Date: 2022-11-02T11:47:34+00:00

Actual source code: interpol.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:    SLEPc nonlinear eigensolver: "interpol"

     13:    Method: Polynomial interpolation

     15:    Algorithm:

     17:        Uses a PEP object to solve the interpolated NEP. Currently supports
     18:        only Chebyshev interpolation on an interval.

     20:    References:

     22:        [1] C. Effenberger and D. Kresser, "Chebyshev interpolation for
     23:            nonlinear eigenvalue problems", BIT 52:933-951, 2012.
     24: */

     26: #include <slepc/private/nepimpl.h>

     28: typedef struct {
     29:   PEP       pep;
     30:   PetscReal tol;       /* tolerance for norm of polynomial coefficients */
     31:   PetscInt  maxdeg;    /* maximum degree of interpolation polynomial */
     32:   PetscInt  deg;       /* actual degree of interpolation polynomial */
     33: } NEP_INTERPOL;

     35: PetscErrorCode NEPSetUp_Interpol(NEP nep)
     36: {
     37:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;
     38:   ST             st;
     39:   RG             rg;
     40:   PetscReal      a,b,c,d,s,tol;
     41:   PetscScalar    zero=0.0;
     42:   PetscBool      flg,istrivial,trackall;
     43:   PetscInt       its,in;

     45:   NEPSetDimensions_Default(nep,nep->nev,&nep->ncv,&nep->mpd);
     47:   if (nep->max_it==PETSC_DEFAULT) nep->max_it = PetscMax(5000,2*nep->n/nep->ncv);
     48:   if (!nep->which) nep->which = NEP_TARGET_MAGNITUDE;
     50:   NEPCheckUnsupported(nep,NEP_FEATURE_CALLBACK | NEP_FEATURE_STOPPING | NEP_FEATURE_TWOSIDED);

     52:   /* transfer PEP options */
     53:   if (!ctx->pep) NEPInterpolGetPEP(nep,&ctx->pep);
     54:   PEPSetBasis(ctx->pep,PEP_BASIS_CHEBYSHEV1);
     55:   PEPSetWhichEigenpairs(ctx->pep,PEP_TARGET_MAGNITUDE);
     56:   PetscObjectTypeCompare((PetscObject)ctx->pep,PEPJD,&flg);
     57:   if (!flg) {
     58:     PEPGetST(ctx->pep,&st);
     59:     STSetType(st,STSINVERT);
     60:   }
     61:   PEPSetDimensions(ctx->pep,nep->nev,nep->ncv,nep->mpd);
     62:   PEPGetTolerances(ctx->pep,&tol,&its);
     63:   if (tol==PETSC_DEFAULT) tol = SlepcDefaultTol(nep->tol);
     64:   if (ctx->tol==PETSC_DEFAULT) ctx->tol = tol;
     65:   if (its==PETSC_DEFAULT) its = nep->max_it;
     66:   PEPSetTolerances(ctx->pep,tol,its);
     67:   NEPGetTrackAll(nep,&trackall);
     68:   PEPSetTrackAll(ctx->pep,trackall);

     70:   /* transfer region options */
     71:   RGIsTrivial(nep->rg,&istrivial);
     73:   PetscObjectTypeCompare((PetscObject)nep->rg,RGINTERVAL,&flg);
     75:   RGIntervalGetEndpoints(nep->rg,&a,&b,&c,&d);
     77:   PEPGetRG(ctx->pep,&rg);
     78:   RGSetType(rg,RGINTERVAL);
     80:   s = 2.0/(b-a);
     81:   c = c*s;
     82:   d = d*s;
     83:   RGIntervalSetEndpoints(rg,-1.0,1.0,c,d);
     84:   RGCheckInside(nep->rg,1,&nep->target,&zero,&in);
     86:   PEPSetTarget(ctx->pep,(nep->target-(a+b)/2)*s);

     88:   NEPAllocateSolution(nep,0);
     89:   return 0;
     90: }

     92: /*
     93:   Input:
     94:     d, number of nodes to compute
     95:     a,b, interval extremes
     96:   Output:
     97:     *x, array containing the d Chebyshev nodes of the interval [a,b]
     98:     *dct2, coefficients to compute a discrete cosine transformation (DCT-II)
     99: */
    100: static PetscErrorCode ChebyshevNodes(PetscInt d,PetscReal a,PetscReal b,PetscScalar *x,PetscReal *dct2)
    101: {
    102:   PetscInt  j,i;
    103:   PetscReal t;

