Actual source code: pepdefault.c
slepc-3.10.1 2018-10-23
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2018, 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>     /*I "slepcpep.h" I*/

     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:    Developers Note:
     26:    This is PETSC_EXTERN because it may be required by user plugin PEP
     27:    implementations.

     29:    Level: developer
     30: @*/
     31: PetscErrorCode PEPSetWorkVecs(PEP pep,PetscInt nw)
     32: {
     34:   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:   return(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;

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

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

     72:   /* initialization of matrix norms */
     73:   if (!pep->nrma[pep->nmat-1]) {
     74:     for (j=0;j<pep->nmat;j++) {
     75:       MatHasOperation(pep->A[j],MATOP_NORM,&flg);
     76:       if (!flg) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONG,"The convergence test related to the matrix norms requires a matrix norm operation");
     77:       MatNorm(pep->A[j],NORM_INFINITY,&pep->nrma[j]);
     78:     }
     79:   }
     80:   t = SlepcAbsEigenvalue(eigr,eigi);
     81:   for (j=pep->nmat-1;j>=0;j--) {
     82:     w = w*t+pep->nrma[j];
     83:   }
     84:   *errest = res/w;
     85:   return(0);
     86: }

     88: /*
     89:   PEPConvergedAbsolute - Checks convergence absolutely.
     90: */
     91: PetscErrorCode PEPConvergedAbsolute(PEP pep,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
     92: {
     94:   *errest = res;
     95:   return(0);
     96: }

     98: /*@C
     99:    PEPStoppingBasic - Default routine to determine whether the outer eigensolver
    100:    iteration must be stopped.

    102:    Collective on PEP

    104:    Input Parameters:
    105: +  pep    - eigensolver context obtained from PEPCreate()
    106: .  its    - current number of iterations
    107: .  max_it - maximum number of iterations
    108: .  nconv  - number of currently converged eigenpairs
    109: .  nev    - number of requested eigenpairs
    110: -  ctx    - context (not used here)

    112:    Output Parameter:
    113: .  reason - result of the stopping test

    115:    Notes:
    116:    A positive value of reason indicates that the iteration has finished successfully
    117:    (converged), and a negative value indicates an error condition (diverged). If
    118:    the iteration needs to be continued, reason must be set to PEP_CONVERGED_ITERATING
    119:    (zero).

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

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

    126:    Level: advanced

    128: .seealso: PEPSetStoppingTest(), PEPConvergedReason, PEPGetConvergedReason()
    129: @*/
    130: PetscErrorCode PEPStoppingBasic(PEP pep,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,PEPConvergedReason *reason,void *ctx)
    131: {

    135:   *reason = PEP_CONVERGED_ITERATING;
    136:   if (nconv >= nev) {
    137:     PetscInfo2(pep,"Polynomial eigensolver finished successfully: %D eigenpairs converged at iteration %D\n",nconv,its);
    138:     *reason = PEP_CONVERGED_TOL;
    139:   } else if (its >= max_it) {
    140:     *reason = PEP_DIVERGED_ITS;
    141:     PetscInfo1(pep,"Polynomial eigensolver iteration reached maximum number of iterations (%D)\n",its);
    142:   }
    143:   return(0);
    144: }

    146: PetscErrorCode PEPBackTransform_Default(PEP pep)
    147: {

    151:   STBackTransform(pep->st,pep->nconv,pep->eigr,pep->eigi);
    152:   return(0);
    153: }

    155: PetscErrorCode PEPComputeVectors_Default(PEP pep)
    156: {
    158:   PetscInt       i;
    159:   Vec            v;
    160: #if !defined(PETSC_USE_COMPLEX)
    161:   Vec            v1;
    162: #endif

    165:   PEPExtractVectors(pep);

