Actual source code: ptoar.c
slepc-3.22.1 2024-10-28
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 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: static PetscErrorCode PEPSetUp_TOAR(PEP pep)
51: {
52: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
53: PetscBool sinv,flg;
54: PetscInt i;
56: PetscFunctionBegin;
57: PEPCheckShiftSinvert(pep);
58: PetscCall(PEPSetDimensions_Default(pep,pep->nev,&pep->ncv,&pep->mpd));
59: PetscCheck(ctx->lock || pep->mpd>=pep->ncv,PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Should not use mpd parameter in non-locking variant");
60: if (pep->max_it==PETSC_DETERMINE) pep->max_it = PetscMax(100,2*(pep->nmat-1)*pep->n/pep->ncv);
61: if (!pep->which) PetscCall(PEPSetWhichEigenpairs_Default(pep));
62: PetscCheck(pep->which!=PEP_ALL,PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"This solver does not support computing all eigenvalues");
63: if (pep->problem_type!=PEP_GENERAL) PetscCall(PetscInfo(pep,"Problem type ignored, performing a non-symmetric linearization\n"));
65: if (!ctx->keep) ctx->keep = 0.5;
67: PetscCall(PEPAllocateSolution(pep,pep->nmat-1));
68: PetscCall(PEPSetWorkVecs(pep,3));
69: PetscCall(DSSetType(pep->ds,DSNHEP));
70: PetscCall(DSSetExtraRow(pep->ds,PETSC_TRUE));
71: PetscCall(DSAllocate(pep->ds,pep->ncv+1));
73: PetscCall(PEPBasisCoefficients(pep,pep->pbc));
74: PetscCall(STGetTransform(pep->st,&flg));
75: if (!flg) {
76: PetscCall(PetscFree(pep->solvematcoeffs));
77: PetscCall(PetscMalloc1(pep->nmat,&pep->solvematcoeffs));
78: PetscCall(PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv));
79: if (sinv) PetscCall(PEPEvaluateBasis(pep,pep->target,0,pep->solvematcoeffs,NULL));
80: else {
81: for (i=0;i<pep->nmat-1;i++) pep->solvematcoeffs[i] = 0.0;
82: pep->solvematcoeffs[pep->nmat-1] = 1.0;
83: }
84: }
85: PetscCall(BVDestroy(&ctx->V));
86: PetscCall(BVCreateTensor(pep->V,pep->nmat-1,&ctx->V));
87: PetscFunctionReturn(PETSC_SUCCESS);
88: }
90: /*
91: Extend the TOAR basis by applying the matrix operator
92: over a vector which is decomposed in the TOAR way
93: Input:
94: - pbc: array containing the polynomial basis coefficients
95: - S,V: define the latest Arnoldi vector (nv vectors in V)
96: Output:
97: - t: new vector extending the TOAR basis
98: - r: temporary coefficients to compute the TOAR coefficients
99: for the new Arnoldi vector
100: Workspace: t_ (two vectors)
101: */
102: 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_)
103: {
104: PetscInt nmat=pep->nmat,deg=nmat-1,k,j,off=0,lss;
105: Vec v=t_[0],ve=t_[1],q=t_[2];
106: PetscScalar alpha=1.0,*ss,a;
107: PetscReal *ca=pep->pbc,*cb=pep->pbc+nmat,*cg=pep->pbc+2*nmat;
108: PetscBool flg;
110: PetscFunctionBegin;
111: PetscCall(BVSetActiveColumns(pep->V,0,nv));
112: PetscCall(STGetTransform(pep->st,&flg));
113: if (sinvert) {
114: for (j=0;j<nv;j++) {
115: if (deg>1) r[lr+j] = S[j]/ca[0];
116: if (deg>2) r[2*lr+j] = (S[ls+j]+(sigma-cb[1])*r[lr+j])/ca[1];
117: }
118: for (k=2;k<deg-1;k++) {
119: 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];
120: }
121: k = deg-1;
122: 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];
123: ss = r; lss = lr; off = 1; alpha = -1.0; a = pep->sfactor;
124: } else {
125: ss = S; lss = ls; off = 0; alpha = -ca[deg-1]; a = 1.0;
126: }
127: PetscCall(BVMultVec(V,1.0,0.0,v,ss+off*lss));
128: if (PetscUnlikely(pep->Dr)) { /* balancing */
129: PetscCall(VecPointwiseMult(v,v,pep->Dr));
130: }
131: PetscCall(STMatMult(pep->st,off,v,q));
132: PetscCall(VecScale(q,a));
