Package org.apache.commons.math.linear

Class QRDecompositionImpl

  • All Implemented Interfaces:
    QRDecomposition
    public class QRDecompositionImpl
extends java.lang.Object
implements QRDecomposition
    Calculates the QR-decomposition of a matrix.

    The QR-decomposition of a matrix A consists of two matrices Q and R that satisfy: A = QR, Q is orthogonal (QTQ = I), and R is upper triangular. If A is m×n, Q is m×m and R m×n.

    This class compute the decomposition using Householder reflectors.

    For efficiency purposes, the decomposition in packed form is transposed. This allows inner loop to iterate inside rows, which is much more cache-efficient in Java.

    Since:
    1.2
    Version:
    $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $
    See Also:
    MathWorld, Wikipedia

    • Constructor Summary

      Constructors 
      Constructor Description
      QRDecompositionImpl​(RealMatrix matrix)
      Calculates the QR-decomposition of the given matrix.

    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      RealMatrix getH()
      Returns the Householder reflector vectors.
      RealMatrix getQ()
      Returns the matrix Q of the decomposition.
      RealMatrix getQT()
      Returns the transpose of the matrix Q of the decomposition.
      RealMatrix getR()
      Returns the matrix R of the decomposition.
      DecompositionSolver getSolver()
      Get a solver for finding the A × X = B solution in least square sense.

      • Methods inherited from class java.lang.Object

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

    • Constructor Detail

      • QRDecompositionImpl

        public QRDecompositionImpl​(RealMatrix matrix)
        Calculates the QR-decomposition of the given matrix.
        Parameters:
        matrix - The matrix to decompose.

    • Method Detail

      • getR

        public RealMatrix getR()
        Returns the matrix R of the decomposition.

        R is an upper-triangular matrix

        Specified by:
        getR in interface QRDecomposition
        Returns:
        the R matrix

      • getQ

        public RealMatrix getQ()
        Returns the matrix Q of the decomposition.

        Q is an orthogonal matrix

        Specified by:
        getQ in interface QRDecomposition
        Returns:
        the Q matrix

      • getQT

        public RealMatrix getQT()
        Returns the transpose of the matrix Q of the decomposition.

        Q is an orthogonal matrix

        Specified by:
        getQT in interface QRDecomposition
        Returns:
        the Q matrix

      • getH

        public RealMatrix getH()
        Returns the Householder reflector vectors.

        H is a lower trapezoidal matrix whose columns represent each successive Householder reflector vector. This matrix is used to compute Q.

        Specified by:
        getH in interface QRDecomposition
        Returns:
        a matrix containing the Householder reflector vectors