Actual source code: qarnoldi.c
slepc-3.21.0 2024-03-30
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 quadratic eigensolver: "qarnoldi"
13: Method: Q-Arnoldi
15: Algorithm:
17: Quadratic Arnoldi with Krylov-Schur type restart.
19: References:
21: [1] K. Meerbergen, "The Quadratic Arnoldi method for the solution
22: of the quadratic eigenvalue problem", SIAM J. Matrix Anal.
23: Appl. 30(4):1462-1482, 2008.
24: */
26: #include <slepc/private/pepimpl.h>
27: #include <petscblaslapack.h>
29: typedef struct {
30: PetscReal keep; /* restart parameter */
31: PetscBool lock; /* locking/non-locking variant */
32: } PEP_QARNOLDI;
34: static PetscErrorCode PEPSetUp_QArnoldi(PEP pep)
35: {
36: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
37: PetscBool flg;
39: PetscFunctionBegin;
40: PEPCheckQuadratic(pep);
41: PEPCheckShiftSinvert(pep);
42: PetscCall(PEPSetDimensions_Default(pep,pep->nev,&pep->ncv,&pep->mpd));
43: PetscCheck(ctx->lock || pep->mpd>=pep->ncv,PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Should not use mpd parameter in non-locking variant");
44: if (pep->max_it==PETSC_DEFAULT) pep->max_it = PetscMax(100,4*pep->n/pep->ncv);
45: if (!pep->which) PetscCall(PEPSetWhichEigenpairs_Default(pep));
46: PetscCheck(pep->which!=PEP_ALL,PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"This solver does not support computing all eigenvalues");
48: PetscCall(STGetTransform(pep->st,&flg));
49: PetscCheck(flg,PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver requires the ST transformation flag set, see STSetTransform()");
51: /* set default extraction */
52: if (!pep->extract) pep->extract = PEP_EXTRACT_NONE;
53: PEPCheckUnsupported(pep,PEP_FEATURE_NONMONOMIAL | PEP_FEATURE_EXTRACT);
55: if (!ctx->keep) ctx->keep = 0.5;
57: PetscCall(PEPAllocateSolution(pep,0));
58: PetscCall(PEPSetWorkVecs(pep,4));
60: PetscCall(DSSetType(pep->ds,DSNHEP));
61: PetscCall(DSSetExtraRow(pep->ds,PETSC_TRUE));
62: PetscCall(DSAllocate(pep->ds,pep->ncv+1));
63: PetscFunctionReturn(PETSC_SUCCESS);
64: }
66: static PetscErrorCode PEPExtractVectors_QArnoldi(PEP pep)
67: {
68: PetscInt k=pep->nconv;
69: Mat X,X0;
71: PetscFunctionBegin;
72: if (pep->nconv==0) PetscFunctionReturn(PETSC_SUCCESS);
73: PetscCall(DSVectors(pep->ds,DS_MAT_X,NULL,NULL));
75: /* update vectors V = V*X */
76: PetscCall(DSGetMat(pep->ds,DS_MAT_X,&X));
77: PetscCall(MatDenseGetSubMatrix(X,0,k,0,k,&X0));
78: PetscCall(BVMultInPlace(pep->V,X0,0,k));
79: PetscCall(MatDenseRestoreSubMatrix(X,&X0));
80: PetscCall(DSRestoreMat(pep->ds,DS_MAT_X,&X));
81: PetscFunctionReturn(PETSC_SUCCESS);
82: }
84: /*
85: Compute a step of Classical Gram-Schmidt orthogonalization
86: */
87: static PetscErrorCode PEPQArnoldiCGS(PEP pep,PetscScalar *H,PetscBLASInt ldh,PetscScalar *h,PetscBLASInt j,BV V,Vec t,Vec v,Vec w,PetscReal *onorm,PetscReal *norm,PetscScalar *work)
88: {
89: PetscBLASInt ione = 1,j_1 = j+1;
90: PetscReal x,y;
91: PetscScalar dot,one = 1.0,zero = 0.0;
93: PetscFunctionBegin;
94: /* compute norm of v and w */
95: if (onorm) {
96: PetscCall(VecNorm(v,NORM_2,&x));
97: PetscCall(VecNorm(w,NORM_2,&y));
98: *onorm = SlepcAbs(x,y);
99: }
101: /* orthogonalize: compute h */
102: PetscCall(BVDotVec(V,v,h));
103: PetscCall(BVDotVec(V,w,work));
104: if (j>0) PetscCallBLAS("BLASgemv",BLASgemv_("C",&j_1,&j,&one,H,&ldh,work,&ione,&one,h,&ione));
105: PetscCall(VecDot(w,t,&dot));
106: h[j] += dot;
108: /* orthogonalize: update v and w */
109: PetscCall(BVMultVec(V,-1.0,1.0,v,h));
110: if (j>0) {
111: PetscCallBLAS("BLASgemv",BLASgemv_("N",&j_1,&j,&one,H,&ldh,h,&ione,&zero,work,&ione));
112: PetscCall(BVMultVec(V,-1.0,1.0,w,work));
113: }
