC_STAR = HPanCopy;
        Herk
        ( LOWER, ADJOINT, 
          C(1), HPan_VC_STAR.LockedMatrix(),
          C(0), SInv_STAR_STAR.Matrix() );     
        SInv_STAR_STAR.SumOverGrid();
        t1_STAR_STAR = t1;
        FixDiagonal( conjugation, t1_STAR_STAR, SInv_STAR_STAR );

        HPan_MR_STAR = HPan_VC_STAR;
        LocalGemm
        ( ADJOINT, ADJOINT,
          C(1), HPan_MR_STAR, ARight, C(0), ZAdj_STAR_MC );
        ZAdj_STAR_VC.SumScatterFrom( ZAdj_STAR_MC );
 
        LocalTrsm
        ( LEFT, LOWER, ADJOINT, NON_UNIT, C(1), SInv_STAR_STAR, ZAdj_STAR_VC );

        ZAdj_STAR_MC = ZAdj_STAR_VC;
        LocalGemm
        ( ADJOINT, ADJOINT, C(-1), ZAdj_STAR_MC, HPan_MR_STAR, C(1), ARight );
        //--------------------------------------------------------------------//
        HPan_MR_STAR.FreeAlignments();
        ZAdj_STAR_MC.FreeAlignments();
        ZAdj_STAR_VC.FreeAlignments();

        SlideLockedPartitionUpDiagonal
        ( HTL, /**/ HTR,  H00, /**/ H01, H02,
         /*************/ /******************/
               /**/       H10, /**/ H11, H12,
          HBL, /**/ HBR,  H20, /**/ H21, H22 );

        SlideLockedPartitionUp
        ( tT,  t0,
         /**/ /**/
               t1,
          tB,  t2 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
예제 #13
0
파일: RLVB.hpp 프로젝트: mcg1969/Elemental
inline void
RLVB
( Conjugation conjugation, int offset, 
  const Matrix<Complex<R> >& H,
  const Matrix<Complex<R> >& t,
        Matrix<Complex<R> >& A )
{
#ifndef RELEASE
    PushCallStack("apply_packed_reflectors::RLVB");
    if( offset > 0 || offset < -H.Height() )
        throw std::logic_error("Transforms out of bounds");
    if( H.Height() != A.Width() )
        throw std::logic_error
        ("Height of transforms must equal width of target matrix");
    if( t.Height() != H.DiagonalLength( offset ) )
        throw std::logic_error("t must be the same length as H's offset diag");
#endif
    typedef Complex<R> C;

    Matrix<C>
        HTL, HTR,  H00, H01, H02,  HPan, HPanCopy,
        HBL, HBR,  H10, H11, H12,
                   H20, H21, H22;
    Matrix<C> ARight;
    Matrix<C>
        tT,  t0,
        tB,  t1,
             t2;
    
    Matrix<C> SInv, Z;

    LockedPartitionUpDiagonal
    ( H, HTL, HTR,
         HBL, HBR, 0 );
    LockedPartitionUp
    ( t, tT,
         tB, 0 );
    while( HBR.Height() < H.Height() && HBR.Width() < H.Width() )
    {
        LockedRepartitionUpDiagonal
        ( HTL, /**/ HTR,  H00, H01, /**/ H02,
               /**/       H10, H11, /**/ H12,
         /*************/ /******************/
          HBL, /**/ HBR,  H20, H21, /**/ H22 );

        const int HPanHeight = H11.Height() + H21.Height();
        const int HPanWidth = 
            std::min( H11.Width(), std::max(HPanHeight+offset,0) );
        const int leftover = A.Width()-HPanHeight;
        LockedView( HPan, H, H00.Height(), H00.Width(), HPanHeight, HPanWidth );

        LockedRepartitionUp
        ( tT,  t0,
               t1,
         /**/ /**/
          tB,  t2, HPanWidth );

        View( ARight, A, 0, leftover, A.Height(), HPanHeight );

