SingularValueDecomposition

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## weka.core.matrix
Class 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: 1.5 $
Author:
  The Mathworks and NIST, Fracpete (fracpete at waikato dot ac dot nz)
See Also:
  Serialized Form

Constructor Summary
`SingularValueDecomposition(Matrix Arg)` Construct the singular value decomposition

Method Summary
`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

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