com.imsl.test.example.math

Class SuperLUEx1

java.lang.Object

com.imsl.test.example.math.SuperLUEx1

public class SuperLUEx1
extends Object

SuperLU Example 1: Computes the LU factorization of a sparse matrix.

The LU Factorization of the sparse $6 \times 6$ matrix $$A=\begin{pmatrix} 10.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\ 0.0 & 10.0 & -3.0 & -1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & 15.0 & 0.0 & 0.0 & 0.0 \\ -2.0 & 0.0 & 0.0 & 10.0 & -1.0 & 0.0 \\ -1.0 & 0.0 & 0.0 & -5.0 & 1.0 & -3.0 \\ -1.0 & -2.0 & 0.0 & 0.0 & 0.0 & 6.0 \end{pmatrix}$$

is computed. The sparse coordinate form for $A$ is given by a series of row, column, and value triplets:

row	column	value
$0$	$0$	$10.0$
$1$	$1$	$10.0$
$1$	$2$	$-3.0$
$1$	$3$	$-1.0$
$2$	$2$	$15.0$
$3$	$0$	$-2.0$
$3$	$3$	$10.0$
$3$	$4$	$-1.0$
$4$	$0$	$-1.0$
$4$	$3$	$-5.0$
$4$	$4$	$1.0$
$4$	$5$	$-3.0$
$5$	$0$	$-1.0$
$5$	$1$	$-2.0$
$5$	$5$	$6.0$

Let $y^T = (1.0, 2.0, 3.0, 4.0, 5.0, 6.0)$. Then we have $b_1 := Ay = {(10.0, 7.0, 45.0, 33.0, -34.0, 31.0)}^T$ and $b_2 := A^Ty = {(-9.0,8.0,39.0, 13.0,1.0, 21.0)}^T$.

In the example, the The LU factorization of $A$ is used to solve the sparse linear system $$\begin{array}{cc} Ax &=& b_1 \\ A^Tx &=& b_2 \end{array}$$

with iterative refinement. The reciprocal pivot growth factor and the reciprocal condition number are also computed. Note that by construction $x=y$ is the solution to this system.

See Also:

Code, Output

Constructor Summary

Constructors

Constructor and Description
SuperLUEx1()

Method Summary

Modifier and Type	Method and Description
static void	main(String[] args)

Methods inherited from class java.lang.Object

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

Constructor Detail

SuperLUEx1

public SuperLUEx1()

Method Detail

main

public static void main(String[] args)
                 throws Exception

Throws:

Exception