        Zeros( ARight.Height(), HPan.Width(), Z );
        Zeros( HPan.Width(), HPan.Width(), SInv );
        //--------------------------------------------------------------------//
        HPanCopy = HPan;
        MakeTrapezoidal( LEFT, LOWER, offset, HPanCopy );
        SetDiagonal( LEFT, offset, HPanCopy, C(1) );

        Herk( LOWER, ADJOINT, C(1), HPanCopy, C(0), SInv );
        FixDiagonal( conjugation, t1, SInv );

        Gemm( NORMAL, NORMAL, C(1), ARight, HPanCopy, C(0), Z );
        Trsm( RIGHT, LOWER, NORMAL, NON_UNIT, C(1), SInv, Z );
        Gemm( NORMAL, ADJOINT, C(-1), Z, HPanCopy, C(1), ARight );
        //--------------------------------------------------------------------//

        SlideLockedPartitionUpDiagonal
        ( HTL, /**/ HTR,  H00, /**/ H01, H02,
         /*************/ /******************/
               /**/       H10, /**/ H11, H12,
          HBL, /**/ HBR,  H20, /**/ H21, H22 );

        SlideLockedPartitionUp
        ( tT,  t0,
         /**/ /**/
               t1,
          tB,  t2 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
예제 #14
0
파일: RLVB.hpp 프로젝트: mcg1969/Elemental
inline void
RLVB
( int offset, 
  const DistMatrix<R>& H,
        DistMatrix<R>& A )
{
#ifndef RELEASE
    PushCallStack("apply_packed_reflectors::RLVB");
    if( H.Grid() != A.Grid() )
        throw std::logic_error("{H,A} must be distributed over the same grid");
    if( offset > 0 || offset < -H.Height() )
        throw std::logic_error("Transforms out of bounds");
    if( H.Height() != A.Width() )
        throw std::logic_error
        ("Height of transforms must equal width of target matrix");
#endif
    const Grid& g = H.Grid();

    DistMatrix<R>
        HTL(g), HTR(g),  H00(g), H01(g), H02(g),  HPan(g), HPanCopy(g),
        HBL(g), HBR(g),  H10(g), H11(g), H12(g),
                         H20(g), H21(g), H22(g);
    DistMatrix<R> ARight(g);

    DistMatrix<R,VC,  STAR> HPan_VC_STAR(g);
    DistMatrix<R,MR,  STAR> HPan_MR_STAR(g);
    DistMatrix<R,STAR,STAR> SInv_STAR_STAR(g);
    DistMatrix<R,STAR,MC  > ZTrans_STAR_MC(g);
    DistMatrix<R,STAR,VC  > ZTrans_STAR_VC(g);

    LockedPartitionUpDiagonal
    ( H, HTL, HTR,
         HBL, HBR, 0 );
    while( HBR.Height() < H.Height() && HBR.Width() < H.Width() )
    {
        LockedRepartitionUpDiagonal
        ( HTL, /**/ HTR,  H00, H01, /**/ H02,
               /**/       H10, H11, /**/ H12,
         /*************/ /******************/
          HBL, /**/ HBR,  H20, H21, /**/ H22 );

        const int HPanHeight = H11.Height() + H21.Height();
        const int HPanWidth = 
            std::min( H11.Width(), std::max(HPanHeight+offset,0) );
        const int leftover = A.Width()-HPanHeight;
        LockedView( HPan, H, H00.Height(), H00.Width(), HPanHeight, HPanWidth );

        View( ARight, A, 0, leftover, A.Height(), HPanHeight );

        HPan_MR_STAR.AlignWith( ARight );
        ZTrans_STAR_MC.AlignWith( ARight );
        ZTrans_STAR_VC.AlignWith( ARight );
        Zeros( HPanWidth, ARight.Height(), ZTrans_STAR_MC );
        Zeros( HPanWidth, HPanWidth, SInv_STAR_STAR );
        //--------------------------------------------------------------------//
        HPanCopy = HPan;
        MakeTrapezoidal( LEFT, LOWER, offset, HPanCopy );
        SetDiagonal( LEFT, offset, HPanCopy, R(1) );

