Package 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	Description
ComplexSuperLUEx1()

Method Summary

Modifier and Type	Method	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 Details

ComplexSuperLUEx1

public ComplexSuperLUEx1()

Method Details

main

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

Throws:

Exception