    105:   for (j=0;j<d+1;j++) {
    106:     t = ((2*j+1)*PETSC_PI)/(2*(d+1));
    107:     x[j] = (a+b)/2.0+((b-a)/2.0)*PetscCosReal(t);
    108:     for (i=0;i<d+1;i++) dct2[j*(d+1)+i] = PetscCosReal(i*t);
    109:   }
    110:   return 0;
    111: }

    113: PetscErrorCode NEPSolve_Interpol(NEP nep)
    114: {
    115:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;
    116:   Mat            *A,*P;
    117:   PetscScalar    *x,*fx,t;
    118:   PetscReal      *cs,a,b,s,aprox,aprox0=1.0,*matnorm;
    119:   PetscInt       i,j,k,deg=ctx->maxdeg;
    120:   PetscBool      hasmnorm=PETSC_FALSE;
    121:   Vec            vr,vi=NULL;
    122:   ST             st;

    124:   PetscMalloc4((deg+1)*(deg+1),&cs,deg+1,&x,(deg+1)*nep->nt,&fx,nep->nt,&matnorm);
    125:   for  (j=0;j<nep->nt;j++) {
    126:     MatHasOperation(nep->A[j],MATOP_NORM,&hasmnorm);
    127:     if (!hasmnorm) break;
    128:     MatNorm(nep->A[j],NORM_INFINITY,matnorm+j);
    129:   }
    130:   if (!hasmnorm) for (j=0;j<nep->nt;j++) matnorm[j] = 1.0;
    131:   RGIntervalGetEndpoints(nep->rg,&a,&b,NULL,NULL);
    132:   ChebyshevNodes(deg,a,b,x,cs);
    133:   for (j=0;j<nep->nt;j++) {
    134:     for (i=0;i<=deg;i++) FNEvaluateFunction(nep->f[j],x[i],&fx[i+j*(deg+1)]);
    135:   }
    136:   /* Polynomial coefficients */
    137:   PetscMalloc1(deg+1,&A);
    138:   if (nep->P) PetscMalloc1(deg+1,&P);
    139:   ctx->deg = deg;
    140:   for (k=0;k<=deg;k++) {
    141:     MatDuplicate(nep->A[0],MAT_COPY_VALUES,&A[k]);
    142:     if (nep->P) MatDuplicate(nep->P[0],MAT_COPY_VALUES,&P[k]);
    143:     t = 0.0;
    144:     for (i=0;i<deg+1;i++) t += fx[i]*cs[i*(deg+1)+k];
    145:     t *= 2.0/(deg+1);
    146:     if (k==0) t /= 2.0;
    147:     aprox = matnorm[0]*PetscAbsScalar(t);
    148:     MatScale(A[k],t);
    149:     if (nep->P) MatScale(P[k],t);
    150:     for (j=1;j<nep->nt;j++) {
    151:       t = 0.0;
    152:       for (i=0;i<deg+1;i++) t += fx[i+j*(deg+1)]*cs[i*(deg+1)+k];
    153:       t *= 2.0/(deg+1);
    154:       if (k==0) t /= 2.0;
    155:       aprox += matnorm[j]*PetscAbsScalar(t);
    156:       MatAXPY(A[k],t,nep->A[j],nep->mstr);
    157:       if (nep->P) MatAXPY(P[k],t,nep->P[j],nep->mstrp);
    158:     }
    159:     if (k==0) aprox0 = aprox;
    160:     if (k>1 && aprox/aprox0<ctx->tol) { ctx->deg = k; deg = k; break; }
    161:   }
    162:   PEPSetOperators(ctx->pep,deg+1,A);
    163:   MatDestroyMatrices(deg+1,&A);
    164:   if (nep->P) {
    165:     PEPGetST(ctx->pep,&st);
    166:     STSetSplitPreconditioner(st,deg+1,P,nep->mstrp);
    167:     MatDestroyMatrices(deg+1,&P);
    168:   }
    169:   PetscFree4(cs,x,fx,matnorm);

