Actual source code: power.c

slepc-main 2024-12-17
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.
  7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
  8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  9: */
 10: /*
 11:    SLEPc eigensolver: "power"

 13:    Method: Power Iteration

 15:    Algorithm:

 17:        This solver implements the power iteration for finding dominant
 18:        eigenpairs. It also includes the following well-known methods:
 19:        - Inverse Iteration: when used in combination with shift-and-invert
 20:          spectral transformation.
 21:        - Rayleigh Quotient Iteration (RQI): also with shift-and-invert plus
 22:          a variable shift.

 24:        It can also be used for nonlinear inverse iteration on the problem
 25:        A(x)*x=lambda*B(x)*x, where A and B are not constant but depend on x.

 27:    References:

 29:        [1] "Single Vector Iteration Methods in SLEPc", SLEPc Technical Report
 30:            STR-2, available at https://slepc.upv.es.
 31: */

 33: #include <slepc/private/epsimpl.h>
 34: #include <slepcblaslapack.h>
 35: /* petsc headers */
 36: #include <petscdm.h>
 37: #include <petscsnes.h>

 39: static PetscErrorCode EPSPowerFormFunction_Update(SNES,Vec,Vec,void*);
 40: static PetscErrorCode EPSSolve_Power(EPS);
 41: static PetscErrorCode EPSSolve_TS_Power(EPS);

 43: typedef struct {
 44:   EPSPowerShiftType shift_type;
 45:   PetscBool         nonlinear;
 46:   PetscBool         update;
 47:   PetscBool         sign_normalization;
 48:   SNES              snes;
 49:   PetscErrorCode    (*formFunctionB)(SNES,Vec,Vec,void*);
 50:   void              *formFunctionBctx;
 51:   PetscErrorCode    (*formFunctionA)(SNES,Vec,Vec,void*);
 52:   void              *formFunctionActx;
 53:   PetscErrorCode    (*formFunctionAB)(SNES,Vec,Vec,Vec,void*);
 54:   PetscErrorCode    (*formNorm)(SNES,Vec,PetscReal*,void*);
 55:   void              *formNormCtx;
 56:   PetscInt          idx;  /* index of the first nonzero entry in the iteration vector */
 57:   PetscMPIInt       p;    /* process id of the owner of idx */
 58:   PetscReal         norm0; /* norm of initial vector */
 59: } EPS_POWER;

 61: static PetscErrorCode SNESMonitor_PowerUpdate(SNES snes,PetscInt its,PetscReal fnorm,void *ctx)
 62: {
 63:   EPS            eps;

 65:   PetscFunctionBegin;
 66:   PetscCall(PetscObjectQuery((PetscObject)snes,"eps",(PetscObject *)&eps));
 67:   PetscCheck(eps,PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_NULL,"No composed EPS");
 68:   /* Call EPS monitor on each SNES iteration */
 69:   PetscCall(EPSMonitor(eps,its,eps->nconv,eps->eigr,eps->eigi,eps->errest,PetscMin(eps->nconv+1,eps->nev)));
 70:   PetscFunctionReturn(PETSC_SUCCESS);
 71: }

 73: static PetscErrorCode EPSSetUp_Power(EPS eps)
 74: {
 75:   EPS_POWER      *power = (EPS_POWER*)eps->data;
 76:   STMatMode      mode;
 77:   Mat            A,B,P;
 78:   Vec            res;
 79:   PetscContainer container;
 80:   PetscErrorCode (*formFunctionA)(SNES,Vec,Vec,void*);
 81:   PetscErrorCode (*formJacobianA)(SNES,Vec,Mat,Mat,void*);
 82:   PetscErrorCode (*formNorm)(SNES,Vec,PetscReal*,void*);
 83:   void           *ctx;

 85:   PetscFunctionBegin;
 86:   EPSCheckNotStructured(eps);
 87:   if (eps->nev==0) eps->nev = 1;
 88:   if (eps->ncv!=PETSC_DETERMINE) {
 89:     PetscCheck(eps->ncv>=eps->nev,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"The value of ncv must be at least nev");
 90:   } else eps->ncv = eps->nev;
 91:   if (eps->mpd!=PETSC_DETERMINE) PetscCall(PetscInfo(eps,"Warning: parameter mpd ignored\n"));
 92:   if (eps->max_it==PETSC_DETERMINE) {
 93:     /* SNES will directly return the solution for us, and we need to do only one iteration */
 94:     if (power->nonlinear && power->update) eps->max_it = 1;
 95:     else eps->max_it = PetscMax(1000*eps->nev,100*eps->n);
 96:   }
 97:   if (!eps->which) PetscCall(EPSSetWhichEigenpairs_Default(eps));
 98:   PetscCheck(eps->which==EPS_LARGEST_MAGNITUDE || eps->which==EPS_TARGET_MAGNITUDE,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver supports only largest magnitude or target magnitude eigenvalues");
 99:   if (power->shift_type != EPS_POWER_SHIFT_CONSTANT) {
100:     PetscCheck(!power->nonlinear,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Variable shifts not allowed in nonlinear problems");
101:     EPSCheckSinvertCayleyCondition(eps,PETSC_TRUE," (with variable shifts)");
102:     PetscCall(STGetMatMode(eps->st,&mode));
103:     PetscCheck(mode!=ST_MATMODE_INPLACE,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"ST matrix mode inplace does not work with variable shifts");
104:   }
105:   EPSCheckUnsupported(eps,EPS_FEATURE_BALANCE | EPS_FEATURE_ARBITRARY | EPS_FEATURE_REGION | EPS_FEATURE_CONVERGENCE | EPS_FEATURE_THRESHOLD);
106:   EPSCheckIgnored(eps,EPS_FEATURE_EXTRACTION);
107:   PetscCall(EPSAllocateSolution(eps,0));
108:   PetscCall(EPS_SetInnerProduct(eps));

110:   if (power->nonlinear) {
111:     PetscCheck(eps->nev==1,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Nonlinear inverse iteration cannot compute more than one eigenvalue");
112:     PetscCall(EPSSetWorkVecs(eps,3));
113:     PetscCheck(!power->update || eps->max_it==1,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"More than one iteration is not allowed for Newton eigensolver (SNES)");

115:     /* Set up SNES solver */
116:     /* If SNES was setup, we need to reset it so that it will be consistent with the current EPS */
117:     if (power->snes) PetscCall(SNESReset(power->snes));
118:     else PetscCall(EPSPowerGetSNES(eps,&power->snes));

120:     /* For nonlinear solver (Newton), we should scale the initial vector back.
121:        The initial vector will be scaled in EPSSetUp. */
122:     if (eps->IS) PetscCall(VecNorm(eps->IS[0],NORM_2,&power->norm0));

124:     PetscCall(EPSGetOperators(eps,&A,&B));

126:     /* form function */
127:     PetscCall(PetscObjectQueryFunction((PetscObject)A,"formFunction",&formFunctionA));
128:     PetscCheck(formFunctionA,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER,"For nonlinear inverse iteration you must compose a callback function 'formFunction' in matrix A");
129:     PetscCall(PetscObjectQuery((PetscObject)A,"formFunctionCtx",(PetscObject*)&container));
130:     if (container) PetscCall(PetscContainerGetPointer(container,&ctx));
131:     else ctx = NULL;
132:     PetscCall(MatCreateVecs(A,&res,NULL));
133:     power->formFunctionA = formFunctionA;
134:     power->formFunctionActx = ctx;
135:     if (power->update) {
136:       PetscCall(SNESSetFunction(power->snes,res,EPSPowerFormFunction_Update,ctx));
137:       PetscCall(PetscObjectQueryFunction((PetscObject)A,"formFunctionAB",&power->formFunctionAB));
138:       PetscCall(SNESMonitorSet(power->snes,SNESMonitor_PowerUpdate,NULL,NULL));
139:     }
140:     else PetscCall(SNESSetFunction(power->snes,res,formFunctionA,ctx));
141:     PetscCall(VecDestroy(&res));