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

    176:   /* normalization */
    177:   for (i=0;i<pep->nconv;i++) {
    178: #if !defined(PETSC_USE_COMPLEX)
    179:     if (pep->eigi[i]!=0.0) {   /* first eigenvalue of a complex conjugate pair */
    180:       BVGetColumn(pep->V,i,&v);
    181:       BVGetColumn(pep->V,i+1,&v1);
    182:       VecNormalizeComplex(v,v1,PETSC_TRUE,NULL);
    183:       BVRestoreColumn(pep->V,i,&v);
    184:       BVRestoreColumn(pep->V,i+1,&v1);
    185:       i++;
    186:     } else   /* real eigenvalue */
    187: #endif
    188:     {
    189:       BVGetColumn(pep->V,i,&v);
    190:       VecNormalizeComplex(v,NULL,PETSC_FALSE,NULL);
    191:       BVRestoreColumn(pep->V,i,&v);
    192:     }
    193:   }
    194:   return(0);
    195: }

    197: /*
    198:    PEPKrylovConvergence - This is the analogue to EPSKrylovConvergence, but
    199:    for polynomial Krylov methods.

    201:    Differences:
    202:    - Always non-symmetric
    203:    - Does not check for STSHIFT
    204:    - No correction factor
    205:    - No support for true residual
    206: */
    207: PetscErrorCode PEPKrylovConvergence(PEP pep,PetscBool getall,PetscInt kini,PetscInt nits,PetscReal beta,PetscInt *kout)
    208: {
    210:   PetscInt       k,newk,marker,inside;
    211:   PetscScalar    re,im;
    212:   PetscReal      resnorm;
    213:   PetscBool      istrivial;

    216:   RGIsTrivial(pep->rg,&istrivial);
    217:   marker = -1;
    218:   if (pep->trackall) getall = PETSC_TRUE;
    219:   for (k=kini;k<kini+nits;k++) {
    220:     /* eigenvalue */
    221:     re = pep->eigr[k];
    222:     im = pep->eigi[k];
    223:     if (!istrivial) {
    224:       STBackTransform(pep->st,1,&re,&im);
    225:       RGCheckInside(pep->rg,1,&re,&im,&inside);
    226:       if (marker==-1 && inside<0) marker = k;
    227:       re = pep->eigr[k];
    228:       im = pep->eigi[k];
    229:     }
    230:     newk = k;
    231:     DSVectors(pep->ds,DS_MAT_X,&newk,&resnorm);
    232:     resnorm *= beta;
    233:     /* error estimate */
    234:     (*pep->converged)(pep,re,im,resnorm,&pep->errest[k],pep->convergedctx);
    235:     if (marker==-1 && pep->errest[k] >= pep->tol) marker = k;
    236:     if (newk==k+1) {
    237:       pep->errest[k+1] = pep->errest[k];
    238:       k++;
    239:     }
    240:     if (marker!=-1 && !getall) break;
    241:   }
    242:   if (marker!=-1) k = marker;
    243:   *kout = k;
    244:   return(0);
    245: }

    247: /*
    248:   PEPBuildDiagonalScaling - compute two diagonal matrices to be applied for balancing
    249:   in polynomial eigenproblems.
    250: */
    251: PetscErrorCode PEPBuildDiagonalScaling(PEP pep)
    252: {
    254:   PetscInt       it,i,j,k,nmat,nr,e,nz,lst,lend,nc=0,*cols,emax,emin,emaxl,eminl;
    255:   const PetscInt *cidx,*ridx;
    256:   Mat            M,*T,A;
    257:   PetscMPIInt    n;
    258:   PetscBool      cont=PETSC_TRUE,flg=PETSC_FALSE;
    259:   PetscScalar    *array,*Dr,*Dl,t;
    260:   PetscReal      l2,d,*rsum,*aux,*csum,w=1.0;
    261:   MatStructure   str;
    262:   MatInfo        info;

