Date: 2024-10-28T09:13:20+00:00

Actual source code: power.c
slepc-3.22.1 2024-10-28
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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->ncv!=PETSC_DETERMINE) {
     88:     PetscCheck(eps->ncv>=eps->nev,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"The value of ncv must be at least nev");
     89:   } else eps->ncv = eps->nev;
     90:   if (eps->mpd!=PETSC_DETERMINE) PetscCall(PetscInfo(eps,"Warning: parameter mpd ignored\n"));
     91:   if (eps->max_it==PETSC_DETERMINE) {
     92:     /* SNES will directly return the solution for us, and we need to do only one iteration */
     93:     if (power->nonlinear && power->update) eps->max_it = 1;
     94:     else eps->max_it = PetscMax(1000*eps->nev,100*eps->n);
     95:   }
     96:   if (!eps->which) PetscCall(EPSSetWhichEigenpairs_Default(eps));
     97:   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");
     98:   if (power->shift_type != EPS_POWER_SHIFT_CONSTANT) {
     99:     PetscCheck(!power->nonlinear,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Variable shifts not allowed in nonlinear problems");
    100:     EPSCheckSinvertCayleyCondition(eps,PETSC_TRUE," (with variable shifts)");
    101:     PetscCall(STGetMatMode(eps->st,&mode));
    102:     PetscCheck(mode!=ST_MATMODE_INPLACE,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"ST matrix mode inplace does not work with variable shifts");
    103:   }
    104:   EPSCheckUnsupported(eps,EPS_FEATURE_BALANCE | EPS_FEATURE_ARBITRARY | EPS_FEATURE_REGION | EPS_FEATURE_CONVERGENCE);
    105:   EPSCheckIgnored(eps,EPS_FEATURE_EXTRACTION);
    106:   PetscCall(EPSAllocateSolution(eps,0));
    107:   PetscCall(EPS_SetInnerProduct(eps));

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

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

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

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

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

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

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

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

    189: /*
    190:    Find the index of the first nonzero entry of x, and the process that owns it.
    191: */
    192: static PetscErrorCode FirstNonzeroIdx(Vec x,PetscInt *idx,PetscMPIInt *p)
    193: {
    194:   PetscInt          i,first,last,N;
    195:   PetscLayout       map;
    196:   const PetscScalar *xx;

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

    214: /*
    215:    Normalize a vector x with respect to a given norm as well as, optionally, the
    216:    sign of the first nonzero entry (assumed to be idx in process p).
    217: */
    218: static PetscErrorCode Normalize(Vec x,PetscReal norm,PetscInt idx,PetscMPIInt p,PetscBool sign_normalization,PetscScalar *sign)
    219: {
    220:   PetscScalar       alpha=1.0;
    221:   PetscInt          first,last;
    222:   PetscReal         absv;
    223:   const PetscScalar *xx;

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

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

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

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

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

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

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

    299: /*
    300:    Use SNES to compute y = A^{-1}*B*x for the nonlinear problem
    301: */
    302: static PetscErrorCode EPSPowerApply_SNES(EPS eps,Vec x,Vec y)
    303: {
    304:   EPS_POWER      *power = (EPS_POWER*)eps->data;
    305:   Vec            Bx;

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

    317: /*
    318:    Use nonlinear inverse power to compute an initial guess
    319: */
    320: static PetscErrorCode EPSPowerComputeInitialGuess_Update(EPS eps)
    321: {
    322:   EPS            powereps;
    323:   Mat            A,B,P;
    324:   Vec            v1,v2;
    325:   SNES           snes;
    326:   DM             dm,newdm;
    327:   PetscBool      sign_normalization;

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

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

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

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

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

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

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

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

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

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

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

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

    465:       /**
    466:        * If the Newton method (update, SNES) is used, we do not compute "relerr"
    467:        * since SNES determines the convergence.
    468:        */
    469:       if (PetscUnlikely(power->update)) relerr = 0.;
    470:       else {
    471:         /* compute relative error as ||y-theta v||_2/|theta| */
    472:         PetscCall(VecCopy(y,e));
    473:         PetscCall(BVGetColumn(eps->V,k,&v));
    474:         PetscCall(VecAXPY(e,power->nonlinear?-1.0:-theta,v));
    475:         PetscCall(BVRestoreColumn(eps->V,k,&v));
    476:         PetscCall(VecNorm(e,NORM_2,&relerr));
    477:         if (PetscUnlikely(power->nonlinear)) relerr *= PetscAbsScalar(theta);
    478:         else relerr /= PetscAbsScalar(theta);
    479:       }

    481:     } else {  /* RQI */

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

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

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

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

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

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

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

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

    562:     /**
    563:      * When a customized stopping test is used, and reason can be set to be converged (EPS_CONVERGED_USER).
    564:      * In this case, we need to increase eps->nconv to "1" so users can retrieve the solution.
    565:      */
    566:     if (PetscUnlikely(power->nonlinear && eps->reason>0)) eps->nconv = 1;
    567:   }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    775: /*@
    776:    EPSPowerSetShiftType - Sets the type of shifts used during the power
    777:    iteration. This can be used to emulate the Rayleigh Quotient Iteration
    778:    (RQI) method.

