Actual source code: stoar.c
slepc-3.7.2 2016-07-19
1: /*
3: SLEPc polynomial eigensolver: "stoar"
5: Method: S-TOAR
7: Algorithm:
9: Symmetric Two-Level Orthogonal Arnoldi.
11: References:
13: [1] C. Campos and J.E. Roman, "Restarted Q-Arnoldi-type methods
14: exploiting symmetry in quadratic eigenvalue problems", BIT
15: Numer. Math. (in press), 2016.
17: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
18: SLEPc - Scalable Library for Eigenvalue Problem Computations
19: Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain
21: This file is part of SLEPc.
23: SLEPc is free software: you can redistribute it and/or modify it under the
24: terms of version 3 of the GNU Lesser General Public License as published by
25: the Free Software Foundation.
27: SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
28: WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
29: FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
30: more details.
32: You should have received a copy of the GNU Lesser General Public License
33: along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
34: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
35: */
37: #include <slepc/private/pepimpl.h> /*I "slepcpep.h" I*/
38: #include ../src/pep/impls/krylov/pepkrylov.h
39: #include <slepcblaslapack.h>
41: static PetscBool cited = PETSC_FALSE;
42: static const char citation[] =
43: "@Article{slepc-stoar,\n"
44: " author = \"C. Campos and J. E. Roman\",\n"
45: " title = \"Restarted {Q-Arnoldi-type} methods exploiting symmetry in quadratic eigenvalue problems\",\n"
46: " journal = \"{BIT} Numer. Math.\",\n"
47: " volume = \"to appear\",\n"
48: " number = \"\",\n"
49: " pages = \"\",\n"
50: " year = \"2016,\"\n"
51: " doi = \"http://dx.doi.org/10.1007/s10543-016-0601-5\"\n"
52: "}\n";
56: /*
57: Compute B-norm of v=[v1;v2] whith B=diag(-pep->T[0],pep->T[2])
58: */
59: static PetscErrorCode PEPSTOARNorm(PEP pep,PetscInt j,PetscReal *norm)
60: {
62: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
63: PetscBLASInt n_,one=1,ld_;
64: PetscScalar sone=1.0,szero=0.0,*sp,*sq,*w1,*w2,*qK,*qM;
65: PetscInt n,i,lds=ctx->d*ctx->ld;
68: qK = ctx->qB;
69: qM = ctx->qB+ctx->ld*ctx->ld;
70: n = j+2;
71: PetscMalloc2(n,&w1,n,&w2);
72: sp = ctx->S+lds*j;
73: sq = sp+ctx->ld;
74: PetscBLASIntCast(n,&n_);
75: PetscBLASIntCast(ctx->ld,&ld_);
76: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&n_,&sone,qK,&ld_,sp,&one,&szero,w1,&one));
77: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&n_,&sone,qM,&ld_,sq,&one,&szero,w2,&one));
78: *norm = 0.0;
79: for (i=0;i<n;i++) *norm += PetscRealPart(w1[i]*PetscConj(sp[i])+w2[i]*PetscConj(sq[i]));
80: *norm = (*norm>0.0)?PetscSqrtReal(*norm):-PetscSqrtReal(-*norm);
81: PetscFree2(w1,w2);
82: return(0);
83: }
87: static PetscErrorCode PEPSTOARqKqMupdates(PEP pep,PetscInt j,Vec *wv)
88: {
90: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
91: PetscInt i,ld=ctx->ld;
92: PetscScalar *qK,*qM;
93: Vec vj,v1,v2;
96: qK = ctx->qB;
97: qM = ctx->qB+ctx->ld*ctx->ld;
98: v1 = wv[0];
99: v2 = wv[1];
100: BVGetColumn(pep->V,j,&vj);
101: STMatMult(pep->st,0,vj,v1);
102: STMatMult(pep->st,2,vj,v2);
103: BVRestoreColumn(pep->V,j,&vj);
104: for (i=0;i<=j;i++) {
105: BVGetColumn(pep->V,i,&vj);
106: VecDot(v1,vj,qK+j*ld+i);
107: VecDot(v2,vj,qM+j*ld+i);
108: *(qM+j*ld+i) *= pep->sfactor*pep->sfactor;
109: BVRestoreColumn(pep->V,i,&vj);
110: }
111: for (i=0;i<j;i++) {
112: qK[i+j*ld] = -qK[i+ld*j];
