Date: 2021-02-01T14:42:16+00:00

Actual source code: interpol.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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>
     27: #include <slepc/private/pepimpl.h>

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

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

     48:   NEPSetDimensions_Default(nep,nep->nev,&nep->ncv,&nep->mpd);
     49:   if (nep->ncv>nep->nev+nep->mpd) SETERRQ(PetscObjectComm((PetscObject)nep),1,"The value of ncv must not be larger than nev+mpd");
     50:   if (nep->max_it==PETSC_DEFAULT) nep->max_it = PetscMax(5000,2*nep->n/nep->ncv);
     51:   if (!nep->which) nep->which = NEP_TARGET_MAGNITUDE;
     52:   if (nep->which!=NEP_TARGET_MAGNITUDE) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"This solver supports only target magnitude eigenvalues");
     53:   NEPCheckUnsupported(nep,NEP_FEATURE_CALLBACK | NEP_FEATURE_STOPPING | NEP_FEATURE_TWOSIDED);

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

     73:   /* transfer region options */
     74:   RGIsTrivial(nep->rg,&istrivial);
     75:   if (istrivial) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"NEPINTERPOL requires a nontrivial region");
     76:   PetscObjectTypeCompare((PetscObject)nep->rg,RGINTERVAL,&flg);
     77:   if (!flg) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"Only implemented for interval regions");
     78:   RGIntervalGetEndpoints(nep->rg,&a,&b,&c,&d);
     79:   if (a<=-PETSC_MAX_REAL || b>=PETSC_MAX_REAL) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"Only implemented for bounded intervals");
     80:   PEPGetRG(ctx->pep,&rg);
     81:   RGSetType(rg,RGINTERVAL);
     82:   if (a==b) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"Only implemented for intervals on the real axis");
     83:   s = 2.0/(b-a);
     84:   c = c*s;
     85:   d = d*s;
     86:   RGIntervalSetEndpoints(rg,-1.0,1.0,c,d);
     87:   RGCheckInside(nep->rg,1,&nep->target,&zero,&in);
     88:   if (in<0) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"The target is not inside the target set");
     89:   PEPSetTarget(ctx->pep,(nep->target-(a+b)/2)*s);

     91:   NEPAllocateSolution(nep,0);
     92:   return(0);
     93: }

     95: /*
     96:   Input:
     97:     d, number of nodes to compute
     98:     a,b, interval extrems
     99:   Output:
    100:     *x, array containing the d Chebyshev nodes of the interval [a,b]
    101:     *dct2, coefficients to compute a discrete cosine transformation (DCT-II)
    102: */
    103: static PetscErrorCode ChebyshevNodes(PetscInt d,PetscReal a,PetscReal b,PetscScalar *x,PetscReal *dct2)
    104: {
    105:   PetscInt  j,i;
    106:   PetscReal t;

    109:   for (j=0;j<d+1;j++) {
    110:     t = ((2*j+1)*PETSC_PI)/(2*(d+1));
    111:     x[j] = (a+b)/2.0+((b-a)/2.0)*PetscCosReal(t);
    112:     for (i=0;i<d+1;i++) dct2[j*(d+1)+i] = PetscCosReal(i*t);
    113:   }
    114:   return(0);
    115: }

