smile.math.matrix

Class LUDecomposition

java.lang.Object

smile.math.matrix.LUDecomposition

public class LUDecomposition
extends java.lang.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 decomposition 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.

Constructor Summary

Constructors

Constructor and Description
LUDecomposition(DenseMatrix A) Constructor.
LUDecomposition(double[][] A) Constructor.

Method Summary

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

LUDecomposition

public LUDecomposition(DenseMatrix A)

Constructor. The decomposition will be stored in the input matrix.

Parameters:

A - input matrix

Method Detail

isSingular

public boolean isSingular()

Returns true if the matrix is singular or false otherwise.

getL

public DenseMatrix getL()

Returns the lower triangular factor.

getU

public DenseMatrix 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 DenseMatrix 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:

java.lang.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:

java.lang.RuntimeException - if matrix is singular.

solve

public void solve(DenseMatrix B,
                  DenseMatrix X)

Solve A * X = B.

Parameters:

B - right hand side of linear system.

X - the solution matrix.

Throws:

java.lang.RuntimeException - if matrix is singular.