1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
|
/*
ARPACK++ v1.0 8/1/1997
c++ interface to ARPACK code.
MODULE UCompShf.cc.
Example program that illustrates how to solve a complex standard
eigenvalue problem in shift and invert mode using the
ARluCompStdEig class.
1) Problem description:
In this example we try to solve A*x = x*lambda in shift and invert
mode, where A is derived from the central difference discretization
of the 1-dimensional convection-diffusion operator
(d^2u/dx^2) + rho*(du/dx)
on the interval [0,1] with zero Dirichlet boundary conditions.
2) Data structure used to represent matrix A:
{nnz, irow, pcol, A}: matrix A data in CSC format.
3) Library called by this example:
The UMFPACK package is called by ARluCompStdEig to solve
some linear systems involving (A-sigma*I). This is needed to
implement the shift and invert strategy.
4) Included header files:
File Contents
----------- ---------------------------------------------
lcmatrxb.h CompMatrixB, a function that generates matrix
A in CSC format.
arunsmat.h The ARumNonSymMatrix class definition.
aruscomp.h The ARluCompStdEig class definition.
lcompsol.h The Solution function.
arcomp.h The "arcomplex" (complex) type definition.
5) ARPACK Authors:
Richard Lehoucq
Kristyn Maschhoff
Danny Sorensen
Chao Yang
Dept. of Computational & Applied Mathematics
Rice University
Houston, Texas
*/
#include "arcomp.h"
#include "arunsmat.h"
#include "aruscomp.h"
#include "lcmatrxb.h"
#include "lcompsol.h"
main()
{
// Defining variables;
int n; // Dimension of the problem.
int nnz; // Number of nonzero elements in A.
int* irow; // pointer to an array that stores the row
// indices of the nonzeros in A.
int* pcol; // pointer to an array of pointers to the
// beginning of each column of A in valA.
arcomplex<double> rho; // parameter used to generate A.
arcomplex<double>* valA; // pointer to an array that stores the
// nonzero elements of A.
// Creating a complex matrix.
n = 100;
rho = 10.0;
CompMatrixB(n, rho, nnz, valA, irow, pcol);
ARumNonSymMatrix<arcomplex<double> > A(n, nnz, valA, irow, pcol);
// Defining what we need: the four eigenvectors of F nearest to 0.0.
ARluCompStdEig<double> dprob(4L, A, arcomplex<double>(0.0, 0.0));
// Finding eigenvalues and eigenvectors.
dprob.FindEigenvectors();
// Printing solution.
Solution(A, dprob);
} // main.
|
