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
93
94
95
96
97
98
|
/*
ARPACK++ v1.0 8/1/1997
c++ interface to ARPACK code.
MODULE ASymGShf.cc.
Example program that illustrates how to solve a real symmetric
generalized eigenvalue problem in Cayley mode using the AREig
function.
1) Problem description:
In this example we try to solve A*x = B*x*lambda in Cayley mode,
where A and B are obtained from the finite element discretization
of the 1-dimensional discrete Laplacian
d^2u / dx^2
on the interval [0,1] with zero Dirichlet boundary conditions
using piecewise linear elements.
2) Data structure used to represent matrices A and B:
{nnzA, irowA, pcolA, valA}: upper triangular part of matrix A
stored in CSC format.
{nnzB, irowB, pcolB, valB}: upper triangular part of matrix B
stored in CSC format.
3) Library called by this example:
The SuperLU package is called by AREig to solve some linear
systems involving (A-sigma*B).
4) Included header files:
File Contents
----------- -------------------------------------------
lsmatrxc.h SymmetricMatrixC, a function that generates
matrix A in CSC format.
lsmatrxd.h SymmetricMatrixD, a function that generates
matrix B in CSC format.
areig.h The AREig function definition.
asymsol.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 "lsmatrxc.h"
#include "lsmatrxd.h"
#include "areig.h"
#include "asymsol.h"
main()
{
// Defining variables;
int n; // Dimension of the problem.
int nconv; // Number of "converged" eigenvalues.
int nnzA, nnzB; // Number of nonzero elements in A and B.
int *irowA, *irowB; // pointer to an array that stores the row
// indices of the nonzeros in A and B.
int *pcolA, *pcolB; // pointer to an array of pointers to the
// beginning of each column of A (B) in valA (valB).
double *valA, *valB; // pointer to an array that stores the nonzero
// elements of A and B.
double EigVal[101]; // Eigenvalues.
double EigVec[1001]; // Eigenvectors stored sequentially.
char uplo; // Variable that indicates whether the upper
// (uplo='U') ot the lower (uplo='L') part of
// A and B will be supplied to AREig.
// Creating matrices A and B.
n = 100;
uplo = 'U';
SymmetricMatrixC(n, nnzA, valA, irowA, pcolA, uplo);
SymmetricMatrixD(n, nnzB, valB, irowB, pcolB, uplo);
// Finding the four eigenvalues of A nearest to 150.0 and the
// related eigenvectors.
nconv = AREig(EigVal, EigVec, n, nnzA, valA, irowA, pcolA,
nnzB, valB, irowB, pcolB, uplo, 'C', 150.0, 4);
// Printing solution.
Solution(nconv, n, nnzA, valA, irowA, pcolA, nnzB,
valB, irowB, pcolB, uplo, EigVal, EigVec);
} // main.
|
