コード例 #1
0
ファイル: HPSDCholesky.hpp プロジェクト: ahmadia/elemental
void MakeExplicitlyHermitian( UpperOrLower uplo, DistMatrix<F,MC,MR>& A )
{
    const Grid& g = A.Grid();
    DistMatrix<F,MC,MR> ATL(g), ATR(g),  A00(g), A01(g), A02(g),
                        ABL(g), ABR(g),  A10(g), A11(g), A12(g),
                                         A20(g), A21(g), A22(g);
    DistMatrix<F,MC,MR> A11Adj(g);
    DistMatrix<F,MR,MC> A11_MR_MC(g);
    DistMatrix<F,MR,MC> A21_MR_MC(g);
    DistMatrix<F,MR,MC> A12_MR_MC(g);

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

        A11Adj.AlignWith( A11 );
        A11_MR_MC.AlignWith( A11 );
        A12_MR_MC.AlignWith( A21 );
        A21_MR_MC.AlignWith( A12 );
        //--------------------------------------------------------------------//
        A11_MR_MC = A11;
        A11Adj.ResizeTo( A11.Height(), A11.Width() );
        Adjoint( A11_MR_MC.LocalMatrix(), A11Adj.LocalMatrix() );

        if( uplo == LOWER )
        {
            MakeTrapezoidal( LEFT, UPPER, 1, A11Adj );
            Axpy( (F)1, A11Adj, A11 );

            A21_MR_MC = A21;
            Adjoint( A21_MR_MC.LocalMatrix(), A12.LocalMatrix() ); 
        }
        else
        {
            MakeTrapezoidal( LEFT, LOWER, -1, A11Adj );
            Axpy( (F)1, A11Adj, A11 );

            A12_MR_MC = A12;
            Adjoint( A12_MR_MC.LocalMatrix(), A21.LocalMatrix() );
        }
        //--------------------------------------------------------------------//
        A21_MR_MC.FreeAlignments();
        A12_MR_MC.FreeAlignments();
        A11_MR_MC.FreeAlignments();
        A11Adj.FreeAlignments();

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, A01, /**/ A02,
               /**/       A10, A11, /**/ A12,
         /*************/ /******************/
          ABL, /**/ ABR,  A20, A21, /**/ A22 );
    }
}
コード例 #2
0
ファイル: LQ.hpp プロジェクト: ahmadia/elemental
inline void
LQ( DistMatrix<R,MC,MR>& A )
{
#ifndef RELEASE
    PushCallStack("LQ");
#endif
    if( IsComplex<R>::val )
        throw std::logic_error("Called real routine with complex datatype");
    const Grid& g = A.Grid();

    // Matrix views
    DistMatrix<R,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);

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

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

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

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, A01, /**/ A02,
               /**/       A10, A11, /**/ A12,
         /*************/ /******************/
          ABL, /**/ ABR,  A20, A21, /**/ A22 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #3
0
ファイル: RU.hpp プロジェクト: certik/Elemental
inline void
HemmRUC
( T alpha, const DistMatrix<T>& A,
           const DistMatrix<T>& B,
  T beta,        DistMatrix<T>& C )
{
#ifndef RELEASE
    PushCallStack("internal::HemmRUC");
    if( A.Grid() != B.Grid() || B.Grid() != C.Grid() )
        throw std::logic_error("{A,B,C} must be distributed on the same grid");
#endif
    const Grid& g = A.Grid();

    // Matrix views
    DistMatrix<T> 
        ATL(g), ATR(g),  A00(g), A01(g), A02(g),  AColPan(g),
        ABL(g), ABR(g),  A10(g), A11(g), A12(g),  ARowPan(g),
                         A20(g), A21(g), A22(g);
    DistMatrix<T> BL(g), BR(g),
                  B0(g), B1(g), B2(g);
    DistMatrix<T> CL(g), CR(g),
                  C0(g), C1(g), C2(g),
                  CLeft(g), CRight(g);

    // Temporary distributions
    DistMatrix<T,MC,STAR> B1_MC_STAR(g);
    DistMatrix<T,VR,  STAR> AColPan_VR_STAR(g);
    DistMatrix<T,STAR,MR  > AColPanAdj_STAR_MR(g);
    DistMatrix<T,MR,  STAR> ARowPanAdj_MR_STAR(g);

    B1_MC_STAR.AlignWith( C );

    // Start the algorithm
    Scale( beta, C );
    LockedPartitionDownDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 );
    LockedPartitionRight( B, BL, BR, 0 );
    PartitionRight( C, CL, CR, 0 );
    while( CR.Width() > 0 )
    {
        LockedRepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ A01, A02,
         /*************/ /******************/
               /**/       A10, /**/ A11, A12,
          ABL, /**/ ABR,  A20, /**/ A21, A22 );

        LockedRepartitionRight
        ( BL, /**/ BR,
          B0, /**/ B1, B2 );

        RepartitionRight
        ( CL, /**/ CR,
          C0, /**/ C1, C2 );

        ARowPan.LockedView1x2( A11, A12 );
        AColPan.LockedView2x1
        ( A01,
          A11 );

        CLeft.View1x2( C0, C1 );
        CRight.View1x2( C1, C2 );

        AColPan_VR_STAR.AlignWith( CLeft );
        AColPanAdj_STAR_MR.AlignWith( CLeft );
        ARowPanAdj_MR_STAR.AlignWith( CRight );
        //--------------------------------------------------------------------//
        B1_MC_STAR = B1;

        AColPan_VR_STAR = AColPan;
        AColPanAdj_STAR_MR.AdjointFrom( AColPan_VR_STAR );
        ARowPanAdj_MR_STAR.AdjointFrom( ARowPan );
        MakeTrapezoidal( LEFT,  LOWER,  0, ARowPanAdj_MR_STAR );
        MakeTrapezoidal( RIGHT, LOWER, -1, AColPanAdj_STAR_MR );

        LocalGemm
        ( NORMAL, ADJOINT, 
          alpha, B1_MC_STAR, ARowPanAdj_MR_STAR, T(1), CRight );

        LocalGemm
        ( NORMAL, NORMAL,
          alpha, B1_MC_STAR, AColPanAdj_STAR_MR, T(1), CLeft );
        //--------------------------------------------------------------------//
        AColPan_VR_STAR.FreeAlignments();
        AColPanAdj_STAR_MR.FreeAlignments();
        ARowPanAdj_MR_STAR.FreeAlignments();

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

        SlideLockedPartitionRight
        ( BL,     /**/ BR,
          B0, B1, /**/ B2 );

        SlidePartitionRight
        ( CL,     /**/ CR,
          C0, C1, /**/ C2 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #4
0
ファイル: LL.hpp プロジェクト: jimgoo/Elemental
inline void
SymmLLC
( T alpha, const DistMatrix<T>& A, const DistMatrix<T>& B,
  T beta,        DistMatrix<T>& C )
{
#ifndef RELEASE
    PushCallStack("internal::SymmLLC");
    if( A.Grid() != B.Grid() || B.Grid() != C.Grid() )
        throw std::logic_error
        ("{A,B,C} must be distributed over the same grid");
#endif
    const Grid& g = A.Grid();

    // Matrix views
    DistMatrix<T> 
        ATL(g), ATR(g),  A00(g), A01(g), A02(g),  AColPan(g),
        ABL(g), ABR(g),  A10(g), A11(g), A12(g),  ARowPan(g),
                         A20(g), A21(g), A22(g);
    DistMatrix<T> 
        BT(g),  B0(g),
        BB(g),  B1(g),
                B2(g);
    DistMatrix<T> 
        CT(g),  C0(g),  CAbove(g),
        CB(g),  C1(g),  CBelow(g),
                C2(g);

    // Temporary distributions
    DistMatrix<T,MC,  STAR> AColPan_MC_STAR(g);
    DistMatrix<T,STAR,MC  > ARowPan_STAR_MC(g);
    DistMatrix<T,MR,  STAR> B1Trans_MR_STAR(g);

    B1Trans_MR_STAR.AlignWith( C );

    // Start the algorithm
    Scale( beta, C );
    LockedPartitionDownDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 );
    LockedPartitionDown
    ( B, BT,
         BB, 0 );
    PartitionDown
    ( C, CT,
         CB, 0 );
    while( CB.Height() > 0 )
    {
        LockedRepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ A01, A02,
         /*************/ /******************/
               /**/       A10, /**/ A11, A12,
          ABL, /**/ ABR,  A20, /**/ A21, A22 );

        LockedRepartitionDown
        ( BT,  B0,
         /**/ /**/
               B1,
          BB,  B2 );

        RepartitionDown
        ( CT,  C0,
         /**/ /**/
               C1,
          CB,  C2 );

        LockedView1x2( ARowPan, A10, A11 );
        LockedView2x1
        ( AColPan, A11,
                   A21 );

        View2x1
        ( CAbove, C0,
                  C1 );
        View2x1
        ( CBelow, C1,
                  C2 );

        AColPan_MC_STAR.AlignWith( CBelow );
        ARowPan_STAR_MC.AlignWith( CAbove );
        //--------------------------------------------------------------------//
        AColPan_MC_STAR = AColPan;
        ARowPan_STAR_MC = ARowPan;
        MakeTrapezoidal( LEFT,  LOWER,  0, AColPan_MC_STAR );
        MakeTrapezoidal( RIGHT, LOWER, -1, ARowPan_STAR_MC );

        B1Trans_MR_STAR.TransposeFrom( B1 );

        LocalGemm
        ( NORMAL, TRANSPOSE, 
          alpha, AColPan_MC_STAR, B1Trans_MR_STAR, T(1), CBelow );

        LocalGemm
        ( TRANSPOSE, TRANSPOSE, 
          alpha, ARowPan_STAR_MC, B1Trans_MR_STAR, T(1), CAbove );
        //--------------------------------------------------------------------//
        AColPan_MC_STAR.FreeAlignments();
        ARowPan_STAR_MC.FreeAlignments();

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

        SlideLockedPartitionDown
        ( BT,  B0,
               B1,
         /**/ /**/
          BB,  B2 );

        SlidePartitionDown
        ( CT,  C0,
               C1,
         /**/ /**/
          CB,  C2 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #5
0
ファイル: UVar1.hpp プロジェクト: khalid-hasanov/Elemental
inline void
TwoSidedTrsmUVar1
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& U )
{
#ifndef RELEASE
    CallStackEntry entry("internal::TwoSidedTrsmUVar1");
    if( A.Height() != A.Width() )
        LogicError("A must be square");
    if( U.Height() != U.Width() )
        LogicError("Triangular matrices must be square");
    if( A.Height() != U.Height() )
        LogicError("A and U must be the same size");
#endif
    const Grid& g = A.Grid();

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

    // Temporary distributions
    DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
    DistMatrix<F,VC,  STAR> A01_VC_STAR(g);
    DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
    DistMatrix<F,MC,  STAR> U01_MC_STAR(g);
    DistMatrix<F,VC,  STAR> U01_VC_STAR(g);
    DistMatrix<F,VR,  STAR> U01_VR_STAR(g);
    DistMatrix<F,STAR,MR  > U01Adj_STAR_MR(g);
    DistMatrix<F,STAR,STAR> X11_STAR_STAR(g);
    DistMatrix<F,MR,  MC  > Z01_MR_MC(g);
    DistMatrix<F,MC,  STAR> Z01_MC_STAR(g);
    DistMatrix<F,MR,  STAR> Z01_MR_STAR(g);
    DistMatrix<F> Y01(g);

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

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

        A01_VC_STAR.AlignWith( A01 );
        U01_MC_STAR.AlignWith( A00 );
        U01_VR_STAR.AlignWith( A00 );
        U01_VC_STAR.AlignWith( A00 );
        U01Adj_STAR_MR.AlignWith( A00 );
        Y01.AlignWith( A01 );
        Z01_MR_MC.AlignWith( A01 );
        Z01_MC_STAR.AlignWith( A00 );
        Z01_MR_STAR.AlignWith( A00 );
        //--------------------------------------------------------------------//
        // Y01 := A00 U01
        U01_MC_STAR = U01;
        U01_VR_STAR = U01_MC_STAR;
        U01Adj_STAR_MR.AdjointFrom( U01_VR_STAR );
        Zeros( Z01_MC_STAR, A01.Height(), A01.Width() );
        Zeros( Z01_MR_STAR, A01.Height(), A01.Width() );
        LocalSymmetricAccumulateLU
        ( ADJOINT, 
          F(1), A00, U01_MC_STAR, U01Adj_STAR_MR, Z01_MC_STAR, Z01_MR_STAR );
        Z01_MR_MC.SumScatterFrom( Z01_MR_STAR );
        Y01 = Z01_MR_MC;
        Y01.SumScatterUpdate( F(1), Z01_MC_STAR );

        // A01 := inv(U00)' A01
        //
        // This is the bottleneck because A01 only has blocksize columns
        Trsm( LEFT, UPPER, ADJOINT, diag, F(1), U00, A01 );

