Package gov.nih.mipav.view.renderer.WildMagic.AAM

Class SingularValueDecomposition

java.lang.Object
gov.nih.mipav.view.renderer.WildMagic.AAM.SingularValueDecomposition
All Implemented Interfaces:
Serializable
public class SingularValueDecomposition extends Object implements 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.

See Also:

  • 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.
    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(CVisDMatrix Arg)
    Construct the singular value decomposition

  • Method Summary

    Modifier and Type
    Method
    Description
    double
    cond()
    Two norm condition number
    CVisDVector
    getS()
    Return the diagonal matrix of singular values
    double[]
    getSingularValues()
    Return the one-dimensional array of singular values
    CVisDMatrix
    getU()
    Return the left singular vectors
    CVisDMatrix
    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 Details

    • 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 Details

    • SingularValueDecomposition

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

  • Method Details

    • getU

      public CVisDMatrix getU()
      Return the left singular vectors
      Returns:
      U

    • getV

      public CVisDMatrix 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 CVisDVector 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.