    780:    Logically Collective

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

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

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

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

    799:    Level: advanced

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

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

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

    821: /*@
    822:    EPSPowerGetShiftType - Gets the type of shifts used during the power
    823:    iteration.

    825:    Not Collective

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

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

    833:    Level: advanced

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

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

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

    860: /*@
    861:    EPSPowerSetNonlinear - Sets a flag to indicate that the problem is nonlinear.

    863:    Logically Collective

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

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

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

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

    886:    Level: advanced

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

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

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

    908: /*@
    909:    EPSPowerGetNonlinear - Returns a flag indicating if the problem is nonlinear.

    911:    Not Collective

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

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

    919:    Level: advanced

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

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

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

    943: /*@
    944:    EPSPowerSetUpdate - Sets a flag to indicate that the residual is updated monolithically
    945:    for nonlinear problems. This potentially has a better convergence.

    947:    Logically Collective

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

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

    956:    Level: advanced

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

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

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

    978: /*@
    979:    EPSPowerGetUpdate - Returns a flag indicating if the residual is updated monolithically
    980:    for nonlinear problems.

    982:    Not Collective

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

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

    990:    Level: advanced

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

    1003: static PetscErrorCode EPSPowerSetSignNormalization_Power(EPS eps,PetscBool sign_normalization)
    1004: {
    1005:   EPS_POWER *power = (EPS_POWER*)eps->data;

    1007:   PetscFunctionBegin;
    1008:   power->sign_normalization = sign_normalization;
    1009:   PetscFunctionReturn(PETSC_SUCCESS);
    1010: }

    1012: /*@
    1013:    EPSPowerSetSignNormalization - Sets a flag to indicate whether the Bx vector
    1014:    should be normalized by the sign of the first non-zero element in the vector.
    1015:    E.g., if this is true, the post-normalization value of the first non-zero element
    1016:    in the vector is guaranteed to be positive.

    1018:    Logically Collective

    1020:    Input Parameters:
    1021: +  eps - the eigenproblem solver context
    1022: -  sign_normalization - whether Bx should be multiplied by the sign of the first non-zero
    1023:                         element when performing normalization steps

    1025:    Options Database Key:
    1026: .  -eps_power_sign_normalization - Sets the sign normalization flag

    1028:    Level: advanced

    1030: .seealso: EPSPowerGetSignNormalization()
    1031: @*/
    1032: PetscErrorCode EPSPowerSetSignNormalization(EPS eps,PetscBool sign_normalization)
    1033: {
    1034:   PetscFunctionBegin;
    1037:   PetscTryMethod(eps,"EPSPowerSetSignNormalization_C",(EPS,PetscBool),(eps,sign_normalization));
    1038:   PetscFunctionReturn(PETSC_SUCCESS);
    1039: }

    1041: static PetscErrorCode EPSPowerGetSignNormalization_Power(EPS eps,PetscBool *sign_normalization)
    1042: {
    1043:   EPS_POWER *power = (EPS_POWER*)eps->data;

    1045:   PetscFunctionBegin;
    1046:   *sign_normalization = power->sign_normalization;
    1047:   PetscFunctionReturn(PETSC_SUCCESS);
    1048: }

    1050: /*@
    1051:    EPSPowerGetSignNormalization - Returns a flag indicating whether the Bx vector
    1052:    is normalized by the sign of the first non-zero element in the vector. E.g.,
    1053:    if this is true, the post-normalization value of the first non-zero element in
    1054:    the vector is guaranteed to be positive.

    1056:    Not Collective

    1058:    Input Parameter:
    1059: .  eps - the eigenproblem solver context

    1061:    Output Parameter:
    1062: .  sign_normalization - the sign normalization flag

    1064:    Level: advanced

    1066: .seealso: EPSPowerSetSignNormalization()
    1067: @*/
    1068: PetscErrorCode EPSPowerGetSignNormalization(EPS eps,PetscBool *sign_normalization)
    1069: {
    1070:   PetscFunctionBegin;
    1072:   PetscAssertPointer(sign_normalization,2);
    1073:   PetscUseMethod(eps,"EPSPowerGetSignNormalization_C",(EPS,PetscBool*),(eps,sign_normalization));
    1074:   PetscFunctionReturn(PETSC_SUCCESS);
    1075: }

    1077: static PetscErrorCode EPSPowerSetSNES_Power(EPS eps,SNES snes)
    1078: {
    1079:   EPS_POWER      *power = (EPS_POWER*)eps->data;

    1081:   PetscFunctionBegin;
    1082:   PetscCall(PetscObjectReference((PetscObject)snes));
    1083:   PetscCall(SNESDestroy(&power->snes));
    1084:   power->snes = snes;
    1085:   eps->state = EPS_STATE_INITIAL;
    1086:   PetscFunctionReturn(PETSC_SUCCESS);
    1087: }

    1089: /*@
    1090:    EPSPowerSetSNES - Associate a nonlinear solver object (SNES) to the
    1091:    eigenvalue solver (to be used in nonlinear inverse iteration).

