Actual source code: ptoar.c
slepc-3.13.2 2020-05-12
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2020, 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 polynomial eigensolver: "toar"
13: Method: TOAR
15: Algorithm:
17: Two-Level Orthogonal Arnoldi.
19: References:
21: [1] Y. Su, J. Zhang and Z. Bai, "A compact Arnoldi algorithm for
22: polynomial eigenvalue problems", talk presented at RANMEP 2008.
24: [2] C. Campos and J.E. Roman, "Parallel Krylov solvers for the
25: polynomial eigenvalue problem in SLEPc", SIAM J. Sci. Comput.
26: 38(5):S385-S411, 2016.
28: [3] D. Lu, Y. Su and Z. Bai, "Stability analysis of the two-level
29: orthogonal Arnoldi procedure", SIAM J. Matrix Anal. App.
30: 37(1):195-214, 2016.
31: */
33: #include <slepc/private/pepimpl.h>
34: #include "../src/pep/impls/krylov/pepkrylov.h"
35: #include <slepcblaslapack.h>
37: static PetscBool cited = PETSC_FALSE;
38: static const char citation[] =
39: "@Article{slepc-pep,\n"
40: " author = \"C. Campos and J. E. Roman\",\n"
41: " title = \"Parallel {Krylov} solvers for the polynomial eigenvalue problem in {SLEPc}\",\n"
42: " journal = \"{SIAM} J. Sci. Comput.\",\n"
43: " volume = \"38\",\n"
44: " number = \"5\",\n"
45: " pages = \"S385--S411\",\n"
46: " year = \"2016,\"\n"
47: " doi = \"https://doi.org/10.1137/15M1022458\"\n"
48: "}\n";
50: PetscErrorCode PEPSetUp_TOAR(PEP pep)
51: {
53: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
54: PetscBool shift,sinv,flg;
55: PetscInt i;
58: pep->lineariz = PETSC_TRUE;
59: PEPSetDimensions_Default(pep,pep->nev,&pep->ncv,&pep->mpd);
60: if (!ctx->lock && pep->mpd<pep->ncv) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Should not use mpd parameter in non-locking variant");
61: if (!pep->max_it) pep->max_it = PetscMax(100,2*(pep->nmat-1)*pep->n/pep->ncv);
63: PetscObjectTypeCompare((PetscObject)pep->st,STSHIFT,&shift);
64: PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
65: if (!shift && !sinv) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Only STSHIFT and STSINVERT spectral transformations can be used");
66: if (!pep->which) {
67: if (sinv) pep->which = PEP_TARGET_MAGNITUDE;
68: else pep->which = PEP_LARGEST_MAGNITUDE;
69: }
70: if (pep->which==PEP_ALL) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Wrong value of pep->which");
71: if (pep->problem_type!=PEP_GENERAL) {
72: PetscInfo(pep,"Problem type ignored, performing a non-symmetric linearization\n");
73: }
75: if (!ctx->keep) ctx->keep = 0.5;
77: PEPAllocateSolution(pep,pep->nmat-1);
78: PEPSetWorkVecs(pep,3);
79: DSSetType(pep->ds,DSNHEP);
80: DSSetExtraRow(pep->ds,PETSC_TRUE);
81: DSAllocate(pep->ds,pep->ncv+1);
83: PEPBasisCoefficients(pep,pep->pbc);
84: STGetTransform(pep->st,&flg);
85: if (!flg) {
86: PetscMalloc1(pep->nmat,&pep->solvematcoeffs);
87: PetscLogObjectMemory((PetscObject)pep,pep->nmat*sizeof(PetscScalar));
88: if (sinv) {
89: PEPEvaluateBasis(pep,pep->target,0,pep->solvematcoeffs,NULL);
90: } else {