114: PetscCall(VecAXPY(w,-h[j],t));
116: /* compute norm of v and w */
117: if (norm) {
118: PetscCall(VecNorm(v,NORM_2,&x));
119: PetscCall(VecNorm(w,NORM_2,&y));
120: *norm = SlepcAbs(x,y);
121: }
122: PetscFunctionReturn(PETSC_SUCCESS);
123: }
125: /*
126: Compute a run of Q-Arnoldi iterations
127: */
128: static PetscErrorCode PEPQArnoldi(PEP pep,Mat A,PetscInt k,PetscInt *M,Vec v,Vec w,PetscReal *beta,PetscBool *breakdown,PetscScalar *work)
129: {
130: PetscInt i,j,l,m = *M,ldh;
131: Vec t = pep->work[2],u = pep->work[3];
132: BVOrthogRefineType refinement;
133: PetscReal norm=0.0,onorm,eta;
134: PetscScalar *H,*c = work + m;
136: PetscFunctionBegin;
137: *beta = 0.0;
138: PetscCall(MatDenseGetArray(A,&H));
139: PetscCall(MatDenseGetLDA(A,&ldh));
140: PetscCall(BVGetOrthogonalization(pep->V,NULL,&refinement,&eta,NULL));
141: PetscCall(BVInsertVec(pep->V,k,v));
142: for (j=k;j<m;j++) {
143: /* apply operator */
144: PetscCall(VecCopy(w,t));
145: if (pep->Dr) PetscCall(VecPointwiseMult(v,v,pep->Dr));
146: PetscCall(STMatMult(pep->st,0,v,u));
147: PetscCall(VecCopy(t,v));
148: if (pep->Dr) PetscCall(VecPointwiseMult(t,t,pep->Dr));
149: PetscCall(STMatMult(pep->st,1,t,w));
150: PetscCall(VecAXPY(u,pep->sfactor,w));
151: PetscCall(STMatSolve(pep->st,u,w));
152: PetscCall(VecScale(w,-1.0/(pep->sfactor*pep->sfactor)));
153: if (pep->Dr) PetscCall(VecPointwiseDivide(w,w,pep->Dr));
154: PetscCall(VecCopy(v,t));
155: PetscCall(BVSetActiveColumns(pep->V,0,j+1));
157: /* orthogonalize */
158: switch (refinement) {
159: case BV_ORTHOG_REFINE_NEVER:
160: PetscCall(PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,NULL,&norm,work));
161: *breakdown = PETSC_FALSE;
162: break;
163: case BV_ORTHOG_REFINE_ALWAYS:
164: PetscCall(PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,NULL,NULL,work));
165: PetscCall(PEPQArnoldiCGS(pep,H,ldh,c,j,pep->V,t,v,w,&onorm,&norm,work));
166: for (i=0;i<=j;i++) H[ldh*j+i] += c[i];
167: if (norm < eta * onorm) *breakdown = PETSC_TRUE;
168: else *breakdown = PETSC_FALSE;
169: break;
170: case BV_ORTHOG_REFINE_IFNEEDED:
171: PetscCall(PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,&onorm,&norm,work));
172: /* ||q|| < eta ||h|| */
173: l = 1;
174: while (l<3 && norm < eta * onorm) {
175: l++;
176: onorm = norm;
177: PetscCall(PEPQArnoldiCGS(pep,H,ldh,c,j,pep->V,t,v,w,NULL,&norm,work));
178: for (i=0;i<=j;i++) H[ldh*j+i] += c[i];
179: }
180: if (norm < eta * onorm) *breakdown = PETSC_TRUE;
181: else *breakdown = PETSC_FALSE;
182: break;
183: }
184: PetscCall(VecScale(v,1.0/norm));
185: PetscCall(VecScale(w,1.0/norm));
187: H[j+1+ldh*j] = norm;
188: if (j<m-1) PetscCall(BVInsertVec(pep->V,j+1,v));
189: }
190: *beta = norm;
191: PetscCall(MatDenseRestoreArray(A,&H));
192: PetscFunctionReturn(PETSC_SUCCESS);
193: }
195: static PetscErrorCode PEPSolve_QArnoldi(PEP pep)
196: {
197: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
198: PetscInt j,k,l,lwork,nv,nconv;
199: Vec v=pep->work[0],w=pep->work[1];
200: Mat Q,S;
201: PetscScalar *work;
202: PetscReal beta,norm,x,y;
203: PetscBool breakdown=PETSC_FALSE,sinv;
205: PetscFunctionBegin;
206: lwork = 7*pep->ncv;
207: PetscCall(PetscMalloc1(lwork,&work));
208: PetscCall(PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv));
209: PetscCall(RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor));
210: PetscCall(STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor));
212: /* Get the starting Arnoldi vector */
213: for (j=0;j<2;j++) {
214: if (j>=pep->nini) PetscCall(BVSetRandomColumn(pep->V,j));
215: }
216: PetscCall(BVCopyVec(pep->V,0,v));
217: PetscCall(BVCopyVec(pep->V,1,w));
218: PetscCall(VecNorm(v,NORM_2,&x));
