SingularValueDecomposition (MIPAV API Documentation)

java.lang.Object
- gov.nih.mipav.view.renderer.WildMagic.AAM.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

Field Summary

Fields
Modifier and Type	Field	Description
`private int`	`m`	Row and column dimensions.
`private int`	`n`	Row and column dimensions.
`private double[]`	`s`	Array for internal storage of singular values.
`private double[][]`	`U`	Arrays for internal storage of U and V.
`private double[][]`	`V`	Arrays for internal storage of U and V.

Constructor Summary

Constructors
Constructor Description

SingularValueDecomposition(CVisDMatrix 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
`CVisDVector`	`getS()`	Return the diagonal matrix of singular values
`double[]`	`getSingularValues()`	Return the one-dimensional array of singular values
`CVisDMatrix`	`getU()`	Return the left singular vectors
`CVisDMatrix`	`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

- Field Detail
  - U
```
private double[][] U
```
    Arrays for internal storage of U and V.
  - V
```
private double[][] V
```
    Arrays for internal storage of U and V.
  - s
```
private double[] s
```
    Array for internal storage of singular values.
  - m
```
private int m
```
    Row and column dimensions.
  - n
```
private int n
```
    Row and column dimensions.
- Constructor Detail
  - SingularValueDecomposition
```
public SingularValueDecomposition(CVisDMatrix Arg)
```
    Construct the singular value decomposition
    
    Parameters:
    
    A - Rectangular matrix
- Method Detail
  - getU
```
public CVisDMatrix getU()
```
    Return the left singular vectors
    
    Returns:
    
    U
  - getV
```
public CVisDMatrix 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 CVisDVector 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.