void LUNMedium
( const AbstractDistMatrix<F>& UPre, AbstractDistMatrix<F>& XPre,
bool checkIfSingular )
{
DEBUG_CSE
const Int m = XPre.Height();
const Int bsize = Blocksize();
const Grid& g = UPre.Grid();
DistMatrixReadProxy<F,F,MC,MR> UProx( UPre );
DistMatrixReadWriteProxy<F,F,MC,MR> XProx( XPre );
auto& U = UProx.GetLocked();
auto& X = XProx.Get();
DistMatrix<F,MC, STAR> U01_MC_STAR(g);
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,MR, STAR> X1Trans_MR_STAR(g);
const Int kLast = LastOffset( m, bsize );
Int k=kLast, kOld=m;
while( true )
{
const bool in2x2 = ( k>0 && U.Get(k,k-1) != F(0) );
if( in2x2 )
--k;
const Int nb = kOld-k;
const Range<Int> ind0( 0, k ),
ind1( k, k+nb );
auto U01 = U( ind0, ind1 );
auto U11 = U( ind1, ind1 );
auto X0 = X( ind0, ALL );
auto X1 = X( ind1, ALL );
U11_STAR_STAR = U11; // U11[* ,* ] <- U11[MC,MR]
X1Trans_MR_STAR.AlignWith( X0 );
Transpose( X1, X1Trans_MR_STAR );
// X1^T[MR,* ] := X1^T[MR,* ] U11^-T[* ,* ]
// = (U11^-1[* ,* ] X1[* ,MR])^T
LocalQuasiTrsm
( RIGHT, UPPER, TRANSPOSE,
F(1), U11_STAR_STAR, X1Trans_MR_STAR, checkIfSingular );
Transpose( X1Trans_MR_STAR, X1 );
U01_MC_STAR.AlignWith( X0 );
U01_MC_STAR = U01; // U01[MC,* ] <- U01[MC,MR]
// X0[MC,MR] -= U01[MC,* ] X1[* ,MR]
LocalGemm
( NORMAL, TRANSPOSE, F(-1), U01_MC_STAR, X1Trans_MR_STAR, F(1), X0 );
if( k == 0 )
break;
kOld = k;
k -= Min(bsize,k);
}
}
void LLNMedium
( const AbstractDistMatrix<F>& LPre,
AbstractDistMatrix<F>& XPre,
bool checkIfSingular )
{
DEBUG_CSE
const Int m = XPre.Height();
const Int bsize = Blocksize();
const Grid& g = LPre.Grid();
DistMatrixReadProxy<F,F,MC,MR> LProx( LPre );
DistMatrixReadWriteProxy<F,F,MC,MR> XProx( XPre );
auto& L = LProx.GetLocked();
auto& X = XProx.Get();
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,MC, STAR> L21_MC_STAR(g);
DistMatrix<F,MR, STAR> X1Trans_MR_STAR(g);
for( Int k=0; k<m; k+=bsize )
{
const Int nbProp = Min(bsize,m-k);
const bool in2x2 = ( k+nbProp<m && L.Get(k+nbProp-1,k+nbProp) != F(0) );
const Int nb = ( in2x2 ? nbProp+1 : nbProp );
const Range<Int> ind1( k, k+nb ),
ind2( k+nb, m );
auto L11 = L( ind1, ind1 );
auto L21 = L( ind2, ind1 );
auto X1 = X( ind1, ALL );
auto X2 = X( ind2, ALL );
L11_STAR_STAR = L11; // L11[* ,* ] <- L11[MC,MR]
X1Trans_MR_STAR.AlignWith( X2 );
Transpose( X1, X1Trans_MR_STAR );
// X1^T[MR,* ] := X1^T[MR,* ] L11^-T[* ,* ]
// = (L11^-1[* ,* ] X1[* ,MR])^T
LocalQuasiTrsm
( RIGHT, LOWER, TRANSPOSE,
F(1), L11_STAR_STAR, X1Trans_MR_STAR, checkIfSingular );
Transpose( X1Trans_MR_STAR, X1 );
L21_MC_STAR.AlignWith( X2 );
L21_MC_STAR = L21; // L21[MC,* ] <- L21[MC,MR]
// X2[MC,MR] -= L21[MC,* ] X1[* ,MR]
