void BackwardSingle
( const DistMatrix<F,VC,STAR>& L,
DistMatrix<F,VC,STAR>& X,
bool conjugate=false )
{
const Grid& g = L.Grid();
const Orientation orientation = ( conjugate ? ADJOINT : TRANSPOSE );
DistMatrix<F,STAR,STAR> D(g), L11_STAR_STAR(g), Z1_STAR_STAR(g);
FormDiagonalBlocks( L, D, conjugate );
const Int m = L.Height();
const Int n = L.Width();
const Int numRHS = X.Width();
const Int bsize = Blocksize();
const Int kLast = LastOffset( n, bsize );
for( Int k=kLast; k>=0; k-=bsize )
{
const Int nb = Min(bsize,n-k);
const Range<Int> ind1(k,k+nb), ind2(k+nb,m);
auto L11Trans_STAR_STAR = D( IR(0,nb), ind1 );
auto L21 = L( ind2, ind1 );
auto X1 = X( ind1, IR(0,numRHS) );
auto X2 = X( ind2, IR(0,numRHS) );
// X1 -= L21' X2
LocalGemm( orientation, NORMAL, F(-1), L21, X2, Z1_STAR_STAR );
axpy::util::UpdateWithLocalData( F(1), X1, Z1_STAR_STAR );
El::AllReduce( Z1_STAR_STAR, X1.DistComm() );
// X1 := L11^-1 X1
LocalTrsm
( LEFT, UPPER, NORMAL, UNIT, F(1), L11Trans_STAR_STAR, Z1_STAR_STAR );
X1 = Z1_STAR_STAR;
}
}
inline void
TrsmLLTSmall
( Orientation orientation, UnitOrNonUnit diag,
F alpha, const DistMatrix<F,VC,STAR>& L, DistMatrix<F,VC,STAR>& X,
bool checkIfSingular )
{
#ifndef RELEASE
PushCallStack("internal::TrsmLLTSmall");
if( L.Grid() != X.Grid() )
throw std::logic_error
("L and X must be distributed over the same grid");
if( orientation == NORMAL )
throw std::logic_error("TrsmLLT expects a (Conjugate)Transpose option");
if( L.Height() != L.Width() || L.Height() != X.Height() )
{
std::ostringstream msg;
msg << "Nonconformal TrsmLLT: \n"
<< " L ~ " << L.Height() << " x " << L.Width() << "\n"
<< " X ~ " << X.Height() << " x " << X.Width() << "\n";
throw std::logic_error( msg.str().c_str() );
}
if( L.ColAlignment() != X.ColAlignment() )
throw std::logic_error("L and X must be aligned");
#endif
const Grid& g = L.Grid();
// Matrix views
DistMatrix<F,VC,STAR>
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);
DistMatrix<F,VC,STAR> XT(g), X0(g),
XB(g), X1(g),
X2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> Z1_STAR_STAR(g);
// Start the algorithm
Scale( alpha, X );
LockedPartitionUpDiagonal
( L, LTL, LTR,
LBL, LBR, 0 );
PartitionUp
( X, XT,
XB, 0 );
while( XT.Height() > 0 )
{
LockedRepartitionUpDiagonal
( LTL, /**/ LTR, L00, L01, /**/ L02,
/**/ L10, L11, /**/ L12,
/*************/ /******************/
LBL, /**/ LBR, L20, L21, /**/ L22 );
RepartitionUp
( XT, X0,
X1,
/**/ /**/
XB, X2 );
//--------------------------------------------------------------------//
// X1 -= L21' X2
Zeros( X1.Height(), X1.Width(), Z1_STAR_STAR );
LocalGemm( orientation, NORMAL, F(-1), L21, X2, F(0), Z1_STAR_STAR );
AddInLocalData( X1, Z1_STAR_STAR );
Z1_STAR_STAR.SumOverGrid();
// X1 := L11^-1 X1
L11_STAR_STAR = L11;
LocalTrsm
( LEFT, LOWER, orientation, diag, F(1), L11_STAR_STAR, Z1_STAR_STAR,
checkIfSingular );
X1 = Z1_STAR_STAR;
//--------------------------------------------------------------------//
SlideLockedPartitionUpDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
SlidePartitionUp
( XT, X0,
/**/ /**/
X1,
XB, X2 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