    171:   /* Solve polynomial eigenproblem */
    172:   PEPSolve(ctx->pep);
    173:   PEPGetConverged(ctx->pep,&nep->nconv);
    174:   PEPGetIterationNumber(ctx->pep,&nep->its);
    175:   PEPGetConvergedReason(ctx->pep,(PEPConvergedReason*)&nep->reason);
    176:   BVSetActiveColumns(nep->V,0,nep->nconv);
    177:   BVCreateVec(nep->V,&vr);
    178: #if !defined(PETSC_USE_COMPLEX)
    179:   VecDuplicate(vr,&vi);
    180: #endif
    181:   s = 2.0/(b-a);
    182:   for (i=0;i<nep->nconv;i++) {
    183:     PEPGetEigenpair(ctx->pep,i,&nep->eigr[i],&nep->eigi[i],vr,vi);
    184:     nep->eigr[i] /= s;
    185:     nep->eigr[i] += (a+b)/2.0;
    186:     nep->eigi[i] /= s;
    187:     BVInsertVec(nep->V,i,vr);
    188: #if !defined(PETSC_USE_COMPLEX)
    189:     if (nep->eigi[i]!=0.0) BVInsertVec(nep->V,++i,vi);
    190: #endif
    191:   }
    192:   VecDestroy(&vr);
    193:   VecDestroy(&vi);

    195:   nep->state = NEP_STATE_EIGENVECTORS;
    196:   return 0;
    197: }

    199: static PetscErrorCode PEPMonitor_Interpol(PEP pep,PetscInt its,PetscInt nconv,PetscScalar *eigr,PetscScalar *eigi,PetscReal *errest,PetscInt nest,void *ctx)
    200: {
    201:   PetscInt       i,n;
    202:   NEP            nep = (NEP)ctx;
    203:   PetscReal      a,b,s;
    204:   ST             st;

    206:   n = PetscMin(nest,nep->ncv);
    207:   for (i=0;i<n;i++) {
    208:     nep->eigr[i]   = eigr[i];
    209:     nep->eigi[i]   = eigi[i];
    210:     nep->errest[i] = errest[i];
    211:   }
    212:   PEPGetST(pep,&st);
    213:   STBackTransform(st,n,nep->eigr,nep->eigi);
    214:   RGIntervalGetEndpoints(nep->rg,&a,&b,NULL,NULL);
    215:   s = 2.0/(b-a);
    216:   for (i=0;i<n;i++) {
    217:     nep->eigr[i] /= s;
    218:     nep->eigr[i] += (a+b)/2.0;
    219:     nep->eigi[i] /= s;
    220:   }
    221:   NEPMonitor(nep,its,nconv,nep->eigr,nep->eigi,nep->errest,nest);
    222:   return 0;
    223: }

    225: PetscErrorCode NEPSetFromOptions_Interpol(NEP nep,PetscOptionItems *PetscOptionsObject)
    226: {
    227:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;
    228:   PetscInt       i;
    229:   PetscBool      flg1,flg2;
    230:   PetscReal      r;

    232:   PetscOptionsHeadBegin(PetscOptionsObject,"NEP Interpol Options");

    234:     NEPInterpolGetInterpolation(nep,&r,&i);
    235:     if (!i) i = PETSC_DEFAULT;
    236:     PetscOptionsInt("-nep_interpol_interpolation_degree","Maximum degree of polynomial interpolation","NEPInterpolSetInterpolation",i,&i,&flg1);
    237:     PetscOptionsReal("-nep_interpol_interpolation_tol","Tolerance for interpolation coefficients","NEPInterpolSetInterpolation",r,&r,&flg2);
    238:     if (flg1 || flg2) NEPInterpolSetInterpolation(nep,r,i);

    240:   PetscOptionsHeadEnd();

    242:   if (!ctx->pep) NEPInterpolGetPEP(nep,&ctx->pep);
    243:   PEPSetFromOptions(ctx->pep);
    244:   return 0;
    245: }

    247: static PetscErrorCode NEPInterpolSetInterpolation_Interpol(NEP nep,PetscReal tol,PetscInt degree)
    248: {
    249:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

