Actual source code: qarnoldi.c
slepc-3.15.2 2021-09-20
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2021, 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: PetscErrorCode PEPSetUp_QArnoldi(PEP pep)
35: {
37: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
38: PetscBool flg;
41: PEPCheckQuadratic(pep);
42: PEPCheckShiftSinvert(pep);
43: PEPSetDimensions_Default(pep,pep->nev,&pep->ncv,&pep->mpd);
44: if (!ctx->lock && pep->mpd<pep->ncv) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Should not use mpd parameter in non-locking variant");
45: if (pep->max_it==PETSC_DEFAULT) pep->max_it = PetscMax(100,4*pep->n/pep->ncv);
46: if (!pep->which) { PEPSetWhichEigenpairs_Default(pep); }
47: if (pep->which==PEP_ALL) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"This solver does not support computing all eigenvalues");
49: STGetTransform(pep->st,&flg);
50: if (!flg) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver requires the ST transformation flag set, see STSetTransform()");
52: /* set default extraction */
53: if (!pep->extract) pep->extract = PEP_EXTRACT_NONE;
54: PEPCheckUnsupported(pep,PEP_FEATURE_NONMONOMIAL | PEP_FEATURE_EXTRACT);
56: if (!ctx->keep) ctx->keep = 0.5;
58: PEPAllocateSolution(pep,0);
59: PEPSetWorkVecs(pep,4);
61: DSSetType(pep->ds,DSNHEP);
62: DSSetExtraRow(pep->ds,PETSC_TRUE);
63: DSAllocate(pep->ds,pep->ncv+1);
65: return(0);
66: }
68: PetscErrorCode PEPExtractVectors_QArnoldi(PEP pep)
69: {
71: PetscInt i,k=pep->nconv,ldds;
72: PetscScalar *X,*pX0;
73: Mat X0;
76: if (pep->nconv==0) return(0);
77: DSGetLeadingDimension(pep->ds,&ldds);
78: DSVectors(pep->ds,DS_MAT_X,NULL,NULL);
79: DSGetArray(pep->ds,DS_MAT_X,&X);
81: /* update vectors V = V*X */
82: MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&X0);
83: MatDenseGetArrayWrite(X0,&pX0);
84: for (i=0;i<k;i++) {
85: PetscArraycpy(pX0+i*k,X+i*ldds,k);
86: }
87: MatDenseRestoreArrayWrite(X0,&pX0);
88: BVMultInPlace(pep->V,X0,0,k);
89: MatDestroy(&X0);
90: DSRestoreArray(pep->ds,DS_MAT_X,&X);
91: return(0);
92: }
94: /*
95: Compute a step of Classical Gram-Schmidt orthogonalization
96: */
97: 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)
98: {
100: PetscBLASInt ione = 1,j_1 = j+1;
101: PetscReal x,y;
102: PetscScalar dot,one = 1.0,zero = 0.0;
105: /* compute norm of v and w */
106: if (onorm) {
107: VecNorm(v,NORM_2,&x);
108: VecNorm(w,NORM_2,&y);
109: *onorm = PetscSqrtReal(x*x+y*y);
110: }
112: /* orthogonalize: compute h */
113: BVDotVec(V,v,h);
114: BVDotVec(V,w,work);
115: if (j>0)
116: PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&j_1,&j,&one,H,&ldh,work,&ione,&one,h,&ione));
117: VecDot(w,t,&dot);
118: h[j] += dot;
120: /* orthogonalize: update v and w */
121: BVMultVec(V,-1.0,1.0,v,h);
122: if (j>0) {
123: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&j_1,&j,&one,H,&ldh,h,&ione,&zero,work,&ione));
124: BVMultVec(V,-1.0,1.0,w,work);
125: }
126: VecAXPY(w,-h[j],t);
128: /* compute norm of v and w */
129: if (norm) {
130: VecNorm(v,NORM_2,&x);
131: VecNorm(w,NORM_2,&y);
132: *norm = PetscSqrtReal(x*x+y*y);
133: }
134: return(0);
135: }
137: /*
138: Compute a run of Q-Arnoldi iterations
139: */
140: static PetscErrorCode PEPQArnoldi(PEP pep,PetscScalar *H,PetscInt ldh,PetscInt k,PetscInt *M,Vec v,Vec w,PetscReal *beta,PetscBool *breakdown,PetscScalar *work)
141: {
142: PetscErrorCode ierr;
143: PetscInt i,j,l,m = *M;
144: Vec t = pep->work[2],u = pep->work[3];
145: BVOrthogRefineType refinement;
146: PetscReal norm=0.0,onorm,eta;
147: PetscScalar *c = work + m;
150: BVGetOrthogonalization(pep->V,NULL,&refinement,&eta,NULL);
