Date: 2026-03-31T13:23:00+00:00

Actual source code: pepdefault.c

      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

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

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

     29:    Level: developer

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

     37:   PetscFunctionBegin;
     40:   PetscCheck(nw>0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"nw must be > 0: nw = %" PetscInt_FMT,nw);
     41:   if (pep->nwork < nw) {
     42:     PetscCall(VecDestroyVecs(pep->nwork,&pep->work));
     43:     pep->nwork = nw;
     44:     PetscCall(BVGetColumn(pep->V,0,&t));
     45:     PetscCall(VecDuplicateVecs(t,nw,&pep->work));
     46:     PetscCall(BVRestoreColumn(pep->V,0,&t));
     47:   }
     48:   PetscFunctionReturn(PETSC_SUCCESS);
     49: }

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

     58:   PetscFunctionBegin;
     59:   w = SlepcAbsEigenvalue(eigr,eigi);
     60:   *errest = (w!=0.0)? res/w: PETSC_MAX_REAL;
     61:   PetscFunctionReturn(PETSC_SUCCESS);
     62: }

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

     73:   PetscFunctionBegin;
     74:   /* initialization of matrix norms */
     75:   if (!pep->nrma[pep->nmat-1]) {
     76:     for (j=0;j<pep->nmat;j++) {
     77:       PetscCall(MatHasOperation(pep->A[j],MATOP_NORM,&flg));
     78:       PetscCheck(flg,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONG,"The convergence test related to the matrix norms requires a matrix norm operation");
     79:       PetscCall(MatNorm(pep->A[j],NORM_INFINITY,&pep->nrma[j]));
     80:     }
     81:   }
     82:   t = SlepcAbsEigenvalue(eigr,eigi);
     83:   for (j=pep->nmat-1;j>=0;j--) {
     84:     w = w*t+pep->nrma[j];
     85:   }
     86:   *errest = res/w;
     87:   PetscFunctionReturn(PETSC_SUCCESS);
     88: }

     90: /*
     91:   PEPSetWhichEigenpairs_Default - Sets the default value for which,
     92:   depending on the ST.
     93:  */
     94: PetscErrorCode PEPSetWhichEigenpairs_Default(PEP pep)
     95: {
     96:   PetscBool      target;

     98:   PetscFunctionBegin;
     99:   PetscCall(PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&target));
    100:   if (target) pep->which = PEP_TARGET_MAGNITUDE;
    101:   else pep->which = PEP_LARGEST_MAGNITUDE;
    102:   PetscFunctionReturn(PETSC_SUCCESS);
    103: }

    105: /*
    106:   PEPConvergedAbsolute - Checks convergence absolutely.
    107: */
    108: PetscErrorCode PEPConvergedAbsolute(PEP pep,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
    109: {
    110:   PetscFunctionBegin;
    111:   *errest = res;
    112:   PetscFunctionReturn(PETSC_SUCCESS);
    113: }

    115: /*@C
    116:    PEPStoppingBasic - Default routine to determine whether the outer eigensolver
    117:    iteration must be stopped.

    119:    Collective

    121:    Input Parameters:
    122: +  pep    - the polynomial eigensolver context
    123: .  its    - current number of iterations
    124: .  max_it - maximum number of iterations
    125: .  nconv  - number of currently converged eigenpairs
    126: .  nev    - number of requested eigenpairs
    127: -  ctx    - context (not used here)

    129:    Output Parameter:
    130: .  reason - result of the stopping test

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

    136:    This is the default stopping test.
    137:    Use `PEPSetStoppingTest()` to provide your own test instead of using this one.