133: for (j=1+off;j<deg+off-1;j++) {
134: PetscCall(BVMultVec(V,1.0,0.0,v,ss+j*lss));
135: if (PetscUnlikely(pep->Dr)) PetscCall(VecPointwiseMult(v,v,pep->Dr));
136: PetscCall(STMatMult(pep->st,j,v,t));
137: a *= pep->sfactor;
138: PetscCall(VecAXPY(q,a,t));
139: }
140: if (sinvert) {
141: PetscCall(BVMultVec(V,1.0,0.0,v,ss));
142: if (PetscUnlikely(pep->Dr)) PetscCall(VecPointwiseMult(v,v,pep->Dr));
143: PetscCall(STMatMult(pep->st,deg,v,t));
144: a *= pep->sfactor;
145: PetscCall(VecAXPY(q,a,t));
146: } else {
147: PetscCall(BVMultVec(V,1.0,0.0,ve,ss+(deg-1)*lss));
148: if (PetscUnlikely(pep->Dr)) PetscCall(VecPointwiseMult(ve,ve,pep->Dr));
149: a *= pep->sfactor;
150: PetscCall(STMatMult(pep->st,deg-1,ve,t));
151: PetscCall(VecAXPY(q,a,t));
152: a *= pep->sfactor;
153: }
154: if (flg || !sinvert) alpha /= a;
155: PetscCall(STMatSolve(pep->st,q,t));
156: PetscCall(VecScale(t,alpha));
157: if (!sinvert) {
158: PetscCall(VecAXPY(t,cg[deg-1],v));
159: PetscCall(VecAXPY(t,cb[deg-1],ve));
160: }
161: if (PetscUnlikely(pep->Dr)) PetscCall(VecPointwiseDivide(t,t,pep->Dr));
162: PetscFunctionReturn(PETSC_SUCCESS);
163: }
165: /*
166: Compute TOAR coefficients of the blocks of the new Arnoldi vector computed
167: */
168: static PetscErrorCode PEPTOARCoefficients(PEP pep,PetscBool sinvert,PetscScalar sigma,PetscInt nv,PetscScalar *S,PetscInt ls,PetscScalar *r,PetscInt lr,PetscScalar *x)
169: {
170: PetscInt k,j,nmat=pep->nmat,d=nmat-1;
171: PetscReal *ca=pep->pbc,*cb=pep->pbc+nmat,*cg=pep->pbc+2*nmat;
172: PetscScalar t=1.0,tp=0.0,tt;
174: PetscFunctionBegin;
175: if (sinvert) {
176: for (k=1;k<d;k++) {
177: tt = t;
178: t = ((sigma-cb[k-1])*t-cg[k-1]*tp)/ca[k-1]; /* k-th basis polynomial */
179: tp = tt;
180: for (j=0;j<=nv;j++) r[k*lr+j] += t*x[j];
181: }
182: } else {
183: for (j=0;j<=nv;j++) r[j] = (cb[0]-sigma)*S[j]+ca[0]*S[ls+j];
184: for (k=1;k<d-1;k++) {
185: 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];
186: }
187: if (sigma!=0.0) for (j=0;j<=nv;j++) r[(d-1)*lr+j] -= sigma*S[(d-1)*ls+j];
188: }
189: PetscFunctionReturn(PETSC_SUCCESS);
190: }
192: /*
193: Compute a run of Arnoldi iterations dim(work)=ld
194: */
195: static PetscErrorCode PEPTOARrun(PEP pep,PetscScalar sigma,Mat A,PetscInt k,PetscInt *M,PetscReal *beta,PetscBool *breakdown,Vec *t_)
196: {
197: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
198: PetscInt j,m=*M,deg=pep->nmat-1,ld;
199: PetscInt ldh,lds,nqt,l;
200: Vec t;
201: PetscReal norm=0.0;
202: PetscBool flg,sinvert=PETSC_FALSE,lindep;
203: PetscScalar *H,*x,*S;
204: Mat MS;
206: PetscFunctionBegin;
207: *beta = 0.0;
208: PetscCall(MatDenseGetArray(A,&H));
209: PetscCall(MatDenseGetLDA(A,&ldh));
210: PetscCall(BVTensorGetFactors(ctx->V,NULL,&MS));
211: PetscCall(MatDenseGetArray(MS,&S));
212: PetscCall(BVGetSizes(pep->V,NULL,NULL,&ld));
213: lds = ld*deg;
214: PetscCall(BVGetActiveColumns(pep->V,&l,&nqt));
215: PetscCall(STGetTransform(pep->st,&flg));
216: if (!flg) {
217: /* spectral transformation handled by the solver */
218: PetscCall(PetscObjectTypeCompareAny((PetscObject)pep->st,&flg,STSINVERT,STSHIFT,""));
219: PetscCheck(flg,PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"ST type not supported for TOAR without transforming matrices");
220: PetscCall(PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinvert));
221: }
222: PetscCall(BVSetActiveColumns(ctx->V,0,m));
223: for (j=k;j<m;j++) {
224: /* apply operator */
225: PetscCall(BVGetColumn(pep->V,nqt,&t));
