Actual source code: interpol.c

slepc-3.20.1 2023-11-27
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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: static 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:   PetscFunctionBegin;
 46:   PetscCall(NEPSetDimensions_Default(nep,nep->nev,&nep->ncv,&nep->mpd));
 47:   PetscCheck(nep->ncv<=nep->nev+nep->mpd,PetscObjectComm((PetscObject)nep),PETSC_ERR_USER_INPUT,"The value of ncv must not be larger than nev+mpd");
 48:   if (nep->max_it==PETSC_DEFAULT) nep->max_it = PetscMax(5000,2*nep->n/nep->ncv);
 49:   if (!nep->which) nep->which = NEP_TARGET_MAGNITUDE;
 50:   PetscCheck(nep->which==NEP_TARGET_MAGNITUDE,PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"This solver supports only target magnitude eigenvalues");
 51:   NEPCheckUnsupported(nep,NEP_FEATURE_CALLBACK | NEP_FEATURE_STOPPING | NEP_FEATURE_TWOSIDED);

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

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

 89:   PetscCall(NEPAllocateSolution(nep,0));
 90:   PetscFunctionReturn(PETSC_SUCCESS);
 91: }

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

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

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

126:   PetscFunctionBegin;
127:   PetscCall(PetscMalloc4((deg+1)*(deg+1),&cs,deg+1,&x,(deg+1)*nep->nt,&fx,nep->nt,&matnorm));
128:   for  (j=0;j<nep->nt;j++) {
129:     PetscCall(MatHasOperation(nep->A[j],MATOP_NORM,&hasmnorm));
130:     if (!hasmnorm) break;
131:     PetscCall(MatNorm(nep->A[j],NORM_INFINITY,matnorm+j));
132:   }
133:   if (!hasmnorm) for (j=0;j<nep->nt;j++) matnorm[j] = 1.0;
134:   PetscCall(RGIntervalGetEndpoints(nep->rg,&a,&b,NULL,NULL));
135:   PetscCall(ChebyshevNodes(deg,a,b,x,cs));
136:   for (j=0;j<nep->nt;j++) {
137:     for (i=0;i<=deg;i++) PetscCall(FNEvaluateFunction(nep->f[j],x[i],&fx[i+j*(deg+1)]));
138:   }
139:   /* Polynomial coefficients */
140:   PetscCall(PetscMalloc1(deg+1,&A));
141:   if (nep->P) PetscCall(PetscMalloc1(deg+1,&P));
142:   ctx->deg = deg;
143:   for (k=0;k<=deg;k++) {
144:     PetscCall(MatDuplicate(nep->A[0],MAT_COPY_VALUES,&A[k]));
145:     if (nep->P) PetscCall(MatDuplicate(nep->P[0],MAT_COPY_VALUES,&P[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:     PetscCall(MatScale(A[k],t));
152:     if (nep->P) PetscCall(MatScale(P[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:       PetscCall(MatAXPY(A[k],t,nep->A[j],nep->mstr));
160:       if (nep->P) PetscCall(MatAXPY(P[k],t,nep->P[j],nep->mstrp));
161:     }
162:     if (k==0) aprox0 = aprox;
163:     if (k>1 && aprox/aprox0<ctx->tol) { ctx->deg = k; deg = k; break; }
164:   }
165:   PetscCall(PEPSetOperators(ctx->pep,deg+1,A));
166:   PetscCall(MatDestroyMatrices(deg+1,&A));
167:   if (nep->P) {
168:     PetscCall(PEPGetST(ctx->pep,&st));
169:     PetscCall(STSetSplitPreconditioner(st,deg+1,P,nep->mstrp));
170:     PetscCall(MatDestroyMatrices(deg+1,&P));
171:   }
172:   PetscCall(PetscFree4(cs,x,fx,matnorm));

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

198:   nep->state = NEP_STATE_EIGENVECTORS;
199:   PetscFunctionReturn(PETSC_SUCCESS);
200: }

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

209:   PetscFunctionBegin;
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:   PetscCall(PEPGetST(pep,&st));
217:   PetscCall(STBackTransform(st,n,nep->eigr,nep->eigi));
218:   PetscCall(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:   PetscCall(NEPMonitor(nep,its,nconv,nep->eigr,nep->eigi,nep->errest,nest));
226:   PetscFunctionReturn(PETSC_SUCCESS);
227: }

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

236:   PetscFunctionBegin;
237:   PetscOptionsHeadBegin(PetscOptionsObject,"NEP Interpol Options");

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

245:   PetscOptionsHeadEnd();

247:   if (!ctx->pep) PetscCall(NEPInterpolGetPEP(nep,&ctx->pep));
248:   PetscCall(PEPSetFromOptions(ctx->pep));
249:   PetscFunctionReturn(PETSC_SUCCESS);
250: }

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

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

279: /*@
280:    NEPInterpolSetInterpolation - Sets the tolerance and maximum degree when building
281:    the interpolation polynomial.

