SingularValueDecomposition
cern.colt.matrix.linalg

Class SingularValueDecomposition

  • All Implemented Interfaces:
    Serializable


    public class SingularValueDecompositionextends Objectimplements Serializable
    For an m x n matrix A with m >= n, the singular value decomposition isan m x n orthogonal matrix U, an n x n diagonal matrix S, andan n x n orthogonal matrix V so that A = U*S*V'.

    The singular values, sigma[k] = S[k][k], are ordered so thatsigma[0] >= sigma[1] >= ... >= sigma[n-1].

    The singular value decomposition always exists, so the constructor willnever fail. The matrix condition number and the effective numericalrank can be computed from this decomposition.

    See Also:
    Serialized Form
    • Constructor Summary

      Constructors 
      Constructor and Description
      SingularValueDecomposition(DoubleMatrix2D Arg)
      Constructs and returns a new singular value decomposition object; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.
    • Constructor Detail

      • SingularValueDecomposition

        public SingularValueDecomposition(DoubleMatrix2D Arg)
        Constructs and returns a new singular value decomposition object; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.
        Parameters:
        A - A rectangular matrix.
        Throws:
        IllegalArgumentException - if A.rows() < A.columns().
    • Method Detail

      • cond

        public double cond()
        Returns the two norm condition number, which is max(S) / min(S).
      • getS

        public DoubleMatrix2D getS()
        Returns the diagonal matrix of singular values.
        Returns:
        S
      • getSingularValues

        public double[] getSingularValues()
        Returns the diagonal of S, which is a one-dimensional array of singular values
        Returns:
        diagonal of S.
      • getU

        public DoubleMatrix2D getU()
        Returns the left singular vectors U.
        Returns:
        U
      • getV

        public DoubleMatrix2D getV()
        Returns the right singular vectors V.
        Returns:
        V
      • norm2

        public double norm2()
        Returns the two norm, which is max(S).
      • rank

        public int rank()
        Returns the effective numerical matrix rank, which is the number of nonnegligible singular values.
      • toString

        public String toString()
        Returns a String with (propertyName, propertyValue) pairs.Useful for debugging or to quickly get the rough picture.For example,
        rank          : 3trace         : 0
        Overrides:
        toString in class Object

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