    139:    Level: advanced

    141: .seealso: [](ch:pep), `PEPSetStoppingTest()`, `PEPConvergedReason`, `PEPGetConvergedReason()`
    142: @*/
    143: PetscErrorCode PEPStoppingBasic(PEP pep,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,PEPConvergedReason *reason,void *ctx)
    144: {
    145:   PetscFunctionBegin;
    146:   *reason = PEP_CONVERGED_ITERATING;
    147:   if (nconv >= nev) {
    148:     PetscCall(PetscInfo(pep,"Polynomial eigensolver finished successfully: %" PetscInt_FMT " eigenpairs converged at iteration %" PetscInt_FMT "\n",nconv,its));
    149:     *reason = PEP_CONVERGED_TOL;
    150:   } else if (its >= max_it) {
    151:     *reason = PEP_DIVERGED_ITS;
    152:     PetscCall(PetscInfo(pep,"Polynomial eigensolver iteration reached maximum number of iterations (%" PetscInt_FMT ")\n",its));
    153:   }
    154:   PetscFunctionReturn(PETSC_SUCCESS);
    155: }

    157: PetscErrorCode PEPBackTransform_Default(PEP pep)
    158: {
    159:   PetscFunctionBegin;
    160:   PetscCall(STBackTransform(pep->st,pep->nconv,pep->eigr,pep->eigi));
    161:   PetscFunctionReturn(PETSC_SUCCESS);
    162: }

    164: PetscErrorCode PEPComputeVectors_Default(PEP pep)
    165: {
    166:   PetscInt       i;
    167:   Vec            v;

    169:   PetscFunctionBegin;
    170:   PetscCall(PEPExtractVectors(pep));

    172:   /* Fix eigenvectors if balancing was used */
    173:   if ((pep->scale==PEP_SCALE_DIAGONAL || pep->scale==PEP_SCALE_BOTH) && pep->Dr && (pep->refine!=PEP_REFINE_MULTIPLE)) {
    174:     for (i=0;i<pep->nconv;i++) {
    175:       PetscCall(BVGetColumn(pep->V,i,&v));
    176:       PetscCall(VecPointwiseMult(v,v,pep->Dr));
    177:       PetscCall(BVRestoreColumn(pep->V,i,&v));
    178:     }
    179:   }

    181:   /* normalization */
    182:   PetscCall(BVNormalize(pep->V,pep->eigi));
    183:   PetscFunctionReturn(PETSC_SUCCESS);
    184: }

