Date: 2020-01-13T12:01:51+00:00

Actual source code: interpol.c
slepc-3.12.2 2020-01-13
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2019, 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>         /*I "slepcnep.h" I*/
     27: #include <slepc/private/pepimpl.h>         /*I "slepcpep.h" I*/

     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) nep->max_it = PetscMax(5000,2*nep->n/nep->ncv);
     51:   if (nep->fui!=NEP_USER_INTERFACE_SPLIT) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"NEPINTERPOL only available for split operator");
     52:   if (nep->stopping!=NEPStoppingBasic) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"This solver does not support user-defined stopping test");

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

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

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

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

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

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

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

    164:   PEPSetOperators(ctx->pep,deg+1,A);
    165:   for (k=0;k<=deg;k++) {
    166:     MatDestroy(&A[k]);
    167:   }
    168:   PetscFree5(A,cs,x,fx,matnorm);

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

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

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

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

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

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

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

    245:   PetscOptionsTail();

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

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

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

    280: /*@
    281:    NEPInterpolSetInterpolation - Sets the tolerance and maximum degree when building
    282:    the interpolation polynomial.

    284:    Collective on nep

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

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

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

    298:    Level: advanced

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

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

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

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

    324: /*@
    325:    NEPInterpolGetInterpolation - Gets the tolerance and maximum degree when building
    326:    the interpolation polynomial.

    328:    Not Collective

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

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

    337:    Level: advanced

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

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

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

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

    365: /*@
    366:    NEPInterpolSetPEP - Associate a polynomial eigensolver object (PEP) to the
    367:    nonlinear eigenvalue solver.

    369:    Collective on nep

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

    375:    Level: advanced

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

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

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

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

    410: /*@
    411:    NEPInterpolGetPEP - Retrieve the polynomial eigensolver object (PEP)
    412:    associated with the nonlinear eigenvalue solver.

    414:    Not Collective

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

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

    422:    Level: advanced

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

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

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

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

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

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

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

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

    481: SLEPC_EXTERN PetscErrorCode NEPCreate_Interpol(NEP nep)
    482: {
    484:   NEP_INTERPOL   *ctx;

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

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

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