Package org.hipparchus.linear

Class FieldQRDecomposition<T extends CalculusFieldElement<T>>

java.lang.Object
org.hipparchus.linear.FieldQRDecomposition<T>
Type Parameters:
T - type of the underlying field elements
public class FieldQRDecomposition<T extends CalculusFieldElement<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:

  • Constructor Details

    • FieldQRDecomposition

      public FieldQRDecomposition(FieldMatrix<T> matrix)
      Calculates the QR-decomposition of the given matrix. The singularity threshold defaults to zero.
      Parameters:
      matrix - The matrix to decompose.
      See Also:

    • 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.

    • FieldQRDecomposition

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

  • Method Details

    • 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