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 );
}
}
inline void
TwoSidedTrsmLVar2
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& L )
{
#ifndef RELEASE
PushCallStack("internal::TwoSidedTrsmLVar2");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( L.Height() != L.Width() )
throw std::logic_error("Triangular matrices must be square");
if( A.Height() != L.Height() )
throw std::logic_error("A and L must be the same size");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<F>
LTL(g), LTR(g), L00(g), L01(g), L02(g),
LBL(g), LBR(g), L10(g), L11(g), L12(g),
L20(g), L21(g), L22(g);
// Temporary distributions
DistMatrix<F,MR, STAR> A10Adj_MR_STAR(g);
DistMatrix<F,STAR,VR > A10_STAR_VR(g);
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,VC, STAR> A21_VC_STAR(g);
DistMatrix<F,MR, STAR> F10Adj_MR_STAR(g);
DistMatrix<F,MR, STAR> L10Adj_MR_STAR(g);
DistMatrix<F,VC, STAR> L10Adj_VC_STAR(g);
DistMatrix<F,STAR,MC > L10_STAR_MC(g);
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,MC, STAR> X11_MC_STAR(g);
DistMatrix<F,MC, STAR> X21_MC_STAR(g);
DistMatrix<F,MC, STAR> Y10Adj_MC_STAR(g);
DistMatrix<F,MR, MC > Y10Adj_MR_MC(g);
DistMatrix<F> X11(g);
DistMatrix<F> Y10Adj(g);
Matrix<F> Y10Local;
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionDownDiagonal
( L, LTL, LTR,
LBL, LBR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionDownDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
A10Adj_MR_STAR.AlignWith( L10 );
F10Adj_MR_STAR.AlignWith( A00 );
L10Adj_MR_STAR.AlignWith( A00 );
L10Adj_VC_STAR.AlignWith( A00 );
L10_STAR_MC.AlignWith( A00 );
X11.AlignWith( A11 );
X11_MC_STAR.AlignWith( L10 );
X21_MC_STAR.AlignWith( A20 );
Y10Adj_MC_STAR.AlignWith( A00 );
Y10Adj_MR_MC.AlignWith( A10 );
//--------------------------------------------------------------------//
// Y10 := L10 A00
L10Adj_MR_STAR.AdjointFrom( L10 );
L10Adj_VC_STAR = L10Adj_MR_STAR;
L10_STAR_MC.AdjointFrom( L10Adj_VC_STAR );
Y10Adj_MC_STAR.ResizeTo( A10.Width(), A10.Height() );
F10Adj_MR_STAR.ResizeTo( A10.Width(), A10.Height() );
Zero( Y10Adj_MC_STAR );
Zero( F10Adj_MR_STAR );
LocalSymmetricAccumulateRL
( ADJOINT,
F(1), A00, L10_STAR_MC, L10Adj_MR_STAR,
Y10Adj_MC_STAR, F10Adj_MR_STAR );
Y10Adj.SumScatterFrom( Y10Adj_MC_STAR );
Y10Adj_MR_MC = Y10Adj;
Y10Adj_MR_MC.SumScatterUpdate( F(1), F10Adj_MR_STAR );
Adjoint( Y10Adj_MR_MC.LockedLocalMatrix(), Y10Local );
// X11 := A10 L10'
X11_MC_STAR.ResizeTo( A11.Height(), A11.Width() );
LocalGemm
( NORMAL, NORMAL, F(1), A10, L10Adj_MR_STAR, F(0), X11_MC_STAR );
// A10 := A10 - Y10
Axpy( F(-1), Y10Local, A10.LocalMatrix() );
A10Adj_MR_STAR.AdjointFrom( A10 );
// A11 := A11 - (X11 + L10 A10') = A11 - (A10 L10' + L10 A10')
LocalGemm
( NORMAL, NORMAL, F(1), L10, A10Adj_MR_STAR, F(1), X11_MC_STAR );
X11.SumScatterFrom( X11_MC_STAR );
MakeTrapezoidal( LEFT, LOWER, 0, X11 );
Axpy( F(-1), X11, A11 );
// A10 := inv(L11) A10
L11_STAR_STAR = L11;
A10_STAR_VR.AdjointFrom( A10Adj_MR_STAR );
LocalTrsm
( LEFT, LOWER, NORMAL, diag, F(1), L11_STAR_STAR, A10_STAR_VR );
A10 = A10_STAR_VR;
// A11 := inv(L11) A11 inv(L11)'
A11_STAR_STAR = A11;
LocalTwoSidedTrsm( LOWER, diag, A11_STAR_STAR, L11_STAR_STAR );
A11 = A11_STAR_STAR;
// A21 := A21 - A20 L10'
X21_MC_STAR.ResizeTo( A21.Height(), A21.Width() );
LocalGemm
( NORMAL, NORMAL, F(1), A20, L10Adj_MR_STAR, F(0), X21_MC_STAR );
A21.SumScatterUpdate( F(-1), X21_MC_STAR );
// A21 := A21 inv(L11)'
A21_VC_STAR = A21;
LocalTrsm
( RIGHT, LOWER, ADJOINT, diag, F(1), L11_STAR_STAR, A21_VC_STAR );
A21 = A21_VC_STAR;
//--------------------------------------------------------------------//
A10Adj_MR_STAR.FreeAlignments();
F10Adj_MR_STAR.FreeAlignments();
L10Adj_MR_STAR.FreeAlignments();
L10Adj_VC_STAR.FreeAlignments();
L10_STAR_MC.FreeAlignments();
X11.FreeAlignments();
X11_MC_STAR.FreeAlignments();
X21_MC_STAR.FreeAlignments();
Y10Adj_MC_STAR.FreeAlignments();
Y10Adj_MR_MC.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionDownDiagonal
( LTL, /**/ LTR, L00, L01, /**/ L02,
/**/ L10, L11, /**/ L12,
/**********************************/
LBL, /**/ LBR, L20, L21, /**/ L22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