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

    129:   PetscMalloc5(deg+1,&A,(deg+1)*(deg+1),&cs,deg+1,&x,(deg+1)*nep->nt,&fx,nep->nt,&matnorm);
    130:   for  (j=0;j<nep->nt;j++) {
    131:     MatHasOperation(nep->A[j],MATOP_NORM,&hasmnorm);
    132:     if (!hasmnorm) break;
    133:     MatNorm(nep->A[j],NORM_INFINITY,matnorm+j);
    134:   }
    135:   if (!hasmnorm) for (j=0;j<nep->nt;j++) matnorm[j] = 1.0;
    136:   RGIntervalGetEndpoints(nep->rg,&a,&b,NULL,NULL);
    137:   ChebyshevNodes(deg,a,b,x,cs);
    138:   for (j=0;j<nep->nt;j++) {
    139:     for (i=0;i<=deg;i++) {
    140:       FNEvaluateFunction(nep->f[j],x[i],&fx[i+j*(deg+1)]);
    141:     }
    142:   }
    143:   /* Polynomial coefficients */
    144:   ctx->deg = deg;
    145:   for (k=0;k<=deg;k++) {
    146:     MatDuplicate(nep->A[0],MAT_COPY_VALUES,&A[k]);
    147:     t = 0.0;
    148:     for (i=0;i<deg+1;i++) t += fx[i]*cs[i*(deg+1)+k];
    149:     t *= 2.0/(deg+1);
    150:     if (k==0) t /= 2.0;
    151:     aprox = matnorm[0]*PetscAbsScalar(t);
    152:     MatScale(A[k],t);
    153:     for (j=1;j<nep->nt;j++) {
    154:       t = 0.0;
    155:       for (i=0;i<deg+1;i++) t += fx[i+j*(deg+1)]*cs[i*(deg+1)+k];
    156:       t *= 2.0/(deg+1);
    157:       if (k==0) t /= 2.0;
    158:       aprox += matnorm[j]*PetscAbsScalar(t);
    159:       MatAXPY(A[k],t,nep->A[j],nep->mstr);
    160:     }
    161:     if (k==0) aprox0 = aprox;
    162:     if (k>1 && aprox/aprox0<ctx->tol) { ctx->deg = k; deg = k; break; }
    163:   }

    165:   PEPSetOperators(ctx->pep,deg+1,A);
    166:   for (k=0;k<=deg;k++) {
    167:     MatDestroy(&A[k]);
    168:   }
    169:   PetscFree5(A,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) {
    190:       BVInsertVec(nep->V,++i,vi);
    191:     }
    192: #endif
    193:   }
    194:   VecDestroy(&vr);
    195:   VecDestroy(&vi);

    197:   nep->state = NEP_STATE_EIGENVECTORS;
    198:   return(0);
    199: }

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

    210:   n = PetscMin(nest,nep->ncv);
    211:   for (i=0;i<n;i++) {
    212:     nep->eigr[i]   = eigr[i];
    213:     nep->eigi[i]   = eigi[i];
    214:     nep->errest[i] = errest[i];
    215:   }
    216:   PEPGetST(pep,&st);
    217:   STBackTransform(st,n,nep->eigr,nep->eigi);
    218:   RGIntervalGetEndpoints(nep->rg,&a,&b,NULL,NULL);
    219:   s = 2.0/(b-a);
    220:   for (i=0;i<n;i++) {
    221:     nep->eigr[i] /= s;
    222:     nep->eigr[i] += (a+b)/2.0;
    223:     nep->eigi[i] /= s;
    224:   }
    225:   NEPMonitor(nep,its,nconv,nep->eigr,nep->eigi,nep->errest,nest);
    226:   return(0);
    227: }

    229: PetscErrorCode NEPSetFromOptions_Interpol(PetscOptionItems *PetscOptionsObject,NEP nep)
    230: {
    232:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;
    233:   PetscInt       i;
    234:   PetscBool      flg1,flg2;
    235:   PetscReal      r;

    238:   PetscOptionsHead(PetscOptionsObject,"NEP Interpol Options");

    240:     NEPInterpolGetInterpolation(nep,&r,&i);
    241:     if (!i) i = PETSC_DEFAULT;
    242:     PetscOptionsInt("-nep_interpol_interpolation_degree","Maximum degree of polynomial interpolation","NEPInterpolSetInterpolation",i,&i,&flg1);
    243:     PetscOptionsReal("-nep_interpol_interpolation_tol","Tolerance for interpolation coefficients","NEPInterpolSetInterpolation",r,&r,&flg2);
    244:     if (flg1 || flg2) { NEPInterpolSetInterpolation(nep,r,i); }

    246:   PetscOptionsTail();

    248:   if (!ctx->pep) { NEPInterpolGetPEP(nep,&ctx->pep); }
    249:   PEPSetFromOptions(ctx->pep);
    250:   return(0);
    251: }

    253: static PetscErrorCode NEPInterpolSetInterpolation_Interpol(NEP nep,PetscReal tol,PetscInt degree)
    254: {
    256:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