        HPan_VC_STAR = HPanCopy;
        Syrk
        ( LOWER, TRANSPOSE, 
          R(1), HPan_VC_STAR.LockedMatrix(),
          R(0), SInv_STAR_STAR.Matrix() );     
        SInv_STAR_STAR.SumOverGrid();
        HalveMainDiagonal( SInv_STAR_STAR );

        HPan_MR_STAR = HPan_VC_STAR;
        LocalGemm
        ( TRANSPOSE, TRANSPOSE,
          R(1), HPan_MR_STAR, ARight, R(0), ZTrans_STAR_MC );
        ZTrans_STAR_VC.SumScatterFrom( ZTrans_STAR_MC );
 
        LocalTrsm
        ( LEFT, LOWER, TRANSPOSE, NON_UNIT,
          R(1), SInv_STAR_STAR, ZTrans_STAR_VC );

        ZTrans_STAR_MC = ZTrans_STAR_VC;
        LocalGemm
        ( TRANSPOSE, TRANSPOSE, 
          R(-1), ZTrans_STAR_MC, HPan_MR_STAR, R(1), ARight );
        //--------------------------------------------------------------------//
        HPan_MR_STAR.FreeAlignments();
        ZTrans_STAR_MC.FreeAlignments();
        ZTrans_STAR_VC.FreeAlignments();

        SlideLockedPartitionUpDiagonal
        ( HTL, /**/ HTR,  H00, /**/ H01, H02,
         /*************/ /******************/
               /**/       H10, /**/ H11, H12,
          HBL, /**/ HBR,  H20, /**/ H21, H22 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
예제 #15
0
파일: LUN.hpp 프로젝트: jimgoo/Elemental
inline void
TrsmLUNSmall
( UnitOrNonUnit diag,
  F alpha, const DistMatrix<F,VC,STAR>& U, DistMatrix<F,VC,STAR>& X,
  bool checkIfSingular )
{
#ifndef RELEASE
    PushCallStack("internal::TrsmLUNSmall");
    if( U.Grid() != X.Grid() )
        throw std::logic_error
        ("U and X must be distributed over the same grid");
    if( U.Height() != U.Width() || U.Width() != X.Height() )
    {
        std::ostringstream msg;
        msg << "Nonconformal TrsmLUN: \n"
            << "  U ~ " << U.Height() << " x " << U.Width() << "\n"
            << "  X ~ " << X.Height() << " x " << X.Width() << "\n";
        throw std::logic_error( msg.str() );
    }
    if( U.ColAlignment() != X.ColAlignment() )
        throw std::logic_error("U and X are assumed to be aligned");
#endif
    const Grid& g = U.Grid();

    // Matrix views
    DistMatrix<F,VC,STAR> 
        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);
    DistMatrix<F,VC,STAR> XT(g),  X0(g),
                          XB(g),  X1(g),
                                  X2(g);

    // Temporary distributions
    DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
    DistMatrix<F,STAR,STAR> X1_STAR_STAR(g);

    // Start the algorithm
    Scale( alpha, X );
    LockedPartitionUpDiagonal
    ( U, UTL, UTR,
         UBL, UBR, 0 );
    PartitionUp
    ( X, XT,
         XB, 0 );
    while( XT.Height() > 0 )
    {
        LockedRepartitionUpDiagonal
        ( UTL, /**/ UTR,   U00, U01, /**/ U02,
               /**/        U10, U11, /**/ U12,
         /*************/  /******************/
          UBL, /**/ UBR,   U20, U21, /**/ U22 );

        RepartitionUp
        ( XT,  X0,
               X1,
         /**/ /**/
          XB,  X2 );

        //--------------------------------------------------------------------//
        U11_STAR_STAR = U11; // U11[* ,* ] <- U11[VC,* ]
        X1_STAR_STAR = X1;   // X1[* ,* ] <- X1[VC,* ]
        
        // X1[* ,* ] := U11^-1[* ,* ] X1[* ,* ]
        LocalTrsm
        ( LEFT, UPPER, NORMAL, diag,
          F(1), U11_STAR_STAR, X1_STAR_STAR, checkIfSingular );
        X1 = X1_STAR_STAR;

