E nvironment for Deve L oping K DD-Applications Supported by I ndex-Structures

## de.lmu.ifi.dbs.elki.math.linearalgebra Class LUDecomposition

```java.lang.Object
de.lmu.ifi.dbs.elki.math.linearalgebra.LUDecomposition
```
All Implemented Interfaces:
Serializable

`public class LUDecompositionextends Objectimplements Serializable`

LU Decomposition.

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, so the constructor will never fail. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations. This will fail if isNonsingular() returns false.

Serialized Form

Field Summary
`private  double[][]` `LU`
Array for internal storage of decomposition.
`private  int` `m`
Row and column dimensions, and pivot sign.
`private  int` `n`
Row and column dimensions, and pivot sign.
`private  int[]` `piv`
Internal storage of pivot vector.
`private  int` `pivsign`
Row and column dimensions, and pivot sign.

Constructor Summary
`LUDecomposition(Matrix A)`
LU Decomposition

Method Summary
` double` `det()`
Determinant
` double[]` `getDoublePivot()`
Return pivot permutation vector as a one-dimensional double array
` Matrix` `getL()`
Return lower triangular factor
` int[]` `getPivot()`
Return pivot permutation vector
` Matrix` `getU()`
Return upper triangular factor
` boolean` `isNonsingular()`
Is the matrix nonsingular?
` Matrix` `solve(Matrix 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

`private double[][] LU`
Array for internal storage of decomposition.

### m

`private int m`
Row and column dimensions, and pivot sign.

### n

`private int n`
Row and column dimensions, and pivot sign.

### pivsign

`private int pivsign`
Row and column dimensions, and pivot sign.

### piv

`private int[] piv`
Internal storage of pivot vector.

Constructor Detail

### LUDecomposition

`public LUDecomposition(Matrix A)`
LU Decomposition

Parameters:
`A` - Rectangular matrix
Method Detail

### isNonsingular

`public boolean isNonsingular()`
Is the matrix nonsingular?

Returns:
true if U, and hence A, is nonsingular.

### getL

`public Matrix getL()`
Return lower triangular factor

Returns:
L

### getU

`public Matrix getU()`
Return upper triangular factor

Returns:
U

### getPivot

`public int[] getPivot()`
Return pivot permutation vector

Returns:
piv

### getDoublePivot

`public double[] getDoublePivot()`
Return pivot permutation vector as a one-dimensional double array

Returns:
(double) piv

### det

`public double det()`
Determinant

Returns:
det(A)
Throws:
`IllegalArgumentException` - Matrix must be square

### solve

`public Matrix solve(Matrix B)`
Solve A*X = B

Parameters:
`B` - A Matrix with as many rows as A and any number of columns.
Returns:
X so that L*U*X = B(piv,:)
Throws:
`IllegalArgumentException` - Matrix row dimensions must agree.
`RuntimeException` - Matrix is singular.

 Release 0.2.1 (2009-07-13_1605)