inline void
TrsvLT
( Orientation orientation, UnitOrNonUnit diag,
const DistMatrix<F>& L, DistMatrix<F>& x )
{
#ifndef RELEASE
PushCallStack("internal::TrsvLT");
if( L.Grid() != x.Grid() )
throw std::logic_error("{L,x} must be distributed over the same grid");
if( orientation == NORMAL )
throw std::logic_error("TrsvLT expects a (conjugate-)transpose option");
if( L.Height() != L.Width() )
throw std::logic_error("L must be square");
if( x.Width() != 1 && x.Height() != 1 )
throw std::logic_error("x must be a vector");
const int xLength = ( x.Width() == 1 ? x.Height() : x.Width() );
if( L.Width() != xLength )
throw std::logic_error("Nonconformal TrsvLT");
#endif
const Grid& g = L.Grid();
if( x.Width() == 1 )
{
// Matrix views
DistMatrix<F> L10(g), L11(g);
DistMatrix<F>
xT(g), x0(g),
xB(g), x1(g),
x2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
DistMatrix<F,MC, STAR> x1_MC_STAR(g);
DistMatrix<F,MC, MR > z1(g);
DistMatrix<F,MR, MC > z1_MR_MC(g);
DistMatrix<F,MR, STAR> z_MR_STAR(g);
// Views of z[MR,* ]
DistMatrix<F,MR,STAR> z0_MR_STAR(g),
z1_MR_STAR(g);
z_MR_STAR.AlignWith( L );
Zeros( x.Height(), 1, z_MR_STAR );
// Start the algorithm
PartitionUp
( x, xT,
xB, 0 );
while( xT.Height() > 0 )
{
RepartitionUp
( xT, x0,
x1,
/**/ /**/
xB, x2 );
const int n0 = x0.Height();
const int n1 = x1.Height();
LockedView( L10, L, n0, 0, n1, n0 );
LockedView( L11, L, n0, n0, n1, n1 );
View( z0_MR_STAR, z_MR_STAR, 0, 0, n0, 1 );
View( z1_MR_STAR, z_MR_STAR, n0, 0, n1, 1 );
x1_MC_STAR.AlignWith( L10 );
z1.AlignWith( x1 );
//----------------------------------------------------------------//
if( x2.Height() != 0 )
{
z1_MR_MC.SumScatterFrom( z1_MR_STAR );
z1 = z1_MR_MC;
Axpy( F(1), z1, x1 );
}
x1_STAR_STAR = x1;
L11_STAR_STAR = L11;
Trsv
( LOWER, orientation, diag,
L11_STAR_STAR.LockedMatrix(),
x1_STAR_STAR.Matrix() );
x1 = x1_STAR_STAR;
x1_MC_STAR = x1_STAR_STAR;
Gemv
( orientation, F(-1),
L10.LockedMatrix(),
x1_MC_STAR.LockedMatrix(),
F(1), z0_MR_STAR.Matrix() );
//----------------------------------------------------------------//
x1_MC_STAR.FreeAlignments();
z1.FreeAlignments();
SlidePartitionUp
( xT, x0,
/**/ /**/
x1,
xB, x2 );
}
}
else
{
// Matrix views
DistMatrix<F> L10(g), L11(g);
DistMatrix<F>
xL(g), xR(g),
x0(g), x1(g), x2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
DistMatrix<F,STAR,MC > x1_STAR_MC(g);
DistMatrix<F,STAR,MR > z_STAR_MR(g);
// Views of z[* ,MR], which will store updates to x
DistMatrix<F,STAR,MR> z0_STAR_MR(g),
z1_STAR_MR(g);
z_STAR_MR.AlignWith( L );
Zeros( 1, x.Width(), z_STAR_MR );
// Start the algorithm
PartitionLeft( x, xL, xR, 0 );
while( xL.Width() > 0 )
{
RepartitionLeft
( xL, /**/ xR,
x0, x1, /**/ x2 );
const int n0 = x0.Width();
const int n1 = x1.Width();
LockedView( L10, L, n0, 0, n1, n0 );
LockedView( L11, L, n0, n0, n1, n1 );
View( z0_STAR_MR, z_STAR_MR, 0, 0, 1, n0 );