226: PetscCall(PEPTOARExtendBasis(pep,sinvert,sigma,S+j*lds,ld,nqt,pep->V,t,S+(j+1)*lds,ld,t_));
227: PetscCall(BVRestoreColumn(pep->V,nqt,&t));
229: /* orthogonalize */
230: if (sinvert) x = S+(j+1)*lds;
231: else x = S+(deg-1)*ld+(j+1)*lds;
232: PetscCall(BVOrthogonalizeColumn(pep->V,nqt,x,&norm,&lindep));
233: if (!lindep) {
234: x[nqt] = norm;
235: PetscCall(BVScaleColumn(pep->V,nqt,1.0/norm));
236: nqt++;
237: }
239: PetscCall(PEPTOARCoefficients(pep,sinvert,sigma,nqt-1,S+j*lds,ld,S+(j+1)*lds,ld,x));
241: /* level-2 orthogonalization */
242: PetscCall(BVOrthogonalizeColumn(ctx->V,j+1,H+j*ldh,&norm,breakdown));
243: H[j+1+ldh*j] = norm;
244: if (PetscUnlikely(*breakdown)) {
245: *M = j+1;
246: break;
247: }
248: PetscCall(BVScaleColumn(ctx->V,j+1,1.0/norm));
249: PetscCall(BVSetActiveColumns(pep->V,l,nqt));
250: }
251: *beta = norm;
252: PetscCall(BVSetActiveColumns(ctx->V,0,*M));
253: PetscCall(MatDenseRestoreArray(MS,&S));
254: PetscCall(BVTensorRestoreFactors(ctx->V,NULL,&MS));
255: PetscCall(MatDenseRestoreArray(A,&H));
256: PetscFunctionReturn(PETSC_SUCCESS);
257: }
259: /*
260: Computes T_j = phi_idx(T). In T_j and T_p are phi_{idx-1}(T)
261: and phi_{idx-2}(T) respectively or null if idx=0,1.
262: Tp and Tj are input/output arguments
263: */
264: static PetscErrorCode PEPEvaluateBasisM(PEP pep,PetscInt k,PetscScalar *T,PetscInt ldt,PetscInt idx,PetscScalar **Tp,PetscScalar **Tj)
265: {
266: PetscInt i;
267: PetscReal *ca,*cb,*cg;
268: PetscScalar *pt,g,a;
269: PetscBLASInt k_,ldt_;
271: PetscFunctionBegin;
272: if (idx==0) {
273: PetscCall(PetscArrayzero(*Tj,k*k));
274: PetscCall(PetscArrayzero(*Tp,k*k));
275: for (i=0;i<k;i++) (*Tj)[i+i*k] = 1.0;
276: } else {
277: PetscCall(PetscBLASIntCast(ldt,&ldt_));
278: PetscCall(PetscBLASIntCast(k,&k_));
279: ca = pep->pbc; cb = pep->pbc+pep->nmat; cg = pep->pbc+2*pep->nmat;
280: for (i=0;i<k;i++) T[i*ldt+i] -= cb[idx-1];
281: a = 1/ca[idx-1];
282: g = (idx==1)?0.0:-cg[idx-1]/ca[idx-1];
283: PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&a,T,&ldt_,*Tj,&k_,&g,*Tp,&k_));
284: pt = *Tj; *Tj = *Tp; *Tp = pt;
285: for (i=0;i<k;i++) T[i*ldt+i] += cb[idx-1];
286: }
287: PetscFunctionReturn(PETSC_SUCCESS);
288: }
290: static PetscErrorCode PEPExtractInvariantPair(PEP pep,PetscScalar sigma,PetscInt sr,PetscInt k,PetscScalar *S,PetscInt ld,PetscInt deg,Mat HH)
291: {
292: PetscInt i,j,jj,ldh,lds,ldt,d=pep->nmat-1,idxcpy=0;
293: PetscScalar *H,*At,*Bt,*Hj,*Hp,*T,sone=1.0,g,a,*pM,*work;
294: PetscBLASInt k_,sr_,lds_,ldh_,info,*p,lwork,ldt_;
295: PetscBool transf=PETSC_FALSE,flg;
296: PetscReal norm,maxnrm,*rwork;
297: BV *R,Y;
298: Mat M,*A;
300: PetscFunctionBegin;
301: if (k==0) PetscFunctionReturn(PETSC_SUCCESS);
302: PetscCall(MatDenseGetArray(HH,&H));
303: PetscCall(MatDenseGetLDA(HH,&ldh));
304: lds = deg*ld;
305: PetscCall(PetscCalloc6(k,&p,sr*k,&At,k*k,&Bt,k*k,&Hj,k*k,&Hp,sr*k,&work));
306: PetscCall(PetscBLASIntCast(sr,&sr_));
307: PetscCall(PetscBLASIntCast(k,&k_));
308: PetscCall(PetscBLASIntCast(lds,&lds_));
309: PetscCall(PetscBLASIntCast(ldh,&ldh_));
310: PetscCall(STGetTransform(pep->st,&flg));
311: if (!flg) {
312: PetscCall(PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&flg));
313: if (flg || sigma!=0.0) transf=PETSC_TRUE;
314: }
315: if (transf) {
316: PetscCall(PetscMalloc1(k*k,&T));
317: ldt = k;
318: for (i=0;i<k;i++) PetscCall(PetscArraycpy(T+k*i,H+i*ldh,k));
319: if (flg) {
320: PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
321: PetscCallBLAS("LAPACKgetrf",LAPACKgetrf_(&k_,&k_,T,&k_,p,&info));
