Package org.apache.commons.math3.linear

Class FieldLUDecomposition<T extends FieldElement<T>>

java.lang.Object
org.apache.commons.math3.linear.FieldLUDecomposition<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  • the solve and isNonSingular methods have been replaced by a getSolver method and the equivalent methods provided by the returned DecompositionSolver.
Since:
2.0 (changed to concrete class in 3.0)
See Also:

  • Constructor Details

    • FieldLUDecomposition

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

  • Method Details

    • 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

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

    • 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