View( z1_STAR_MR, z_STAR_MR, 0, n0, 1, n1 );
x1_STAR_MC.AlignWith( L10 );
//----------------------------------------------------------------//
if( x2.Width() != 0 )
x1.SumScatterUpdate( F(1), z1_STAR_MR );
x1_STAR_STAR = x1;
L11_STAR_STAR = L11;
Trsv
( LOWER, orientation, diag,
L11_STAR_STAR.LockedMatrix(),
x1_STAR_STAR.Matrix() );
x1 = x1_STAR_STAR;
x1_STAR_MC = x1_STAR_STAR;
Gemv
( orientation, F(-1),
L10.LockedMatrix(),
x1_STAR_MC.LockedMatrix(),
F(1), z0_STAR_MR.Matrix() );
//----------------------------------------------------------------//
x1_STAR_MC.FreeAlignments();
SlidePartitionLeft
( xL, /**/ xR,
x0, /**/ x1, x2 );
}
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TrsvUN( UnitOrNonUnit diag, const DistMatrix<F>& U, DistMatrix<F>& x )
{
#ifndef RELEASE
PushCallStack("internal::TrsvUN");
if( U.Grid() != x.Grid() )
throw std::logic_error("{U,x} must be distributed over the same grid");
if( U.Height() != U.Width() )
throw std::logic_error("U must be square");
if( x.Width() != 1 && x.Height() != 1 )
throw std::logic_error("x must be a vector");
const int xLength = ( x.Width() == 1 ? x.Height() : x.Width() );
if( U.Width() != xLength )
throw std::logic_error("Nonconformal TrsvUN");
#endif
const Grid& g = U.Grid();
if( x.Width() == 1 )
{
// Matrix views
DistMatrix<F> U01(g),
U11(g);
DistMatrix<F>
xT(g), x0(g),
xB(g), x1(g),
x2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
DistMatrix<F,MR, STAR> x1_MR_STAR(g);
DistMatrix<F,MC, STAR> z_MC_STAR(g);
// Views of z[MC,* ], which will store updates to x
DistMatrix<F,MC,STAR> z0_MC_STAR(g),
z1_MC_STAR(g);
z_MC_STAR.AlignWith( U );
Zeros( x.Height(), 1, z_MC_STAR );
// Start the algorithm
PartitionUp
( x, xT,
xB, 0 );
while( xT.Height() > 0 )
{
RepartitionUp
( xT, x0,
x1,
/**/ /**/
xB, x2 );
const int n0 = x0.Height();
const int n1 = x1.Height();
LockedView( U01, U, 0, n0, n0, n1 );
LockedView( U11, U, n0, n0, n1, n1 );
View( z0_MC_STAR, z_MC_STAR, 0, 0, n0, 1 );
View( z1_MC_STAR, z_MC_STAR, n0, 0, n1, 1 );
x1_MR_STAR.AlignWith( U01 );
//----------------------------------------------------------------//
if( x2.Height() != 0 )
x1.SumScatterUpdate( F(1), z1_MC_STAR );
x1_STAR_STAR = x1;
U11_STAR_STAR = U11;
Trsv
( UPPER, NORMAL, diag,
U11_STAR_STAR.LockedLocalMatrix(),
x1_STAR_STAR.LocalMatrix() );
x1 = x1_STAR_STAR;
x1_MR_STAR = x1_STAR_STAR;
Gemv
( NORMAL, F(-1),
U01.LockedLocalMatrix(),
x1_MR_STAR.LockedLocalMatrix(),
F(1), z0_MC_STAR.LocalMatrix() );
//----------------------------------------------------------------//
x1_MR_STAR.FreeAlignments();
SlidePartitionUp
( xT, x0,
/**/ /**/
x1,
xB, x2 );
}
}
else
{
// Matrix views
DistMatrix<F> U01(g),
U11(g);
DistMatrix<F>
xL(g), xR(g),
x0(g), x1(g), x2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
DistMatrix<F,STAR,MR > x1_STAR_MR(g);
