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
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
|
/*
ARPACK++ v1.2 2/20/2000
c++ interface to ARPACK code.
MODULE LNSymSol.h
Template functions that exemplify how to print information
about nonsymmetric standard and generalized eigenvalue problems.
ARPACK Authors
Richard Lehoucq
Danny Sorensen
Chao Yang
Dept. of Computational & Applied Mathematics
Rice University
Houston, Texas
*/
#ifndef LNSYMSOL_H
#define LNSYMSOL_H
#include <math.h>
#include "blas1c.h"
#include "lapackc.h"
#ifdef ARLNSMAT_H
#include "arlsnsym.h"
#include "arlgnsym.h"
#elif defined ARUNSMAT_H
#include "arusnsym.h"
#include "arugnsym.h"
#elif defined ARDNSMAT_H
#include "ardsnsym.h"
#include "ardgnsym.h"
#else
#include "arbsnsym.h"
#include "arbgnsym.h"
#endif
template<class ARMATRIX, class ARFLOAT>
void Solution(ARMATRIX &A, ARluNonSymStdEig<ARFLOAT> &Prob)
/*
Prints eigenvalues and eigenvectors of nonsymmetric eigen-problems
on standard "cout" stream.
*/
{
int i, n, nconv, mode;
ARFLOAT *Ax;
ARFLOAT *ResNorm;
n = Prob.GetN();
nconv = Prob.ConvergedEigenvalues();
mode = Prob.GetMode();
std::cout << std::endl << std::endl << "Testing ARPACK++ class ARluNonSymStdEig \n";
std::cout << "Real nonsymmetric eigenvalue problem: A*x - lambda*x" << std::endl;
switch (mode) {
case 1:
std::cout << "Regular mode" << std::endl << std::endl;
break;
case 3:
std::cout << "Shift and invert mode" << std::endl << std::endl;
}
std::cout << "Dimension of the system : " << n << std::endl;
std::cout << "Number of 'requested' eigenvalues : " << Prob.GetNev() << std::endl;
std::cout << "Number of 'converged' eigenvalues : " << nconv << std::endl;
std::cout << "Number of Arnoldi vectors generated: " << Prob.GetNcv() << std::endl;
std::cout << "Number of iterations taken : " << Prob.GetIter() << std::endl;
std::cout << std::endl;
if (Prob.EigenvaluesFound()) {
// Printing eigenvalues.
std::cout << "Eigenvalues:" << std::endl;
for (i=0; i<nconv; i++) {
std::cout << " lambda[" << (i+1) << "]: " << Prob.EigenvalueReal(i);
if (Prob.EigenvalueImag(i)>=0.0) {
std::cout << " + " << Prob.EigenvalueImag(i) << " I" << std::endl;
}
else {
std::cout << " - " << fabs(Prob.EigenvalueImag(i)) << " I" << std::endl;
}
}
std::cout << std::endl;
}
if (Prob.EigenvectorsFound()) {
// Printing the residual norm || A*x - lambda*x ||
// for the nconv accurately computed eigenvectors.
Ax = new ARFLOAT[n];
ResNorm = new ARFLOAT[nconv+1];
for (i=0; i<nconv; i++) {
if (Prob.EigenvalueImag(i)==0.0) { // Eigenvalue is real.
A.MultMv(Prob.RawEigenvector(i), Ax);
axpy(n, -Prob.EigenvalueReal(i), Prob.RawEigenvector(i), 1, Ax, 1);
ResNorm[i] = nrm2(n, Ax, 1)/fabs(Prob.EigenvalueReal(i));
}
else { // Eigenvalue is complex.
A.MultMv(Prob.RawEigenvector(i), Ax);
axpy(n, -Prob.EigenvalueReal(i), Prob.RawEigenvector(i), 1, Ax, 1);
axpy(n, Prob.EigenvalueImag(i), Prob.RawEigenvector(i+1), 1, Ax, 1);
ResNorm[i] = nrm2(n, Ax, 1);
A.MultMv(Prob.RawEigenvector(i+1), Ax);
axpy(n, -Prob.EigenvalueImag(i), Prob.RawEigenvector(i), 1, Ax, 1);
axpy(n, -Prob.EigenvalueReal(i), Prob.RawEigenvector(i+1), 1, Ax, 1);
ResNorm[i] = lapy2(ResNorm[i], nrm2(n, Ax, 1))/
lapy2(Prob.EigenvalueReal(i), Prob.EigenvalueImag(i));
ResNorm[i+1] = ResNorm[i];
i++;
}
}
for (i=0; i<nconv; i++) {
std::cout << "||A*x(" << (i+1) << ") - lambda(" << (i+1);
std::cout << ")*x(" << (i+1) << ")||: " << ResNorm[i] << "\n";
}
std::cout << "\n";
delete[] Ax;
delete[] ResNorm;
}
} // Solution
template<class MATRA, class MATRB, class ARFLOAT>
void Solution(MATRA &A, MATRB &B, ARluNonSymGenEig<ARFLOAT> &Prob)
/*
Prints eigenvalues and eigenvectors of nonsymmetric generalized
eigen-problems on standard "std::cout" stream.