143:     /* form Jacobian */
144:     PetscCall(PetscObjectQueryFunction((PetscObject)A,"formJacobian",&formJacobianA));
145:     PetscCheck(formJacobianA,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER,"For nonlinear inverse iteration you must compose a callback function 'formJacobian' in matrix A");
146:     PetscCall(PetscObjectQuery((PetscObject)A,"formJacobianCtx",(PetscObject*)&container));
147:     if (container) PetscCall(PetscContainerGetPointer(container,&ctx));
148:     else ctx = NULL;
149:     /* This allows users to compute a different preconditioning matrix than A.
150:      * It is useful when A and B are shell matrices.
151:      */
152:     PetscCall(STGetPreconditionerMat(eps->st,&P));
153:     /* If users do not provide a matrix, we simply use A */
154:     PetscCall(SNESSetJacobian(power->snes,A,P? P:A,formJacobianA,ctx));
155:     PetscCall(SNESSetFromOptions(power->snes));
156:     PetscCall(SNESSetUp(power->snes));

158:     ctx = NULL;
159:     formNorm = NULL;
160:     if (B) {
161:       PetscCall(PetscObjectQueryFunction((PetscObject)B,"formFunction",&power->formFunctionB));
162:       PetscCall(PetscObjectQuery((PetscObject)B,"formFunctionCtx",(PetscObject*)&container));
163:       if (power->formFunctionB && container) PetscCall(PetscContainerGetPointer(container,&power->formFunctionBctx));
164:       else power->formFunctionBctx = NULL;

166:       /* form norm */
167:       PetscCall(PetscObjectQueryFunction((PetscObject)B,"formNorm",&formNorm));
168:       if (formNorm) {
169:         PetscCall(PetscObjectQuery((PetscObject)B,"formNormCtx",(PetscObject*)&container));
170:         if (container) PetscCall(PetscContainerGetPointer(container,&ctx));
171:       }
172:     }
173:     power->formNorm = formNorm;
174:     power->formNormCtx = ctx;
175:   } else {
176:     if (eps->twosided) PetscCall(EPSSetWorkVecs(eps,3));
177:     else PetscCall(EPSSetWorkVecs(eps,2));
178:     PetscCall(DSSetType(eps->ds,DSNHEP));
179:     PetscCall(DSAllocate(eps->ds,eps->nev));
180:   }
181:   /* dispatch solve method */
182:   if (eps->twosided) {
183:     PetscCheck(!power->nonlinear,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Nonlinear inverse iteration does not have two-sided variant");
184:     PetscCheck(power->shift_type!=EPS_POWER_SHIFT_WILKINSON,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Two-sided variant does not support Wilkinson shifts");
185:     eps->ops->solve = EPSSolve_TS_Power;
186:   } else eps->ops->solve = EPSSolve_Power;
187:   PetscFunctionReturn(PETSC_SUCCESS);
188: }

190: /*
191:    Find the index of the first nonzero entry of x, and the process that owns it.
192: */
193: static PetscErrorCode FirstNonzeroIdx(Vec x,PetscInt *idx,PetscMPIInt *p)
194: {
195:   PetscInt          i,first,last,N;
196:   PetscLayout       map;
197:   const PetscScalar *xx;

199:   PetscFunctionBegin;
200:   PetscCall(VecGetSize(x,&N));
201:   PetscCall(VecGetOwnershipRange(x,&first,&last));
202:   PetscCall(VecGetArrayRead(x,&xx));
203:   for (i=first;i<last;i++) {
204:     if (PetscAbsScalar(xx[i-first])>10*PETSC_MACHINE_EPSILON) break;
205:   }
206:   PetscCall(VecRestoreArrayRead(x,&xx));
207:   if (i==last) i=N;
208:   PetscCallMPI(MPIU_Allreduce(&i,idx,1,MPIU_INT,MPI_MIN,PetscObjectComm((PetscObject)x)));
209:   PetscCheck(*idx!=N,PetscObjectComm((PetscObject)x),PETSC_ERR_PLIB,"Zero vector found");
210:   PetscCall(VecGetLayout(x,&map));
211:   PetscCall(PetscLayoutFindOwner(map,*idx,p));
212:   PetscFunctionReturn(PETSC_SUCCESS);
213: }

215: /*
216:    Normalize a vector x with respect to a given norm as well as, optionally, the
217:    sign of the first nonzero entry (assumed to be idx in process p).
218: */
219: static PetscErrorCode Normalize(Vec x,PetscReal norm,PetscInt idx,PetscMPIInt p,PetscBool sign_normalization,PetscScalar *sign)
220: {
221:   PetscScalar       alpha=1.0;
222:   PetscInt          first,last;
223:   PetscReal         absv;
224:   const PetscScalar *xx;

226:   PetscFunctionBegin;
227:   if (sign_normalization) {
228:     PetscCall(VecGetOwnershipRange(x,&first,&last));
229:     if (idx>=first && idx<last) {
230:       PetscCall(VecGetArrayRead(x,&xx));
231:       absv = PetscAbsScalar(xx[idx-first]);
232:       if (absv>10*PETSC_MACHINE_EPSILON) alpha = xx[idx-first]/absv;
233:       PetscCall(VecRestoreArrayRead(x,&xx));
234:     }
235:     PetscCallMPI(MPI_Bcast(&alpha,1,MPIU_SCALAR,p,PetscObjectComm((PetscObject)x)));
236:   }
237:   if (sign) *sign = alpha;
238:   alpha *= norm;
239:   PetscCall(VecScale(x,1.0/alpha));
240:   PetscFunctionReturn(PETSC_SUCCESS);
241: }

243: static PetscErrorCode EPSPowerUpdateFunctionB(EPS eps,Vec x,Vec Bx)
244: {
245:   EPS_POWER      *power = (EPS_POWER*)eps->data;
246:   Mat            B;

248:   PetscFunctionBegin;
249:   PetscCall(STResetMatrixState(eps->st));
250:   PetscCall(EPSGetOperators(eps,NULL,&B));
251:   if (B) {
252:     if (power->formFunctionB) PetscCall((*power->formFunctionB)(power->snes,x,Bx,power->formFunctionBctx));
253:     else PetscCall(MatMult(B,x,Bx));
254:   } else PetscCall(VecCopy(x,Bx));
255:   PetscFunctionReturn(PETSC_SUCCESS);
256: }

258: static PetscErrorCode EPSPowerUpdateFunctionA(EPS eps,Vec x,Vec Ax)
259: {
260:   EPS_POWER      *power = (EPS_POWER*)eps->data;
261:   Mat            A;

263:   PetscFunctionBegin;
264:   PetscCall(STResetMatrixState(eps->st));
265:   PetscCall(EPSGetOperators(eps,&A,NULL));
266:   PetscCheck(A,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_NULL,"Matrix A is required for an eigenvalue problem");
267:   if (power->formFunctionA) PetscCall((*power->formFunctionA)(power->snes,x,Ax,power->formFunctionActx));
268:   else PetscCall(MatMult(A,x,Ax));
269:   PetscFunctionReturn(PETSC_SUCCESS);
270: }

272: static PetscErrorCode EPSPowerFormFunction_Update(SNES snes,Vec x,Vec y,void *ctx)
273: {
274:   EPS            eps;
275:   PetscReal      bx;
276:   Vec            Bx;
277:   PetscScalar    sign;
278:   EPS_POWER      *power;