322: SlepcCheckLapackInfo("getrf",info);
323: PetscCall(PetscBLASIntCast(sr*k,&lwork));
324: PetscCallBLAS("LAPACKgetri",LAPACKgetri_(&k_,T,&k_,p,work,&lwork,&info));
325: SlepcCheckLapackInfo("getri",info);
326: PetscCall(PetscFPTrapPop());
327: }
328: if (sigma!=0.0) for (i=0;i<k;i++) T[i+k*i] += sigma;
329: } else {
330: T = H; ldt = ldh;
331: }
332: PetscCall(PetscBLASIntCast(ldt,&ldt_));
333: switch (pep->extract) {
334: case PEP_EXTRACT_NONE:
335: break;
336: case PEP_EXTRACT_NORM:
337: if (pep->basis == PEP_BASIS_MONOMIAL) {
338: PetscCall(PetscBLASIntCast(ldt,&ldt_));
339: PetscCall(PetscMalloc1(k,&rwork));
340: norm = LAPACKlange_("F",&k_,&k_,T,&ldt_,rwork);
341: PetscCall(PetscFree(rwork));
342: if (norm>1.0) idxcpy = d-1;
343: } else {
344: PetscCall(PetscBLASIntCast(ldt,&ldt_));
345: PetscCall(PetscMalloc1(k,&rwork));
346: maxnrm = 0.0;
347: for (i=0;i<pep->nmat-1;i++) {
348: PetscCall(PEPEvaluateBasisM(pep,k,T,ldt,i,&Hp,&Hj));
349: norm = LAPACKlange_("F",&k_,&k_,Hj,&k_,rwork);
350: if (norm > maxnrm) {
351: idxcpy = i;
352: maxnrm = norm;
353: }
354: }
355: PetscCall(PetscFree(rwork));
356: }
357: if (idxcpy>0) {
358: /* copy block idxcpy of S to the first one */
359: for (j=0;j<k;j++) PetscCall(PetscArraycpy(S+j*lds,S+idxcpy*ld+j*lds,sr));
360: }
361: break;
362: case PEP_EXTRACT_RESIDUAL:
363: PetscCall(STGetTransform(pep->st,&flg));
364: if (flg) {
365: PetscCall(PetscMalloc1(pep->nmat,&A));
366: for (i=0;i<pep->nmat;i++) PetscCall(STGetMatrixTransformed(pep->st,i,A+i));
367: } else A = pep->A;
368: PetscCall(PetscMalloc1(pep->nmat-1,&R));
369: for (i=0;i<pep->nmat-1;i++) PetscCall(BVDuplicateResize(pep->V,k,R+i));
370: PetscCall(BVDuplicateResize(pep->V,sr,&Y));
371: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,sr,k,NULL,&M));
372: g = 0.0; a = 1.0;
373: PetscCall(BVSetActiveColumns(pep->V,0,sr));
374: for (j=0;j<pep->nmat;j++) {
375: PetscCall(BVMatMult(pep->V,A[j],Y));
376: PetscCall(PEPEvaluateBasisM(pep,k,T,ldt,i,&Hp,&Hj));
377: for (i=0;i<pep->nmat-1;i++) {
378: PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&sr_,&k_,&k_,&a,S+i*ld,&lds_,Hj,&k_,&g,At,&sr_));
379: PetscCall(MatDenseGetArray(M,&pM));
380: for (jj=0;jj<k;jj++) PetscCall(PetscArraycpy(pM+jj*sr,At+jj*sr,sr));
381: PetscCall(MatDenseRestoreArray(M,&pM));
382: PetscCall(BVMult(R[i],1.0,(i==0)?0.0:1.0,Y,M));
383: }
384: }
386: /* frobenius norm */
387: maxnrm = 0.0;
388: for (i=0;i<pep->nmat-1;i++) {
389: PetscCall(BVNorm(R[i],NORM_FROBENIUS,&norm));
390: if (maxnrm > norm) {
391: maxnrm = norm;
392: idxcpy = i;
393: }
394: }
395: if (idxcpy>0) {
396: /* copy block idxcpy of S to the first one */
397: for (j=0;j<k;j++) PetscCall(PetscArraycpy(S+j*lds,S+idxcpy*ld+j*lds,sr));
398: }
399: if (flg) PetscCall(PetscFree(A));
400: for (i=0;i<pep->nmat-1;i++) PetscCall(BVDestroy(&R[i]));
401: PetscCall(PetscFree(R));
402: PetscCall(BVDestroy(&Y));
403: PetscCall(MatDestroy(&M));
404: break;
405: case PEP_EXTRACT_STRUCTURED:
406: for (j=0;j<k;j++) Bt[j+j*k] = 1.0;
407: for (j=0;j<sr;j++) {
408: for (i=0;i<k;i++) At[j*k+i] = PetscConj(S[i*lds+j]);
409: }
410: PetscCall(PEPEvaluateBasisM(pep,k,T,ldt,0,&Hp,&Hj));
411: for (i=1;i<deg;i++) {
412: PetscCall(PEPEvaluateBasisM(pep,k,T,ldt,i,&Hp,&Hj));
413: PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&k_,&sr_,&k_,&sone,Hj,&k_,S+i*ld,&lds_,&sone,At,&k_));
414: PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&k_,&k_,&k_,&sone,Hj,&k_,Hj,&k_,&sone,Bt,&k_));
415: }
