Date: 2016-03-29T14:59:21+00:00

Actual source code: interpol.c
slepc-3.6.3 2016-03-29
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      1: /*

      3:    SLEPc nonlinear eigensolver: "interpol"

      5:    Method: Polynomial interpolation

      7:    Algorithm:

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

     12:    References:

     14:        [1] C. Effenberger and D. Kresser, "Chebyshev interpolation for
     15:            nonlinear eigenvalue problems", BIT 52:933-951, 2012.

     17:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     18:    SLEPc - Scalable Library for Eigenvalue Problem Computations
     19:    Copyright (c) 2002-2015, Universitat Politecnica de Valencia, Spain

     21:    This file is part of SLEPc.

     23:    SLEPc is free software: you can redistribute it and/or modify it under  the
     24:    terms of version 3 of the GNU Lesser General Public License as published by
     25:    the Free Software Foundation.

     27:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     28:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     29:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     30:    more details.

     32:    You  should have received a copy of the GNU Lesser General  Public  License
     33:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     34:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     35: */

     37: #include <slepc/private/nepimpl.h>         /*I "slepcnep.h" I*/
     38: #include <slepc/private/pepimpl.h>

     40: typedef struct {
     41:   PEP       pep;
     42:   PetscInt  deg;
     43: } NEP_INTERPOL;

     47: PetscErrorCode NEPSetUp_Interpol(NEP nep)
     48: {
     50:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;
     51:   ST             st;
     52:   RG             rg;
     53:   PetscReal      a,b,c,d,s,tol;
     54:   PetscScalar    zero=0.0;
     55:   PetscBool      flg,istrivial;
     56:   PetscInt       its,in;

     59:   if (nep->ncv) { /* ncv set */
     60:     if (nep->ncv<nep->nev) SETERRQ(PetscObjectComm((PetscObject)nep),1,"The value of ncv must be at least nev");
     61:   } else if (nep->mpd) { /* mpd set */
     62:     nep->ncv = PetscMin(nep->n,nep->nev+nep->mpd);
     63:   } else { /* neither set: defaults depend on nev being small or large */
     64:     if (nep->nev<500) nep->ncv = PetscMin(nep->n,PetscMax(2*nep->nev,nep->nev+15));
     65:     else {
     66:       nep->mpd = 500;
     67:       nep->ncv = PetscMin(nep->n,nep->nev+nep->mpd);
     68:     }
     69:   }
     70:   if (!nep->mpd) nep->mpd = nep->ncv;
     71:   if (nep->ncv>nep->nev+nep->mpd) SETERRQ(PetscObjectComm((PetscObject)nep),1,"The value of ncv must not be larger than nev+mpd");
     72:   if (!nep->max_it) nep->max_it = PetscMax(5000,2*nep->n/nep->ncv);
     73:   if (!nep->max_funcs) nep->max_funcs = nep->max_it;
     74:   if (!nep->split) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"NEPINTERPOL only available for split operator");

     76:   /* transfer PEP options */
     77:   if (!ctx->pep) { NEPInterpolGetPEP(nep,&ctx->pep); }
     78:   PEPSetBV(ctx->pep,nep->V);
     79:   PEPSetBasis(ctx->pep,PEP_BASIS_CHEBYSHEV1);
     80:   PEPSetWhichEigenpairs(ctx->pep,PEP_TARGET_MAGNITUDE);
     81:   PEPGetST(ctx->pep,&st);
     82:   STSetType(st,STSINVERT);
     83:   PEPSetDimensions(ctx->pep,nep->nev,nep->ncv?nep->ncv:PETSC_DEFAULT,nep->mpd?nep->mpd:PETSC_DEFAULT);
     84:   tol=ctx->pep->tol;
     85:   if (tol==PETSC_DEFAULT) tol = (nep->rtol==PETSC_DEFAULT)?SLEPC_DEFAULT_TOL/10.0:nep->rtol/10.0;
     86:   its=ctx->pep->max_it;
     87:   if (!its) its = nep->max_it?nep->max_it:PETSC_DEFAULT;
     88:   PEPSetTolerances(ctx->pep,tol,its);