151: BVInsertVec(pep->V,k,v);
152: for (j=k;j<m;j++) {
153: /* apply operator */
154: VecCopy(w,t);
155: if (pep->Dr) {
156: VecPointwiseMult(v,v,pep->Dr);
157: }
158: STMatMult(pep->st,0,v,u);
159: VecCopy(t,v);
160: if (pep->Dr) {
161: VecPointwiseMult(t,t,pep->Dr);
162: }
163: STMatMult(pep->st,1,t,w);
164: VecAXPY(u,pep->sfactor,w);
165: STMatSolve(pep->st,u,w);
166: VecScale(w,-1.0/(pep->sfactor*pep->sfactor));
167: if (pep->Dr) {
168: VecPointwiseDivide(w,w,pep->Dr);
169: }
170: VecCopy(v,t);
171: BVSetActiveColumns(pep->V,0,j+1);
173: /* orthogonalize */
174: switch (refinement) {
175: case BV_ORTHOG_REFINE_NEVER:
176: PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,NULL,&norm,work);
177: *breakdown = PETSC_FALSE;
178: break;
179: case BV_ORTHOG_REFINE_ALWAYS:
180: PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,NULL,NULL,work);
181: PEPQArnoldiCGS(pep,H,ldh,c,j,pep->V,t,v,w,&onorm,&norm,work);
182: for (i=0;i<=j;i++) H[ldh*j+i] += c[i];
183: if (norm < eta * onorm) *breakdown = PETSC_TRUE;
184: else *breakdown = PETSC_FALSE;
185: break;
186: case BV_ORTHOG_REFINE_IFNEEDED:
187: PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,&onorm,&norm,work);
188: /* ||q|| < eta ||h|| */
189: l = 1;
190: while (l<3 && norm < eta * onorm) {
191: l++;
192: onorm = norm;
193: PEPQArnoldiCGS(pep,H,ldh,c,j,pep->V,t,v,w,NULL,&norm,work);
194: for (i=0;i<=j;i++) H[ldh*j+i] += c[i];
195: }
196: if (norm < eta * onorm) *breakdown = PETSC_TRUE;
197: else *breakdown = PETSC_FALSE;
198: break;
199: }
200: VecScale(v,1.0/norm);
201: VecScale(w,1.0/norm);
203: H[j+1+ldh*j] = norm;
204: if (j<m-1) {
205: BVInsertVec(pep->V,j+1,v);
206: }
207: }
208: *beta = norm;
209: return(0);
210: }
212: PetscErrorCode PEPSolve_QArnoldi(PEP pep)
213: {
215: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
216: PetscInt j,k,l,lwork,nv,ld,nconv;
217: Vec v=pep->work[0],w=pep->work[1];
218: Mat Q;
219: PetscScalar *S,*work;
220: PetscReal beta=0.0,norm,x,y;
221: PetscBool breakdown=PETSC_FALSE,sinv;
224: DSGetLeadingDimension(pep->ds,&ld);
225: lwork = 7*pep->ncv;
226: PetscMalloc1(lwork,&work);
227: PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
228: RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor);
229: STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor);
231: /* Get the starting Arnoldi vector */
232: for (j=0;j<2;j++) {
233: if (j>=pep->nini) {
234: BVSetRandomColumn(pep->V,j);
235: }
236: }
237: BVCopyVec(pep->V,0,v);
238: BVCopyVec(pep->V,1,w);
239: VecNorm(v,NORM_2,&x);
240: VecNorm(w,NORM_2,&y);
241: norm = PetscSqrtReal(x*x+y*y);
242: VecScale(v,1.0/norm);
243: VecScale(w,1.0/norm);
245: /* clean projected matrix (including the extra-arrow) */
246: DSGetArray(pep->ds,DS_MAT_A,&S);
247: PetscArrayzero(S,ld*ld);
248: DSRestoreArray(pep->ds,DS_MAT_A,&S);
250: /* Restart loop */
251: l = 0;
252: while (pep->reason == PEP_CONVERGED_ITERATING) {
253: pep->its++;
255: /* Compute an nv-step Arnoldi factorization */
256: nv = PetscMin(pep->nconv+pep->mpd,pep->ncv);
257: DSGetArray(pep->ds,DS_MAT_A,&S);
258: PEPQArnoldi(pep,S,ld,pep->nconv+l,&nv,v,w,&beta,&breakdown,work);
259: DSRestoreArray(pep->ds,DS_MAT_A,&S);
260: DSSetDimensions(pep->ds,nv,0,pep->nconv,pep->nconv+l);
261: if (l==0) {
262: DSSetState(pep->ds,DS_STATE_INTERMEDIATE);
263: } else {
264: DSSetState(pep->ds,DS_STATE_RAW);
265: }
266: BVSetActiveColumns(pep->V,pep->nconv,nv);
268: /* Solve projected problem */
269: DSSolve(pep->ds,pep->eigr,pep->eigi);
270: DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
271: DSUpdateExtraRow(pep->ds);
272: DSSynchronize(pep->ds,pep->eigr,pep->eigi);
