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
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
|
/*
ARPACK++ v1.2 2/20/2000
c++ interface to ARPACK code.
MODULE ARGNSym.h.
Arpack++ class ARNonSymGenEig definition.
ARPACK Authors
Richard Lehoucq
Danny Sorensen
Chao Yang
Dept. of Computational & Applied Mathematics
Rice University
Houston, Texas
*/
#ifndef ARGNSYM_H
#define ARGNSYM_H
#include <cstddef>
#include "arch.h"
#include "blas1c.h"
#include "lapackc.h"
#include "arsnsym.h"
#include "argeig.h"
#include "arrgnsym.h"
template<class ARFLOAT, class ARFOP, class ARFB>
class ARNonSymGenEig:
virtual public ARGenEig<ARFLOAT, ARFLOAT, ARFOP, ARFB>,
virtual public ARNonSymStdEig<ARFLOAT, ARFOP>,
virtual public ARrcNonSymGenEig<ARFLOAT> {
public:
// a) Notation.
typedef void (ARFB::* TypeBx)(ARFLOAT[], ARFLOAT[]);
protected:
// b) Protected variables:
ARFB *objA; // Object that has MultAx as a member function.
TypeBx MultAx; // Function that evaluates the product A*x.
// c) Protected functions:
void RecoverEigenvalues();
// Uses Rayleigh quotient to recover eigenvalues of the original
// problem when shift is complex.
virtual void Copy(const ARNonSymGenEig& other);
// Makes a deep copy of "other" over "this" object.
// Old values are not deleted (this function is to be used
// by the copy constructor and the assignment operator only).
public:
// d) Public functions:
// d.1) Functions that allow changes in problem parameters.
virtual void SetShiftInvertMode(ARFLOAT sigmaRp, ARFOP* objOPp,
void (ARFOP::* MultOPxp)(ARFLOAT[],ARFLOAT[]));
// Turns the problem to real shift-and-invert mode with sigmaRp as shift.
virtual void SetComplexShiftMode(char partp, ARFLOAT sigmaRp,
ARFLOAT sigmaIp, ARFOP* objOPp,
void (ARFOP::* MultOPxp)(ARFLOAT[],ARFLOAT[]),
ARFB* objAp,
void (ARFB::* MultAxp)(ARFLOAT[],ARFLOAT[]));
// Turns the problem to complex shift-and-invert mode with shift
// defined by sigmaRp and sigmaIp. MultAx is used to obtain eigenvalues.
// d.2) Functions that perform all calculations in one step.
virtual int FindEigenvalues();
// Determines nev approximated eigenvalues of the given eigen-problem.
virtual int FindEigenvectors(bool schurp = false);
// Determines nev approximated eigenvectors of the given eigen-problem
// Optionally also determines nev Schur vectors that span the desired
// invariant subspace.
virtual int FindSchurVectors();
// Determines nev Schur vectors that span the desired invariant subspace.
// Redefined in ARSymEig.
// d.3) Constructors and destructor.
ARNonSymGenEig() { this->part = 'R'; }
// Short constructor (Does nothing but calling base classes constructors).
ARNonSymGenEig(int np, int nevp, ARFOP* objOPp,
void (ARFOP::* MultOPxp)(ARFLOAT[], ARFLOAT[]),
ARFB* objBp, void (ARFB::* MultBxp)(ARFLOAT[], ARFLOAT[]),
char* whichp = "LM", int ncvp = 0, ARFLOAT tolp = 0.0,
int maxitp = 0, ARFLOAT* residp = NULL, bool ishiftp = true);
// Long constructor (regular mode).
ARNonSymGenEig(int np, int nevp, ARFOP* objOPp,
void (ARFOP::* MultOPxp)(ARFLOAT[], ARFLOAT[]),
ARFB* objBp, void (ARFB::* MultBxp)(ARFLOAT[], ARFLOAT[]),
ARFLOAT sigmap, char* whichp = "LM", int ncvp = 0,
ARFLOAT tolp = 0.0, int maxitp = 0, ARFLOAT* residp = NULL,
bool ishiftp = true);
// Long constructor (real shift and invert mode).
ARNonSymGenEig(int np, int nevp, ARFOP* objOPp,
void (ARFOP::* MultOPxp)(ARFLOAT[], ARFLOAT[]), ARFB* objAp,
void (ARFB::* MultAxp)(ARFLOAT[], ARFLOAT[]), ARFB* objBp,
void (ARFB::* MultBxp)(ARFLOAT[], ARFLOAT[]), char partp,
ARFLOAT sigmaRp, ARFLOAT sigmaIp, char* whichp = "LM",
int ncvp = 0, ARFLOAT tolp = 0.0, int maxitp = 0,
ARFLOAT* residp = NULL, bool ishiftp = true);
// Long constructor (complex shift and invert mode).
