vnl_symmetric_eigensystem.h File Reference

Find eigenvalues of a symmetric matrix. More...

Go to the source code of this file.

Compounds
class	vnl_symmetric_eigensystem
Functions
bool	vnl_symmetric_eigensystem_compute (vnl_matrix< float > const &A, vnl_matrix< float > &V, vnl_vector< float > &D)
bool	vnl_symmetric_eigensystem_compute (vnl_matrix< double > const &A, vnl_matrix< double > &V, vnl_vector< double > &D)

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Detailed Description

Find eigenvalues of a symmetric matrix.

Author:

Andrew W. Fitzgibbon, Oxford RRG, 29 Aug 96

    Modifications
    fsm@robots, 5 March 2000: templated
    dac (Manchester) 28/03/2001: tidied up documentation
    

Definition in file vnl_symmetric_eigensystem.h.

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Function Documentation

bool vnl_symmetric_eigensystem_compute (  vnl_matrix< double > const &    A, vnl_matrix< double > &    V, vnl_vector< double > &    D )

Find eigenvalues of a symmetric matrix. Solve the eigenproblem , with symmetric. The resulting eigenvectors and values are sorted in increasing order so V.column(0) is the eigenvector corresponding to the smallest the smallest eigenvalue.

bool vnl_symmetric_eigensystem_compute (  vnl_matrix< float > const &    A, vnl_matrix< float > &    V, vnl_vector< float > &    D )

Find eigenvalues of a symmetric matrix. Solve the eigenproblem , with symmetric. The resulting eigenvectors and values are sorted in increasing order so V.column(0) is the eigenvector corresponding to the smallest the smallest eigenvalue. As a matrix decomposition, this is Uses the EISPACK routine RS, which in turn calls TRED2 to reduce A to tridiagonal form, followed by TQL2, to find the eigensystem. This is summarized in Golub and van Loan, \S8.2. The following are the original subroutine headers: Remarks: TRED2 is a translation of the Algol procedure tred2, Num. Math. 11, 181-195(1968) by Martin, Reinsch, and Wilkinson. Handbook for Auto. Comp., Vol.ii-Linear Algebra, 212-226(1971). Remarks: This subroutine reduces a real symmetric matrix to a symmetric tridiagonal matrix using and accumulating orthogonal similarity transformations. Remarks: TQL2 is a translation of the Algol procedure tql2, Num. Math. 11, 293-306(1968) by Bowdler, Martin, Reinsch, and Wilkinson. Handbook for Auto. Comp., Vol.ii-Linear Algebra, 227-240(1971). Remarks: This subroutine finds the eigenvalues and eigenvectors of a symmetric tridiagonal matrix by the QL method. the eigenvectors of a full symmetric matrix can also be found if tred2 has been used to reduce this full matrix to tridiagonal form.

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