Line data Source code
1 : /*
2 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3 : SLEPc - Scalable Library for Eigenvalue Problem Computations
4 : Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
5 :
6 : This file is part of SLEPc.
7 : SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9 : */
10 : /*
11 : This file contains some simple default routines for common operations
12 : */
13 :
14 : #include <slepc/private/epsimpl.h> /*I "slepceps.h" I*/
15 : #include <slepcvec.h>
16 :
17 574 : PetscErrorCode EPSBackTransform_Default(EPS eps)
18 : {
19 574 : PetscFunctionBegin;
20 574 : PetscCall(STBackTransform(eps->st,eps->nconv,eps->eigr,eps->eigi));
21 574 : PetscFunctionReturn(PETSC_SUCCESS);
22 : }
23 :
24 : /*
25 : EPSComputeVectors_Hermitian - Copies the Lanczos vectors as eigenvectors
26 : using purification for generalized eigenproblems.
27 : */
28 260 : PetscErrorCode EPSComputeVectors_Hermitian(EPS eps)
29 : {
30 260 : PetscBool iscayley,indef;
31 260 : Mat B,C;
32 :
33 260 : PetscFunctionBegin;
34 260 : if (eps->purify) {
35 55 : PetscCall(EPS_Purify(eps,eps->nconv));
36 55 : PetscCall(BVNormalize(eps->V,NULL));
37 : } else {
38 : /* In the case of Cayley transform, eigenvectors need to be B-normalized */
39 205 : PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&iscayley));
40 205 : if (iscayley && eps->isgeneralized) {
41 1 : PetscCall(STGetMatrix(eps->st,1,&B));
42 1 : PetscCall(BVGetMatrix(eps->V,&C,&indef));
43 1 : PetscCheck(!indef,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"The inner product should not be indefinite");
44 1 : PetscCall(BVSetMatrix(eps->V,B,PETSC_FALSE));
45 1 : PetscCall(BVNormalize(eps->V,NULL));
46 1 : PetscCall(BVSetMatrix(eps->V,C,PETSC_FALSE)); /* restore original matrix */
47 : }
48 : }
49 260 : PetscFunctionReturn(PETSC_SUCCESS);
50 : }
51 :
52 : /*
53 : EPSComputeVectors_Indefinite - similar to the Schur version but
54 : for indefinite problems
55 : */
56 13 : PetscErrorCode EPSComputeVectors_Indefinite(EPS eps)
57 : {
58 13 : PetscInt n;
59 13 : Mat X;
60 :
61 13 : PetscFunctionBegin;
62 13 : PetscCall(DSGetDimensions(eps->ds,&n,NULL,NULL,NULL));
63 13 : PetscCall(DSVectors(eps->ds,DS_MAT_X,NULL,NULL));
64 13 : PetscCall(DSGetMat(eps->ds,DS_MAT_X,&X));
65 13 : PetscCall(BVMultInPlace(eps->V,X,0,n));
66 13 : PetscCall(DSRestoreMat(eps->ds,DS_MAT_X,&X));
67 :
68 : /* purification */
69 13 : if (eps->purify) PetscCall(EPS_Purify(eps,eps->nconv));
70 :
71 : /* normalization */
72 13 : PetscCall(BVNormalize(eps->V,eps->eigi));
73 13 : PetscFunctionReturn(PETSC_SUCCESS);
74 : }
75 :
76 : /*
77 : EPSComputeVectors_Twosided - Adjust left eigenvectors in generalized problems: y = B^-* y.
