LUDecomposition
jhplot.math

Class LUDecomposition



  • public class LUDecompositionextends Object
    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. In other words, assuming P the permutation Matrix, P*A = 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.

    • Constructor Detail

      • LUDecomposition

        public LUDecomposition(double[][] A)
        LU Decomposition
        Parameters:
        A - Rectangular matrix
    • Method Detail

      • isNonsingular

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

        public double[][] getL()
        Return lower triangular factor
        Returns:
        L
      • getU

        public double[][] getU()
        Return upper triangular factor
        Returns:
        U
      • getP

        public double[][] getP()
        Return pivot permutation vector
        Returns:
        piv
      • solve

        public double[][] solve(double[][] 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:
        IllegalArgumentException - Matrix row dimensions must agree.
        RuntimeException - Matrix is singular.

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