RWDenseTriDiagDecomp< TypeT > Class Template Reference
[Decomposition]

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

#include <rw/lapack/td.h>

Inheritance diagram for RWDenseTriDiagDecomp< TypeT >:

List of all members.

Public Types
typedef rw_numeric_traits < TypeT >::norm_type	rt
Public Member Functions
	RWDenseTriDiagDecomp (const typename rw_linear_algebra_traits< TypeT >::hermitian_type &A)
virtual RWMathVec< TypeT >	transform (const RWMathVec< rt > &) const
virtual RWGenMat< TypeT >	transform (const RWGenMat< rt > &) const

---

Detailed Description

template<class TypeT>
class RWDenseTriDiagDecomp< TypeT >

The class RWDenseTriDiagDecomp<T> encapsulates the symmetric tridiagonal decomposition of a dense symmetric matrix A, where:

and Q is orthogonal and T is real tridiagonal symmetric. These classes are used internally by the symmetric eigenvalue classes.

Synopsis

 #include <rw/lapack/td.h>

 RWDenseTriDiagDecomp<double> QTQ(A);    // A is a
                                   // RWSymMat<double>

Examples

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

 int main()
 {
     RWSymMat<double> A;
     std::cin >> A;
     RWDenseTriDiagDecomp<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 RWDenseTriDiagDecomp< 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>

RWDenseTriDiagDecomp< TypeT >::RWDenseTriDiagDecomp

(

const typename rw_linear_algebra_traits< TypeT >::hermitian_type &

A

)

Constructs a tridiagonal decomposition of A.

---

Member Function Documentation

template<class TypeT>

virtual RWGenMat<TypeT> RWDenseTriDiagDecomp< 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> RWDenseTriDiagDecomp< 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 >.