smile.math.matrix

Class LU

java.lang.Object

smile.math.matrix.LU

public class LU
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.

Field Summary

Fields

Modifier and Type	Field and Description
protected DenseMatrix	lu Array for internal storage of decomposition.
protected int[]	piv Internal storage of pivot vector.
protected int	pivsign pivot sign.
protected boolean	singular True if the matrix is singular.

Constructor Summary

Constructors

Constructor and Description
LU(DenseMatrix lu, int[] piv, boolean singular) Constructor.
LU(DenseMatrix lu, int[] piv, int pivsign, boolean singular) Constructor.

Method Summary

Modifier and Type	Method and Description
double	det() Returns the matrix determinant
DenseMatrix	inverse() Returns the matrix inverse.
boolean	isSingular() Returns true if the matrix is singular or false otherwise.
void	solve(DenseMatrix B) Solve A * X = B.
void	solve(double[] b) Solve A * x = b.

Methods inherited from class java.lang.Object

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

Field Detail

lu

protected DenseMatrix lu

Array for internal storage of decomposition.

pivsign

protected int pivsign

pivot sign.

piv

protected int[] piv

Internal storage of pivot vector.

singular

protected boolean singular

True if the matrix is singular.

Constructor Detail

LU

public LU(DenseMatrix lu,
          int[] piv,
          int pivsign,
          boolean singular)

Constructor.

Parameters:

lu - LU decomposition matrix

piv - pivot vector

pivsign - pivot sign. +1 if even number of row interchanges, -1 if odd number of row interchanges.

singular - True if the matrix is singular

LU

public LU(DenseMatrix lu,
          int[] piv,
          boolean singular)

Constructor.

Parameters:

lu - LU decomposition matrix

piv - pivot vector

singular - True if the matrix is singular

Method Detail

isSingular

public boolean isSingular()

Returns true if the matrix is singular or false otherwise.

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.

Parameters:

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

Throws:

java.lang.RuntimeException - if matrix is singular.

solve

public void solve(DenseMatrix 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:

java.lang.RuntimeException - if matrix is singular.