com.numericalmethod.suanshu.matrix.doubles.linearsystem
Class LU

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.linearsystem.LU

public class LU
extends java.lang.Object

Use the LU decomposition to solve

Ax = b

where A is square and det(A) != 0.

The dimensions of A and b must match.

That is,

 Ax = b;
 LUx = PAx = Pb
 

We first solve Ly = b by forward substitution then Ux = y by backward substitution.

See Also:

Wikipedia: Solving linear equations

Field Summary

LowerTriangularMatrix	L matrix L as in LUx = PAx = Pb
PermutationMatrix	P matrix P as in LUx = PAx = Pb
UpperTriangularMatrix	U matrix U as in LUx = PAx = Pb

Constructor Summary

LU(Matrix A)
Construct an LU instance to solve for different Vector b's.

Method Summary

Vector

solve(Vector b) Solve Ax = b

Methods inherited from class java.lang.Object

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

Field Detail

L

public final LowerTriangularMatrix L

matrix L as in LUx = PAx = Pb

U

public final UpperTriangularMatrix U

matrix U as in LUx = PAx = Pb

P

public final PermutationMatrix P

matrix P as in LUx = PAx = Pb

Constructor Detail

LU

public LU(Matrix A)

Construct an LU instance to solve for different Vector b's.

Parameters:

A - a matrix A as in Ax = b

Throws:

Solver.NoSolution - if there is no solution to this system

Method Detail

solve

public Vector solve(Vector b)

Solve

Ax = b

Parameters:

b - a vector

Returns:

x such that

Ax = b