自学教程：C++ A11函数代码示例

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 );    }}

int main(){	DoubleMatrix A(3,3);	DoubleInterval A00(2,3);	DoubleInterval A10(5,9);	DoubleInterval A11(3,4);	DoubleInterval A20(-2,5);	DoubleInterval A21(3,8);	A(0,0) = A00;	A(0,1) = 0;	A(0,2) = 0;	A(1,0) = A10;	A(1,1) = A11;	A(1,2) = 0;	A(2,0) = A20;	A(2,1) = A21;	A(2,2) = 5;	DoubleInterval X(0,0);	mtl::dense_vector<DoubleInterval> b(3,X);	b[0] = 5;	b[1] = 3;	b[2] = -6;	mtl::dense_vector<DoubleInterval> x(3,X);	x = mtl::mat::upper_trisolve(A,b);	std::cout << x << std::endl;	return 0;}

		std::string makeFormattedString(		const char* aFormat,		const A1& a1 = A1(),		const A2& a2 = A2(),		const A3& a3 = A3(),		const A4& a4 = A4(),		const A5& a5 = A5(),		const A6& a6 = A6(),		const A7& a7 = A7(),		const A8& a8 = A8(),		const A9& a9 = A9(),		const A10& a10 = A10(),		const A11& a11 = A11(),		const A12& a12 = A12(),		const A13& a13 = A13(),		const A14& a14 = A14(),		const A15& a15 = A15(),		const A16& a16 = A16(),		const A17& a17 = A17(),		const A18& a18 = A18(),		const A19& a19 = A19(),		const A20& a20 = A20()		)		{			return makeStringByPrintf(aFormat,				a1, a2, a3, a4, a5, a6, a7, a8, a9, a10,				a11, a12, a13, a14, a15, a16, a17, a18, a19, a20				);		}

void graphics::NgoiLang(QPainter& painter,int x,int y,int c,int r){    QPoint A(x-r/2,y+c);    QPoint B(x+r/2,y+c);    QPoint C(x+r/2,y+c/3);    QPoint D(x,y);    QPoint E(x-r/2,y+c/3);    QPolygon poly1;    poly1 << D << E << A << B << C;    painter.drawPolygon(poly1);// ve cai cua    QPoint A1(x,y+c);    QPoint B1(x,y+2*c/3);    QPoint C1(x-r/4,y+2*c/3);    QPoint D1(x-r/4,y+c);    QPolygon poly2;    poly2 << A1 << B1 << C1 << D1;    painter.drawPolyline(poly2); // ve cua so   QPoint A11(x-r/4,y+c/6);    QPoint B11(x-r/4,y);   QPoint C11(x-r/8,y);    QPoint D11(x-r/8,y+c/12);   QPolygon poly21;    poly21 << A11 << B11 << C11 << D11;    painter.drawPolygon(poly21);    painter.drawRect(x+r/4,y+c/2.5,c/10,r/10);}

int main(){	Rat a1(-1,2);	Rat a2(2,9);	Rat b2(3,2);	Rat c1(-1,9);	DoubleInterval A11(a2,b2);	DoubleInterval A12(a1,0);	DoubleInterval A21(-1,c1);	DoubleInterval A22(a2,b2);	DoubleMatrix A(2,2);	A(0,0) = A11;	A(0,1) = A12;	A(1,0) = A21;	A(1,1) = A22;	DoubleInterval B1(1,3);	DoubleInterval B2(3,4);	DoubleVector b(2, (DoubleInterval)0);	b[0] = B1;	b[1] = B2;	std::cout << A << std::endl;	std::cout << b << std::endl;	DoubleVector x(2, (DoubleInterval)0);	x = A * b;	std::cout << x << std::endl;	//Need to sort this out	DoubleInterval test(-1,2);	DoubleInterval testb(5,100);	DoubleInterval ans;	ans = testb/test;	std::cout << ans << std::endl;	DoubleInterval k00(0,2);	DoubleInterval k01(1,3);	DoubleInterval k10(3,5);	DoubleInterval k11(5,7);	std::cout << "INVERSE IS " << std::endl;	std::cout << boost::numeric::Doubleinterval_lib::multiplicative_inverse(k11) << std::endl;	std::cout << boost::numeric::norm(k11) << std::endl;	std::cout << k00 * k11 << std::endl;	std::cout << k01 * k10 << std::endl;	std::cout << (k00 * k11) - (k01 * k10) << std::endl;	return 0;}

