SingularValueDecomposition (original) (raw)

• 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:11815Revision: 11815 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 and Description
  SingularValueDecomposition(Matrix Arg) Construct the singular value decomposition

  • Method Summary

  All Methods Instance Methods Concrete Methods

  Modifier and Type	Method and 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](../../../weka/core/matrix/Matrix.html "class in weka.core.matrix") Arg)  
     Construct the singular value decomposition  
     Parameters:  
     `Arg` \- Rectangular matrix  

  • Method Detail

    * #### getU  
    public [Matrix](../../../weka/core/matrix/Matrix.html "class in weka.core.matrix") getU()  
    Return the left singular vectors  
    Returns:  
    U  
    * #### getV  
    public [Matrix](../../../weka/core/matrix/Matrix.html "class in weka.core.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](../../../weka/core/matrix/Matrix.html "class in weka.core.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](../../../weka/core/RevisionHandler.html#getRevision--)` in interface `[RevisionHandler](../../../weka/core/RevisionHandler.html "interface in weka.core")`  
    Returns:  
    the revision