JAMA::SVD< Real > Class Template Reference

#include <jama_svd.h>

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

Public Member Functions

 SVD (const Array2D< Real > &Arg)
void getU (Array2D< Real > &A)
void getV (Array2D< Real > &A)
void getSingularValues (Array1D< Real > &x)
void getS (Array2D< Real > &A)
double norm2 ()
double cond ()
int rank ()

Private Attributes

Array2D< Real > U
Array2D< Real > V
Array1D< Real > s
int m
int n


Detailed Description

template<class Real>
class JAMA::SVD< Real >

Singular Value Decomposition.

For an m-by-n matrix A with m >= n, the singular value decomposition is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and an n-by-n orthogonal matrix V so that A = U*S*V'.

The singular values, sigma[k] = S[k][k], are ordered so that sigma[0] >= sigma[1] >= ... >= sigma[n-1].

The singular value decompostion always exists, so the constructor will never fail. The matrix condition number and the effective numerical rank can be computed from this decomposition.

(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 39 of file jama_svd.h.


Constructor & Destructor Documentation

template<class Real>
JAMA::SVD< Real >::SVD ( const Array2D< Real > &  Arg  )  [inline]

Definition at line 50 of file jama_svd.h.


Member Function Documentation

template<class Real>
double JAMA::SVD< Real >::cond (  )  [inline]

Two norm of condition number (max(S)/min(S))

Definition at line 514 of file jama_svd.h.

template<class Real>
void JAMA::SVD< Real >::getS ( Array2D< Real > &  A  )  [inline]

Return the diagonal matrix of singular values

Returns:
S

Definition at line 496 of file jama_svd.h.

template<class Real>
void JAMA::SVD< Real >::getSingularValues ( Array1D< Real > &  x  )  [inline]

Return the one-dimensional array of singular values

Definition at line 487 of file jama_svd.h.

template<class Real>
void JAMA::SVD< Real >::getU ( Array2D< Real > &  A  )  [inline]

Definition at line 466 of file jama_svd.h.

template<class Real>
void JAMA::SVD< Real >::getV ( Array2D< Real > &  A  )  [inline]

Definition at line 480 of file jama_svd.h.

template<class Real>
double JAMA::SVD< Real >::norm2 (  )  [inline]

Two norm (max(S))

Definition at line 508 of file jama_svd.h.

template<class Real>
int JAMA::SVD< Real >::rank (  )  [inline]

Effective numerical matrix rank

Returns:
Number of nonnegligible singular values.

Definition at line 522 of file jama_svd.h.


Member Data Documentation

template<class Real>
int JAMA::SVD< Real >::m [private]

Definition at line 45 of file jama_svd.h.

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

Definition at line 45 of file jama_svd.h.

template<class Real>
Array1D<Real> JAMA::SVD< Real >::s [private]

Definition at line 44 of file jama_svd.h.

template<class Real>
Array2D<Real> JAMA::SVD< Real >::U [private]

Definition at line 43 of file jama_svd.h.

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

Definition at line 43 of file jama_svd.h.


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

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