Date: 2022-08-09T09:05:48+00:00

Actual source code: pepdefault.c
slepc-3.17.2 2022-08-09
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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;

     37:   if (pep->nwork < nw) {
     38:     VecDestroyVecs(pep->nwork,&pep->work);
     39:     pep->nwork = nw;
     40:     BVGetColumn(pep->V,0,&t);
     41:     VecDuplicateVecs(t,nw,&pep->work);
     42:     BVRestoreColumn(pep->V,0,&t);
     43:     PetscLogObjectParents(pep,nw,pep->work);
     44:   }
     45:   PetscFunctionReturn(0);
     46: }

     48: /*
     49:   PEPConvergedRelative - Checks convergence relative to the eigenvalue.
     50: */
     51: PetscErrorCode PEPConvergedRelative(PEP pep,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
     52: {
     53:   PetscReal w;

     55:   w = SlepcAbsEigenvalue(eigr,eigi);
     56:   *errest = res/w;
     57:   PetscFunctionReturn(0);
     58: }

     60: /*
     61:   PEPConvergedNorm - Checks convergence relative to the matrix norms.
     62: */
     63: PetscErrorCode PEPConvergedNorm(PEP pep,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
     64: {
     65:   PetscReal      w=0.0,t;
     66:   PetscInt       j;
     67:   PetscBool      flg;

     69:   /* initialization of matrix norms */
     70:   if (!pep->nrma[pep->nmat-1]) {
     71:     for (j=0;j<pep->nmat;j++) {
     72:       MatHasOperation(pep->A[j],MATOP_NORM,&flg);
     74:       MatNorm(pep->A[j],NORM_INFINITY,&pep->nrma[j]);
     75:     }
     76:   }
     77:   t = SlepcAbsEigenvalue(eigr,eigi);
     78:   for (j=pep->nmat-1;j>=0;j--) {
     79:     w = w*t+pep->nrma[j];
     80:   }
     81:   *errest = res/w;
     82:   PetscFunctionReturn(0);
     83: }

     85: /*
     86:   PEPSetWhichEigenpairs_Default - Sets the default value for which,
     87:   depending on the ST.
     88:  */
     89: PetscErrorCode PEPSetWhichEigenpairs_Default(PEP pep)
     90: {
     91:   PetscBool      target;

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

     99: /*
    100:   PEPConvergedAbsolute - Checks convergence absolutely.
    101: */
    102: PetscErrorCode PEPConvergedAbsolute(PEP pep,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
    103: {
    104:   *errest = res;
    105:   PetscFunctionReturn(0);
    106: }

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

    112:    Collective on pep

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

    122:    Output Parameter:
    123: .  reason - result of the stopping test

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

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

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

    136:    Level: advanced

    138: .seealso: PEPSetStoppingTest(), PEPConvergedReason, PEPGetConvergedReason()
    139: @*/
    140: PetscErrorCode PEPStoppingBasic(PEP pep,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,PEPConvergedReason *reason,void *ctx)
    141: {
    142:   *reason = PEP_CONVERGED_ITERATING;
    143:   if (nconv >= nev) {
    144:     PetscInfo(pep,"Polynomial eigensolver finished successfully: %" PetscInt_FMT " eigenpairs converged at iteration %" PetscInt_FMT "\n",nconv,its);
    145:     *reason = PEP_CONVERGED_TOL;
    146:   } else if (its >= max_it) {
    147:     *reason = PEP_DIVERGED_ITS;
    148:     PetscInfo(pep,"Polynomial eigensolver iteration reached maximum number of iterations (%" PetscInt_FMT ")\n",its);
    149:   }
    150:   PetscFunctionReturn(0);
    151: }

    153: PetscErrorCode PEPBackTransform_Default(PEP pep)
    154: {
    155:   STBackTransform(pep->st,pep->nconv,pep->eigr,pep->eigi);
    156:   PetscFunctionReturn(0);
    157: }

    159: PetscErrorCode PEPComputeVectors_Default(PEP pep)
    160: {
    161:   PetscInt       i;
    162:   Vec            v;

    164:   PEPExtractVectors(pep);

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

    175:   /* normalization */
    176:   BVNormalize(pep->V,pep->eigi);
    177:   PetscFunctionReturn(0);
    178: }

    180: /*
    181:   PEPBuildDiagonalScaling - compute two diagonal matrices to be applied for balancing
    182:   in polynomial eigenproblems.
    183: */
    184: PetscErrorCode PEPBuildDiagonalScaling(PEP pep)
    185: {
    186:   PetscInt       it,i,j,k,nmat,nr,e,nz,lst,lend,nc=0,*cols,emax,emin,emaxl,eminl;
    187:   const PetscInt *cidx,*ridx;
    188:   Mat            M,*T,A;
    189:   PetscMPIInt    n;
    190:   PetscBool      cont=PETSC_TRUE,flg=PETSC_FALSE;
    191:   PetscScalar    *array,*Dr,*Dl,t;
    192:   PetscReal      l2,d,*rsum,*aux,*csum,w=1.0;
    193:   MatStructure   str;
    194:   MatInfo        info;

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

    318: /*
    319:    PEPComputeScaleFactor - compute sfactor as described in [Betcke 2008].
    320: */
    321: PetscErrorCode PEPComputeScaleFactor(PEP pep)
    322: {
    323:   PetscBool      has0,has1,flg;
    324:   PetscReal      norm0,norm1;
    325:   Mat            T[2];
    326:   PEPBasis       basis;
    327:   PetscInt       i;

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

    373: /*
    374:    PEPBasisCoefficients - compute polynomial basis coefficients
    375: */
    376: PetscErrorCode PEPBasisCoefficients(PEP pep,PetscReal *pbc)
    377: {
    378:   PetscReal *ca,*cb,*cg;
    379:   PetscInt  k,nmat=pep->nmat;

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