91: for (i=0;i<pep->nmat-1;i++) pep->solvematcoeffs[i] = 0.0;
92: pep->solvematcoeffs[pep->nmat-1] = 1.0;
93: }
94: }
95: BVDestroy(&ctx->V);
96: BVCreateTensor(pep->V,pep->nmat-1,&ctx->V);
97: return(0);
98: }
100: /*
101: Extend the TOAR basis by applying the the matrix operator
102: over a vector which is decomposed in the TOAR way
103: Input:
104: - pbc: array containing the polynomial basis coefficients
105: - S,V: define the latest Arnoldi vector (nv vectors in V)
106: Output:
107: - t: new vector extending the TOAR basis
108: - r: temporary coefficients to compute the TOAR coefficients
109: for the new Arnoldi vector
110: Workspace: t_ (two vectors)
111: */
112: static PetscErrorCode PEPTOARExtendBasis(PEP pep,PetscBool sinvert,PetscScalar sigma,PetscScalar *S,PetscInt ls,PetscInt nv,BV V,Vec t,PetscScalar *r,PetscInt lr,Vec *t_)
113: {
115: PetscInt nmat=pep->nmat,deg=nmat-1,k,j,off=0,lss;
116: Vec v=t_[0],ve=t_[1],q=t_[2];
117: PetscScalar alpha=1.0,*ss,a;
118: PetscReal *ca=pep->pbc,*cb=pep->pbc+nmat,*cg=pep->pbc+2*nmat;
119: PetscBool flg;
122: BVSetActiveColumns(pep->V,0,nv);
123: STGetTransform(pep->st,&flg);
124: if (sinvert) {
125: for (j=0;j<nv;j++) {
126: if (deg>1) r[lr+j] = S[j]/ca[0];
127: if (deg>2) r[2*lr+j] = (S[ls+j]+(sigma-cb[1])*r[lr+j])/ca[1];
128: }
129: for (k=2;k<deg-1;k++) {
130: for (j=0;j<nv;j++) r[(k+1)*lr+j] = (S[k*ls+j]+(sigma-cb[k])*r[k*lr+j]-cg[k]*r[(k-1)*lr+j])/ca[k];
131: }
132: k = deg-1;
133: for (j=0;j<nv;j++) r[j] = (S[k*ls+j]+(sigma-cb[k])*r[k*lr+j]-cg[k]*r[(k-1)*lr+j])/ca[k];
134: ss = r; lss = lr; off = 1; alpha = -1.0; a = pep->sfactor;
135: } else {
136: ss = S; lss = ls; off = 0; alpha = -ca[deg-1]; a = 1.0;
137: }
138: BVMultVec(V,1.0,0.0,v,ss+off*lss);
139: if (pep->Dr) { /* balancing */
140: VecPointwiseMult(v,v,pep->Dr);
141: }
142: STMatMult(pep->st,off,v,q);
143: VecScale(q,a);
144: for (j=1+off;j<deg+off-1;j++) {
145: BVMultVec(V,1.0,0.0,v,ss+j*lss);
146: if (pep->Dr) {
147: VecPointwiseMult(v,v,pep->Dr);
148: }
149: STMatMult(pep->st,j,v,t);
150: a *= pep->sfactor;
151: VecAXPY(q,a,t);
152: }
153: if (sinvert) {
154: BVMultVec(V,1.0,0.0,v,ss);
155: if (pep->Dr) {
156: VecPointwiseMult(v,v,pep->Dr);
157: }
158: STMatMult(pep->st,deg,v,t);
159: a *= pep->sfactor;
160: VecAXPY(q,a,t);
161: } else {
162: BVMultVec(V,1.0,0.0,ve,ss+(deg-1)*lss);
163: if (pep->Dr) {
164: VecPointwiseMult(ve,ve,pep->Dr);
165: }
166: a *= pep->sfactor;
167: STMatMult(pep->st,deg-1,ve,t);
168: VecAXPY(q,a,t);
169: a *= pep->sfactor;
170: }
171: if (flg || !sinvert) alpha /= a;
172: STMatSolve(pep->st,q,t);
173: VecScale(t,alpha);
174: if (!sinvert) {
175: if (cg[deg-1]!=0) { VecAXPY(t,cg[deg-1],v); }
176: if (cb[deg-1]!=0) { VecAXPY(t,cb[deg-1],ve); }
177: }
178: if (pep->Dr) {
179: VecPointwiseDivide(t,t,pep->Dr);
180: }
181: return(0);
182: }
184: /*
185: Compute TOAR coefficients of the blocks of the new Arnoldi vector computed
186: */
