Package org.apache.commons.math.linear

Class QRDecompositionImpl

java.lang.Object
org.apache.commons.math.linear.QRDecompositionImpl
All Implemented Interfaces:
QRDecomposition
public class QRDecompositionImpl extends 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
See Also:

  • Constructor Details

    • QRDecompositionImpl

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

  • Method Details

    • 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

    • getSolver

      public DecompositionSolver getSolver()
      Get a solver for finding the A × X = B solution in least square sense.
      Specified by:
      getSolver in interface QRDecomposition
      Returns:
      a solver