LUDecomposition (math 11.1.5 API)

java.lang.Object
- de.gsi.math.matrix.LUDecomposition

All Implemented Interfaces:

java.io.Serializable
```
public class LUDecomposition
extends java.lang.Object
implements java.io.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.

See Also:

Serialized Form

Constructor Summary

Constructors
Constructor Description

LUDecomposition(MatrixD A)
LU Decomposition

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`double`	`det()`	Determinant
`double[]`	`getDoublePivot()`	Return pivot permutation vector as a one-dimensional double array
`MatrixD`	`getL()`	Return lower triangular factor
`int[]`	`getPivot()`	Return pivot permutation vector
`MatrixD`	`getU()`	Return upper triangular factor
`boolean`	`isNonsingular()`	Is the matrix nonsingular?
`MatrixD`	`solve(MatrixD B)`	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(MatrixD A)
```
    LU Decomposition
    
    Parameters:
    
    A - Rectangular matrix Structure to access L, U and piv.
- Method Detail
  - det
```
public double det()
```
    Determinant
    
    Returns:
    
    det(A)
    
    Throws:
    
    java.lang.IllegalArgumentException - Matrix must be square
  - getDoublePivot
```
public double[] getDoublePivot()
```
    Return pivot permutation vector as a one-dimensional double array
    
    Returns:
    
    (double) piv
  - getL
```
public MatrixD getL()
```
    Return lower triangular factor
    
    Returns:
    
    L
  - getPivot
```
public int[] getPivot()
```
    Return pivot permutation vector
    
    Returns:
    
    piv
  - getU
```
public MatrixD getU()
```
    Return upper triangular factor
    
    Returns:
    
    U
  - isNonsingular
```
public boolean isNonsingular()
```
    Is the matrix nonsingular?
    
    Returns:
    
    true if U, and hence A, is nonsingular.
  - solve
```
public MatrixD solve(MatrixD 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:
    
    java.lang.IllegalArgumentException - Matrix row dimensions must agree.
    
    java.lang.RuntimeException - Matrix is singular.