com.imsl.test.example.math

Class ComplexSuperLUEx1

java.lang.Object

com.imsl.test.example.math.ComplexSuperLUEx1

public class ComplexSuperLUEx1
extends Object

Computes the LU factorization of a sparse complex matrix.

The LU Factorization of the sparse complex $6 \times 6$ matrix $$A=\begin{pmatrix} 10+7i & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\ 0.0 & 3+2i & -3+0i & -1+2i & 0.0 & 0.0 \\ 0.0 & 0.0 & 4+2i & 0.0 & 0.0 & 0.0 \\ -2-4i & 0.0 & 0.0 & 1+6i & -1+3i & 0.0 \\ -5+4i & 0.0 & 0.0 & -5+0i & 12+2i & -7+7i \\ -1+12i & -2+8i & 0.0 & 0.0 & 0.0 & 3+7i \end{pmatrix}$$ is computed. The sparse coordinate form for A is given by row, column, value triplets:

row	column	value
$0$	$0$	$10+7i$
$1$	$1$	$3+2i$
$1$	$2$	$-3+0i$
$1$	$3$	$-1+2i$
$2$	$2$	$4+2i$
$3$	$0$	$-2-4i$
$3$	$3$	$1+6i$
$3$	$4$	$-1+3i$
$4$	$0$	$-5+4i$
$4$	$3$	$-5+0i$
$4$	$4$	$12+2i$
$4$	$5$	$-7+7i$
$5$	$0$	$-1+12i$
$5$	$1$	$-2+8i$
$5$	$5$	$3+7i$

Let $$x^T = (1+i, 2+2i, 3+3i, 4+4i, 5+5i, 6+6i)$$ so that $$b_1:=Ax = {(3+17i, -19+5i, 6+18i, -38+32i, -63+49i, -57+83i)}^T$$ and $$b_2:=A^Hx = {(54-112i, 46-58i, 12, 5-51i, 78+34i, 60-94i)}^T\,.$$

The LU factorization of $A$ is used to solve the complex sparse linear systems $Ax=b_1$ and $A^Hx=b_2$ with iterative refinement. The reciprocal pivot growth factor and the reciprocal condition number are also computed.

See Also:

Code, Output

Constructor Summary

Constructors

Constructor and Description
ComplexSuperLUEx1()

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

ComplexSuperLUEx1

public ComplexSuperLUEx1()

Method Detail

main

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

Throws:

Exception