        // X0[VC,* ] -= U01[VC,* ] X1[* ,* ]
        LocalGemm( NORMAL, NORMAL, F(-1), U01, X1_STAR_STAR, F(1), X0 );
        //--------------------------------------------------------------------//

        SlideLockedPartitionUpDiagonal
        ( UTL, /**/ UTR,  U00, /**/ U01, U02,
         /*************/ /******************/
               /**/       U10, /**/ U11, U12,
          UBL, /**/ UBR,  U20, /**/ U21, U22 );

        SlidePartitionUp
        ( XT,  X0,
         /**/ /**/
               X1,
          XB,  X2 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
예제 #16
0
파일: LLN.hpp 프로젝트: ahmadia/Elemental-1
inline void
TrmmLLNC
( UnitOrNonUnit diag,
  T alpha, const DistMatrix<T>& L,
                 DistMatrix<T>& X )
{
#ifndef RELEASE
    CallStackEntry entry("internal::TrmmLLNC");
    if( L.Grid() != X.Grid() )
        throw std::logic_error
        ("L and X must be distributed over the same grid");
    if( L.Height() != L.Width() || L.Width() != X.Height() )
    {
        std::ostringstream msg;
        msg << "Nonconformal TrmmLLNC: \n"
            << "  L ~ " << L.Height() << " x " << L.Width() << "\n"
            << "  X ~ " << X.Height() << " x " << X.Width() << "\n";
        throw std::logic_error( msg.str().c_str() );
    }
#endif
    const Grid& g = L.Grid();

    // Matrix views
    DistMatrix<T> 
        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);
    DistMatrix<T> XT(g),  X0(g),
                  XB(g),  X1(g),
                          X2(g);

    // Temporary distributions
    DistMatrix<T,MC,  STAR> L21_MC_STAR(g);
    DistMatrix<T,STAR,STAR> L11_STAR_STAR(g);
    DistMatrix<T,STAR,VR  > X1_STAR_VR(g);
    DistMatrix<T,MR,  STAR> X1Trans_MR_STAR(g);

    // Start the algorithm
    Scale( alpha, X );
    LockedPartitionUpDiagonal
    ( L, LTL, LTR,
         LBL, LBR, 0 );
    PartitionUp
    ( X, XT,
         XB, 0 );
    while( XT.Height() > 0 )
    {
        LockedRepartitionUpDiagonal
        ( LTL, /**/ LTR,  L00, L01, /**/ L02,
               /**/       L10, L11, /**/ L12,
         /*************/ /******************/
          LBL, /**/ LBR,  L20, L21, /**/ L22 );

        RepartitionUp
        ( XT,  X0,
               X1,
         /**/ /**/
          XB,  X2 );

        L21_MC_STAR.AlignWith( X2 );
        X1Trans_MR_STAR.AlignWith( X2 );
        X1_STAR_VR.AlignWith( X1 );
        //--------------------------------------------------------------------//
        L21_MC_STAR = L21;
        X1Trans_MR_STAR.TransposeFrom( X1 );
        LocalGemm
        ( NORMAL, TRANSPOSE, T(1), L21_MC_STAR, X1Trans_MR_STAR, T(1), X2 );

        L11_STAR_STAR = L11;
        X1_STAR_VR.TransposeFrom( X1Trans_MR_STAR );
        LocalTrmm( LEFT, LOWER, NORMAL, diag, T(1), L11_STAR_STAR, X1_STAR_VR );
        X1 = X1_STAR_VR;
        //--------------------------------------------------------------------//
        L21_MC_STAR.FreeAlignments();
        X1Trans_MR_STAR.FreeAlignments();
        X1_STAR_VR.FreeAlignments();

        SlideLockedPartitionUpDiagonal
        ( LTL, /**/ LTR,  L00, /**/ L01, L02,
         /*************/ /******************/
               /**/       L10, /**/ L11, L12, 
          LBL, /**/ LBR,  L20, /**/ L21, L22 );