    251:   if (tol == PETSC_DEFAULT) {
    252:     ctx->tol   = PETSC_DEFAULT;
    253:     nep->state = NEP_STATE_INITIAL;
    254:   } else {
    256:     ctx->tol = tol;
    257:   }
    258:   if (degree == PETSC_DEFAULT || degree == PETSC_DECIDE) {
    259:     ctx->maxdeg = 0;
    260:     if (nep->state) NEPReset(nep);
    261:     nep->state = NEP_STATE_INITIAL;
    262:   } else {
    264:     if (ctx->maxdeg != degree) {
    265:       ctx->maxdeg = degree;
    266:       if (nep->state) NEPReset(nep);
    267:       nep->state = NEP_STATE_INITIAL;
    268:     }
    269:   }
    270:   return 0;
    271: }

    273: /*@
    274:    NEPInterpolSetInterpolation - Sets the tolerance and maximum degree when building
    275:    the interpolation polynomial.

    277:    Collective on nep

    279:    Input Parameters:
    280: +  nep - nonlinear eigenvalue solver
    281: .  tol - tolerance to stop computing polynomial coefficients
    282: -  deg - maximum degree of interpolation

    284:    Options Database Key:
    285: +  -nep_interpol_interpolation_tol <tol> - Sets the tolerance to stop computing polynomial coefficients
    286: -  -nep_interpol_interpolation_degree <degree> - Sets the maximum degree of interpolation

    288:    Notes:
    289:    Use PETSC_DEFAULT for either argument to assign a reasonably good value.

    291:    Level: advanced

    293: .seealso: NEPInterpolGetInterpolation()
    294: @*/
    295: PetscErrorCode NEPInterpolSetInterpolation(NEP nep,PetscReal tol,PetscInt deg)
    296: {
    300:   PetscTryMethod(nep,"NEPInterpolSetInterpolation_C",(NEP,PetscReal,PetscInt),(nep,tol,deg));
    301:   return 0;
    302: }

    304: static PetscErrorCode NEPInterpolGetInterpolation_Interpol(NEP nep,PetscReal *tol,PetscInt *deg)
    305: {
    306:   NEP_INTERPOL *ctx = (NEP_INTERPOL*)nep->data;

    308:   if (tol) *tol = ctx->tol;
    309:   if (deg) *deg = ctx->maxdeg;
    310:   return 0;
    311: }

    313: /*@
    314:    NEPInterpolGetInterpolation - Gets the tolerance and maximum degree when building
    315:    the interpolation polynomial.

    317:    Not Collective

    319:    Input Parameter:
    320: .  nep - nonlinear eigenvalue solver

    322:    Output Parameters:
    323: +  tol - tolerance to stop computing polynomial coefficients
    324: -  deg - maximum degree of interpolation

    326:    Level: advanced

    328: .seealso: NEPInterpolSetInterpolation()
    329: @*/
    330: PetscErrorCode NEPInterpolGetInterpolation(NEP nep,PetscReal *tol,PetscInt *deg)
    331: {
    333:   PetscUseMethod(nep,"NEPInterpolGetInterpolation_C",(NEP,PetscReal*,PetscInt*),(nep,tol,deg));
    334:   return 0;
    335: }

    337: static PetscErrorCode NEPInterpolSetPEP_Interpol(NEP nep,PEP pep)
    338: {
    339:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

    341:   PetscObjectReference((PetscObject)pep);
    342:   PEPDestroy(&ctx->pep);
    343:   ctx->pep = pep;
    344:   nep->state = NEP_STATE_INITIAL;
    345:   return 0;
    346: }

    348: /*@
    349:    NEPInterpolSetPEP - Associate a polynomial eigensolver object (PEP) to the
    350:    nonlinear eigenvalue solver.