280:   PetscFunctionBegin;
281:   PetscCall(PetscObjectQuery((PetscObject)snes,"eps",(PetscObject *)&eps));
282:   PetscCheck(eps,PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_NULL,"No composed EPS");
283:   PetscCall(STResetMatrixState(eps->st));
284:   power = (EPS_POWER*)eps->data;
285:   Bx = eps->work[2];
286:   if (power->formFunctionAB) PetscCall((*power->formFunctionAB)(snes,x,y,Bx,ctx));
287:   else {
288:     PetscCall(EPSPowerUpdateFunctionA(eps,x,y));
289:     PetscCall(EPSPowerUpdateFunctionB(eps,x,Bx));
290:   }
291:   if (power->formNorm) PetscCall((*power->formNorm)(snes,Bx,&bx,power->formNormCtx));
292:   else PetscCall(VecNorm(Bx,NORM_2,&bx));
293:   PetscCall(Normalize(Bx,bx,power->idx,power->p,power->sign_normalization,&sign));
294:   PetscCall(VecAXPY(y,-1.0,Bx));
295:   /* Keep tracking eigenvalue update. It would be useful when we want to monitor solver progress via snes monitor. */
296:   eps->eigr[(eps->nconv < eps->nev)? eps->nconv:(eps->nconv-1)] = 1.0/(bx*sign);
297:   PetscFunctionReturn(PETSC_SUCCESS);
298: }

300: /*
301:    Use SNES to compute y = A^{-1}*B*x for the nonlinear problem
302: */
303: static PetscErrorCode EPSPowerApply_SNES(EPS eps,Vec x,Vec y)
304: {
305:   EPS_POWER      *power = (EPS_POWER*)eps->data;
306:   Vec            Bx;

308:   PetscFunctionBegin;
309:   PetscCall(VecCopy(x,y));
310:   if (power->update) PetscCall(SNESSolve(power->snes,NULL,y));
311:   else {
312:     Bx = eps->work[2];
313:     PetscCall(SNESSolve(power->snes,Bx,y));
314:   }
315:   PetscFunctionReturn(PETSC_SUCCESS);
316: }

318: /*
319:    Use nonlinear inverse power to compute an initial guess
320: */
321: static PetscErrorCode EPSPowerComputeInitialGuess_Update(EPS eps)
322: {
323:   EPS            powereps;
324:   Mat            A,B,P;
325:   Vec            v1,v2;
326:   SNES           snes;
327:   DM             dm,newdm;
328:   PetscBool      sign_normalization;

330:   PetscFunctionBegin;
331:   PetscCall(EPSCreate(PetscObjectComm((PetscObject)eps),&powereps));
332:   PetscCall(EPSGetOperators(eps,&A,&B));
333:   PetscCall(EPSSetType(powereps,EPSPOWER));
334:   PetscCall(EPSSetOperators(powereps,A,B));
335:   PetscCall(EPSSetTolerances(powereps,1e-6,4));
336:   PetscCall(EPSSetOptionsPrefix(powereps,((PetscObject)eps)->prefix));
337:   PetscCall(EPSAppendOptionsPrefix(powereps,"init_"));
338:   PetscCall(EPSSetProblemType(powereps,EPS_GNHEP));
339:   PetscCall(EPSSetWhichEigenpairs(powereps,EPS_TARGET_MAGNITUDE));
340:   PetscCall(EPSPowerSetNonlinear(powereps,PETSC_TRUE));
341:   PetscCall(STGetPreconditionerMat(eps->st,&P));
342:   /* attach dm to initial solve */
343:   PetscCall(EPSPowerGetSNES(eps,&snes));
344:   PetscCall(SNESGetDM(snes,&dm));
345:   /* use  dmshell to temporarily store snes context */
346:   PetscCall(DMCreate(PetscObjectComm((PetscObject)eps),&newdm));
347:   PetscCall(DMSetType(newdm,DMSHELL));
348:   PetscCall(DMSetUp(newdm));
349:   PetscCall(DMCopyDMSNES(dm,newdm));
350:   PetscCall(EPSPowerGetSNES(powereps,&snes));
351:   PetscCall(SNESSetDM(snes,dm));
352:   PetscCall(EPSPowerGetSignNormalization(eps,&sign_normalization));
353:   PetscCall(EPSPowerSetSignNormalization(powereps,sign_normalization));
354:   PetscCall(EPSSetFromOptions(powereps));
355:   if (P) PetscCall(STSetPreconditionerMat(powereps->st,P));
356:   PetscCall(EPSSolve(powereps));
357:   PetscCall(BVGetColumn(eps->V,0,&v2));
358:   PetscCall(BVGetColumn(powereps->V,0,&v1));
359:   PetscCall(VecCopy(v1,v2));
360:   PetscCall(BVRestoreColumn(powereps->V,0,&v1));
361:   PetscCall(BVRestoreColumn(eps->V,0,&v2));
362:   PetscCall(EPSDestroy(&powereps));
363:   /* restore context back to the old nonlinear solver */
364:   PetscCall(DMCopyDMSNES(newdm,dm));
365:   PetscCall(DMDestroy(&newdm));
366:   PetscFunctionReturn(PETSC_SUCCESS);
367: }

369: static PetscErrorCode EPSSolve_Power(EPS eps)
370: {
371:   EPS_POWER           *power = (EPS_POWER*)eps->data;
372:   PetscInt            k,ld;
373:   Vec                 v,y,e,Bx;
374:   Mat                 A;
375:   KSP                 ksp;
376:   PetscReal           relerr,norm,norm1,rt1,rt2,cs1;
377:   PetscScalar         theta,rho,delta,sigma,alpha2,beta1,sn1,*T,sign;
378:   PetscBool           breakdown;
379:   KSPConvergedReason  reason;
380:   SNESConvergedReason snesreason;

382:   PetscFunctionBegin;
383:   e = eps->work[0];
384:   y = eps->work[1];
385:   if (power->nonlinear) Bx = eps->work[2];
386:   else Bx = NULL;

388:   if (power->shift_type != EPS_POWER_SHIFT_CONSTANT) PetscCall(STGetKSP(eps->st,&ksp));
389:   if (power->nonlinear) {
390:     PetscCall(PetscObjectCompose((PetscObject)power->snes,"eps",(PetscObject)eps));
391:     /* Compute an initial guess only when users do not provide one */
392:     if (power->update && !eps->nini) PetscCall(EPSPowerComputeInitialGuess_Update(eps));
393:   } else PetscCall(DSGetLeadingDimension(eps->ds,&ld));
394:   if (!power->update) PetscCall(EPSGetStartVector(eps,0,NULL));
395:   if (power->nonlinear) {
396:     PetscCall(BVGetColumn(eps->V,0,&v));
397:     if (eps->nini) {
398:       /* We scale the initial vector back if the initial vector was provided by users */
399:       PetscCall(VecScale(v,power->norm0));
400:     }
401:     /* Do a couple things:
402:      * 1) Determine the first non-zero index for Bx and the proc that owns it. This will be
403:      *    used if performing normalization by the sign of the first nonzero element of Bx.
404:      * 2) Scale Bx by its norm. For non-update power iterations, Bx (in code terms) is used
405:      *    as the RHS argument to SNESSolve. And recall that the formula for generalized
406:      *    inverse power iterations in this case is: (Ax)_n = (Bx)_{n-1}/|(Bx)_{n-1}| (in
407:      *    math terms)
408:      */
409:     PetscCall(EPSPowerUpdateFunctionB(eps,v,Bx));
410:     PetscCall(BVRestoreColumn(eps->V,0,&v));
411:     if (power->formNorm) PetscCall((*power->formNorm)(power->snes,Bx,&norm,power->formNormCtx));
412:     else PetscCall(VecNorm(Bx,NORM_2,&norm));
413:     PetscCall(FirstNonzeroIdx(Bx,&power->idx,&power->p));
414:     PetscCall(Normalize(Bx,norm,power->idx,power->p,power->sign_normalization,NULL));
415:   }

417:   PetscCall(STGetShift(eps->st,&sigma));    /* original shift */
418:   rho = sigma;

420:   while (eps->reason == EPS_CONVERGED_ITERATING) {
421:     eps->its++;
422:     k = eps->nconv;

424:     /* y = OP v */
425:     PetscCall(BVGetColumn(eps->V,k,&v));
426:     if (power->nonlinear) PetscCall(EPSPowerApply_SNES(eps,v,y));
427:     else PetscCall(STApply(eps->st,v,y));
428:     PetscCall(BVRestoreColumn(eps->V,k,&v));