int main(){  const int sz=7;    CArray A(sz);    A(0) = complex<float>(1,2);    A(1) = complex<float>(3,4);    Array<float,1> Ar = real(A);    BZTEST(int(Ar(0)) == 1 && int(Ar(1)) == 3);    Array<float,1> Ai = imag(A);    BZTEST(int(Ai(0)) == 2 && int(Ai(1)) == 4);    CArray Ac(sz);    Ac = conj(A);    BZTEST(Ac(0) == complex<float>(1,-2));    BZTEST(Ac(1) == complex<float>(3,-4));    Array<float,1> Ab(sz);    Ab = abs(A);    BZTEST(fabs(Ab(0) - 2.236068) < eps);    BZTEST(fabs(Ab(1) - 5.0) < eps);    Ab = arg(A);    BZTEST(fabs(Ab(0) - atan(2.0)) < eps);    BZTEST(fabs(Ab(1) - atan(4.0/3.0)) < eps);    Array<float,1> r(sz), theta(sz);    r(0) = 4.0f;    r(1) = 15.0f;    theta(0) = float(3.141592/3.0);    theta(1) = float(3.0*3.141592/2.0);    Ac = blitz::polar(r,theta);    BZTEST(fabs(real(Ac(0)) - 2) < eps);    BZTEST(fabs(imag(Ac(0)) - 3.4641012) < eps);    BZTEST(fabs(real(Ac(1)) - 0.0) < eps);    BZTEST(fabs(imag(Ac(1)) + 15.0) < eps);    Array<complex<long double>,1> A11(5),B11(5),C11(5);    A11=1,2,3,4,5;    B11=1,2,3,4,5;    C11=A11+B11;    BZTEST(fabs(real(C11(0)) - 2.) < eps);    C11=A11/B11;    BZTEST(fabs(real(C11(1)) - 1.) < eps);    C11=1.0l/A11;    BZTEST(fabs(real(C11(2)) - 1/3.) < eps);    C11=A11/1.0l;    BZTEST(fabs(real(C11(3)) - 4.) < eps);    C11=complex<long double>(0,1)/A11;    BZTEST(fabs(imag(C11(4)) - 1/5.) < eps);    C11=A11/complex<long double>(0,1);    BZTEST(fabs(imag(C11(0)) - -1.) < eps);    return 0;}

inline voidLQ( 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}

inline voidSymmLLC( 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,//.........这里部分代码省略.........

inline voidTwoSidedTrsmUVar1( 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 );//.........这里部分代码省略.........

inline voidHouseholder( 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 );    }}

inline voidinternal::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();//.........这里部分代码省略.........

int main(){    std::cout << "============== Test 1 ==============" << std::endl << std::endl;    DoubleInterval A00(2,3);    DoubleInterval A01(0,1);    DoubleInterval A10(1,2);    DoubleInterval A11(2,3);    DoubleInterval B0(0,120);    DoubleInterval B1(60,240);    DoubleMatrix *A = new DoubleMatrix(2,2);    (*A)(0,0) = A00;    (*A)(0,1) = A01;    (*A)(1,0) = A10;    (*A)(1,1) = A11;    std::cout << "A: " << std::endl;    std::cout << *A << std::endl;    DoubleVector *b = new DoubleVector(2, (DoubleInterval)0);    (*b)[0] = B0;    (*b)[1] = B1;    std::cout << "b: " << std::endl;    std::cout << *b << std::endl << std::endl;    DoubleVector *x = new DoubleVector(2, (DoubleInterval)0);    try    {        x = hansen_gaussian_elimination_v1(*A,*b);        if(x != NULL)        {            std::cout << "x = " << std::endl;            std::cout << *x << std::endl << std::endl;        }    }    catch(const std::exception& e)    {        std::cout << e.what() << std::endl << std::endl;    }    catch(std::string& error)    {        std::cout << error << std::endl << std::endl;    }    //Solution should be [[-120,90], [-60,240]]^T    delete A;    delete b;    delete x;    /*std::cout << "============== Test 2 ==============" << std::endl << std::endl;    A = new DoubleMatrix(3,3);    (*A)(0,0) = 2;    (*A)(0,1) = 1;    (*A)(0,2) = -1;    (*A)(1,0) = -3;    (*A)(1,1) = -1;    (*A)(1,2) = 2;    (*A)(2,0) = -2;    (*A)(2,1) = 1;    (*A)(2,2) = 2;    std::cout << "A = " << std::endl;    std::cout << *A << std::endl;    b = new DoubleVector(3, (DoubleInterval)0);    (*b)[0] = 8;    (*b)[1] = -11;    (*b)[2] = -3;    std::cout << "b = " << std::endl;    std::cout << *b << std::endl << std::endl;    x = new DoubleVector(3, (DoubleInterval)0);    try    {    	x = hansen_gaussian_elimination_v1(*A,*b);    	if(x != NULL)    	{    		std::cout << "x = " << std::endl;    		std::cout << *x << std::endl << std::endl;    	}    }    catch(const std::exception& e)    {    	std::cout << e.what() << std::endl << std::endl;    }    catch(std::string& error)    {    	std::cout << error << std::endl << std::endl;    }    delete A;    delete b;    delete x;    //Solution should be [2, 3, -1]^T    std::cout << "============== Test 3 ==============" << std::endl << std::endl;//.........这里部分代码省略.........

