Date: 2022-11-02T11:47:18+00:00

Actual source code: pepdefault.c
slepc-3.18.1 2022-11-02
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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:    Simple default routines for common PEP operations
     12: */

     14: #include <slepc/private/pepimpl.h>

     16: /*@
     17:    PEPSetWorkVecs - Sets a number of work vectors into a PEP object.

     19:    Collective on pep

     21:    Input Parameters:
     22: +  pep - polynomial eigensolver context
     23: -  nw  - number of work vectors to allocate

     25:    Developer Notes:
     26:    This is SLEPC_EXTERN because it may be required by user plugin PEP
     27:    implementations.

     29:    Level: developer

     31: .seealso: PEPSetUp()
     32: @*/
     33: PetscErrorCode PEPSetWorkVecs(PEP pep,PetscInt nw)
     34: {
     35:   Vec            t;

     40:   if (pep->nwork < nw) {
     41:     VecDestroyVecs(pep->nwork,&pep->work);
     42:     pep->nwork = nw;
     43:     BVGetColumn(pep->V,0,&t);
     44:     VecDuplicateVecs(t,nw,&pep->work);
     45:     BVRestoreColumn(pep->V,0,&t);
     46:   }
     47:   return 0;
     48: }

     50: /*
     51:   PEPConvergedRelative - Checks convergence relative to the eigenvalue.
     52: */
     53: PetscErrorCode PEPConvergedRelative(PEP pep,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
     54: {
     55:   PetscReal w;

     57:   w = SlepcAbsEigenvalue(eigr,eigi);
     58:   *errest = res/w;
     59:   return 0;
     60: }

     62: /*
     63:   PEPConvergedNorm - Checks convergence relative to the matrix norms.
     64: */
     65: PetscErrorCode PEPConvergedNorm(PEP pep,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
     66: {
     67:   PetscReal      w=0.0,t;
     68:   PetscInt       j;
     69:   PetscBool      flg;

     71:   /* initialization of matrix norms */
     72:   if (!pep->nrma[pep->nmat-1]) {
     73:     for (j=0;j<pep->nmat;j++) {
     74:       MatHasOperation(pep->A[j],MATOP_NORM,&flg);
     76:       MatNorm(pep->A[j],NORM_INFINITY,&pep->nrma[j]);
     77:     }
     78:   }
     79:   t = SlepcAbsEigenvalue(eigr,eigi);
     80:   for (j=pep->nmat-1;j>=0;j--) {
     81:     w = w*t+pep->nrma[j];
     82:   }
     83:   *errest = res/w;
     84:   return 0;
     85: }

     87: /*
     88:   PEPSetWhichEigenpairs_Default - Sets the default value for which,
     89:   depending on the ST.
     90:  */
     91: PetscErrorCode PEPSetWhichEigenpairs_Default(PEP pep)
     92: {
     93:   PetscBool      target;

     95:   PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&target);
     96:   if (target) pep->which = PEP_TARGET_MAGNITUDE;
     97:   else pep->which = PEP_LARGEST_MAGNITUDE;
     98:   return 0;
     99: }

    101: /*
    102:   PEPConvergedAbsolute - Checks convergence absolutely.
    103: */
    104: PetscErrorCode PEPConvergedAbsolute(PEP pep,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
    105: {
    106:   *errest = res;
    107:   return 0;
    108: }

    110: /*@C
    111:    PEPStoppingBasic - Default routine to determine whether the outer eigensolver
    112:    iteration must be stopped.

    114:    Collective on pep

    116:    Input Parameters:
    117: +  pep    - eigensolver context obtained from PEPCreate()
    118: .  its    - current number of iterations
    119: .  max_it - maximum number of iterations
    120: .  nconv  - number of currently converged eigenpairs
    121: .  nev    - number of requested eigenpairs
    122: -  ctx    - context (not used here)

    124:    Output Parameter:
    125: .  reason - result of the stopping test

    127:    Notes:
    128:    A positive value of reason indicates that the iteration has finished successfully
    129:    (converged), and a negative value indicates an error condition (diverged). If
    130:    the iteration needs to be continued, reason must be set to PEP_CONVERGED_ITERATING
    131:    (zero).