        SlidePartitionUp
        ( XT,  X0,
         /**/ /**/
               X1,
          XB,  X2 );
    }
}
예제 #17
0
파일: LUHB.hpp 프로젝트: certik/Elemental
inline void
ApplyPackedReflectorsLUHB
( Conjugation conjugation, int offset, 
  const Matrix<Complex<R> >& H,
  const Matrix<Complex<R> >& t,
        Matrix<Complex<R> >& A )
{
#ifndef RELEASE
    PushCallStack("internal::ApplyPackedReflectorsLUHB");
    if( offset < 0 || offset > H.Width() )
        throw std::logic_error("Transforms out of bounds");
    if( H.Width() != A.Height() )
        throw std::logic_error
        ("Width of transforms must equal height of target matrix");
    if( t.Height() != H.DiagonalLength( offset ) )
        throw std::logic_error("t must be the same length as H's offset diag");
#endif
    typedef Complex<R> C;

    Matrix<C>
        HTL, HTR,  H00, H01, H02,  HPan, HPanCopy,
        HBL, HBR,  H10, H11, H12,
                   H20, H21, H22;
    Matrix<C> ABottom;
    Matrix<C>
        tT,  t0,
        tB,  t1,
             t2;

    Matrix<C> SInv, Z;

    LockedPartitionUpDiagonal
    ( H, HTL, HTR,
         HBL, HBR, 0 );
    LockedPartitionUp
    ( t, tT,
         tB, 0 );
    while( HBR.Height() < H.Height() && HBR.Width() < H.Width() )
    {
        LockedRepartitionUpDiagonal
        ( HTL, /**/ HTR,  H00, H01, /**/ H02,
               /**/       H10, H11, /**/ H12,
         /*************/ /******************/
          HBL, /**/ HBR,  H20, H21, /**/ H22 );
    
        const int HPanWidth = H11.Width() + H12.Width();
        const int HPanHeight = 
            std::min( H11.Height(), std::max(HPanWidth-offset,0) );
        const int leftover = A.Height()-HPanWidth;
        HPan.LockedView( H, H00.Height(), H00.Width(), HPanHeight, HPanWidth );

        LockedRepartitionUp
        ( tT,  t0,
               t1,
         /**/ /**/
          tB,  t2, HPanHeight );

        ABottom.View( A, leftover, 0, HPanWidth, A.Width() );

        Zeros( HPanHeight, ABottom.Width(), Z );
        Zeros( HPanHeight, HPanHeight, SInv );
        //--------------------------------------------------------------------//
        HPanCopy = HPan;
        MakeTrapezoidal( LEFT, UPPER, offset, HPanCopy );
        SetDiagonalToOne( LEFT, offset, HPanCopy );

        Herk( UPPER, NORMAL, C(1), HPanCopy, C(0), SInv );
        FixDiagonal( conjugation, t1, SInv );

        Gemm( NORMAL, NORMAL, C(1), HPanCopy, ABottom, C(0), Z );
        Trsm( LEFT, UPPER, NORMAL, NON_UNIT, C(1), SInv, Z );
        Gemm( ADJOINT, NORMAL, C(-1), HPanCopy, Z, C(1), ABottom );
        //--------------------------------------------------------------------//

        SlideLockedPartitionUpDiagonal
        ( HTL, /**/ HTR,  H00, /**/ H01, H02,
         /*************/ /******************/
               /**/       H10, /**/ H11, H12,
          HBL, /**/ HBR,  H20, /**/ H21, H22 );

        SlideLockedPartitionUp
        ( tT,  t0,
         /**/ /**/
               t1,
          tB,  t2 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
예제 #18
0
파일: LLT.hpp 프로젝트: mcg1969/Elemental
inline void
TrsmLLTSmall
( Orientation orientation, UnitOrNonUnit diag,
  F alpha, const DistMatrix<F,STAR,VR>& L, DistMatrix<F,VR,STAR>& X,
  bool checkIfSingular )
{
#ifndef RELEASE
    PushCallStack("internal::TrsmLLTSmall");
    if( L.Grid() != X.Grid() )
        throw std::logic_error
        ("L and X must be distributed over the same grid");
    if( orientation == NORMAL )
        throw std::logic_error("TrsmLLT expects a (Conjugate)Transpose option");
    if( L.Height() != L.Width() || L.Height() != X.Height() )
    {
        std::ostringstream msg;
        msg << "Nonconformal TrsmLLT: \n"
            << "  L ~ " << L.Height() << " x " << L.Width() << "\n"
            << "  X ~ " << X.Height() << " x " << X.Width() << "\n";
        throw std::logic_error( msg.str().c_str() );
    }
    if( L.RowAlignment() != X.ColAlignment() )
        throw std::logic_error("L and X must be aligned");
#endif
    const Grid& g = L.Grid();

