Package Jama

Class SingularValueDecomposition

java.lang.Object
Jama.SingularValueDecomposition
All Implemented Interfaces:
java.io.Serializable
public class SingularValueDecomposition
extends java.lang.Object
implements java.io.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:
Serialized Form

  • Constructor Summary

    Constructors 
    Constructor Description
    SingularValueDecomposition​(Matrix Arg)
    Construct the singular value decomposition

  • Method Summary

    Modifier and Type Method Description
    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

  • Constructor Details

  • 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.