Package org.hipparchus.linear

Class LUDecomposition

java.lang.Object
org.hipparchus.linear.LUDecomposition
public class LUDecomposition 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: P×A = L×U. L is lower triangular (with unit diagonal terms), U is upper triangular and P is a permutation matrix. All matrices are m×m.

As shown by the presence of the P matrix, this decomposition is implemented using partial pivoting.

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  • the solve and isNonSingular methods have been replaced by a getSolver method and the equivalent methods provided by the returned DecompositionSolver.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:

  • Constructor Details

    • LUDecomposition

      public LUDecomposition(RealMatrix matrix)
      Calculates the LU-decomposition of the given matrix. This constructor uses 1e-11 as default value for the singularity threshold.
      Parameters:
      matrix - Matrix to decompose.
      Throws:
      MathIllegalArgumentException - if matrix is not square.

    • LUDecomposition

      public LUDecomposition(RealMatrix matrix, double singularityThreshold)
      Calculates the LU-decomposition of the given matrix.
      Parameters:
      matrix - The matrix to decompose.
      singularityThreshold - threshold (based on partial row norm) under which a matrix is considered singular
      Throws:
      MathIllegalArgumentException - if matrix is not square

  • Method Details

    • getL

      public RealMatrix 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 RealMatrix 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 RealMatrix 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 double getDeterminant()
      Return the determinant of the matrix
      Returns:
      determinant of the matrix

    • getSolver

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