Package org.hipparchus.linear

Class FieldQRDecomposition<T extends RealFieldElement<T>>

  • Type Parameters:
    T - type of the underlying field elements
    public class FieldQRDecomposition<T extends RealFieldElement<T>>
extends Object
    Calculates the QR-decomposition of a field 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.

    This class is based on the class QRDecomposition.

    See Also:
    MathWorld, Wikipedia

    • Constructor Detail

      • FieldQRDecomposition

        public FieldQRDecomposition​(FieldMatrix<T> matrix,
                            T threshold)
        Calculates the QR-decomposition of the given matrix.
        Parameters:
        matrix - The matrix to decompose.
        threshold - Singularity threshold.

    • Method Detail

      • decompose

        protected void decompose​(T[][] matrix)
        Decompose matrix.
        Parameters:
        matrix - transposed matrix

      • performHouseholderReflection

        protected void performHouseholderReflection​(int minor,
                                            T[][] matrix)
        Perform Householder reflection for a minor A(minor, minor) of A.
        Parameters:
        minor - minor index
        matrix - transposed matrix

      • getR

        public FieldMatrix<T> getR()
        Returns the matrix R of the decomposition.

        R is an upper-triangular matrix

        Returns:
        the R matrix

      • getQ

        public FieldMatrix<T> getQ()
        Returns the matrix Q of the decomposition.

        Q is an orthogonal matrix

        Returns:
        the Q matrix

      • getQT

        public FieldMatrix<T> getQT()
        Returns the transpose of the matrix Q of the decomposition.

        Q is an orthogonal matrix

        Returns:
        the transpose of the Q matrix, QT

      • getH

        public FieldMatrix<T> 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.

        Returns:
        a matrix containing the Householder reflector vectors

      • getSolver

        public FieldDecompositionSolver<T> getSolver()
        Get a solver for finding the A × X = B solution in least square sense.

        Least Square sense means a solver can be computed for an overdetermined system, (i.e. a system with more equations than unknowns, which corresponds to a tall A matrix with more rows than columns). In any case, if the matrix is singular within the tolerance set at construction, an error will be triggered when the solve method will be called.

        Returns:
        a solver