edu.rit.numeric

Class LinearSolve

java.lang.Object

edu.rit.numeric.LinearSolve

public class LinearSolve
extends java.lang.Object

Class LinearSolve provides an object for solving a system of linear equations using LU decomposition. The solve() method finds a solution to the system of linear equations Ax = b, where A is a square matrix supplied to the constructor and b is a vector supplied to the solve() method. Thus, an instance of class LinearSolve can be used to solve many linear systems with the same left-hand-side matrix and different right-hand-side vectors.

The Java code for LU decomposition was translated from routine gsl_linalg_LU_decomp() in the GNU Scientific Library.

Constructor Summary

Constructors

Constructor and Description
LinearSolve(double[][] A) Construct a new LinearSolve object.

Method Summary

Modifier and Type	Method and Description
double	determinant() Compute det A, the determinant of A.
void	invert(double[][] Ainv) Compute A-1, the inverse of A.
void	invertMultiply(double[][] AinvB, double[][] B) Compute A-1B.
void	solve(double[] x, double[] b) Solve the linear system Ax = b.

Methods inherited from class java.lang.Object

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

Constructor Detail

LinearSolve

public LinearSolve(double[][] A)

Construct a new LinearSolve object. A must be an N-by-N matrix with N > 0. This constructor calculates the LU decomposition of A and stores the result internally; A is unchanged.

Parameters:

A - Left-hand-side matrix.

Throws:

java.lang.NullPointerException - (unchecked exception) Thrown if A or any row thereof is null.

java.lang.IllegalArgumentException - (unchecked exception) Thrown if A is zero length or is not a square matrix.

DomainException - (unchecked exception) Thrown if a zero pivot was encountered during the LU decomposition.

Method Detail

solve

public void solve(double[] x,
                  double[] b)

Solve the linear system Ax = b. A is the N-by-N matrix supplied to the constructor. b must be an N-element array initialized to the right-hand-side vector. The solution vector is stored in the N-element array x. b and x must be different arrays.

Parameters:

x - Solution vector (output).

b - Right-hand-side vector (input).

Throws:

java.lang.NullPointerException - (unchecked exception) Thrown if x or b is null.

java.lang.IllegalArgumentException - (unchecked exception) Thrown if x's length or b's length is not N.

invert

public void invert(double[][] Ainv)

Compute A^-1, the inverse of A. A is the N-by-N matrix supplied to the constructor. The inverse of A is stored in the N-by-N matrix Ainv.

Parameters:

Ainv - Inverse matrix (output).

Throws:

java.lang.NullPointerException - (unchecked exception) Thrown if Ainv or any row thereof is null.

java.lang.IllegalArgumentException - (unchecked exception) Thrown if Ainv is not an N-by-N matrix.

invertMultiply

public void invertMultiply(double[][] AinvB,
                           double[][] B)

Compute A^-1B. A is the N-by-N matrix supplied to the constructor. B must be an N-by-N matrix. The matrix product of A^-1 and B is stored in the N-by-N matrix AinvB.

Parameters:

AinvB - Product matrix (output).

B - Matrix (input).

Throws:

java.lang.NullPointerException - (unchecked exception) Thrown if AinvB, B, or any row thereof is null.

java.lang.IllegalArgumentException - (unchecked exception) Thrown if AinvB or B is not an N-by-N matrix.

determinant

public double determinant()

Compute det A, the determinant of A. A is the N-by-N matrix supplied to the constructor. Note that for larger matrices, det A may overflow or underflow the dynamic range of type double.

Returns:

The determinant of A.