416: PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
417: PetscCallBLAS("LAPACKgesv",LAPACKgesv_(&k_,&sr_,Bt,&k_,p,At,&k_,&info));
418: PetscCall(PetscFPTrapPop());
419: SlepcCheckLapackInfo("gesv",info);
420: for (j=0;j<sr;j++) {
421: for (i=0;i<k;i++) S[i*lds+j] = PetscConj(At[j*k+i]);
422: }
423: break;
424: }
425: if (transf) PetscCall(PetscFree(T));
426: PetscCall(PetscFree6(p,At,Bt,Hj,Hp,work));
427: PetscCall(MatDenseRestoreArray(HH,&H));
428: PetscFunctionReturn(PETSC_SUCCESS);
429: }
431: static PetscErrorCode PEPSolve_TOAR(PEP pep)
432: {
433: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
434: PetscInt i,j,k,l,nv=0,ld,lds,nq=0,nconv=0;
435: PetscInt nmat=pep->nmat,deg=nmat-1;
436: PetscScalar *S,sigma;
437: PetscReal beta;
438: PetscBool breakdown=PETSC_FALSE,flg,falselock=PETSC_FALSE,sinv=PETSC_FALSE;
439: Mat H,MS,MQ;
441: PetscFunctionBegin;
442: PetscCall(PetscCitationsRegister(citation,&cited));
443: if (ctx->lock) {
444: /* undocumented option to use a cheaper locking instead of the true locking */
445: PetscCall(PetscOptionsGetBool(NULL,NULL,"-pep_toar_falselocking",&falselock,NULL));
446: }
447: PetscCall(STGetShift(pep->st,&sigma));
449: /* update polynomial basis coefficients */
450: PetscCall(STGetTransform(pep->st,&flg));
451: if (pep->sfactor!=1.0) {
452: for (i=0;i<nmat;i++) {
453: pep->pbc[nmat+i] /= pep->sfactor;
454: pep->pbc[2*nmat+i] /= pep->sfactor*pep->sfactor;
455: }
456: if (!flg) {
457: pep->target /= pep->sfactor;
458: PetscCall(RGPushScale(pep->rg,1.0/pep->sfactor));
459: PetscCall(STScaleShift(pep->st,1.0/pep->sfactor));
460: sigma /= pep->sfactor;
461: } else {
462: PetscCall(PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv));
463: pep->target = sinv?pep->target*pep->sfactor:pep->target/pep->sfactor;
464: PetscCall(RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor));
465: PetscCall(STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor));
466: }
467: }
469: if (flg) sigma = 0.0;
471: /* clean projected matrix (including the extra-arrow) */
472: PetscCall(DSSetDimensions(pep->ds,PETSC_DETERMINE,PETSC_DETERMINE,PETSC_DETERMINE));
473: PetscCall(DSGetMat(pep->ds,DS_MAT_A,&H));
474: PetscCall(MatZeroEntries(H));
475: PetscCall(DSRestoreMat(pep->ds,DS_MAT_A,&H));
477: /* Get the starting Arnoldi vector */
478: PetscCall(BVTensorBuildFirstColumn(ctx->V,pep->nini));
480: /* restart loop */
481: l = 0;
482: while (pep->reason == PEP_CONVERGED_ITERATING) {
483: pep->its++;
485: /* compute an nv-step Lanczos factorization */
486: nv = PetscMax(PetscMin(nconv+pep->mpd,pep->ncv),nv);
487: PetscCall(DSGetMat(pep->ds,DS_MAT_A,&H));
488: PetscCall(PEPTOARrun(pep,sigma,H,pep->nconv+l,&nv,&beta,&breakdown,pep->work));
489: PetscCall(DSRestoreMat(pep->ds,DS_MAT_A,&H));
490: PetscCall(DSSetDimensions(pep->ds,nv,pep->nconv,pep->nconv+l));
491: PetscCall(DSSetState(pep->ds,l?DS_STATE_RAW:DS_STATE_INTERMEDIATE));
492: PetscCall(BVSetActiveColumns(ctx->V,pep->nconv,nv));
494: /* solve projected problem */
495: PetscCall(DSSolve(pep->ds,pep->eigr,pep->eigi));
496: PetscCall(DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL));
497: PetscCall(DSUpdateExtraRow(pep->ds));
498: PetscCall(DSSynchronize(pep->ds,pep->eigr,pep->eigi));
500: /* check convergence */
501: PetscCall(PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,nv-pep->nconv,beta,&k));
502: PetscCall((*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx));
504: /* update l */
505: if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
