RWTriDiagDecomp< TypeT > Class Template Reference

Encapsulates the tridiagonal decomposition of a symmetric matrix. More...

#include <rw/lapack/td.h>

Inheritance diagram for RWTriDiagDecomp< TypeT >:

Public Types
typedef rw_numeric_traits< TypeT >::norm_type	rt

Public Member Functions
unsigned	cols () const
const RWMathVec< rt >	diagonal () const
const RWMathVec< rt >	offDiagonal () const
unsigned	rows () const
void	set (const RWMathVec< rt > &diag_, const RWMathVec< rt > &offdiag_)
virtual RWGenMat< TypeT >	transform (const RWGenMat< rt > &) const =0
virtual RWMathVec< TypeT >	transform (const RWMathVec< rt > &) const

Detailed Description

template<class TypeT>
class RWTriDiagDecomp< TypeT >

The class RWTriDiagDecomp encapsulates the tridiagonal decomposition of a symmetric matrix A:

\[ A = Q^{\prime}TQ \]

where Q is orthogonal and T is tridiagonal and real, even in the complex case. This decomposition is often done as a precursor to computing eigenvalues, since the eigenvalues of T and A are the same, and those of T are easier to compute. This class is used internally by the symmetric eigenvalue classes.

The class RWTriDiagDecomp is an abstract base class. Subclasses must implement the pure virtual function decompose. This separates the implementation of the storage of Q from the interface, so that band and dense decompositions can use different storage techniques. The Linear Algebra Module provides the derived classes RWDenseTriDiagDecomp and RWBandTriDiagDecomp.

Synopsis

#include <rw/lapack/td.h>

Example

See specific subclasses for examples.

Member Typedef Documentation

rt

template<class TypeT >

typedef rw_numeric_traits<TypeT>::norm_type RWTriDiagDecomp< TypeT >::rt

Typedef for the usual return type of numerical norm-like functions. For more information, see rw_numeric_traits<T>::norm_type.

Member Function Documentation

cols()

template<class TypeT >

unsigned RWTriDiagDecomp< TypeT >::cols ( ) const

inline

Returns the number of columns in the decomposition.

diagonal()

template<class TypeT >

const RWMathVec< rt > RWTriDiagDecomp< TypeT >::diagonal ( ) const

inline

Returns the diagonal of the symmetric tridiagonal matrix T.

offDiagonal()

template<class TypeT >

const RWMathVec< rt > RWTriDiagDecomp< TypeT >::offDiagonal ( ) const

inline

Returns the subdiagonal or superdiagonal of the symmetric tridiagonal matrix T.

rows()

template<class TypeT >

unsigned RWTriDiagDecomp< TypeT >::rows ( ) const

inline

Returns the number of rows in the decomposition.

set()

template<class TypeT >

void RWTriDiagDecomp< TypeT >::set	(	const RWMathVec< rt > &	diag_,
		const RWMathVec< rt > &	offdiag_ )

Sets the tridiagonal matrix directly.

transform() [1/2]

template<class TypeT >

virtual RWGenMat< TypeT > RWTriDiagDecomp< TypeT >::transform ( const RWGenMat< rt > & ) const

pure virtual

Transforms the vector from tridiagonal decomposition space back to the original matrix space. This amounts to multiplying it by the matrix Q.

Implemented in RWBandTriDiagDecomp< TypeT >, and RWDenseTriDiagDecomp< TypeT >.

transform() [2/2]

template<class TypeT >

virtual RWMathVec< TypeT > RWTriDiagDecomp< TypeT >::transform ( const RWMathVec< rt > & ) const

virtual

Transforms the vector from tridiagonal decomposition space back to the original matrix space. This amounts to multiplying it by the matrix Q.

Reimplemented in RWBandTriDiagDecomp< TypeT >, and RWDenseTriDiagDecomp< TypeT >.