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
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
|
/*
ARPACK++ v1.2 2/18/2000
c++ interface to ARPACK code.
MODULE RNSymShf.cc.
Example program that illustrates how to solve a real
nonsymmetric standard eigenvalue problem in shift and invert
mode using the ARrcNonSymStdEig class.
1) Problem description:
In this example we try to solve A*x = x*lambda in regular mode,
where A is derived from the centered 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 condition.
The shift sigma is a real number.
2) Data structure used to represent matrix A:
class ARrcNonSymStdEig requires the user to provide a way to
perform the matrix-vector product w = OPv, where OP =
inv[A - sigma*I]. In this example a class called NonSymMatrixB was
created with this purpose. NonSymMatrixB contains a member function,
MultOPv, that takes a vector v and returns the product OPv in w.
3) The reverse communication interface:
This example uses the reverse communication interface, which
means that the desired eigenvalues cannot be obtained directly
from an ARPACK++ class.
Here, the overall process of finding eigenvalues by using the
Arnoldi method is splitted into two parts. In the first, a
sequence of calls to a function called TakeStep is combined
with matrix-vector products in order to find an Arnoldi basis.
In the second part, an ARPACK++ function like FindEigenvectors
(or EigenValVectors) is used to extract eigenvalues and
eigenvectors.
4) Included header files:
File Contents
----------- -------------------------------------------
nmatrixb.h The NonSymMatrixB class definition.
arrsnsym.h The ARrcNonSymStdEig class definition.
rnsymsol.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 "nmatrixb.h"
#include "rnsymsol.h"
#include "arrsnsym.h"
template<class T>
void Test(T type)
{
// Defining a nonsymmetric matrix.
NonSymMatrixB<T> B(100, 1.0, 10.0); // n = 100, shift = 1, rho = 10.
// Creating a nonsymmetric eigenvalue problem and defining what we need:
// the four eigenvectors of B nearest to 1.0.
ARrcNonSymStdEig<T> prob(B.ncols(), 4, (T)1.0);
// Finding an Arnoldi basis.
while (!prob.ArnoldiBasisFound()) {
// Calling ARPACK FORTRAN code. Almost all work needed to
// find an Arnoldi basis is performed by TakeStep.
prob.TakeStep();
if ((prob.GetIdo() == 1)||(prob.GetIdo() == -1)) {
// Performing matrix-vector multiplication.
// In shift and invert mode, w = OPv must be performed
// whenever GetIdo is equal to 1 or -1. GetVector supplies
// a pointer to the input vector, v, and PutVector a pointer
// to the output vector, w.
B.MultOPv(prob.GetVector(), prob.PutVector());
}
}
// Finding eigenvalues and eigenvectors.
prob.FindEigenvectors();
// Printing solution.
Solution(prob);
} // Test.
int main()
{
// Solving a double precision problem with n = 100.
Test((double)0.0);
// Solving a single precision problem with n = 100.
Test((float)0.0);
} // main
|