ARNonSymGenEig(const ARNonSymGenEig& other) { Copy(other); }
// Copy constructor.
virtual ~ARNonSymGenEig() { }
// Destructor.
// e) Operators.
ARNonSymGenEig& operator=(const ARNonSymGenEig& other);
// Assignment operator.
}; // class ARNonSymGenEig.
// ------------------------------------------------------------------------ //
// ARNonSymGenEig member functions definition. //
// ------------------------------------------------------------------------ //
template<class ARFLOAT, class ARFOP, class ARFB>
inline void ARNonSymGenEig<ARFLOAT, ARFOP, ARFB>::
Copy(const ARNonSymGenEig<ARFLOAT, ARFOP, ARFB>& other)
{
ARGenEig<ARFLOAT, ARFLOAT, ARFOP, ARFB>::Copy(other);
objA = other.objA;
MultAx = other.MultAx;
this->part = other.part;
} // Copy.
template<class ARFLOAT, class ARFOP, class ARFB>
void ARNonSymGenEig<ARFLOAT, ARFOP, ARFB>::RecoverEigenvalues()
{
int j, ColJ, ColJp1;
ARFLOAT numr, numi, denr, deni;
ARFLOAT* Ax;
Ax = new ARFLOAT[this->n];
for (j=0; j<this->nconv; j++) {
ColJ = j*this->n;
ColJp1 = ColJ+this->n;
if (this->EigValI[j] == (ARFLOAT)0.0) {
// Eigenvalue is real. Computing EigVal = x'(Ax)/x'(Mx).
(this->objB->*this->MultAx)(&this->EigVec[ColJ], Ax);
numr = dot(this->n, &this->EigVec[ColJ], 1, Ax, 1);
(this->objB->*this->MultBx)(&this->EigVec[ColJ], Ax);
denr = dot(this->n, &this->EigVec[ColJ], 1, Ax, 1);
this->EigValR[j] = numr / denr;
}
else {
// Eigenvalue is complex.
// Computing x'(Ax).
(this->objB->*this->MultAx)(&this->EigVec[ColJ], Ax);
numr = dot(this->n, &this->EigVec[ColJ], 1, Ax, 1);
numi = dot(this->n, &this->EigVec[ColJp1], 1, Ax, 1);
(this->objB->*this->MultAx)(&this->EigVec[ColJp1], Ax);
numr = numr + dot(this->n, &this->EigVec[ColJp1], 1, Ax, 1);
numi = -numi + dot(this->n, &this->EigVec[ColJ], 1, Ax, 1);
// Computing x'(Mx).
(this->objB->*this->MultBx)(&this->EigVec[ColJ], Ax);
denr = dot(this->n, &this->EigVec[ColJ], 1, Ax, 1);
deni = dot(this->n, &this->EigVec[ColJp1], 1, Ax, 1);
(this->objB->*this->MultBx)(&this->EigVec[ColJp1], Ax);
denr = denr + dot(this->n, &this->EigVec[ColJp1], 1, Ax, 1);
deni = -deni + dot(this->n, &this->EigVec[ColJ], 1, Ax, 1);
// Computing the first eigenvalue of the conjugate pair.
this->EigValR[j] = (numr*denr+numi*deni) / lapy2(denr, deni);
this->EigValI[j] = (numi*denr-numr*deni) / lapy2(denr, deni);
// Getting the second eigenvalue of the conjugate pair by taking
// the conjugate of the first.
this->EigValR[j+1] = this->EigValR[j];
this->EigValI[j+1] = -this->EigValI[j];
j++;
}
}
delete[] Ax;
} // RecoverEigenvalues.
template<class ARFLOAT, class ARFOP, class ARFB>
inline void ARNonSymGenEig<ARFLOAT, ARFOP, ARFB>::
SetShiftInvertMode(ARFLOAT sigmaRp, ARFOP* objOPp,
void (ARFOP::* MultOPxp)(ARFLOAT[], ARFLOAT[]))
{
this->part = 'R';
this->objOP = objOPp;
this->MultOPx = MultOPxp;
this->ChangeShift(sigmaRp);
} // SetShiftInvertMode.
template<class ARFLOAT, class ARFOP, class ARFB>
inline void ARNonSymGenEig<ARFLOAT, ARFOP, ARFB>::
SetComplexShiftMode(char partp, ARFLOAT sigmaRp, ARFLOAT sigmaIp,
ARFOP* objOPp,
void (ARFOP::* MultOPxp)(ARFLOAT[], ARFLOAT[]),
ARFB* objAp, void (ARFB::* MultAxp)(ARFLOAT[], ARFLOAT[]))
{
this->objOP = objOPp;
this->MultOPx = MultOPxp;
this->objA = objAp;
this->MultAx = MultAxp;
this->part = this->CheckPart(partp);
this->ChangeShift(sigmaRp, sigmaIp);
} // SetComplexShiftMode.
