Пример #1
0
inline void
PanelHouseholder( DistMatrix<F>& A, DistMatrix<F,MD,STAR>& t )
{
#ifndef RELEASE
    CallStackEntry entry("lq::PanelHouseholder");
    if( A.Grid() != t.Grid() )
        LogicError("{A,t} must be distributed over the same grid");
    if( t.Height() != Min(A.Height(),A.Width()) || t.Width() != 1 )
        LogicError
        ("t must be a vector of height equal to the minimum dimension of A");
    if( !t.AlignedWithDiagonal( A, 0 ) )
        LogicError("t must be aligned with A's main diagonal");
#endif
    const Grid& g = A.Grid();

    // Matrix views
    DistMatrix<F>
        ATL(g), ATR(g),  A00(g), a01(g),     A02(g),  aTopRow(g), ABottomPan(g),
        ABL(g), ABR(g),  a10(g), alpha11(g), a12(g),
                         A20(g), a21(g),     A22(g);
    DistMatrix<F,MD,STAR>
        tT(g),  t0(g),
        tB(g),  tau1(g),
                t2(g);

    // Temporary distributions
    DistMatrix<F> aTopRowConj(g);
    DistMatrix<F,STAR,MR  > aTopRowConj_STAR_MR(g);
    DistMatrix<F,MC,  STAR> z_MC_STAR(g);

    PartitionDownDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 );
    PartitionDown
    ( t, tT,
         tB, 0 );
    while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
    {
        RepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ a01,     A02,
         /*************/ /**********************/
               /**/       a10, /**/ alpha11, a12,
          ABL, /**/ ABR,  A20, /**/ a21,     A22, 1 );

        RepartitionDown
        ( tT,  t0,
         /**/ /****/
               tau1,
          tB,  t2, 1 );

        View1x2( aTopRow, alpha11, a12 );
        View1x2( ABottomPan, a21, A22 );

        aTopRowConj_STAR_MR.AlignWith( ABottomPan );
        z_MC_STAR.AlignWith( ABottomPan );
        //--------------------------------------------------------------------//
        // Compute the Householder reflector
        const F tau = Reflector( alpha11, a12 );
        tau1.Set( 0, 0, tau );

        // Apply the Householder reflector
        const bool myDiagonalEntry = ( g.Row() == alpha11.ColAlignment() &&
                                       g.Col() == alpha11.RowAlignment() );
        F alpha = 0;
        if( myDiagonalEntry )
        {
            alpha = alpha11.GetLocal(0,0);
            alpha11.SetLocal(0,0,1);
        }
        Conjugate( aTopRow, aTopRowConj );
        aTopRowConj_STAR_MR = aTopRowConj;
        Zeros( z_MC_STAR, ABottomPan.Height(), 1 );
        LocalGemv
        ( NORMAL, F(1), ABottomPan, aTopRowConj_STAR_MR, F(0), z_MC_STAR );
        z_MC_STAR.SumOverRow();
        Ger
        ( -Conj(tau),
          z_MC_STAR.LockedMatrix(),
          aTopRowConj_STAR_MR.LockedMatrix(),
          ABottomPan.Matrix() );
        if( myDiagonalEntry )
            alpha11.SetLocal(0,0,alpha);
        //--------------------------------------------------------------------//

        SlidePartitionDown
        ( tT,  t0,
               tau1,
         /**/ /****/
          tB,  t2 );

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, a01,     /**/ A02,
               /**/       a10, alpha11, /**/ a12,
         /*************/ /**********************/
          ABL, /**/ ABR,  A20, a21,     /**/ A22 );
    }
}
inline void
internal::ApplyPackedReflectorsLLVF
( Conjugation conjugation, int offset, 
  const DistMatrix<Complex<R>,MC,MR  >& H,
  const DistMatrix<Complex<R>,MD,STAR>& t,
        DistMatrix<Complex<R>,MC,MR  >& A )
{
#ifndef RELEASE
    PushCallStack("internal::ApplyPackedReflectorsLLVF");
    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 )
        throw std::logic_error("Transforms cannot extend above matrix");
    if( offset < -H.Height() )
        throw std::logic_error("Transforms cannot extend below matrix");
    if( H.Height() != A.Height() )
        throw std::logic_error
        ("Height 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();