430:     /* purge previously converged eigenvectors */
431:     if (PetscUnlikely(power->nonlinear)) {
432:       /* We do not need to call this for Newton eigensolver since eigenvalue is
433:        * updated in function evaluations.
434:        */
435:       if (!power->update) {
436:         PetscCall(EPSPowerUpdateFunctionB(eps,y,Bx));
437:         if (power->formNorm) PetscCall((*power->formNorm)(power->snes,Bx,&norm,power->formNormCtx));
438:         else PetscCall(VecNorm(Bx,NORM_2,&norm));
439:         PetscCall(Normalize(Bx,norm,power->idx,power->p,power->sign_normalization,&sign));
440:       }
441:     } else {
442:       PetscCall(DSGetArray(eps->ds,DS_MAT_A,&T));
443:       PetscCall(BVSetActiveColumns(eps->V,0,k));
444:       PetscCall(BVOrthogonalizeVec(eps->V,y,T+k*ld,&norm,NULL));
445:     }

447:     /* theta = (v,y)_B */
448:     PetscCall(BVSetActiveColumns(eps->V,k,k+1));
449:     PetscCall(BVDotVec(eps->V,y,&theta));
450:     if (!power->nonlinear) {
451:       T[k+k*ld] = theta;
452:       PetscCall(DSRestoreArray(eps->ds,DS_MAT_A,&T));
453:     }

455:     /* Eigenvalue is already stored in function evaluations.
456:      * Assign eigenvalue to theta to make the rest of the code consistent
457:      */
458:     if (power->update) theta = eps->eigr[eps->nconv];
459:     else if (power->nonlinear) theta = 1.0/(norm*sign); /* Eigenvalue: 1/|Bx| */

461:     if (power->shift_type == EPS_POWER_SHIFT_CONSTANT) { /* direct & inverse iteration */

463:       /* approximate eigenvalue is the Rayleigh quotient */
464:       eps->eigr[eps->nconv] = theta;

466:       /**
467:        * If the Newton method (update, SNES) is used, we do not compute "relerr"
468:        * since SNES determines the convergence.
469:        */
470:       if (PetscUnlikely(power->update)) relerr = 0.;
471:       else {
472:         /* compute relative error as ||y-theta v||_2/|theta| */
473:         PetscCall(VecCopy(y,e));
474:         PetscCall(BVGetColumn(eps->V,k,&v));
475:         PetscCall(VecAXPY(e,power->nonlinear?-1.0:-theta,v));
476:         PetscCall(BVRestoreColumn(eps->V,k,&v));
477:         PetscCall(VecNorm(e,NORM_2,&relerr));
478:         if (PetscUnlikely(power->nonlinear)) relerr *= PetscAbsScalar(theta);
479:         else relerr /= PetscAbsScalar(theta);
480:       }

482:     } else {  /* RQI */

484:       /* delta = ||y||_B */
485:       delta = norm;

487:       /* compute relative error */
488:       if (rho == 0.0) relerr = PETSC_MAX_REAL;
489:       else relerr = 1.0 / (norm*PetscAbsScalar(rho));

491:       /* approximate eigenvalue is the shift */
492:       eps->eigr[eps->nconv] = rho;

494:       /* compute new shift */
495:       if (relerr<eps->tol) {
496:         rho = sigma;  /* if converged, restore original shift */
497:         PetscCall(STSetShift(eps->st,rho));
498:       } else {
499:         rho = rho + PetscConj(theta)/(delta*delta);  /* Rayleigh quotient R(v) */
500:         if (power->shift_type == EPS_POWER_SHIFT_WILKINSON) {
501:           /* beta1 is the norm of the residual associated with R(v) */
502:           PetscCall(BVGetColumn(eps->V,k,&v));
503:           PetscCall(VecAXPY(v,-PetscConj(theta)/(delta*delta),y));
504:           PetscCall(BVRestoreColumn(eps->V,k,&v));
505:           PetscCall(BVScaleColumn(eps->V,k,1.0/delta));
506:           PetscCall(BVNormColumn(eps->V,k,NORM_2,&norm1));
507:           beta1 = norm1;

509:           /* alpha2 = (e'*A*e)/(beta1*beta1), where e is the residual */
510:           PetscCall(STGetMatrix(eps->st,0,&A));
511:           PetscCall(BVGetColumn(eps->V,k,&v));
512:           PetscCall(MatMult(A,v,e));
513:           PetscCall(VecDot(v,e,&alpha2));
514:           PetscCall(BVRestoreColumn(eps->V,k,&v));
515:           alpha2 = alpha2 / (beta1 * beta1);

517:           /* choose the eigenvalue of [rho beta1; beta1 alpha2] closest to rho */
518:           PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
519:           PetscCallBLAS("LAPACKlaev2",LAPACKlaev2_(&rho,&beta1,&alpha2,&rt1,&rt2,&cs1,&sn1));
520:           PetscCall(PetscFPTrapPop());
521:           if (PetscAbsScalar(rt1-rho) < PetscAbsScalar(rt2-rho)) rho = rt1;
522:           else rho = rt2;
523:         }
524:         /* update operator according to new shift */
525:         PetscCall(KSPSetErrorIfNotConverged(ksp,PETSC_FALSE));
526:         PetscCall(STSetShift(eps->st,rho));
527:         PetscCall(KSPGetConvergedReason(ksp,&reason));
528:         if (reason) {
529:           PetscCall(PetscInfo(eps,"Factorization failed, repeat with a perturbed shift\n"));
530:           rho *= 1+10*PETSC_MACHINE_EPSILON;
531:           PetscCall(STSetShift(eps->st,rho));
532:           PetscCall(KSPGetConvergedReason(ksp,&reason));
533:           PetscCheck(!reason,PetscObjectComm((PetscObject)ksp),PETSC_ERR_CONV_FAILED,"Second factorization failed");
534:         }
535:         PetscCall(KSPSetErrorIfNotConverged(ksp,PETSC_TRUE));
536:       }
537:     }
538:     eps->errest[eps->nconv] = relerr;

540:     /* normalize */
541:     if (!power->nonlinear) PetscCall(Normalize(y,norm,power->idx,power->p,power->sign_normalization,NULL));
542:     PetscCall(BVInsertVec(eps->V,k,y));

544:     if (PetscUnlikely(power->update)) {
545:       PetscCall(SNESGetConvergedReason(power->snes,&snesreason));
546:       /* For Newton eigensolver, we are ready to return once SNES converged. */
547:       if (snesreason>0) eps->nconv = 1;
548:     } else if (PetscUnlikely(relerr<eps->tol)) {   /* accept eigenpair */
549:       eps->nconv = eps->nconv + 1;
550:       if (eps->nconv<eps->nev) {
551:         PetscCall(EPSGetStartVector(eps,eps->nconv,&breakdown));
552:         if (breakdown) {
553:           eps->reason = EPS_DIVERGED_BREAKDOWN;
554:           PetscCall(PetscInfo(eps,"Unable to generate more start vectors\n"));
555:           break;
556:         }
557:       }
558:     }
559:     /* For Newton eigensolver, monitor will be called from SNES monitor */
560:     if (!power->update) PetscCall(EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,PetscMin(eps->nconv+1,eps->nev)));
561:     PetscCall((*eps->stopping)(eps,eps->its,eps->max_it,eps->nconv,eps->nev,&eps->reason,eps->stoppingctx));

563:     /**
564:      * When a customized stopping test is used, and reason can be set to be converged (EPS_CONVERGED_USER).
565:      * In this case, we need to increase eps->nconv to "1" so users can retrieve the solution.
566:      */
567:     if (PetscUnlikely(power->nonlinear && eps->reason>0)) eps->nconv = 1;
568:   }

