smile.math.matrix

Class LUDecomposition

java.lang.Object

smile.math.matrix.LUDecomposition

public class LUDecomposition
extends Object

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. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations if it is not singular.

This decomposition can also be used to calculate the determinant.

Author:

Haifeng Li

Constructor Summary

Constructors

Constructor and Description
LUDecomposition(double[][] A) Constructor.
LUDecomposition(double[][] A, boolean overwrite) Constructor.

Method Summary

Methods

Modifier and Type	Method and Description
double	det() Returns the matrix determinant
double[][]	getL() Returns the lower triangular factor.
int[]	getPivot() Returns the pivot permutation vector.
double[][]	getU() Returns the upper triangular factor.
double[][]	inverse() Returns the matrix inverse.
boolean	isSingular() Returns true if the matrix is singular or false otherwise.
void	solve(double[] b) Solve A * x = b.
void	solve(double[][] B) Solve A * X = B.
void	solve(double[][] B, double[][] X) Solve A * X = B.
void	solve(double[] b, double[] x) Solve A * x = b.

Methods inherited from class java.lang.Object

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

Constructor Detail

LUDecomposition

public LUDecomposition(double[][] A)

Constructor. The decomposition will be stored in a new create matrix. The input matrix will not be modified.

Parameters:

A - rectangular matrix

LUDecomposition

public LUDecomposition(double[][] A,
               boolean overwrite)

Constructor. The user can specify if the decomposition takes in place, i.e. if the decomposition will be stored in the input matrix. Otherwise, a new matrix will be allocated to store the decomposition.

Parameters:

A - rectangular matrix

overwrite - if the decomposition will be taken in place. If true, the decomposition will be stored in the input matrix to save space. It is very useful in practice if the matrix is huge. Otherwise, a new matrix will created to store the decomposition.

Method Detail

isSingular

public boolean isSingular()

Returns true if the matrix is singular or false otherwise.

getL

public double[][] getL()

Returns the lower triangular factor.

getU

public double[][] getU()

Returns the upper triangular factor.

getPivot

public int[] getPivot()

Returns the pivot permutation vector.

det

public double det()

Returns the matrix determinant

inverse

public double[][] inverse()

Returns the matrix inverse. For pseudo inverse, use QRDecomposition.

solve

public void solve(double[] b)

Solve A * x = b. b will be overwritten with the solution vector on output.

Parameters:

b - right hand side of linear system. On output, it will be overwritten with the solution vector

Throws:

RuntimeException - if matrix is singular.

solve

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

Solve A * x = b.

Parameters:

b - right hand side of linear system.

x - the solution vector.

Throws:

RuntimeException - if matrix is singular.

solve

public void solve(double[][] B)

Solve A * X = B. B will be overwritten with the solution matrix on output.

Parameters:

B - right hand side of linear system. On output, B will be overwritten with the solution matrix.

Throws:

RuntimeException - if matrix is singular.

solve

public void solve(double[][] B,
         double[][] X)

Solve A * X = B.

Parameters:

B - right hand side of linear system.

X - the solution matrix.

Throws:

RuntimeException - if matrix is singular.