Jama

Class SingularValueDecomposition

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

Constructor Details

SingularValueDecomposition

public SingularValueDecomposition(Matrix Arg)
Construct the singular value decomposition
Parameters:

Method Details

cond

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

getS

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

getSingularValues

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

getU

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

getV

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

norm2

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

rank

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