570:   if (power->nonlinear) PetscCall(PetscObjectCompose((PetscObject)power->snes,"eps",NULL));
571:   else {
572:     PetscCall(DSSetDimensions(eps->ds,eps->nconv,0,0));
573:     PetscCall(DSSetState(eps->ds,DS_STATE_RAW));
574:   }
575:   PetscFunctionReturn(PETSC_SUCCESS);
576: }

578: static PetscErrorCode EPSSolve_TS_Power(EPS eps)
579: {
580:   EPS_POWER          *power = (EPS_POWER*)eps->data;
581:   PetscInt           k,ld;
582:   Vec                v,w,y,e,z;
583:   KSP                ksp;
584:   PetscReal          relerr=1.0,relerrl,delta;
585:   PetscScalar        theta,rho,alpha,sigma;
586:   PetscBool          breakdown,breakdownl;
587:   KSPConvergedReason reason;

589:   PetscFunctionBegin;
590:   e = eps->work[0];
591:   v = eps->work[1];
592:   w = eps->work[2];

594:   if (power->shift_type != EPS_POWER_SHIFT_CONSTANT) PetscCall(STGetKSP(eps->st,&ksp));
595:   PetscCall(DSGetLeadingDimension(eps->ds,&ld));
596:   PetscCall(EPSGetStartVector(eps,0,NULL));
597:   PetscCall(EPSGetLeftStartVector(eps,0,NULL));
598:   PetscCall(BVBiorthonormalizeColumn(eps->V,eps->W,0,NULL));
599:   PetscCall(BVCopyVec(eps->V,0,v));
600:   PetscCall(BVCopyVec(eps->W,0,w));
601:   PetscCall(STGetShift(eps->st,&sigma));    /* original shift */
602:   rho = sigma;

604:   while (eps->reason == EPS_CONVERGED_ITERATING) {
605:     eps->its++;
606:     k = eps->nconv;

608:     /* y = OP v, z = OP' w */
609:     PetscCall(BVGetColumn(eps->V,k,&y));
610:     PetscCall(STApply(eps->st,v,y));
611:     PetscCall(BVRestoreColumn(eps->V,k,&y));
612:     PetscCall(BVGetColumn(eps->W,k,&z));
613:     PetscCall(STApplyHermitianTranspose(eps->st,w,z));
614:     PetscCall(BVRestoreColumn(eps->W,k,&z));

616:     /* purge previously converged eigenvectors */
617:     PetscCall(BVBiorthogonalizeColumn(eps->V,eps->W,k));

619:     /* theta = (w,y)_B */
620:     PetscCall(BVSetActiveColumns(eps->V,k,k+1));
621:     PetscCall(BVDotVec(eps->V,w,&theta));
622:     theta = PetscConj(theta);

624:     if (power->shift_type == EPS_POWER_SHIFT_CONSTANT) { /* direct & inverse iteration */

626:       /* approximate eigenvalue is the Rayleigh quotient */
627:       eps->eigr[eps->nconv] = theta;

629:       /* compute relative errors as ||y-theta v||_2/|theta| and ||z-conj(theta) w||_2/|theta|*/
630:       PetscCall(BVCopyVec(eps->V,k,e));
631:       PetscCall(VecAXPY(e,-theta,v));
632:       PetscCall(VecNorm(e,NORM_2,&relerr));
633:       PetscCall(BVCopyVec(eps->W,k,e));
634:       PetscCall(VecAXPY(e,-PetscConj(theta),w));
635:       PetscCall(VecNorm(e,NORM_2,&relerrl));
636:       relerr = PetscMax(relerr,relerrl)/PetscAbsScalar(theta);
637:     }

639:     /* normalize */
640:     PetscCall(BVSetActiveColumns(eps->V,k,k+1));
641:     PetscCall(BVGetColumn(eps->W,k,&z));
642:     PetscCall(BVDotVec(eps->V,z,&alpha));
643:     PetscCall(BVRestoreColumn(eps->W,k,&z));
644:     delta = PetscSqrtReal(PetscAbsScalar(alpha));
645:     PetscCheck(delta!=0.0,PetscObjectComm((PetscObject)eps),PETSC_ERR_CONV_FAILED,"Breakdown in two-sided Power/RQI");
646:     PetscCall(BVScaleColumn(eps->V,k,1.0/PetscConj(alpha/delta)));
647:     PetscCall(BVScaleColumn(eps->W,k,1.0/delta));
648:     PetscCall(BVCopyVec(eps->V,k,v));
649:     PetscCall(BVCopyVec(eps->W,k,w));

651:     if (power->shift_type == EPS_POWER_SHIFT_RAYLEIGH) { /* RQI */

653:       /* compute relative error */
654:       if (rho == 0.0) relerr = PETSC_MAX_REAL;
655:       else relerr = 1.0 / PetscAbsScalar(delta*rho);

657:       /* approximate eigenvalue is the shift */
658:       eps->eigr[eps->nconv] = rho;

660:       /* compute new shift */
661:       if (relerr<eps->tol) {
662:         rho = sigma;  /* if converged, restore original shift */
663:         PetscCall(STSetShift(eps->st,rho));
664:       } else {
665:         rho = rho + PetscConj(theta)/(delta*delta);  /* Rayleigh quotient R(v) */
666:         /* update operator according to new shift */
667:         PetscCall(KSPSetErrorIfNotConverged(ksp,PETSC_FALSE));
668:         PetscCall(STSetShift(eps->st,rho));
669:         PetscCall(KSPGetConvergedReason(ksp,&reason));
670:         if (reason) {
671:           PetscCall(PetscInfo(eps,"Factorization failed, repeat with a perturbed shift\n"));
672:           rho *= 1+10*PETSC_MACHINE_EPSILON;
673:           PetscCall(STSetShift(eps->st,rho));
674:           PetscCall(KSPGetConvergedReason(ksp,&reason));
675:           PetscCheck(!reason,PetscObjectComm((PetscObject)ksp),PETSC_ERR_CONV_FAILED,"Second factorization failed");
676:         }
677:         PetscCall(KSPSetErrorIfNotConverged(ksp,PETSC_TRUE));
678:       }
679:     }
680:     eps->errest[eps->nconv] = relerr;

682:     /* if relerr<tol, accept eigenpair */
683:     if (relerr<eps->tol) {
684:       eps->nconv = eps->nconv + 1;
685:       if (eps->nconv<eps->nev) {
686:         PetscCall(EPSGetStartVector(eps,eps->nconv,&breakdown));
687:         PetscCall(EPSGetLeftStartVector(eps,eps->nconv,&breakdownl));
688:         if (breakdown || breakdownl) {
689:           eps->reason = EPS_DIVERGED_BREAKDOWN;
690:           PetscCall(PetscInfo(eps,"Unable to generate more start vectors\n"));
691:           break;
692:         }
693:         PetscCall(BVBiorthonormalizeColumn(eps->V,eps->W,eps->nconv,NULL));
694:       }
695:     }
696:     PetscCall(EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,PetscMin(eps->nconv+1,eps->nev)));
697:     PetscCall((*eps->stopping)(eps,eps->its,eps->max_it,eps->nconv,eps->nev,&eps->reason,eps->stoppingctx));
698:   }

700:   PetscCall(DSSetDimensions(eps->ds,eps->nconv,0,0));
701:   PetscCall(DSSetState(eps->ds,DS_STATE_RAW));
702:   PetscFunctionReturn(PETSC_SUCCESS);
703: }

705: static PetscErrorCode EPSStopping_Power(EPS eps,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,EPSConvergedReason *reason,void *ctx)
706: {
707:   EPS_POWER      *power = (EPS_POWER*)eps->data;
708:   SNESConvergedReason snesreason;

710:   PetscFunctionBegin;
711:   if (PetscUnlikely(power->update)) {
712:     PetscCall(SNESGetConvergedReason(power->snes,&snesreason));
713:     if (snesreason < 0) {
714:       *reason = EPS_DIVERGED_BREAKDOWN;
715:       PetscFunctionReturn(PETSC_SUCCESS);
716:     }
717:   }
718:   PetscCall(EPSStoppingBasic(eps,its,max_it,nconv,nev,reason,ctx));
719:   PetscFunctionReturn(PETSC_SUCCESS);
720: }