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

    202:   PetscFunctionBegin;
    203:   l2 = 2*PetscLogReal(2.0);
    204:   nmat = pep->nmat;
    205:   PetscCall(PetscMPIIntCast(pep->n,&n));
    206:   PetscCall(STGetMatStructure(pep->st,&str));
    207:   PetscCall(PetscMalloc1(nmat,&T));
    208:   for (k=0;k<nmat;k++) PetscCall(STGetMatrixTransformed(pep->st,k,&T[k]));
    209:   /* Form local auxiliary matrix M */
    210:   PetscCall(PetscObjectBaseTypeCompareAny((PetscObject)T[0],&cont,MATMPIAIJ,MATSEQAIJ,""));
    211:   PetscCheck(cont,PetscObjectComm((PetscObject)T[0]),PETSC_ERR_SUP,"Only for MPIAIJ or SEQAIJ matrix types");
    212:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)T[0],MATMPIAIJ,&cont));
    213:   if (cont) {
    214:     PetscCall(MatMPIAIJGetLocalMat(T[0],MAT_INITIAL_MATRIX,&M));
    215:     flg = PETSC_TRUE;
    216:   } else PetscCall(MatDuplicate(T[0],MAT_COPY_VALUES,&M));
    217:   PetscCall(MatGetInfo(M,MAT_LOCAL,&info));
    218:   nz = (PetscInt)info.nz_used;
    219:   PetscCall(MatSeqAIJGetArray(M,&array));
    220:   for (i=0;i<nz;i++) {
    221:     t = PetscAbsScalar(array[i]);
    222:     array[i] = t*t;
    223:   }
    224:   PetscCall(MatSeqAIJRestoreArray(M,&array));
    225:   for (k=1;k<nmat;k++) {
    226:     if (flg) PetscCall(MatMPIAIJGetLocalMat(T[k],MAT_INITIAL_MATRIX,&A));
    227:     else {
    228:       if (str==SAME_NONZERO_PATTERN) PetscCall(MatCopy(T[k],A,SAME_NONZERO_PATTERN));
    229:       else PetscCall(MatDuplicate(T[k],MAT_COPY_VALUES,&A));
    230:     }
    231:     PetscCall(MatGetInfo(A,MAT_LOCAL,&info));
    232:     nz = (PetscInt)info.nz_used;
    233:     PetscCall(MatSeqAIJGetArray(A,&array));
    234:     for (i=0;i<nz;i++) {
    235:       t = PetscAbsScalar(array[i]);
    236:       array[i] = t*t;
    237:     }
    238:     PetscCall(MatSeqAIJRestoreArray(A,&array));
    239:     w *= pep->slambda*pep->slambda*pep->sfactor;
    240:     PetscCall(MatAXPY(M,w,A,str));
    241:     if (flg || str!=SAME_NONZERO_PATTERN || k==nmat-2) PetscCall(MatDestroy(&A));
    242:   }
    243:   PetscCall(MatGetRowIJ(M,0,PETSC_FALSE,PETSC_FALSE,&nr,&ridx,&cidx,&cont));
    244:   PetscCheck(cont,PetscObjectComm((PetscObject)T[0]),PETSC_ERR_SUP,"It is not possible to compute scaling diagonals for these PEP matrices");
    245:   PetscCall(MatGetInfo(M,MAT_LOCAL,&info));
    246:   nz = (PetscInt)info.nz_used;
    247:   PetscCall(VecGetOwnershipRange(pep->Dl,&lst,&lend));
    248:   PetscCall(PetscMalloc4(nr,&rsum,pep->n,&csum,pep->n,&aux,PetscMin(pep->n-lend+lst,nz),&cols));
    249:   PetscCall(VecSet(pep->Dr,1.0));
    250:   PetscCall(VecSet(pep->Dl,1.0));
    251:   PetscCall(VecGetArray(pep->Dl,&Dl));
    252:   PetscCall(VecGetArray(pep->Dr,&Dr));
    253:   PetscCall(MatSeqAIJGetArray(M,&array));
    254:   PetscCall(PetscArrayzero(aux,pep->n));
    255:   for (j=0;j<nz;j++) {
    256:     /* Search non-zero columns outsize lst-lend */
