Exemple #1
0
inline void
TwoSidedTrmmUVar5
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& U )
{
#ifndef RELEASE
    PushCallStack("internal::TwoSidedTrmmUVar5");
    if( A.Height() != A.Width() )
        throw std::logic_error("A must be square");
    if( U.Height() != U.Width() )
        throw std::logic_error("Triangular matrices must be square");
    if( A.Height() != U.Height() )
        throw std::logic_error("A and U must be the same size");
#endif
    const Grid& g = A.Grid();

    // Matrix views
    DistMatrix<F>
        ATL(g), ATR(g),  A00(g), A01(g), A02(g),
        ABL(g), ABR(g),  A10(g), A11(g), A12(g),
                         A20(g), A21(g), A22(g);
    DistMatrix<F>
        UTL(g), UTR(g),  U00(g), U01(g), U02(g),
        UBL(g), UBR(g),  U10(g), U11(g), U12(g),
                         U20(g), U21(g), U22(g);

    // Temporary distributions
    DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
    DistMatrix<F,MC,  STAR> A01_MC_STAR(g);
    DistMatrix<F,MR,  STAR> A01_MR_STAR(g);
    DistMatrix<F,VC,  STAR> A01_VC_STAR(g);
    DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
    DistMatrix<F,MC,  STAR> U01_MC_STAR(g);
    DistMatrix<F,MR,  STAR> U01_MR_STAR(g);
    DistMatrix<F,VC,  STAR> U01_VC_STAR(g);
    DistMatrix<F,VC,  STAR> Y01_VC_STAR(g);
    DistMatrix<F> Y01(g);

    PartitionDownDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 );
    LockedPartitionDownDiagonal
    ( U, UTL, UTR,
         UBL, UBR, 0 );
    while( ATL.Height() < A.Height() )
    {
        RepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ A01, A02,
         /*************/ /******************/
               /**/       A10, /**/ A11, A12,
          ABL, /**/ ABR,  A20, /**/ A21, A22 );

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

        A01_MC_STAR.AlignWith( A00 );
        A01_MR_STAR.AlignWith( A00 );
        A01_VC_STAR.AlignWith( A00 );
        U01_MC_STAR.AlignWith( A00 );
        U01_MR_STAR.AlignWith( A00 );
        U01_VC_STAR.AlignWith( A00 );
        Y01.AlignWith( A01 );
        Y01_VC_STAR.AlignWith( A01 );
        //--------------------------------------------------------------------//
        // Y01 := U01 A11
        A11_STAR_STAR = A11;
        U01_VC_STAR = U01;
        Y01_VC_STAR.ResizeTo( A01.Height(), A01.Width() );
        Hemm
        ( RIGHT, UPPER,
          F(1), A11_STAR_STAR.LocalMatrix(), U01_VC_STAR.LocalMatrix(),
          F(0), Y01_VC_STAR.LocalMatrix() );
        Y01 = Y01_VC_STAR;

        // A01 := U00 A01
        Trmm( LEFT, UPPER, NORMAL, diag, F(1), U00, A01 );

        // A01 := A01 + 1/2 Y01
        Axpy( F(1)/F(2), Y01, A01 );

        // A00 := A00 + (U01 A01' + A01 U01')
        A01_MC_STAR = A01;
        U01_MC_STAR = U01;
        A01_VC_STAR = A01_MC_STAR;
        A01_MR_STAR = A01_VC_STAR;
        U01_MR_STAR = U01_MC_STAR;
        LocalTrr2k
        ( UPPER, ADJOINT, ADJOINT,
          F(1), U01_MC_STAR, A01_MR_STAR, 
                A01_MC_STAR, U01_MR_STAR,
          F(1), A00 );

        // A01 := A01 + 1/2 Y01
        Axpy( F(1)/F(2), Y01_VC_STAR, A01_VC_STAR );

        // A01 := A01 U11'
        U11_STAR_STAR = U11;
        LocalTrmm
        ( RIGHT, UPPER, ADJOINT, diag, F(1), U11_STAR_STAR, A01_VC_STAR );
        A01 = A01_VC_STAR;

