java.lang.Object
- cern.colt.matrix.linalg.SingularValueDecomposition

All Implemented Interfaces:

java.io.Serializable
```
public class SingularValueDecomposition
extends java.lang.Object
implements java.io.Serializable
```
For an m x n matrix A with m >= n, the singular value decomposition is an m x n orthogonal matrix U, an n x n diagonal matrix S, and an n x 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 decomposition 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.
`(package private) static long`	`serialVersionUID`
`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(DoubleMatrix2D Arg)`	Constructs and returns a new singular value decomposition object; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`double`	`cond()`	Returns the two norm condition number, which is `max(S) / min(S)`.
`DoubleMatrix2D`	`getS()`	Returns the diagonal matrix of singular values.
`double[]`	`getSingularValues()`	Returns the diagonal of `S`, which is a one-dimensional array of singular values
`DoubleMatrix2D`	`getU()`	Returns the left singular vectors `U`.
`DoubleMatrix2D`	`getV()`	Returns the right singular vectors `V`.
`double`	`norm2()`	Returns the two norm, which is `max(S)`.
`int`	`rank()`	Returns the effective numerical matrix rank, which is the number of nonnegligible singular values.
`java.lang.String`	`toString()`	Returns a String with (propertyName, propertyValue) pairs.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Field Detail
  - serialVersionUID
```
static final long serialVersionUID
```
    See Also:
    
    Constant Field Values
  - 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(DoubleMatrix2D Arg)
```
    Constructs and returns a new singular value decomposition object; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.
    
    Parameters:
    
    A - A rectangular matrix.
    
    Throws:
    
    java.lang.IllegalArgumentException - if A.rows() < A.columns().
- Method Detail
  - cond
```
public double cond()
```
    Returns the two norm condition number, which is max(S) / min(S).
  - getS
```
public DoubleMatrix2D getS()
```
    Returns the diagonal matrix of singular values.
    
    Returns:
    
    S
  - getSingularValues
```
public double[] getSingularValues()
```
    Returns the diagonal of S, which is a one-dimensional array of singular values
    
    Returns:
    
    diagonal of S.
  - getU
```
public DoubleMatrix2D getU()
```
    Returns the left singular vectors U.
    
    Returns:
    
    U
  - getV
```
public DoubleMatrix2D getV()
```
    Returns the right singular vectors V.
    
    Returns:
    
    V
  - norm2
```
public double norm2()
```
    Returns the two norm, which is max(S).
  - rank
```
public int rank()
```
    Returns the effective numerical matrix rank, which is the number of nonnegligible singular values.
  - toString
```
public java.lang.String toString()
```
    Returns a String with (propertyName, propertyValue) pairs. Useful for debugging or to quickly get the rough picture. For example,
    rank : 3 trace : 0
    Overrides:
    
    toString in class java.lang.Object

Class SingularValueDecomposition

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

serialVersionUID

U

V

s

m

n

Constructor Detail

SingularValueDecomposition

Method Detail

cond

getS

getSingularValues

getU

getV

norm2

rank

toString