void L( Matrix<F>& A, Matrix<F>& t )
{
#ifndef RELEASE
CallStackEntry entry("hermitian_tridiag::L");
if( A.Height() != A.Width() )
LogicError("A must be square");
#endif
typedef BASE(F) R;
const Int tHeight = Max(A.Height()-1,0);
t.ResizeTo( tHeight, 1 );
// Matrix views
Matrix<F>
ATL, ATR, A00, a01, A02, alpha21T,
ABL, ABR, a10, alpha11, a12, a21B,
A20, a21, A22;
// Temporary matrices
Matrix<F> w21;
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ATL.Height()+1 < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ a01, A02,
/*************/ /**********************/
/**/ a10, /**/ alpha11, a12,
ABL, /**/ ABR, A20, /**/ a21, A22, 1 );
PartitionDown
( a21, alpha21T,
a21B, 1 );
//--------------------------------------------------------------------//
const F tau = Reflector( alpha21T, a21B );
const R epsilon1 = alpha21T.GetRealPart(0,0);
t.Set(A00.Height(),0,tau);
alpha21T.Set(0,0,F(1));
Zeros( w21, a21.Height(), 1 );
Hemv( LOWER, tau, A22, a21, F(0), w21 );
const F alpha = -tau*Dot( w21, a21 )/F(2);
Axpy( alpha, a21, w21 );
Her2( LOWER, F(-1), a21, w21, A22 );
alpha21T.Set(0,0,epsilon1);
//--------------------------------------------------------------------//
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, a01, /**/ A02,
/**/ a10, alpha11, /**/ a12,
/*************/ /**********************/
ABL, /**/ ABR, A20, a21, /**/ A22 );
}
}
inline void HermitianTridiagU
( Matrix<Complex<R> >& A, Matrix<Complex<R> >& t )
{
#ifndef RELEASE
PushCallStack("HermitianTridiagU");
#endif
const int tHeight = std::max(A.Height()-1,0);
#ifndef RELEASE
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( t.Viewing() && (t.Height() != tHeight || t.Width() != 1) )
throw std::logic_error("t is of the wrong size");
#endif
typedef Complex<R> C;
if( !t.Viewing() )
t.ResizeTo( tHeight, 1 );
// Matrix views
Matrix<C>
ATL, ATR, A00, a01, A02, a01T,
ABL, ABR, a10, alpha11, a12, alpha01B,
A20, a21, A22;
// Temporary matrices
Matrix<C> w01;
PushBlocksizeStack( 1 );
PartitionUpDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ABR.Height()+1 < A.Height() )
{
RepartitionUpDiagonal
( ATL, /**/ ATR, A00, a01, /**/ A02,
/**/ a10, alpha11, /**/ a12,
/*************/ /**********************/
ABL, /**/ ABR, A20, a21, /**/ A22 );
PartitionUp
( a01, a01T,
alpha01B, 1 );
w01.ResizeTo( a01.Height(), 1 );
//--------------------------------------------------------------------//
const C tau = Reflector( alpha01B, a01T );
const R epsilon1 = alpha01B.GetRealPart(0,0);
t.Set(t.Height()-1-A22.Height(),0,tau);
alpha01B.Set(0,0,C(1));
Hemv( UPPER, tau, A00, a01, C(0), w01 );
const C alpha = -tau*Dot( w01, a01 )/C(2);
Axpy( alpha, a01, w01 );
Her2( UPPER, C(-1), a01, w01, A00 );
alpha01B.Set(0,0,epsilon1);
//--------------------------------------------------------------------//
SlidePartitionUpDiagonal
( ATL, /**/ ATR, A00, /**/ a01, A02,
/*************/ /**********************/
/**/ a10, /**/ alpha11, a12,
ABL, /**/ ABR, A20, /**/ a21, A22 );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}
