JAMA::Eigenvalue< Real > Class Template Reference

#include <jama_eig.h>

Collaboration diagram for JAMA::Eigenvalue< Real >:
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List of all members.

Public Member Functions

 Eigenvalue (const TNT::Array2D< Real > &A)
void getV (TNT::Array2D< Real > &V_)
void getRealEigenvalues (TNT::Array1D< Real > &d_)
void getImagEigenvalues (TNT::Array1D< Real > &e_)
void getD (TNT::Array2D< Real > &D)

Private Member Functions

void tred2 ()
void tql2 ()
void orthes ()
void cdiv (Real xr, Real xi, Real yr, Real yi)
void hqr2 ()

Private Attributes

int n
int issymmetric
TNT::Array1D< Real > d
TNT::Array1D< Real > e
TNT::Array2D< Real > V
TNT::Array2D< Real > H
TNT::Array1D< Real > ort
Real cdivr
Real cdivi


Detailed Description

template<class Real>
class JAMA::Eigenvalue< Real >

Computes eigenvalues and eigenvectors of a real (non-complex) matrix.

If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. That is, the diagonal values of D are the eigenvalues, and V*V' = I, where I is the identity matrix. The columns of V represent the eigenvectors in the sense that A*V = V*D.

If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, a + i*b, in 2-by-2 blocks, [a, b; -b, a]. That is, if the complex eigenvalues look like

          u + iv     .        .          .      .    .
            .      u - iv     .          .      .    .
            .        .      a + ib       .      .    .
            .        .        .        a - ib   .    .
            .        .        .          .      x    .
            .        .        .          .      .    y
then D looks like

            u        v        .          .      .    .
           -v        u        .          .      .    . 
            .        .        a          b      .    .
            .        .       -b          a      .    .
            .        .        .          .      x    .
            .        .        .          .      .    y
This keeps V a real matrix in both symmetric and non-symmetric cases, and A*V = V*D.

The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon the condition number of V.

(Adapted from JAMA, a Java Matrix Library, developed by jointly by the Mathworks and NIST; see http://math.nist.gov/javanumerics/jama).

Definition at line 72 of file jama_eig.h.


Constructor & Destructor Documentation

template<class Real >
JAMA::Eigenvalue< Real >::Eigenvalue ( const TNT::Array2D< Real > &  A  )  [inline]

Check for symmetry, then construct the eigenvalue decomposition

Parameters:
A Square real (non-complex) matrix

Definition at line 903 of file jama_eig.h.


Member Function Documentation

template<class Real >
void JAMA::Eigenvalue< Real >::cdiv ( Real  xr,
Real  xi,
Real  yr,
Real  yi 
) [inline, private]

Definition at line 438 of file jama_eig.h.

template<class Real >
void JAMA::Eigenvalue< Real >::getD ( TNT::Array2D< Real > &  D  )  [inline]

Computes the block diagonal eigenvalue matrix. If the original matrix A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, a + i*b, in 2-by-2 blocks, [a, b; -b, a]. That is, if the complex eigenvalues look like

          u + iv     .        .          .      .    .
            .      u - iv     .          .      .    .
            .        .      a + ib       .      .    .
            .        .        .        a - ib   .    .
            .        .        .          .      x    .
            .        .        .          .      .    y
then D looks like

            u        v        .          .      .    .
           -v        u        .          .      .    . 
            .        .        a          b      .    .
            .        .       -b          a      .    .
            .        .        .          .      x    .
            .        .        .          .      .    y
This keeps V a real matrix in both symmetric and non-symmetric cases, and A*V = V*D.

Parameters:
D,: upon return, the matrix is filled with the block diagonal eigenvalue matrix.

Definition at line 1010 of file jama_eig.h.

template<class Real >
void JAMA::Eigenvalue< Real >::getImagEigenvalues ( TNT::Array1D< Real > &  e_  )  [inline]

Return the imaginary parts of the eigenvalues in parameter e_.

e_: new matrix with imaginary parts of the eigenvalues.

Definition at line 971 of file jama_eig.h.

template<class Real >
void JAMA::Eigenvalue< Real >::getRealEigenvalues ( TNT::Array1D< Real > &  d_  )  [inline]

Return the real parts of the eigenvalues

Returns:
real(diag(D))

Definition at line 961 of file jama_eig.h.

template<class Real >
void JAMA::Eigenvalue< Real >::getV ( TNT::Array2D< Real > &  V_  )  [inline]

Return the eigenvector matrix

Returns:
V

Definition at line 952 of file jama_eig.h.

template<class Real >
void JAMA::Eigenvalue< Real >::hqr2 (  )  [inline, private]

Definition at line 456 of file jama_eig.h.

template<class Real >
void JAMA::Eigenvalue< Real >::orthes (  )  [inline, private]

Definition at line 343 of file jama_eig.h.

template<class Real >
void JAMA::Eigenvalue< Real >::tql2 (  )  [inline, private]

Definition at line 220 of file jama_eig.h.

template<class Real >
void JAMA::Eigenvalue< Real >::tred2 (  )  [inline, private]

Definition at line 103 of file jama_eig.h.


Member Data Documentation

template<class Real >
Real JAMA::Eigenvalue< Real >::cdivi [private]

Definition at line 437 of file jama_eig.h.

template<class Real >
Real JAMA::Eigenvalue< Real >::cdivr [private]

Definition at line 437 of file jama_eig.h.

template<class Real >
TNT::Array1D<Real> JAMA::Eigenvalue< Real >::d [private]

Arrays for internal storage of eigenvalues.

Definition at line 83 of file jama_eig.h.

template<class Real >
TNT::Array1D<Real> JAMA::Eigenvalue< Real >::e [private]

Definition at line 84 of file jama_eig.h.

template<class Real >
TNT::Array2D<Real> JAMA::Eigenvalue< Real >::H [private]

Array for internal storage of nonsymmetric Hessenberg form. internal storage of nonsymmetric Hessenberg form.

Definition at line 92 of file jama_eig.h.

template<class Real >
int JAMA::Eigenvalue< Real >::issymmetric [private]

Definition at line 79 of file jama_eig.h.

template<class Real >
int JAMA::Eigenvalue< Real >::n [private]

Row and column dimension (square matrix).

Definition at line 77 of file jama_eig.h.

template<class Real >
TNT::Array1D<Real> JAMA::Eigenvalue< Real >::ort [private]

Working storage for nonsymmetric algorithm. working storage for nonsymmetric algorithm.

Definition at line 98 of file jama_eig.h.

template<class Real >
TNT::Array2D<Real> JAMA::Eigenvalue< Real >::V [private]

Array for internal storage of eigenvectors.

Definition at line 87 of file jama_eig.h.


The documentation for this class was generated from the following file:

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