    133:    PEPStoppingBasic() will stop if all requested eigenvalues are converged, or if
    134:    the maximum number of iterations has been reached.

    136:    Use PEPSetStoppingTest() to provide your own test instead of using this one.

    138:    Level: advanced

    140: .seealso: PEPSetStoppingTest(), PEPConvergedReason, PEPGetConvergedReason()
    141: @*/
    142: PetscErrorCode PEPStoppingBasic(PEP pep,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,PEPConvergedReason *reason,void *ctx)
    143: {
    144:   *reason = PEP_CONVERGED_ITERATING;
    145:   if (nconv >= nev) {
    146:     PetscInfo(pep,"Polynomial eigensolver finished successfully: %" PetscInt_FMT " eigenpairs converged at iteration %" PetscInt_FMT "\n",nconv,its);
    147:     *reason = PEP_CONVERGED_TOL;
    148:   } else if (its >= max_it) {
    149:     *reason = PEP_DIVERGED_ITS;
    150:     PetscInfo(pep,"Polynomial eigensolver iteration reached maximum number of iterations (%" PetscInt_FMT ")\n",its);
    151:   }
    152:   return 0;
    153: }

    155: PetscErrorCode PEPBackTransform_Default(PEP pep)
    156: {
    157:   STBackTransform(pep->st,pep->nconv,pep->eigr,pep->eigi);
    158:   return 0;
    159: }

    161: PetscErrorCode PEPComputeVectors_Default(PEP pep)
    162: {
    163:   PetscInt       i;
    164:   Vec            v;

    166:   PEPExtractVectors(pep);

    168:   /* Fix eigenvectors if balancing was used */
    169:   if ((pep->scale==PEP_SCALE_DIAGONAL || pep->scale==PEP_SCALE_BOTH) && pep->Dr && (pep->refine!=PEP_REFINE_MULTIPLE)) {
    170:     for (i=0;i<pep->nconv;i++) {
    171:       BVGetColumn(pep->V,i,&v);
    172:       VecPointwiseMult(v,v,pep->Dr);
    173:       BVRestoreColumn(pep->V,i,&v);
    174:     }
    175:   }

    177:   /* normalization */
    178:   BVNormalize(pep->V,pep->eigi);
    179:   return 0;
    180: }

    182: /*
    183:   PEPBuildDiagonalScaling - compute two diagonal matrices to be applied for balancing
    184:   in polynomial eigenproblems.
    185: */
    186: PetscErrorCode PEPBuildDiagonalScaling(PEP pep)
    187: {
    188:   PetscInt       it,i,j,k,nmat,nr,e,nz,lst,lend,nc=0,*cols,emax,emin,emaxl,eminl;
    189:   const PetscInt *cidx,*ridx;
    190:   Mat            M,*T,A;
    191:   PetscMPIInt    n;
    192:   PetscBool      cont=PETSC_TRUE,flg=PETSC_FALSE;
    193:   PetscScalar    *array,*Dr,*Dl,t;
    194:   PetscReal      l2,d,*rsum,*aux,*csum,w=1.0;
    195:   MatStructure   str;
    196:   MatInfo        info;