274: /* Check convergence */
275: PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,nv-pep->nconv,beta,&k);
276: (*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx);
277: nconv = k;
279: /* Update l */
280: if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
281: else {
282: l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
283: DSGetTruncateSize(pep->ds,k,nv,&l);
284: }
285: if (!ctx->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
286: if (l) { PetscInfo1(pep,"Preparing to restart keeping l=%D vectors\n",l); }
288: if (pep->reason == PEP_CONVERGED_ITERATING) {
289: if (breakdown) {
290: /* Stop if breakdown */
291: PetscInfo2(pep,"Breakdown Quadratic Arnoldi method (it=%D norm=%g)\n",pep->its,(double)beta);
292: pep->reason = PEP_DIVERGED_BREAKDOWN;
293: } else {
294: /* Prepare the Rayleigh quotient for restart */
295: DSTruncate(pep->ds,k+l,PETSC_FALSE);
296: }
297: }
298: /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
299: DSGetMat(pep->ds,DS_MAT_Q,&Q);
300: BVMultInPlace(pep->V,Q,pep->nconv,k+l);
301: MatDestroy(&Q);
303: pep->nconv = k;
304: PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv);
305: }
306: BVSetActiveColumns(pep->V,0,pep->nconv);
307: for (j=0;j<pep->nconv;j++) {
308: pep->eigr[j] *= pep->sfactor;
309: pep->eigi[j] *= pep->sfactor;
310: }
312: STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor);
313: RGPopScale(pep->rg);
315: DSTruncate(pep->ds,pep->nconv,PETSC_TRUE);
316: PetscFree(work);
317: return(0);
318: }
320: static PetscErrorCode PEPQArnoldiSetRestart_QArnoldi(PEP pep,PetscReal keep)
321: {
322: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
325: if (keep==PETSC_DEFAULT) ctx->keep = 0.5;
326: else {
327: if (keep<0.1 || keep>0.9) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The keep argument must be in the range [0.1,0.9]");
328: ctx->keep = keep;
329: }
330: return(0);
331: }
333: /*@
334: PEPQArnoldiSetRestart - Sets the restart parameter for the Q-Arnoldi
335: method, in particular the proportion of basis vectors that must be kept
336: after restart.
338: Logically Collective on pep
340: Input Parameters:
341: + pep - the eigenproblem solver context
342: - keep - the number of vectors to be kept at restart
344: Options Database Key:
345: . -pep_qarnoldi_restart - Sets the restart parameter
347: Notes:
348: Allowed values are in the range [0.1,0.9]. The default is 0.5.
350: Level: advanced
352: .seealso: PEPQArnoldiGetRestart()
353: @*/
354: PetscErrorCode PEPQArnoldiSetRestart(PEP pep,PetscReal keep)
355: {
361: PetscTryMethod(pep,"PEPQArnoldiSetRestart_C",(PEP,PetscReal),(pep,keep));
362: return(0);
363: }
365: static PetscErrorCode PEPQArnoldiGetRestart_QArnoldi(PEP pep,PetscReal *keep)
366: {
367: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
370: *keep = ctx->keep;
371: return(0);
372: }
374: /*@
375: PEPQArnoldiGetRestart - Gets the restart parameter used in the Q-Arnoldi method.
377: Not Collective
379: Input Parameter:
380: . pep - the eigenproblem solver context
382: Output Parameter:
383: . keep - the restart parameter
385: Level: advanced
387: .seealso: PEPQArnoldiSetRestart()
388: @*/
389: PetscErrorCode PEPQArnoldiGetRestart(PEP pep,PetscReal *keep)
390: {
396: PetscUseMethod(pep,"PEPQArnoldiGetRestart_C",(PEP,PetscReal*),(pep,keep));
397: return(0);
398: }
400: static PetscErrorCode PEPQArnoldiSetLocking_QArnoldi(PEP pep,PetscBool lock)
401: {
402: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
405: ctx->lock = lock;
406: return(0);
407: }
409: /*@
410: PEPQArnoldiSetLocking - Choose between locking and non-locking variants of
411: the Q-Arnoldi method.