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

        // A11 := A11 - (U01' A01 + A01' U01)
        A01_VC_STAR = A01;
        U01_VC_STAR = U01_MC_STAR;
        Zeros( X11_STAR_STAR, A11.Height(), A11.Width() );
        Her2k
        ( UPPER, ADJOINT,
          F(-1), A01_VC_STAR.Matrix(), U01_VC_STAR.Matrix(),
          F(0), X11_STAR_STAR.Matrix() );
        A11.SumScatterUpdate( F(1), X11_STAR_STAR );

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

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

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

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

        SlideLockedPartitionDownDiagonal
        ( UTL, /**/ UTR,  U00, U01, /**/ U02,
               /**/       U10, U11, /**/ U12,
         /*************/ /******************/
          UBL, /**/ UBR,  U20, U21, /**/ U22 );
    }
}
コード例 #6
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 );
    }
}
コード例 #7
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 );
    }
}
コード例 #8
0
ファイル: LSquare.hpp プロジェクト: ahmadia/Elemental-1
void LSquare( DistMatrix<R>& A )
{
#ifndef RELEASE
    CallStackEntry entry("hermitian_tridiag::LSquare");
    if( A.Height() != A.Width() )
        throw std::logic_error("A must be square");
    if( A.Grid().Height() != A.Grid().Width() )
        throw std::logic_error("The process grid must be square");
#endif
    const Grid& g = A.Grid();

    // Matrix views 
    DistMatrix<R> 
        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> WPan(g);
    DistMatrix<R,STAR,STAR> A11_STAR_STAR(g);
    DistMatrix<R,MC,  STAR> APan_MC_STAR(g),  A11_MC_STAR(g),
                                              A21_MC_STAR(g);
    DistMatrix<R,MR,  STAR> APan_MR_STAR(g),  A11_MR_STAR(g),
                                              A21_MR_STAR(g);
    DistMatrix<R,MC,  STAR> WPan_MC_STAR(g),  W11_MC_STAR(g),
                                              W21_MC_STAR(g);
    DistMatrix<R,MR,  STAR> WPan_MR_STAR(g),  W11_MR_STAR(g),
                                              W21_MR_STAR(g);

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

        if( A22.Height() > 0 )
        {
            WPan.AlignWith( A11 );
            APan_MC_STAR.AlignWith( A11 );
            WPan_MC_STAR.AlignWith( A11 );
            APan_MR_STAR.AlignWith( A11 );
            WPan_MR_STAR.AlignWith( A11 );
            //----------------------------------------------------------------//
            WPan.ResizeTo( ABR.Height(), A11.Width() );
            APan_MC_STAR.ResizeTo( ABR.Height(), A11.Width() );
            WPan_MC_STAR.ResizeTo( ABR.Height(), A11.Width() );
            APan_MR_STAR.ResizeTo( ABR.Height(), A11.Width() );
            WPan_MR_STAR.ResizeTo( ABR.Height(), A11.Width() );

            hermitian_tridiag::PanelLSquare
            ( ABR, WPan, 
              APan_MC_STAR, APan_MR_STAR, WPan_MC_STAR, WPan_MR_STAR );

            PartitionDown
            ( APan_MC_STAR, A11_MC_STAR,
                            A21_MC_STAR, A11.Height() );
            PartitionDown
            ( APan_MR_STAR, A11_MR_STAR,
                            A21_MR_STAR, A11.Height() );
            PartitionDown
            ( WPan_MC_STAR, W11_MC_STAR,
                            W21_MC_STAR, A11.Height() );
            PartitionDown
            ( WPan_MR_STAR, W11_MR_STAR,
                            W21_MR_STAR, A11.Height() );

            LocalTrr2k
            ( LOWER, TRANSPOSE, TRANSPOSE,
              R(-1), A21_MC_STAR, W21_MR_STAR,
                     W21_MC_STAR, A21_MR_STAR,
              R(1), A22 );
            //----------------------------------------------------------------//
            WPan_MR_STAR.FreeAlignments();
            APan_MR_STAR.FreeAlignments();
            WPan_MC_STAR.FreeAlignments();
            APan_MC_STAR.FreeAlignments();
            WPan.FreeAlignments();
        }
        else
        {
            A11_STAR_STAR = A11;
            HermitianTridiag( LOWER, A11_STAR_STAR.Matrix() );
            A11 = A11_STAR_STAR;
        }

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, A01, /**/ A02,
               /**/       A10, A11, /**/ A12,
         /*************/ /******************/
          ABL, /**/ ABR,  A20, A21, /**/ A22 );
    }
}
コード例 #9
0
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
}
コード例 #10
0
ファイル: UnblockedU.hpp プロジェクト: jimgoo/Elemental
inline void UnblockedBidiagU
( DistMatrix<Complex<R> >& A, 
  DistMatrix<Complex<R>,MD,STAR>& tP,
  DistMatrix<Complex<R>,MD,STAR>& tQ )
{
#ifndef RELEASE
    PushCallStack("BidiagU");
#endif
    const int tPHeight = std::max(A.Width()-1,0);
    const int tQHeight = A.Width();
#ifndef RELEASE
    if( A.Grid() != tP.Grid() || tP.Grid() != tQ.Grid() )
        throw std::logic_error("Process grids do not match");
    if( A.Height() < A.Width() )
        throw std::logic_error("A must be at least as tall as it is wide");
    if( tP.Viewing() && (tP.Height() != tPHeight || tP.Width() != 1) )
        throw std::logic_error("tP is the wrong height");
    if( tQ.Viewing() && (tQ.Height() != tQHeight || tQ.Width() != 1) )
        throw std::logic_error("tQ is the wrong height");
#endif
    typedef Complex<R> C;
    const Grid& g = A.Grid();

    if( !tP.Viewing() )
        tP.ResizeTo( tPHeight, 1 );
    if( !tQ.Viewing() )
        tQ.ResizeTo( tQHeight, 1 );

    // Matrix views 
    DistMatrix<C>
        ATL(g), ATR(g),  A00(g), a01(g),     A02(g),  alpha12L(g), a12R(g),
        ABL(g), ABR(g),  a10(g), alpha11(g), a12(g),  aB1(g), AB2(g),
                         A20(g), a21(g),     A22(g);

    // Temporary matrices
    DistMatrix<C,STAR,MR  > a12_STAR_MR(g);
    DistMatrix<C,MC,  STAR> aB1_MC_STAR(g);
    DistMatrix<C,MR,  STAR> x12Adj_MR_STAR(g);
    DistMatrix<C,MC,  STAR> w21_MC_STAR(g);

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

        View2x1
        ( aB1, alpha11,
               a21 );
        View2x1
        ( AB2, a12,
               A22 );

        aB1_MC_STAR.AlignWith( aB1 );
        a12_STAR_MR.AlignWith( a12 );
        x12Adj_MR_STAR.AlignWith( AB2 );
        w21_MC_STAR.AlignWith( A22 );
        Zeros( a12.Width(), 1, x12Adj_MR_STAR );
        Zeros( a21.Height(), 1, w21_MC_STAR );
        const bool thisIsMyRow = ( g.Row() == alpha11.ColAlignment() );
        const bool thisIsMyCol = ( g.Col() == alpha11.RowAlignment() );
        const bool nextIsMyCol = ( g.Col() == a12.RowAlignment() );
        //--------------------------------------------------------------------//

        // Find tauQ, u, and epsilonQ such that
        //     I - conj(tauQ) | 1 | | 1, u^H | | alpha11 | = | epsilonQ |
        //                    | u |            |    a21  |   |    0     |
        const C tauQ = Reflector( alpha11, a21 );
        tQ.Set(A00.Height(),0,tauQ );
        C epsilonQ=0;
        if( thisIsMyCol && thisIsMyRow )
            epsilonQ = alpha11.GetLocal(0,0);

        // Set aB1 = | 1 | and form x12^H := (aB1^H AB2)^H = AB2^H aB1
        //           | u |
        alpha11.Set(0,0,C(1));
        aB1_MC_STAR = aB1;
        internal::LocalGemv
        ( ADJOINT, C(1), AB2, aB1_MC_STAR, C(0), x12Adj_MR_STAR );
        x12Adj_MR_STAR.SumOverCol();

        // Update AB2 := AB2 - conj(tauQ) aB1 x12
        //             = AB2 - conj(tauQ) aB1 aB1^H AB2 
        //             = (I - conj(tauQ) aB1 aB1^H) AB2
        internal::LocalGer( -Conj(tauQ), aB1_MC_STAR, x12Adj_MR_STAR, AB2 );

        // Put epsilonQ back instead of the temporary value, 1
        if( thisIsMyCol && thisIsMyRow )
            alpha11.SetLocal(0,0,epsilonQ);

        if( A22.Width() != 0 )
        {
            // Due to the deficiencies in the BLAS ?gemv routines, this section
            // is easier if we temporarily conjugate a12
            Conjugate( a12 ); 

            // Expose the subvector we seek to zero, a12R
            PartitionRight( a12, alpha12L, a12R );

            // Find tauP, v, and epsilonP such that
            //     I - conj(tauP) | 1 | | 1, v^H | | alpha12L | = | epsilonP |
            //                    | v |            |  a12R^T  |   |    0     |
            const C tauP = Reflector( alpha12L, a12R );
            tP.Set(A00.Height(),0,tauP);
            C epsilonP=0;
            if( nextIsMyCol && thisIsMyRow )
                epsilonP = alpha12L.GetLocal(0,0);

            // Set a12^T = | 1 | and form w21 := A22 a12^T = A22 | 1 |
            //             | v |                                 | v |
            alpha12L.Set(0,0,C(1));
            a12_STAR_MR = a12;
            internal::LocalGemv
            ( NORMAL, C(1), A22, a12_STAR_MR, C(0), w21_MC_STAR );
            w21_MC_STAR.SumOverRow();

            // A22 := A22 - tauP w21 conj(a12)
            //      = A22 - tauP A22 a12^T conj(a12)
            //      = A22 (I - tauP a12^T conj(a12))
            //      = A22 conj(I - conj(tauP) a12^H a12)
            // which compensates for the fact that the reflector was generated
            // on the conjugated a12.
            internal::LocalGer( -tauP, w21_MC_STAR, a12_STAR_MR, A22 );

            // Put epsilonP back instead of the temporary value, 1
            if( nextIsMyCol && thisIsMyRow )
                alpha12L.SetLocal(0,0,epsilonP);

            // Undue the temporary conjugation
            Conjugate( a12 );
        }
        //--------------------------------------------------------------------//
        aB1_MC_STAR.FreeAlignments();
        a12_STAR_MR.FreeAlignments();
        x12Adj_MR_STAR.FreeAlignments();
        w21_MC_STAR.FreeAlignments();

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, a01,     /**/ A02,
               /**/       a10, alpha11, /**/ a12,
         /*************/ /**********************/
          ABL, /**/ ABR,  A20, a21,     /**/ A22 );
    }
    PopBlocksizeStack();
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #11
0
ファイル: UnblockedU.hpp プロジェクト: jimgoo/Elemental
inline void UnblockedBidiagU( DistMatrix<R>& A )
{
#ifndef RELEASE
    PushCallStack("bidiag::UnblockedBidiagU");
    if( A.Height() < A.Width() )
        throw std::logic_error("A must be at least as tall as it is wide");
#endif
    const Grid& g = A.Grid();

    // Matrix views 
    DistMatrix<R>
        ATL(g), ATR(g),  A00(g), a01(g),     A02(g),  alpha12L(g), a12R(g),
        ABL(g), ABR(g),  a10(g), alpha11(g), a12(g),  aB1(g), AB2(g),
                         A20(g), a21(g),     A22(g);

    // Temporary matrices
    DistMatrix<R,STAR,MR  > a12_STAR_MR(g);
    DistMatrix<R,MC,  STAR> aB1_MC_STAR(g);
    DistMatrix<R,MR,  STAR> x12Trans_MR_STAR(g);
    DistMatrix<R,MC,  STAR> w21_MC_STAR(g);

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

        View2x1
        ( aB1, alpha11,
               a21 );
        View2x1
        ( AB2, a12,
               A22 );

        aB1_MC_STAR.AlignWith( aB1 );
        a12_STAR_MR.AlignWith( a12 );
        x12Trans_MR_STAR.AlignWith( AB2 );
        w21_MC_STAR.AlignWith( A22 );
        Zeros( a12.Width(), 1, x12Trans_MR_STAR );
        Zeros( a21.Height(), 1, w21_MC_STAR );
        const bool thisIsMyRow = ( g.Row() == alpha11.ColAlignment() );
        const bool thisIsMyCol = ( g.Col() == alpha11.RowAlignment() );
        const bool nextIsMyCol = ( g.Col() == a12.RowAlignment() );
        //--------------------------------------------------------------------//