187: static PetscErrorCode PEPTOARCoefficients(PEP pep,PetscBool sinvert,PetscScalar sigma,PetscInt nv,PetscScalar *S,PetscInt ls,PetscScalar *r,PetscInt lr,PetscScalar *x)
188: {
189: PetscInt k,j,nmat=pep->nmat,d=nmat-1;
190: PetscReal *ca=pep->pbc,*cb=pep->pbc+nmat,*cg=pep->pbc+2*nmat;
191: PetscScalar t=1.0,tp=0.0,tt;
194: if (sinvert) {
195: for (k=1;k<d;k++) {
196: tt = t;
197: t = ((sigma-cb[k-1])*t-cg[k-1]*tp)/ca[k-1]; /* k-th basis polynomial */
198: tp = tt;
199: for (j=0;j<=nv;j++) r[k*lr+j] += t*x[j];
200: }
201: } else {
202: for (j=0;j<=nv;j++) r[j] = (cb[0]-sigma)*S[j]+ca[0]*S[ls+j];
203: for (k=1;k<d-1;k++) {
204: for (j=0;j<=nv;j++) r[k*lr+j] = (cb[k]-sigma)*S[k*ls+j]+ca[k]*S[(k+1)*ls+j]+cg[k]*S[(k-1)*ls+j];
205: }
206: if (sigma!=0.0) for (j=0;j<=nv;j++) r[(d-1)*lr+j] -= sigma*S[(d-1)*ls+j];
207: }
208: return(0);
209: }
211: /*
212: Compute a run of Arnoldi iterations dim(work)=ld
213: */
214: static PetscErrorCode PEPTOARrun(PEP pep,PetscScalar sigma,PetscScalar *H,PetscInt ldh,PetscInt k,PetscInt *M,PetscBool *breakdown,Vec *t_)
215: {
217: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
218: PetscInt j,m=*M,deg=pep->nmat-1,ld;
219: PetscInt lds,nqt,l;
220: Vec t;
221: PetscReal norm;
222: PetscBool flg,sinvert=PETSC_FALSE,lindep;
223: PetscScalar *x,*S;
224: Mat MS;
227: BVTensorGetFactors(ctx->V,NULL,&MS);
228: MatDenseGetArray(MS,&S);
229: BVGetSizes(pep->V,NULL,NULL,&ld);
230: lds = ld*deg;
231: BVGetActiveColumns(pep->V,&l,&nqt);
232: STGetTransform(pep->st,&flg);
233: if (!flg) {
234: /* spectral transformation handled by the solver */
235: PetscObjectTypeCompareAny((PetscObject)pep->st,&flg,STSINVERT,STSHIFT,"");
236: if (!flg) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"ST type not supported for TOAR without transforming matrices");
237: PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinvert);
238: }
239: BVSetActiveColumns(ctx->V,0,m);
240: for (j=k;j<m;j++) {
241: /* apply operator */
242: BVGetColumn(pep->V,nqt,&t);
243: PEPTOARExtendBasis(pep,sinvert,sigma,S+j*lds,ld,nqt,pep->V,t,S+(j+1)*lds,ld,t_);
244: BVRestoreColumn(pep->V,nqt,&t);
246: /* orthogonalize */
247: if (sinvert) x = S+(j+1)*lds;
248: else x = S+(deg-1)*ld+(j+1)*lds;
249: BVOrthogonalizeColumn(pep->V,nqt,x,&norm,&lindep);
250: if (!lindep) {
251: x[nqt] = norm;
252: BVScaleColumn(pep->V,nqt,1.0/norm);
253: nqt++;
254: }
256: PEPTOARCoefficients(pep,sinvert,sigma,nqt-1,S+j*lds,ld,S+(j+1)*lds,ld,x);
258: /* level-2 orthogonalization */
259: BVOrthogonalizeColumn(ctx->V,j+1,H+j*ldh,&norm,breakdown);
260: H[j+1+ldh*j] = norm;
261: if (*breakdown) {
262: *M = j+1;
263: break;
264: }
265: BVScaleColumn(ctx->V,j+1,1.0/norm);
266: BVSetActiveColumns(pep->V,l,nqt);
267: }
268: BVSetActiveColumns(ctx->V,0,*M);
269: MatDenseRestoreArray(MS,&S);
270: BVTensorRestoreFactors(ctx->V,NULL,&MS);
271: return(0);
272: }
274: /*
275: Computes T_j = phi_idx(T). In T_j and T_p are phi_{idx-1}(T)
276: and phi_{idx-2}(T) respectively or null if idx=0,1.