DistMatrix<F,MC, MR > z1(g);
DistMatrix<F,MR, MC > z1_MR_MC(g);
DistMatrix<F,STAR,MC > z_STAR_MC(g);
// Views of z[* ,MC]
DistMatrix<F,STAR,MC> z0_STAR_MC(g),
z1_STAR_MC(g);
z_STAR_MC.AlignWith( U );
Zeros( 1, x.Width(), z_STAR_MC );
// Start the algorithm
PartitionLeft( x, xL, xR, 0 );
while( xL.Width() > 0 )
{
RepartitionLeft
( xL, /**/ xR,
x0, x1, /**/ x2 );
const int n0 = x0.Width();
const int n1 = x1.Width();
LockedView( U01, U, 0, n0, n0, n1 );
LockedView( U11, U, n0, n0, n1, n1 );
View( z0_STAR_MC, z_STAR_MC, 0, 0, 1, n0 );
View( z1_STAR_MC, z_STAR_MC, 0, n0, 1, n1 );
x1_STAR_MR.AlignWith( U01 );
z1.AlignWith( x1 );
//----------------------------------------------------------------//
if( x2.Width() != 0 )
{
z1_MR_MC.SumScatterFrom( z1_STAR_MC );
z1 = z1_MR_MC;
Axpy( F(1), z1, x1 );
}
x1_STAR_STAR = x1;
U11_STAR_STAR = U11;
Trsv
( UPPER, NORMAL, diag,
U11_STAR_STAR.LockedLocalMatrix(),
x1_STAR_STAR.LocalMatrix() );
x1 = x1_STAR_STAR;
x1_STAR_MR = x1_STAR_STAR;
Gemv
( NORMAL, F(-1),
U01.LockedLocalMatrix(),
x1_STAR_MR.LockedLocalMatrix(),
F(1), z0_STAR_MC.LocalMatrix() );
//----------------------------------------------------------------//
x1_STAR_MR.FreeAlignments();
z1.FreeAlignments();
SlidePartitionLeft
( xL, /**/ xR,
x0, /**/ x1, x2 );
}
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
internal::TrsvUN
( UnitOrNonUnit diag,
const DistMatrix<F,MC,MR>& U,
DistMatrix<F,MC,MR>& x )
{
#ifndef RELEASE
PushCallStack("internal::TrsvUN");
if( U.Grid() != x.Grid() )
throw std::logic_error("{U,x} must be distributed over the same grid");
if( U.Height() != U.Width() )
throw std::logic_error("U must be square");
if( x.Width() != 1 && x.Height() != 1 )
throw std::logic_error("x must be a vector");
const int xLength = ( x.Width() == 1 ? x.Height() : x.Width() );
if( U.Width() != xLength )
throw std::logic_error("Nonconformal TrsvUN");
#endif
const Grid& g = U.Grid();
if( x.Width() == 1 )
{
// Matrix views
DistMatrix<F,MC,MR>
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,MC,MR>
xT(g), x0(g),
xB(g), x1(g),
x2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
DistMatrix<F,MR, STAR> x1_MR_STAR(g);
DistMatrix<F,MC, STAR> z0_MC_STAR(g);
// Start the algorithm
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 );
x1_MR_STAR.AlignWith( U01 );
z0_MC_STAR.AlignWith( U01 );
z0_MC_STAR.ResizeTo( x0.Height(), 1 );
//----------------------------------------------------------------//
x1_STAR_STAR = x1;
U11_STAR_STAR = U11;
Trsv
( UPPER, NORMAL, diag,
U11_STAR_STAR.LockedLocalMatrix(),
x1_STAR_STAR.LocalMatrix() );
x1 = x1_STAR_STAR;
x1_MR_STAR = x1_STAR_STAR;
Gemv
( NORMAL, (F)-1,
U01.LockedLocalMatrix(),
x1_MR_STAR.LockedLocalMatrix(),
(F)0, z0_MC_STAR.LocalMatrix() );
x0.SumScatterUpdate( (F)1, z0_MC_STAR );
//----------------------------------------------------------------//