    265:   l2 = 2*PetscLogReal(2.0);
    266:   nmat = pep->nmat;
    267:   PetscMPIIntCast(pep->n,&n);
    268:   STGetMatStructure(pep->st,&str);
    269:   PetscMalloc1(nmat,&T);
    270:   for (k=0;k<nmat;k++) {
    271:     STGetMatrixTransformed(pep->st,k,&T[k]);
    272:   }
    273:   /* Form local auxiliar matrix M */
    274:   PetscObjectTypeCompareAny((PetscObject)T[0],&cont,MATMPIAIJ,MATSEQAIJ,"");
    275:   if (!cont) SETERRQ(PetscObjectComm((PetscObject)T[0]),PETSC_ERR_SUP,"Only for MPIAIJ or SEQAIJ matrix types");
    276:   PetscObjectTypeCompare((PetscObject)T[0],MATMPIAIJ,&cont);
    277:   if (cont) {
    278:     MatMPIAIJGetLocalMat(T[0],MAT_INITIAL_MATRIX,&M);
    279:     flg = PETSC_TRUE;
    280:   } else {
    281:     MatDuplicate(T[0],MAT_COPY_VALUES,&M);
    282:   }
    283:   MatGetInfo(M,MAT_LOCAL,&info);
    284:   nz = (PetscInt)info.nz_used;
    285:   MatSeqAIJGetArray(M,&array);
    286:   for (i=0;i<nz;i++) {
    287:     t = PetscAbsScalar(array[i]);
    288:     array[i] = t*t;
    289:   }
    290:   MatSeqAIJRestoreArray(M,&array);
    291:   for (k=1;k<nmat;k++) {
    292:     if (flg) {
    293:       MatMPIAIJGetLocalMat(T[k],MAT_INITIAL_MATRIX,&A);
    294:     } else {
    295:       if (str==SAME_NONZERO_PATTERN) {
    296:         MatCopy(T[k],A,SAME_NONZERO_PATTERN);
    297:       } else {
    298:         MatDuplicate(T[k],MAT_COPY_VALUES,&A);
    299:       }
    300:     }
    301:     MatGetInfo(A,MAT_LOCAL,&info);
    302:     nz = (PetscInt)info.nz_used;
    303:     MatSeqAIJGetArray(A,&array);
    304:     for (i=0;i<nz;i++) {
    305:       t = PetscAbsScalar(array[i]);
    306:       array[i] = t*t;
    307:     }
    308:     MatSeqAIJRestoreArray(A,&array);
    309:     w *= pep->slambda*pep->slambda*pep->sfactor;
    310:     MatAXPY(M,w,A,str);
    311:     if (flg || str!=SAME_NONZERO_PATTERN || k==nmat-2) {
    312:       MatDestroy(&A);
    313:     }
    314:   }
    315:   MatGetRowIJ(M,0,PETSC_FALSE,PETSC_FALSE,&nr,&ridx,&cidx,&cont);
    316:   if (!cont) SETERRQ(PetscObjectComm((PetscObject)T[0]),PETSC_ERR_SUP,"It is not possible to compute scaling diagonals for these PEP matrices");
    317:   MatGetInfo(M,MAT_LOCAL,&info);
    318:   nz = (PetscInt)info.nz_used;
    319:   VecGetOwnershipRange(pep->Dl,&lst,&lend);
    320:   PetscMalloc4(nr,&rsum,pep->n,&csum,pep->n,&aux,PetscMin(pep->n-lend+lst,nz),&cols);
    321:   VecSet(pep->Dr,1.0);
    322:   VecSet(pep->Dl,1.0);
    323:   VecGetArray(pep->Dl,&Dl);
    324:   VecGetArray(pep->Dr,&Dr);
    325:   MatSeqAIJGetArray(M,&array);
    326:   PetscMemzero(aux,pep->n*sizeof(PetscReal));
    327:   for (j=0;j<nz;j++) {
    328:     /* Search non-zero columns outsize lst-lend */
