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
}
inline void
internal::CholeskyLVar3( DistMatrix<F,MC,MR>& A )
{
#ifndef RELEASE
PushCallStack("internal::CholeskyLVar3");
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,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 matrices
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,VC, STAR> A21_VC_STAR(g);
DistMatrix<F,VR, STAR> A21_VR_STAR(g);
DistMatrix<F,STAR,MC > A21Trans_STAR_MC(g);
DistMatrix<F,STAR,MR > A21Adj_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 );
A21_VR_STAR.AlignWith( A22 );
A21_VC_STAR.AlignWith( A22 );
A21Trans_STAR_MC.AlignWith( A22 );
A21Adj_STAR_MR.AlignWith( A22 );
//--------------------------------------------------------------------//
A11_STAR_STAR = A11;
internal::LocalCholesky( LOWER, A11_STAR_STAR );
A11 = A11_STAR_STAR;
A21_VC_STAR = A21;
internal::LocalTrsm
( RIGHT, LOWER, ADJOINT, NON_UNIT, (F)1, A11_STAR_STAR, A21_VC_STAR );
A21_VR_STAR = A21_VC_STAR;
A21Trans_STAR_MC.TransposeFrom( A21_VC_STAR );
A21Adj_STAR_MR.AdjointFrom( A21_VR_STAR );
// (A21^T[* ,MC])^T A21^H[* ,MR] = A21[MC,* ] A21^H[* ,MR]
// = (A21 A21^H)[MC,MR]
internal::LocalTrrk
( LOWER, TRANSPOSE,
(F)-1, A21Trans_STAR_MC, A21Adj_STAR_MR, (F)1, A22 );
A21.TransposeFrom( A21Trans_STAR_MC );
//--------------------------------------------------------------------//
A21_VR_STAR.FreeAlignments();
A21_VC_STAR.FreeAlignments();
A21Trans_STAR_MC.FreeAlignments();
A21Adj_STAR_MR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