template<class ARFLOAT, class ARFOP, class ARFB>
inline int ARNonSymGenEig<ARFLOAT, ARFOP, ARFB>::FindEigenvalues()
{
this->nconv = ARStdEig<ARFLOAT, ARFLOAT, ARFOP>::FindEigenvalues();
if (this->sigmaI != 0.0) RecoverEigenvalues();
return this->nconv;
} // FindEigenvalues.
template<class ARFLOAT, class ARFOP, class ARFB>
inline int ARNonSymGenEig<ARFLOAT, ARFOP, ARFB>::FindEigenvectors(bool schurp)
{
this->nconv = ARStdEig<ARFLOAT, ARFLOAT, ARFOP>::FindEigenvectors(schurp);
if (this->sigmaI != 0.0) RecoverEigenvalues();
return this->nconv;
} // FindEigenvectors.
template<class ARFLOAT, class ARFOP, class ARFB>
int ARNonSymGenEig<ARFLOAT, ARFOP, ARFB>::FindSchurVectors()
{
this->nconv = ARStdEig<ARFLOAT, ARFLOAT, ARFOP>::FindSchurVectors();
if (this->sigmaI != 0.0) RecoverEigenvalues();
return this->nconv;
} // FindSchurVectors.
template<class ARFLOAT, class ARFOP, class ARFB>
inline ARNonSymGenEig<ARFLOAT, ARFOP, ARFB>::
ARNonSymGenEig(int np, int nevp, ARFOP* objOPp,
void (ARFOP::* MultOPxp)(ARFLOAT[], ARFLOAT[]),
ARFB* objBp, void (ARFB::* MultBxp)(ARFLOAT[], ARFLOAT[]),
char* whichp, int ncvp, ARFLOAT tolp, int maxitp,
ARFLOAT* residp, bool ishiftp)
{
this->part = 'R'; // Considering mode = 3 in ChangeShift.
this->NoShift();
this->DefineParameters(np, nevp, objOPp, MultOPxp, objBp, MultBxp,
whichp, ncvp, tolp, maxitp, residp, ishiftp);
} // Long constructor (regular mode).
template<class ARFLOAT, class ARFOP, class ARFB>
inline ARNonSymGenEig<ARFLOAT, ARFOP, ARFB>::
ARNonSymGenEig(int np, int nevp, ARFOP* objOPp,
void (ARFOP::* MultOPxp)(ARFLOAT[], ARFLOAT[]),
ARFB* objBp, void (ARFB::* MultBxp)(ARFLOAT[], ARFLOAT[]),
ARFLOAT sigmap, char* whichp, int ncvp,
ARFLOAT tolp, int maxitp, ARFLOAT* residp, bool ishiftp)
{
SetShiftInvertMode(sigmap, objOPp, MultOPxp);
this->DefineParameters(np, nevp, objOPp, MultOPxp, objBp, MultBxp,
whichp, ncvp, tolp, maxitp, residp, ishiftp);
} // Long constructor (real shift and invert mode).
template<class ARFLOAT, class ARFOP, class ARFB>
inline ARNonSymGenEig<ARFLOAT, ARFOP, ARFB>::
ARNonSymGenEig(int np, int nevp, ARFOP* objOPp,
void (ARFOP::* MultOPxp)(ARFLOAT[], ARFLOAT[]),
ARFB* objAp, void (ARFB::* MultAxp)(ARFLOAT[], ARFLOAT[]),
ARFB* objBp, void (ARFB::* MultBxp)(ARFLOAT[], ARFLOAT[]),
char partp, ARFLOAT sigmaRp, ARFLOAT sigmaIp,
char* whichp, int ncvp, ARFLOAT tolp, int maxitp,
ARFLOAT* residp, bool ishiftp)
{
SetComplexShiftMode(partp, sigmaRp, sigmaIp, objOPp,
MultOPxp, objAp, MultAxp);
this->DefineParameters(np, nevp, objOPp, MultOPxp, objBp, MultBxp,
whichp, ncvp, tolp, maxitp, residp, ishiftp);
} // Long constructor (shift and invert mode).
template<class ARFLOAT, class ARFOP, class ARFB>
ARNonSymGenEig<ARFLOAT, ARFOP, ARFB>& ARNonSymGenEig<ARFLOAT, ARFOP, ARFB>::
operator=(const ARNonSymGenEig<ARFLOAT, ARFOP, ARFB>& other)
{
if (this != &other) { // Stroustrup suggestion.
this->ClearMem();
Copy(other);
}
return *this;
} // operator=.
#endif // ARGNSYM_H
|