        // Find tauQ, u, and epsilonQ such that
        //     I - tauQ | 1 | | 1, u^T | | alpha11 | = | epsilonQ |
        //              | u |            |   a21   | = |    0     |
        const R tauQ = Reflector( alpha11, a21 );
        R epsilonQ=0;
        if( thisIsMyCol && thisIsMyRow )
            epsilonQ = alpha11.GetLocal(0,0);

        // Set aB1 = | 1 | and form x12^T := (aB1^T AB2)^T = AB2^T aB1
        //           | u |
        alpha11.Set(0,0,R(1));
        aB1_MC_STAR = aB1;
        internal::LocalGemv
        ( TRANSPOSE, R(1), AB2, aB1_MC_STAR, R(0), x12Trans_MR_STAR );
        x12Trans_MR_STAR.SumOverCol();

        // Update AB2 := AB2 - tauQ aB1 x12
        //             = AB2 - tauQ aB1 aB1^T AB2
        //             = (I - tauQ aB1 aB1^T) AB2
        internal::LocalGer( -tauQ, aB1_MC_STAR, x12Trans_MR_STAR, AB2 );

        // Put epsilonQ back instead of the temporary value, 1
        if( thisIsMyCol && thisIsMyRow )
            alpha11.SetLocal(0,0,epsilonQ);

        if( A22.Width() != 0 )
        {
            // Expose the subvector we seek to zero, a12R
            PartitionRight( a12, alpha12L, a12R );

            // Find tauP, v, and epsilonP such that
            //     I - tauP | 1 | | 1, v^T | | alpha12L | = | epsilonP |
            //              | v |            |  a12R^T  | = |    0     |
            const R tauP = Reflector( alpha12L, a12R );
            R epsilonP=0;
            if( nextIsMyCol && thisIsMyRow )
                epsilonP = alpha12L.GetLocal(0,0);

            // Set a12^T = | 1 | and form w21 := A22 a12^T = A22 | 1 |
            //             | v |                                 | v |
            alpha12L.Set(0,0,R(1));
            a12_STAR_MR = a12;
            internal::LocalGemv
            ( NORMAL, R(1), A22, a12_STAR_MR, R(0), w21_MC_STAR );
            w21_MC_STAR.SumOverRow();

            // A22 := A22 - tauP w21 a12
            //      = A22 - tauP A22 a12^T a12
            //      = A22 (I - tauP a12^T a12)
            internal::LocalGer( -tauP, w21_MC_STAR, a12_STAR_MR, A22 );

            // Put epsilonP back instead of the temporary value, 1
            if( nextIsMyCol && thisIsMyRow )
                alpha12L.SetLocal(0,0,epsilonP);
        }
        //--------------------------------------------------------------------//
        aB1_MC_STAR.FreeAlignments();
        a12_STAR_MR.FreeAlignments();
        x12Trans_MR_STAR.FreeAlignments();
        w21_MC_STAR.FreeAlignments();

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, a01,     /**/ A02,
               /**/       a10, alpha11, /**/ a12,
         /*************/ /**********************/
          ABL, /**/ ABR,  A20, a21,     /**/ A22 );
    }
    PopBlocksizeStack();
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #12
0
ファイル: Panel.hpp プロジェクト: jimgoo/Elemental
inline void
PanelLU
( DistMatrix<F,  STAR,STAR>& A, 
  DistMatrix<F,  MC,  STAR>& B, 
  DistMatrix<int,STAR,STAR>& p, 
  int pivotOffset )
{
#ifndef RELEASE
    PushCallStack("internal::PanelLU");
    if( A.Grid() != p.Grid() || p.Grid() != B.Grid() )
        throw std::logic_error
        ("Matrices must be distributed over the same grid");
    if( A.Width() != B.Width() )
        throw std::logic_error("A and B must be the same width");
    if( A.Height() != p.Height() || p.Width() != 1 )
        throw std::logic_error("p must be a vector that conforms with A");
#endif
    const Grid& g = A.Grid();
    const int r = g.Height();
    const int colShift = B.ColShift();
    const int colAlignment = B.ColAlignment();

    // Matrix views
    DistMatrix<F,STAR,STAR> 
        ATL(g), ATR(g),  A00(g), a01(g),     A02(g),  
        ABL(g), ABR(g),  a10(g), alpha11(g), a12(g),  
                         A20(g), a21(g),     A22(g);

    DistMatrix<F,MC,STAR>
        BL(g), BR(g),
        B0(g), b1(g), B2(g);

    const int width = A.Width();
    const int numBytes = (width+1)*sizeof(F)+sizeof(int);
    std::vector<byte> sendData(numBytes);
    std::vector<byte> recvData(numBytes);

    // Extract pointers to send and recv data
    // TODO: Think of how to make this safer with respect to alignment issues
    F* sendBufFloat = (F*)&sendData[0];
    F* recvBufFloat = (F*)&recvData[0];
    int* sendBufInt = (int*)&sendData[(width+1)*sizeof(F)];
    int* recvBufInt = (int*)&recvData[(width+1)*sizeof(F)];

    // Start the algorithm
    PushBlocksizeStack( 1 );
    PartitionDownDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 );
    PartitionRight( B, BL, BR, 0 );
    while( ATL.Height() < A.Height() )
    {
        RepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ a01,     A02,
         /*************/ /**********************/
               /**/       a10, /**/ alpha11, a12,
          ABL, /**/ ABR,  A20, /**/ a21,     A22 );

        RepartitionRight
        ( BL, /**/ BR,  
          B0, /**/ b1, B2 );

        //--------------------------------------------------------------------//
        const int currentRow = a01.Height();
        
        // Store the index/value of the pivot candidate in A
        F pivot = alpha11.GetLocal(0,0);
        int pivotRow = currentRow;
        for( int i=0; i<a21.Height(); ++i )
        {
            F value = a21.GetLocal(i,0);
            if( FastAbs(value) > FastAbs(pivot) )
            {
                pivot = value;
                pivotRow = currentRow + i + 1;
            }
        }

        // Update the pivot candidate to include local data from B
        for( int i=0; i<B.LocalHeight(); ++i )
        {
            F value = b1.GetLocal(i,0);
            if( FastAbs(value) > FastAbs(pivot) )
            {
                pivot = value;
                pivotRow = A.Height() + colShift + i*r;
            }
        }

        // Fill the send buffer with:
        // [ pivotValue | pivot row data | pivotRow ]
        if( pivotRow < A.Height() )
        {
            sendBufFloat[0] = A.GetLocal(pivotRow,a10.Width());

            const int ALDim = A.LocalLDim();
            const F* ABuffer = A.LocalBuffer(pivotRow,0);
            for( int j=0; j<width; ++j )
                sendBufFloat[j+1] = ABuffer[j*ALDim];
        }
        else
        {
            const int localRow = ((pivotRow-A.Height())-colShift)/r;
            sendBufFloat[0] = b1.GetLocal(localRow,0);

            const int BLDim = B.LocalLDim();
            const F* BBuffer = B.LocalBuffer(localRow,0);
            for( int j=0; j<width; ++j )
                sendBufFloat[j+1] = BBuffer[j*BLDim];
        }
        *sendBufInt = pivotRow;

        // Communicate to establish the pivot information
        mpi::AllReduce
        ( &sendData[0], &recvData[0], numBytes, PivotOp<F>(), g.ColComm() );

        // Update the pivot vector
        pivotRow = *recvBufInt;
        p.SetLocal(currentRow,0,pivotRow+pivotOffset);

        // Copy the current row into the pivot row
        if( pivotRow < A.Height() )
        {
            const int ALDim = A.LocalLDim();
            F* ASetBuffer = A.LocalBuffer(pivotRow,0);
            const F* AGetBuffer = A.LocalBuffer(currentRow,0);
            for( int j=0; j<width; ++j )
                ASetBuffer[j*ALDim] = AGetBuffer[j*ALDim];
        }
        else
        {
            const int ownerRank = (colAlignment+(pivotRow-A.Height())) % r;
            if( g.Row() == ownerRank )
            {
                const int localRow = ((pivotRow-A.Height())-colShift) / r;

                const int ALDim = A.LocalLDim();
                const int BLDim = B.LocalLDim();
                F* BBuffer = B.LocalBuffer(localRow,0);
                const F* ABuffer = A.LocalBuffer(currentRow,0);
                for( int j=0; j<width; ++j )
                    BBuffer[j*BLDim] = ABuffer[j*ALDim];
            }
        }

        // Copy the pivot row into the current row
        {
            F* ABuffer = A.LocalBuffer(currentRow,0);
            const int ALDim = A.LocalLDim();
            for( int j=0; j<width; ++j )
                ABuffer[j*ALDim] = recvBufFloat[j+1];
        }

        // Now we can perform the update of the current panel
        const F alpha = alpha11.GetLocal(0,0);
        if( alpha == F(0) )
            throw SingularMatrixException();
        const F alpha11Inv = F(1) / alpha;
        Scale( alpha11Inv, a21.LocalMatrix() );
        Scale( alpha11Inv, b1.LocalMatrix()  );
        Geru( F(-1), a21.LocalMatrix(), a12.LocalMatrix(), A22.LocalMatrix() );
        Geru( F(-1), b1.LocalMatrix(), a12.LocalMatrix(), B2.LocalMatrix() );
        //--------------------------------------------------------------------//

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, a01,     /**/ A02,
               /**/       a10, alpha11, /**/ a12,
         /*************/ /**********************/
          ABL, /**/ ABR,  A20, a21,     /**/ A22 );

        SlidePartitionRight
        ( BL,     /**/ BR,  
          B0, b1, /**/ B2 );
    }
    PopBlocksizeStack();

#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #13
0
ファイル: LVar2.hpp プロジェクト: jimgoo/Elemental
inline void
TwoSidedTrsmLVar2
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& L )
{
#ifndef RELEASE
    PushCallStack("internal::TwoSidedTrsmLVar2");
    if( A.Height() != A.Width() )
        throw std::logic_error("A must be square");
    if( L.Height() != L.Width() )
        throw std::logic_error("Triangular matrices must be square");
    if( A.Height() != L.Height() )
        throw std::logic_error("A and L must be the same size");
#endif
    const Grid& g = A.Grid();
    
    // Matrix views
    DistMatrix<F>
        ATL(g), ATR(g),  A00(g), A01(g), A02(g),
        ABL(g), ABR(g),  A10(g), A11(g), A12(g),
                         A20(g), A21(g), A22(g);

    DistMatrix<F>
        LTL(g), LTR(g),  L00(g), L01(g), L02(g),
        LBL(g), LBR(g),  L10(g), L11(g), L12(g),
                         L20(g), L21(g), L22(g);

    // Temporary distributions
    DistMatrix<F,MR,  STAR> A10Adj_MR_STAR(g);
    DistMatrix<F,STAR,VR  > A10_STAR_VR(g);
    DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
    DistMatrix<F,VC,  STAR> A21_VC_STAR(g);
    DistMatrix<F,MR,  STAR> F10Adj_MR_STAR(g);
    DistMatrix<F,MR,  STAR> L10Adj_MR_STAR(g);
    DistMatrix<F,VC,  STAR> L10Adj_VC_STAR(g);
    DistMatrix<F,STAR,MC  > L10_STAR_MC(g);
    DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
    DistMatrix<F,MC,  STAR> X11_MC_STAR(g);
    DistMatrix<F,MC,  STAR> X21_MC_STAR(g);
    DistMatrix<F,MC,  STAR> Y10Adj_MC_STAR(g);
    DistMatrix<F,MR,  MC  > Y10Adj_MR_MC(g);
    DistMatrix<F> X11(g);
    DistMatrix<F> Y10Adj(g);

    Matrix<F> Y10Local;

    PartitionDownDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 );
    LockedPartitionDownDiagonal
    ( L, LTL, LTR,
         LBL, LBR, 0 );
    while( ATL.Height() < A.Height() )
    {
        RepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ A01, A02,
         /*************/ /******************/
               /**/       A10, /**/ A11, A12,
          ABL, /**/ ABR,  A20, /**/ A21, A22 );

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

        A10Adj_MR_STAR.AlignWith( L10 );
        F10Adj_MR_STAR.AlignWith( A00 );
        L10Adj_MR_STAR.AlignWith( A00 );
        L10Adj_VC_STAR.AlignWith( A00 );
        L10_STAR_MC.AlignWith( A00 );
        X11.AlignWith( A11 );
        X11_MC_STAR.AlignWith( L10 );
        X21_MC_STAR.AlignWith( A20 );
        Y10Adj_MC_STAR.AlignWith( A00 );
        Y10Adj_MR_MC.AlignWith( A10 );
        //--------------------------------------------------------------------//
        // Y10 := L10 A00
        L10Adj_MR_STAR.AdjointFrom( L10 );
        L10Adj_VC_STAR = L10Adj_MR_STAR;
        L10_STAR_MC.AdjointFrom( L10Adj_VC_STAR );
        Y10Adj_MC_STAR.ResizeTo( A10.Width(), A10.Height() );
        F10Adj_MR_STAR.ResizeTo( A10.Width(), A10.Height() );
        Zero( Y10Adj_MC_STAR );
        Zero( F10Adj_MR_STAR );
        LocalSymmetricAccumulateRL
        ( ADJOINT,
          F(1), A00, L10_STAR_MC, L10Adj_MR_STAR, 
          Y10Adj_MC_STAR, F10Adj_MR_STAR );
        Y10Adj.SumScatterFrom( Y10Adj_MC_STAR );
        Y10Adj_MR_MC = Y10Adj;
        Y10Adj_MR_MC.SumScatterUpdate( F(1), F10Adj_MR_STAR );
        Adjoint( Y10Adj_MR_MC.LockedLocalMatrix(), Y10Local );

