RWBandTriDiagDecomp< TypeT > Class Template Reference
[Decomposition]

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

#include <rw/lapack/td.h>

Inheritance diagram for RWBandTriDiagDecomp< TypeT >:

List of all members.

Public Types
typedef rw_numeric_traits < TypeT >::norm_type	rt
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

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Detailed Description

template<class TypeT>
class RWBandTriDiagDecomp< TypeT >

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

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

Examples

 #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;
 }

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Member Typedef Documentation

template<class TypeT >

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

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

Reimplemented from RWTriDiagDecomp< TypeT >.

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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.

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Member Function Documentation

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 >.

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 >.