x1_MR_STAR.FreeAlignments();
z0_MC_STAR.FreeAlignments();
SlideLockedPartitionUpDiagonal
( UTL, /**/ UTR, U00, /**/ U01, U02,
/*************/ /******************/
/**/ U10, /**/ U11, U12,
UBL, /**/ UBR, U20, /**/ U21, U22 );
SlidePartitionUp
( xT, x0,
/**/ /**/
x1,
xB, x2 );
}
}
else
{
// Matrix views
DistMatrix<F,MC,MR>
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,MC,MR>
xL(g), xR(g),
x0(g), x1(g), x2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
DistMatrix<F,STAR,MR > x1_STAR_MR(g);
DistMatrix<F,STAR,MC > z0_STAR_MC(g);
DistMatrix<F,MR, MC > z0_MR_MC(g);
DistMatrix<F,MC, MR > z0(g);
// Start the algorithm
LockedPartitionUpDiagonal
( U, UTL, UTR,
UBL, UBR, 0 );
PartitionLeft( x, xL, xR, 0 );
while( xL.Width() > 0 )
{
LockedRepartitionUpDiagonal
( UTL, /**/ UTR, U00, U01, /**/ U02,
/**/ U10, U11, /**/ U12,
/*************/ /******************/
UBL, /**/ UBR, U20, U21, /**/ U22 );
RepartitionLeft
( xL, /**/ xR,
x0, x1, /**/ x2 );
x1_STAR_MR.AlignWith( U01 );
z0_STAR_MC.AlignWith( U01 );
z0.AlignWith( x0 );
z0_STAR_MC.ResizeTo( 1, x0.Width() );
//----------------------------------------------------------------//
x1_STAR_STAR = x1;
U11_STAR_STAR = U11;
Trsv
( UPPER, NORMAL, diag,
U11_STAR_STAR.LockedLocalMatrix(),
x1_STAR_STAR.LocalMatrix() );
x1 = x1_STAR_STAR;
x1_STAR_MR = x1_STAR_STAR;
Gemv
( NORMAL, (F)-1,
U01.LockedLocalMatrix(),
x1_STAR_MR.LockedLocalMatrix(),
(F)0, z0_STAR_MC.LocalMatrix() );
z0_MR_MC.SumScatterFrom( z0_STAR_MC );
z0 = z0_MR_MC;
Axpy( (F)1, z0, x0 );
//----------------------------------------------------------------//
x1_STAR_MR.FreeAlignments();
z0_STAR_MC.FreeAlignments();
z0.FreeAlignments();
SlideLockedPartitionUpDiagonal
( UTL, /**/ UTR, U00, /**/ U01, U02,
/*************/ /******************/
/**/ U10, /**/ U11, U12,
UBL, /**/ UBR, U20, /**/ U21, U22 );
SlidePartitionLeft
( xL, /**/ xR,
x0, /**/ x1, x2 );
}
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TrmmRUNC
( UnitOrNonUnit diag,
T alpha, const DistMatrix<T>& U,
DistMatrix<T>& X )
{
#ifndef RELEASE
CallStackEntry entry("internal::TrmmRUNC");
if( U.Grid() != X.Grid() )
throw std::logic_error
("U and X must be distributed over the same grid");
if( U.Height() != U.Width() || X.Width() != U.Height() )
{
std::ostringstream msg;
msg << "Nonconformal TrmmRUNC: \n"
<< " U ~ " << U.Height() << " x " << U.Width() << "\n"
<< " X ~ " << X.Height() << " x " << X.Width() << "\n";
throw std::logic_error( msg.str().c_str() );
}
#endif
const Grid& g = U.Grid();
// Matrix views
DistMatrix<T>
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<T> XL(g), XR(g),
X0(g), X1(g), X2(g);
// Temporary distributions
DistMatrix<T,MR, STAR> U12Trans_MR_STAR(g);
DistMatrix<T,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<T,VC, STAR> X1_VC_STAR(g);
DistMatrix<T,MC, STAR> X1_MC_STAR(g);
// Start the algorithm