        // X11 := A10 L10'
        X11_MC_STAR.ResizeTo( A11.Height(), A11.Width() );
        LocalGemm
        ( NORMAL, NORMAL, F(1), A10, L10Adj_MR_STAR, F(0), X11_MC_STAR );

        // A10 := A10 - Y10
        Axpy( F(-1), Y10Local, A10.LocalMatrix() );
        A10Adj_MR_STAR.AdjointFrom( A10 );
        
        // A11 := A11 - (X11 + L10 A10') = A11 - (A10 L10' + L10 A10')
        LocalGemm
        ( NORMAL, NORMAL, F(1), L10, A10Adj_MR_STAR, F(1), X11_MC_STAR );
        X11.SumScatterFrom( X11_MC_STAR );
        MakeTrapezoidal( LEFT, LOWER, 0, X11 );
        Axpy( F(-1), X11, A11 );

        // A10 := inv(L11) A10
        L11_STAR_STAR = L11;
        A10_STAR_VR.AdjointFrom( A10Adj_MR_STAR );
        LocalTrsm
        ( LEFT, LOWER, NORMAL, diag, F(1), L11_STAR_STAR, A10_STAR_VR );
        A10 = A10_STAR_VR;

        // A11 := inv(L11) A11 inv(L11)'
        A11_STAR_STAR = A11;
        LocalTwoSidedTrsm( LOWER, diag, A11_STAR_STAR, L11_STAR_STAR );
        A11 = A11_STAR_STAR;

        // A21 := A21 - A20 L10'
        X21_MC_STAR.ResizeTo( A21.Height(), A21.Width() );
        LocalGemm
        ( NORMAL, NORMAL, F(1), A20, L10Adj_MR_STAR, F(0), X21_MC_STAR );
        A21.SumScatterUpdate( F(-1), X21_MC_STAR );

        // A21 := A21 inv(L11)'
        A21_VC_STAR =  A21;
        LocalTrsm
        ( RIGHT, LOWER, ADJOINT, diag, F(1), L11_STAR_STAR, A21_VC_STAR );
        A21 = A21_VC_STAR;
        //--------------------------------------------------------------------//
        A10Adj_MR_STAR.FreeAlignments();
        F10Adj_MR_STAR.FreeAlignments();
        L10Adj_MR_STAR.FreeAlignments();
        L10Adj_VC_STAR.FreeAlignments();
        L10_STAR_MC.FreeAlignments();
        X11.FreeAlignments();
        X11_MC_STAR.FreeAlignments();
        X21_MC_STAR.FreeAlignments();
        Y10Adj_MC_STAR.FreeAlignments();
        Y10Adj_MR_MC.FreeAlignments();

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

        SlideLockedPartitionDownDiagonal
        ( LTL, /**/ LTR,  L00, L01, /**/ L02,
               /**/       L10, L11, /**/ L12,
         /**********************************/
          LBL, /**/ LBR,  L20, L21, /**/ L22 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #14
0
ファイル: LVar5.hpp プロジェクト: khalid-hasanov/Elemental
inline void
TwoSidedTrsmLVar5
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& L )
{
#ifndef RELEASE
    CallStackEntry entry("internal::TwoSidedTrsmLVar5");
    if( A.Height() != A.Width() )
        LogicError("A must be square");
    if( L.Height() != L.Width() )
        LogicError("Triangular matrices must be square");
    if( A.Height() != L.Height() )
        LogicError("A and L must be the same size");
#endif
    const Grid& g = A.Grid();

    // Matrix views
    DistMatrix<F>
    ATL(g), ATR(g),  A00(g), A01(g), A02(g),
        ABL(g), ABR(g),  A10(g), A11(g), A12(g),
        A20(g), A21(g), A22(g);
    DistMatrix<F>
    LTL(g), LTR(g),  L00(g), L01(g), L02(g),
        LBL(g), LBR(g),  L10(g), L11(g), L12(g),
        L20(g), L21(g), L22(g);

    // Temporary distributions
    DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
    DistMatrix<F,MC,  STAR> A21_MC_STAR(g);
    DistMatrix<F,VC,  STAR> A21_VC_STAR(g);
    DistMatrix<F,VR,  STAR> A21_VR_STAR(g);
    DistMatrix<F,STAR,MR  > A21Adj_STAR_MR(g);
    DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
    DistMatrix<F,MC,  STAR> L21_MC_STAR(g);
    DistMatrix<F,VC,  STAR> L21_VC_STAR(g);
    DistMatrix<F,VR,  STAR> L21_VR_STAR(g);
    DistMatrix<F,STAR,MR  > L21Adj_STAR_MR(g);
    DistMatrix<F,VC,  STAR> Y21_VC_STAR(g);
    DistMatrix<F> Y21(g);

    PartitionDownDiagonal
    ( A, ATL, ATR,
      ABL, ABR, 0 );
    LockedPartitionDownDiagonal
    ( L, LTL, LTR,
      LBL, LBR, 0 );
    while( ATL.Height() < A.Height() )
    {
        RepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ A01, A02,
          /*************/ /******************/
          /**/       A10, /**/ A11, A12,
          ABL, /**/ ABR,  A20, /**/ A21, A22 );

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

        A21_MC_STAR.AlignWith( A22 );
        A21_VC_STAR.AlignWith( A22 );
        A21_VR_STAR.AlignWith( A22 );
        A21Adj_STAR_MR.AlignWith( A22 );
        L21_MC_STAR.AlignWith( A22 );
        L21_VC_STAR.AlignWith( A22 );
        L21_VR_STAR.AlignWith( A22 );
        L21Adj_STAR_MR.AlignWith( A22 );
        Y21.AlignWith( A21 );
        Y21_VC_STAR.AlignWith( A22 );
        //--------------------------------------------------------------------//
        // A11 := inv(L11) A11 inv(L11)'
        L11_STAR_STAR = L11;
        A11_STAR_STAR = A11;
        LocalTwoSidedTrsm( LOWER, diag, A11_STAR_STAR, L11_STAR_STAR );
        A11 = A11_STAR_STAR;

        // Y21 := L21 A11
        L21_VC_STAR = L21;
        Zeros( Y21_VC_STAR, A21.Height(), A21.Width() );
        Hemm
        ( RIGHT, LOWER,
          F(1), A11_STAR_STAR.Matrix(), L21_VC_STAR.Matrix(),
          F(0), Y21_VC_STAR.Matrix() );
        Y21 = Y21_VC_STAR;

        // A21 := A21 inv(L11)'
        A21_VC_STAR = A21;
        LocalTrsm
        ( RIGHT, LOWER, ADJOINT, diag, F(1), L11_STAR_STAR, A21_VC_STAR );
        A21 = A21_VC_STAR;

        // A21 := A21 - 1/2 Y21
        Axpy( F(-1)/F(2), Y21, A21 );

        // A22 := A22 - (L21 A21' + A21 L21')
        A21_MC_STAR = A21;
        L21_MC_STAR = L21;
        A21_VC_STAR = A21_MC_STAR;
        A21_VR_STAR = A21_VC_STAR;
        L21_VR_STAR = L21_VC_STAR;
        A21Adj_STAR_MR.AdjointFrom( A21_VR_STAR );
        L21Adj_STAR_MR.AdjointFrom( L21_VR_STAR );
        LocalTrr2k
        ( LOWER,
          F(-1), L21_MC_STAR, A21Adj_STAR_MR,
          A21_MC_STAR, L21Adj_STAR_MR,
          F(1), A22 );

        // A21 := A21 - 1/2 Y21
        Axpy( F(-1)/F(2), Y21, A21 );

        // A21 := inv(L22) A21
        //
        // This is the bottleneck because A21 only has blocksize columns
        Trsm( LEFT, LOWER, NORMAL, diag, F(1), L22, A21 );
        //--------------------------------------------------------------------//

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

        SlideLockedPartitionDownDiagonal
        ( LTL, /**/ LTR,  L00, L01, /**/ L02,
          /**/       L10, L11, /**/ L12,
          /**********************************/
          LBL, /**/ LBR,  L20, L21, /**/ L22 );
    }
}
コード例 #15
0
ファイル: HegstRLVar3.hpp プロジェクト: ahmadia/elemental
inline void
internal::HegstRLVar3( DistMatrix<F,MC,MR>& A, const DistMatrix<F,MC,MR>& L )
{
#ifndef RELEASE
    PushCallStack("internal::HegstRLVar4");
    if( A.Height() != A.Width() )
        throw std::logic_error("A must be square");
    if( L.Height() != L.Width() )
        throw std::logic_error("Triangular matrices must be square");
    if( A.Height() != L.Height() )
        throw std::logic_error("A and L must be the same size");
#endif
    const Grid& g = A.Grid();

    // Matrix views
    DistMatrix<F,MC,MR>
    ATL(g), ATR(g),  A00(g), A01(g), A02(g),
        ABL(g), ABR(g),  A10(g), A11(g), A12(g),
        A20(g), A21(g), A22(g);
    DistMatrix<F,MC,MR>
    YTL(g), YTR(g),  Y00(g), Y01(g), Y02(g),
        YBL(g), YBR(g),  Y10(g), Y11(g), Y12(g),
        Y20(g), Y21(g), Y22(g);
    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);

    // Temporary distributions
    DistMatrix<F,STAR,MR  > A11_STAR_MR(g);
    DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
    DistMatrix<F,VC,  STAR> A21_VC_STAR(g);
    DistMatrix<F,STAR,VR  > A10_STAR_VR(g);
    DistMatrix<F,STAR,MR  > A10_STAR_MR(g);
    DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
    DistMatrix<F,STAR,VR  > L10_STAR_VR(g);
    DistMatrix<F,STAR,MR  > L10_STAR_MR(g);
    DistMatrix<F,MC,  STAR> L21_MC_STAR(g);
    DistMatrix<F,STAR,STAR> X11_STAR_STAR(g);
    DistMatrix<F,MC,  STAR> X21_MC_STAR(g);
    DistMatrix<F,MC,  STAR> Z21_MC_STAR(g);

    // We will use an entire extra matrix as temporary storage. If this is not
    // acceptable, use HegstRLVar4 instead.
    DistMatrix<F,MC,MR> Y(g);
    Y.AlignWith( A );
    Y.ResizeTo( A.Height(), A.Width() );
    Zero( Y );

    PartitionDownDiagonal
    ( A, ATL, ATR,
      ABL, ABR, 0 );
    PartitionDownDiagonal
    ( Y, YTL, YTR,
      YBL, YBR, 0 );
    LockedPartitionDownDiagonal
    ( L, LTL, LTR,
      LBL, LBR, 0 );
    while( ATL.Height() < A.Height() )
    {
        RepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ A01, A02,
          /*************/ /******************/
          /**/       A10, /**/ A11, A12,
          ABL, /**/ ABR,  A20, /**/ A21, A22 );

        RepartitionDownDiagonal
        ( YTL, /**/ YTR,  Y00, /**/ Y01, Y02,
          /*************/ /******************/
          /**/       Y10, /**/ Y11, Y12,
          YBL, /**/ YBR,  Y20, /**/ Y21, Y22 );

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

        A11_STAR_MR.AlignWith( Y21 );
        A21_VC_STAR.AlignWith( A21 );
        A10_STAR_VR.AlignWith( A10 );
        A10_STAR_MR.AlignWith( A10 );
        L10_STAR_VR.AlignWith( A10 );
        L10_STAR_MR.AlignWith( A10 );
        L21_MC_STAR.AlignWith( Y21 );
        X21_MC_STAR.AlignWith( A20 );
        Z21_MC_STAR.AlignWith( L20 );
        //--------------------------------------------------------------------//
        // A10 := A10 - 1/2 Y10
        Axpy( (F)-0.5, Y10, A10 );

        // A11 := A11 - (A10 L10' + L10 A10')
        A10_STAR_VR = A10;
        L10_STAR_VR = L10;
        X11_STAR_STAR.ResizeTo( A11.Height(), A11.Width() );
        Her2k
        ( LOWER, NORMAL,
          (F)1, A10_STAR_VR.LocalMatrix(), L10_STAR_VR.LocalMatrix(),
          (F)0, X11_STAR_STAR.LocalMatrix() );
        MakeTrapezoidal( LEFT, LOWER, 0, X11_STAR_STAR );
        A11.SumScatterUpdate( (F)-1, X11_STAR_STAR );