    1093:    Collective

    1095:    Input Parameters:
    1096: +  eps  - the eigenvalue solver
    1097: -  snes - the nonlinear solver object

    1099:    Level: advanced

    1101: .seealso: EPSPowerGetSNES()
    1102: @*/
    1103: PetscErrorCode EPSPowerSetSNES(EPS eps,SNES snes)
    1104: {
    1105:   PetscFunctionBegin;
    1108:   PetscCheckSameComm(eps,1,snes,2);
    1109:   PetscTryMethod(eps,"EPSPowerSetSNES_C",(EPS,SNES),(eps,snes));
    1110:   PetscFunctionReturn(PETSC_SUCCESS);
    1111: }

    1113: static PetscErrorCode EPSPowerGetSNES_Power(EPS eps,SNES *snes)
    1114: {
    1115:   EPS_POWER      *power = (EPS_POWER*)eps->data;

    1117:   PetscFunctionBegin;
    1118:   if (!power->snes) {
    1119:     PetscCall(SNESCreate(PetscObjectComm((PetscObject)eps),&power->snes));
    1120:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)power->snes,(PetscObject)eps,1));
    1121:     PetscCall(SNESSetOptionsPrefix(power->snes,((PetscObject)eps)->prefix));
    1122:     PetscCall(SNESAppendOptionsPrefix(power->snes,"eps_power_"));
    1123:     PetscCall(PetscObjectSetOptions((PetscObject)power->snes,((PetscObject)eps)->options));
    1124:   }
    1125:   *snes = power->snes;
    1126:   PetscFunctionReturn(PETSC_SUCCESS);
    1127: }

    1129: /*@
    1130:    EPSPowerGetSNES - Retrieve the nonlinear solver object (SNES) associated
    1131:    with the eigenvalue solver.

    1133:    Not Collective

    1135:    Input Parameter:
    1136: .  eps - the eigenvalue solver

    1138:    Output Parameter:
    1139: .  snes - the nonlinear solver object

    1141:    Level: advanced

    1143: .seealso: EPSPowerSetSNES()
    1144: @*/
    1145: PetscErrorCode EPSPowerGetSNES(EPS eps,SNES *snes)
    1146: {
    1147:   PetscFunctionBegin;
    1149:   PetscAssertPointer(snes,2);
    1150:   PetscUseMethod(eps,"EPSPowerGetSNES_C",(EPS,SNES*),(eps,snes));
    1151:   PetscFunctionReturn(PETSC_SUCCESS);
    1152: }

    1154: static PetscErrorCode EPSReset_Power(EPS eps)
    1155: {
    1156:   EPS_POWER      *power = (EPS_POWER*)eps->data;

    1158:   PetscFunctionBegin;
    1159:   if (power->snes) PetscCall(SNESReset(power->snes));
    1160:   PetscFunctionReturn(PETSC_SUCCESS);
    1161: }

    1163: static PetscErrorCode EPSDestroy_Power(EPS eps)
    1164: {
    1165:   EPS_POWER      *power = (EPS_POWER*)eps->data;

    1167:   PetscFunctionBegin;
    1168:   if (power->nonlinear) PetscCall(SNESDestroy(&power->snes));
    1169:   PetscCall(PetscFree(eps->data));
    1170:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetShiftType_C",NULL));
    1171:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetShiftType_C",NULL));
    1172:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetNonlinear_C",NULL));
    1173:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetNonlinear_C",NULL));
    1174:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetUpdate_C",NULL));
    1175:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetUpdate_C",NULL));
    1176:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetSignNormalization_C",NULL));
    1177:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetSignNormalization_C",NULL));
    1178:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetSNES_C",NULL));
    1179:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetSNES_C",NULL));
    1180:   PetscFunctionReturn(PETSC_SUCCESS);
    1181: }

    1183: static PetscErrorCode EPSView_Power(EPS eps,PetscViewer viewer)
    1184: {
    1185:   EPS_POWER      *power = (EPS_POWER*)eps->data;
    1186:   PetscBool      isascii;