        // A11 := U11 A11 U11'
        LocalTwoSidedTrmm( UPPER, diag, A11_STAR_STAR, U11_STAR_STAR );
        A11 = A11_STAR_STAR;
        //--------------------------------------------------------------------//
        A01_MC_STAR.FreeAlignments();
        A01_MR_STAR.FreeAlignments();
        A01_VC_STAR.FreeAlignments();
        U01_MC_STAR.FreeAlignments();
        U01_MR_STAR.FreeAlignments();
        U01_VC_STAR.FreeAlignments();
        Y01.FreeAlignments();
        Y01_VC_STAR.FreeAlignments();

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, A01, /**/ A02,
               /**/       A10, A11, /**/ A12,
         /*************/ /******************/
          ABL, /**/ ABR,  A20, A21, /**/ A22 );

        SlideLockedPartitionDownDiagonal
        ( UTL, /**/ UTR,  U00, U01, /**/ U02,
               /**/       U10, U11, /**/ U12,
         /*************/ /******************/
          UBL, /**/ UBR,  U20, U21, /**/ U22 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
inline void
internal::HermitianTridiagU
( DistMatrix<Complex<R>,MC,  MR  >& A,
  DistMatrix<Complex<R>,STAR,STAR>& t )
{
#ifndef RELEASE
    PushCallStack("internal::HermitianTridiagU");
    if( A.Grid() != t.Grid() )
        throw std::logic_error("{A,t} must be distributed over the same grid");
    if( A.Height() != A.Width() )
        throw std::logic_error("A must be square");
    if( t.Viewing() )
        throw std::logic_error("t must not be a view");
#endif
    typedef Complex<R> C;

    const Grid& g = A.Grid();
    DistMatrix<C,MD,STAR> tDiag(g);
    tDiag.AlignWithDiagonal( A, 1 );
    tDiag.ResizeTo( A.Height()-1, 1 );

    if( g.InGrid() )
    {
        // Matrix views
        DistMatrix<C,MC,MR>
        ATL(g), ATR(g),  A00(g), A01(g), A02(g),
            ABL(g), ABR(g),  A10(g), A11(g), A12(g),
            A20(g), A21(g), A22(g);
        DistMatrix<C,MD,STAR> tT(g),  t0(g),
                   tB(g),  t1(g),
                   t2(g);

        // Temporary distributions
        DistMatrix<C,MC,  MR  > WPan(g);
        DistMatrix<C,STAR,STAR> t1_STAR_STAR(g);
        DistMatrix<C,STAR,STAR> A11_STAR_STAR(g);
        DistMatrix<C,MC,  STAR> APan_MC_STAR(g),  A01_MC_STAR(g),
                   A11_MC_STAR(g);
        DistMatrix<C,MR,  STAR> APan_MR_STAR(g),  A01_MR_STAR(g),
                   A11_MR_STAR(g);
        DistMatrix<C,MC,  STAR> WPan_MC_STAR(g),  W01_MC_STAR(g),
                   W11_MC_STAR(g);
        DistMatrix<C,MR,  STAR> WPan_MR_STAR(g),  W01_MR_STAR(g),
                   W11_MR_STAR(g);

        PartitionUpDiagonal
        ( A, ATL, ATR,
          ABL, ABR, 0 );
        PartitionUp
        ( tDiag, tT,
          tB, 0 );
        while( ABR.Height() < A.Height() )
        {
            RepartitionUpDiagonal
            ( ATL, /**/ ATR,  A00, A01, /**/ A02,
              /**/       A10, A11, /**/ A12,
              /*************/ /******************/
              ABL, /**/ ABR,  A20, A21, /**/ A22 );

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

            if( A00.Height() > 0 )
            {
                WPan.AlignWith( A01 );
                APan_MC_STAR.AlignWith( A00 );
                WPan_MC_STAR.AlignWith( A00 );
                APan_MR_STAR.AlignWith( A00 );
                WPan_MR_STAR.AlignWith( A00 );
                //------------------------------------------------------------//
                WPan.ResizeTo( ATL.Height(), A11.Width() );
                APan_MC_STAR.ResizeTo( ATL.Height(), A11.Width() );
                WPan_MC_STAR.ResizeTo( ATL.Height(), A11.Width() );
                APan_MR_STAR.ResizeTo( ATL.Height(), A11.Width() );
                WPan_MR_STAR.ResizeTo( ATL.Height(), A11.Width() );

                internal::HermitianPanelTridiagU
                ( ATL, WPan, t1,
                  APan_MC_STAR, APan_MR_STAR, WPan_MC_STAR, WPan_MR_STAR );

