SingularValueDecomposition

java.lang.Object
- weka.core.matrix.SingularValueDecomposition

All Implemented Interfaces:

java.io.Serializable, RevisionHandler
```
public class SingularValueDecomposition
extends java.lang.Object
implements java.io.Serializable, RevisionHandler
```
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 the JAMA package.

Version:

$Revision: 11815 $

Author:

The Mathworks and NIST, Fracpete (fracpete at waikato dot ac dot nz), eibe@cs.waikato.ac.nz

See Also:

Serialized Form

Constructor Summary

Constructors
Constructor Description

SingularValueDecomposition(Matrix Arg)
Construct the singular value decomposition

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`double`	`cond()`	Two norm condition number
`java.lang.String`	`getRevision()`	Returns the revision string.
`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
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - SingularValueDecomposition
```
public SingularValueDecomposition(Matrix Arg)
```
    Construct the singular value decomposition
    
    Parameters:
    
    Arg - 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.
  - getRevision
```
public java.lang.String getRevision()
```
    Returns the revision string.
    
    Specified by:
    
    getRevision in interface RevisionHandler
    
    Returns:
    
    the revision