コード例 #1
0
ファイル: LVar2.hpp プロジェクト: jimgoo/Elemental
inline void
CholeskyLVar2( Matrix<F>& A )
{
#ifndef RELEASE
    PushCallStack("internal::CholeskyLVar2");
    if( A.Height() != A.Width() )
        throw std::logic_error
        ("Can only compute Cholesky factor of square matrices");
#endif
    // Matrix views
    Matrix<F> 
        ATL, ATR,   A00, A01, A02,
        ABL, ABR,   A10, A11, A12,
                    A20, A21, A22;

    // 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 );

        //--------------------------------------------------------------------//
        Herk( LOWER, NORMAL, F(-1), A10, F(1), A11 );
        CholeskyLVar3Unb( A11 );
        Gemm( NORMAL, ADJOINT, F(-1), A20, A10, F(1), A21 );
        Trsm( RIGHT, LOWER, ADJOINT, NON_UNIT, F(1), A11, A21 );
        //--------------------------------------------------------------------//

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, A01, /**/ A02,
               /**/       A10, A11, /**/ A12,
         /*************/ /******************/
          ABL, /**/ ABR,  A20, A21, /**/ A22 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #2
0
ファイル: LVar1.hpp プロジェクト: khalid-hasanov/Elemental
inline void
TrdtrmmLVar1( Orientation orientation, Matrix<F>& L )
{
#ifndef RELEASE
    CallStackEntry entry("internal::TrdtrmmLVar1");
    if( L.Height() != L.Width() )
        LogicError("L must be square");
    if( orientation == NORMAL )
        LogicError("Orientation must be (conjugate-)transpose");
#endif
    Matrix<F>
        LTL, LTR,  L00, L01, L02,
        LBL, LBR,  L10, L11, L12,
                   L20, L21, L22;
    Matrix<F> d1, S10;

    PartitionDownDiagonal
    ( L, LTL, LTR,
         LBL, LBR, 0 );
    while( LTL.Height() < L.Height() && LTL.Width() < L.Height() )
    {
        RepartitionDownDiagonal
        ( LTL, /**/ LTR,  L00, /**/ L01, L02,
         /*************/ /******************/
               /**/       L10, /**/ L11, L12,
          LBL, /**/ LBR,  L20, /**/ L21, L22 );

        //--------------------------------------------------------------------/
        L11.GetDiagonal( d1 );
        S10 = L10;
        DiagonalSolve( LEFT, NORMAL, d1, L10, true );
        Trrk( LOWER, orientation, NORMAL, F(1), S10, L10, F(1), L00 );
        Trmm( LEFT, LOWER, orientation, UNIT, F(1), L11, L10 );
        TrdtrmmLUnblocked( orientation, L11 );
        //--------------------------------------------------------------------/

        SlidePartitionDownDiagonal
        ( LTL, /**/ LTR,  L00, L01, /**/ L02,
               /**/       L10, L11, /**/ L12,
         /*************/ /******************/
          LBL, /**/ LBR,  L20, L21, /**/ L22 );
    }
}
コード例 #3
0
ファイル: LocalLU.hpp プロジェクト: ahmadia/elemental
inline void
LU( Matrix<F>& A )
{
#ifndef RELEASE
    PushCallStack("LU");
#endif
    // Matrix views 
    Matrix<F>
        ATL, ATR,  A00, a01,     A02,  alpha21T,
        ABL, ABR,  a10, alpha11, a12,  a21B,
                   A20, a21,     A22;

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

        //--------------------------------------------------------------------//
        F alpha = alpha11.Get(0,0);
        if( alpha == static_cast<F>(0) )
            throw SingularMatrixException();
        Scal( static_cast<F>(1)/alpha, a21 );
        Geru( (F)-1, a21, a12, A22 );
        //--------------------------------------------------------------------//