277: Tp and Tj are input/output arguments
278: */
279: static PetscErrorCode PEPEvaluateBasisM(PEP pep,PetscInt k,PetscScalar *T,PetscInt ldt,PetscInt idx,PetscScalar **Tp,PetscScalar **Tj)
280: {
282: PetscInt i;
283: PetscReal *ca,*cb,*cg;
284: PetscScalar *pt,g,a;
285: PetscBLASInt k_,ldt_;
288: if (idx==0) {
289: PetscArrayzero(*Tj,k*k);
290: PetscArrayzero(*Tp,k*k);
291: for (i=0;i<k;i++) (*Tj)[i+i*k] = 1.0;
292: } else {
293: PetscBLASIntCast(ldt,&ldt_);
294: PetscBLASIntCast(k,&k_);
295: ca = pep->pbc; cb = pep->pbc+pep->nmat; cg = pep->pbc+2*pep->nmat;
296: for (i=0;i<k;i++) T[i*ldt+i] -= cb[idx-1];
297: a = 1/ca[idx-1];
298: g = (idx==1)?0.0:-cg[idx-1]/ca[idx-1];
299: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&a,T,&ldt_,*Tj,&k_,&g,*Tp,&k_));
300: pt = *Tj; *Tj = *Tp; *Tp = pt;
301: for (i=0;i<k;i++) T[i*ldt+i] += cb[idx-1];
302: }
303: return(0);
304: }
306: static PetscErrorCode PEPExtractInvariantPair(PEP pep,PetscScalar sigma,PetscInt sr,PetscInt k,PetscScalar *S,PetscInt ld,PetscInt deg,PetscScalar *H,PetscInt ldh)
307: {
309: PetscInt i,j,jj,lds,ldt,d=pep->nmat-1,idxcpy=0;
310: PetscScalar *At,*Bt,*Hj,*Hp,*T,sone=1.0,g,a,*pM,*work;
311: PetscBLASInt k_,sr_,lds_,ldh_,info,*p,lwork,ldt_;
312: PetscBool transf=PETSC_FALSE,flg;
313: PetscReal nrm,norm,maxnrm,*rwork;
314: BV *R,Y;
315: Mat M,*A;
316: Vec v;
319: if (k==0) return(0);
320: lds = deg*ld;
321: PetscCalloc6(k,&p,sr*k,&At,k*k,&Bt,k*k,&Hj,k*k,&Hp,sr*k,&work);
322: PetscBLASIntCast(sr,&sr_);
323: PetscBLASIntCast(k,&k_);
324: PetscBLASIntCast(lds,&lds_);
325: PetscBLASIntCast(ldh,&ldh_);
326: STGetTransform(pep->st,&flg);
327: if (!flg) {
328: PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&flg);
329: if (flg || sigma!=0.0) transf=PETSC_TRUE;
330: }
331: if (transf) {
332: PetscMalloc1(k*k,&T);
333: ldt = k;
334: for (i=0;i<k;i++) {
335: PetscArraycpy(T+k*i,H+i*ldh,k);
336: }
337: if (flg) {
338: PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&k_,&k_,T,&k_,p,&info));
339: SlepcCheckLapackInfo("getrf",info);
340: PetscBLASIntCast(sr*k,&lwork);
341: PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&k_,T,&k_,p,work,&lwork,&info));
342: SlepcCheckLapackInfo("getri",info);
343: }
344: if (sigma!=0.0) for (i=0;i<k;i++) T[i+k*i] += sigma;
345: } else {
346: T = H; ldt = ldh;
347: }
348: PetscBLASIntCast(ldt,&ldt_);
349: switch (pep->extract) {
350: case PEP_EXTRACT_NONE:
351: break;
352: case PEP_EXTRACT_NORM:
353: if (pep->basis == PEP_BASIS_MONOMIAL) {
354: PetscBLASIntCast(ldt,&ldt_);
355: PetscMalloc1(k,&rwork);
356: norm = LAPACKlange_("F",&k_,&k_,T,&ldt_,rwork);
357: PetscFree(rwork);
358: if (norm>1.0) idxcpy = d-1;
359: } else {
360: PetscBLASIntCast(ldt,&ldt_);
361: PetscMalloc1(k,&rwork);
362: maxnrm = 0.0;
363: for (i=0;i<pep->nmat-1;i++) {
364: PEPEvaluateBasisM(pep,k,T,ldt,i,&Hp,&Hj);
365: norm = LAPACKlange_("F",&k_,&k_,Hj,&k_,rwork);
366: if (norm > maxnrm) {
367: idxcpy = i;
368: maxnrm = norm;
369: }
370: }
371: PetscFree(rwork);
372: }
373: if (idxcpy>0) {
374: /* copy block idxcpy of S to the first one */
375: for (j=0;j<k;j++) {
376: PetscArraycpy(S+j*lds,S+idxcpy*ld+j*lds,sr);
377: }
378: }
379: break;
380: case PEP_EXTRACT_RESIDUAL:
381: STGetTransform(pep->st,&flg);
382: if (flg) {
383: PetscMalloc1(pep->nmat,&A);
384: for (i=0;i<pep->nmat;i++) {
385: STGetMatrixTransformed(pep->st,i,A+i);
386: }
387: } else A = pep->A;
388: PetscMalloc1(pep->nmat-1,&R);
389: for (i=0;i<pep->nmat-1;i++) {
390: BVDuplicateResize(pep->V,k,R+i);
391: }
392: BVDuplicateResize(pep->V,sr,&Y);
393: MatCreateSeqDense(PETSC_COMM_SELF,sr,k,NULL,&M);