113: qK[j+i*ld] = PetscConj(qK[i+j*ld]);
114: qM[j+i*ld] = PetscConj(qM[i+j*ld]);
115: }
116: qK[j+j*ld] = -PetscRealPart(qK[j+ld*j]);
117: qM[j+j*ld] = PetscRealPart(qM[j+ld*j]);
118: return(0);
119: }
123: PetscErrorCode PEPSetUp_STOAR(PEP pep)
124: {
126: PetscBool shift,sinv,flg,lindep;
127: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
128: PetscInt ld,i;
129: PetscReal norm,*omega;
132: pep->lineariz = PETSC_TRUE;
133: PEPSetDimensions_Default(pep,pep->nev,&pep->ncv,&pep->mpd);
134: if (!ctx->lock && pep->mpd<pep->ncv) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Should not use mpd parameter in non-locking variant");
135: if (!pep->max_it) pep->max_it = PetscMax(100,2*pep->n/pep->ncv);
136: /* Set STSHIFT as the default ST */
137: if (!((PetscObject)pep->st)->type_name) {
138: STSetType(pep->st,STSHIFT);
139: }
140: PetscObjectTypeCompare((PetscObject)pep->st,STSHIFT,&shift);
141: PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
142: if (!shift && !sinv) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Only STSHIFT and STSINVERT spectral transformations can be used");
143: if (!pep->which) {
144: if (sinv) pep->which = PEP_TARGET_MAGNITUDE;
145: else pep->which = PEP_LARGEST_MAGNITUDE;
146: }
147: if (pep->problem_type!=PEP_HERMITIAN) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Requested method is only available for Hermitian problems");
149: if (pep->nmat!=3) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver only available for quadratic problems");
150: if (pep->basis!=PEP_BASIS_MONOMIAL) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver not implemented for non-monomial bases");
151: STGetTransform(pep->st,&flg);
152: if (!flg) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver requires the ST transformation flag set, see STSetTransform()");
154: PEPAllocateSolution(pep,2);
155: PEPSetWorkVecs(pep,4);
156: ld = pep->ncv+2;
157: DSSetType(pep->ds,DSGHIEP);
158: DSSetCompact(pep->ds,PETSC_TRUE);
159: DSAllocate(pep->ds,ld);
160: STGetNumMatrices(pep->st,&ctx->d);
161: ctx->d--;
162: ctx->ld = ld;
163: PetscCalloc1(ctx->d*ld*ld,&ctx->S);
164: PetscCalloc1(2*ld*ld,&ctx->qB);
166: /* process starting vector */
167: if (pep->nini>-2) {
168: BVSetRandomColumn(pep->V,0);
169: BVSetRandomColumn(pep->V,1);
170: } else {
171: BVInsertVec(pep->V,0,pep->IS[0]);
172: BVInsertVec(pep->V,1,pep->IS[1]);
173: }
174: BVOrthogonalizeColumn(pep->V,0,NULL,&norm,&lindep);
175: if (!lindep) {
176: BVScaleColumn(pep->V,0,1.0/norm);
177: ctx->S[0] = norm;
178: PEPSTOARqKqMupdates(pep,0,pep->work);
179: } else SETERRQ(PetscObjectComm((PetscObject)pep),1,"Problem with initial vector");
180: BVOrthogonalizeColumn(pep->V,1,ctx->S+ld,&norm,&lindep);
181: if (!lindep) {
182: BVScaleColumn(pep->V,1,1.0/norm);
183: ctx->S[1] = norm;
184: PEPSTOARqKqMupdates(pep,1,pep->work);
185: } else SETERRQ(PetscObjectComm((PetscObject)pep),1,"Problem with initial vector");
187: PEPSTOARNorm(pep,0,&norm);
188: for (i=0;i<2;i++) { ctx->S[i+ld] /= norm; ctx->S[i] /= norm; }
189: DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
190: omega[0] = (norm>0)?1.0:-1.0;
191: DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
192: if (pep->nini<0) {
193: SlepcBasisDestroy_Private(&pep->nini,&pep->IS);
194: }
195: return(0);
196: }
200: /*
201: Computes GS orthogonalization x = [z;x] - [Sp;Sq]*y,
202: where y = Omega\([Sp;Sq]'*[qK zeros(size(qK,1)) ;zeros(size(qK,1)) qM]*[z;x]).