    // Matrix views
    DistMatrix<F,STAR,VR> 
        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);

    DistMatrix<F,VR,STAR> XT(g),  X0(g),
                          XB(g),  X1(g),
                                  X2(g);

    // Temporary distributions
    DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
    DistMatrix<F,STAR,STAR> X1_STAR_STAR(g);

    // Start the algorithm
    Scale( alpha, X );
    LockedPartitionUpDiagonal
    ( L, LTL, LTR,
         LBL, LBR, 0 );
    PartitionUp
    ( X, XT,
         XB, 0 );
    while( XT.Height() > 0 )
    {
        LockedRepartitionUpDiagonal
        ( LTL, /**/ LTR,  L00, L01, /**/ L02,
               /**/       L10, L11, /**/ L12,
         /*************/ /******************/
          LBL, /**/ LBR,  L20, L21, /**/ L22 );

        RepartitionUp
        ( XT,  X0,
               X1,
         /**/ /**/
          XB,  X2 ); 

        //--------------------------------------------------------------------//
        L11_STAR_STAR = L11; // L11[* ,* ] <- L11[* ,VR]
        X1_STAR_STAR = X1;   // X1[* ,* ] <- X1[VR,* ]

        // X1[* ,* ] := L11^-[T/H][* ,* ] X1[* ,* ]
        LocalTrsm
        ( LEFT, LOWER, orientation, diag,
          F(1), L11_STAR_STAR, X1_STAR_STAR, checkIfSingular );

        X1 = X1_STAR_STAR;

        // X0[VR,* ] -= L10[* ,VR]^(T/H) X1[* ,* ]
        LocalGemm( orientation, NORMAL, F(-1), L10, X1_STAR_STAR, F(1), X0 );
        //--------------------------------------------------------------------//

        SlideLockedPartitionUpDiagonal
        ( LTL, /**/ LTR,  L00, /**/ L01, L02,
         /*************/ /******************/
               /**/       L10, /**/ L11, L12,
          LBL, /**/ LBR,  L20, /**/ L21, L22 );

        SlidePartitionUp
        ( XT,  X0,
         /**/ /**/
               X1,
          XB,  X2 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
예제 #19
0
파일: LUHB.hpp 프로젝트: certik/Elemental
inline void
ApplyPackedReflectorsLUHB
( Conjugation conjugation, int offset, 
  const DistMatrix<Complex<R> >& H,
  const DistMatrix<Complex<R>,MD,STAR>& t,
        DistMatrix<Complex<R> >& A )
{
#ifndef RELEASE
    PushCallStack("internal::ApplyPackedReflectorsLUHB");
    if( H.Grid() != t.Grid() || t.Grid() != A.Grid() )
        throw std::logic_error
        ("{H,t,A} must be distributed over the same grid");
    if( offset < 0 || offset > H.Width() )
        throw std::logic_error("Transforms out of bounds");
    if( H.Width() != A.Height() )
        throw std::logic_error
        ("Width of transforms must equal height of target matrix");
    if( t.Height() != H.DiagonalLength( offset ) )
        throw std::logic_error("t must be the same length as H's offset diag");
    if( !t.AlignedWithDiagonal( H, offset ) )
        throw std::logic_error("t must be aligned with H's offset diagonal");
#endif
    typedef Complex<R> C;
    const Grid& g = H.Grid();