394: g = 0.0; a = 1.0;
395: BVSetActiveColumns(pep->V,0,sr);
396: for (j=0;j<pep->nmat;j++) {
397: BVMatMult(pep->V,A[j],Y);
398: PEPEvaluateBasisM(pep,k,T,ldt,i,&Hp,&Hj);
399: for (i=0;i<pep->nmat-1;i++) {
400: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&sr_,&k_,&k_,&a,S+i*ld,&lds_,Hj,&k_,&g,At,&sr_));
401: MatDenseGetArray(M,&pM);
402: for (jj=0;jj<k;jj++) {
403: PetscArraycpy(pM+jj*sr,At+jj*sr,sr);
404: }
405: MatDenseRestoreArray(M,&pM);
406: BVMult(R[i],1.0,(i==0)?0.0:1.0,Y,M);
407: }
408: }
410: /* frobenius norm */
411: maxnrm = 0.0;
412: for (i=0;i<pep->nmat-1;i++) {
413: norm = 0.0;
414: for (j=0;j<k;j++) {
415: BVGetColumn(R[i],j,&v);
416: VecNorm(v,NORM_2,&nrm);
417: BVRestoreColumn(R[i],j,&v);
418: norm += nrm*nrm;
419: }
420: norm = PetscSqrtReal(norm);
421: if (maxnrm > norm) {
422: maxnrm = norm;
423: idxcpy = i;
424: }
425: }
426: if (idxcpy>0) {
427: /* copy block idxcpy of S to the first one */
428: for (j=0;j<k;j++) {
429: PetscArraycpy(S+j*lds,S+idxcpy*ld+j*lds,sr);
430: }
431: }
432: if (flg) PetscFree(A);
433: for (i=0;i<pep->nmat-1;i++) {
434: BVDestroy(&R[i]);
435: }
436: PetscFree(R);
437: BVDestroy(&Y);
438: MatDestroy(&M);
439: break;
440: case PEP_EXTRACT_STRUCTURED:
441: for (j=0;j<k;j++) Bt[j+j*k] = 1.0;
442: for (j=0;j<sr;j++) {
443: for (i=0;i<k;i++) At[j*k+i] = PetscConj(S[i*lds+j]);
444: }
445: PEPEvaluateBasisM(pep,k,T,ldt,0,&Hp,&Hj);
446: for (i=1;i<deg;i++) {
447: PEPEvaluateBasisM(pep,k,T,ldt,i,&Hp,&Hj);
448: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","C",&k_,&sr_,&k_,&sone,Hj,&k_,S+i*ld,&lds_,&sone,At,&k_));
449: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","C",&k_,&k_,&k_,&sone,Hj,&k_,Hj,&k_,&sone,Bt,&k_));
450: }
451: PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&k_,&sr_,Bt,&k_,p,At,&k_,&info));
452: SlepcCheckLapackInfo("gesv",info);
453: for (j=0;j<sr;j++) {
454: for (i=0;i<k;i++) S[i*lds+j] = PetscConj(At[j*k+i]);
455: }
456: break;
457: }
458: if (transf) { PetscFree(T); }
459: PetscFree6(p,At,Bt,Hj,Hp,work);
460: return(0);
461: }
463: PetscErrorCode PEPSolve_TOAR(PEP pep)
464: {
466: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
467: PetscInt i,j,k,l,nv=0,ld,lds,ldds,newn,nq=0,nconv=0;
468: PetscInt nmat=pep->nmat,deg=nmat-1;
469: PetscScalar *S,*H,sigma;
470: PetscReal beta;
471: PetscBool breakdown=PETSC_FALSE,flg,falselock=PETSC_FALSE,sinv=PETSC_FALSE;
472: Mat MS,MQ;
475: PetscCitationsRegister(citation,&cited);
476: if (ctx->lock) {
477: /* undocumented option to use a cheaper locking instead of the true locking */
478: PetscOptionsGetBool(NULL,NULL,"-pep_toar_falselocking",&falselock,NULL);
479: }
480: DSGetLeadingDimension(pep->ds,&ldds);
481: STGetShift(pep->st,&sigma);
483: /* update polynomial basis coefficients */
484: STGetTransform(pep->st,&flg);
485: if (pep->sfactor!=1.0) {
486: for (i=0;i<nmat;i++) {
487: pep->pbc[nmat+i] /= pep->sfactor;
488: pep->pbc[2*nmat+i] /= pep->sfactor*pep->sfactor;
489: }
490: if (!flg) {
491: pep->target /= pep->sfactor;
492: RGPushScale(pep->rg,1.0/pep->sfactor);
493: STScaleShift(pep->st,1.0/pep->sfactor);
494: sigma /= pep->sfactor;
495: } else {
496: PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
497: pep->target = sinv?pep->target*pep->sfactor:pep->target/pep->sfactor;
498: RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor);
499: STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor);
500: }
501: }
503: if (flg) sigma = 0.0;
505: /* clean projected matrix (including the extra-arrow) */
506: DSGetArray(pep->ds,DS_MAT_A,&H);
507: PetscArrayzero(H,ldds*ldds);
508: DSRestoreArray(pep->ds,DS_MAT_A,&H);