    329:     if (aux[cidx[j]]==0 && (cidx[j]<lst || lend<=cidx[j])) cols[nc++] = cidx[j];
    330:     /* Local column sums */
    331:     aux[cidx[j]] += PetscAbsScalar(array[j]);
    332:   }
    333:   for (it=0;it<pep->sits && cont;it++) {
    334:     emaxl = 0; eminl = 0;
    335:     /* Column sum  */
    336:     if (it>0) { /* it=0 has been already done*/
    337:       MatSeqAIJGetArray(M,&array);
    338:       PetscMemzero(aux,pep->n*sizeof(PetscReal));
    339:       for (j=0;j<nz;j++) aux[cidx[j]] += PetscAbsScalar(array[j]);
    340:       MatSeqAIJRestoreArray(M,&array);
    341:     }
    342:     MPI_Allreduce(aux,csum,n,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)pep->Dr));
    343:     /* Update Dr */
    344:     for (j=lst;j<lend;j++) {
    345:       d = PetscLogReal(csum[j])/l2;
    346:       e = -(PetscInt)((d < 0)?(d-0.5):(d+0.5));
    347:       d = PetscPowReal(2.0,e);
    348:       Dr[j-lst] *= d;
    349:       aux[j] = d*d;
    350:       emaxl = PetscMax(emaxl,e);
    351:       eminl = PetscMin(eminl,e);
    352:     }
    353:     for (j=0;j<nc;j++) {
    354:       d = PetscLogReal(csum[cols[j]])/l2;
    355:       e = -(PetscInt)((d < 0)?(d-0.5):(d+0.5));
    356:       d = PetscPowReal(2.0,e);
    357:       aux[cols[j]] = d*d;
    358:       emaxl = PetscMax(emaxl,e);
    359:       eminl = PetscMin(eminl,e);
    360:     }
    361:     /* Scale M */
    362:     MatSeqAIJGetArray(M,&array);
    363:     for (j=0;j<nz;j++) {
    364:       array[j] *= aux[cidx[j]];
    365:     }
    366:     MatSeqAIJRestoreArray(M,&array);
    367:     /* Row sum */
    368:     PetscMemzero(rsum,nr*sizeof(PetscReal));
    369:     MatSeqAIJGetArray(M,&array);
    370:     for (i=0;i<nr;i++) {
    371:       for (j=ridx[i];j<ridx[i+1];j++) rsum[i] += PetscAbsScalar(array[j]);
    372:       /* Update Dl */
    373:       d = PetscLogReal(rsum[i])/l2;
    374:       e = -(PetscInt)((d < 0)?(d-0.5):(d+0.5));
    375:       d = PetscPowReal(2.0,e);
    376:       Dl[i] *= d;
    377:       /* Scale M */
    378:       for (j=ridx[i];j<ridx[i+1];j++) array[j] *= d*d;
    379:       emaxl = PetscMax(emaxl,e);
    380:       eminl = PetscMin(eminl,e);
    381:     }
    382:     MatSeqAIJRestoreArray(M,&array);
    383:     /* Compute global max and min */
    384:     MPI_Allreduce(&emaxl,&emax,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)pep->Dl));
    385:     MPI_Allreduce(&eminl,&emin,1,MPIU_INT,MPI_MIN,PetscObjectComm((PetscObject)pep->Dl));
    386:     if (emax<=emin+2) cont = PETSC_FALSE;
    387:   }
    388:   VecRestoreArray(pep->Dr,&Dr);
    389:   VecRestoreArray(pep->Dl,&Dl);
    390:   /* Free memory*/
    391:   MatDestroy(&M);
    392:   PetscFree4(rsum,csum,aux,cols);
    393:   PetscFree(T);
    394:   return(0);
    395: }