                PartitionUp
                ( APan_MC_STAR, A01_MC_STAR,
                  A11_MC_STAR, A11.Height() );
                PartitionUp
                ( APan_MR_STAR, A01_MR_STAR,
                  A11_MR_STAR, A11.Height() );
                PartitionUp
                ( WPan_MC_STAR, W01_MC_STAR,
                  W11_MC_STAR, A11.Height() );
                PartitionUp
                ( WPan_MR_STAR, W01_MR_STAR,
                  W11_MR_STAR, A11.Height() );

                internal::LocalTrr2k
                ( UPPER, ADJOINT, ADJOINT,
                  (C)-1, A01_MC_STAR, W01_MR_STAR,
                  W01_MC_STAR, A01_MR_STAR,
                  (C)1,  A00 );
                //------------------------------------------------------------//
                WPan_MR_STAR.FreeAlignments();
                APan_MR_STAR.FreeAlignments();
                WPan_MC_STAR.FreeAlignments();
                APan_MC_STAR.FreeAlignments();
                WPan.FreeAlignments();
            }
            else
            {
                A11_STAR_STAR = A11;
                t1_STAR_STAR.ResizeTo( t1.Height(), 1 );

                HermitianTridiag
                ( UPPER, A11_STAR_STAR.LocalMatrix(),
                  t1_STAR_STAR.LocalMatrix() );

                A11 = A11_STAR_STAR;
                t1 = t1_STAR_STAR;
            }

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

            SlidePartitionUpDiagonal
            ( ATL, /**/ ATR,  A00, /**/ A01, A02,
              /*************/ /******************/
              /**/       A10, /**/ A11, A12,
              ABL, /**/ ABR,  A20, /**/ A21, A22 );
        }
    }
    // Redistribute from matrix-diagonal form to fully replicated
    t = tDiag;
#ifndef RELEASE
    PopCallStack();
#endif
}
inline void
internal::HermitianTridiagU( DistMatrix<R,MC,MR>& A )
{
#ifndef RELEASE
    PushCallStack("internal::HermitianTridiagU");
    if( A.Height() != A.Width() )
        throw std::logic_error( "A must be square." );
#endif
    const Grid& g = A.Grid();

    if( g.InGrid() )
    {
        // Matrix views
        DistMatrix<R,MC,MR>
        ATL(g), ATR(g),  A00(g), A01(g), A02(g),
            ABL(g), ABR(g),  A10(g), A11(g), A12(g),
            A20(g), A21(g), A22(g);

        // Temporary distributions
        DistMatrix<R,MC,  MR  > WPan(g);
        DistMatrix<R,STAR,STAR> A11_STAR_STAR(g);
        DistMatrix<R,MC,  STAR> APan_MC_STAR(g),  A01_MC_STAR(g),
                   A11_MC_STAR(g);
        DistMatrix<R,MR,  STAR> APan_MR_STAR(g),  A01_MR_STAR(g),
                   A11_MR_STAR(g);
        DistMatrix<R,MC,  STAR> WPan_MC_STAR(g),  W01_MC_STAR(g),
                   W11_MC_STAR(g);
        DistMatrix<R,MR,  STAR> WPan_MR_STAR(g),  W01_MR_STAR(g),
                   W11_MR_STAR(g);