    // Matrix views    
    DistMatrix<C,MC,MR>
        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,MC,MR>
        AT(g),  A0(g),
        AB(g),  A1(g),
                A2(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,MC,  STAR> HPan_MC_STAR(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);

    LockedPartitionDownDiagonal
    ( H, HTL, HTR,
         HBL, HBR, 0 );
    LockedPartitionDown
    ( t, tT,
         tB, 0 );
    PartitionDown
    ( A, AT,
         AB, 0 );
    while( HTL.Height() < H.Height() && HTL.Width() < H.Width() )
    {
        LockedRepartitionDownDiagonal
        ( HTL, /**/ HTR,  H00, /**/ H01, H02,
         /*************/ /******************/
               /**/       H10, /**/ H11, H12,
          HBL, /**/ HBR,  H20, /**/ H21, H22 );

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

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

        RepartitionDown
        ( AT,  A0,
         /**/ /**/
               A1,
          AB,  A2 );

        HPan_MC_STAR.AlignWith( AB );
        Z_STAR_MR.AlignWith( AB );
        Z_STAR_VR.AlignWith( AB );
        Z_STAR_MR.ResizeTo( HPan.Width(), AB.Width() );
        SInv_STAR_STAR.ResizeTo( HPan.Width(), HPan.Width() );
        Zero( SInv_STAR_STAR );
        //--------------------------------------------------------------------//
        HPanCopy = HPan;
        MakeTrapezoidal( LEFT, LOWER, offset, HPanCopy );
        SetDiagonalToOne( LEFT, offset, HPanCopy );

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

        HPan_MC_STAR = HPanCopy;
        internal::LocalGemm
        ( ADJOINT, NORMAL, (C)1, HPan_MC_STAR, AB, (C)0, Z_STAR_MR );
        Z_STAR_VR.SumScatterFrom( Z_STAR_MR );
        
        internal::LocalTrsm
        ( LEFT, UPPER, ADJOINT, NON_UNIT, (C)1, SInv_STAR_STAR, Z_STAR_VR );

        Z_STAR_MR = Z_STAR_VR;
        internal::LocalGemm
        ( NORMAL, NORMAL, (C)-1, HPan_MC_STAR, Z_STAR_MR, (C)1, AB );
        //--------------------------------------------------------------------//
        HPan_MC_STAR.FreeAlignments();
        Z_STAR_MR.FreeAlignments();
        Z_STAR_VR.FreeAlignments();

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

        SlideLockedPartitionDown
        ( tT,  t0,
               t1,
         /**/ /**/
          tB,  t2 ); 

        SlidePartitionDown
        ( AT,  A0,
               A1,
         /**/ /**/
          AB,  A2 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
Пример #3
0
inline void
RUVF
( Conjugation conjugation, Int offset, 
  const DistMatrix<F>& H, const DistMatrix<F,MD,STAR>& t, DistMatrix<F>& A )
{
#ifndef RELEASE
    CallStackEntry cse("apply_packed_reflectors::RUVF");
    if( H.Grid() != t.Grid() || t.Grid() != A.Grid() )
        LogicError("{H,t,A} must be distributed over the same grid");
    // TODO: Proper dimension checks
    if( t.Height() != H.DiagonalLength(offset) )
        LogicError("t must be the same length as H's offset diag");
    if( !t.AlignedWithDiagonal( H, offset ) )
        LogicError("t must be aligned with H's 'offset' diagonal");
#endif
    const Grid& g = H.Grid();
    DistMatrix<F>
        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<F> ALeft(g);
    DistMatrix<F,MD,STAR>
        tT(g),  t0(g),
        tB(g),  t1(g),
                t2(g);

