RWDenseTriDiagDecomp< TypeT > Class Template Reference

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

#include <rw/lapack/td.h>

Inheritance diagram for RWDenseTriDiagDecomp< TypeT >:

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

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

\[ A = QTQ^\prime \]

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>

Example

#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;
}

Constructor & Destructor Documentation

RWDenseTriDiagDecomp()

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

transform() [1/2]

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 >.

transform() [2/2]

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 >.