506: else {
507: l = (nv==k)?0:PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
508: PetscCall(DSGetTruncateSize(pep->ds,k,nv,&l));
509: if (!breakdown) {
510: /* prepare the Rayleigh quotient for restart */
511: PetscCall(DSTruncate(pep->ds,k+l,PETSC_FALSE));
512: }
513: }
514: nconv = k;
515: if (!ctx->lock && pep->reason == PEP_CONVERGED_ITERATING && !breakdown) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
516: if (l) PetscCall(PetscInfo(pep,"Preparing to restart keeping l=%" PetscInt_FMT " vectors\n",l));
518: /* update S */
519: PetscCall(DSGetMat(pep->ds,DS_MAT_Q,&MQ));
520: PetscCall(BVMultInPlace(ctx->V,MQ,pep->nconv,k+l));
521: PetscCall(DSRestoreMat(pep->ds,DS_MAT_Q,&MQ));
523: /* copy last column of S */
524: PetscCall(BVCopyColumn(ctx->V,nv,k+l));
526: if (PetscUnlikely(breakdown && pep->reason == PEP_CONVERGED_ITERATING)) {
527: /* stop if breakdown */
528: PetscCall(PetscInfo(pep,"Breakdown TOAR method (it=%" PetscInt_FMT " norm=%g)\n",pep->its,(double)beta));
529: pep->reason = PEP_DIVERGED_BREAKDOWN;
530: }
531: if (pep->reason != PEP_CONVERGED_ITERATING) l--;
532: /* truncate S */
533: PetscCall(BVGetActiveColumns(pep->V,NULL,&nq));
534: if (k+l+deg<=nq) {
535: PetscCall(BVSetActiveColumns(ctx->V,pep->nconv,k+l+1));
536: if (!falselock && ctx->lock) PetscCall(BVTensorCompress(ctx->V,k-pep->nconv));
537: else PetscCall(BVTensorCompress(ctx->V,0));
538: }
539: pep->nconv = k;
540: PetscCall(PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv));
541: }
542: if (pep->nconv>0) {
543: /* {V*S_nconv^i}_{i=0}^{d-1} has rank nconv instead of nconv+d-1. Force zeros in each S_nconv^i block */
544: PetscCall(BVSetActiveColumns(ctx->V,0,pep->nconv));
545: PetscCall(BVGetActiveColumns(pep->V,NULL,&nq));
546: PetscCall(BVSetActiveColumns(pep->V,0,nq));
547: if (nq>pep->nconv) {
548: PetscCall(BVTensorCompress(ctx->V,pep->nconv));
549: PetscCall(BVSetActiveColumns(pep->V,0,pep->nconv));
550: nq = pep->nconv;
551: }
553: /* perform Newton refinement if required */
554: if (pep->refine==PEP_REFINE_MULTIPLE && pep->rits>0) {
555: /* extract invariant pair */
556: PetscCall(BVTensorGetFactors(ctx->V,NULL,&MS));
557: PetscCall(MatDenseGetArray(MS,&S));
558: PetscCall(DSGetMat(pep->ds,DS_MAT_A,&H));
559: PetscCall(BVGetSizes(pep->V,NULL,NULL,&ld));
560: lds = deg*ld;
561: PetscCall(PEPExtractInvariantPair(pep,sigma,nq,pep->nconv,S,ld,deg,H));
562: PetscCall(DSRestoreMat(pep->ds,DS_MAT_A,&H));
563: PetscCall(DSSetDimensions(pep->ds,pep->nconv,0,0));
564: PetscCall(DSSetState(pep->ds,DS_STATE_RAW));
565: PetscCall(PEPNewtonRefinement_TOAR(pep,sigma,&pep->rits,NULL,pep->nconv,S,lds));
566: PetscCall(DSSolve(pep->ds,pep->eigr,pep->eigi));
567: PetscCall(DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL));
568: PetscCall(DSSynchronize(pep->ds,pep->eigr,pep->eigi));
569: PetscCall(DSGetMat(pep->ds,DS_MAT_Q,&MQ));
570: PetscCall(BVMultInPlace(ctx->V,MQ,0,pep->nconv));
571: PetscCall(DSRestoreMat(pep->ds,DS_MAT_Q,&MQ));
572: PetscCall(MatDenseRestoreArray(MS,&S));
573: PetscCall(BVTensorRestoreFactors(ctx->V,NULL,&MS));
574: }
575: }
576: PetscCall(STGetTransform(pep->st,&flg));
577: if (pep->refine!=PEP_REFINE_MULTIPLE || pep->rits==0) {
578: if (!flg) PetscTryTypeMethod(pep,backtransform);
579: if (pep->sfactor!=1.0) {
580: for (j=0;j<pep->nconv;j++) {
581: pep->eigr[j] *= pep->sfactor;
582: pep->eigi[j] *= pep->sfactor;
583: }
584: /* restore original values */
585: for (i=0;i<pep->nmat;i++) {
586: pep->pbc[pep->nmat+i] *= pep->sfactor;