203: n: Column from S to be orthogonalized against previous columns.
204: */
205: static PetscErrorCode PEPSTOAROrth2(PEP pep,PetscInt k,PetscReal *Omega,PetscScalar *y)
206: {
208: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
209: PetscBLASInt n_,lds_,k_,one=1,ld_;
210: PetscScalar *S=ctx->S,sonem=-1.0,sone=1.0,szero=0.0,*tp,*tq,*xp,*xq,*c,*qK,*qM;
211: PetscInt i,lds=ctx->d*ctx->ld,n,j;
214: qK = ctx->qB;
215: qM = ctx->qB+ctx->ld*ctx->ld;
216: n = k+2;
217: PetscMalloc3(n,&tp,n,&tq,k,&c);
218: PetscBLASIntCast(n,&n_); /* Size of qK and qM */
219: PetscBLASIntCast(ctx->ld,&ld_);
220: PetscBLASIntCast(lds,&lds_);
221: PetscBLASIntCast(k,&k_); /* Number of vectors to orthogonalize against */
222: xp = S+k*lds;
223: xq = S+ctx->ld+k*lds;
224: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&n_,&sone,qK,&ld_,xp,&one,&szero,tp,&one));
225: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&n_,&sone,qM,&ld_,xq,&one,&szero,tq,&one));
226: PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n_,&k_,&sone,ctx->S,&lds_,tp,&one,&szero,y,&one));
227: PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n_,&k_,&sone,S+ctx->ld,&lds_,tq,&one,&sone,y,&one));
228: for (i=0;i<k;i++) y[i] /= Omega[i];
229: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&k_,&sonem,S,&lds_,y,&one,&sone,xp,&one));
230: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&k_,&sonem,S+ctx->ld,&lds_,y,&one,&sone,xq,&one));
231: /* three times */
232: for (j=0;j<2;j++) {
233: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&n_,&sone,qK,&ld_,xp,&one,&szero,tp,&one));
234: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&n_,&sone,qM,&ld_,xq,&one,&szero,tq,&one));
235: PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n_,&k_,&sone,ctx->S,&lds_,tp,&one,&szero,c,&one));
236: PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n_,&k_,&sone,S+ctx->ld,&lds_,tq,&one,&sone,c,&one));
237: for (i=0;i<k;i++) c[i] /= Omega[i];
238: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&k_,&sonem,S,&lds_,c,&one,&sone,xp,&one));
239: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&k_,&sonem,S+ctx->ld,&lds_,c,&one,&sone,xq,&one));
240: for (i=0;i<k;i++) y[i] += c[i];
241: }
242: PetscFree3(tp,tq,c);
243: return(0);
244: }
248: /*
249: Compute a run of Lanczos iterations. dim(work)=(ctx->ld)*4
250: */
251: static PetscErrorCode PEPSTOARrun(PEP pep,PetscReal *a,PetscReal *b,PetscReal *omega,PetscInt k,PetscInt *M,PetscBool *breakdown,PetscBool *symmlost,PetscScalar *work,Vec *t_)
252: {
254: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
255: PetscInt i,j,m=*M,l;
256: PetscInt lds=ctx->d*ctx->ld,offq=ctx->ld;
257: Vec v=t_[0],t=t_[1],q=t_[2];
258: PetscReal norm,sym=0.0,fro=0.0,*f;