        PartitionUpDiagonal
        ( A, ATL, ATR,
          ABL, ABR, 0 );
        while( ABR.Height() < A.Height() )
        {
            RepartitionUpDiagonal
            ( ATL, /**/ ATR,  A00, A01, /**/ A02,
              /**/       A10, A11, /**/ A12,
              /*************/ /******************/
              ABL, /**/ ABR,  A20, A21, /**/ A22 );

            if( A00.Height() > 0 )
            {
                WPan.AlignWith( A01 );
                APan_MC_STAR.AlignWith( A00 );
                WPan_MC_STAR.AlignWith( A00 );
                APan_MR_STAR.AlignWith( A00 );
                WPan_MR_STAR.AlignWith( A00 );
                //------------------------------------------------------------//
                WPan.ResizeTo( ATL.Height(), A11.Width() );
                APan_MC_STAR.ResizeTo( ATL.Height(), A11.Width() );
                WPan_MC_STAR.ResizeTo( ATL.Height(), A11.Width() );
                APan_MR_STAR.ResizeTo( ATL.Height(), A11.Width() );
                WPan_MR_STAR.ResizeTo( ATL.Height(), A11.Width() );

                internal::HermitianPanelTridiagU
                ( ATL, WPan,
                  APan_MC_STAR, APan_MR_STAR, WPan_MC_STAR, WPan_MR_STAR );

                PartitionUp
                ( APan_MC_STAR, A01_MC_STAR,
                  A11_MC_STAR, A11.Height() );
                PartitionUp
                ( APan_MR_STAR, A01_MR_STAR,
                  A11_MR_STAR, A11.Height() );
                PartitionUp
                ( WPan_MC_STAR, W01_MC_STAR,
                  W11_MC_STAR, A11.Height() );
                PartitionUp
                ( WPan_MR_STAR, W01_MR_STAR,
                  W11_MR_STAR, A11.Height() );

                internal::LocalTrr2k
                ( UPPER, TRANSPOSE, TRANSPOSE,
                  (R)-1, A01_MC_STAR, W01_MR_STAR,
                  W01_MC_STAR, A01_MR_STAR,
                  (R)1,  A00 );
                //------------------------------------------------------------//
                WPan_MR_STAR.FreeAlignments();
                APan_MR_STAR.FreeAlignments();
                WPan_MC_STAR.FreeAlignments();
                APan_MC_STAR.FreeAlignments();
                WPan.FreeAlignments();
            }
            else
            {
                A11_STAR_STAR = A11;
                HermitianTridiag( UPPER, A11_STAR_STAR.LocalMatrix() );
                A11 = A11_STAR_STAR;
            }

            SlidePartitionUpDiagonal
            ( ATL, /**/ ATR,  A00, /**/ A01, A02,
              /*************/ /******************/
              /**/       A10, /**/ A11, A12,
              ABL, /**/ ABR,  A20, /**/ A21, A22 );
        }
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
Exemple #4
0
inline void
TwoSidedTrsmUVar2
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& U )
{
#ifndef RELEASE
    CallStackEntry entry("internal::TwoSidedTrsmUVar2");
    if( A.Height() != A.Width() )
        LogicError("A must be square");
    if( U.Height() != U.Width() )
        LogicError("Triangular matrices must be square");
    if( A.Height() != U.Height() )
        LogicError("A and U must be the same size");
#endif
    const Grid& g = A.Grid();

    // Matrix views
    DistMatrix<F>
        ATL(g), ATR(g),  A00(g), A01(g), A02(g),
        ABL(g), ABR(g),  A10(g), A11(g), A12(g),
                         A20(g), A21(g), A22(g);
    DistMatrix<F>
        UTL(g), UTR(g),  U00(g), U01(g), U02(g),
        UBL(g), UBR(g),  U10(g), U11(g), U12(g),
                         U20(g), U21(g), U22(g);

    // Temporary distributions
    DistMatrix<F,MC,  STAR> A01_MC_STAR(g);
    DistMatrix<F,VC,  STAR> A01_VC_STAR(g);
    DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
    DistMatrix<F,STAR,VR  > A12_STAR_VR(g);
    DistMatrix<F,MC,  STAR> F01_MC_STAR(g);
    DistMatrix<F,MC,  STAR> U01_MC_STAR(g);
    DistMatrix<F,VR,  STAR> U01_VR_STAR(g);
    DistMatrix<F,STAR,MR  > U01Adj_STAR_MR(g);
    DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
    DistMatrix<F,STAR,MR  > X11_STAR_MR(g);
    DistMatrix<F,MR,  STAR> X12Adj_MR_STAR(g);
    DistMatrix<F,MR,  MC  > X12Adj_MR_MC(g);
    DistMatrix<F,MR,  MC  > Y01_MR_MC(g);
    DistMatrix<F,MR,  STAR> Y01_MR_STAR(g);
    DistMatrix<F> X11(g);
    DistMatrix<F> Y01(g);