    257:     if (aux[cidx[j]]==0 && (cidx[j]<lst || lend<=cidx[j])) cols[nc++] = cidx[j];
    258:     /* Local column sums */
    259:     aux[cidx[j]] += PetscAbsScalar(array[j]);
    260:   }
    261:   for (it=0;it<pep->sits && cont;it++) {
    262:     emaxl = 0; eminl = 0;
    263:     /* Column sum  */
    264:     if (it>0) { /* it=0 has been already done*/
    265:       PetscCall(MatSeqAIJGetArray(M,&array));
    266:       PetscCall(PetscArrayzero(aux,pep->n));
    267:       for (j=0;j<nz;j++) aux[cidx[j]] += PetscAbsScalar(array[j]);
    268:       PetscCall(MatSeqAIJRestoreArray(M,&array));
    269:     }
    270:     PetscCallMPI(MPIU_Allreduce(aux,csum,n,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)pep->Dr)));
    271:     /* Update Dr */
    272:     for (j=lst;j<lend;j++) {
    273:       d = PetscLogReal(csum[j])/l2;
    274:       e = -(PetscInt)((d < 0)?(d-0.5):(d+0.5));
    275:       d = PetscPowReal(2.0,e);
    276:       Dr[j-lst] *= d;
    277:       aux[j] = d*d;
    278:       emaxl = PetscMax(emaxl,e);
    279:       eminl = PetscMin(eminl,e);
    280:     }
    281:     for (j=0;j<nc;j++) {
    282:       d = PetscLogReal(csum[cols[j]])/l2;
    283:       e = -(PetscInt)((d < 0)?(d-0.5):(d+0.5));
    284:       d = PetscPowReal(2.0,e);
    285:       aux[cols[j]] = d*d;
    286:       emaxl = PetscMax(emaxl,e);
    287:       eminl = PetscMin(eminl,e);
    288:     }
    289:     /* Scale M */
    290:     PetscCall(MatSeqAIJGetArray(M,&array));
    291:     for (j=0;j<nz;j++) {
    292:       array[j] *= aux[cidx[j]];
    293:     }
    294:     PetscCall(MatSeqAIJRestoreArray(M,&array));
    295:     /* Row sum */
    296:     PetscCall(PetscArrayzero(rsum,nr));
    297:     PetscCall(MatSeqAIJGetArray(M,&array));
    298:     for (i=0;i<nr;i++) {
    299:       for (j=ridx[i];j<ridx[i+1];j++) rsum[i] += PetscAbsScalar(array[j]);
    300:       /* Update Dl */
    301:       d = PetscLogReal(rsum[i])/l2;
    302:       e = -(PetscInt)((d < 0)?(d-0.5):(d+0.5));
    303:       d = PetscPowReal(2.0,e);
    304:       Dl[i] *= d;
    305:       /* Scale M */
    306:       for (j=ridx[i];j<ridx[i+1];j++) array[j] *= d*d;
    307:       emaxl = PetscMax(emaxl,e);
    308:       eminl = PetscMin(eminl,e);
    309:     }
    310:     PetscCall(MatSeqAIJRestoreArray(M,&array));
    311:     /* Compute global max and min */
    312:     PetscCallMPI(MPIU_Allreduce(&emaxl,&emax,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)pep->Dl)));
    313:     PetscCallMPI(MPIU_Allreduce(&eminl,&emin,1,MPIU_INT,MPI_MIN,PetscObjectComm((PetscObject)pep->Dl)));
    314:     if (emax<=emin+2) cont = PETSC_FALSE;
    315:   }
    316:   PetscCall(VecRestoreArray(pep->Dr,&Dr));
    317:   PetscCall(VecRestoreArray(pep->Dl,&Dl));
    318:   /* Free memory*/
    319:   PetscCall(MatDestroy(&M));
    320:   PetscCall(PetscFree4(rsum,csum,aux,cols));
    321:   PetscCall(PetscFree(T));
    322:   PetscFunctionReturn(PETSC_SUCCESS);
    323: }