259: PetscScalar *y,*S=ctx->S;
260: PetscBLASInt j_,one=1;
261: PetscBool lindep;
264: *breakdown = PETSC_FALSE; /* ----- */
265: DSGetDimensions(pep->ds,NULL,NULL,&l,NULL,NULL);
266: y = work;
267: for (j=k;j<m;j++) {
268: /* apply operator */
269: BVSetActiveColumns(pep->V,0,j+2);
270: BVMultVec(pep->V,1.0,0.0,v,S+j*lds);
271: STMatMult(pep->st,0,v,t);
272: BVMultVec(pep->V,1.0,0.0,v,S+offq+j*lds);
273: STMatMult(pep->st,1,v,q);
274: VecAXPY(t,pep->sfactor,q);
275: STMatSolve(pep->st,t,q);
276: VecScale(q,-1.0/(pep->sfactor*pep->sfactor));
278: /* orthogonalize */
279: BVOrthogonalizeVec(pep->V,q,S+offq+(j+1)*lds,&norm,&lindep);
280: if (lindep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"STOAR does not support detection of linearly dependent TOAR vectors");
281: *(S+offq+(j+1)*lds+j+2) = norm;
282: VecScale(q,1.0/norm);
283: BVInsertVec(pep->V,j+2,q);
284: for (i=0;i<=j+1;i++) *(S+(j+1)*lds+i) = *(S+offq+j*lds+i);
286: /* update qK and qM */
287: PEPSTOARqKqMupdates(pep,j+2,t_);
289: /* level-2 orthogonalization */
290: PEPSTOAROrth2(pep,j+1,omega,y);
291: a[j] = PetscRealPart(y[j])/omega[j];
292: PEPSTOARNorm(pep,j+1,&norm);
293: omega[j+1] = (norm > 0)?1.0:-1.0;
294: for (i=0;i<=j+2;i++) {
295: S[i+(j+1)*lds] /= norm;
296: S[i+offq+(j+1)*lds] /= norm;
297: }
298: b[j] = PetscAbsReal(norm);
300: /* check symmetry */
301: DSGetArrayReal(pep->ds,DS_MAT_T,&f);
302: if (j==k) {
303: for (i=l;i<j-1;i++) y[i] = PetscAbsScalar(y[i])-PetscAbsReal(f[2*ctx->ld+i]);
304: for (i=0;i<l;i++) y[i] = 0.0;
305: }
306: DSRestoreArrayReal(pep->ds,DS_MAT_T,&f);
307: if (j>0) y[j-1] = PetscAbsScalar(y[j-1])-PetscAbsReal(b[j-1]);
308: PetscBLASIntCast(j,&j_);
309: sym = SlepcAbs(BLASnrm2_(&j_,y,&one),sym);
310: fro = SlepcAbs(fro,SlepcAbs(a[j],b[j]));
311: if (j>0) fro = SlepcAbs(fro,b[j-1]);
312: if (sym/fro>PetscMax(PETSC_SQRT_MACHINE_EPSILON,10*pep->tol)) {
313: *symmlost = PETSC_TRUE;
314: *M=j+1;
315: break;
316: }
317: }
318: return(0);
319: }
323: static PetscErrorCode PEPSTOARTrunc(PEP pep,PetscInt rs1,PetscInt cs1,PetscScalar *work,PetscReal *rwork)
324: {
325: #if defined(PETSC_MISSING_LAPACK_GESVD)
327: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GESVD - Lapack routine is unavailable");
328: #else
330: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
331: Mat G;
332: PetscInt lwa,nwu=0,nrwu=0;
333: PetscInt i,n,lds=2*ctx->ld;
334: PetscScalar *M,*V,*U,*S=ctx->S,sone=1.0,zero=0.0,t,*qK,*qM;
335: PetscReal *sg;
336: PetscBLASInt cs1_,rs1_,cs1t2,cs1p1,n_,info,lw_,lds_,ld_;
339: qK = ctx->qB;
340: qM = ctx->qB+ctx->ld*ctx->ld;
341: n = (rs1>2*cs1)?2*cs1:rs1;
342: lwa = cs1*rs1*4+n*(rs1+2*cs1)+(cs1+1)*(cs1+2);
343: M = work+nwu;
344: nwu += rs1*cs1*2;
345: U = work+nwu;