    397: /*
    398:    PEPComputeScaleFactor - compute sfactor as described in [Betcke 2008].
    399: */
    400: PetscErrorCode PEPComputeScaleFactor(PEP pep)
    401: {
    403:   PetscBool      has0,has1,flg;
    404:   PetscReal      norm0,norm1;
    405:   Mat            T[2];
    406:   PEPBasis       basis;
    407:   PetscInt       i;

    410:   if (pep->scale==PEP_SCALE_NONE || pep->scale==PEP_SCALE_DIAGONAL) {  /* no scalar scaling */
    411:     pep->sfactor = 1.0;
    412:     pep->dsfactor = 1.0;
    413:     return(0);
    414:   }
    415:   if (pep->sfactor_set) return(0);  /* user provided value */
    416:   pep->sfactor = 1.0;
    417:   pep->dsfactor = 1.0;
    418:   PEPGetBasis(pep,&basis);
    419:   if (basis==PEP_BASIS_MONOMIAL) {
    420:     STGetTransform(pep->st,&flg);
    421:     if (flg) {
    422:       STGetMatrixTransformed(pep->st,0,&T[0]);
    423:       STGetMatrixTransformed(pep->st,pep->nmat-1,&T[1]);
    424:     } else {
    425:       T[0] = pep->A[0];
    426:       T[1] = pep->A[pep->nmat-1];
    427:     }
    428:     if (pep->nmat>2) {
    429:       MatHasOperation(T[0],MATOP_NORM,&has0);
    430:       MatHasOperation(T[1],MATOP_NORM,&has1);
    431:       if (has0 && has1) {
    432:         MatNorm(T[0],NORM_INFINITY,&norm0);
    433:         MatNorm(T[1],NORM_INFINITY,&norm1);
    434:         pep->sfactor = PetscPowReal(norm0/norm1,1.0/(pep->nmat-1));
    435:         pep->dsfactor = norm1;
    436:         for (i=pep->nmat-2;i>0;i--) {
    437:           STGetMatrixTransformed(pep->st,i,&T[1]);
    438:           MatHasOperation(T[1],MATOP_NORM,&has1);
    439:           if (has1) {
    440:             MatNorm(T[1],NORM_INFINITY,&norm1);
    441:             pep->dsfactor = pep->dsfactor*pep->sfactor+norm1;
    442:           } else break;
    443:         }
    444:         if (has1) {
    445:           pep->dsfactor = pep->dsfactor*pep->sfactor+norm0;
    446:           pep->dsfactor = pep->nmat/pep->dsfactor;
    447:         } else pep->dsfactor = 1.0;
    448:       }
    449:     }
    450:   }
    451:   return(0);
    452: }

    454: /*
    455:    PEPBasisCoefficients - compute polynomial basis coefficients
    456: */
    457: PetscErrorCode PEPBasisCoefficients(PEP pep,PetscReal *pbc)
    458: {
    459:   PetscReal *ca,*cb,*cg;
    460:   PetscInt  k,nmat=pep->nmat;

    463:   ca = pbc;
    464:   cb = pbc+nmat;
    465:   cg = pbc+2*nmat;
    466:   switch (pep->basis) {
    467:   case PEP_BASIS_MONOMIAL:
    468:     for (k=0;k<nmat;k++) {
    469:       ca[k] = 1.0; cb[k] = 0.0; cg[k] = 0.0;
    470:     }
    471:     break;
    472:   case PEP_BASIS_CHEBYSHEV1:
    473:     ca[0] = 1.0; cb[0] = 0.0; cg[0] = 0.0;
    474:     for (k=1;k<nmat;k++) {
    475:       ca[k] = .5; cb[k] = 0.0; cg[k] = .5;
    476:     }
    477:     break;
    478:   case PEP_BASIS_CHEBYSHEV2:
    479:     ca[0] = .5; cb[0] = 0.0; cg[0] = 0.0;
    480:     for (k=1;k<nmat;k++) {
    481:       ca[k] = .5; cb[k] = 0.0; cg[k] = .5;
    482:     }
    483:     break;
    484:   case PEP_BASIS_LEGENDRE:
    485:     ca[0] = 1.0; cb[0] = 0.0; cg[0] = 0.0;
    486:     for (k=1;k<nmat;k++) {
    487:       ca[k] = k+1; cb[k] = -2*k; cg[k] = k;
    488:     }
    489:     break;
    490:   case PEP_BASIS_LAGUERRE:
    491:     ca[0] = -1.0; cb[0] = 0.0; cg[0] = 0.0;
    492:     for (k=1;k<nmat;k++) {
    493:       ca[k] = -(k+1); cb[k] = 2*k+1; cg[k] = -k;
    494:     }
    495:     break;
    496:   case PEP_BASIS_HERMITE:
    497:     ca[0] = .5; cb[0] = 0.0; cg[0] = 0.0;
    498:     for (k=1;k<nmat;k++) {
    499:       ca[k] = .5; cb[k] = 0.0; cg[k] = -k;
    500:     }
    501:     break;
    502:   }
    503:   return(0);
    504: }