    DistMatrix<F,VC,  STAR> HPan_VC_STAR(g);
    DistMatrix<F,MR,  STAR> HPan_MR_STAR(g);
    DistMatrix<F,STAR,STAR> t1_STAR_STAR(g);
    DistMatrix<F,STAR,STAR> SInv_STAR_STAR(g);
    DistMatrix<F,STAR,MC  > ZAdj_STAR_MC(g);
    DistMatrix<F,STAR,VC  > ZAdj_STAR_VC(g);

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

        LockedRepartitionDown
        ( tT,  t0,
         /**/ /**/
               t1,
          tB,  t2 );

        LockedView2x1( HPan, H01, H11 );
        View( ALeft, A, 0, 0, A.Height(), HPan.Height() );

        HPan_MR_STAR.AlignWith( ALeft );
        ZAdj_STAR_MC.AlignWith( ALeft );
        ZAdj_STAR_VC.AlignWith( ALeft );
        //--------------------------------------------------------------------//
        HPanCopy = HPan;
        MakeTrapezoidal( UPPER, HPanCopy, 0, RIGHT );
        SetDiagonal( HPanCopy, F(1), 0, RIGHT );
 
        HPan_VC_STAR = HPanCopy;
        Zeros( SInv_STAR_STAR, HPan.Width(), HPan.Width() );
        Herk
        ( UPPER, ADJOINT, 
          F(1), HPan_VC_STAR.LockedMatrix(),
          F(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, F(1), HPan_MR_STAR, ALeft, ZAdj_STAR_MC );
        ZAdj_STAR_VC.SumScatterFrom( ZAdj_STAR_MC );
        
        LocalTrsm
        ( LEFT, UPPER, ADJOINT, NON_UNIT, 
          F(1), SInv_STAR_STAR, ZAdj_STAR_VC );

        ZAdj_STAR_MC = ZAdj_STAR_VC;
        LocalGemm
        ( ADJOINT, ADJOINT, F(-1), ZAdj_STAR_MC, HPan_MR_STAR, F(1), ALeft );
        //--------------------------------------------------------------------//

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

        SlideLockedPartitionDown
        ( tT,  t0,
               t1,
         /**/ /**/
          tB,  t2 );
    }
}
Пример #4
0
inline void
Householder( DistMatrix<F>& A, DistMatrix<F,MD,STAR>& t )
{
#ifndef RELEASE
    CallStackEntry entry("qr::Householder");
    if( A.Grid() != t.Grid() )
        LogicError("{A,s} must be distributed over the same grid");
#endif
    const Grid& g = A.Grid();
    if( t.Viewing() )
    {
        if( !t.AlignedWithDiagonal( A ) ) 
            LogicError("t was not aligned with A");
    }
    else
    {
        t.AlignWithDiagonal( A );
    }
    t.ResizeTo( Min(A.Height(),A.Width()), 1 );

    // Matrix views
    DistMatrix<F>
        ATL(g), ATR(g),  A00(g), A01(g), A02(g),  ALeftPan(g), ARightPan(g),
        ABL(g), ABR(g),  A10(g), A11(g), A12(g),
                         A20(g), A21(g), A22(g);
    DistMatrix<F,MD,STAR>
        tT(g),  t0(g),
        tB(g),  t1(g),
                t2(g);

    PartitionDownDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 );
    PartitionDown
    ( t, tT,
         tB, 0 );
    while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
    {
        RepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ A01, A02,
         /*************/ /******************/
               /**/       A10, /**/ A11, A12,
          ABL, /**/ ABR,  A20, /**/ A21, A22 );

        RepartitionDown
        ( tT,  t0,
         /**/ /**/
               t1,
          tB,  t2 );

        View2x1
        ( ALeftPan, A11,
                    A21 );

        View2x1
        ( ARightPan, A12,
                     A22 );

        //--------------------------------------------------------------------//
        PanelHouseholder( ALeftPan, t1 );
        ApplyQ( LEFT, ADJOINT, ALeftPan, t1, ARightPan );
        //--------------------------------------------------------------------//

        SlidePartitionDown
        ( tT,  t0,
               t1,
         /**/ /**/
          tB,  t2 );