    Matrix<F> X12Local;

    PartitionDownDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 );
    LockedPartitionDownDiagonal
    ( U, UTL, UTR,
         UBL, UBR, 0 );
    while( ATL.Height() < A.Height() )
    {
        RepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ A01, A02,
         /*************/ /******************/
               /**/       A10, /**/ A11, A12,
          ABL, /**/ ABR,  A20, /**/ A21, A22 );

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

        A01_MC_STAR.AlignWith( U01 );
        Y01.AlignWith( A01 );
        Y01_MR_STAR.AlignWith( A00 );
        U01_MC_STAR.AlignWith( A00 );
        U01_VR_STAR.AlignWith( A00 );
        U01Adj_STAR_MR.AlignWith( A00 );
        X11_STAR_MR.AlignWith( U01 );
        X11.AlignWith( A11 );
        X12Adj_MR_STAR.AlignWith( A02 );
        X12Adj_MR_MC.AlignWith( A12 );
        F01_MC_STAR.AlignWith( A00 );
        //--------------------------------------------------------------------//
        // Y01 := A00 U01
        U01_MC_STAR = U01;
        U01_VR_STAR = U01_MC_STAR;
        U01Adj_STAR_MR.AdjointFrom( U01_VR_STAR );
        Zeros( Y01_MR_STAR, A01.Height(), A01.Width() );
        Zeros( F01_MC_STAR, A01.Height(), A01.Width() );
        LocalSymmetricAccumulateLU
        ( ADJOINT, 
          F(1), A00, U01_MC_STAR, U01Adj_STAR_MR, F01_MC_STAR, Y01_MR_STAR );
        Y01_MR_MC.SumScatterFrom( Y01_MR_STAR );
        Y01 = Y01_MR_MC;
        Y01.SumScatterUpdate( F(1), F01_MC_STAR );

        // X11 := U01' A01
        LocalGemm( ADJOINT, NORMAL, F(1), U01_MC_STAR, A01, X11_STAR_MR );

        // A01 := A01 - Y01
        Axpy( F(-1), Y01, A01 );
        A01_MC_STAR = A01;
        
        // A11 := A11 - triu(X11 + A01' U01) = A11 - (U01 A01 + A01' U01)
        LocalGemm( ADJOINT, NORMAL, F(1), A01_MC_STAR, U01, F(1), X11_STAR_MR );
        X11.SumScatterFrom( X11_STAR_MR );
        MakeTriangular( UPPER, X11 );
        Axpy( F(-1), X11, A11 );

        // A01 := A01 inv(U11)
        U11_STAR_STAR = U11;
        A01_VC_STAR = A01_MC_STAR;
        LocalTrsm
        ( RIGHT, UPPER, NORMAL, diag, F(1), U11_STAR_STAR, A01_VC_STAR );
        A01 = A01_VC_STAR;

        // A11 := inv(U11)' A11 inv(U11)
        A11_STAR_STAR = A11;
        LocalTwoSidedTrsm( UPPER, diag, A11_STAR_STAR, U11_STAR_STAR );
        A11 = A11_STAR_STAR;

        // A12 := A12 - A02' U01
        LocalGemm( ADJOINT, NORMAL, F(1), A02, U01_MC_STAR, X12Adj_MR_STAR );
        X12Adj_MR_MC.SumScatterFrom( X12Adj_MR_STAR );
        Adjoint( X12Adj_MR_MC.LockedMatrix(), X12Local );
        Axpy( F(-1), X12Local, A12.Matrix() );

        // A12 := inv(U11)' A12
        A12_STAR_VR = A12;
        LocalTrsm
        ( LEFT, UPPER, ADJOINT, diag, F(1), U11_STAR_STAR, A12_STAR_VR );
        A12 = A12_STAR_VR;
        //--------------------------------------------------------------------//

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, A01, /**/ A02,
               /**/       A10, A11, /**/ A12,
         /*************/ /******************/
          ABL, /**/ ABR,  A20, A21, /**/ A22 );

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