Class QRDecomposition

  • All Implemented Interfaces:
    java.io.Serializable, RevisionHandler

    public class QRDecomposition
    extends java.lang.Object
    implements java.io.Serializable, RevisionHandler
    QR Decomposition.

    For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n orthogonal matrix Q and an n-by-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.

    Adapted from the JAMA package.

    Version:
    $Revision: 1.4 $
    Author:
    The Mathworks and NIST, Fracpete (fracpete at waikato dot ac dot nz)
    See Also:
    Serialized Form
    • Constructor Summary

      Constructors 
      Constructor Description
      QRDecomposition​(Matrix A)
      QR Decomposition, computed by Householder reflections.
    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      Matrix getH()
      Return the Householder vectors
      Matrix getQ()
      Generate and return the (economy-sized) orthogonal factor
      Matrix getR()
      Return the upper triangular factor
      java.lang.String getRevision()
      Returns the revision string.
      boolean isFullRank()
      Is the matrix full rank?
      Matrix solve​(Matrix B)
      Least squares solution of A*X = B
      • Methods inherited from class java.lang.Object

        equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
    • Constructor Detail

      • QRDecomposition

        public QRDecomposition​(Matrix A)
        QR Decomposition, computed by Householder reflections.
        Parameters:
        A - Rectangular matrix
    • Method Detail

      • isFullRank

        public boolean isFullRank()
        Is the matrix full rank?
        Returns:
        true if R, and hence A, has full rank.
      • getH

        public Matrix getH()
        Return the Householder vectors
        Returns:
        Lower trapezoidal matrix whose columns define the reflections
      • getR

        public Matrix getR()
        Return the upper triangular factor
        Returns:
        R
      • getQ

        public Matrix getQ()
        Generate and return the (economy-sized) orthogonal factor
        Returns:
        Q
      • solve

        public Matrix solve​(Matrix B)
        Least squares solution of A*X = B
        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 - Matrix row dimensions must agree.
        java.lang.RuntimeException - Matrix is rank deficient.
      • getRevision

        public java.lang.String getRevision()
        Returns the revision string.
        Specified by:
        getRevision in interface RevisionHandler
        Returns:
        the revision