722: static PetscErrorCode EPSBackTransform_Power(EPS eps)
723: {
724:   EPS_POWER      *power = (EPS_POWER*)eps->data;

726:   PetscFunctionBegin;
727:   if (power->nonlinear) eps->eigr[0] = 1.0/eps->eigr[0];
728:   else if (power->shift_type == EPS_POWER_SHIFT_CONSTANT) PetscCall(EPSBackTransform_Default(eps));
729:   PetscFunctionReturn(PETSC_SUCCESS);
730: }

732: static PetscErrorCode EPSSetFromOptions_Power(EPS eps,PetscOptionItems *PetscOptionsObject)
733: {
734:   EPS_POWER         *power = (EPS_POWER*)eps->data;
735:   PetscBool         flg,val;
736:   EPSPowerShiftType shift;

738:   PetscFunctionBegin;
739:   PetscOptionsHeadBegin(PetscOptionsObject,"EPS Power Options");

741:     PetscCall(PetscOptionsEnum("-eps_power_shift_type","Shift type","EPSPowerSetShiftType",EPSPowerShiftTypes,(PetscEnum)power->shift_type,(PetscEnum*)&shift,&flg));
742:     if (flg) PetscCall(EPSPowerSetShiftType(eps,shift));

744:     PetscCall(PetscOptionsBool("-eps_power_nonlinear","Use nonlinear inverse iteration","EPSPowerSetNonlinear",power->nonlinear,&val,&flg));
745:     if (flg) PetscCall(EPSPowerSetNonlinear(eps,val));

747:     PetscCall(PetscOptionsBool("-eps_power_update","Update residual monolithically","EPSPowerSetUpdate",power->update,&val,&flg));
748:     if (flg) PetscCall(EPSPowerSetUpdate(eps,val));

750:     PetscCall(PetscOptionsBool("-eps_power_sign_normalization","Normalize Bx with sign of first nonzero entry","EPSPowerSetSignNormalization",power->sign_normalization,&power->sign_normalization,&flg));

752:   PetscOptionsHeadEnd();
753:   PetscFunctionReturn(PETSC_SUCCESS);
754: }

756: static PetscErrorCode EPSPowerSetShiftType_Power(EPS eps,EPSPowerShiftType shift)
757: {
758:   EPS_POWER *power = (EPS_POWER*)eps->data;

760:   PetscFunctionBegin;
761:   switch (shift) {
762:     case EPS_POWER_SHIFT_CONSTANT:
763:     case EPS_POWER_SHIFT_RAYLEIGH:
764:     case EPS_POWER_SHIFT_WILKINSON:
765:       if (power->shift_type != shift) {
766:         power->shift_type = shift;
767:         eps->state = EPS_STATE_INITIAL;
768:       }
769:       break;
770:     default:
771:       SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Invalid shift type");
772:   }
773:   PetscFunctionReturn(PETSC_SUCCESS);
774: }

776: /*@
777:    EPSPowerSetShiftType - Sets the type of shifts used during the power
778:    iteration. This can be used to emulate the Rayleigh Quotient Iteration
779:    (RQI) method.

781:    Logically Collective

783:    Input Parameters:
784: +  eps - the eigenproblem solver context
785: -  shift - the type of shift

787:    Options Database Key:
788: .  -eps_power_shift_type - Sets the shift type (either 'constant' or
789:                            'rayleigh' or 'wilkinson')

791:    Notes:
792:    By default, shifts are constant (EPS_POWER_SHIFT_CONSTANT) and the iteration
793:    is the simple power method (or inverse iteration if a shift-and-invert
794:    transformation is being used).

796:    A variable shift can be specified (EPS_POWER_SHIFT_RAYLEIGH or
797:    EPS_POWER_SHIFT_WILKINSON). In this case, the iteration behaves rather like
798:    a cubic converging method such as RQI.

800:    Level: advanced

802: .seealso: EPSPowerGetShiftType(), STSetShift(), EPSPowerShiftType
803: @*/
804: PetscErrorCode EPSPowerSetShiftType(EPS eps,EPSPowerShiftType shift)
805: {
806:   PetscFunctionBegin;
809:   PetscTryMethod(eps,"EPSPowerSetShiftType_C",(EPS,EPSPowerShiftType),(eps,shift));
810:   PetscFunctionReturn(PETSC_SUCCESS);
811: }

813: static PetscErrorCode EPSPowerGetShiftType_Power(EPS eps,EPSPowerShiftType *shift)
814: {
815:   EPS_POWER *power = (EPS_POWER*)eps->data;

817:   PetscFunctionBegin;
818:   *shift = power->shift_type;
819:   PetscFunctionReturn(PETSC_SUCCESS);
820: }

822: /*@
823:    EPSPowerGetShiftType - Gets the type of shifts used during the power
824:    iteration.

826:    Not Collective

828:    Input Parameter:
829: .  eps - the eigenproblem solver context

831:    Output Parameter:
832: .  shift - the type of shift

834:    Level: advanced

836: .seealso: EPSPowerSetShiftType(), EPSPowerShiftType
837: @*/
838: PetscErrorCode EPSPowerGetShiftType(EPS eps,EPSPowerShiftType *shift)
839: {
840:   PetscFunctionBegin;
842:   PetscAssertPointer(shift,2);
843:   PetscUseMethod(eps,"EPSPowerGetShiftType_C",(EPS,EPSPowerShiftType*),(eps,shift));
844:   PetscFunctionReturn(PETSC_SUCCESS);
845: }

847: static PetscErrorCode EPSPowerSetNonlinear_Power(EPS eps,PetscBool nonlinear)
848: {
849:   EPS_POWER *power = (EPS_POWER*)eps->data;

851:   PetscFunctionBegin;
852:   if (power->nonlinear != nonlinear) {
853:     power->nonlinear = nonlinear;
854:     eps->useds = PetscNot(nonlinear);
855:     eps->ops->setupsort = nonlinear? NULL: EPSSetUpSort_Default;
856:     eps->state = EPS_STATE_INITIAL;
857:   }
858:   PetscFunctionReturn(PETSC_SUCCESS);
859: }

861: /*@
862:    EPSPowerSetNonlinear - Sets a flag to indicate that the problem is nonlinear.

864:    Logically Collective

866:    Input Parameters:
867: +  eps - the eigenproblem solver context
868: -  nonlinear - whether the problem is nonlinear or not

870:    Options Database Key:
871: .  -eps_power_nonlinear - Sets the nonlinear flag

873:    Notes:
874:    If this flag is set, the solver assumes that the problem is nonlinear,
875:    that is, the operators that define the eigenproblem are not constant
876:    matrices, but depend on the eigenvector, A(x)*x=lambda*B(x)*x. This is
877:    different from the case of nonlinearity with respect to the eigenvalue
878:    (use the NEP solver class for this kind of problems).

880:    The way in which nonlinear operators are specified is very similar to
881:    the case of PETSc's SNES solver. The difference is that the callback
882:    functions are provided via composed functions "formFunction" and
883:    "formJacobian" in each of the matrix objects passed as arguments of
884:    EPSSetOperators(). The application context required for these functions
885:    can be attached via a composed PetscContainer.

887:    Level: advanced

889: .seealso: EPSPowerGetNonlinear(), EPSSetOperators()
890: @*/
891: PetscErrorCode EPSPowerSetNonlinear(EPS eps,PetscBool nonlinear)
892: {
893:   PetscFunctionBegin;
896:   PetscTryMethod(eps,"EPSPowerSetNonlinear_C",(EPS,PetscBool),(eps,nonlinear));
897:   PetscFunctionReturn(PETSC_SUCCESS);
898: }

900: static PetscErrorCode EPSPowerGetNonlinear_Power(EPS eps,PetscBool *nonlinear)
901: {
902:   EPS_POWER *power = (EPS_POWER*)eps->data;

904:   PetscFunctionBegin;
905:   *nonlinear = power->nonlinear;
906:   PetscFunctionReturn(PETSC_SUCCESS);
907: }

909: /*@
910:    EPSPowerGetNonlinear - Returns a flag indicating if the problem is nonlinear.

