RWBandTriDiagDecomp< TypeT > Class Template Reference

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

#include <rw/lapack/td.h>

Inheritance diagram for RWBandTriDiagDecomp< TypeT >:

Public Member Functions
	RWBandTriDiagDecomp (const typename rw_linear_algebra_traits< TypeT >::banded_hermitian_type &A, bool keepQ=true)
virtual RWGenMat< TypeT >	transform (const RWGenMat< rt > &x) const
virtual RWMathVec< TypeT >	transform (const RWMathVec< rt > &x) const
Public Member Functions inherited from RWTriDiagDecomp< TypeT >
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_)

Additional Inherited Members
Public Types inherited from RWTriDiagDecomp< TypeT >
typedef rw_numeric_traits< TypeT >::norm_type	rt

Detailed Description

template<class TypeT>
class RWBandTriDiagDecomp< TypeT >

The class RWBandTriDiagDecomp encapsulates a symmetric tridiagonal decomposition of a symmetric banded matrix A:

\[ A = QTQ^\prime \]

where Q is orthogonal and T is real tridiagonal symmetric. This class is used internally by the symmetric eigenvalue classes.

Synopsis

#include <rw/lapack/td.h>

RWBandTriDiagDecomp<double>(A);  // A is a DoubleSymMat

Example

#include <rw/lapack/sbndmat.h>
#include <rw/lapack/td.h>
#include <iostream>

int main()
{
    RWSymBandMat<double> A;
    std::cin >> A;
    RWSymBandTriDiagDecomp<double> decomp(A);
    std::cout << "T's diagonal is" << decomp.diagonal() << std::endl;
    std::cout << "T's off diagonal is " << decomp.offDiagonal()
               << std::endl;
    return 0;
}

Constructor & Destructor Documentation

template<class TypeT >

RWBandTriDiagDecomp< TypeT >::RWBandTriDiagDecomp	(	const typename rw_linear_algebra_traits< TypeT >::banded_hermitian_type &	A,
		bool	keepQ = true
	)

Constructs a tridiagonal decomposition of A. By setting the optional boolean parameter keepQ to false, the data necessary to transform via Q is not stored. This can save substantial storage costs, but an exception is thrown if you attempt to use the member function transform.

Member Function Documentation

template<class TypeT >

virtual RWGenMat<TypeT> RWBandTriDiagDecomp< TypeT >::transform ( const RWGenMat< 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.

Implements RWTriDiagDecomp< TypeT >.

template<class TypeT >

virtual RWMathVec<TypeT> RWBandTriDiagDecomp< 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 from RWTriDiagDecomp< TypeT >.