RWTriDiagDecomp< TypeT > Class Template Reference
[Symmetric Eigenvalue Decomposition]

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

#include <rw/lapack/td.h>

Inheritance diagram for RWTriDiagDecomp< TypeT >:

List of all members.

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

---

Detailed Description

template<class TypeT>
class RWTriDiagDecomp< TypeT >

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

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<T> 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<T> and RWBandTriDiagDecomp<T> .

Synopsis

 #include <rw/lapack/td.h>

Examples

See specific subclasses for examples.

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Member Typedef Documentation

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.

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

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Member Function Documentation

template<class TypeT >

unsigned RWTriDiagDecomp< TypeT >::cols

(

)

const [inline]

Returns the number of columns in the decomposition.

template<class TypeT >

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

(

)

const [inline]

Returns the diagonal of the symmetric tridiagonal matrix T.

template<class TypeT >

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

(

)

const [inline]

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

template<class TypeT >

unsigned RWTriDiagDecomp< TypeT >::rows

(

)

const [inline]

Returns the number of rows in the decomposition.

template<class TypeT >

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

Sets the tridiagonal matrix directly.

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 RWDenseTriDiagDecomp< TypeT >, and RWBandTriDiagDecomp< TypeT >.

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 RWDenseTriDiagDecomp< TypeT >, and RWBandTriDiagDecomp< TypeT >.