510: /* Get the starting Arnoldi vector */
511: BVTensorBuildFirstColumn(ctx->V,pep->nini);
513: /* restart loop */
514: l = 0;
515: while (pep->reason == PEP_CONVERGED_ITERATING) {
516: pep->its++;
518: /* compute an nv-step Lanczos factorization */
519: nv = PetscMax(PetscMin(nconv+pep->mpd,pep->ncv),nv);
520: DSGetArray(pep->ds,DS_MAT_A,&H);
521: PEPTOARrun(pep,sigma,H,ldds,pep->nconv+l,&nv,&breakdown,pep->work);
522: beta = PetscAbsScalar(H[(nv-1)*ldds+nv]);
523: DSRestoreArray(pep->ds,DS_MAT_A,&H);
524: DSSetDimensions(pep->ds,nv,0,pep->nconv,pep->nconv+l);
525: if (l==0) {
526: DSSetState(pep->ds,DS_STATE_INTERMEDIATE);
527: } else {
528: DSSetState(pep->ds,DS_STATE_RAW);
529: }
530: BVSetActiveColumns(ctx->V,pep->nconv,nv);
532: /* solve projected problem */
533: DSSolve(pep->ds,pep->eigr,pep->eigi);
534: DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
535: DSUpdateExtraRow(pep->ds);
536: DSSynchronize(pep->ds,pep->eigr,pep->eigi);
538: /* check convergence */
539: PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,nv-pep->nconv,beta,&k);
540: (*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx);
542: /* update l */
543: if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
544: else {
545: l = (nv==k)?0:PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
546: if (!breakdown) {
547: /* prepare the Rayleigh quotient for restart */
548: DSTruncate(pep->ds,k+l);
549: DSGetDimensions(pep->ds,&newn,NULL,NULL,NULL,NULL);
550: l = newn-k;
551: }
552: }
553: nconv = k;
554: if (!ctx->lock && pep->reason == PEP_CONVERGED_ITERATING && !breakdown) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
556: /* update S */
557: DSGetMat(pep->ds,DS_MAT_Q,&MQ);
558: BVMultInPlace(ctx->V,MQ,pep->nconv,k+l);
559: MatDestroy(&MQ);
561: /* copy last column of S */
562: BVCopyColumn(ctx->V,nv,k+l);
564: if (breakdown && pep->reason == PEP_CONVERGED_ITERATING) {
565: /* stop if breakdown */
566: PetscInfo2(pep,"Breakdown TOAR method (it=%D norm=%g)\n",pep->its,(double)beta);
567: pep->reason = PEP_DIVERGED_BREAKDOWN;
568: }
569: if (pep->reason != PEP_CONVERGED_ITERATING) l--;
570: /* truncate S */
571: BVGetActiveColumns(pep->V,NULL,&nq);
572: if (k+l+deg<=nq) {
573: BVSetActiveColumns(ctx->V,pep->nconv,k+l+1);
574: if (!falselock && ctx->lock) {
575: BVTensorCompress(ctx->V,k-pep->nconv);
576: } else {
577: BVTensorCompress(ctx->V,0);
578: }
579: }
580: pep->nconv = k;
581: PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv);
582: }
583: if (pep->nconv>0) {
584: /* {V*S_nconv^i}_{i=0}^{d-1} has rank nconv instead of nconv+d-1. Force zeros in each S_nconv^i block */
585: BVSetActiveColumns(ctx->V,0,pep->nconv);
586: BVGetActiveColumns(pep->V,NULL,&nq);
587: BVSetActiveColumns(pep->V,0,nq);
588: if (nq>pep->nconv) {
589: BVTensorCompress(ctx->V,pep->nconv);
590: BVSetActiveColumns(pep->V,0,pep->nconv);
591: nq = pep->nconv;
592: }
594: /* perform Newton refinement if required */
595: if (pep->refine==PEP_REFINE_MULTIPLE && pep->rits>0) {
596: /* extract invariant pair */
597: BVTensorGetFactors(ctx->V,NULL,&MS);
598: MatDenseGetArray(MS,&S);
599: DSGetArray(pep->ds,DS_MAT_A,&H);
600: BVGetSizes(pep->V,NULL,NULL,&ld);
601: lds = deg*ld;
602: PEPExtractInvariantPair(pep,sigma,nq,pep->nconv,S,ld,deg,H,ldds);
603: DSRestoreArray(pep->ds,DS_MAT_A,&H);
604: DSSetDimensions(pep->ds,pep->nconv,0,0,0);
605: DSSetState(pep->ds,DS_STATE_RAW);
606: PEPNewtonRefinement_TOAR(pep,sigma,&pep->rits,NULL,pep->nconv,S,lds);
607: DSSolve(pep->ds,pep->eigr,pep->eigi);
608: DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