78 : */
79 16 : PetscErrorCode EPSComputeVectors_Twosided(EPS eps)
80 : {
81 16 : PetscInt i;
82 16 : Vec w,y;
83 :
84 16 : PetscFunctionBegin;
85 16 : if (!eps->twosided || !eps->isgeneralized) PetscFunctionReturn(PETSC_SUCCESS);
86 1 : PetscCall(EPSSetWorkVecs(eps,1));
87 1 : w = eps->work[0];
88 7 : for (i=0;i<eps->nconv;i++) {
89 6 : PetscCall(BVCopyVec(eps->W,i,w));
90 6 : PetscCall(BVGetColumn(eps->W,i,&y));
91 6 : PetscCall(STMatSolveHermitianTranspose(eps->st,w,y));
92 6 : PetscCall(BVRestoreColumn(eps->W,i,&y));
93 : }
94 1 : PetscFunctionReturn(PETSC_SUCCESS);
95 : }
96 :
97 : /*
98 : EPSComputeVectors_Schur - Compute eigenvectors from the vectors
99 : provided by the eigensolver. This version is intended for solvers
100 : that provide Schur vectors. Given the partial Schur decomposition
101 : OP*V=V*T, the following steps are performed:
102 : 1) compute eigenvectors of T: T*Z=Z*D
103 : 2) compute eigenvectors of OP: X=V*Z
104 : */
105 302 : PetscErrorCode EPSComputeVectors_Schur(EPS eps)
106 : {
107 302 : PetscInt i;
108 302 : Mat Z;
109 302 : Vec z;
110 :
111 302 : PetscFunctionBegin;
112 302 : if (eps->ishermitian) {
113 51 : if (eps->isgeneralized && !eps->ispositive) PetscCall(EPSComputeVectors_Indefinite(eps));
114 51 : else PetscCall(EPSComputeVectors_Hermitian(eps));
115 51 : PetscFunctionReturn(PETSC_SUCCESS);
116 : }
117 :
118 : /* right eigenvectors */
119 251 : PetscCall(DSVectors(eps->ds,DS_MAT_X,NULL,NULL));
120 :
121 : /* V = V * Z */
122 251 : PetscCall(DSGetMat(eps->ds,DS_MAT_X,&Z));
123 251 : PetscCall(BVMultInPlace(eps->V,Z,0,eps->nconv));
124 251 : PetscCall(DSRestoreMat(eps->ds,DS_MAT_X,&Z));
125 :
126 : /* Purify eigenvectors */
127 251 : if (eps->purify) PetscCall(EPS_Purify(eps,eps->nconv));
128 :
129 : /* Fix eigenvectors if balancing was used */
130 251 : if (eps->balance!=EPS_BALANCE_NONE && eps->D) {
131 74 : for (i=0;i<eps->nconv;i++) {
132 62 : PetscCall(BVGetColumn(eps->V,i,&z));
133 62 : PetscCall(VecPointwiseDivide(z,z,eps->D));
134 62 : PetscCall(BVRestoreColumn(eps->V,i,&z));
135 : }
136 : }
137 :
138 : /* normalize eigenvectors (when using purification or balancing) */
139 251 : if (eps->purify || (eps->balance!=EPS_BALANCE_NONE && eps->D)) PetscCall(BVNormalize(eps->V,eps->eigi));
140 :
141 : /* left eigenvectors */
142 251 : if (eps->twosided) {
143 13 : PetscCall(DSVectors(eps->ds,DS_MAT_Y,NULL,NULL));
144 : /* W = W * Z */
145 13 : PetscCall(DSGetMat(eps->ds,DS_MAT_Y,&Z));
146 13 : PetscCall(BVMultInPlace(eps->W,Z,0,eps->nconv));
147 13 : PetscCall(DSRestoreMat(eps->ds,DS_MAT_Y,&Z));
148 : /* Fix left eigenvectors if balancing was used */
149 13 : if (eps->balance!=EPS_BALANCE_NONE && eps->D) {
150 10 : for (i=0;i<eps->nconv;i++) {
151 8 : PetscCall(BVGetColumn(eps->W,i,&z));
152 8 : PetscCall(VecPointwiseMult(z,z,eps->D));
153 8 : PetscCall(BVRestoreColumn(eps->W,i,&z));
154 : }
155 : }
156 13 : PetscCall(EPSComputeVectors_Twosided(eps));
157 : /* normalize */
158 13 : PetscCall(BVNormalize(eps->W,eps->eigi));
159 : #if !defined(PETSC_USE_COMPLEX)
160 : for (i=0;i<eps->nconv-1;i++) {
161 : if (eps->eigi[i] != 0.0) {
162 : if (eps->eigi[i] > 0.0) PetscCall(BVScaleColumn(eps->W,i+1,-1.0));
163 : i++;
164 : }
165 : }
166 : #endif
167 : }
168 251 : PetscFunctionReturn(PETSC_SUCCESS);
169 : }
170 :
171 : /*@
172 : EPSSetWorkVecs - Sets a number of work vectors into an EPS object.
