Package Jama

Class LUDecomposition

java.lang.Object
Jama.LUDecomposition
All Implemented Interfaces:
java.io.Serializable
public class LUDecomposition
extends java.lang.Object
implements java.io.Serializable
LU Decomposition.

For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n unit lower triangular matrix L, an n-by-n upper triangular matrix U, and a permutation vector piv of length m so that A(piv,:) = L*U. If m < n, then L is m-by-m and U is m-by-n.

The LU decompostion with pivoting always exists, even if the matrix is singular, so the constructor will never fail. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations. This will fail if isNonsingular() returns false.

See Also:
Serialized Form

  • Constructor Summary

    Constructors 
    Constructor Description
    LUDecomposition​(Matrix A)
    LU Decomposition

  • Method Summary

    Modifier and Type Method Description
    double det()
    Determinant
    double[] getDoublePivot()
    Return pivot permutation vector as a one-dimensional double array
    Matrix getL()
    Return lower triangular factor
    int[] getPivot()
    Return pivot permutation vector
    Matrix getU()
    Return upper triangular factor
    boolean isNonsingular()
    Is the matrix nonsingular?
    Matrix solve​(Matrix B)
    Solve A*X = B

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • LUDecomposition

      public LUDecomposition​(Matrix A)
      LU Decomposition
      Parameters:
      A - Rectangular matrix

  • Method Details

    • isNonsingular

      public boolean isNonsingular()
      Is the matrix nonsingular?
      Returns:
      true if U, and hence A, is nonsingular.

    • getL

      public Matrix getL()
      Return lower triangular factor
      Returns:
      L

    • getU

      public Matrix getU()
      Return upper triangular factor
      Returns:
      U

    • getPivot

      public int[] getPivot()
      Return pivot permutation vector
      Returns:
      piv

    • getDoublePivot

      public double[] getDoublePivot()
      Return pivot permutation vector as a one-dimensional double array
      Returns:
      (double) piv

    • det

      public double det()
      Determinant
      Returns:
      det(A)
      Throws:
      java.lang.IllegalArgumentException - Matrix must be square

    • solve

      public Matrix solve​(Matrix B)
      Solve A*X = B
      Parameters:
      B - A Matrix with as many rows as A and any number of columns.
      Returns:
      X so that L*U*X = B(piv,:)
      Throws:
      java.lang.IllegalArgumentException - Matrix row dimensions must agree.
      java.lang.RuntimeException - Matrix is singular.