Class QRDecomposition

  • All Implemented Interfaces:
    java.io.Serializable

    public class QRDecomposition
    extends java.lang.Object
    implements java.io.Serializable
    For an m x n matrix A with m >= n, the QR decomposition is an m x n orthogonal matrix Q and an n x n upper triangular matrix R so that A = Q*R.

    The QR decompostion always exists, even if the matrix does not have full rank, so the constructor will never fail. The primary use of the QR decomposition is in the least squares solution of nonsquare systems of simultaneous linear equations. This will fail if isFullRank() returns false.

    See Also:
    Serialized Form
    • Field Summary

      Fields 
      Modifier and Type Field Description
      private int m
      Row and column dimensions.
      private int n
      Row and column dimensions.
      private DoubleMatrix2D QR
      Array for internal storage of decomposition.
      private DoubleMatrix1D Rdiag
      Array for internal storage of diagonal of R.
      (package private) static long serialVersionUID  
    • Constructor Summary

      Constructors 
      Constructor Description
      QRDecomposition​(DoubleMatrix2D A)
      Constructs and returns a new QR decomposition object; computed by Householder reflections; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.
    • Field Detail

      • QR

        private DoubleMatrix2D QR
        Array for internal storage of decomposition.
      • m

        private int m
        Row and column dimensions.
      • n

        private int n
        Row and column dimensions.
      • Rdiag

        private DoubleMatrix1D Rdiag
        Array for internal storage of diagonal of R.
    • Constructor Detail

      • QRDecomposition

        public QRDecomposition​(DoubleMatrix2D A)
        Constructs and returns a new QR decomposition object; computed by Householder reflections; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.
        Parameters:
        A - A rectangular matrix.
        Throws:
        java.lang.IllegalArgumentException - if A.rows() < A.columns().
    • Method Detail

      • getH

        public DoubleMatrix2D getH()
        Returns the Householder vectors H.
        Returns:
        A lower trapezoidal matrix whose columns define the householder reflections.
      • getQ

        public DoubleMatrix2D getQ()
        Generates and returns the (economy-sized) orthogonal factor Q.
        Returns:
        Q
      • getR

        public DoubleMatrix2D getR()
        Returns the upper triangular factor, R.
        Returns:
        R
      • hasFullRank

        public boolean hasFullRank()
        Returns whether the matrix A has full rank.
        Returns:
        true if R, and hence A, has full rank.
      • solve

        public DoubleMatrix2D solve​(DoubleMatrix2D B)
        Least squares solution of A*X = B; returns X.
        Parameters:
        B - A matrix with as many rows as A and any number of columns.
        Returns:
        X that minimizes the two norm of Q*R*X - B.
        Throws:
        java.lang.IllegalArgumentException - if B.rows() != A.rows().
        java.lang.IllegalArgumentException - if !this.hasFullRank() (A is rank deficient).
      • toString

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