912:    Not Collective

914:    Input Parameter:
915: .  eps - the eigenproblem solver context

917:    Output Parameter:
918: .  nonlinear - the nonlinear flag

920:    Level: advanced

922: .seealso: EPSPowerSetUpdate(), EPSPowerSetNonlinear()
923: @*/
924: PetscErrorCode EPSPowerGetNonlinear(EPS eps,PetscBool *nonlinear)
925: {
926:   PetscFunctionBegin;
928:   PetscAssertPointer(nonlinear,2);
929:   PetscUseMethod(eps,"EPSPowerGetNonlinear_C",(EPS,PetscBool*),(eps,nonlinear));
930:   PetscFunctionReturn(PETSC_SUCCESS);
931: }

933: static PetscErrorCode EPSPowerSetUpdate_Power(EPS eps,PetscBool update)
934: {
935:   EPS_POWER *power = (EPS_POWER*)eps->data;

937:   PetscFunctionBegin;
938:   PetscCheck(power->nonlinear,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_INCOMP,"This option does not make sense for linear problems");
939:   power->update = update;
940:   eps->state = EPS_STATE_INITIAL;
941:   PetscFunctionReturn(PETSC_SUCCESS);
942: }

944: /*@
945:    EPSPowerSetUpdate - Sets a flag to indicate that the residual is updated monolithically
946:    for nonlinear problems. This potentially has a better convergence.

948:    Logically Collective

950:    Input Parameters:
951: +  eps - the eigenproblem solver context
952: -  update - whether the residual is updated monolithically or not

954:    Options Database Key:
955: .  -eps_power_update - Sets the update flag

957:    Level: advanced

959: .seealso: EPSPowerGetUpdate(), EPSPowerGetNonlinear(), EPSSetOperators()
960: @*/
961: PetscErrorCode EPSPowerSetUpdate(EPS eps,PetscBool update)
962: {
963:   PetscFunctionBegin;
966:   PetscTryMethod(eps,"EPSPowerSetUpdate_C",(EPS,PetscBool),(eps,update));
967:   PetscFunctionReturn(PETSC_SUCCESS);
968: }

970: static PetscErrorCode EPSPowerGetUpdate_Power(EPS eps,PetscBool *update)
971: {
972:   EPS_POWER *power = (EPS_POWER*)eps->data;

974:   PetscFunctionBegin;
975:   *update = power->update;
976:   PetscFunctionReturn(PETSC_SUCCESS);
977: }

979: /*@
980:    EPSPowerGetUpdate - Returns a flag indicating if the residual is updated monolithically
981:    for nonlinear problems.

983:    Not Collective

985:    Input Parameter:
986: .  eps - the eigenproblem solver context

988:    Output Parameter:
989: .  update - the update flag

991:    Level: advanced

993: .seealso: EPSPowerSetUpdate(), EPSPowerSetNonlinear()
994: @*/
995: PetscErrorCode EPSPowerGetUpdate(EPS eps,PetscBool *update)
996: {
997:   PetscFunctionBegin;
999:   PetscAssertPointer(update,2);
1000:   PetscUseMethod(eps,"EPSPowerGetUpdate_C",(EPS,PetscBool*),(eps,update));
1001:   PetscFunctionReturn(PETSC_SUCCESS);
1002: }

1004: static PetscErrorCode EPSPowerSetSignNormalization_Power(EPS eps,PetscBool sign_normalization)
1005: {
1006:   EPS_POWER *power = (EPS_POWER*)eps->data;

1008:   PetscFunctionBegin;
1009:   power->sign_normalization = sign_normalization;
1010:   PetscFunctionReturn(PETSC_SUCCESS);
1011: }

1013: /*@
1014:    EPSPowerSetSignNormalization - Sets a flag to indicate whether the Bx vector
1015:    should be normalized by the sign of the first non-zero element in the vector.
1016:    E.g., if this is true, the post-normalization value of the first non-zero element
1017:    in the vector is guaranteed to be positive.

1019:    Logically Collective

1021:    Input Parameters:
1022: +  eps - the eigenproblem solver context
1023: -  sign_normalization - whether Bx should be multiplied by the sign of the first non-zero
1024:                         element when performing normalization steps

1026:    Options Database Key:
1027: .  -eps_power_sign_normalization - Sets the sign normalization flag

1029:    Level: advanced

1031: .seealso: EPSPowerGetSignNormalization()
1032: @*/
1033: PetscErrorCode EPSPowerSetSignNormalization(EPS eps,PetscBool sign_normalization)
1034: {
1035:   PetscFunctionBegin;
1038:   PetscTryMethod(eps,"EPSPowerSetSignNormalization_C",(EPS,PetscBool),(eps,sign_normalization));
1039:   PetscFunctionReturn(PETSC_SUCCESS);
1040: }

1042: static PetscErrorCode EPSPowerGetSignNormalization_Power(EPS eps,PetscBool *sign_normalization)
1043: {
1044:   EPS_POWER *power = (EPS_POWER*)eps->data;

1046:   PetscFunctionBegin;
1047:   *sign_normalization = power->sign_normalization;
1048:   PetscFunctionReturn(PETSC_SUCCESS);
1049: }

1051: /*@
1052:    EPSPowerGetSignNormalization - Returns a flag indicating whether the Bx vector
1053:    is normalized by the sign of the first non-zero element in the vector. E.g.,
1054:    if this is true, the post-normalization value of the first non-zero element in
1055:    the vector is guaranteed to be positive.

1057:    Not Collective

1059:    Input Parameter:
1060: .  eps - the eigenproblem solver context

1062:    Output Parameter:
1063: .  sign_normalization - the sign normalization flag

1065:    Level: advanced

1067: .seealso: EPSPowerSetSignNormalization()
1068: @*/
1069: PetscErrorCode EPSPowerGetSignNormalization(EPS eps,PetscBool *sign_normalization)
1070: {
1071:   PetscFunctionBegin;
1073:   PetscAssertPointer(sign_normalization,2);
1074:   PetscUseMethod(eps,"EPSPowerGetSignNormalization_C",(EPS,PetscBool*),(eps,sign_normalization));
1075:   PetscFunctionReturn(PETSC_SUCCESS);
1076: }

1078: static PetscErrorCode EPSPowerSetSNES_Power(EPS eps,SNES snes)
1079: {
1080:   EPS_POWER      *power = (EPS_POWER*)eps->data;

1082:   PetscFunctionBegin;
1083:   PetscCall(PetscObjectReference((PetscObject)snes));
1084:   PetscCall(SNESDestroy(&power->snes));
1085:   power->snes = snes;
1086:   eps->state = EPS_STATE_INITIAL;
1087:   PetscFunctionReturn(PETSC_SUCCESS);
1088: }

1090: /*@
1091:    EPSPowerSetSNES - Associate a nonlinear solver object (SNES) to the
1092:    eigenvalue solver (to be used in nonlinear inverse iteration).

