dev.nm.algebra.linear.matrix.doubles.linearsystem

Class LUSolver

java.lang.Object

dev.nm.algebra.linear.matrix.doubles.linearsystem.LUSolver

public class LUSolver
extends Object

Use LU decomposition to solve Ax = b where A is square and det(A) != 0. The dimensions of A and b must match. The algorithm goes as follows. \[ \begin{gathered} Ax = b; \\ LUx = PAx = Pb \end{gathered} \] We first solve Ly = b by forward substitution and then Ux = y by backward substitution.

See Also:

Wikipedia: Solving linear equations

Constructor Summary

Constructors

Constructor and Description
LUSolver()

Method Summary

Modifier and Type	Method and Description
Vector	solve(LSProblem problem) Solve Ax = b.
Matrix	solve(Matrix A, Matrix B) Solves AX = B.

Methods inherited from class java.lang.Object

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

Constructor Detail

LUSolver

public LUSolver()

Method Detail

solve

public Vector solve(LSProblem problem)

Solve Ax = b.

Parameters:

problem - a system of linear equations

Returns:

x a solution such that Ax = b

Throws:

LinearSystemSolver.NoSolution - if there is no solution to the system

solve

public Matrix solve(Matrix A,
                    Matrix B)

Solves AX = B.

Parameters:

A - the left-hand side coefficient matrix

B - the right-hand side of the equation

Returns:

the solution, X