283:    Collective

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

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

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

297:    Level: advanced

299: .seealso: NEPInterpolGetInterpolation()
300: @*/
301: PetscErrorCode NEPInterpolSetInterpolation(NEP nep,PetscReal tol,PetscInt deg)
302: {
303:   PetscFunctionBegin;
307:   PetscTryMethod(nep,"NEPInterpolSetInterpolation_C",(NEP,PetscReal,PetscInt),(nep,tol,deg));
308:   PetscFunctionReturn(PETSC_SUCCESS);
309: }

311: static PetscErrorCode NEPInterpolGetInterpolation_Interpol(NEP nep,PetscReal *tol,PetscInt *deg)
312: {
313:   NEP_INTERPOL *ctx = (NEP_INTERPOL*)nep->data;

315:   PetscFunctionBegin;
316:   if (tol) *tol = ctx->tol;
317:   if (deg) *deg = ctx->maxdeg;
318:   PetscFunctionReturn(PETSC_SUCCESS);
319: }

321: /*@
322:    NEPInterpolGetInterpolation - Gets the tolerance and maximum degree when building
323:    the interpolation polynomial.

325:    Not Collective

327:    Input Parameter:
328: .  nep - nonlinear eigenvalue solver

330:    Output Parameters:
331: +  tol - tolerance to stop computing polynomial coefficients
332: -  deg - maximum degree of interpolation

334:    Level: advanced

336: .seealso: NEPInterpolSetInterpolation()
337: @*/
338: PetscErrorCode NEPInterpolGetInterpolation(NEP nep,PetscReal *tol,PetscInt *deg)
339: {
340:   PetscFunctionBegin;
342:   PetscUseMethod(nep,"NEPInterpolGetInterpolation_C",(NEP,PetscReal*,PetscInt*),(nep,tol,deg));
343:   PetscFunctionReturn(PETSC_SUCCESS);
344: }

346: static PetscErrorCode NEPInterpolSetPEP_Interpol(NEP nep,PEP pep)
347: {
348:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

350:   PetscFunctionBegin;
351:   PetscCall(PetscObjectReference((PetscObject)pep));
352:   PetscCall(PEPDestroy(&ctx->pep));
353:   ctx->pep = pep;
354:   nep->state = NEP_STATE_INITIAL;
355:   PetscFunctionReturn(PETSC_SUCCESS);
356: }

358: /*@
359:    NEPInterpolSetPEP - Associate a polynomial eigensolver object (PEP) to the
360:    nonlinear eigenvalue solver.

362:    Collective

364:    Input Parameters:
365: +  nep - nonlinear eigenvalue solver
366: -  pep - the polynomial eigensolver object

368:    Level: advanced

370: .seealso: NEPInterpolGetPEP()
371: @*/
372: PetscErrorCode NEPInterpolSetPEP(NEP nep,PEP pep)
373: {
374:   PetscFunctionBegin;
377:   PetscCheckSameComm(nep,1,pep,2);
378:   PetscTryMethod(nep,"NEPInterpolSetPEP_C",(NEP,PEP),(nep,pep));
379:   PetscFunctionReturn(PETSC_SUCCESS);
380: }

382: static PetscErrorCode NEPInterpolGetPEP_Interpol(NEP nep,PEP *pep)
383: {
384:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

386:   PetscFunctionBegin;
387:   if (!ctx->pep) {
388:     PetscCall(PEPCreate(PetscObjectComm((PetscObject)nep),&ctx->pep));
389:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)ctx->pep,(PetscObject)nep,1));
390:     PetscCall(PEPSetOptionsPrefix(ctx->pep,((PetscObject)nep)->prefix));
391:     PetscCall(PEPAppendOptionsPrefix(ctx->pep,"nep_interpol_"));
392:     PetscCall(PetscObjectSetOptions((PetscObject)ctx->pep,((PetscObject)nep)->options));
393:     PetscCall(PEPMonitorSet(ctx->pep,PEPMonitor_Interpol,nep,NULL));
394:   }
395:   *pep = ctx->pep;
396:   PetscFunctionReturn(PETSC_SUCCESS);
397: }

399: /*@
400:    NEPInterpolGetPEP - Retrieve the polynomial eigensolver object (PEP)
401:    associated with the nonlinear eigenvalue solver.