LocalGemm
( NORMAL, TRANSPOSE, F(-1), L21_MC_STAR, X1Trans_MR_STAR, F(1), X2 );
}
}
void LUNMedium
( UnitOrNonUnit diag,
const AbstractDistMatrix<F>& UPre,
AbstractDistMatrix<F>& XPre,
bool checkIfSingular )
{
EL_DEBUG_CSE
const Int m = XPre.Height();
const Int bsize = Blocksize();
const Grid& g = UPre.Grid();
DistMatrixReadProxy<F,F,MC,MR> UProx( UPre );
DistMatrixReadWriteProxy<F,F,MC,MR> XProx( XPre );
auto& U = UProx.GetLocked();
auto& X = XProx.Get();
DistMatrix<F,MC, STAR> U01_MC_STAR(g);
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,MR, STAR> X1Trans_MR_STAR(g);
const Int kLast = LastOffset( m, bsize );
for( Int k=kLast; k>=0; k-=bsize )
{
const Int nb = Min(bsize,m-k);
const Range<Int> ind0( 0, k ),
ind1( k, k+nb );
auto U01 = U( ind0, ind1 );
auto U11 = U( ind1, ind1 );
auto X0 = X( ind0, ALL );
auto X1 = X( ind1, ALL );
U11_STAR_STAR = U11; // U11[* ,* ] <- U11[MC,MR]
X1Trans_MR_STAR.AlignWith( X0 );
Transpose( X1, X1Trans_MR_STAR );
// X1^T[MR,* ] := X1^T[MR,* ] U11^-T[* ,* ]
// = (U11^-1[* ,* ] X1[* ,MR])^T
LocalTrsm
( RIGHT, UPPER, TRANSPOSE, diag,
F(1), U11_STAR_STAR, X1Trans_MR_STAR, checkIfSingular );
Transpose( X1Trans_MR_STAR, X1 );
U01_MC_STAR.AlignWith( X0 );
U01_MC_STAR = U01; // U01[MC,* ] <- U01[MC,MR]
// X0[MC,MR] -= U01[MC,* ] X1[* ,MR]
LocalGemm
( NORMAL, TRANSPOSE, F(-1), U01_MC_STAR, X1Trans_MR_STAR, F(1), X0 );
}
}
inline void
TrmmLLTC
( Orientation orientation,
UnitOrNonUnit diag,
T alpha,
const DistMatrix<T>& L,
DistMatrix<T>& X )
{
#ifndef RELEASE
PushCallStack("internal::TrmmLLTC");
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("TrmmLLT expects a (Conjugate)Transpose option");
if( L.Height() != L.Width() || L.Height() != X.Height() )
{
std::ostringstream msg;
msg << "Nonconformal TrmmLLTC: \n"
<< " L ~ " << L.Height() << " x " << L.Width() << "\n"
<< " X ~ " << X.Height() << " x " << X.Width() << "\n";
throw std::logic_error( msg.str().c_str() );
}
#endif
const Grid& g = L.Grid();
// Matrix views
DistMatrix<T>
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<T> XT(g), X0(g),
XB(g), X1(g),
X2(g);
// Temporary distributions
DistMatrix<T,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<T,STAR,MC > L10_STAR_MC(g);
DistMatrix<T,STAR,VR > X1_STAR_VR(g);
DistMatrix<T,MR, STAR> X1Trans_MR_STAR(g);
// Start the algorithm
Scale( alpha, X );
LockedPartitionDownDiagonal
( L, LTL, LTR,
LBL, LBR, 0 );
PartitionDown
( X, XT,
XB, 0 );
while( XB.Height() > 0 )
{
LockedRepartitionDownDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
RepartitionDown
( XT, X0,
/**/ /**/
X1,
XB, X2 );
L10_STAR_MC.AlignWith( X0 );
X1Trans_MR_STAR.AlignWith( X0 );