    198:   l2 = 2*PetscLogReal(2.0);
    199:   nmat = pep->nmat;
    200:   PetscMPIIntCast(pep->n,&n);
    201:   STGetMatStructure(pep->st,&str);
    202:   PetscMalloc1(nmat,&T);
    203:   for (k=0;k<nmat;k++) STGetMatrixTransformed(pep->st,k,&T[k]);
    204:   /* Form local auxiliary matrix M */
    205:   PetscObjectBaseTypeCompareAny((PetscObject)T[0],&cont,MATMPIAIJ,MATSEQAIJ,"");
    207:   PetscObjectBaseTypeCompare((PetscObject)T[0],MATMPIAIJ,&cont);
    208:   if (cont) {
    209:     MatMPIAIJGetLocalMat(T[0],MAT_INITIAL_MATRIX,&M);
    210:     flg = PETSC_TRUE;
    211:   } else MatDuplicate(T[0],MAT_COPY_VALUES,&M);
    212:   MatGetInfo(M,MAT_LOCAL,&info);
    213:   nz = (PetscInt)info.nz_used;
    214:   MatSeqAIJGetArray(M,&array);
    215:   for (i=0;i<nz;i++) {
    216:     t = PetscAbsScalar(array[i]);
    217:     array[i] = t*t;
    218:   }
    219:   MatSeqAIJRestoreArray(M,&array);
    220:   for (k=1;k<nmat;k++) {
    221:     if (flg) MatMPIAIJGetLocalMat(T[k],MAT_INITIAL_MATRIX,&A);
    222:     else {
    223:       if (str==SAME_NONZERO_PATTERN) MatCopy(T[k],A,SAME_NONZERO_PATTERN);
    224:       else MatDuplicate(T[k],MAT_COPY_VALUES,&A);
    225:     }
    226:     MatGetInfo(A,MAT_LOCAL,&info);
    227:     nz = (PetscInt)info.nz_used;
    228:     MatSeqAIJGetArray(A,&array);
    229:     for (i=0;i<nz;i++) {
    230:       t = PetscAbsScalar(array[i]);
    231:       array[i] = t*t;
    232:     }
    233:     MatSeqAIJRestoreArray(A,&array);
    234:     w *= pep->slambda*pep->slambda*pep->sfactor;
    235:     MatAXPY(M,w,A,str);
    236:     if (flg || str!=SAME_NONZERO_PATTERN || k==nmat-2) MatDestroy(&A);
    237:   }
    238:   MatGetRowIJ(M,0,PETSC_FALSE,PETSC_FALSE,&nr,&ridx,&cidx,&cont);
    240:   MatGetInfo(M,MAT_LOCAL,&info);
    241:   nz = (PetscInt)info.nz_used;
    242:   VecGetOwnershipRange(pep->Dl,&lst,&lend);
    243:   PetscMalloc4(nr,&rsum,pep->n,&csum,pep->n,&aux,PetscMin(pep->n-lend+lst,nz),&cols);
    244:   VecSet(pep->Dr,1.0);
    245:   VecSet(pep->Dl,1.0);
    246:   VecGetArray(pep->Dl,&Dl);
    247:   VecGetArray(pep->Dr,&Dr);
    248:   MatSeqAIJGetArray(M,&array);
    249:   PetscArrayzero(aux,pep->n);
    250:   for (j=0;j<nz;j++) {
    251:     /* Search non-zero columns outsize lst-lend */
    252:     if (aux[cidx[j]]==0 && (cidx[j]<lst || lend<=cidx[j])) cols[nc++] = cidx[j];
    253:     /* Local column sums */
    254:     aux[cidx[j]] += PetscAbsScalar(array[j]);
    255:   }
    256:   for (it=0;it<pep->sits && cont;it++) {