219: PetscCall(VecNorm(w,NORM_2,&y));
220: norm = SlepcAbs(x,y);
221: PetscCall(VecScale(v,1.0/norm));
222: PetscCall(VecScale(w,1.0/norm));
224: /* clean projected matrix (including the extra-arrow) */
225: PetscCall(DSSetDimensions(pep->ds,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT));
226: PetscCall(DSGetMat(pep->ds,DS_MAT_A,&S));
227: PetscCall(MatZeroEntries(S));
228: PetscCall(DSRestoreMat(pep->ds,DS_MAT_A,&S));
230: /* Restart loop */
231: l = 0;
232: while (pep->reason == PEP_CONVERGED_ITERATING) {
233: pep->its++;
235: /* Compute an nv-step Arnoldi factorization */
236: nv = PetscMin(pep->nconv+pep->mpd,pep->ncv);
237: PetscCall(DSGetMat(pep->ds,DS_MAT_A,&S));
238: PetscCall(PEPQArnoldi(pep,S,pep->nconv+l,&nv,v,w,&beta,&breakdown,work));
239: PetscCall(DSRestoreMat(pep->ds,DS_MAT_A,&S));
240: PetscCall(DSSetDimensions(pep->ds,nv,pep->nconv,pep->nconv+l));
241: PetscCall(DSSetState(pep->ds,l?DS_STATE_RAW:DS_STATE_INTERMEDIATE));
242: PetscCall(BVSetActiveColumns(pep->V,pep->nconv,nv));
244: /* Solve projected problem */
245: PetscCall(DSSolve(pep->ds,pep->eigr,pep->eigi));
246: PetscCall(DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL));
247: PetscCall(DSUpdateExtraRow(pep->ds));
248: PetscCall(DSSynchronize(pep->ds,pep->eigr,pep->eigi));
250: /* Check convergence */
251: PetscCall(PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,nv-pep->nconv,beta,&k));
252: PetscCall((*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx));
253: nconv = k;
255: /* Update l */
256: if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
257: else {
258: l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
259: PetscCall(DSGetTruncateSize(pep->ds,k,nv,&l));
260: }
261: if (!ctx->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
262: if (l) PetscCall(PetscInfo(pep,"Preparing to restart keeping l=%" PetscInt_FMT " vectors\n",l));
264: if (pep->reason == PEP_CONVERGED_ITERATING) {
265: if (PetscUnlikely(breakdown)) {
266: /* Stop if breakdown */
267: PetscCall(PetscInfo(pep,"Breakdown Quadratic Arnoldi method (it=%" PetscInt_FMT " norm=%g)\n",pep->its,(double)beta));
268: pep->reason = PEP_DIVERGED_BREAKDOWN;
269: } else {
270: /* Prepare the Rayleigh quotient for restart */
271: PetscCall(DSTruncate(pep->ds,k+l,PETSC_FALSE));
272: }
273: }
274: /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
275: PetscCall(DSGetMat(pep->ds,DS_MAT_Q,&Q));
276: PetscCall(BVMultInPlace(pep->V,Q,pep->nconv,k+l));
277: PetscCall(DSRestoreMat(pep->ds,DS_MAT_Q,&Q));
279: pep->nconv = k;
280: PetscCall(PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv));
281: }
282: PetscCall(BVSetActiveColumns(pep->V,0,pep->nconv));
283: for (j=0;j<pep->nconv;j++) {
284: pep->eigr[j] *= pep->sfactor;
285: pep->eigi[j] *= pep->sfactor;
286: }
288: PetscCall(STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor));
289: PetscCall(RGPopScale(pep->rg));
291: PetscCall(DSTruncate(pep->ds,pep->nconv,PETSC_TRUE));
292: PetscCall(PetscFree(work));
293: PetscFunctionReturn(PETSC_SUCCESS);
294: }
296: static PetscErrorCode PEPQArnoldiSetRestart_QArnoldi(PEP pep,PetscReal keep)
297: {
298: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
300: PetscFunctionBegin;
301: if (keep==(PetscReal)PETSC_DEFAULT) ctx->keep = 0.5;
302: else {
303: PetscCheck(keep>=0.1 && keep<=0.9,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The keep argument must be in the range [0.1,0.9]");
304: ctx->keep = keep;
305: }
306: PetscFunctionReturn(PETSC_SUCCESS);
307: }
309: /*@
310: PEPQArnoldiSetRestart - Sets the restart parameter for the Q-Arnoldi
311: method, in particular the proportion of basis vectors that must be kept
312: after restart.
