Package org.hipparchus.linear

Class FieldLUDecomposition<T extends FieldElement<T>>

  • Type Parameters:
    T - the type of the field elements
    public class FieldLUDecomposition<T extends FieldElement<T>>
extends Object
    Calculates the LUP-decomposition of a square matrix.

    The LUP-decomposition of a matrix A consists of three matrices L, U and P that satisfy: PA = LU, L is lower triangular, and U is upper triangular and P is a permutation matrix. All matrices are m×m.

    Since field elements do not provide an ordering operator, the permutation matrix is computed here only in order to avoid a zero pivot element, no attempt is done to get the largest pivot element.

    This class is based on the class with similar name from the JAMA library.

    • a getP method has been added,
    • the det method has been renamed as getDeterminant,
    • the getDoublePivot method has been removed (but the int based getPivot method has been kept),
    • the solve and isNonSingular methods have been replaced by a getSolver method and the equivalent methods provided by the returned DecompositionSolver.
    See Also:
    MathWorld, Wikipedia

    • Constructor Detail

      • FieldLUDecomposition

        public FieldLUDecomposition​(FieldMatrix<T> matrix)
        Calculates the LU-decomposition of the given matrix.
        Parameters:
        matrix - The matrix to decompose.
        Throws:
        MathIllegalArgumentException - if matrix is not square

    • Method Detail

      • getL

        public FieldMatrix<T> getL()
        Returns the matrix L of the decomposition.

        L is a lower-triangular matrix

        Returns:
        the L matrix (or null if decomposed matrix is singular)

      • getU

        public FieldMatrix<T> getU()
        Returns the matrix U of the decomposition.

        U is an upper-triangular matrix

        Returns:
        the U matrix (or null if decomposed matrix is singular)

      • getP

        public FieldMatrix<T> getP()
        Returns the P rows permutation matrix.

        P is a sparse matrix with exactly one element set to 1.0 in each row and each column, all other elements being set to 0.0.

        The positions of the 1 elements are given by the pivot permutation vector.

        Returns:
        the P rows permutation matrix (or null if decomposed matrix is singular)
        See Also:
        getPivot()

      • getPivot

        public int[] getPivot()
        Returns the pivot permutation vector.
        Returns:
        the pivot permutation vector
        See Also:
        getP()

      • getDeterminant

        public T getDeterminant()
        Return the determinant of the matrix.
        Returns:
        determinant of the matrix

      • getSolver

        public FieldDecompositionSolver<T> getSolver()
        Get a solver for finding the A × X = B solution in exact linear sense.
        Returns:
        a solver