Jama
Class SingularValueDecomposition

java.lang.Object
  |
  +--Jama.SingularValueDecomposition
All Implemented Interfaces:
java.io.Serializable

public class SingularValueDecomposition
extends java.lang.Object
implements java.io.Serializable

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.

See Also:
Serialized Form

Constructor Summary
SingularValueDecomposition(Matrix Arg)
          Construct the singular value decomposition
 
Method Summary
 double cond()
          Two norm condition number
 Matrix getS()
          Return the diagonal matrix of singular values
 double[] getSingularValues()
          Return the one-dimensional array of singular values
 Matrix getU()
          Return the left singular vectors
 Matrix getV()
          Return the right singular vectors
 double norm2()
          Two norm
 int rank()
          Effective numerical matrix rank
 
Methods inherited from class java.lang.Object
, clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

SingularValueDecomposition

public SingularValueDecomposition(Matrix Arg)
Construct the singular value decomposition
Parameters:
A - Rectangular matrix
Method Detail

getU

public Matrix getU()
Return the left singular vectors
Returns:
U

getV

public Matrix getV()
Return the right singular vectors
Returns:
V

getSingularValues

public double[] getSingularValues()
Return the one-dimensional array of singular values
Returns:
diagonal of S.

getS

public Matrix getS()
Return the diagonal matrix of singular values
Returns:
S

norm2

public double norm2()
Two norm
Returns:
max(S)

cond

public double cond()
Two norm condition number
Returns:
max(S)/min(S)

rank

public int rank()
Effective numerical matrix rank
Returns:
Number of nonnegligible singular values.