    257:     emaxl = 0; eminl = 0;
    258:     /* Column sum  */
    259:     if (it>0) { /* it=0 has been already done*/
    260:       MatSeqAIJGetArray(M,&array);
    261:       PetscArrayzero(aux,pep->n);
    262:       for (j=0;j<nz;j++) aux[cidx[j]] += PetscAbsScalar(array[j]);
    263:       MatSeqAIJRestoreArray(M,&array);
    264:     }
    265:     MPIU_Allreduce(aux,csum,n,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)pep->Dr));
    266:     /* Update Dr */
    267:     for (j=lst;j<lend;j++) {
    268:       d = PetscLogReal(csum[j])/l2;
    269:       e = -(PetscInt)((d < 0)?(d-0.5):(d+0.5));
    270:       d = PetscPowReal(2.0,e);
    271:       Dr[j-lst] *= d;
    272:       aux[j] = d*d;
    273:       emaxl = PetscMax(emaxl,e);
    274:       eminl = PetscMin(eminl,e);
    275:     }
    276:     for (j=0;j<nc;j++) {
    277:       d = PetscLogReal(csum[cols[j]])/l2;
    278:       e = -(PetscInt)((d < 0)?(d-0.5):(d+0.5));
    279:       d = PetscPowReal(2.0,e);
    280:       aux[cols[j]] = d*d;
    281:       emaxl = PetscMax(emaxl,e);
    282:       eminl = PetscMin(eminl,e);
    283:     }
    284:     /* Scale M */
    285:     MatSeqAIJGetArray(M,&array);
    286:     for (j=0;j<nz;j++) {
    287:       array[j] *= aux[cidx[j]];
    288:     }
    289:     MatSeqAIJRestoreArray(M,&array);
    290:     /* Row sum */
    291:     PetscArrayzero(rsum,nr);
    292:     MatSeqAIJGetArray(M,&array);
    293:     for (i=0;i<nr;i++) {
    294:       for (j=ridx[i];j<ridx[i+1];j++) rsum[i] += PetscAbsScalar(array[j]);
    295:       /* Update Dl */
    296:       d = PetscLogReal(rsum[i])/l2;
    297:       e = -(PetscInt)((d < 0)?(d-0.5):(d+0.5));
    298:       d = PetscPowReal(2.0,e);
    299:       Dl[i] *= d;
    300:       /* Scale M */
    301:       for (j=ridx[i];j<ridx[i+1];j++) array[j] *= d*d;
    302:       emaxl = PetscMax(emaxl,e);
    303:       eminl = PetscMin(eminl,e);
    304:     }
    305:     MatSeqAIJRestoreArray(M,&array);
    306:     /* Compute global max and min */
    307:     MPIU_Allreduce(&emaxl,&emax,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)pep->Dl));
    308:     MPIU_Allreduce(&eminl,&emin,1,MPIU_INT,MPI_MIN,PetscObjectComm((PetscObject)pep->Dl));
    309:     if (emax<=emin+2) cont = PETSC_FALSE;
    310:   }
    311:   VecRestoreArray(pep->Dr,&Dr);
    312:   VecRestoreArray(pep->Dl,&Dl);
    313:   /* Free memory*/
    314:   MatDestroy(&M);
    315:   PetscFree4(rsum,csum,aux,cols);
    316:   PetscFree(T);
    317:   return 0;
    318: }