X1_STAR_VR.AlignWith( X1 );
//--------------------------------------------------------------------//
L10_STAR_MC = L10;
X1Trans_MR_STAR.TransposeFrom( X1 );
LocalGemm
( orientation, TRANSPOSE,
T(1), L10_STAR_MC, X1Trans_MR_STAR, T(1), X0 );
L11_STAR_STAR = L11;
X1_STAR_VR.TransposeFrom( X1Trans_MR_STAR );
LocalTrmm
( LEFT, LOWER, orientation, diag, T(1), L11_STAR_STAR, X1_STAR_VR );
X1 = X1_STAR_VR;
//--------------------------------------------------------------------//
L10_STAR_MC.FreeAlignments();
X1Trans_MR_STAR.FreeAlignments();
X1_STAR_VR.FreeAlignments();
SlideLockedPartitionDownDiagonal
( LTL, /**/ LTR, L00, L01, /**/ L02,
/**/ L10, L11, /**/ L12,
/*************/ /******************/
LBL, /**/ LBR, L20, L21, /**/ L22 );
SlidePartitionDown
( XT, X0,
X1,
/**/ /**/
XB, X2 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TrsmLUNMedium
( UnitOrNonUnit diag, F alpha, const DistMatrix<F>& U, DistMatrix<F>& X,
bool checkIfSingular )
{
#ifndef RELEASE
PushCallStack("internal::TrsmLUNMedium");
#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> XT(g), X0(g),
XB(g), X1(g),
X2(g);
// Temporary distributions
DistMatrix<F,MC, STAR> U01_MC_STAR(g);
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,MR, STAR> X1Trans_MR_STAR(g);
// Start the algorithm
Scale( alpha, X );
LockedPartitionUpDiagonal
( U, UTL, UTR,
UBL, UBR, 0 );
PartitionUp
( X, XT,
XB, 0 );
while( XT.Height() > 0 )
{
LockedRepartitionUpDiagonal
( UTL, /**/ UTR, U00, U01, /**/ U02,
/**/ U10, U11, /**/ U12,
/*************/ /******************/
UBL, /**/ UBR, U20, U21, /**/ U22 );
RepartitionUp
( XT, X0,
X1,
/**/ /**/
XB, X2 );
U01_MC_STAR.AlignWith( X0 );
X1Trans_MR_STAR.AlignWith( X0 );
//--------------------------------------------------------------------//
U11_STAR_STAR = U11; // U11[* ,* ] <- U11[MC,MR]
X1Trans_MR_STAR.TransposeFrom( X1 ); // X1[* ,MR] <- X1[MC,MR]
// X1[* ,MR] := U11^-1[* ,* ] X1[* ,MR]
//
// X1^T[MR,* ] := X1^T[MR,* ] U11^-T[* ,* ]
LocalTrsm
( RIGHT, UPPER, TRANSPOSE, diag,
F(1), U11_STAR_STAR, X1Trans_MR_STAR, checkIfSingular );
X1.TransposeFrom( X1Trans_MR_STAR );
U01_MC_STAR = U01; // U01[MC,* ] <- U01[MC,MR]
// X0[MC,MR] -= U01[MC,* ] X1[* ,MR]
LocalGemm
( NORMAL, TRANSPOSE, F(-1), U01_MC_STAR, X1Trans_MR_STAR, F(1), X0 );
//--------------------------------------------------------------------//
U01_MC_STAR.FreeAlignments();
X1Trans_MR_STAR.FreeAlignments();
SlideLockedPartitionUpDiagonal
( UTL, /**/ UTR, U00, /**/ U01, U02,
/*************/ /******************/
/**/ U10, /**/ U11, U12,
UBL, /**/ UBR, U20, /**/ U21, U22 );
SlidePartitionUp
( XT, X0,
/**/ /**/
X1,
XB, X2 );
}
#ifndef RELEASE
PopCallStack();
#endif
}