    1188:   PetscFunctionBegin;
    1189:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
    1190:   if (isascii) {
    1191:     if (power->nonlinear) {
    1192:       if (power->sign_normalization) PetscCall(PetscViewerASCIIPrintf(viewer,"  normalizing Bx by the sign of the first nonzero element\n"));
    1193:       else PetscCall(PetscViewerASCIIPrintf(viewer,"  not normalizing Bx by the sign of the first nonzero element\n"));
    1194:       PetscCall(PetscViewerASCIIPrintf(viewer,"  using nonlinear inverse iteration\n"));
    1195:       if (power->update) PetscCall(PetscViewerASCIIPrintf(viewer,"  updating the residual monolithically\n"));
    1196:       if (!power->snes) PetscCall(EPSPowerGetSNES(eps,&power->snes));
    1197:       PetscCall(PetscViewerASCIIPushTab(viewer));
    1198:       PetscCall(SNESView(power->snes,viewer));
    1199:       PetscCall(PetscViewerASCIIPopTab(viewer));
    1200:     } else PetscCall(PetscViewerASCIIPrintf(viewer,"  %s shifts\n",EPSPowerShiftTypes[power->shift_type]));
    1201:   }
    1202:   PetscFunctionReturn(PETSC_SUCCESS);
    1203: }

    1205: static PetscErrorCode EPSComputeVectors_Power(EPS eps)
    1206: {
    1207:   EPS_POWER      *power = (EPS_POWER*)eps->data;

    1209:   PetscFunctionBegin;
    1210:   if (eps->twosided) {
    1211:     PetscCall(EPSComputeVectors_Twosided(eps));
    1212:     PetscCall(BVNormalize(eps->V,NULL));
    1213:     PetscCall(BVNormalize(eps->W,NULL));
    1214:   } else if (!power->nonlinear) PetscCall(EPSComputeVectors_Schur(eps));
    1215:   PetscFunctionReturn(PETSC_SUCCESS);
    1216: }

    1218: static PetscErrorCode EPSSetDefaultST_Power(EPS eps)
    1219: {
    1220:   EPS_POWER      *power = (EPS_POWER*)eps->data;
    1221:   KSP            ksp;
    1222:   PC             pc;

    1224:   PetscFunctionBegin;
    1225:   if (power->nonlinear) {
    1226:     eps->categ=EPS_CATEGORY_PRECOND;
    1227:     PetscCall(STGetKSP(eps->st,&ksp));
    1228:     /* Set ST as STPRECOND so it can carry one preconditioning matrix
    1229:      * It is useful when A and B are shell matrices
    1230:      */
    1231:     PetscCall(STSetType(eps->st,STPRECOND));
    1232:     PetscCall(KSPGetPC(ksp,&pc));
    1233:     PetscCall(PCSetType(pc,PCNONE));
    1234:   }
    1235:   PetscFunctionReturn(PETSC_SUCCESS);
    1236: }

    1238: SLEPC_EXTERN PetscErrorCode EPSCreate_Power(EPS eps)
    1239: {
    1240:   EPS_POWER      *ctx;

    1242:   PetscFunctionBegin;
    1243:   PetscCall(PetscNew(&ctx));
    1244:   eps->data = (void*)ctx;

    1246:   eps->useds = PETSC_TRUE;
    1247:   eps->categ = EPS_CATEGORY_OTHER;

    1249:   eps->ops->setup          = EPSSetUp_Power;
    1250:   eps->ops->setupsort      = EPSSetUpSort_Default;
    1251:   eps->ops->setfromoptions = EPSSetFromOptions_Power;
    1252:   eps->ops->reset          = EPSReset_Power;
    1253:   eps->ops->destroy        = EPSDestroy_Power;
    1254:   eps->ops->view           = EPSView_Power;
    1255:   eps->ops->backtransform  = EPSBackTransform_Power;
    1256:   eps->ops->computevectors = EPSComputeVectors_Power;
    1257:   eps->ops->setdefaultst   = EPSSetDefaultST_Power;
    1258:   eps->stopping            = EPSStopping_Power;
    1259:   ctx->sign_normalization  = PETSC_TRUE;

    1261:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetShiftType_C",EPSPowerSetShiftType_Power));
    1262:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetShiftType_C",EPSPowerGetShiftType_Power));
    1263:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetNonlinear_C",EPSPowerSetNonlinear_Power));
    1264:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetNonlinear_C",EPSPowerGetNonlinear_Power));
    1265:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetUpdate_C",EPSPowerSetUpdate_Power));
    1266:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetUpdate_C",EPSPowerGetUpdate_Power));
    1267:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetSignNormalization_C",EPSPowerSetSignNormalization_Power));
    1268:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetSignNormalization_C",EPSPowerGetSignNormalization_Power));
    1269:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerSetSNES_C",EPSPowerSetSNES_Power));
    1270:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSPowerGetSNES_C",EPSPowerGetSNES_Power));
    1271:   PetscFunctionReturn(PETSC_SUCCESS);
    1272: }