inline voidTwoSidedTrsmLVar2( 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() );//.........这里部分代码省略.........

int main(){	DoubleMatrix X(3,3);	DoubleInterval A(2,5);	X = A;	DoubleMatrix Y(3,3);	DoubleInterval B(5,9);	Y = B;	std::cout << X << std::endl;	std::cout << Y << std::endl;	DoubleMatrix Z(3,3);	Z = mtl::mat::trans(X);	std::cout << Z << std::endl;	mtl::mat::swap_row(Z,1,2);	std::cout << Z << std::endl;	DoubleInterval C;	C = boost::numeric::max(A,B);	std::cout << C << std::endl;	std::cout << "============== Test 1 ==============" << std::endl << std::endl;	DoubleInterval A00(2,3);	DoubleInterval A01(0,1);	DoubleInterval A10(1,2);	DoubleInterval A11(2,3);	DoubleMatrix *Test = new DoubleMatrix(2,2);	(*Test)(0,0) = A00;	(*Test)(0,1) = A01;	(*Test)(1,0) = A10;	(*Test)(1,1) = A11;	std::cout << "Test: " << std::endl;	std::cout << *Test << std::endl;	bool diag = diagonally_dominant(*Test);	if(diag == true)		std::cout << "Test is diagonally dominant" << std::endl << std::endl;	else		std::cout << "Test is NOT diagonally dominant" << std::endl << std::endl;		std::cout << "Max on row 2 is " << row_max_element(*Test,1,0) << std::endl;	std::cout << "The max is located on element " << row_max_term(*Test,1,0) << std::endl;	std::cout << std::endl;	std::cout << "determinant = " << det(*Test) << std::endl;		delete Test;	std::cout << "============== Test 2 ==============" << std::endl << std::endl;		Test = new DoubleMatrix(3,3);	(*Test)(0,0) = 1;	(*Test)(0,1) = 2;	(*Test)(0,2) = 3;	(*Test)(1,0) = 4;	(*Test)(1,1) = 5;	(*Test)(1,2) = 6;	(*Test)(2,0) = 7;	(*Test)(2,1) = 8;	(*Test)(2,2) = 9;	std::cout << "Test: " << std::endl;	std::cout << *Test << std::endl;	diag = diagonally_dominant(*Test);	if(diag == true)		std::cout << "Test is diagonally dominant" << std::endl << std::endl;	else		std::cout << "Test is NOT diagonally dominant" << std::endl << std::endl;	for(unsigned int i = 0; i < mtl::mat::num_rows(*Test); i++)	{		std::cout << "Max on row " << i << " is " << row_max_element(*Test,i,0) << std::endl;		std::cout << "The max is located on element " << row_max_term(*Test,i,0) << std::endl;	}	std::cout << std::endl;	std::cout << "determinant = " << det(*Test) << std::endl;	delete Test;	std::cout << "============== Test 3 ==============" << std::endl << std::endl;		Test = new DoubleMatrix(3,3);	(*Test)(0,0) = 1;	(*Test)(0,1) = 2;	(*Test)(0,2) = 3;	(*Test)(1,0) = 10;	(*Test)(1,1) = 5;	(*Test)(1,2) = 6;	(*Test)(2,0) = 10;	(*Test)(2,1) = 8;	(*Test)(2,2) = 9;	std::cout << "Test: " << std::endl;	std::cout << *Test << std::endl;	diag = diagonally_dominant(*Test);//.........这里部分代码省略.........

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,//.........这里部分代码省略.........

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 );    }}

inline voidinternal::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,         /*************/ /******************///.........这里部分代码省略.........

inline voidTwoSidedTrmmUVar5( 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//.........这里部分代码省略.........

inline voidinternal::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 );//.........这里部分代码省略.........

inline voidTwoSidedTrsmUVar4( 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, //.........这里部分代码省略.........

inline voidLocalSymmetricAccumulateLU( 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//.........这里部分代码省略.........

inline voidLU( 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,//.........这里部分代码省略.........

inline voidCholeskyUVar3( 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}

inline voidHPDInverseLVar2( 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 );//.........这里部分代码省略.........

inline voidTwoSidedTrmmLVar4( 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;//.........这里部分代码省略.........

inline voidLVar2( 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 );    }}

inline voidTwoSidedTrsmUVar5( 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;//.........这里部分代码省略.........