Scale( alpha, X );
LockedPartitionUpDiagonal
( U, UTL, UTR,
UBL, UBR, 0 );
PartitionLeft( X, XL, XR, 0 );
while( XL.Width() > 0 )
{
LockedRepartitionUpDiagonal
( UTL, /**/ UTR, U00, U01, /**/ U02,
/**/ U10, U11, /**/ U12,
/*************/ /******************/
UBL, /**/ UBR, U20, U21, /**/ U22 );
RepartitionLeft
( XL, /**/ XR,
X0, X1, /**/ X2 );
X1_MC_STAR.AlignWith( X2 );
U12Trans_MR_STAR.AlignWith( X2 );
X1_VC_STAR.AlignWith( X1 );
//--------------------------------------------------------------------//
X1_MC_STAR = X1;
U12Trans_MR_STAR.TransposeFrom( U12 );
LocalGemm
( NORMAL, TRANSPOSE, T(1), X1_MC_STAR, U12Trans_MR_STAR, T(1), X2 );
U11_STAR_STAR = U11;
X1_VC_STAR = X1_MC_STAR;
LocalTrmm
( RIGHT, UPPER, NORMAL, diag, T(1), U11_STAR_STAR, X1_VC_STAR );
X1 = X1_VC_STAR;
//--------------------------------------------------------------------//
X1_MC_STAR.FreeAlignments();
U12Trans_MR_STAR.FreeAlignments();
X1_VC_STAR.FreeAlignments();
SlideLockedPartitionUpDiagonal
( UTL, /**/ UTR, U00, /**/ U01, U02,
/*************/ /******************/
/**/ U10, /**/ U11, U12,
UBL, /**/ UBR, U20, /**/ U21, U22 );
SlidePartitionLeft
( XL, /**/ XR,
X0, /**/ X1, X2 );
}
}
inline void
internal::TrsvLT
( Orientation orientation,
UnitOrNonUnit diag,
const DistMatrix<F,MC,MR>& L,
DistMatrix<F,MC,MR>& x )
{
#ifndef RELEASE
PushCallStack("internal::TrsvLT");
if( L.Grid() != x.Grid() )
throw std::logic_error("{L,x} must be distributed over the same grid");
if( orientation == NORMAL )
throw std::logic_error("TrsvLT expects a (conjugate-)transpose option");
if( L.Height() != L.Width() )
throw std::logic_error("L must be square");
if( x.Width() != 1 && x.Height() != 1 )
throw std::logic_error("x must be a vector");
const int xLength = ( x.Width() == 1 ? x.Height() : x.Width() );
if( L.Width() != xLength )
throw std::logic_error("Nonconformal TrsvLT");
#endif
const Grid& g = L.Grid();
if( x.Width() == 1 )
{
// Matrix views
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);
DistMatrix<F,MC,MR>
xT(g), x0(g),
xB(g), x1(g),
x2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
DistMatrix<F,MC, STAR> x1_MC_STAR(g);
DistMatrix<F,MR, STAR> z0_MR_STAR(g);
DistMatrix<F,MR, MC > z0_MR_MC(g);
DistMatrix<F,MC, MR > z0(g);
// Start the algorithm
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_MC_STAR.AlignWith( L10 );
z0_MR_STAR.AlignWith( L10 );
z0_MR_STAR.ResizeTo( x0.Height(), 1 );
z0.AlignWith( x0 );
//----------------------------------------------------------------//
x1_STAR_STAR = x1;
L11_STAR_STAR = L11;
Trsv
( LOWER, orientation, diag,
L11_STAR_STAR.LockedLocalMatrix(),
x1_STAR_STAR.LocalMatrix() );
x1 = x1_STAR_STAR;
x1_MC_STAR = x1_STAR_STAR;
Gemv
( orientation, (F)-1,
L10.LockedLocalMatrix(),
x1_MC_STAR.LockedLocalMatrix(),
(F)0, z0_MR_STAR.LocalMatrix() );
z0_MR_MC.SumScatterFrom( z0_MR_STAR );