    DistMatrix<C>
        HTL(g), HTR(g),  H00(g), H01(g), H02(g),  HPan(g), HPanCopy(g),
        HBL(g), HBR(g),  H10(g), H11(g), H12(g),
                         H20(g), H21(g), H22(g);
    DistMatrix<C> ABottom(g);
    DistMatrix<C,MD,STAR>
        tT(g),  t0(g),
        tB(g),  t1(g),
                t2(g);

    DistMatrix<C,STAR,VR  > HPan_STAR_VR(g);
    DistMatrix<C,STAR,MC  > HPan_STAR_MC(g);
    DistMatrix<C,STAR,STAR> t1_STAR_STAR(g);
    DistMatrix<C,STAR,STAR> SInv_STAR_STAR(g);
    DistMatrix<C,STAR,MR  > Z_STAR_MR(g);
    DistMatrix<C,STAR,VR  > Z_STAR_VR(g);

    LockedPartitionUpDiagonal
    ( H, HTL, HTR,
         HBL, HBR, 0 );
    LockedPartitionUp
    ( t, tT,
         tB, 0 );
    while( HBR.Height() < H.Height() && HBR.Width() < H.Width() )
    {
        LockedRepartitionUpDiagonal
        ( HTL, /**/ HTR,  H00, H01, /**/ H02,
               /**/       H10, H11, /**/ H12,
         /*************/ /******************/
          HBL, /**/ HBR,  H20, H21, /**/ H22 );
    
        const int HPanWidth = H11.Width() + H12.Width();
        const int HPanHeight = 
            std::min( H11.Height(), std::max(HPanWidth-offset,0) );
        const int leftover = A.Height()-HPanWidth;
        HPan.LockedView( H, H00.Height(), H00.Width(), HPanHeight, HPanWidth );

        LockedRepartitionUp
        ( tT,  t0,
               t1,
         /**/ /**/
          tB,  t2, HPanHeight );

        ABottom.View( A, leftover, 0, HPanWidth, A.Width() );

        HPan_STAR_MC.AlignWith( ABottom );
        Z_STAR_MR.AlignWith( ABottom );
        Z_STAR_VR.AlignWith( ABottom );
        Zeros( HPanHeight, ABottom.Width(), Z_STAR_MR );
        Zeros( HPanHeight, HPanHeight, SInv_STAR_STAR );
        //--------------------------------------------------------------------//
        HPanCopy = HPan;
        MakeTrapezoidal( LEFT, UPPER, offset, HPanCopy );
        SetDiagonalToOne( LEFT, offset, HPanCopy );

        HPan_STAR_VR = HPanCopy;
        Herk
        ( UPPER, NORMAL,
          C(1), HPan_STAR_VR.LockedLocalMatrix(),
          C(0), SInv_STAR_STAR.LocalMatrix() );
        SInv_STAR_STAR.SumOverGrid();
        t1_STAR_STAR = t1;
        FixDiagonal( conjugation, t1_STAR_STAR, SInv_STAR_STAR );

        HPan_STAR_MC = HPan_STAR_VR;
        LocalGemm
        ( NORMAL, NORMAL, C(1), HPan_STAR_MC, ABottom, C(0), Z_STAR_MR );
        Z_STAR_VR.SumScatterFrom( Z_STAR_MR );

        LocalTrsm
        ( LEFT, UPPER, NORMAL, NON_UNIT, C(1), SInv_STAR_STAR, Z_STAR_VR );

        Z_STAR_MR = Z_STAR_VR;
        LocalGemm
        ( ADJOINT, NORMAL, C(-1), HPan_STAR_MC, Z_STAR_MR, C(1), ABottom );
        //--------------------------------------------------------------------//
        HPan_STAR_MC.FreeAlignments();
        Z_STAR_MR.FreeAlignments();
        Z_STAR_VR.FreeAlignments();

        SlideLockedPartitionUpDiagonal
        ( HTL, /**/ HTR,  H00, /**/ H01, H02,
         /*************/ /******************/
               /**/       H10, /**/ H11, H12,
          HBL, /**/ HBR,  H20, /**/ H21, H22 );

        SlideLockedPartitionUp
        ( tT,  t0,
         /**/ /**/
               t1,
          tB,  t2 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}