    352:    Collective on nep

    354:    Input Parameters:
    355: +  nep - nonlinear eigenvalue solver
    356: -  pep - the polynomial eigensolver object

    358:    Level: advanced

    360: .seealso: NEPInterpolGetPEP()
    361: @*/
    362: PetscErrorCode NEPInterpolSetPEP(NEP nep,PEP pep)
    363: {
    367:   PetscTryMethod(nep,"NEPInterpolSetPEP_C",(NEP,PEP),(nep,pep));
    368:   return 0;
    369: }

    371: static PetscErrorCode NEPInterpolGetPEP_Interpol(NEP nep,PEP *pep)
    372: {
    373:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

    375:   if (!ctx->pep) {
    376:     PEPCreate(PetscObjectComm((PetscObject)nep),&ctx->pep);
    377:     PetscObjectIncrementTabLevel((PetscObject)ctx->pep,(PetscObject)nep,1);
    378:     PEPSetOptionsPrefix(ctx->pep,((PetscObject)nep)->prefix);
    379:     PEPAppendOptionsPrefix(ctx->pep,"nep_interpol_");
    380:     PetscObjectSetOptions((PetscObject)ctx->pep,((PetscObject)nep)->options);
    381:     PEPMonitorSet(ctx->pep,PEPMonitor_Interpol,nep,NULL);
    382:   }
    383:   *pep = ctx->pep;
    384:   return 0;
    385: }

    387: /*@
    388:    NEPInterpolGetPEP - Retrieve the polynomial eigensolver object (PEP)
    389:    associated with the nonlinear eigenvalue solver.

    391:    Not Collective

    393:    Input Parameter:
    394: .  nep - nonlinear eigenvalue solver

    396:    Output Parameter:
    397: .  pep - the polynomial eigensolver object

    399:    Level: advanced

    401: .seealso: NEPInterpolSetPEP()
    402: @*/
    403: PetscErrorCode NEPInterpolGetPEP(NEP nep,PEP *pep)
    404: {
    407:   PetscUseMethod(nep,"NEPInterpolGetPEP_C",(NEP,PEP*),(nep,pep));
    408:   return 0;
    409: }

    411: PetscErrorCode NEPView_Interpol(NEP nep,PetscViewer viewer)
    412: {
    413:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;
    414:   PetscBool      isascii;

    416:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    417:   if (isascii) {
    418:     if (!ctx->pep) NEPInterpolGetPEP(nep,&ctx->pep);
    419:     PetscViewerASCIIPrintf(viewer,"  polynomial degree %" PetscInt_FMT ", max=%" PetscInt_FMT "\n",ctx->deg,ctx->maxdeg);
    420:     PetscViewerASCIIPrintf(viewer,"  tolerance for norm of polynomial coefficients %g\n",(double)ctx->tol);
    421:     PetscViewerASCIIPushTab(viewer);
    422:     PEPView(ctx->pep,viewer);
    423:     PetscViewerASCIIPopTab(viewer);
    424:   }
    425:   return 0;
    426: }

    428: PetscErrorCode NEPReset_Interpol(NEP nep)
    429: {
    430:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

    432:   PEPReset(ctx->pep);
    433:   return 0;
    434: }

    436: PetscErrorCode NEPDestroy_Interpol(NEP nep)
    437: {
    438:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

    440:   PEPDestroy(&ctx->pep);
    441:   PetscFree(nep->data);
    442:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetInterpolation_C",NULL);
    443:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetInterpolation_C",NULL);
    444:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetPEP_C",NULL);
    445:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetPEP_C",NULL);
    446:   return 0;
    447: }

    449: SLEPC_EXTERN PetscErrorCode NEPCreate_Interpol(NEP nep)
    450: {
    451:   NEP_INTERPOL   *ctx;

    453:   PetscNew(&ctx);
    454:   nep->data   = (void*)ctx;
    455:   ctx->maxdeg = 5;
    456:   ctx->tol    = PETSC_DEFAULT;

    458:   nep->ops->solve          = NEPSolve_Interpol;
    459:   nep->ops->setup          = NEPSetUp_Interpol;
    460:   nep->ops->setfromoptions = NEPSetFromOptions_Interpol;
    461:   nep->ops->reset          = NEPReset_Interpol;
    462:   nep->ops->destroy        = NEPDestroy_Interpol;
    463:   nep->ops->view           = NEPView_Interpol;

    465:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetInterpolation_C",NEPInterpolSetInterpolation_Interpol);
    466:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetInterpolation_C",NEPInterpolGetInterpolation_Interpol);
    467:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetPEP_C",NEPInterpolSetPEP_Interpol);
    468:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetPEP_C",NEPInterpolGetPEP_Interpol);
    469:   return 0;
    470: }