403:    Collective

405:    Input Parameter:
406: .  nep - nonlinear eigenvalue solver

408:    Output Parameter:
409: .  pep - the polynomial eigensolver object

411:    Level: advanced

413: .seealso: NEPInterpolSetPEP()
414: @*/
415: PetscErrorCode NEPInterpolGetPEP(NEP nep,PEP *pep)
416: {
417:   PetscFunctionBegin;
419:   PetscAssertPointer(pep,2);
420:   PetscUseMethod(nep,"NEPInterpolGetPEP_C",(NEP,PEP*),(nep,pep));
421:   PetscFunctionReturn(PETSC_SUCCESS);
422: }

424: static PetscErrorCode NEPView_Interpol(NEP nep,PetscViewer viewer)
425: {
426:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;
427:   PetscBool      isascii;

429:   PetscFunctionBegin;
430:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
431:   if (isascii) {
432:     if (!ctx->pep) PetscCall(NEPInterpolGetPEP(nep,&ctx->pep));
433:     PetscCall(PetscViewerASCIIPrintf(viewer,"  polynomial degree %" PetscInt_FMT ", max=%" PetscInt_FMT "\n",ctx->deg,ctx->maxdeg));
434:     PetscCall(PetscViewerASCIIPrintf(viewer,"  tolerance for norm of polynomial coefficients %g\n",(double)ctx->tol));
435:     PetscCall(PetscViewerASCIIPushTab(viewer));
436:     PetscCall(PEPView(ctx->pep,viewer));
437:     PetscCall(PetscViewerASCIIPopTab(viewer));
438:   }
439:   PetscFunctionReturn(PETSC_SUCCESS);
440: }

442: static PetscErrorCode NEPReset_Interpol(NEP nep)
443: {
444:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

446:   PetscFunctionBegin;
447:   PetscCall(PEPReset(ctx->pep));
448:   PetscFunctionReturn(PETSC_SUCCESS);
449: }

451: static PetscErrorCode NEPDestroy_Interpol(NEP nep)
452: {
453:   NEP_INTERPOL   *ctx = (NEP_INTERPOL*)nep->data;

455:   PetscFunctionBegin;
456:   PetscCall(PEPDestroy(&ctx->pep));
457:   PetscCall(PetscFree(nep->data));
458:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetInterpolation_C",NULL));
459:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetInterpolation_C",NULL));
460:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetPEP_C",NULL));
461:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetPEP_C",NULL));
462:   PetscFunctionReturn(PETSC_SUCCESS);
463: }

465: SLEPC_EXTERN PetscErrorCode NEPCreate_Interpol(NEP nep)
466: {
467:   NEP_INTERPOL   *ctx;

469:   PetscFunctionBegin;
470:   PetscCall(PetscNew(&ctx));
471:   nep->data   = (void*)ctx;
472:   ctx->maxdeg = 5;
473:   ctx->tol    = PETSC_DEFAULT;

475:   nep->ops->solve          = NEPSolve_Interpol;
476:   nep->ops->setup          = NEPSetUp_Interpol;
477:   nep->ops->setfromoptions = NEPSetFromOptions_Interpol;
478:   nep->ops->reset          = NEPReset_Interpol;
479:   nep->ops->destroy        = NEPDestroy_Interpol;
480:   nep->ops->view           = NEPView_Interpol;

482:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetInterpolation_C",NEPInterpolSetInterpolation_Interpol));
483:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetInterpolation_C",NEPInterpolGetInterpolation_Interpol));
484:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetPEP_C",NEPInterpolSetPEP_Interpol));
485:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetPEP_C",NEPInterpolGetPEP_Interpol));
486:   PetscFunctionReturn(PETSC_SUCCESS);
487: }