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

    336:   PetscFunctionBegin;
    337:   if (pep->scale==PEP_SCALE_NONE || pep->scale==PEP_SCALE_DIAGONAL) {  /* no scalar scaling */
    338:     pep->sfactor = 1.0;
    339:     pep->dsfactor = 1.0;
    340:     PetscFunctionReturn(PETSC_SUCCESS);
    341:   }
    342:   if (pep->sfactor_set) PetscFunctionReturn(PETSC_SUCCESS);  /* user provided value */
    343:   pep->sfactor = 1.0;
    344:   pep->dsfactor = 1.0;
    345:   PetscCall(PEPGetBasis(pep,&basis));
    346:   if (basis==PEP_BASIS_MONOMIAL) {
    347:     PetscCall(STGetTransform(pep->st,&flg));
    348:     if (flg) {
    349:       PetscCall(STGetMatrixTransformed(pep->st,0,&T[0]));
    350:       PetscCall(STGetMatrixTransformed(pep->st,pep->nmat-1,&T[1]));
    351:     } else {
    352:       T[0] = pep->A[0];
    353:       T[1] = pep->A[pep->nmat-1];
    354:     }
    355:     if (pep->nmat>2) {
    356:       PetscCall(MatHasOperation(T[0],MATOP_NORM,&has0));
    357:       PetscCall(MatHasOperation(T[1],MATOP_NORM,&has1));
    358:       if (has0 && has1) {
    359:         PetscCall(MatNorm(T[0],NORM_INFINITY,&norm0));
    360:         PetscCall(MatNorm(T[1],NORM_INFINITY,&norm1));
    361:         pep->sfactor = PetscPowReal(norm0/norm1,1.0/(pep->nmat-1));
    362:         pep->dsfactor = norm1;
    363:         for (i=pep->nmat-2;i>0;i--) {
    364:           PetscCall(STGetMatrixTransformed(pep->st,i,&T[1]));
    365:           PetscCall(MatHasOperation(T[1],MATOP_NORM,&has1));
    366:           if (has1) {
    367:             PetscCall(MatNorm(T[1],NORM_INFINITY,&norm1));
    368:             pep->dsfactor = pep->dsfactor*pep->sfactor+norm1;
    369:           } else break;
    370:         }
    371:         if (has1) {
    372:           pep->dsfactor = pep->dsfactor*pep->sfactor+norm0;
    373:           pep->dsfactor = pep->nmat/pep->dsfactor;
    374:         } else pep->dsfactor = 1.0;
    375:       }
    376:     }
    377:   }
    378:   PetscFunctionReturn(PETSC_SUCCESS);
    379: }

    381: /*
    382:    PEPBasisCoefficients - compute polynomial basis coefficients
    383: */
    384: PetscErrorCode PEPBasisCoefficients(PEP pep,PetscReal *pbc)
    385: {
    386:   PetscReal *ca,*cb,*cg;
    387:   PetscInt  k,nmat=pep->nmat;

    389:   PetscFunctionBegin;
    390:   ca = pbc;
    391:   cb = pbc+nmat;
    392:   cg = pbc+2*nmat;
    393:   switch (pep->basis) {
    394:   case PEP_BASIS_MONOMIAL:
    395:     for (k=0;k<nmat;k++) {
    396:       ca[k] = 1.0; cb[k] = 0.0; cg[k] = 0.0;
    397:     }
    398:     break;
    399:   case PEP_BASIS_CHEBYSHEV1:
    400:     ca[0] = 1.0; cb[0] = 0.0; cg[0] = 0.0;
    401:     for (k=1;k<nmat;k++) {
    402:       ca[k] = .5; cb[k] = 0.0; cg[k] = .5;
    403:     }
    404:     break;
    405:   case PEP_BASIS_CHEBYSHEV2:
    406:     ca[0] = .5; cb[0] = 0.0; cg[0] = 0.0;
    407:     for (k=1;k<nmat;k++) {
    408:       ca[k] = .5; cb[k] = 0.0; cg[k] = .5;
    409:     }
    410:     break;
    411:   case PEP_BASIS_LEGENDRE:
    412:     ca[0] = 1.0; cb[0] = 0.0; cg[0] = 0.0;
    413:     for (k=1;k<nmat;k++) {
    414:       ca[k] = k+1; cb[k] = -2*k; cg[k] = k;
    415:     }
    416:     break;
    417:   case PEP_BASIS_LAGUERRE:
    418:     ca[0] = -1.0; cb[0] = 0.0; cg[0] = 0.0;
    419:     for (k=1;k<nmat;k++) {
    420:       ca[k] = -(k+1); cb[k] = 2*k+1; cg[k] = -k;
    421:     }
    422:     break;
    423:   case PEP_BASIS_HERMITE:
    424:     ca[0] = .5; cb[0] = 0.0; cg[0] = 0.0;
    425:     for (k=1;k<nmat;k++) {
    426:       ca[k] = .5; cb[k] = 0.0; cg[k] = -k;
    427:     }
    428:     break;
    429:   }
    430:   PetscFunctionReturn(PETSC_SUCCESS);
    431: }