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, A01, /**/ A02,
               /**/       A10, A11, /**/ A12,
         /*************/ /******************/
          ABL, /**/ ABR,  A20, A21, /**/ A22 );
    }
}
Пример #5
0
inline void
LQ( DistMatrix<Complex<R>,MC,MR  >& A, 
    DistMatrix<Complex<R>,MD,STAR>& t )
{
#ifndef RELEASE
    PushCallStack("LQ");
    if( A.Grid() != t.Grid() )
        throw std::logic_error("{A,t} must be distributed over the same grid");
#endif
    typedef Complex<R> C;
    const Grid& g = A.Grid();
    if( t.Viewing() )
    {
        if( !t.AlignedWithDiagonal( A ) )
            throw std::logic_error("t was not aligned with A");
        if( t.Height() != std::min(A.Height(),A.Width()) || t.Width() != 1 )
            throw std::logic_error("t was not the appropriate shape");
    }
    else
    {
        t.AlignWithDiagonal( A );
        t.ResizeTo( std::min(A.Height(),A.Width()), 1 );
    }

    // Matrix views
    DistMatrix<C,MC,MR>
        ATL(g), ATR(g),  A00(g), A01(g), A02(g),  ATopPan(g), ABottomPan(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);

    PartitionDownLeftDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 );
    PartitionDown
    ( t, tT,
         tB, 0 );
    while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
    {
        RepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ A01, A02,
         /*************/ /******************/
               /**/       A10, /**/ A11, A12,
          ABL, /**/ ABR,  A20, /**/ A21, A22 );

        RepartitionDown
        ( tT,  t0,
         /**/ /**/
               t1,
          tB,  t2 );

        ATopPan.View1x2( A11, A12 );
        ABottomPan.View1x2( A21, A22 );

        //--------------------------------------------------------------------//
        internal::PanelLQ( ATopPan, t1 );
        ApplyPackedReflectors
        ( RIGHT, UPPER, HORIZONTAL, FORWARD, CONJUGATED,
          0, ATopPan, t1, ABottomPan );
        //--------------------------------------------------------------------//

        SlidePartitionDown
        ( tT,  t0,
               t1,
         /**/ /**/
          tB,  t2 );

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, A01, /**/ A02,
               /**/       A10, A11, /**/ A12,
         /*************/ /******************/
          ABL, /**/ ABR,  A20, A21, /**/ A22 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
Пример #6
0
inline void
RLHF
( 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::RLHF");
    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.Width() )
        throw std::logic_error
        ("Width 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> ALeft(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,MR  > HPan_STAR_MR(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);

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

        const int HPanWidth = H10.Width() + H11.Width();
        const int HPanOffset = 
            std::min( H11.Height(), std::max(-offset-H00.Height(),0) );
        const int HPanHeight = H11.Height()-HPanOffset;
        LockedView
        ( HPan, H, H00.Height()+HPanOffset, 0, HPanHeight, HPanWidth );

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

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

        HPan_STAR_MR.AlignWith( ALeft );
        ZAdj_STAR_MC.AlignWith( ALeft );
        ZAdj_STAR_VC.AlignWith( ALeft );
        Zeros( HPan.Height(), ALeft.Height(), ZAdj_STAR_MC );
        Zeros( HPan.Height(), HPan.Height(), SInv_STAR_STAR );
        //--------------------------------------------------------------------//
        HPanCopy = HPan;
        MakeTrapezoidal( RIGHT, LOWER, offset, HPanCopy );
        SetDiagonal( RIGHT, offset, HPanCopy, C(1) );

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

        HPan_STAR_MR = HPan_STAR_VR;
        LocalGemm
        ( NORMAL, ADJOINT,
          C(1), HPan_STAR_MR, ALeft, C(0), ZAdj_STAR_MC );
        ZAdj_STAR_VC.SumScatterFrom( ZAdj_STAR_MC );

        LocalTrsm
        ( LEFT, UPPER, ADJOINT, NON_UNIT,
          C(1), SInv_STAR_STAR, ZAdj_STAR_VC );

