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## de.lmu.ifi.dbs.elki.math.linearalgebra Class SingularValueDecomposition

```java.lang.Object
de.lmu.ifi.dbs.elki.math.linearalgebra.SingularValueDecomposition
```
All Implemented Interfaces:
Serializable

`public class SingularValueDecompositionextends Objectimplements 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.

Serialized Form

Field Summary
`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
`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

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(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.

 Release 0.3 (2010-03-31_1612)