173 :
174 : Collective
175 :
176 : Input Parameters:
177 : + eps - eigensolver context
178 : - nw - number of work vectors to allocate
179 :
180 : Developer Notes:
181 : This is SLEPC_EXTERN because it may be required by user plugin EPS
182 : implementations.
183 :
184 : Level: developer
185 :
186 : .seealso: EPSSetUp()
187 : @*/
188 3949 : PetscErrorCode EPSSetWorkVecs(EPS eps,PetscInt nw)
189 : {
190 3949 : Vec t;
191 :
192 3949 : PetscFunctionBegin;
193 3949 : PetscValidHeaderSpecific(eps,EPS_CLASSID,1);
194 11847 : PetscValidLogicalCollectiveInt(eps,nw,2);
195 3949 : PetscCheck(nw>0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"nw must be > 0: nw = %" PetscInt_FMT,nw);
196 3949 : if (eps->nwork < nw) {
197 659 : PetscCall(VecDestroyVecs(eps->nwork,&eps->work));
198 659 : eps->nwork = nw;
199 659 : PetscCall(BVGetColumn(eps->V,0,&t));
200 659 : PetscCall(VecDuplicateVecs(t,nw,&eps->work));
201 659 : PetscCall(BVRestoreColumn(eps->V,0,&t));
202 : }
203 3949 : PetscFunctionReturn(PETSC_SUCCESS);
204 : }
205 :
206 : /*
207 : EPSSetWhichEigenpairs_Default - Sets the default value for which,
208 : depending on the ST.
209 : */
210 113 : PetscErrorCode EPSSetWhichEigenpairs_Default(EPS eps)
211 : {
212 113 : PetscBool target;
213 :
214 113 : PetscFunctionBegin;
215 113 : PetscCall(PetscObjectTypeCompareAny((PetscObject)eps->st,&target,STSINVERT,STCAYLEY,""));
216 113 : if (target) eps->which = EPS_TARGET_MAGNITUDE;
217 94 : else eps->which = EPS_LARGEST_MAGNITUDE;
218 113 : PetscFunctionReturn(PETSC_SUCCESS);
219 : }
220 :
221 : /*
222 : EPSConvergedRelative - Checks convergence relative to the eigenvalue.
223 : */
224 49981 : PetscErrorCode EPSConvergedRelative(EPS eps,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
225 : {
226 49981 : PetscReal w;
227 :
228 49981 : PetscFunctionBegin;
229 49981 : w = SlepcAbsEigenvalue(eigr,eigi);
230 49981 : *errest = (w!=0.0)? res/w: PETSC_MAX_REAL;
231 49981 : PetscFunctionReturn(PETSC_SUCCESS);
232 : }
233 :
234 : /*
235 : EPSConvergedAbsolute - Checks convergence absolutely.
236 : */
237 4336 : PetscErrorCode EPSConvergedAbsolute(EPS eps,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
238 : {
239 4336 : PetscFunctionBegin;
240 4336 : *errest = res;
241 4336 : PetscFunctionReturn(PETSC_SUCCESS);
242 : }
243 :
244 : /*
245 : EPSConvergedNorm - Checks convergence relative to the eigenvalue and
246 : the matrix norms.
247 : */
248 5138 : PetscErrorCode EPSConvergedNorm(EPS eps,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
249 : {
250 5138 : PetscReal w;
251 :
252 5138 : PetscFunctionBegin;
253 5138 : w = SlepcAbsEigenvalue(eigr,eigi);
254 5138 : *errest = res / (eps->nrma + w*eps->nrmb);
255 5138 : PetscFunctionReturn(PETSC_SUCCESS);
256 : }
257 :
258 : /*@C
259 : EPSStoppingBasic - Default routine to determine whether the outer eigensolver
260 : iteration must be stopped.
