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
|
/*
ARPACK++ v1.2 2/18/2000
c++ interface to ARPACK code.
MODULE DSymShf.cc.
Example program that illustrates how to solve a real symmetric
dense standard eigenvalue problem in shift and invert mode using
the ARluSymStdEig 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 standard central
difference discretization of the 2-dimensional Laplacian on
the unit square with zero Dirichlet boundary conditions.
2) Data structure used to represent matrix A:
Although A is very sparse in this example, it is stored
here as a dense symmetric matrix. The lower triangular part
of A is stored, by columns, in the vector A.
3) Library called by this example:
The LAPACK package is called by ARluSymStdEig 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
----------- --------------------------------------------
dsmatrxa.h DenseMatrixA, a function that generates
matrix A.
ardsmat.h The ARdsSymMatrix class definition.
ardssym.h The ARluSymStdEig class definition.
lsymsol.h The Solution function.
5) ARPACK Authors:
Richard Lehoucq
Kristyn Maschhoff
Danny Sorensen
Chao Yang
Dept. of Computational & Applied Mathematics
Rice University
Houston, Texas
*/
#include "dsmatrxa.h"
#include "ardsmat.h"
#include "ardssym.h"
#include "lsymsol.h"
int main()
{
// Defining variables;
int nx;
int n; // Dimension of the problem.
double* A; // Pointer to an array that stores the elements of A.
// Creating a 100x100 matrix.
nx = 10;
DenseMatrixA(nx, n, A);
ARdsSymMatrix<double> matrix(n, A);
// Defining what we need: the four eigenvectors of A nearest to 1.0.
ARluSymStdEig<double> dprob(4L, matrix, 1.0);
// Finding eigenvalues and eigenvectors.
dprob.FindEigenvectors();
// Printing solution.
Solution(matrix, dprob);
} // main
|