587: pep->pbc[2*pep->nmat+i] *= pep->sfactor*pep->sfactor;
588: }
589: }
590: }
591: /* restore original values */
592: if (!flg) {
593: pep->target *= pep->sfactor;
594: PetscCall(STScaleShift(pep->st,pep->sfactor));
595: } else {
596: PetscCall(STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor));
597: pep->target = (sinv)?pep->target/pep->sfactor:pep->target*pep->sfactor;
598: }
599: if (pep->sfactor!=1.0) PetscCall(RGPopScale(pep->rg));
601: /* change the state to raw so that DSVectors() computes eigenvectors from scratch */
602: PetscCall(DSSetDimensions(pep->ds,pep->nconv,0,0));
603: PetscCall(DSSetState(pep->ds,DS_STATE_RAW));
604: PetscFunctionReturn(PETSC_SUCCESS);
605: }
607: static PetscErrorCode PEPTOARSetRestart_TOAR(PEP pep,PetscReal keep)
608: {
609: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
611: PetscFunctionBegin;
612: if (keep==(PetscReal)PETSC_DEFAULT || keep==(PetscReal)PETSC_DECIDE) ctx->keep = 0.5;
613: else {
614: 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]");
615: ctx->keep = keep;
616: }
617: PetscFunctionReturn(PETSC_SUCCESS);
618: }
620: /*@
621: PEPTOARSetRestart - Sets the restart parameter for the TOAR
622: method, in particular the proportion of basis vectors that must be kept
623: after restart.
625: Logically Collective
627: Input Parameters:
628: + pep - the eigenproblem solver context
629: - keep - the number of vectors to be kept at restart
631: Options Database Key:
632: . -pep_toar_restart - Sets the restart parameter
634: Notes:
635: Allowed values are in the range [0.1,0.9]. The default is 0.5.
637: Level: advanced
639: .seealso: PEPTOARGetRestart()
640: @*/
641: PetscErrorCode PEPTOARSetRestart(PEP pep,PetscReal keep)
642: {
643: PetscFunctionBegin;
646: PetscTryMethod(pep,"PEPTOARSetRestart_C",(PEP,PetscReal),(pep,keep));
647: PetscFunctionReturn(PETSC_SUCCESS);
648: }
650: static PetscErrorCode PEPTOARGetRestart_TOAR(PEP pep,PetscReal *keep)
651: {
652: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
654: PetscFunctionBegin;
655: *keep = ctx->keep;
656: PetscFunctionReturn(PETSC_SUCCESS);
657: }
659: /*@
660: PEPTOARGetRestart - Gets the restart parameter used in the TOAR method.
662: Not Collective
664: Input Parameter:
665: . pep - the eigenproblem solver context
667: Output Parameter:
668: . keep - the restart parameter
670: Level: advanced
672: .seealso: PEPTOARSetRestart()
673: @*/
674: PetscErrorCode PEPTOARGetRestart(PEP pep,PetscReal *keep)
675: {
676: PetscFunctionBegin;
678: PetscAssertPointer(keep,2);
679: PetscUseMethod(pep,"PEPTOARGetRestart_C",(PEP,PetscReal*),(pep,keep));
680: PetscFunctionReturn(PETSC_SUCCESS);
681: }
683: static PetscErrorCode PEPTOARSetLocking_TOAR(PEP pep,PetscBool lock)
684: {
685: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
687: PetscFunctionBegin;
688: ctx->lock = lock;
689: PetscFunctionReturn(PETSC_SUCCESS);
690: }
692: /*@
693: PEPTOARSetLocking - Choose between locking and non-locking variants of
694: the TOAR method.
696: Logically Collective
698: Input Parameters:
699: + pep - the eigenproblem solver context
700: - lock - true if the locking variant must be selected
702: Options Database Key:
703: . -pep_toar_locking - Sets the locking flag
705: Notes:
706: The default is to lock converged eigenpairs when the method restarts.
707: This behaviour can be changed so that all directions are kept in the
708: working subspace even if already converged to working accuracy (the
709: non-locking variant).