        // A11 := inv(L11) A11 inv(L11)'
        A11_STAR_STAR = A11;
        L11_STAR_STAR = L11;
        internal::LocalHegst( RIGHT, LOWER, A11_STAR_STAR, L11_STAR_STAR );
        A11 = A11_STAR_STAR;

        // A21 := A21 - A20 L10'
        L10_STAR_MR = L10_STAR_VR;
        X21_MC_STAR.ResizeTo( A21.Height(), A21.Width() );
        internal::LocalGemm
        ( NORMAL, ADJOINT, (F)1, A20, L10_STAR_MR, (F)0, X21_MC_STAR );
        A21.SumScatterUpdate( (F)-1, X21_MC_STAR );

        // A21 := A21 inv(L11)'
        A21_VC_STAR = A21;
        internal::LocalTrsm
        ( RIGHT, LOWER, ADJOINT, NON_UNIT, (F)1, L11_STAR_STAR, A21_VC_STAR );
        A21 = A21_VC_STAR;

        // A10 := A10 - 1/2 Y10
        Axpy( (F)-0.5, Y10, A10 );

        // A10 := inv(L11) A10
        A10_STAR_VR = A10;
        internal::LocalTrsm
        ( LEFT, LOWER, NORMAL, NON_UNIT,
          (F)1, L11_STAR_STAR, A10_STAR_VR );

        // Y20 := Y20 + L21 A10
        A10_STAR_MR = A10_STAR_VR;
        A10 = A10_STAR_MR;
        L21_MC_STAR = L21;
        internal::LocalGemm
        ( NORMAL, NORMAL, (F)1, L21_MC_STAR, A10_STAR_MR, (F)1, Y20 );

        // Y21 := L21 A11
        //
        // Symmetrize A11[* ,* ] by copying the lower triangle into the upper
        // so that we can call a local gemm instead of worrying about
        // reproducing a hemm with nonsymmetric local matrices.
        {
            const int height = A11_STAR_STAR.LocalHeight();
            const int ldim = A11_STAR_STAR.LocalLDim();
            F* A11Buffer = A11_STAR_STAR.LocalBuffer();
            for( int i=1; i<height; ++i )
                for( int j=0; j<i; ++j )
                    A11Buffer[j+i*ldim] = Conj(A11Buffer[i+j*ldim]);
        }
        A11_STAR_MR = A11_STAR_STAR;
        internal::LocalGemm
        ( NORMAL, NORMAL, (F)1, L21_MC_STAR, A11_STAR_MR, (F)0, Y21 );

        // Y21 := Y21 + L20 A10'
        Z21_MC_STAR.ResizeTo( A21.Height(), A21.Width() );
        internal::LocalGemm
        ( NORMAL, ADJOINT, (F)1, L20, A10_STAR_MR, (F)0, Z21_MC_STAR );
        Y21.SumScatterUpdate( (F)1, Z21_MC_STAR );
        //--------------------------------------------------------------------//
        A11_STAR_MR.FreeAlignments();
        A21_VC_STAR.FreeAlignments();
        A10_STAR_VR.FreeAlignments();
        A10_STAR_MR.FreeAlignments();
        L10_STAR_VR.FreeAlignments();
        L10_STAR_MR.FreeAlignments();
        L21_MC_STAR.FreeAlignments();
        X21_MC_STAR.FreeAlignments();
        Z21_MC_STAR.FreeAlignments();

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

        SlidePartitionDownDiagonal
        ( YTL, /**/ YTR,  Y00, Y01, /**/ Y02,
          /**/       Y10, Y11, /**/ Y12,
          /*************/ /******************/
          YBL, /**/ YBR,  Y20, Y21, /**/ Y22 );

        SlideLockedPartitionDownDiagonal
        ( LTL, /**/ LTR,  L00, L01, /**/ L02,
          /**/       L10, L11, /**/ L12,
          /**********************************/
          LBL, /**/ LBR,  L20, L21, /**/ L22 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #16
0
ファイル: UVar5.hpp プロジェクト: certik/Elemental
inline void
TwoSidedTrsmUVar5
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& U )
{
#ifndef RELEASE
    PushCallStack("internal::TwoSidedTrsmUVar5");
    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,STAR,MC  > A12_STAR_MC(g);
    DistMatrix<F,STAR,MR  > A12_STAR_MR(g);
    DistMatrix<F,STAR,VC  > A12_STAR_VC(g);
    DistMatrix<F,STAR,VR  > A12_STAR_VR(g);
    DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
    DistMatrix<F,STAR,MC  > U12_STAR_MC(g);
    DistMatrix<F,STAR,MR  > U12_STAR_MR(g);
    DistMatrix<F,STAR,VC  > U12_STAR_VC(g);
    DistMatrix<F,STAR,VR  > U12_STAR_VR(g);
    DistMatrix<F,STAR,VR  > Y12_STAR_VR(g);
    DistMatrix<F> Y12(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 );

        A12_STAR_MC.AlignWith( A22 );
        A12_STAR_MR.AlignWith( A22 );
        A12_STAR_VC.AlignWith( A22 );
        A12_STAR_VR.AlignWith( A22 );
        U12_STAR_MC.AlignWith( A22 );
        U12_STAR_MR.AlignWith( A22 );
        U12_STAR_VC.AlignWith( A22 );
        U12_STAR_VR.AlignWith( A22 );
        Y12.AlignWith( A12 );
        Y12_STAR_VR.AlignWith( A12 );
        //--------------------------------------------------------------------//
        // A11 := inv(U11)' A11 inv(U11)
        U11_STAR_STAR = U11;
        A11_STAR_STAR = A11;
        LocalTwoSidedTrsm( UPPER, diag, A11_STAR_STAR, U11_STAR_STAR );
        A11 = A11_STAR_STAR;

        // Y12 := A11 U12
        U12_STAR_VR = U12;
        Y12_STAR_VR.ResizeTo( A12.Height(), A12.Width() );
        Hemm
        ( LEFT, UPPER,
          F(1), A11_STAR_STAR.LocalMatrix(), U12_STAR_VR.LocalMatrix(),
          F(0), Y12_STAR_VR.LocalMatrix() );
        Y12 = Y12_STAR_VR;

        // 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;

        // A12 := A12 - 1/2 Y12
        Axpy( F(-1)/F(2), Y12, A12 );

        // A22 := A22 - (A12' U12 + U12' A12)
        A12_STAR_VR = A12;
        A12_STAR_VC = A12_STAR_VR;
        U12_STAR_VC = U12_STAR_VR;
        A12_STAR_MC = A12_STAR_VC;
        U12_STAR_MC = U12_STAR_VC;
        A12_STAR_MR = A12_STAR_VR;
        U12_STAR_MR = U12_STAR_VR;
        LocalTrr2k
        ( UPPER, ADJOINT, ADJOINT,
          F(-1), U12_STAR_MC, A12_STAR_MR,
                 A12_STAR_MC, U12_STAR_MR,
          F(1), A22 );

        // A12 := A12 - 1/2 Y12
        Axpy( F(-1)/F(2), Y12, A12 );

        // A12 := A12 inv(U22)
        //
        // This is the bottleneck because A12 only has blocksize rows
        Trsm( RIGHT, UPPER, NORMAL, diag, F(1), U22, A12 );
        //--------------------------------------------------------------------//
        A12_STAR_MC.FreeAlignments();
        A12_STAR_MR.FreeAlignments();
        A12_STAR_VC.FreeAlignments();
        A12_STAR_VR.FreeAlignments();
        U12_STAR_MC.FreeAlignments();
        U12_STAR_MR.FreeAlignments();
        U12_STAR_VC.FreeAlignments();
        U12_STAR_VR.FreeAlignments();
        Y12.FreeAlignments();
        Y12_STAR_VR.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
}
コード例 #17
0
ファイル: LSquare.hpp プロジェクト: ahmadia/Elemental-1
void LSquare
( DistMatrix<Complex<R> >& A,
  DistMatrix<Complex<R>,STAR,STAR>& t )
{
#ifndef RELEASE
    CallStackEntry entry("hermitian_tridiag::LSquare");
    if( A.Grid() != t.Grid() )
        throw std::logic_error("{A,t} must be distributed over the same grid");
#endif
    const Grid& g = A.Grid();
#ifndef RELEASE
    if( g.Height() != g.Width() )
        throw std::logic_error("The process grid must be square");
    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;

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

    // Matrix views 
    DistMatrix<C> 
        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> 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),  A11_MC_STAR(g),
                                              A21_MC_STAR(g);
    DistMatrix<C,MR,  STAR> APan_MR_STAR(g),  A11_MR_STAR(g),
                                              A21_MR_STAR(g);
    DistMatrix<C,MC,  STAR> WPan_MC_STAR(g),  W11_MC_STAR(g),
                                              W21_MC_STAR(g);
    DistMatrix<C,MR,  STAR> WPan_MR_STAR(g),  W11_MR_STAR(g),
                                              W21_MR_STAR(g);

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

        RepartitionDown
        ( tT,  t0,
         /**/ /**/
               t1,
          tB,  t2 );
            
        if( A22.Height() > 0 )
        {
            WPan.AlignWith( A11 );
            APan_MC_STAR.AlignWith( A11 );
            WPan_MC_STAR.AlignWith( A11 );
            APan_MR_STAR.AlignWith( A11 );
            WPan_MR_STAR.AlignWith( A11 );
            //----------------------------------------------------------------//
            WPan.ResizeTo( ABR.Height(), A11.Width() );
            APan_MC_STAR.ResizeTo( ABR.Height(), A11.Width() );
            WPan_MC_STAR.ResizeTo( ABR.Height(), A11.Width() );
            APan_MR_STAR.ResizeTo( ABR.Height(), A11.Width() );
            WPan_MR_STAR.ResizeTo( ABR.Height(), A11.Width() );

            hermitian_tridiag::PanelLSquare
            ( ABR, WPan, t1,
              APan_MC_STAR, APan_MR_STAR, WPan_MC_STAR, WPan_MR_STAR );

            PartitionDown
            ( APan_MC_STAR, A11_MC_STAR,
                            A21_MC_STAR, A11.Height() );
            PartitionDown
            ( APan_MR_STAR, A11_MR_STAR,
                            A21_MR_STAR, A11.Height() );
            PartitionDown
            ( WPan_MC_STAR, W11_MC_STAR,
                            W21_MC_STAR, A11.Height() );
            PartitionDown
            ( WPan_MR_STAR, W11_MR_STAR,
                            W21_MR_STAR, A11.Height() );

            LocalTrr2k
            ( LOWER, ADJOINT, ADJOINT,
              C(-1), A21_MC_STAR, W21_MR_STAR,
                     W21_MC_STAR, A21_MR_STAR,
              C(1), A22 );
            //----------------------------------------------------------------//
            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
            ( LOWER, A11_STAR_STAR.Matrix(), t1_STAR_STAR.Matrix() );

            A11 = A11_STAR_STAR;
            t1 = t1_STAR_STAR;
        }

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

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

    // Redistribute from matrix-diagonal form to fully replicated
    t = tDiag;
}
コード例 #18
0
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
}
コード例 #19
0
ファイル: UVar5.hpp プロジェクト: jimgoo/Elemental
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
}
コード例 #20
0
inline void
internal::CholeskyUVar3Square( DistMatrix<F,MC,MR>& A )
{
#ifndef RELEASE
    PushCallStack("internal::CholeskyUVar3Square");
    if( A.Height() != A.Width() )
        throw std::logic_error
        ("Can only compute Cholesky factor of square matrices.");
    if( A.Grid().Height() != A.Grid().Width() )
        throw std::logic_error
        ("CholeskyUVar3Square assumes a square process grid.");
#endif
    const Grid& g = A.Grid();

    // Find the process holding our transposed data
    const int r = g.Height();
    int transposeRank;
    {
        const int colAlignment = A.ColAlignment();
        const int rowAlignment = A.RowAlignment();
        const int colShift = A.ColShift();
        const int rowShift = A.RowShift();

        const int transposeRow = (colAlignment+rowShift) % r;
        const int transposeCol = (rowAlignment+colShift) % r;
        transposeRank = transposeRow + r*transposeCol;
    }
    const bool onDiagonal = ( transposeRank == g.VCRank() );

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

    // Temporary matrix distributions
    DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
    DistMatrix<F,STAR,VR  > A12_STAR_VR(g);
    DistMatrix<F,STAR,MC  > A12_STAR_MC(g);
    DistMatrix<F,STAR,MR  > A12_STAR_MR(g);

    // Start the algorithm
    PartitionDownDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 ); 
    while( ABR.Height() > 0 )
    {
        RepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ A01, A02,
         /*************/ /******************/
               /**/       A10, /**/ A11, A12,
          ABL, /**/ ABR,  A20, /**/ A21, A22 );