1094:    Collective

1096:    Input Parameters:
1097: +  eps  - the eigenvalue solver
1098: -  snes - the nonlinear solver object

1100:    Level: advanced

1102: .seealso: EPSPowerGetSNES()
1103: @*/
1104: PetscErrorCode EPSPowerSetSNES(EPS eps,SNES snes)
1105: {
1106:   PetscFunctionBegin;
1109:   PetscCheckSameComm(eps,1,snes,2);
1110:   PetscTryMethod(eps,"EPSPowerSetSNES_C",(EPS,SNES),(eps,snes));
1111:   PetscFunctionReturn(PETSC_SUCCESS);
1112: }

1114: static PetscErrorCode EPSPowerGetSNES_Power(EPS eps,SNES *snes)
1115: {
1116:   EPS_POWER      *power = (EPS_POWER*)eps->data;

1118:   PetscFunctionBegin;
1119:   if (!power->snes) {
1120:     PetscCall(SNESCreate(PetscObjectComm((PetscObject)eps),&power->snes));
1121:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)power->snes,(PetscObject)eps,1));
1122:     PetscCall(SNESSetOptionsPrefix(power->snes,((PetscObject)eps)->prefix));
1123:     PetscCall(SNESAppendOptionsPrefix(power->snes,"eps_power_"));
1124:     PetscCall(PetscObjectSetOptions((PetscObject)power->snes,((PetscObject)eps)->options));
1125:   }
1126:   *snes = power->snes;
1127:   PetscFunctionReturn(PETSC_SUCCESS);
1128: }

1130: /*@
1131:    EPSPowerGetSNES - Retrieve the nonlinear solver object (SNES) associated
1132:    with the eigenvalue solver.

1134:    Not Collective

1136:    Input Parameter:
1137: .  eps - the eigenvalue solver

1139:    Output Parameter:
1140: .  snes - the nonlinear solver object

1142:    Level: advanced

1144: .seealso: EPSPowerSetSNES()
1145: @*/
1146: PetscErrorCode EPSPowerGetSNES(EPS eps,SNES *snes)
1147: {
1148:   PetscFunctionBegin;
1150:   PetscAssertPointer(snes,2);
1151:   PetscUseMethod(eps,"EPSPowerGetSNES_C",(EPS,SNES*),(eps,snes));
1152:   PetscFunctionReturn(PETSC_SUCCESS);
1153: }

1155: static PetscErrorCode EPSReset_Power(EPS eps)
1156: {
1157:   EPS_POWER      *power = (EPS_POWER*)eps->data;

1159:   PetscFunctionBegin;
1160:   if (power->snes) PetscCall(SNESReset(power->snes));
1161:   PetscFunctionReturn(PETSC_SUCCESS);
1162: }

1164: static PetscErrorCode EPSDestroy_Power(EPS eps)
1165: {
1166:   EPS_POWER      *power = (EPS_POWER*)eps->data;

1168:   PetscFunctionBegin;
1169:   if (power->nonlinear) PetscCall(SNESDestroy(&power->snes));
1170:   PetscCall(PetscFree(eps->data));
1171:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetShiftType_C",NULL));
1172:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetShiftType_C",NULL));
1173:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetNonlinear_C",NULL));
1174:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetNonlinear_C",NULL));
1175:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetUpdate_C",NULL));
1176:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetUpdate_C",NULL));
1177:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetSignNormalization_C",NULL));
1178:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetSignNormalization_C",NULL));
1179:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetSNES_C",NULL));
1180:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetSNES_C",NULL));
1181:   PetscFunctionReturn(PETSC_SUCCESS);
1182: }

1184: static PetscErrorCode EPSView_Power(EPS eps,PetscViewer viewer)
1185: {
1186:   EPS_POWER      *power = (EPS_POWER*)eps->data;
1187:   PetscBool      isascii;

1189:   PetscFunctionBegin;
1190:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
1191:   if (isascii) {
1192:     if (power->nonlinear) {
1193:       if (power->sign_normalization) PetscCall(PetscViewerASCIIPrintf(viewer,"  normalizing Bx by the sign of the first nonzero element\n"));
1194:       else PetscCall(PetscViewerASCIIPrintf(viewer,"  not normalizing Bx by the sign of the first nonzero element\n"));
1195:       PetscCall(PetscViewerASCIIPrintf(viewer,"  using nonlinear inverse iteration\n"));
1196:       if (power->update) PetscCall(PetscViewerASCIIPrintf(viewer,"  updating the residual monolithically\n"));
1197:       if (!power->snes) PetscCall(EPSPowerGetSNES(eps,&power->snes));
1198:       PetscCall(PetscViewerASCIIPushTab(viewer));
1199:       PetscCall(SNESView(power->snes,viewer));
1200:       PetscCall(PetscViewerASCIIPopTab(viewer));
1201:     } else PetscCall(PetscViewerASCIIPrintf(viewer,"  %s shifts\n",EPSPowerShiftTypes[power->shift_type]));
1202:   }
1203:   PetscFunctionReturn(PETSC_SUCCESS);
1204: }

1206: static PetscErrorCode EPSComputeVectors_Power(EPS eps)
1207: {
1208:   EPS_POWER      *power = (EPS_POWER*)eps->data;

1210:   PetscFunctionBegin;
1211:   if (eps->twosided) {
1212:     PetscCall(EPSComputeVectors_Twosided(eps));
1213:     PetscCall(BVNormalize(eps->V,NULL));
1214:     PetscCall(BVNormalize(eps->W,NULL));
1215:   } else if (!power->nonlinear) PetscCall(EPSComputeVectors_Schur(eps));
1216:   PetscFunctionReturn(PETSC_SUCCESS);
1217: }

1219: static PetscErrorCode EPSSetDefaultST_Power(EPS eps)
1220: {
1221:   EPS_POWER      *power = (EPS_POWER*)eps->data;
1222:   KSP            ksp;
1223:   PC             pc;

1225:   PetscFunctionBegin;
1226:   if (power->nonlinear) {
1227:     eps->categ=EPS_CATEGORY_PRECOND;
1228:     PetscCall(STGetKSP(eps->st,&ksp));
1229:     /* Set ST as STPRECOND so it can carry one preconditioning matrix
1230:      * It is useful when A and B are shell matrices
1231:      */
1232:     PetscCall(STSetType(eps->st,STPRECOND));
1233:     PetscCall(KSPGetPC(ksp,&pc));
1234:     PetscCall(PCSetType(pc,PCNONE));
1235:   }
1236:   PetscFunctionReturn(PETSC_SUCCESS);
1237: }

1239: SLEPC_EXTERN PetscErrorCode EPSCreate_Power(EPS eps)
1240: {
1241:   EPS_POWER      *ctx;

1243:   PetscFunctionBegin;
1244:   PetscCall(PetscNew(&ctx));
1245:   eps->data = (void*)ctx;

1247:   eps->useds = PETSC_TRUE;
1248:   eps->categ = EPS_CATEGORY_OTHER;

1250:   eps->ops->setup          = EPSSetUp_Power;
1251:   eps->ops->setupsort      = EPSSetUpSort_Default;
1252:   eps->ops->setfromoptions = EPSSetFromOptions_Power;
1253:   eps->ops->reset          = EPSReset_Power;
1254:   eps->ops->destroy        = EPSDestroy_Power;
1255:   eps->ops->view           = EPSView_Power;
1256:   eps->ops->backtransform  = EPSBackTransform_Power;
1257:   eps->ops->computevectors = EPSComputeVectors_Power;
1258:   eps->ops->setdefaultst   = EPSSetDefaultST_Power;
1259:   eps->stopping            = EPSStopping_Power;
1260:   ctx->sign_normalization  = PETSC_TRUE;

1262:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetShiftType_C",EPSPowerSetShiftType_Power));
1263:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetShiftType_C",EPSPowerGetShiftType_Power));
1264:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetNonlinear_C",EPSPowerSetNonlinear_Power));
1265:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetNonlinear_C",EPSPowerGetNonlinear_Power));
1266:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetUpdate_C",EPSPowerSetUpdate_Power));
1267:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetUpdate_C",EPSPowerGetUpdate_Power));
1268:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetSignNormalization_C",EPSPowerSetSignNormalization_Power));
1269:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetSignNormalization_C",EPSPowerGetSignNormalization_Power));
1270:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetSNES_C",EPSPowerSetSNES_Power));
1271:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetSNES_C",EPSPowerGetSNES_Power));
1272:   PetscFunctionReturn(PETSC_SUCCESS);
1273: }