609: DSSynchronize(pep->ds,pep->eigr,pep->eigi);
610: DSGetMat(pep->ds,DS_MAT_Q,&MQ);
611: BVMultInPlace(ctx->V,MQ,0,pep->nconv);
612: MatDestroy(&MQ);
613: MatDenseRestoreArray(MS,&S);
614: BVTensorRestoreFactors(ctx->V,NULL,&MS);
615: }
616: }
617: STGetTransform(pep->st,&flg);
618: if (pep->refine!=PEP_REFINE_MULTIPLE || pep->rits==0) {
619: if (!flg && pep->ops->backtransform) {
620: (*pep->ops->backtransform)(pep);
621: }
622: if (pep->sfactor!=1.0) {
623: for (j=0;j<pep->nconv;j++) {
624: pep->eigr[j] *= pep->sfactor;
625: pep->eigi[j] *= pep->sfactor;
626: }
627: /* restore original values */
628: for (i=0;i<pep->nmat;i++){
629: pep->pbc[pep->nmat+i] *= pep->sfactor;
630: pep->pbc[2*pep->nmat+i] *= pep->sfactor*pep->sfactor;
631: }
632: }
633: }
634: /* restore original values */
635: if (!flg) {
636: pep->target *= pep->sfactor;
637: STScaleShift(pep->st,pep->sfactor);
638: } else {
639: STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor);
640: pep->target = (sinv)?pep->target/pep->sfactor:pep->target*pep->sfactor;
641: }
642: if (pep->sfactor!=1.0) { RGPopScale(pep->rg); }
644: /* change the state to raw so that DSVectors() computes eigenvectors from scratch */
645: DSSetDimensions(pep->ds,pep->nconv,0,0,0);
646: DSSetState(pep->ds,DS_STATE_RAW);
647: return(0);
648: }
650: static PetscErrorCode PEPTOARSetRestart_TOAR(PEP pep,PetscReal keep)
651: {
652: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
655: if (keep==PETSC_DEFAULT) ctx->keep = 0.5;
656: else {
657: 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]");
658: ctx->keep = keep;
659: }
660: return(0);
661: }
663: /*@
664: PEPTOARSetRestart - Sets the restart parameter for the TOAR
665: method, in particular the proportion of basis vectors that must be kept
666: after restart.
668: Logically Collective on pep
670: Input Parameters:
671: + pep - the eigenproblem solver context
672: - keep - the number of vectors to be kept at restart
674: Options Database Key:
675: . -pep_toar_restart - Sets the restart parameter
677: Notes:
678: Allowed values are in the range [0.1,0.9]. The default is 0.5.
680: Level: advanced
682: .seealso: PEPTOARGetRestart()
683: @*/
684: PetscErrorCode PEPTOARSetRestart(PEP pep,PetscReal keep)
685: {
691: PetscTryMethod(pep,"PEPTOARSetRestart_C",(PEP,PetscReal),(pep,keep));
692: return(0);
693: }
695: static PetscErrorCode PEPTOARGetRestart_TOAR(PEP pep,PetscReal *keep)
696: {
697: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
700: *keep = ctx->keep;
701: return(0);
702: }
704: /*@
705: PEPTOARGetRestart - Gets the restart parameter used in the TOAR method.
707: Not Collective
709: Input Parameter:
710: . pep - the eigenproblem solver context
712: Output Parameter:
713: . keep - the restart parameter
715: Level: advanced
717: .seealso: PEPTOARSetRestart()
718: @*/
719: PetscErrorCode PEPTOARGetRestart(PEP pep,PetscReal *keep)
720: {
726: PetscUseMethod(pep,"PEPTOARGetRestart_C",(PEP,PetscReal*),(pep,keep));
727: return(0);
728: }
730: static PetscErrorCode PEPTOARSetLocking_TOAR(PEP pep,PetscBool lock)
731: {
732: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
735: ctx->lock = lock;
736: return(0);
737: }
739: /*@
740: PEPTOARSetLocking - Choose between locking and non-locking variants of
741: the TOAR method.
743: Logically Collective on pep
745: Input Parameters:
746: + pep - the eigenproblem solver context
747: - lock - true if the locking variant must be selected
749: Options Database Key:
750: . -pep_toar_locking - Sets the locking flag
752: Notes:
753: The default is to lock converged eigenpairs when the method restarts.