        ZAdj_STAR_MC = ZAdj_STAR_VC;
        LocalGemm
        ( ADJOINT, NORMAL,
          C(-1), ZAdj_STAR_MC, HPan_STAR_MR, C(1), ALeft );
        //--------------------------------------------------------------------//
        HPan_STAR_MR.FreeAlignments();
        ZAdj_STAR_MC.FreeAlignments();
        ZAdj_STAR_VC.FreeAlignments();

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

        SlideLockedPartitionDown
        ( tT,  t0,
               t1,
         /**/ /**/
          tB,  t2 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
Пример #7
0
inline void
LUHF
( Conjugation conjugation, Int offset, 
  const DistMatrix<F>& H, const DistMatrix<F,MD,STAR>& t, DistMatrix<F>& A )
{
#ifndef RELEASE
    CallStackEntry cse("apply_packed_reflectors::LUHF");
    if( H.Grid() != t.Grid() || t.Grid() != A.Grid() )
        LogicError("{H,t,A} must be distributed over the same grid");
    // TODO: Proper dimension checks
    if( t.Height() != H.DiagonalLength(offset) )
        LogicError("t must be the same length as H's offset diag");
    if( !t.AlignedWithDiagonal( H, offset ) )
        LogicError("t must be aligned with H's offset diagonal");
#endif
    const Grid& g = H.Grid(); 
    DistMatrix<F>
        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<F> 
        AT(g),  A0(g),
        AB(g),  A1(g),
                A2(g);
    DistMatrix<F,MD,STAR>
        tT(g),  t0(g),
        tB(g),  t1(g),
                t2(g);

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

    LockedPartitionDownOffsetDiagonal
    ( offset,
      H, HTL, HTR,
         HBL, HBR, 0 );
    LockedPartitionDown
    ( t, tT,
         tB, 0 );
    PartitionDown
    ( A, AT,
         AB, 0 );
    while( HTL.Height() < H.Height() && HTL.Width() < H.Width() )
    {
        LockedRepartitionDownDiagonal
        ( HTL, /**/ HTR,  H00, /**/ H01, H02,
         /*************/ /******************/
               /**/       H10, /**/ H11, H12,
          HBL, /**/ HBR,  H20, /**/ H21, H22 );

        LockedRepartitionDown
        ( tT,  t0,
         /**/ /**/
               t1,
          tB,  t2 );

        RepartitionDown
        ( AT,  A0,
         /**/ /**/
               A1,
          AB,  A2, H11.Height() );

        LockedView1x2( HPan, H11, H12 );

        HPan_STAR_MC.AlignWith( AB );
        Z_STAR_MR.AlignWith( AB );
        Z_STAR_VR.AlignWith( AB );
        //--------------------------------------------------------------------//
        HPanCopy = HPan;
        MakeTriangular( UPPER, HPanCopy );
        SetDiagonal( HPanCopy, F(1) );

        HPan_STAR_VR = HPanCopy;
        Zeros( SInv_STAR_STAR, HPan.Height(), HPan.Height() );
        Herk
        ( LOWER, NORMAL,
          F(1), HPan_STAR_VR.LockedMatrix(),
          F(0), SInv_STAR_STAR.Matrix() );
        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, F(1), HPan_STAR_MC, AB, Z_STAR_MR );
        Z_STAR_VR.SumScatterFrom( Z_STAR_MR );

        LocalTrsm
        ( LEFT, LOWER, NORMAL, NON_UNIT, F(1), SInv_STAR_STAR, Z_STAR_VR );

        Z_STAR_MR = Z_STAR_VR;
        LocalGemm( ADJOINT, NORMAL, F(-1), HPan_STAR_MC, Z_STAR_MR, F(1), AB );
        //--------------------------------------------------------------------//

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

        SlideLockedPartitionDown
        ( tT,  t0,
               t1,
         /**/ /**/
          tB,  t2 );

