Package com.macrofocus.high_d.mds.pca

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.

    • Constructor Summary

      Constructors 
      Constructor Description
      SingularValueDecomposition​(PCAMatrix 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 Description
      double cond()
      Two norm condition number
      PCAMatrix getS()
      Return the diagonal matrix of singular values
      double[] getSingularValues()
      Return the one-dimensional array of singular values
      PCAMatrix getU()
      Return the left singular vectors
      PCAMatrix 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 Detail

      • SingularValueDecomposition

        public SingularValueDecomposition​(PCAMatrix Arg)
        Construct the singular value decomposition Structure to access U, S and V.
        Parameters:
        Arg - Rectangular matrix

    • Method Detail

      • getU

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

      • getV

        public PCAMatrix 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 PCAMatrix 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.