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
LocalSymvColAccumulateU
( T alpha,
const DistMatrix<T>& A,
const DistMatrix<T,MC,STAR>& x_MC_STAR,
const DistMatrix<T,MR,STAR>& x_MR_STAR,
DistMatrix<T,MC,STAR>& z_MC_STAR,
DistMatrix<T,MR,STAR>& z_MR_STAR )
{
#ifndef RELEASE
PushCallStack("internal::LocalSymvColAccumulateU");
if( A.Grid() != x_MC_STAR.Grid() ||
x_MC_STAR.Grid() != x_MR_STAR.Grid() ||
x_MR_STAR.Grid() != z_MC_STAR.Grid() ||
z_MC_STAR.Grid() != z_MR_STAR.Grid() )
throw std::logic_error
("{A,x,z} must be distributed over the same grid");
if( x_MC_STAR.Width() != 1 || x_MR_STAR.Width() != 1 ||
z_MC_STAR.Width() != 1 || z_MR_STAR.Width() != 1 )
throw std::logic_error("Expected x and z to be column vectors");
if( A.Height() != A.Width() ||
A.Height() != x_MC_STAR.Height() ||
A.Height() != x_MR_STAR.Height() ||
A.Height() != z_MC_STAR.Height() ||
A.Height() != z_MR_STAR.Height() )
{
std::ostringstream msg;
msg << "Nonconformal LocalSymvColAccumulateU: \n"
<< " A ~ " << A.Height() << " x " << A.Width() << "\n"
<< " x[MC,* ] ~ " << x_MC_STAR.Height() << " x "
<< x_MC_STAR.Width() << "\n"
<< " x[MR,* ] ~ " << x_MR_STAR.Height() << " x "
<< x_MR_STAR.Width() << "\n"
<< " z[MC,* ] ~ " << z_MC_STAR.Height() << " x "
<< z_MC_STAR.Width() << "\n"
<< " z[MR,* ] ~ " << z_MR_STAR.Height() << " x "
<< z_MR_STAR.Width() << "\n";
throw std::logic_error( msg.str() );
}
if( x_MC_STAR.ColAlignment() != A.ColAlignment() ||
x_MR_STAR.ColAlignment() != A.RowAlignment() ||
z_MC_STAR.ColAlignment() != A.ColAlignment() ||
z_MR_STAR.ColAlignment() != A.RowAlignment() )
throw std::logic_error("Partial matrix distributions are misaligned");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<T> A11(g), A12(g);
DistMatrix<T> D11(g);
DistMatrix<T,MC,STAR> x1_MC_STAR(g);
DistMatrix<T,MR,STAR>
xT_MR_STAR(g), x0_MR_STAR(g),
xB_MR_STAR(g), x1_MR_STAR(g),
x2_MR_STAR(g);
DistMatrix<T,MC,STAR> z1_MC_STAR(g);
DistMatrix<T,MR,STAR> z1_MR_STAR(g),
z2_MR_STAR(g);
// We want our local gemvs to be of width blocksize, so we will
// temporarily change to max(r,c) times the current blocksize
const int ratio = std::max( g.Height(), g.Width() );
PushBlocksizeStack( ratio*LocalSymvBlocksize<T>() );
LockedPartitionDown
( x_MR_STAR, xT_MR_STAR,
xB_MR_STAR, 0 );
while( xT_MR_STAR.Height() < x_MR_STAR.Height() )
{
LockedRepartitionDown
( xT_MR_STAR, x0_MR_STAR,
/**********/ /**********/
x1_MR_STAR,
xB_MR_STAR, x2_MR_STAR );
const int n0 = x0_MR_STAR.Height();
const int n1 = x1_MR_STAR.Height();
const int n2 = x2_MR_STAR.Height();
LockedView( A11, A, n0, n0, n1, n1 );
LockedView( A12, A, n0, n0+n1, n1, n2 );
LockedView( x1_MC_STAR, x_MC_STAR, n0, 0, n1, 1 );
View( z1_MC_STAR, z_MC_STAR, n0, 0, n1, 1 );
View( z1_MR_STAR, z_MR_STAR, n0, 0, n1, 1 );
View( z2_MR_STAR, z_MR_STAR, n0+n1, 0, n2, 1 );
D11.AlignWith( A11 );
//--------------------------------------------------------------------//
// TODO: These diagonal block updates can be greatly improved
D11 = A11;
MakeTrapezoidal( LEFT, UPPER, 0, D11 );
Gemv
( NORMAL,
alpha, D11.LockedLocalMatrix(),
x1_MR_STAR.LockedLocalMatrix(),
T(1), z1_MC_STAR.LocalMatrix() );
MakeTrapezoidal( LEFT, UPPER, 1, D11 );
Gemv
( TRANSPOSE,
alpha, D11.LockedLocalMatrix(),
x1_MC_STAR.LockedLocalMatrix(),
T(1), z1_MR_STAR.LocalMatrix() );
Gemv
( NORMAL,
alpha, A12.LockedLocalMatrix(),
x2_MR_STAR.LockedLocalMatrix(),
T(1), z1_MC_STAR.LocalMatrix() );
Gemv
( TRANSPOSE,
alpha, A12.LockedLocalMatrix(),
x1_MC_STAR.LockedLocalMatrix(),
T(1), z2_MR_STAR.LocalMatrix() );
//--------------------------------------------------------------------//
D11.FreeAlignments();
SlideLockedPartitionDown
( xT_MR_STAR, x0_MR_STAR,
x1_MR_STAR,
/**********/ /**********/
xB_MR_STAR, x2_MR_STAR );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}