413: Logically Collective on pep
415: Input Parameters:
416: + pep - the eigenproblem solver context
417: - lock - true if the locking variant must be selected
419: Options Database Key:
420: . -pep_qarnoldi_locking - Sets the locking flag
422: Notes:
423: The default is to lock converged eigenpairs when the method restarts.
424: This behaviour can be changed so that all directions are kept in the
425: working subspace even if already converged to working accuracy (the
426: non-locking variant).
428: Level: advanced
430: .seealso: PEPQArnoldiGetLocking()
431: @*/
432: PetscErrorCode PEPQArnoldiSetLocking(PEP pep,PetscBool lock)
433: {
439: PetscTryMethod(pep,"PEPQArnoldiSetLocking_C",(PEP,PetscBool),(pep,lock));
440: return(0);
441: }
443: static PetscErrorCode PEPQArnoldiGetLocking_QArnoldi(PEP pep,PetscBool *lock)
444: {
445: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
448: *lock = ctx->lock;
449: return(0);
450: }
452: /*@
453: PEPQArnoldiGetLocking - Gets the locking flag used in the Q-Arnoldi method.
455: Not Collective
457: Input Parameter:
458: . pep - the eigenproblem solver context
460: Output Parameter:
461: . lock - the locking flag
463: Level: advanced
465: .seealso: PEPQArnoldiSetLocking()
466: @*/
467: PetscErrorCode PEPQArnoldiGetLocking(PEP pep,PetscBool *lock)
468: {
474: PetscUseMethod(pep,"PEPQArnoldiGetLocking_C",(PEP,PetscBool*),(pep,lock));
475: return(0);
476: }
478: PetscErrorCode PEPSetFromOptions_QArnoldi(PetscOptionItems *PetscOptionsObject,PEP pep)
479: {
481: PetscBool flg,lock;
482: PetscReal keep;
485: PetscOptionsHead(PetscOptionsObject,"PEP Q-Arnoldi Options");
487: PetscOptionsReal("-pep_qarnoldi_restart","Proportion of vectors kept after restart","PEPQArnoldiSetRestart",0.5,&keep,&flg);
488: if (flg) { PEPQArnoldiSetRestart(pep,keep); }
490: PetscOptionsBool("-pep_qarnoldi_locking","Choose between locking and non-locking variants","PEPQArnoldiSetLocking",PETSC_FALSE,&lock,&flg);
491: if (flg) { PEPQArnoldiSetLocking(pep,lock); }
493: PetscOptionsTail();
494: return(0);
495: }
497: PetscErrorCode PEPView_QArnoldi(PEP pep,PetscViewer viewer)
498: {
500: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
501: PetscBool isascii;
504: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
505: if (isascii) {
506: PetscViewerASCIIPrintf(viewer," %d%% of basis vectors kept after restart\n",(int)(100*ctx->keep));
507: PetscViewerASCIIPrintf(viewer," using the %slocking variant\n",ctx->lock?"":"non-");
508: }
509: return(0);
510: }
512: PetscErrorCode PEPDestroy_QArnoldi(PEP pep)
513: {
517: PetscFree(pep->data);
518: PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetRestart_C",NULL);
519: PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetRestart_C",NULL);
520: PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetLocking_C",NULL);
521: PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetLocking_C",NULL);
522: return(0);
523: }
525: SLEPC_EXTERN PetscErrorCode PEPCreate_QArnoldi(PEP pep)
526: {
527: PEP_QARNOLDI *ctx;
531: PetscNewLog(pep,&ctx);
532: pep->data = (void*)ctx;
534: pep->lineariz = PETSC_TRUE;
535: ctx->lock = PETSC_TRUE;
537: pep->ops->solve = PEPSolve_QArnoldi;
538: pep->ops->setup = PEPSetUp_QArnoldi;
539: pep->ops->setfromoptions = PEPSetFromOptions_QArnoldi;
540: pep->ops->destroy = PEPDestroy_QArnoldi;
541: pep->ops->view = PEPView_QArnoldi;
542: pep->ops->backtransform = PEPBackTransform_Default;
543: pep->ops->computevectors = PEPComputeVectors_Default;
544: pep->ops->extractvectors = PEPExtractVectors_QArnoldi;
545: pep->ops->setdefaultst = PEPSetDefaultST_Transform;
547: PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetRestart_C",PEPQArnoldiSetRestart_QArnoldi);
548: PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetRestart_C",PEPQArnoldiGetRestart_QArnoldi);
549: PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetLocking_C",PEPQArnoldiSetLocking_QArnoldi);
550: PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetLocking_C",PEPQArnoldiGetLocking_QArnoldi);
551: return(0);
552: }