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, a01,     /**/ A02,
               /**/       a10, alpha11, /**/ a12,
         /*************/ /**********************/
          ABL, /**/ ABR,  A20, a21,     /**/ A22 );
    }
    PopBlocksizeStack();
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #4
0
ファイル: LU.hpp プロジェクト: jimgoo/Elemental
inline void
LU( Matrix<F>& A )
{
#ifndef RELEASE
    PushCallStack("LU");
#endif
    // Matrix views
    Matrix<F>
        ATL, ATR,  A00, A01, A02, 
        ABL, ABR,  A10, A11, A12,  
                   A20, A21, A22;

    // 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 );

        //--------------------------------------------------------------------//
        internal::LUUnb( A11 );
        Trsm( RIGHT, UPPER, NORMAL, NON_UNIT, F(1), A11, A21 );
        Trsm( LEFT, LOWER, NORMAL, UNIT, F(1), A11, A12 );
        Gemm( NORMAL, NORMAL, F(-1), A21, A12, F(1), A22 );
        //--------------------------------------------------------------------//

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, A01, /**/ A02,
               /**/       A10, A11, /**/ A12,
         /*************/ /******************/
          ABL, /**/ ABR,  A20, A21, /**/ A22 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #5
0
ファイル: UVar3.hpp プロジェクト: ahmadia/Elemental-1
inline void
UVar3( Matrix<F>& A )
{
#ifndef RELEASE
    CallStackEntry entry("cholesky::UVar3");
    if( A.Height() != A.Width() )
        throw std::logic_error
        ("Can only compute Cholesky factor of square matrices");
#endif
    // Matrix views
    Matrix<F> 
        ATL, ATR,  A00, A01, A02,
        ABL, ABR,  A10, A11, A12,
                   A20, A21, A22;

    // 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 );

        //--------------------------------------------------------------------//
        cholesky::UVar3Unb( A11 );
        Trsm( LEFT, UPPER, ADJOINT, NON_UNIT, F(1), A11, A12 );
        Herk( UPPER, ADJOINT, F(-1), A12, F(1), A22 );
        //--------------------------------------------------------------------//

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, A01, /**/ A02,
               /**/       A10, A11, /**/ A12,
         /*************/ /******************/
          ABL, /**/ ABR,  A20, A21, /**/ A22 );
    }
}
コード例 #6
0
ファイル: Local.hpp プロジェクト: khalid-hasanov/Elemental
inline void
UnbFLAME( Matrix<F>& A )
{
#ifndef RELEASE
    CallStackEntry entry("lu::UnbFLAME");
#endif
    // Matrix views 
    Matrix<F>
        ATL, ATR,  A00, a01,     A02,  alpha21T,
        ABL, ABR,  a10, alpha11, a12,  a21B,
                   A20, a21,     A22;

    PartitionDownDiagonal
    ( A, ATL, ATR,
         ABL, ABR, 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 );

        //--------------------------------------------------------------------//
        F alpha = alpha11.Get(0,0);
        if( alpha == F(0) )
            throw SingularMatrixException();
        Scale( 1/alpha, a21 );
        Geru( F(-1), a21, a12, A22 );
        //--------------------------------------------------------------------//

        SlidePartitionDownDiagonal
        ( ATL, /**/ ATR,  A00, a01,     /**/ A02,
               /**/       a10, alpha11, /**/ a12,
         /*************/ /**********************/
          ABL, /**/ ABR,  A20, a21,     /**/ A22 );
    }
}
コード例 #7
0
ファイル: UVar1.hpp プロジェクト: jimgoo/Elemental
inline void
TrtrmmUVar1( Orientation orientation, Matrix<T>& U )
{
#ifndef RELEASE
    PushCallStack("internal::TrtrmmUVar1");
#endif
     Matrix<T>
        UTL, UTR,  U00, U01, U02,
        UBL, UBR,  U10, U11, U12,
                   U20, U21, U22;

    PartitionDownDiagonal
    ( U, UTL, UTR,
         UBL, UBR, 0 );
    while( UTL.Height() < U.Height() && UTL.Width() < U.Height() )
    {
        RepartitionDownDiagonal
        ( UTL, /**/ UTR,  U00, /**/ U01, U02,
         /*************/ /******************/
               /**/       U10, /**/ U11, U12,
          UBL, /**/ UBR,  U20, /**/ U21, U22 );