     90:   /* transfer region options */
     91:   RGIsTrivial(nep->rg,&istrivial);
     92:   if (istrivial) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"NEPINTERPOL requires a nontrivial region");
     93:   PetscObjectTypeCompare((PetscObject)nep->rg,RGINTERVAL,&flg);
     94:   if (!flg) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"Only implemented for interval regions");
     95:   RGIntervalGetEndpoints(nep->rg,&a,&b,&c,&d);
     96:   if (a<=-PETSC_MAX_REAL || b>=PETSC_MAX_REAL) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"Only implemented for bounded intervals");
     97:   PEPGetRG(ctx->pep,&rg);
     98:   RGSetType(rg,RGINTERVAL);
     99:   if (a==b) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"Only implemented for intervals on the real axis");
    100:   s = 2.0/(b-a);
    101:   c = (c==0)? -PETSC_MAX_REAL: c*s;
    102:   d = (d==0)? PETSC_MAX_REAL: d*s;
    103:   RGIntervalSetEndpoints(rg,-1.0,1.0,c,d);
    104:   RGCheckInside(nep->rg,1,&nep->target,&zero,&in);
    105:   if (in<0) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"The target is not inside the target set");
    106:   PEPSetTarget(ctx->pep,(nep->target-(a+b)/2)*s);

    108:   NEPAllocateSolution(nep,0);
    109:   return(0);
    110: }

    114: /*
    115:   Input:
    116:     d, number of nodes to compute
    117:     a,b, interval extrems
    118:   Output:
    119:     *x, array containing the d Chebyshev nodes of the interval [a,b]
    120:     *dct2, coefficients to compute a discrete cosine transformation (DCT-II)
    121: */
    122: static PetscErrorCode ChebyshevNodes(PetscInt d,PetscReal a,PetscReal b,PetscScalar *x,PetscReal *dct2)
    123: {
    124:   PetscInt  j,i;
    125:   PetscReal t;

    128:   for (j=0;j<d+1;j++) {
    129:     t = ((2*j+1)*PETSC_PI)/(2*(d+1));
    130:     x[j] = (a+b)/2.0+((b-a)/2.0)*PetscCosReal(t);
    131:     for (i=0;i<d+1;i++) dct2[j*(d+1)+i] = PetscCosReal(i*t);
    132:   }
    133:   return(0);
    134: }

    138: PetscErrorCode NEPSolve_Interpol(NEP nep)
    139: {
    141:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;
    142:   Mat            *A;   /*T=nep->function,Tp=nep->jacobian;*/
    143:   PetscScalar    *x,*fx,t;
    144:   PetscReal      *cs,a,b,s;
    145:   PetscInt       i,j,k,deg=ctx->deg;

    148:   PetscMalloc4(deg+1,&A,(deg+1)*(deg+1),&cs,deg+1,&x,(deg+1)*nep->nt,&fx);
    149:   RGIntervalGetEndpoints(nep->rg,&a,&b,NULL,NULL);
    150:   ChebyshevNodes(deg,a,b,x,cs);
    151:   for (j=0;j<nep->nt;j++) {
    152:     for (i=0;i<=deg;i++) {
    153:       FNEvaluateFunction(nep->f[j],x[i],&fx[i+j*(deg+1)]);
    154:     }
    155:   }

    157:   /* Polynomial coefficients */
    158:   for (k=0;k<=deg;k++) {
    159:     MatDuplicate(nep->A[0],MAT_COPY_VALUES,&A[k]);
    160:     t = 0.0;
    161:     for (i=0;i<deg+1;i++) t += fx[i]*cs[i*(deg+1)+k];
    162:     t *= 2.0/(deg+1);
    163:     if (k==0) t /= 2.0;
    164:     MatScale(A[k],t);
    165:     for (j=1;j<nep->nt;j++) {
    166:       t = 0.0;
    167:       for (i=0;i<deg+1;i++) t += fx[i+j*(deg+1)]*cs[i*(deg+1)+k];
    168:       t *= 2.0/(deg+1);
    169:       if (k==0) t /= 2.0;
    170:       MatAXPY(A[k],t,nep->A[j],SUBSET_NONZERO_PATTERN);
    171:     }
    172:   }