    320: /*
    321:    PEPComputeScaleFactor - compute sfactor as described in [Betcke 2008].
    322: */
    323: PetscErrorCode PEPComputeScaleFactor(PEP pep)
    324: {
    325:   PetscBool      has0,has1,flg;
    326:   PetscReal      norm0,norm1;
    327:   Mat            T[2];
    328:   PEPBasis       basis;
    329:   PetscInt       i;

    331:   if (pep->scale==PEP_SCALE_NONE || pep->scale==PEP_SCALE_DIAGONAL) {  /* no scalar scaling */
    332:     pep->sfactor = 1.0;
    333:     pep->dsfactor = 1.0;
    334:     return 0;
    335:   }
    336:   if (pep->sfactor_set) return 0;  /* user provided value */
    337:   pep->sfactor = 1.0;
    338:   pep->dsfactor = 1.0;
    339:   PEPGetBasis(pep,&basis);
    340:   if (basis==PEP_BASIS_MONOMIAL) {
    341:     STGetTransform(pep->st,&flg);
    342:     if (flg) {
    343:       STGetMatrixTransformed(pep->st,0,&T[0]);
    344:       STGetMatrixTransformed(pep->st,pep->nmat-1,&T[1]);
    345:     } else {
    346:       T[0] = pep->A[0];
    347:       T[1] = pep->A[pep->nmat-1];
    348:     }
    349:     if (pep->nmat>2) {
    350:       MatHasOperation(T[0],MATOP_NORM,&has0);
    351:       MatHasOperation(T[1],MATOP_NORM,&has1);
    352:       if (has0 && has1) {
    353:         MatNorm(T[0],NORM_INFINITY,&norm0);
    354:         MatNorm(T[1],NORM_INFINITY,&norm1);
    355:         pep->sfactor = PetscPowReal(norm0/norm1,1.0/(pep->nmat-1));
    356:         pep->dsfactor = norm1;
    357:         for (i=pep->nmat-2;i>0;i--) {
    358:           STGetMatrixTransformed(pep->st,i,&T[1]);
    359:           MatHasOperation(T[1],MATOP_NORM,&has1);
    360:           if (has1) {
    361:             MatNorm(T[1],NORM_INFINITY,&norm1);
    362:             pep->dsfactor = pep->dsfactor*pep->sfactor+norm1;
    363:           } else break;
    364:         }
    365:         if (has1) {
    366:           pep->dsfactor = pep->dsfactor*pep->sfactor+norm0;
    367:           pep->dsfactor = pep->nmat/pep->dsfactor;
    368:         } else pep->dsfactor = 1.0;
    369:       }
    370:     }
    371:   }
    372:   return 0;
    373: }

    375: /*
    376:    PEPBasisCoefficients - compute polynomial basis coefficients
    377: */
    378: PetscErrorCode PEPBasisCoefficients(PEP pep,PetscReal *pbc)
    379: {
    380:   PetscReal *ca,*cb,*cg;
    381:   PetscInt  k,nmat=pep->nmat;

    383:   ca = pbc;
    384:   cb = pbc+nmat;
    385:   cg = pbc+2*nmat;
    386:   switch (pep->basis) {
    387:   case PEP_BASIS_MONOMIAL:
    388:     for (k=0;k<nmat;k++) {
    389:       ca[k] = 1.0; cb[k] = 0.0; cg[k] = 0.0;
    390:     }
    391:     break;
    392:   case PEP_BASIS_CHEBYSHEV1:
    393:     ca[0] = 1.0; cb[0] = 0.0; cg[0] = 0.0;
    394:     for (k=1;k<nmat;k++) {
    395:       ca[k] = .5; cb[k] = 0.0; cg[k] = .5;
    396:     }
    397:     break;
    398:   case PEP_BASIS_CHEBYSHEV2:
    399:     ca[0] = .5; cb[0] = 0.0; cg[0] = 0.0;
    400:     for (k=1;k<nmat;k++) {
    401:       ca[k] = .5; cb[k] = 0.0; cg[k] = .5;
    402:     }
    403:     break;
    404:   case PEP_BASIS_LEGENDRE:
    405:     ca[0] = 1.0; cb[0] = 0.0; cg[0] = 0.0;
    406:     for (k=1;k<nmat;k++) {
    407:       ca[k] = k+1; cb[k] = -2*k; cg[k] = k;
    408:     }
    409:     break;
    410:   case PEP_BASIS_LAGUERRE:
    411:     ca[0] = -1.0; cb[0] = 0.0; cg[0] = 0.0;
    412:     for (k=1;k<nmat;k++) {
    413:       ca[k] = -(k+1); cb[k] = 2*k+1; cg[k] = -k;
    414:     }
    415:     break;
    416:   case PEP_BASIS_HERMITE:
    417:     ca[0] = .5; cb[0] = 0.0; cg[0] = 0.0;
    418:     for (k=1;k<nmat;k++) {
    419:       ca[k] = .5; cb[k] = 0.0; cg[k] = -k;
    420:     }
    421:     break;
    422:   }
    423:   return 0;
    424: }