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.
| Constructor and Description |
|---|
ComplexSuperLUEx1() |
Copyright © 2020 Rogue Wave Software. All rights reserved.