314: Logically Collective
316: Input Parameters:
317: + pep - the eigenproblem solver context
318: - keep - the number of vectors to be kept at restart
320: Options Database Key:
321: . -pep_qarnoldi_restart - Sets the restart parameter
323: Notes:
324: Allowed values are in the range [0.1,0.9]. The default is 0.5.
326: Level: advanced
328: .seealso: PEPQArnoldiGetRestart()
329: @*/
330: PetscErrorCode PEPQArnoldiSetRestart(PEP pep,PetscReal keep)
331: {
332: PetscFunctionBegin;
335: PetscTryMethod(pep,"PEPQArnoldiSetRestart_C",(PEP,PetscReal),(pep,keep));
336: PetscFunctionReturn(PETSC_SUCCESS);
337: }
339: static PetscErrorCode PEPQArnoldiGetRestart_QArnoldi(PEP pep,PetscReal *keep)
340: {
341: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
343: PetscFunctionBegin;
344: *keep = ctx->keep;
345: PetscFunctionReturn(PETSC_SUCCESS);
346: }
348: /*@
349: PEPQArnoldiGetRestart - Gets the restart parameter used in the Q-Arnoldi method.
351: Not Collective
353: Input Parameter:
354: . pep - the eigenproblem solver context
356: Output Parameter:
357: . keep - the restart parameter
359: Level: advanced
361: .seealso: PEPQArnoldiSetRestart()
362: @*/
363: PetscErrorCode PEPQArnoldiGetRestart(PEP pep,PetscReal *keep)
364: {
365: PetscFunctionBegin;
367: PetscAssertPointer(keep,2);
368: PetscUseMethod(pep,"PEPQArnoldiGetRestart_C",(PEP,PetscReal*),(pep,keep));
369: PetscFunctionReturn(PETSC_SUCCESS);
370: }
372: static PetscErrorCode PEPQArnoldiSetLocking_QArnoldi(PEP pep,PetscBool lock)
373: {
374: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
376: PetscFunctionBegin;
377: ctx->lock = lock;
378: PetscFunctionReturn(PETSC_SUCCESS);
379: }
381: /*@
382: PEPQArnoldiSetLocking - Choose between locking and non-locking variants of
383: the Q-Arnoldi method.
385: Logically Collective
387: Input Parameters:
388: + pep - the eigenproblem solver context
389: - lock - true if the locking variant must be selected
391: Options Database Key:
392: . -pep_qarnoldi_locking - Sets the locking flag
394: Notes:
395: The default is to lock converged eigenpairs when the method restarts.
396: This behaviour can be changed so that all directions are kept in the
397: working subspace even if already converged to working accuracy (the
398: non-locking variant).
400: Level: advanced
402: .seealso: PEPQArnoldiGetLocking()
403: @*/
404: PetscErrorCode PEPQArnoldiSetLocking(PEP pep,PetscBool lock)
405: {
406: PetscFunctionBegin;
409: PetscTryMethod(pep,"PEPQArnoldiSetLocking_C",(PEP,PetscBool),(pep,lock));
410: PetscFunctionReturn(PETSC_SUCCESS);
411: }
413: static PetscErrorCode PEPQArnoldiGetLocking_QArnoldi(PEP pep,PetscBool *lock)
414: {
415: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
417: PetscFunctionBegin;
418: *lock = ctx->lock;
419: PetscFunctionReturn(PETSC_SUCCESS);
420: }
422: /*@
423: PEPQArnoldiGetLocking - Gets the locking flag used in the Q-Arnoldi method.