        //--------------------------------------------------------------------/
        Trrk( UPPER, NORMAL, orientation, T(1), U01, U01, T(1), U00 );
        Trmm( RIGHT, UPPER, orientation, NON_UNIT, T(1), U11, U01 );
        TrtrmmUUnblocked( orientation, U11 );
        //--------------------------------------------------------------------/

        SlidePartitionDownDiagonal
        ( UTL, /**/ UTR,  U00, U01, /**/ U02,
               /**/       U10, U11, /**/ U12,
         /*************/ /******************/
          UBL, /**/ UBR,  U20, U21, /**/ U22 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #8
0
ファイル: LVar1.hpp プロジェクト: khalid-hasanov/Elemental
inline void
TrtrmmLVar1( Orientation orientation, Matrix<T>& L )
{
#ifndef RELEASE
    CallStackEntry entry("internal::TrtrmmLVar1");
    if( orientation == NORMAL )
        LogicError("Must be (conjugate-)transposed");
#endif
    Matrix<T>
        LTL, LTR,  L00, L01, L02,
        LBL, LBR,  L10, L11, L12,
                   L20, L21, L22;

    PartitionDownDiagonal
    ( L, LTL, LTR,
         LBL, LBR, 0 );
    while( LTL.Height() < L.Height() && LTL.Width() < L.Height() )
    {
        RepartitionDownDiagonal
        ( LTL, /**/ LTR,  L00, /**/ L01, L02,
         /*************/ /******************/
               /**/       L10, /**/ L11, L12,
          LBL, /**/ LBR,  L20, /**/ L21, L22 );

        //--------------------------------------------------------------------/
        Trrk( LOWER, orientation, NORMAL, T(1), L10, L10, T(1), L00 );
        Trmm( LEFT, LOWER, orientation, NON_UNIT, T(1), L11, L10 );
        TrtrmmLUnblocked( orientation, L11 );
        //--------------------------------------------------------------------/

        SlidePartitionDownDiagonal
        ( LTL, /**/ LTR,  L00, L01, /**/ L02,
               /**/       L10, L11, /**/ L12,
         /*************/ /******************/
          LBL, /**/ LBR,  L20, L21, /**/ L22 );
    }
}
コード例 #9
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 #10
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 #11
0
ファイル: UVar1.hpp プロジェクト: mcg1969/Elemental
inline void
TrdtrmmUVar1( Orientation orientation, DistMatrix<F>& U )
{
#ifndef RELEASE
    PushCallStack("internal::TrdtrmmUVar1");
    if( U.Height() != U.Width() )
        throw std::logic_error("U must be square");
    if( orientation == NORMAL )
        throw std::logic_error("Orientation must be (conjugate-)transpose");
#endif
    const Grid& g = U.Grid();

    // Matrix views
    DistMatrix<F>
        UTL(g), UTR(g),  U00(g), U01(g), U02(g),
        UBL(g), UBR(g),  U10(g), U11(g), U12(g),
                         U20(g), U21(g), U22(g);
    DistMatrix<F,MD,STAR> d1(g);

    // Temporary distributions
    DistMatrix<F,MC,  STAR> S01_MC_STAR(g);
    DistMatrix<F,VC,  STAR> S01_VC_STAR(g);
    DistMatrix<F,VR,  STAR> U01_VR_STAR(g);
    DistMatrix<F,STAR,MR  > U01AdjOrTrans_STAR_MR(g);
    DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);

    S01_MC_STAR.AlignWith( U );
    S01_VC_STAR.AlignWith( U );
    U01_VR_STAR.AlignWith( U );
    U01AdjOrTrans_STAR_MR.AlignWith( U );

    PartitionDownDiagonal
    ( U, UTL, UTR,
         UBL, UBR, 0 );
    while( UTL.Height() < U.Height() && UTL.Width() < U.Height() )
    {
        RepartitionDownDiagonal 
        ( UTL, /**/ UTR,  U00, /**/ U01, U02,
         /*************/ /******************/
               /**/       U10, /**/ U11, U12,
          UBL, /**/ UBR,  U20, /**/ U21, U22 );