    174:   PEPSetOperators(ctx->pep,deg+1,A);
    175:   for (k=0;k<=deg;k++) {
    176:     MatDestroy(&A[k]);
    177:   }
    178:   PetscFree4(A,cs,x,fx);

    180:   /* Solve polynomial eigenproblem */
    181:   PEPSolve(ctx->pep);
    182:   PEPGetConverged(ctx->pep,&nep->nconv);
    183:   PEPGetIterationNumber(ctx->pep,&nep->its);
    184:   PEPGetConvergedReason(ctx->pep,(PEPConvergedReason*)&nep->reason);
    185:   s = 2.0/(b-a);
    186:   for (i=0;i<nep->nconv;i++) {
    187:     PEPGetEigenpair(ctx->pep,i,&nep->eigr[i],&nep->eigi[i],NULL,NULL);
    188:     nep->eigr[i] /= s;
    189:     nep->eigr[i] += (a+b)/2.0;
    190:     nep->eigi[i] /= s;
    191:   }
    192:   nep->state = NEP_STATE_EIGENVECTORS;
    193:   return(0);
    194: }

    198: PetscErrorCode NEPSetFromOptions_Interpol(PetscOptions *PetscOptionsObject,NEP nep)
    199: {
    201:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

    204:   if (!ctx->pep) { NEPInterpolGetPEP(nep,&ctx->pep); }
    205:   PEPSetFromOptions(ctx->pep);
    206:   PetscOptionsHead(PetscOptionsObject,"NEP Interpol Options");
    207:   PetscOptionsInt("-nep_interpol_degree","Degree of interpolation polynomial","NEPInterpolSetDegree",ctx->deg,&ctx->deg,NULL);
    208:   PetscOptionsTail();
    209:   return(0);
    210: }

    214: static PetscErrorCode NEPInterpolSetDegree_Interpol(NEP nep,PetscInt deg)
    215: {
    216:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

    219:   ctx->deg = deg;
    220:   return(0);
    221: }

    225: /*@
    226:    NEPInterpolSetDegree - Sets the degree of the interpolation polynomial.

    228:    Collective on NEP

    230:    Input Parameters:
    231: +  nep - nonlinear eigenvalue solver
    232: -  deg - polynomial degree

    234:    Level: advanced

    236: .seealso: NEPInterpolGetDegree()
    237: @*/
    238: PetscErrorCode NEPInterpolSetDegree(NEP nep,PetscInt deg)
    239: {

    245:   PetscTryMethod(nep,"NEPInterpolSetDegree_C",(NEP,PetscInt),(nep,deg));
    246:   return(0);
    247: }

    251: static PetscErrorCode NEPInterpolGetDegree_Interpol(NEP nep,PetscInt *deg)
    252: {
    253:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

    256:   *deg = ctx->deg;
    257:   return(0);
    258: }

    262: /*@
    263:    NEPInterpolGetDegree - Gets the degree of the interpolation polynomial.

    265:    Not Collective

    267:    Input Parameter:
    268: .  nep - nonlinear eigenvalue solver

    270:    Output Parameter:
    271: .  pep - the polynomial degree

    273:    Level: advanced

    275: .seealso: NEPInterpolSetDegree()
    276: @*/
    277: PetscErrorCode NEPInterpolGetDegree(NEP nep,PetscInt *deg)
    278: {

    284:   PetscTryMethod(nep,"NEPInterpolGetDegree_C",(NEP,PetscInt*),(nep,deg));
    285:   return(0);
    286: }

    290: static PetscErrorCode NEPInterpolSetPEP_Interpol(NEP nep,PEP pep)
    291: {
    293:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

    296:   PetscObjectReference((PetscObject)pep);
    297:   PEPDestroy(&ctx->pep);
    298:   ctx->pep = pep;
    299:   PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->pep);
    300:   nep->state = NEP_STATE_INITIAL;
    301:   return(0);
    302: }

    306: /*@
    307:    NEPInterpolSetPEP - Associate a polynomial eigensolver object (PEP) to the
    308:    nonlinear eigenvalue solver.

