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.
| Constructor and Description |
|---|
SuperLUEx1() |
Copyright © 2020 Rogue Wave Software. All rights reserved.