711: Level: advanced
713: .seealso: PEPTOARGetLocking()
714: @*/
715: PetscErrorCode PEPTOARSetLocking(PEP pep,PetscBool lock)
716: {
717: PetscFunctionBegin;
720: PetscTryMethod(pep,"PEPTOARSetLocking_C",(PEP,PetscBool),(pep,lock));
721: PetscFunctionReturn(PETSC_SUCCESS);
722: }
724: static PetscErrorCode PEPTOARGetLocking_TOAR(PEP pep,PetscBool *lock)
725: {
726: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
728: PetscFunctionBegin;
729: *lock = ctx->lock;
730: PetscFunctionReturn(PETSC_SUCCESS);
731: }
733: /*@
734: PEPTOARGetLocking - Gets the locking flag used in the TOAR method.
736: Not Collective
738: Input Parameter:
739: . pep - the eigenproblem solver context
741: Output Parameter:
742: . lock - the locking flag
744: Level: advanced
746: .seealso: PEPTOARSetLocking()
747: @*/
748: PetscErrorCode PEPTOARGetLocking(PEP pep,PetscBool *lock)
749: {
750: PetscFunctionBegin;
752: PetscAssertPointer(lock,2);
753: PetscUseMethod(pep,"PEPTOARGetLocking_C",(PEP,PetscBool*),(pep,lock));
754: PetscFunctionReturn(PETSC_SUCCESS);
755: }
757: static PetscErrorCode PEPSetFromOptions_TOAR(PEP pep,PetscOptionItems *PetscOptionsObject)
758: {
759: PetscBool flg,lock;
760: PetscReal keep;
762: PetscFunctionBegin;
763: PetscOptionsHeadBegin(PetscOptionsObject,"PEP TOAR Options");
765: PetscCall(PetscOptionsReal("-pep_toar_restart","Proportion of vectors kept after restart","PEPTOARSetRestart",0.5,&keep,&flg));
766: if (flg) PetscCall(PEPTOARSetRestart(pep,keep));
768: PetscCall(PetscOptionsBool("-pep_toar_locking","Choose between locking and non-locking variants","PEPTOARSetLocking",PETSC_FALSE,&lock,&flg));
769: if (flg) PetscCall(PEPTOARSetLocking(pep,lock));
771: PetscOptionsHeadEnd();
772: PetscFunctionReturn(PETSC_SUCCESS);
773: }
775: static PetscErrorCode PEPView_TOAR(PEP pep,PetscViewer viewer)
776: {
777: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
778: PetscBool isascii;
780: PetscFunctionBegin;
781: PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
782: if (isascii) {
783: PetscCall(PetscViewerASCIIPrintf(viewer," %d%% of basis vectors kept after restart\n",(int)(100*ctx->keep)));
784: PetscCall(PetscViewerASCIIPrintf(viewer," using the %slocking variant\n",ctx->lock?"":"non-"));
785: }
786: PetscFunctionReturn(PETSC_SUCCESS);
787: }
789: static PetscErrorCode PEPDestroy_TOAR(PEP pep)
790: {
791: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
793: PetscFunctionBegin;
794: PetscCall(BVDestroy(&ctx->V));
795: PetscCall(PetscFree(pep->data));
796: PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPTOARSetRestart_C",NULL));
797: PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPTOARGetRestart_C",NULL));
798: PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPTOARSetLocking_C",NULL));
799: PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPTOARGetLocking_C",NULL));
800: PetscFunctionReturn(PETSC_SUCCESS);
801: }
803: SLEPC_EXTERN PetscErrorCode PEPCreate_TOAR(PEP pep)
804: {
805: PEP_TOAR *ctx;
807: PetscFunctionBegin;
808: PetscCall(PetscNew(&ctx));
809: pep->data = (void*)ctx;
811: pep->lineariz = PETSC_TRUE;
812: ctx->lock = PETSC_TRUE;
814: pep->ops->solve = PEPSolve_TOAR;
815: pep->ops->setup = PEPSetUp_TOAR;
816: pep->ops->setfromoptions = PEPSetFromOptions_TOAR;
817: pep->ops->destroy = PEPDestroy_TOAR;
818: pep->ops->view = PEPView_TOAR;
819: pep->ops->backtransform = PEPBackTransform_Default;
820: pep->ops->computevectors = PEPComputeVectors_Default;
821: pep->ops->extractvectors = PEPExtractVectors_TOAR;
823: PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPTOARSetRestart_C",PEPTOARSetRestart_TOAR));
824: PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPTOARGetRestart_C",PEPTOARGetRestart_TOAR));
825: PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPTOARSetLocking_C",PEPTOARSetLocking_TOAR));
826: PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPTOARGetLocking_C",PEPTOARGetLocking_TOAR));
827: PetscFunctionReturn(PETSC_SUCCESS);
828: }