    259:   if (tol == PETSC_DEFAULT) {
    260:     ctx->tol   = PETSC_DEFAULT;
    261:     nep->state = NEP_STATE_INITIAL;
    262:   } else {
    263:     if (tol <= 0.0) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of tol. Must be > 0");
    264:     ctx->tol = tol;
    265:   }
    266:   if (degree == PETSC_DEFAULT || degree == PETSC_DECIDE) {
    267:     ctx->maxdeg = 0;
    268:     if (nep->state) { NEPReset(nep); }
    269:     nep->state = NEP_STATE_INITIAL;
    270:   } else {
    271:     if (degree <= 0) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of degree. Must be > 0");
    272:     if (ctx->maxdeg != degree) {
    273:       ctx->maxdeg = degree;
    274:       if (nep->state) { NEPReset(nep); }
    275:       nep->state = NEP_STATE_INITIAL;
    276:     }
    277:   }
    278:   return(0);
    279: }

    281: /*@
    282:    NEPInterpolSetInterpolation - Sets the tolerance and maximum degree when building
    283:    the interpolation polynomial.

    285:    Collective on nep

    287:    Input Parameters:
    288: +  nep - nonlinear eigenvalue solver
    289: .  tol - tolerance to stop computing polynomial coefficients
    290: -  deg - maximum degree of interpolation

    292:    Options Database Key:
    293: +  -nep_interpol_interpolation_tol <tol> - Sets the tolerance to stop computing polynomial coefficients
    294: -  -nep_interpol_interpolation_degree <degree> - Sets the maximum degree of interpolation

    296:    Notes:
    297:    Use PETSC_DEFAULT for either argument to assign a reasonably good value.

    299:    Level: advanced

    301: .seealso: NEPInterpolGetInterpolation()
    302: @*/
    303: PetscErrorCode NEPInterpolSetInterpolation(NEP nep,PetscReal tol,PetscInt deg)
    304: {

    311:   PetscTryMethod(nep,"NEPInterpolSetInterpolation_C",(NEP,PetscReal,PetscInt),(nep,tol,deg));
    312:   return(0);
    313: }

    315: static PetscErrorCode NEPInterpolGetInterpolation_Interpol(NEP nep,PetscReal *tol,PetscInt *deg)
    316: {
    317:   NEP_INTERPOL *ctx = (NEP_INTERPOL*)nep->data;

    320:   if (tol) *tol = ctx->tol;
    321:   if (deg) *deg = ctx->maxdeg;
    322:   return(0);
    323: }

    325: /*@
    326:    NEPInterpolGetInterpolation - Gets the tolerance and maximum degree when building
    327:    the interpolation polynomial.

    329:    Not Collective

    331:    Input Parameter:
    332: .  nep - nonlinear eigenvalue solver

    334:    Output Parameter:
    335: +  tol - tolerance to stop computing polynomial coefficients
    336: -  deg - maximum degree of interpolation

    338:    Level: advanced

    340: .seealso: NEPInterpolSetInterpolation()
    341: @*/
    342: PetscErrorCode NEPInterpolGetInterpolation(NEP nep,PetscReal *tol,PetscInt *deg)
    343: {

    348:   PetscUseMethod(nep,"NEPInterpolGetInterpolation_C",(NEP,PetscReal*,PetscInt*),(nep,tol,deg));
    349:   return(0);
    350: }

    352: static PetscErrorCode NEPInterpolSetPEP_Interpol(NEP nep,PEP pep)
    353: {
    355:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

    358:   PetscObjectReference((PetscObject)pep);
    359:   PEPDestroy(&ctx->pep);
    360:   ctx->pep = pep;
    361:   PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->pep);
    362:   nep->state = NEP_STATE_INITIAL;
    363:   return(0);
    364: }

    366: /*@
    367:    NEPInterpolSetPEP - Associate a polynomial eigensolver object (PEP) to the
    368:    nonlinear eigenvalue solver.