z0 = z0_MR_MC;
Axpy( (F)1, z0, x0 );
//----------------------------------------------------------------//
x1_MC_STAR.FreeAlignments();
z0_MR_STAR.FreeAlignments();
z0.FreeAlignments();
SlideLockedPartitionUpDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
SlidePartitionUp
( xT, x0,
/**/ /**/
x1,
xB, x2 );
}
}
else
{
// Matrix views
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);
DistMatrix<F,MC,MR>
xL(g), xR(g),
x0(g), x1(g), x2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
DistMatrix<F,STAR,MC > x1_STAR_MC(g);
DistMatrix<F,STAR,MR > z0_STAR_MR(g);
// Start the algorithm
LockedPartitionUpDiagonal
( L, LTL, LTR,
LBL, LBR, 0 );
PartitionLeft( x, xL, xR, 0 );
while( xL.Width() > 0 )
{
LockedRepartitionUpDiagonal
( LTL, /**/ LTR, L00, L01, /**/ L02,
/**/ L10, L11, /**/ L12,
/*************/ /******************/
LBL, /**/ LBR, L20, L21, /**/ L22 );
RepartitionLeft
( xL, /**/ xR,
x0, x1, /**/ x2 );
x1_STAR_MC.AlignWith( L10 );
z0_STAR_MR.AlignWith( L10 );
//----------------------------------------------------------------//
x1_STAR_STAR = x1;
L11_STAR_STAR = L11;
Trsv
( LOWER, orientation, diag,
L11_STAR_STAR.LockedLocalMatrix(),
x1_STAR_STAR.LocalMatrix() );
x1 = x1_STAR_STAR;
x1_STAR_MC = x1_STAR_STAR;
Gemv
( orientation, (F)-1,
L10.LockedLocalMatrix(),
x1_STAR_MC.LockedLocalMatrix(),
(F)0, z0_STAR_MR.LocalMatrix() );
x0.SumScatterUpdate( (F)1, z0_STAR_MR );
//----------------------------------------------------------------//
x1_STAR_MC.FreeAlignments();
z0_STAR_MR.FreeAlignments();
SlideLockedPartitionUpDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
SlidePartitionLeft
( xL, /**/ xR,
x0, /**/ x1, x2 );
}
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TrsmRUT
( Orientation orientation, UnitOrNonUnit diag,
F alpha, const DistMatrix<F>& U, DistMatrix<F>& X,
bool checkIfSingular )
{
#ifndef RELEASE
PushCallStack("internal::TrsmRUT");
if( orientation == NORMAL )
throw std::logic_error("TrsmRUT expects a (Conjugate)Transpose option");
#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> XL(g), XR(g),
X0(g), X1(g), X2(g);
// Temporary distributions
DistMatrix<F,VR, STAR> U01_VR_STAR(g);
DistMatrix<F,STAR,MR > U01AdjOrTrans_STAR_MR(g);
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,VC, STAR> X1_VC_STAR(g);
DistMatrix<F,STAR,MC > X1Trans_STAR_MC(g);
// Start the algorithm
Scale( alpha, X );
LockedPartitionUpDiagonal
( U, UTL, UTR,
UBL, UBR, 0 );
PartitionLeft( X, XL, XR, 0 );
while( XL.Width() > 0 )
{
LockedRepartitionUpDiagonal
( UTL, /**/ UTR, U00, U01, /**/ U02,
/**/ U10, U11, /**/ U12,
/*************/ /******************/
UBL, /**/ UBR, U20, U21, /**/ U22 );
RepartitionLeft
( XL, /**/ XR,
X0, X1, /**/ X2 );
X1_VC_STAR.AlignWith( X0 );
X1Trans_STAR_MC.AlignWith( X0 );
U01_VR_STAR.AlignWith( X0 );
U01AdjOrTrans_STAR_MR.AlignWith( X0 );