        A12_STAR_MC.AlignWith( A22 );
        A12_STAR_MR.AlignWith( A22 );
        A12_STAR_VR.AlignWith( A22 );
        //--------------------------------------------------------------------//
        A11_STAR_STAR = A11;
        internal::LocalCholesky( UPPER, A11_STAR_STAR );
        A11 = A11_STAR_STAR;

        A12_STAR_VR = A12;
        internal::LocalTrsm
        ( LEFT, UPPER, ADJOINT, NON_UNIT, (F)1, A11_STAR_STAR, A12_STAR_VR );

        A12_STAR_MR = A12_STAR_VR;
        // SendRecv to form A12[* ,MC] from A12[* ,MR]
        A12_STAR_MC.ResizeTo( A12.Height(), A12.Width() );
        {
            if( onDiagonal )
            {
                const int size = A11.Height()*A22.LocalWidth();
                MemCopy
                ( A12_STAR_MC.LocalBuffer(), 
                  A12_STAR_MR.LocalBuffer(), size );
            }
            else
            {
                const int sendSize = A11.Height()*A22.LocalWidth();
                const int recvSize = A11.Width()*A22.LocalHeight();
                // We know that the ldim is the height since we have manually
                // created both temporary matrices.
                mpi::SendRecv
                ( A12_STAR_MR.LocalBuffer(), sendSize, transposeRank, 0,
                  A12_STAR_MC.LocalBuffer(), recvSize, transposeRank, 0,
                  g.VCComm() );
            }
        }
        internal::LocalTrrk
        ( UPPER, ADJOINT, (F)-1, A12_STAR_MC, A12_STAR_MR, (F)1, A22 );
        A12 = A12_STAR_MR;
        //--------------------------------------------------------------------//
        A12_STAR_MC.FreeAlignments();
        A12_STAR_MR.FreeAlignments();
        A12_STAR_VR.FreeAlignments();

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, A01, /**/ A02,
               /**/       A10, A11, /**/ A12,
         /*************/ /******************/
          ABL, /**/ ABR,  A20, A21, /**/ A22 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #21
0
ファイル: LQ.hpp プロジェクト: ahmadia/elemental
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
}
コード例 #22
0
ファイル: HegstLLVar4.hpp プロジェクト: ahmadia/elemental
inline void
internal::HegstLLVar4( DistMatrix<F,MC,MR>& A, const DistMatrix<F,MC,MR>& L )
{
#ifndef RELEASE
    PushCallStack("internal::HegstLLVar4");
    if( A.Height() != A.Width() )
        throw std::logic_error("A must be square");
    if( L.Height() != L.Width() )
        throw std::logic_error("Triangular matrices must be square");
    if( A.Height() != L.Height() )
        throw std::logic_error("A and L must be the same size");
#endif
    const Grid& g = A.Grid();

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

    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);

    // Temporary distributions
    DistMatrix<F,STAR,VR  > A10_STAR_VR(g);
    DistMatrix<F,STAR,MR  > A10_STAR_MR(g);
    DistMatrix<F,STAR,MC  > A10_STAR_MC(g);
    DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
    DistMatrix<F,VC,  STAR> A21_VC_STAR(g);
    DistMatrix<F,MC,  STAR> A21_MC_STAR(g);
    DistMatrix<F,STAR,VR  > L10_STAR_VR(g);
    DistMatrix<F,STAR,MR  > L10_STAR_MR(g);
    DistMatrix<F,STAR,MC  > L10_STAR_MC(g);
    DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
    DistMatrix<F,STAR,VR  > Y10_STAR_VR(g);

    PartitionDownDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 );
    LockedPartitionDownDiagonal
    ( L, LTL, LTR,
         LBL, LBR, 0 );
    while( ATL.Height() < A.Height() )
    {
        RepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ A01, A02,
         /*************/ /******************/
               /**/       A10, /**/ A11, A12,
          ABL, /**/ ABR,  A20, /**/ A21, A22 );

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

        A10_STAR_VR.AlignWith( A00 );
        A10_STAR_MR.AlignWith( A00 );
        A10_STAR_MC.AlignWith( A00 );
        A21_MC_STAR.AlignWith( A20 );
        L10_STAR_VR.AlignWith( A00 );
        L10_STAR_MR.AlignWith( A00 );
        L10_STAR_MC.AlignWith( A00 );
        Y10_STAR_VR.AlignWith( A10 );
        //--------------------------------------------------------------------//
        // Y10 := A11 L10
        A11_STAR_STAR = A11;
        L10_STAR_VR = L10;
        Y10_STAR_VR.ResizeTo( A10.Height(), A10.Width() );
        Zero( Y10_STAR_VR );
        Hemm
        ( LEFT, LOWER,
          (F)0.5, A11_STAR_STAR.LockedLocalMatrix(),
                  L10_STAR_VR.LockedLocalMatrix(),
          (F)0,   Y10_STAR_VR.LocalMatrix() );

        // A10 := A10 + 1/2 Y10
        A10_STAR_VR = A10;
        Axpy( (F)1, Y10_STAR_VR, A10_STAR_VR );

        // A00 := A00 + (A10' L10 + L10' A10)
        A10_STAR_MR = A10_STAR_VR;
        A10_STAR_MC = A10_STAR_VR;
        L10_STAR_MR = L10_STAR_VR;
        L10_STAR_MC = L10_STAR_VR;
        internal::LocalTrr2k
        ( LOWER, ADJOINT, ADJOINT,
          (F)1, A10_STAR_MC, L10_STAR_MR, 
                L10_STAR_MC, A10_STAR_MR, 
          (F)1, A00 );

        // A10 := A10 + 1/2 Y10
        Axpy( (F)1, Y10_STAR_VR, A10_STAR_VR );

        // A10 := L11' A10
        L11_STAR_STAR = L11;
        internal::LocalTrmm
        ( LEFT, LOWER, ADJOINT, NON_UNIT, (F)1, L11_STAR_STAR, A10_STAR_VR );
        A10 = A10_STAR_VR;

        // A20 := A20 + A21 L10
        A21_MC_STAR = A21;
        internal::LocalGemm
        ( NORMAL, NORMAL, (F)1, A21_MC_STAR, L10_STAR_MR, (F)1, A20 );

        // A11 := L11' A11 L11
        internal::LocalHegst
        ( LEFT, LOWER, A11_STAR_STAR, L11_STAR_STAR );
        A11 = A11_STAR_STAR;

        // A21 := A21 L11
        A21_VC_STAR = A21_MC_STAR;
        internal::LocalTrmm
        ( RIGHT, LOWER, NORMAL, NON_UNIT, (F)1, L11_STAR_STAR, A21_VC_STAR );
        A21 = A21_VC_STAR;
        //--------------------------------------------------------------------//
        A10_STAR_VR.FreeAlignments();
        A10_STAR_MR.FreeAlignments();
        A10_STAR_MC.FreeAlignments();
        A21_MC_STAR.FreeAlignments();
        L10_STAR_VR.FreeAlignments();
        L10_STAR_MR.FreeAlignments();
        L10_STAR_MC.FreeAlignments();
        Y10_STAR_VR.FreeAlignments();

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

        SlideLockedPartitionDownDiagonal
        ( LTL, /**/ LTR,  L00, L01, /**/ L02,
               /**/       L10, L11, /**/ L12,
         /*************/ /******************/
          LBL, /**/ LBR,  L20, L21, /**/ L22 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #23
0
ファイル: LU.hpp プロジェクト: jimgoo/Elemental
inline void
LocalSymmetricAccumulateLU
( Orientation orientation, T alpha,
  const DistMatrix<T>& A,
  const DistMatrix<T,MC,  STAR>& B_MC_STAR,
  const DistMatrix<T,STAR,MR  >& BAdjOrTrans_STAR_MR,
        DistMatrix<T,MC,  STAR>& Z_MC_STAR,
        DistMatrix<T,MR,  STAR>& Z_MR_STAR )
{
#ifndef RELEASE
    PushCallStack("internal::LocalSymmetricAccumulateLU");
    if( A.Grid() != B_MC_STAR.Grid() ||
        B_MC_STAR.Grid() != BAdjOrTrans_STAR_MR.Grid() ||
        BAdjOrTrans_STAR_MR.Grid() != Z_MC_STAR.Grid() ||
        Z_MC_STAR.Grid() != Z_MR_STAR.Grid() )
        throw std::logic_error
        ("{A,B,Z} must be distributed over the same grid");
    if( A.Height() != A.Width() ||
        A.Height() != B_MC_STAR.Height() ||
        A.Height() != BAdjOrTrans_STAR_MR.Width() ||
        A.Height() != Z_MC_STAR.Height() ||
        A.Height() != Z_MR_STAR.Height() ||
        B_MC_STAR.Width() != BAdjOrTrans_STAR_MR.Height() ||
        BAdjOrTrans_STAR_MR.Height() != Z_MC_STAR.Width() ||
        Z_MC_STAR.Width() != Z_MR_STAR.Width() )
    {
        std::ostringstream msg;
        msg << "Nonconformal LocalSymmetricAccumulateLU: \n"
            << "  A ~ " << A.Height() << " x " << A.Width() << "\n"
            << "  B[MC,* ] ~ " << B_MC_STAR.Height() << " x "
                               << B_MC_STAR.Width() << "\n"
            << "  B^H/T[* ,MR] ~ " << BAdjOrTrans_STAR_MR.Height() << " x "
                                   << BAdjOrTrans_STAR_MR.Width() << "\n"
            << "  Z[MC,* ] ~ " << Z_MC_STAR.Height() << " x "
                               << Z_MC_STAR.Width() << "\n"
            << "  Z[MR,* ] ` " << Z_MR_STAR.Height() << " x "
                               << Z_MR_STAR.Width() << "\n";
        throw std::logic_error( msg.str().c_str() );
    }
    if( B_MC_STAR.ColAlignment() != A.ColAlignment() ||
        BAdjOrTrans_STAR_MR.RowAlignment() != A.RowAlignment() ||
        Z_MC_STAR.ColAlignment() != A.ColAlignment() ||
        Z_MR_STAR.ColAlignment() != A.RowAlignment() )
        throw std::logic_error("Partial matrix distributions are misaligned");
#endif
    const Grid& g = A.Grid();

    DistMatrix<T>
        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<T> D11(g);

    DistMatrix<T,MC,STAR>
        BT_MC_STAR(g),  B0_MC_STAR(g),
        BB_MC_STAR(g),  B1_MC_STAR(g),
                        B2_MC_STAR(g);

    DistMatrix<T,STAR,MR>
        BLAdjOrTrans_STAR_MR(g), BRAdjOrTrans_STAR_MR(g),
        B0AdjOrTrans_STAR_MR(g), B1AdjOrTrans_STAR_MR(g), 
        B2AdjOrTrans_STAR_MR(g);

    DistMatrix<T,MC,STAR>
        ZT_MC_STAR(g),  Z0_MC_STAR(g),
        ZB_MC_STAR(g),  Z1_MC_STAR(g),
                        Z2_MC_STAR(g);

    DistMatrix<T,MR,STAR>
        ZT_MR_STAR(g),  Z0_MR_STAR(g),
        ZB_MR_STAR(g),  Z1_MR_STAR(g),
                        Z2_MR_STAR(g);

    const int ratio = std::max( g.Height(), g.Width() );
    PushBlocksizeStack( ratio*Blocksize() );

    LockedPartitionDownDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 );
    LockedPartitionDown
    ( B_MC_STAR, BT_MC_STAR,
                 BB_MC_STAR, 0 );
    LockedPartitionRight
    ( BAdjOrTrans_STAR_MR, BLAdjOrTrans_STAR_MR, BRAdjOrTrans_STAR_MR, 0 );
    PartitionDown
    ( Z_MC_STAR, ZT_MC_STAR,
                 ZB_MC_STAR, 0 );
    PartitionDown
    ( Z_MR_STAR, ZT_MR_STAR,
                 ZB_MR_STAR, 0 );
    while( ATL.Height() < A.Height() )
    {
        LockedRepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ A01, A02,
          /************/ /******************/
               /**/       A10, /**/ A11, A12,
          ABL, /**/ ABR,  A20, /**/ A21, A22 );

        LockedRepartitionDown
        ( BT_MC_STAR,  B0_MC_STAR,
         /**********/ /**********/
                       B1_MC_STAR,
          BB_MC_STAR,  B2_MC_STAR );

        LockedRepartitionRight
        ( BLAdjOrTrans_STAR_MR, /**/ BRAdjOrTrans_STAR_MR,
          B0AdjOrTrans_STAR_MR, /**/ B1AdjOrTrans_STAR_MR, 
                                     B2AdjOrTrans_STAR_MR );

        RepartitionDown
        ( ZT_MC_STAR,  Z0_MC_STAR,
         /**********/ /**********/
                       Z1_MC_STAR,
          ZB_MC_STAR,  Z2_MC_STAR );