        SlidePartitionDown
        ( AT,  A0,
               A1,
         /**/ /**/
          AB,  A2 );
    }
}
Пример #8
0
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
}
Пример #9
0
inline void
PanelLQ
( DistMatrix<Complex<Real> >& A,
  DistMatrix<Complex<Real>,MD,STAR>& t )
{
#ifndef RELEASE
    PushCallStack("internal::PanelLQ");
    if( A.Grid() != t.Grid() )
        throw std::logic_error("{A,t} must be distributed over the same grid");
    if( t.Height() != std::min(A.Height(),A.Width()) || t.Width() != 1 )
        throw std::logic_error
        ("t must be a vector of height equal to the minimum dimension of A");
    if( !t.AlignedWithDiagonal( A, 0 ) )
        throw std::logic_error("t must be aligned with A's main diagonal");
#endif
    typedef Complex<Real> C;
    const Grid& g = A.Grid();

    // Matrix views
    DistMatrix<C>
        ATL(g), ATR(g),  A00(g), a01(g),     A02(g),  aTopRow(g), ABottomPan(g),
        ABL(g), ABR(g),  a10(g), alpha11(g), a12(g),
                         A20(g), a21(g),     A22(g);
    DistMatrix<C,MD,STAR>
        tT(g),  t0(g),
        tB(g),  tau1(g),
                t2(g);

    // Temporary distributions
    DistMatrix<C> aTopRowConj(g);
    DistMatrix<C,STAR,MR  > aTopRowConj_STAR_MR(g);
    DistMatrix<C,MC,  STAR> z_MC_STAR(g);

    PushBlocksizeStack( 1 );
    PartitionDownLeftDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 );
    PartitionDown
    ( t, tT,
         tB, 0 );
    while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
    {
        RepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ a01,     A02,
         /*************/ /**********************/
               /**/       a10, /**/ alpha11, a12,
          ABL, /**/ ABR,  A20, /**/ a21,     A22 );

        RepartitionDown
        ( tT,  t0,
         /**/ /****/
               tau1,
          tB,  t2 );

        aTopRow.View1x2( alpha11, a12 );
        ABottomPan.View1x2( a21, A22 );

        aTopRowConj_STAR_MR.AlignWith( ABottomPan );
        z_MC_STAR.AlignWith( ABottomPan );
        Zeros( ABottomPan.Height(), 1, z_MC_STAR );
        //--------------------------------------------------------------------//
        const C tau = Reflector( alpha11, a12 );
        tau1.Set( 0, 0, tau );

        const bool myDiagonalEntry = ( g.Row() == alpha11.ColAlignment() &&
                                       g.Col() == alpha11.RowAlignment() );
        C alpha = 0;
        if( myDiagonalEntry )
        {
            alpha = alpha11.GetLocal(0,0);
            alpha11.SetLocal(0,0,1);
        }

        Conjugate( aTopRow, aTopRowConj );
        aTopRowConj_STAR_MR = aTopRowConj;

        Gemv
        ( NORMAL,
          C(1), ABottomPan.LockedLocalMatrix(),
                aTopRowConj_STAR_MR.LockedLocalMatrix(),
          C(0), z_MC_STAR.LocalMatrix() );
        z_MC_STAR.SumOverRow();

        Ger
        ( -Conj(tau),
          z_MC_STAR.LockedLocalMatrix(),
          aTopRowConj_STAR_MR.LockedLocalMatrix(),
          ABottomPan.LocalMatrix() );

        if( myDiagonalEntry )
            alpha11.SetLocal(0,0,alpha);
        //--------------------------------------------------------------------//
        aTopRowConj_STAR_MR.FreeAlignments();
        z_MC_STAR.FreeAlignments();

        SlidePartitionDown
        ( tT,  t0,
               tau1,
         /**/ /****/
          tB,  t2 );

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, a01,     /**/ A02,
               /**/       a10, alpha11, /**/ a12,
         /*************/ /**********************/
          ABL, /**/ ABR,  A20, a21,     /**/ A22 );
    }
    PopBlocksizeStack();
#ifndef RELEASE
    PopCallStack();
#endif
}