//--------------------------------------------------------------------//
U11_STAR_STAR = U11;
X1_VC_STAR = X1;
LocalTrsm
( RIGHT, UPPER, orientation, diag,
F(1), U11_STAR_STAR, X1_VC_STAR, checkIfSingular );
X1Trans_STAR_MC.TransposeFrom( X1_VC_STAR );
X1.TransposeFrom( X1Trans_STAR_MC );
U01_VR_STAR = U01;
if( orientation == ADJOINT )
U01AdjOrTrans_STAR_MR.AdjointFrom( U01_VR_STAR );
else
U01AdjOrTrans_STAR_MR.TransposeFrom( U01_VR_STAR );
// X0[MC,MR] -= X1[MC,* ] (U01[MR,* ])^(T/H)
// = X1^T[* ,MC] (U01^(T/H))[* ,MR]
LocalGemm
( TRANSPOSE, NORMAL,
F(-1), X1Trans_STAR_MC, U01AdjOrTrans_STAR_MR, F(1), X0 );
//--------------------------------------------------------------------//
X1_VC_STAR.FreeAlignments();
X1Trans_STAR_MC.FreeAlignments();
U01_VR_STAR.FreeAlignments();
U01AdjOrTrans_STAR_MR.FreeAlignments();
SlideLockedPartitionUpDiagonal
( UTL, /**/ UTR, U00, /**/ U01, U02,
/*************/ /******************/
/**/ U10, /**/ U11, U12,
UBL, /**/ UBR, U20, /**/ U21, U22 );
SlidePartitionLeft
( XL, /**/ XR,
X0, /**/ X1, X2 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TrsmRLN
( UnitOrNonUnit diag, F alpha, const DistMatrix<F>& L, DistMatrix<F>& X,
bool checkIfSingular )
{
#ifndef RELEASE
PushCallStack("internal::TrsmRLN");
#endif
const Grid& g = L.Grid();
// Matrix views
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);
DistMatrix<F> XL(g), XR(g),
X0(g), X1(g), X2(g);
// Temporary distributions
DistMatrix<F,MR, STAR> L10Trans_MR_STAR(g);
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,STAR,MC > X1Trans_STAR_MC(g);
DistMatrix<F,VC, STAR> X1_VC_STAR(g);
// Start the algorithm
Scale( alpha, X );
LockedPartitionUpDiagonal
( L, LTL, LTR,
LBL, LBR, 0 );
PartitionLeft( X, XL, XR, 0 );
while( XL.Width() > 0 )
{
LockedRepartitionUpDiagonal
( LTL, /**/ LTR, L00, L01, /**/ L02,
/**/ L10, L11, /**/ L12,
/*************/ /******************/
LBL, /**/ LBR, L20, L21, /**/ L22 );
RepartitionLeft
( XL, /**/ XR,
X0, X1, /**/ X2 );
X1Trans_STAR_MC.AlignWith( X0 );
L10Trans_MR_STAR.AlignWith( X0 );
//--------------------------------------------------------------------//
L11_STAR_STAR = L11;
X1_VC_STAR = X1;
LocalTrsm
( RIGHT, LOWER, NORMAL, diag, F(1), L11_STAR_STAR, X1_VC_STAR,
checkIfSingular );
// X0[MC,MR] -= X1[MC,* ] L10[*,MR]
// = X1^T[* ,MC] L10^T[MR,* ]
X1Trans_STAR_MC.TransposeFrom( X1_VC_STAR );
X1.TransposeFrom( X1Trans_STAR_MC );
L10Trans_MR_STAR.TransposeFrom( L10 );
LocalGemm
( TRANSPOSE, TRANSPOSE,
F(-1), X1Trans_STAR_MC, L10Trans_MR_STAR, F(1), X0 );
//--------------------------------------------------------------------//
X1Trans_STAR_MC.FreeAlignments();
L10Trans_MR_STAR.FreeAlignments();
SlideLockedPartitionUpDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
SlidePartitionLeft
( XL, /**/ XR,
X0, /**/ X1, X2 );
}
#ifndef RELEASE
PopCallStack();
#endif
}