org.openmali.decomposition
Class SingularValueDecomposition

java.lang.Object
  extended by org.openmali.decomposition.SingularValueDecomposition

public class SingularValueDecomposition
extends java.lang.Object

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.


Constructor Summary
SingularValueDecomposition(MatrixMxNf M)
          Constructs the singular value decomposition.
 
Method Summary
 float cond()
          Two norm condition number
 MatrixMxNf getS()
           
 float[] getSingularValues()
          Return the one-dimensional array of singular values
 MatrixMxNf getU()
           
 MatrixMxNf getV()
           
 float 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(MatrixMxNf M)
Constructs the singular value decomposition.

Parameters:
M - Rectangular matrix
Method Detail

getU

public final MatrixMxNf getU()
Returns:
the left singular vectors.

getV

public MatrixMxNf getV()
Returns:
the right singular vectors.

getSingularValues

public float[] getSingularValues()
Return the one-dimensional array of singular values

Returns:
diagonal of S.

getS

public MatrixMxNf getS()
Returns:
the diagonal matrix of singular values.

norm2

public final float norm2()
Two norm

Returns:
max(S)

cond

public final float cond()
Two norm condition number

Returns:
max(S)/min(S)

rank

public int rank()
Effective numerical matrix rank

Returns:
Number of nonnegligible singular values.