    370:    Collective on nep

    372:    Input Parameters:
    373: +  nep - nonlinear eigenvalue solver
    374: -  pep - the polynomial eigensolver object

    376:    Level: advanced

    378: .seealso: NEPInterpolGetPEP()
    379: @*/
    380: PetscErrorCode NEPInterpolSetPEP(NEP nep,PEP pep)
    381: {

    388:   PetscTryMethod(nep,"NEPInterpolSetPEP_C",(NEP,PEP),(nep,pep));
    389:   return(0);
    390: }

    392: static PetscErrorCode NEPInterpolGetPEP_Interpol(NEP nep,PEP *pep)
    393: {
    395:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

    398:   if (!ctx->pep) {
    399:     PEPCreate(PetscObjectComm((PetscObject)nep),&ctx->pep);
    400:     PetscObjectIncrementTabLevel((PetscObject)ctx->pep,(PetscObject)nep,1);
    401:     PEPSetOptionsPrefix(ctx->pep,((PetscObject)nep)->prefix);
    402:     PEPAppendOptionsPrefix(ctx->pep,"nep_interpol_");
    403:     PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->pep);
    404:     PetscObjectSetOptions((PetscObject)ctx->pep,((PetscObject)nep)->options);
    405:     PEPMonitorSet(ctx->pep,PEPMonitor_Interpol,nep,NULL);
    406:   }
    407:   *pep = ctx->pep;
    408:   return(0);
    409: }

    411: /*@
    412:    NEPInterpolGetPEP - Retrieve the polynomial eigensolver object (PEP)
    413:    associated with the nonlinear eigenvalue solver.

    415:    Not Collective

    417:    Input Parameter:
    418: .  nep - nonlinear eigenvalue solver

    420:    Output Parameter:
    421: .  pep - the polynomial eigensolver object

    423:    Level: advanced

    425: .seealso: NEPInterpolSetPEP()
    426: @*/
    427: PetscErrorCode NEPInterpolGetPEP(NEP nep,PEP *pep)
    428: {

    434:   PetscUseMethod(nep,"NEPInterpolGetPEP_C",(NEP,PEP*),(nep,pep));
    435:   return(0);
    436: }

    438: PetscErrorCode NEPView_Interpol(NEP nep,PetscViewer viewer)
    439: {
    441:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;
    442:   PetscBool      isascii;

    445:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    446:   if (isascii) {
    447:     if (!ctx->pep) { NEPInterpolGetPEP(nep,&ctx->pep); }
    448:     PetscViewerASCIIPrintf(viewer,"  polynomial degree %D, max=%D\n",ctx->deg,ctx->maxdeg);
    449:     PetscViewerASCIIPrintf(viewer,"  tolerance for norm of polynomial coefficients %g\n",ctx->tol);
    450:     PetscViewerASCIIPushTab(viewer);
    451:     PEPView(ctx->pep,viewer);
    452:     PetscViewerASCIIPopTab(viewer);
    453:   }
    454:   return(0);
    455: }

    457: PetscErrorCode NEPReset_Interpol(NEP nep)
    458: {
    460:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

    463:   PEPReset(ctx->pep);
    464:   return(0);
    465: }

    467: PetscErrorCode NEPDestroy_Interpol(NEP nep)
    468: {
    470:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

    473:   PEPDestroy(&ctx->pep);
    474:   PetscFree(nep->data);
    475:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetInterpolation_C",NULL);
    476:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetInterpolation_C",NULL);
    477:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetPEP_C",NULL);
    478:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetPEP_C",NULL);
    479:   return(0);
    480: }

    482: SLEPC_EXTERN PetscErrorCode NEPCreate_Interpol(NEP nep)
    483: {
    485:   NEP_INTERPOL   *ctx;

    488:   PetscNewLog(nep,&ctx);
    489:   nep->data   = (void*)ctx;
    490:   ctx->maxdeg = 5;
    491:   ctx->tol    = PETSC_DEFAULT;

    493:   nep->ops->solve          = NEPSolve_Interpol;
    494:   nep->ops->setup          = NEPSetUp_Interpol;
    495:   nep->ops->setfromoptions = NEPSetFromOptions_Interpol;
    496:   nep->ops->reset          = NEPReset_Interpol;
    497:   nep->ops->destroy        = NEPDestroy_Interpol;
    498:   nep->ops->view           = NEPView_Interpol;

    500:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetInterpolation_C",NEPInterpolSetInterpolation_Interpol);
    501:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetInterpolation_C",NEPInterpolGetInterpolation_Interpol);
    502:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetPEP_C",NEPInterpolSetPEP_Interpol);
    503:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetPEP_C",NEPInterpolGetPEP_Interpol);
    504:   return(0);
    505: }