        //--------------------------------------------------------------------//
        U11.GetDiagonal( d1 );
        S01_MC_STAR = U01;
        S01_VC_STAR = S01_MC_STAR;
        U01_VR_STAR = S01_VC_STAR;
        if( orientation == TRANSPOSE )
        {
            DiagonalSolve( RIGHT, NORMAL, d1, U01_VR_STAR );
            U01AdjOrTrans_STAR_MR.TransposeFrom( U01_VR_STAR );
        }
        else
        {
            DiagonalSolve( RIGHT, ADJOINT, d1, U01_VR_STAR );
            U01AdjOrTrans_STAR_MR.AdjointFrom( U01_VR_STAR );
        }
        LocalTrrk( UPPER, F(1), S01_MC_STAR, U01AdjOrTrans_STAR_MR, F(1), U00 );

        U11_STAR_STAR = U11;
        LocalTrmm
        ( RIGHT, UPPER, ADJOINT, UNIT, F(1), U11_STAR_STAR, U01_VR_STAR );
        U01 = U01_VR_STAR;

        LocalTrdtrmm( orientation, UPPER, U11_STAR_STAR );
        U11 = U11_STAR_STAR;
        //--------------------------------------------------------------------//
        d1.FreeAlignments();

        SlidePartitionDownDiagonal
        ( UTL, /**/ UTR,  U00, U01, /**/ U02,
               /**/       U10, U11, /**/ U12,
         /*************/ /******************/
          UBL, /**/ UBR,  U20, U21, /**/ U22 );
    }
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #12
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 #13
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 #14
0
ファイル: UVar5.hpp プロジェクト: jimgoo/Elemental
inline void
TwoSidedTrmmUVar5( UnitOrNonUnit diag, Matrix<F>& A, const Matrix<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
    // Matrix views
    Matrix<F>
        ATL, ATR,  A00, A01, A02,
        ABL, ABR,  A10, A11, A12,
                   A20, A21, A22;
    Matrix<F>
        UTL, UTR,  U00, U01, U02,
        UBL, UBR,  U10, U11, U12,
                   U20, U21, U22;

    // Temporary products
    Matrix<F> Y01;

    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 );

        //--------------------------------------------------------------------//
        // Y01 := U01 A11
        Zeros( A01.Height(), A01.Width(), Y01 );
        Hemm( RIGHT, UPPER, F(1), A11, U01, F(0), Y01 );

        // 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')
        Her2k( UPPER, NORMAL, F(1), U01, A01, F(1), A00 );

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

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

        // A11 := U11 A11 U11'
        TwoSidedTrmmUUnb( diag, A11, U11 );
        //--------------------------------------------------------------------//

        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 #15
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 #16
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 #17
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 #18
0
ファイル: LU.hpp プロジェクト: ahmadia/Elemental-1
inline void
LU( Matrix<F>& A, Matrix<int>& p )
{
#ifndef RELEASE
    CallStackEntry entry("LU");
    if( p.Viewing() && 
        (p.Height() != std::min(A.Height(),A.Width()) || p.Width() != 1) ) 
        throw std::logic_error
        ("p must be a vector of the same height as the min dimension of A");
#endif
    if( !p.Viewing() )
        p.ResizeTo( std::min(A.Height(),A.Width()), 1 );

    // Matrix views
    Matrix<F>
        ATL, ATR,  A00, A01, A02,  ABRL, ABRR,
        ABL, ABR,  A10, A11, A12,  
                   A20, A21, A22;

    Matrix<int>
        pT,  p0, 
        pB,  p1,
             p2;

    // 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 );

        PartitionRight( ABR, ABRL, ABRR, A11.Width() );

        const int pivotOffset = A01.Height();
        //--------------------------------------------------------------------//
        lu::Panel( ABRL, p1, pivotOffset );
        ComposePivots( p1, pivotOffset, image, preimage );
        ApplyRowPivots( ABL, image, preimage );
        ApplyRowPivots( ABRR, image, preimage );

        Trsm( LEFT, LOWER, NORMAL, UNIT, F(1), A11, A12 );
        Gemm( NORMAL, NORMAL, F(-1), A21, A12, F(1), A22 );
        //--------------------------------------------------------------------//