754: This behaviour can be changed so that all directions are kept in the
755: working subspace even if already converged to working accuracy (the
756: non-locking variant).
758: Level: advanced
760: .seealso: PEPTOARGetLocking()
761: @*/
762: PetscErrorCode PEPTOARSetLocking(PEP pep,PetscBool lock)
763: {
769: PetscTryMethod(pep,"PEPTOARSetLocking_C",(PEP,PetscBool),(pep,lock));
770: return(0);
771: }
773: static PetscErrorCode PEPTOARGetLocking_TOAR(PEP pep,PetscBool *lock)
774: {
775: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
778: *lock = ctx->lock;
779: return(0);
780: }
782: /*@
783: PEPTOARGetLocking - Gets the locking flag used in the TOAR method.
785: Not Collective
787: Input Parameter:
788: . pep - the eigenproblem solver context
790: Output Parameter:
791: . lock - the locking flag
793: Level: advanced
795: .seealso: PEPTOARSetLocking()
796: @*/
797: PetscErrorCode PEPTOARGetLocking(PEP pep,PetscBool *lock)
798: {
804: PetscUseMethod(pep,"PEPTOARGetLocking_C",(PEP,PetscBool*),(pep,lock));
805: return(0);
806: }
808: PetscErrorCode PEPSetFromOptions_TOAR(PetscOptionItems *PetscOptionsObject,PEP pep)
809: {
811: PetscBool flg,lock;
812: PetscReal keep;
815: PetscOptionsHead(PetscOptionsObject,"PEP TOAR Options");
817: PetscOptionsReal("-pep_toar_restart","Proportion of vectors kept after restart","PEPTOARSetRestart",0.5,&keep,&flg);
818: if (flg) { PEPTOARSetRestart(pep,keep); }
820: PetscOptionsBool("-pep_toar_locking","Choose between locking and non-locking variants","PEPTOARSetLocking",PETSC_FALSE,&lock,&flg);
821: if (flg) { PEPTOARSetLocking(pep,lock); }
823: PetscOptionsTail();
824: return(0);
825: }
827: PetscErrorCode PEPView_TOAR(PEP pep,PetscViewer viewer)
828: {
830: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
831: PetscBool isascii;
834: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
835: if (isascii) {
836: PetscViewerASCIIPrintf(viewer," %d%% of basis vectors kept after restart\n",(int)(100*ctx->keep));
837: PetscViewerASCIIPrintf(viewer," using the %slocking variant\n",ctx->lock?"":"non-");
838: }
839: return(0);
840: }
842: PetscErrorCode PEPDestroy_TOAR(PEP pep)
843: {
845: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
848: BVDestroy(&ctx->V);
849: PetscFree(pep->data);
850: PetscObjectComposeFunction((PetscObject)pep,"PEPTOARSetRestart_C",NULL);
851: PetscObjectComposeFunction((PetscObject)pep,"PEPTOARGetRestart_C",NULL);
852: PetscObjectComposeFunction((PetscObject)pep,"PEPTOARSetLocking_C",NULL);
853: PetscObjectComposeFunction((PetscObject)pep,"PEPTOARGetLocking_C",NULL);
854: return(0);
855: }
857: SLEPC_EXTERN PetscErrorCode PEPCreate_TOAR(PEP pep)
858: {
859: PEP_TOAR *ctx;
863: PetscNewLog(pep,&ctx);
864: pep->data = (void*)ctx;
865: ctx->lock = PETSC_TRUE;
867: pep->ops->solve = PEPSolve_TOAR;
868: pep->ops->setup = PEPSetUp_TOAR;
869: pep->ops->setfromoptions = PEPSetFromOptions_TOAR;
870: pep->ops->destroy = PEPDestroy_TOAR;
871: pep->ops->view = PEPView_TOAR;
872: pep->ops->backtransform = PEPBackTransform_Default;
873: pep->ops->computevectors = PEPComputeVectors_Default;
874: pep->ops->extractvectors = PEPExtractVectors_TOAR;
876: PetscObjectComposeFunction((PetscObject)pep,"PEPTOARSetRestart_C",PEPTOARSetRestart_TOAR);
877: PetscObjectComposeFunction((PetscObject)pep,"PEPTOARGetRestart_C",PEPTOARGetRestart_TOAR);
878: PetscObjectComposeFunction((PetscObject)pep,"PEPTOARSetLocking_C",PEPTOARSetLocking_TOAR);
879: PetscObjectComposeFunction((PetscObject)pep,"PEPTOARGetLocking_C",PEPTOARGetLocking_TOAR);
880: return(0);
881: }