425: Not Collective
427: Input Parameter:
428: . pep - the eigenproblem solver context
430: Output Parameter:
431: . lock - the locking flag
433: Level: advanced
435: .seealso: PEPQArnoldiSetLocking()
436: @*/
437: PetscErrorCode PEPQArnoldiGetLocking(PEP pep,PetscBool *lock)
438: {
439: PetscFunctionBegin;
441: PetscAssertPointer(lock,2);
442: PetscUseMethod(pep,"PEPQArnoldiGetLocking_C",(PEP,PetscBool*),(pep,lock));
443: PetscFunctionReturn(PETSC_SUCCESS);
444: }
446: static PetscErrorCode PEPSetFromOptions_QArnoldi(PEP pep,PetscOptionItems *PetscOptionsObject)
447: {
448: PetscBool flg,lock;
449: PetscReal keep;
451: PetscFunctionBegin;
452: PetscOptionsHeadBegin(PetscOptionsObject,"PEP Q-Arnoldi Options");
454: PetscCall(PetscOptionsReal("-pep_qarnoldi_restart","Proportion of vectors kept after restart","PEPQArnoldiSetRestart",0.5,&keep,&flg));
455: if (flg) PetscCall(PEPQArnoldiSetRestart(pep,keep));
457: PetscCall(PetscOptionsBool("-pep_qarnoldi_locking","Choose between locking and non-locking variants","PEPQArnoldiSetLocking",PETSC_FALSE,&lock,&flg));
458: if (flg) PetscCall(PEPQArnoldiSetLocking(pep,lock));
460: PetscOptionsHeadEnd();
461: PetscFunctionReturn(PETSC_SUCCESS);
462: }
464: static PetscErrorCode PEPView_QArnoldi(PEP pep,PetscViewer viewer)
465: {
466: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
467: PetscBool isascii;
469: PetscFunctionBegin;
470: PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
471: if (isascii) {
472: PetscCall(PetscViewerASCIIPrintf(viewer," %d%% of basis vectors kept after restart\n",(int)(100*ctx->keep)));
473: PetscCall(PetscViewerASCIIPrintf(viewer," using the %slocking variant\n",ctx->lock?"":"non-"));
474: }
475: PetscFunctionReturn(PETSC_SUCCESS);
476: }
478: static PetscErrorCode PEPDestroy_QArnoldi(PEP pep)
479: {
480: PetscFunctionBegin;
481: PetscCall(PetscFree(pep->data));
482: PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetRestart_C",NULL));
483: PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetRestart_C",NULL));
484: PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetLocking_C",NULL));
485: PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetLocking_C",NULL));
486: PetscFunctionReturn(PETSC_SUCCESS);
487: }
489: SLEPC_EXTERN PetscErrorCode PEPCreate_QArnoldi(PEP pep)
490: {
491: PEP_QARNOLDI *ctx;
493: PetscFunctionBegin;
494: PetscCall(PetscNew(&ctx));
495: pep->data = (void*)ctx;
497: pep->lineariz = PETSC_TRUE;
498: ctx->lock = PETSC_TRUE;
500: pep->ops->solve = PEPSolve_QArnoldi;
501: pep->ops->setup = PEPSetUp_QArnoldi;
502: pep->ops->setfromoptions = PEPSetFromOptions_QArnoldi;
503: pep->ops->destroy = PEPDestroy_QArnoldi;
504: pep->ops->view = PEPView_QArnoldi;
505: pep->ops->backtransform = PEPBackTransform_Default;
506: pep->ops->computevectors = PEPComputeVectors_Default;
507: pep->ops->extractvectors = PEPExtractVectors_QArnoldi;
508: pep->ops->setdefaultst = PEPSetDefaultST_Transform;
510: PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetRestart_C",PEPQArnoldiSetRestart_QArnoldi));
511: PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetRestart_C",PEPQArnoldiGetRestart_QArnoldi));
512: PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetLocking_C",PEPQArnoldiSetLocking_QArnoldi));
513: PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetLocking_C",PEPQArnoldiGetLocking_QArnoldi));
514: PetscFunctionReturn(PETSC_SUCCESS);
515: }