Documentation of 'org.encog.mathutil.matrices.decomposition.SingularValueDecomposition' Java class
SingularValueDecomposition
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org.encog.mathutil.matrices.decomposition

Class SingularValueDecomposition


  • public class SingularValueDecomposition
extends java.lang.Object
    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. This file based on a class from the public domain JAMA package. http://math.nist.gov/javanumerics/jama/

    • Constructor Summary

      Constructors 
      Constructor and Description
      SingularValueDecomposition(Matrix Arg)
      Construct the singular value decomposition Structure to access U, S and V.

    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method and 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

        equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

    • Constructor Detail

      • SingularValueDecomposition

        public SingularValueDecomposition(Matrix Arg)
        Construct the singular value decomposition Structure to access U, S and V.
        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.
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