Package weka.core.matrix

Class SingularValueDecomposition

java.lang.Object
weka.core.matrix.SingularValueDecomposition
All Implemented Interfaces:
Serializable, RevisionHandler
public class SingularValueDecomposition extends Object implements 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: 11815 $
Author:
The Mathworks and NIST, Fracpete (fracpete at waikato dot ac dot nz), eibe@cs.waikato.ac.nz
See Also:

  • Constructor Details

    • SingularValueDecomposition

      public SingularValueDecomposition(Matrix Arg)
      Construct the singular value decomposition
      Parameters:
      Arg - Rectangular matrix

  • Method Details

    • 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 String getRevision()
      Returns the revision string.
      Specified by:
      getRevision in interface RevisionHandler
      Returns:
      the revision