261 :
262 : Collective
263 :
264 : Input Parameters:
265 : + eps - eigensolver context obtained from EPSCreate()
266 : . its - current number of iterations
267 : . max_it - maximum number of iterations
268 : . nconv - number of currently converged eigenpairs
269 : . nev - number of requested eigenpairs
270 : - ctx - context (not used here)
271 :
272 : Output Parameter:
273 : . reason - result of the stopping test
274 :
275 : Notes:
276 : A positive value of reason indicates that the iteration has finished successfully
277 : (converged), and a negative value indicates an error condition (diverged). If
278 : the iteration needs to be continued, reason must be set to EPS_CONVERGED_ITERATING
279 : (zero).
280 :
281 : EPSStoppingBasic() will stop if all requested eigenvalues are converged, or if
282 : the maximum number of iterations has been reached.
283 :
284 : Use EPSSetStoppingTest() to provide your own test instead of using this one.
285 :
286 : Level: advanced
287 :
288 : .seealso: EPSSetStoppingTest(), EPSConvergedReason, EPSGetConvergedReason()
289 : @*/
290 44290 : PetscErrorCode EPSStoppingBasic(EPS eps,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,EPSConvergedReason *reason,void *ctx)
291 : {
292 44290 : PetscFunctionBegin;
293 44290 : *reason = EPS_CONVERGED_ITERATING;
294 44290 : if (nconv >= nev) {
295 712 : PetscCall(PetscInfo(eps,"Linear eigensolver finished successfully: %" PetscInt_FMT " eigenpairs converged at iteration %" PetscInt_FMT "\n",nconv,its));
296 712 : *reason = EPS_CONVERGED_TOL;
297 43578 : } else if (its >= max_it) {
298 12 : *reason = EPS_DIVERGED_ITS;
299 12 : PetscCall(PetscInfo(eps,"Linear eigensolver iteration reached maximum number of iterations (%" PetscInt_FMT ")\n",its));
300 : }
301 44290 : PetscFunctionReturn(PETSC_SUCCESS);
302 : }
303 :
304 : /*
305 : EPSComputeRitzVector - Computes the current Ritz vector.
306 :
307 : Simple case (complex scalars or real scalars with Zi=NULL):
308 : x = V*Zr (V is a basis of nv vectors, Zr has length nv)
309 :
310 : Split case:
311 : x = V*Zr y = V*Zi (Zr and Zi have length nv)
312 : */
313 407 : PetscErrorCode EPSComputeRitzVector(EPS eps,PetscScalar *Zr,PetscScalar *Zi,BV V,Vec x,Vec y)
314 : {
315 407 : PetscInt l,k;
316 407 : PetscReal norm;
317 : #if !defined(PETSC_USE_COMPLEX)
318 : Vec z;
319 : #endif
320 :
321 407 : PetscFunctionBegin;
322 : /* compute eigenvector */
323 407 : PetscCall(BVGetActiveColumns(V,&l,&k));
324 407 : PetscCall(BVSetActiveColumns(V,0,k));
325 407 : PetscCall(BVMultVec(V,1.0,0.0,x,Zr));
326 :
327 : /* purify eigenvector if necessary */
328 407 : if (eps->purify) {
329 12 : PetscCall(STApply(eps->st,x,y));
330 12 : if (eps->ishermitian) PetscCall(BVNormVec(eps->V,y,NORM_2,&norm));
331 0 : else PetscCall(VecNorm(y,NORM_2,&norm));
332 12 : PetscCall(VecScale(y,1.0/norm));
333 12 : PetscCall(VecCopy(y,x));
334 : }
335 : /* fix eigenvector if balancing is used */
336 407 : if (!eps->ishermitian && eps->balance!=EPS_BALANCE_NONE && eps->D) PetscCall(VecPointwiseDivide(x,x,eps->D));
337 : #if !defined(PETSC_USE_COMPLEX)
338 : /* compute imaginary part of eigenvector */
339 : if (Zi) {
340 : PetscCall(BVMultVec(V,1.0,0.0,y,Zi));
341 : if (eps->ispositive) {
342 : PetscCall(BVCreateVec(V,&z));
343 : PetscCall(STApply(eps->st,y,z));
344 : PetscCall(VecNorm(z,NORM_2,&norm));
345 : PetscCall(VecScale(z,1.0/norm));
346 : PetscCall(VecCopy(z,y));
347 : PetscCall(VecDestroy(&z));
348 : }
349 : if (eps->balance!=EPS_BALANCE_NONE && eps->D) PetscCall(VecPointwiseDivide(y,y,eps->D));
350 : } else
351 : #endif
352 407 : PetscCall(VecSet(y,0.0));
353 :
354 : /* normalize eigenvectors (when using balancing) */
355 407 : if (eps->balance!=EPS_BALANCE_NONE && eps->D) {
356 : #if !defined(PETSC_USE_COMPLEX)
357 : if (Zi) PetscCall(VecNormalizeComplex(x,y,PETSC_TRUE,NULL));
358 : else
359 : #endif
360 16 : PetscCall(VecNormalize(x,NULL));
361 : }
362 407 : PetscCall(BVSetActiveColumns(V,l,k));
363 407 : PetscFunctionReturn(PETSC_SUCCESS);
364 : }
365 :
366 : /*
367 : EPSBuildBalance_Krylov - uses a Krylov subspace method to compute the
368 : diagonal matrix to be applied for balancing in non-Hermitian problems.