        RepartitionDown
        ( ZT_MR_STAR,  Z0_MR_STAR,
         /**********/ /**********/
                       Z1_MR_STAR,
          ZB_MR_STAR,  Z2_MR_STAR );

        D11.AlignWith( A11 );
        //--------------------------------------------------------------------//
        D11 = A11;
        MakeTrapezoidal( LEFT, UPPER, 0, D11 );
        LocalGemm
        ( NORMAL, orientation, 
          alpha, D11, B1AdjOrTrans_STAR_MR, T(1), Z1_MC_STAR );
        MakeTrapezoidal( LEFT, UPPER, 1, D11 );

        LocalGemm
        ( orientation, NORMAL, alpha, D11, B1_MC_STAR, T(1), Z1_MR_STAR );

        LocalGemm
        ( NORMAL, orientation, 
          alpha, A12, B2AdjOrTrans_STAR_MR, T(1), Z1_MC_STAR );

        LocalGemm
        ( orientation, NORMAL, alpha, A12, B1_MC_STAR, T(1), Z2_MR_STAR );
        //--------------------------------------------------------------------//
        D11.FreeAlignments();

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

        SlideLockedPartitionDown
        ( BT_MC_STAR,  B0_MC_STAR,
                       B1_MC_STAR,
         /**********/ /**********/
          BB_MC_STAR,  B2_MC_STAR );

        SlideLockedPartitionRight
        ( BLAdjOrTrans_STAR_MR,                       /**/ BRAdjOrTrans_STAR_MR,
          B0AdjOrTrans_STAR_MR, B1AdjOrTrans_STAR_MR, /**/ B2AdjOrTrans_STAR_MR         );

        SlidePartitionDown
        ( ZT_MC_STAR,  Z0_MC_STAR,
                       Z1_MC_STAR,
         /**********/ /**********/
          ZB_MC_STAR,  Z2_MC_STAR );

        SlidePartitionDown
        ( ZT_MR_STAR,  Z0_MR_STAR,
                       Z1_MR_STAR,
         /**********/ /**********/
          ZB_MR_STAR,  Z2_MR_STAR );
    }
    PopBlocksizeStack();
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #24
0
ファイル: UVar4.hpp プロジェクト: khalid-hasanov/Elemental
inline void
TwoSidedTrsmUVar4
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& U )
{
#ifndef RELEASE
    CallStackEntry entry("internal::TwoSidedTrsmUVar4");
    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,VC,  STAR> A01_VC_STAR(g);
    DistMatrix<F,STAR,MC  > A01Trans_STAR_MC(g);
    DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
    DistMatrix<F,STAR,VR  > A12_STAR_VR(g);
    DistMatrix<F,STAR,VC  > A12_STAR_VC(g);
    DistMatrix<F,STAR,MC  > A12_STAR_MC(g);
    DistMatrix<F,STAR,MR  > A12_STAR_MR(g);
    DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
    DistMatrix<F,MR,  STAR> U12Trans_MR_STAR(g);
    DistMatrix<F,VR,  STAR> U12Trans_VR_STAR(g);
    DistMatrix<F,STAR,VR  > U12_STAR_VR(g);
    DistMatrix<F,STAR,VC  > U12_STAR_VC(g);
    DistMatrix<F,STAR,MC  > U12_STAR_MC(g);
    DistMatrix<F,STAR,VR  > Y12_STAR_VR(g);

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

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

        A01_VC_STAR.AlignWith( A02 );
        A01Trans_STAR_MC.AlignWith( A02 );
        A12_STAR_VR.AlignWith( A22 );
        A12_STAR_VC.AlignWith( A22 );
        A12_STAR_MC.AlignWith( A22 );
        A12_STAR_MR.AlignWith( A22 );
        U12Trans_MR_STAR.AlignWith( A02 );
        U12Trans_VR_STAR.AlignWith( A02 );
        U12_STAR_VR.AlignWith( A02 );
        U12_STAR_VC.AlignWith( A22 );
        U12_STAR_MC.AlignWith( A22 );
        Y12_STAR_VR.AlignWith( A12 );
        //--------------------------------------------------------------------//
        // A01 := A01 inv(U11)
        A01_VC_STAR = A01;
        U11_STAR_STAR = U11;
        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;

        // A02 := A02 - A01 U12
        A01Trans_STAR_MC.TransposeFrom( A01_VC_STAR );
        U12Trans_MR_STAR.TransposeFrom( U12 );
        LocalGemm
        ( TRANSPOSE, TRANSPOSE, 
          F(-1), A01Trans_STAR_MC, U12Trans_MR_STAR, F(1), A02 );

        // Y12 := A11 U12
        U12Trans_VR_STAR = U12Trans_MR_STAR;
        Zeros( U12_STAR_VR, A12.Height(), A12.Width() );
        Transpose( U12Trans_VR_STAR.Matrix(), U12_STAR_VR.Matrix() );
        Zeros( Y12_STAR_VR, A12.Height(), A12.Width() );
        Hemm
        ( LEFT, UPPER, 
          F(1), A11_STAR_STAR.Matrix(), U12_STAR_VR.Matrix(), 
          F(0), Y12_STAR_VR.Matrix() );

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

        // A12 := A12 - 1/2 Y12
        Axpy( F(-1)/F(2), Y12_STAR_VR, A12_STAR_VR );

        // A22 := A22 - (A12' U12 + U12' A12)
        A12_STAR_MR = A12_STAR_VR;
        A12_STAR_VC = A12_STAR_VR;
        U12_STAR_VC = U12_STAR_VR;
        A12_STAR_MC = A12_STAR_VC;
        U12_STAR_MC = U12_STAR_VC;
        LocalTrr2k
        ( UPPER, ADJOINT, TRANSPOSE, ADJOINT,
          F(-1), A12_STAR_MC, U12Trans_MR_STAR,
                 U12_STAR_MC, A12_STAR_MR,
          F(1), A22 );

        // A12 := A12 - 1/2 Y12
        Axpy( F(-1)/F(2), Y12_STAR_VR, 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 );
    }
}
コード例 #25
0
ファイル: UVar3.hpp プロジェクト: jimgoo/Elemental
inline void
CholeskyUVar3( DistMatrix<F>& A )
{
#ifndef RELEASE
    PushCallStack("internal::CholeskyUVar3");
    if( A.Height() != A.Width() )
        throw std::logic_error
        ("Can only compute Cholesky factor of square matrices");
#endif
    const Grid& g = A.Grid();

    // Matrix views
    DistMatrix<F> 
        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 matrix distributions
    DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
    DistMatrix<F,STAR,VR  > A12_STAR_VR(g);
    DistMatrix<F,STAR,MC  > A12_STAR_MC(g);
    DistMatrix<F,STAR,MR  > A12_STAR_MR(g);

    // Start the algorithm
    PartitionDownDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 ); 
    while( ABR.Height() > 0 )
    {
        RepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ A01, A02,
         /*************/ /******************/
               /**/       A10, /**/ A11, A12,
          ABL, /**/ ABR,  A20, /**/ A21, A22 );

        A12_STAR_MC.AlignWith( A22 );
        A12_STAR_MR.AlignWith( A22 );
        A12_STAR_VR.AlignWith( A22 );
        //--------------------------------------------------------------------//
        A11_STAR_STAR = A11;
        LocalCholesky( UPPER, A11_STAR_STAR );
        A11 = A11_STAR_STAR;

        A12_STAR_VR = A12;
        LocalTrsm
        ( LEFT, UPPER, ADJOINT, NON_UNIT, F(1), A11_STAR_STAR, A12_STAR_VR );

        A12_STAR_MC = A12_STAR_VR;
        A12_STAR_MR = A12_STAR_VR;
        LocalTrrk
        ( UPPER, ADJOINT, F(-1), A12_STAR_MC, A12_STAR_MR, F(1), A22 );
        A12 = A12_STAR_MR;
        //--------------------------------------------------------------------//
        A12_STAR_MC.FreeAlignments();
        A12_STAR_MR.FreeAlignments();
        A12_STAR_VR.FreeAlignments();

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, A01, /**/ A02,
               /**/       A10, A11, /**/ A12,
         /*************/ /******************/
          ABL, /**/ ABR,  A20, A21, /**/ A22 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #26
0
ファイル: LU.hpp プロジェクト: ahmadia/Elemental-1
inline void
LU( DistMatrix<F>& A, DistMatrix<int,VC,STAR>& p )
{
#ifndef RELEASE
    CallStackEntry entry("LU");
    if( A.Grid() != p.Grid() )
        throw std::logic_error("{A,p} must be distributed over the same grid");
    if( p.Viewing() && 
        (std::min(A.Height(),A.Width()) != p.Height() || p.Width() != 1) ) 
        throw std::logic_error
        ("p must be a vector of the same height as the min dimension of A.");
#endif
    const Grid& g = A.Grid();
    if( !p.Viewing() )
        p.ResizeTo( std::min(A.Height(),A.Width()), 1 );

    // Matrix views
    DistMatrix<F>
        ATL(g), ATR(g),  A00(g), A01(g), A02(g),  AB(g),
        ABL(g), ABR(g),  A10(g), A11(g), A12(g),  
                         A20(g), A21(g), A22(g);

    DistMatrix<int,VC,STAR>
        pT(g),  p0(g), 
        pB(g),  p1(g),
                p2(g);

    // Temporary distributions
    DistMatrix<F,  STAR,STAR> A11_STAR_STAR(g);
    DistMatrix<F,  MC,  STAR> A21_MC_STAR(g);
    DistMatrix<F,  STAR,VR  > A12_STAR_VR(g);
    DistMatrix<F,  STAR,MR  > A12_STAR_MR(g);
    DistMatrix<int,STAR,STAR> p1_STAR_STAR(g);

    // Pivot composition
    std::vector<int> image, preimage;

    // Start the algorithm
    PartitionDownDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 );
    PartitionDown
    ( p, pT,
         pB, 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
        ( pT,  p0,
         /**/ /**/
               p1,
          pB,  p2 );

        View1x2( AB, ABL, ABR );

        const int pivotOffset = A01.Height();
        A12_STAR_VR.AlignWith( A22 );
        A12_STAR_MR.AlignWith( A22 );
        A21_MC_STAR.AlignWith( A22 );
        A11_STAR_STAR.ResizeTo( A11.Height(), A11.Width() );
        p1_STAR_STAR.ResizeTo( p1.Height(), 1 );
        //--------------------------------------------------------------------//
        A21_MC_STAR = A21;
        A11_STAR_STAR = A11;
        lu::Panel( A11_STAR_STAR, A21_MC_STAR, p1_STAR_STAR, pivotOffset );
        ComposePivots( p1_STAR_STAR, pivotOffset, image, preimage );
        ApplyRowPivots( AB, image, preimage );

        // Perhaps we should give up perfectly distributing this operation since
        // it's total contribution is only O(n^2)
        A12_STAR_VR = A12;
        LocalTrsm
        ( LEFT, LOWER, NORMAL, UNIT, F(1), A11_STAR_STAR, A12_STAR_VR );

        A12_STAR_MR = A12_STAR_VR;
        LocalGemm( NORMAL, NORMAL, F(-1), A21_MC_STAR, A12_STAR_MR, F(1), A22 );

        A11 = A11_STAR_STAR;
        A12 = A12_STAR_MR;
        A21 = A21_MC_STAR;
        p1 = p1_STAR_STAR;
        //--------------------------------------------------------------------//
        A12_STAR_VR.FreeAlignments();
        A12_STAR_MR.FreeAlignments();
        A21_MC_STAR.FreeAlignments();

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

        SlidePartitionDown
        ( pT,  p0,
               p1,
         /**/ /**/
          pB,  p2 );
    }
}
コード例 #27
0
ファイル: LVar2.hpp プロジェクト: certik/Elemental
inline void
HPDInverseLVar2( DistMatrix<F>& A )
{
#ifndef RELEASE
    PushCallStack("internal::HPDInverseLVar2");
    if( A.Height() != A.Width() )
        throw std::logic_error("Nonsquare matrices cannot be triangular");
#endif
    const Grid& g = A.Grid();

    // Matrix views
    DistMatrix<F> 
        ATL(g), ATR(g),  A00(g), A01(g), A02(g),
        ABL(g), ABR(g),  A10(g), A11(g), A12(g),
                         A20(g), A21(g), A22(g);

    // Temporary distributions
    DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
    DistMatrix<F,STAR,VR  > A10_STAR_VR(g);
    DistMatrix<F,VC,  STAR> A21_VC_STAR(g);
    DistMatrix<F,STAR,MC  > A10_STAR_MC(g);
    DistMatrix<F,STAR,MR  > A10_STAR_MR(g);
    DistMatrix<F,STAR,MC  > A21Trans_STAR_MC(g);
    DistMatrix<F,VR,  STAR> A21_VR_STAR(g);
    DistMatrix<F,STAR,MR  > A21Adj_STAR_MR(g);