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

        SlidePartitionDown
        ( pT,  p0,
               p1,
         /**/ /**/
          pB,  p2 );
    }
}
コード例 #19
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 #20
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 #21
0
inline void
Householder( Matrix<F>& A, Matrix<F>& t )
{
#ifndef RELEASE
    CallStackEntry entry("qr::Householder");
#endif
    t.ResizeTo( Min(A.Height(),A.Width()), 1 );

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

    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 #22
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 #23
0
inline void
PanelHouseholder( Matrix<F>& A, Matrix<F>& t )
{
#ifndef RELEASE
    CallStackEntry entry("lq::PanelHouseholder");
    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");
#endif
    Matrix<F>
        ATL, ATR,  A00, a01,     A02,  aTopRow, ABottomPan,
        ABL, ABR,  a10, alpha11, a12,
                   A20, a21,     A22;
    Matrix<F>
        tT,  t0,
        tB,  tau1,
             t2;

    Matrix<F> z, aTopRowConj;

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

        // Apply the Householder reflector
        const F alpha = alpha11.Get(0,0);
        alpha11.Set(0,0,1);
        Conjugate( aTopRow, aTopRowConj );
        Zeros( z, ABottomPan.Height(), 1 );
        Gemv( NORMAL, F(1), ABottomPan, aTopRowConj, F(0), z );
        Ger( -Conj(tau), z, aTopRowConj, ABottomPan );
        alpha11.Set(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 #24
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 );
    }
}
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: LVar4.hpp プロジェクト: khalid-hasanov/Elemental
inline void
TwoSidedTrmmLVar4( UnitOrNonUnit diag, Matrix<F>& A, const Matrix<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
    // Matrix views
    Matrix<F>
        ATL, ATR,  A00, A01, A02,
        ABL, ABR,  A10, A11, A12,
                   A20, A21, A22;
    Matrix<F>
        LTL, LTR,  L00, L01, L02,
        LBL, LBR,  L10, L11, L12,
                   L20, L21, L22;

    // Temporary products
    Matrix<F> Y10;

    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 );

        //--------------------------------------------------------------------//
        // Y10 := A11 L10
        Zeros( Y10, A10.Height(), A10.Width() );
        Hemm( LEFT, LOWER, F(1), A11, L10, F(0), Y10 );

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

        // A00 := A00 + (A10' L10 + L10' A10)
        Her2k( LOWER, ADJOINT, F(1), A10, L10, F(1), A00 );

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

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

        // A20 := A20 + A21 L10
        Gemm( NORMAL, NORMAL, F(1), A21, L10, F(1), A20 );

        // A11 := L11' A11 L11
        TwoSidedTrmmLUnb( diag, A11, L11 );

        // A21 := A21 L11
        Trmm( RIGHT, LOWER, NORMAL, diag, F(1), L11, 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 #27
0
ファイル: UVar1.hpp プロジェクト: khalid-hasanov/Elemental
inline void
TwoSidedTrsmUVar1( UnitOrNonUnit diag, Matrix<F>& A, const Matrix<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
    // Matrix views
    Matrix<F>
        ATL, ATR,  A00, A01, A02,
        ABL, ABR,  A10, A11, A12,
                   A20, A21, A22;
    Matrix<F>
        UTL, UTR,  U00, U01, U02,
        UBL, UBR,  U10, U11, U12,
                   U20, U21, U22;

    // Temporary products
    Matrix<F> Y01;

    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 );

        //--------------------------------------------------------------------//
        // Y01 := A00 U01
        Zeros( Y01, A01.Height(), A01.Width() );
        Hemm( LEFT, UPPER, F(1), A00, U01, F(0), Y01 );

        // A01 := inv(U00)' A01
        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)
        Her2k( UPPER, ADJOINT, F(-1), U01, A01, F(1), A11 );

        // A11 := inv(U11)' A11 inv(U11)
        TwoSidedTrsmUUnb( diag, A11, U11 );

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

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

        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 #28
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 #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: 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;
}