369 : */
370 13 : PetscErrorCode EPSBuildBalance_Krylov(EPS eps)
371 : {
372 13 : Vec z,p,r;
373 13 : PetscInt i,j;
374 13 : PetscReal norma;
375 13 : PetscScalar *pz,*pD;
376 13 : const PetscScalar *pr,*pp;
377 13 : PetscRandom rand;
378 :
379 13 : PetscFunctionBegin;
380 13 : PetscCall(EPSSetWorkVecs(eps,3));
381 13 : PetscCall(BVGetRandomContext(eps->V,&rand));
382 13 : r = eps->work[0];
383 13 : p = eps->work[1];
384 13 : z = eps->work[2];
385 13 : PetscCall(VecSet(eps->D,1.0));
386 :
387 78 : for (j=0;j<eps->balance_its;j++) {
388 :
389 : /* Build a random vector of +-1's */
390 65 : PetscCall(VecSetRandom(z,rand));
391 65 : PetscCall(VecGetArray(z,&pz));
392 5095 : for (i=0;i<eps->nloc;i++) {
393 5030 : if (PetscRealPart(pz[i])<0.5) pz[i]=-1.0;
394 2491 : else pz[i]=1.0;
395 : }
396 65 : PetscCall(VecRestoreArray(z,&pz));
397 :
398 : /* Compute p=DA(D\z) */
399 65 : PetscCall(VecPointwiseDivide(r,z,eps->D));
400 65 : PetscCall(STApply(eps->st,r,p));
401 65 : PetscCall(VecPointwiseMult(p,p,eps->D));
402 65 : if (eps->balance == EPS_BALANCE_TWOSIDE) {
403 40 : if (j==0) {
404 : /* Estimate the matrix inf-norm */
405 8 : PetscCall(VecAbs(p));
406 8 : PetscCall(VecMax(p,NULL,&norma));
407 : }
408 : /* Compute r=D\(A'Dz) */
409 40 : PetscCall(VecPointwiseMult(z,z,eps->D));
410 40 : PetscCall(STApplyHermitianTranspose(eps->st,z,r));
411 40 : PetscCall(VecPointwiseDivide(r,r,eps->D));
412 : }
413 :
414 : /* Adjust values of D */
415 65 : PetscCall(VecGetArrayRead(r,&pr));
416 65 : PetscCall(VecGetArrayRead(p,&pp));
417 65 : PetscCall(VecGetArray(eps->D,&pD));
418 5095 : for (i=0;i<eps->nloc;i++) {
419 5030 : if (eps->balance == EPS_BALANCE_TWOSIDE) {
420 2900 : if (PetscAbsScalar(pp[i])>eps->balance_cutoff*norma && pr[i]!=0.0)
421 2834 : pD[i] *= PetscSqrtReal(PetscAbsScalar(pr[i]/pp[i]));
422 : } else {
423 2130 : if (pp[i]!=0.0) pD[i] /= PetscAbsScalar(pp[i]);
424 : }
425 : }
426 65 : PetscCall(VecRestoreArrayRead(r,&pr));
427 65 : PetscCall(VecRestoreArrayRead(p,&pp));
428 65 : PetscCall(VecRestoreArray(eps->D,&pD));
429 : }
430 13 : PetscFunctionReturn(PETSC_SUCCESS);
431 : }
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