    // Start the algorithm
    PartitionDownDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 );
    while( ATL.Height() < A.Height() )
    {
        RepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ A01, A02,
         /*************/ /******************/
               /**/       A10, /**/ A11, A12,
          ABL, /**/ ABR,  A20, /**/ A21, A22 );

        A10_STAR_VR.AlignWith( A00 );
        A21_VC_STAR.AlignWith( A20 );
        A10_STAR_MC.AlignWith( A00 );
        A10_STAR_MR.AlignWith( A00 );
        A21Trans_STAR_MC.AlignWith( A20 );
        A21_VR_STAR.AlignWith( A22 );
        A21Adj_STAR_MR.AlignWith( A22 );
        //--------------------------------------------------------------------//
        A11_STAR_STAR = A11;
        LocalCholesky( LOWER, A11_STAR_STAR );

        A10_STAR_VR = A10;
        LocalTrsm
        ( LEFT, LOWER, NORMAL, NON_UNIT, F(1), A11_STAR_STAR, A10_STAR_VR );

        A21_VC_STAR = A21;
        LocalTrsm
        ( RIGHT, LOWER, ADJOINT, NON_UNIT, F(1), A11_STAR_STAR, A21_VC_STAR );

        A10_STAR_MC = A10_STAR_VR;
        A10_STAR_MR = A10_STAR_VR;
        LocalTrrk
        ( LOWER, ADJOINT,
          F(1), A10_STAR_MC, A10_STAR_MR, F(1), A00 );

        A21Trans_STAR_MC.TransposeFrom( A21_VC_STAR );
        LocalGemm
        ( TRANSPOSE, NORMAL, F(-1), A21Trans_STAR_MC, A10_STAR_MR, F(1), A20 );

        A21_VR_STAR = A21_VC_STAR;
        A21Adj_STAR_MR.AdjointFrom( A21_VR_STAR );
        LocalTrrk
        ( LOWER, TRANSPOSE,
          F(-1), A21Trans_STAR_MC, A21Adj_STAR_MR, F(1), A22 );

        LocalTrsm
        ( LEFT, LOWER, ADJOINT, NON_UNIT, F(1), A11_STAR_STAR, A10_STAR_VR );

        LocalTrsm
        ( RIGHT, LOWER, NORMAL, NON_UNIT, F(-1), A11_STAR_STAR, A21_VC_STAR );

        LocalTriangularInverse( LOWER, NON_UNIT, A11_STAR_STAR );

        LocalTrtrmm( ADJOINT, LOWER, A11_STAR_STAR );

        A11 = A11_STAR_STAR;
        A10 = A10_STAR_VR;
        A21 = A21_VC_STAR;
        //--------------------------------------------------------------------//
        A10_STAR_VR.FreeAlignments();
        A21_VC_STAR.FreeAlignments();
        A10_STAR_MC.FreeAlignments();
        A10_STAR_MR.FreeAlignments();
        A21Trans_STAR_MC.FreeAlignments();
        A21_VR_STAR.FreeAlignments();
        A21Adj_STAR_MR.FreeAlignments();

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, A01, /**/ A02,
               /**/       A10, A11, /**/ A12,
         /*************/ /******************/
          ABL, /**/ ABR,  A20, A21, /**/ A22 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #28
0
ファイル: LU.hpp プロジェクト: ahmadia/Elemental-1
inline void
LU( DistMatrix<F>& A )
{
#ifndef RELEASE
    CallStackEntry entry("LU");
#endif
    const Grid& g = A.Grid();

    // Matrix views
    DistMatrix<F>
        ATL(g), ATR(g),  A00(g), A01(g), A02(g), 
        ABL(g), ABR(g),  A10(g), A11(g), A12(g),  
                         A20(g), A21(g), A22(g);

    // Temporary distributions
    DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
    DistMatrix<F,MC,  STAR> A21_MC_STAR(g);
    DistMatrix<F,STAR,VR  > A12_STAR_VR(g);
    DistMatrix<F,STAR,MR  > A12_STAR_MR(g);

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

        A12_STAR_VR.AlignWith( A22 );
        A12_STAR_MR.AlignWith( A22 );
        A21_MC_STAR.AlignWith( A22 );
        A11_STAR_STAR.ResizeTo( A11.Height(), A11.Width() );
        //--------------------------------------------------------------------//
        A11_STAR_STAR = A11;
        LocalLU( A11_STAR_STAR );
        A11 = A11_STAR_STAR;

        A21_MC_STAR = A21;
        LocalTrsm
        ( RIGHT, UPPER, NORMAL, NON_UNIT, F(1), A11_STAR_STAR, A21_MC_STAR );
        A21 = A21_MC_STAR;

        // Perhaps we should give up perfectly distributing this operation since
        // it's total contribution is only O(n^2)
        A12_STAR_VR = A12;
        LocalTrsm
        ( LEFT, LOWER, NORMAL, UNIT, F(1), A11_STAR_STAR, A12_STAR_VR );

        A12_STAR_MR = A12_STAR_VR;
        LocalGemm( NORMAL, NORMAL, F(-1), A21_MC_STAR, A12_STAR_MR, F(1), A22 );
        A12 = A12_STAR_MR;
        //--------------------------------------------------------------------//
        A12_STAR_VR.FreeAlignments();
        A12_STAR_MR.FreeAlignments();
        A21_MC_STAR.FreeAlignments();

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, A01, /**/ A02,
               /**/       A10, A11, /**/ A12,
         /*************/ /******************/
          ABL, /**/ ABR,  A20, A21, /**/ A22 );
    }
}
コード例 #29
0
ファイル: LVar2.hpp プロジェクト: khalid-hasanov/Elemental
inline void
LVar2( DistMatrix<F>& A )
{
#ifndef RELEASE
    CallStackEntry entry("cholesky::LVar2");
    if( A.Height() != A.Width() )
        LogicError("Can only compute Cholesky factor of square matrices");
#endif
    const Grid& g = A.Grid();

    // Matrix views
    DistMatrix<F> 
        ATL(g), ATR(g),   A00(g), A01(g), A02(g),
        ABL(g), ABR(g),   A10(g), A11(g), A12(g),
                          A20(g), A21(g), A22(g);

    // Temporary distributions
    DistMatrix<F,MR,  STAR> A10Adj_MR_STAR(g);
    DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
    DistMatrix<F,VC,  STAR> A21_VC_STAR(g);
    DistMatrix<F,MC,  STAR> X11_MC_STAR(g);
    DistMatrix<F,MC,  STAR> X21_MC_STAR(g);

    // Start the algorithm
    PartitionDownDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 );
    while( ATL.Height() < A.Height() )
    {
        RepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ A01, A02,
         /*************/ /******************/
               /**/       A10, /**/ A11, A12,
          ABL, /**/ ABR,  A20, /**/ A21, A22 );

        A10Adj_MR_STAR.AlignWith( A10 );
        X11_MC_STAR.AlignWith( A10 );
        X21_MC_STAR.AlignWith( A20 );
        //--------------------------------------------------------------------//
        A10Adj_MR_STAR.AdjointFrom( A10 );
        LocalGemm( NORMAL, NORMAL, F(1), A10, A10Adj_MR_STAR, X11_MC_STAR );
        A11.SumScatterUpdate( F(-1), X11_MC_STAR );

        A11_STAR_STAR = A11;
        LocalCholesky( LOWER, A11_STAR_STAR );
        A11 = A11_STAR_STAR;

        LocalGemm( NORMAL, NORMAL, F(1), A20, A10Adj_MR_STAR, X21_MC_STAR );
        A21.SumScatterUpdate( F(-1), X21_MC_STAR );

        A21_VC_STAR = A21;
        LocalTrsm
        ( RIGHT, LOWER, ADJOINT, NON_UNIT, F(1), A11_STAR_STAR, A21_VC_STAR );
        A21 = A21_VC_STAR;
        //--------------------------------------------------------------------//

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, A01, /**/ A02,
               /**/       A10, A11, /**/ A12,
         /*************/ /******************/
          ABL, /**/ ABR,  A20, A21, /**/ A22 );
    }
}
コード例 #30
0
ファイル: LVar4.hpp プロジェクト: khalid-hasanov/Elemental
inline void
TwoSidedTrmmLVar4
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& L )
{
#ifndef RELEASE
    CallStackEntry entry("internal::TwoSidedTrmmLVar4");
    if( A.Height() != A.Width() )
        LogicError("A must be square");
    if( L.Height() != L.Width() )
        LogicError("Triangular matrices must be square");
    if( A.Height() != L.Height() )
        LogicError("A and L must be the same size");
#endif
    const Grid& g = A.Grid();

    // Matrix views
    DistMatrix<F>
        ATL(g), ATR(g),  A00(g), A01(g), A02(g),
        ABL(g), ABR(g),  A10(g), A11(g), A12(g),
                         A20(g), A21(g), A22(g);
    DistMatrix<F>
        LTL(g), LTR(g),  L00(g), L01(g), L02(g),
        LBL(g), LBR(g),  L10(g), L11(g), L12(g),
                         L20(g), L21(g), L22(g);

    // Temporary distributions
    DistMatrix<F,STAR,VR  > A10_STAR_VR(g);
    DistMatrix<F,STAR,MR  > A10_STAR_MR(g);
    DistMatrix<F,STAR,MC  > A10_STAR_MC(g);
    DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
    DistMatrix<F,VC,  STAR> A21_VC_STAR(g);
    DistMatrix<F,MC,  STAR> A21_MC_STAR(g);
    DistMatrix<F,STAR,VR  > L10_STAR_VR(g);
    DistMatrix<F,MR,  STAR> L10Adj_MR_STAR(g);
    DistMatrix<F,STAR,MC  > L10_STAR_MC(g);
    DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
    DistMatrix<F,STAR,VR  > Y10_STAR_VR(g);

    PartitionDownDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 0 );
    LockedPartitionDownDiagonal
    ( L, LTL, LTR,
         LBL, LBR, 0 );
    while( ATL.Height() < A.Height() )
    {
        RepartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, /**/ A01, A02,
         /*************/ /******************/
               /**/       A10, /**/ A11, A12,
          ABL, /**/ ABR,  A20, /**/ A21, A22 );

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

        A10_STAR_VR.AlignWith( A00 );
        A10_STAR_MR.AlignWith( A00 );
        A10_STAR_MC.AlignWith( A00 );
        A21_MC_STAR.AlignWith( A20 );
        L10_STAR_VR.AlignWith( A00 );
        L10Adj_MR_STAR.AlignWith( A00 );
        L10_STAR_MC.AlignWith( A00 );
        Y10_STAR_VR.AlignWith( A10 );
        //--------------------------------------------------------------------//
        // Y10 := A11 L10
        A11_STAR_STAR = A11;
        L10Adj_MR_STAR.AdjointFrom( L10 );
        L10_STAR_VR.AdjointFrom( L10Adj_MR_STAR );
        Zeros( Y10_STAR_VR, A10.Height(), A10.Width() );
        Hemm
        ( LEFT, LOWER,
          F(1), A11_STAR_STAR.LockedMatrix(), L10_STAR_VR.LockedMatrix(),
          F(0), Y10_STAR_VR.Matrix() );

        // A10 := A10 + 1/2 Y10
        A10_STAR_VR = A10;
        Axpy( F(1)/F(2), Y10_STAR_VR, A10_STAR_VR );

        // A00 := A00 + (A10' L10 + L10' A10)
        A10_STAR_MR = A10_STAR_VR;
        A10_STAR_MC = A10_STAR_VR;
        L10_STAR_MC = L10_STAR_VR;
        LocalTrr2k
        ( LOWER, ADJOINT, ADJOINT, ADJOINT,
          F(1), A10_STAR_MC, L10Adj_MR_STAR, 
                L10_STAR_MC, A10_STAR_MR, 
          F(1), A00 );

        // A10 := A10 + 1/2 Y10
        Axpy( F(1)/F(2), Y10_STAR_VR, A10_STAR_VR );

        // A10 := L11' A10
        L11_STAR_STAR = L11;
        LocalTrmm
        ( LEFT, LOWER, ADJOINT, diag, F(1), L11_STAR_STAR, A10_STAR_VR );
        A10 = A10_STAR_VR;

        // A20 := A20 + A21 L10
        A21_MC_STAR = A21;
        LocalGemm
        ( NORMAL, ADJOINT, F(1), A21_MC_STAR, L10Adj_MR_STAR, F(1), A20 );

        // A11 := L11' A11 L11
        LocalTwoSidedTrmm( LOWER, diag, A11_STAR_STAR, L11_STAR_STAR );
        A11 = A11_STAR_STAR;

        // A21 := A21 L11
        A21_VC_STAR = A21_MC_STAR;
        LocalTrmm
        ( RIGHT, LOWER, NORMAL, diag, F(1), L11_STAR_STAR, A21_VC_STAR );
        A21 = A21_VC_STAR;
        //--------------------------------------------------------------------//

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

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