*/
{
int i, n, nconv, mode;
ARFLOAT *Ax;
ARFLOAT *Bx, *Bx1;
ARFLOAT *ResNorm;
n = Prob.GetN();
nconv = Prob.ConvergedEigenvalues();
mode = Prob.GetMode();
std::cout << std::endl << std::endl << "Testing ARPACK++ class ARluNonSymGenEig \n";
std::cout << "Real nonsymmetric generalized eigenvalue problem: A*x - lambda*B*x";
std::cout << std::endl;
switch (mode) {
case 2:
std::cout << "Regular mode" << std::endl;
break;
case 3:
std::cout << "Shift and invert mode (using the real part of OP)" << std::endl;
break;
case 4:
std::cout << "Shift and invert mode (using the imaginary part of OP)" << std::endl;
}
std::cout << std::endl;
std::cout << "Dimension of the system : " << n << std::endl;
std::cout << "Number of 'requested' eigenvalues : " << Prob.GetNev() << std::endl;
std::cout << "Number of 'converged' eigenvalues : " << nconv << std::endl;
std::cout << "Number of Arnoldi vectors generated: " << Prob.GetNcv() << std::endl;
std::cout << "Number of iterations taken : " << Prob.GetIter() << std::endl;
std::cout << std::endl;
if (Prob.EigenvaluesFound()) {
// Printing eigenvalues.
std::cout << "Eigenvalues:" << std::endl;
for (i=0; i<nconv; i++) {
std::cout << " lambda[" << (i+1) << "]: " << Prob.EigenvalueReal(i);
if (Prob.EigenvalueImag(i)>=0.0) {
std::cout << " + " << Prob.EigenvalueImag(i) << " I" << std::endl;
}
else {
std::cout << " - " << fabs(Prob.EigenvalueImag(i)) << " I" << std::endl;
}
}
std::cout << std::endl;
}
if (Prob.EigenvectorsFound()) {
// Printing the residual norm || A*x - lambda*B*x ||
// for the nconv accurately computed eigenvectors.
Ax = new ARFLOAT[n];
Bx = new ARFLOAT[n];
Bx1 = new ARFLOAT[n];
ResNorm = new ARFLOAT[nconv+1];
for (i=0; i<nconv; i++) {
if (Prob.EigenvalueImag(i)==0.0) { // Eigenvalue is real.
A.MultMv(Prob.RawEigenvector(i), Ax);
B.MultMv(Prob.RawEigenvector(i), Bx);
axpy(n, -Prob.EigenvalueReal(i), Bx, 1, Ax, 1);
ResNorm[i] = nrm2(n, Ax, 1)/fabs(Prob.EigenvalueReal(i));
}
else { // Eigenvalue is complex.
A.MultMv(Prob.RawEigenvector(i), Ax);
B.MultMv(Prob.RawEigenvector(i), Bx);
B.MultMv(Prob.RawEigenvector(i+1), Bx1);
axpy(n, -Prob.EigenvalueReal(i), Bx, 1, Ax, 1);
axpy(n, Prob.EigenvalueImag(i), Bx1, 1, Ax, 1);
ResNorm[i] = nrm2(n, Ax, 1);
A.MultMv(Prob.RawEigenvector(i+1), Ax);
axpy(n, -Prob.EigenvalueImag(i), Bx, 1, Ax, 1);
axpy(n, -Prob.EigenvalueReal(i), Bx1, 1, Ax, 1);
ResNorm[i] = lapy2(ResNorm[i], nrm2(n, Ax, 1))/
lapy2(Prob.EigenvalueReal(i), Prob.EigenvalueImag(i));
ResNorm[i+1] = ResNorm[i];
i++;
}
}
for (i=0; i<nconv; i++) {
std::cout << "||A*x(" << i << ") - lambda(" << i;
std::cout << ")*B*x(" << i << ")||: " << ResNorm[i] << "\n";
}
std::cout << "\n";
delete[] Ax;
delete[] Bx;
delete[] Bx1;
delete[] ResNorm;
}
} // Solution
#endif // LNSYMSOL_H
|