    310:    Collective on NEP

    312:    Input Parameters:
    313: +  nep - nonlinear eigenvalue solver
    314: -  pep - the polynomial eigensolver object

    316:    Level: advanced

    318: .seealso: NEPInterpolGetPEP()
    319: @*/
    320: PetscErrorCode NEPInterpolSetPEP(NEP nep,PEP pep)
    321: {

    328:   PetscTryMethod(nep,"NEPInterpolSetPEP_C",(NEP,PEP),(nep,pep));
    329:   return(0);
    330: }

    334: static PetscErrorCode NEPInterpolGetPEP_Interpol(NEP nep,PEP *pep)
    335: {
    337:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;
    338:   ST             st;

    341:   if (!ctx->pep) {
    342:     PEPCreate(PetscObjectComm((PetscObject)nep),&ctx->pep);
    343:     PEPSetOptionsPrefix(ctx->pep,((PetscObject)nep)->prefix);
    344:     PEPAppendOptionsPrefix(ctx->pep,"nep_");
    345:     PEPGetST(ctx->pep,&st);
    346:     STSetOptionsPrefix(st,((PetscObject)ctx->pep)->prefix);
    347:     PetscObjectIncrementTabLevel((PetscObject)ctx->pep,(PetscObject)nep,1);
    348:     PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->pep);
    349:   }
    350:   *pep = ctx->pep;
    351:   return(0);
    352: }

    356: /*@
    357:    NEPInterpolGetPEP - Retrieve the polynomial eigensolver object (PEP)
    358:    associated with the nonlinear eigenvalue solver.

    360:    Not Collective

    362:    Input Parameter:
    363: .  nep - nonlinear eigenvalue solver

    365:    Output Parameter:
    366: .  pep - the polynomial eigensolver object

    368:    Level: advanced

    370: .seealso: NEPInterpolSetPEP()
    371: @*/
    372: PetscErrorCode NEPInterpolGetPEP(NEP nep,PEP *pep)
    373: {

    379:   PetscTryMethod(nep,"NEPInterpolGetPEP_C",(NEP,PEP*),(nep,pep));
    380:   return(0);
    381: }

    385: PetscErrorCode NEPView_Interpol(NEP nep,PetscViewer viewer)
    386: {
    388:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

    391:   if (!ctx->pep) { NEPInterpolGetPEP(nep,&ctx->pep); }
    392:   PetscViewerASCIIPrintf(viewer,"  Interpol: polynomial degree %D\n",ctx->deg);
    393:   PetscViewerASCIIPushTab(viewer);
    394:   PEPView(ctx->pep,viewer);
    395:   PetscViewerASCIIPopTab(viewer);
    396:   return(0);
    397: }

    401: PetscErrorCode NEPReset_Interpol(NEP nep)
    402: {
    404:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

    407:   if (!ctx->pep) { PEPReset(ctx->pep); }
    408:   return(0);
    409: }

    413: PetscErrorCode NEPDestroy_Interpol(NEP nep)
    414: {
    416:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

    419:   PEPDestroy(&ctx->pep);
    420:   PetscFree(nep->data);
    421:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetDegree_C",NULL);
    422:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetDegree_C",NULL);
    423:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetPEP_C",NULL);
    424:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetPEP_C",NULL);
    425:   return(0);
    426: }

    430: PETSC_EXTERN PetscErrorCode NEPCreate_Interpol(NEP nep)
    431: {
    433:   NEP_INTERPOL   *ctx;

    436:   PetscNewLog(nep,&ctx);
    437:   ctx->deg  = 5;
    438:   nep->data = (void*)ctx;

    440:   nep->ops->solve          = NEPSolve_Interpol;
    441:   nep->ops->setup          = NEPSetUp_Interpol;
    442:   nep->ops->setfromoptions = NEPSetFromOptions_Interpol;
    443:   nep->ops->reset          = NEPReset_Interpol;
    444:   nep->ops->destroy        = NEPDestroy_Interpol;
    445:   nep->ops->view           = NEPView_Interpol;
    446:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetDegree_C",NEPInterpolSetDegree_Interpol);
    447:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetDegree_C",NEPInterpolGetDegree_Interpol);
    448:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetPEP_C",NEPInterpolSetPEP_Interpol);
    449:   PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetPEP_C",NEPInterpolGetPEP_Interpol);
    450:   return(0);
    451: }