346: nwu += rs1*n;
347: V = work+nwu;
348: nwu += 2*cs1*n;
349: sg = rwork+nrwu;
350: nrwu += n;
351: for (i=0;i<cs1;i++) {
352: PetscMemcpy(M+i*rs1,S+i*lds,rs1*sizeof(PetscScalar));
353: PetscMemcpy(M+(i+cs1)*rs1,S+i*lds+ctx->ld,rs1*sizeof(PetscScalar));
354: }
355: PetscBLASIntCast(n,&n_);
356: PetscBLASIntCast(cs1,&cs1_);
357: PetscBLASIntCast(rs1,&rs1_);
358: PetscBLASIntCast(cs1*2,&cs1t2);
359: PetscBLASIntCast(cs1+1,&cs1p1);
360: PetscBLASIntCast(lds,&lds_);
361: PetscBLASIntCast(ctx->ld,&ld_);
362: PetscBLASIntCast(lwa-nwu,&lw_);
363: #if !defined(PETSC_USE_COMPLEX)
364: PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&rs1_,&cs1t2,M,&rs1_,sg,U,&rs1_,V,&n_,work+nwu,&lw_,&info));
365: #else
366: PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&rs1_,&cs1t2,M,&rs1_,sg,U,&rs1_,V,&n_,work+nwu,&lw_,rwork+nrwu,&info));
367: #endif
368: if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGESVD %d",info);
370: /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
371: MatCreateSeqDense(PETSC_COMM_SELF,rs1,2*cs1,U,&G);
372: BVSetActiveColumns(pep->V,0,rs1);
373: BVMultInPlace(pep->V,G,0,cs1+1);
374: MatDestroy(&G);
376: /* Update S */
377: PetscMemzero(S,lds*ctx->ld*sizeof(PetscScalar));
379: for (i=0;i<cs1+1;i++) {
380: t = sg[i];
381: PetscStackCallBLAS("BLASscal",BLASscal_(&cs1t2,&t,V+i,&n_));
382: }
383: for (i=0;i<cs1;i++) {
384: PetscMemcpy(S+i*lds,V+i*n,(cs1+1)*sizeof(PetscScalar));
385: PetscMemcpy(S+ctx->ld+i*lds,V+(cs1+i)*n,(cs1+1)*sizeof(PetscScalar));
386: }
388: /* Update qM and qK */
389: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&rs1_,&cs1p1,&rs1_,&sone,qK,&ld_,U,&rs1_,&zero,work+nwu,&rs1_));
390: PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&cs1p1,&cs1p1,&rs1_,&sone,U,&rs1_,work+nwu,&rs1_,&zero,qK,&ld_));
391: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&rs1_,&cs1p1,&rs1_,&sone,qM,&ld_,U,&rs1_,&zero,work+nwu,&rs1_));
392: PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&cs1p1,&cs1p1,&rs1_,&sone,U,&rs1_,work+nwu,&rs1_,&zero,qM,&ld_));
393: return(0);
394: #endif
395: }
399: /*
400: S <- S*Q
401: columns s-s+ncu of S
402: rows 0-sr of S
403: size(Q) qr x ncu
404: dim(work)=sr*ncu;
405: */
406: static PetscErrorCode PEPSTOARSupdate(PetscScalar *S,PetscInt ld,PetscInt sr,PetscInt s,PetscInt ncu,PetscInt qr,PetscScalar *Q,PetscInt ldq,PetscScalar *work)
407: {
409: PetscScalar a=1.0,b=0.0;
410: PetscBLASInt sr_,ncu_,ldq_,lds_,qr_;
411: PetscInt j,lds=2*ld;
414: PetscBLASIntCast(sr,&sr_);
415: PetscBLASIntCast(qr,&qr_);
416: PetscBLASIntCast(ncu,&ncu_);
417: PetscBLASIntCast(lds,&lds_);
418: PetscBLASIntCast(ldq,&ldq_);
419: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&sr_,&ncu_,&qr_,&a,S,&lds_,Q,&ldq_,&b,work,&sr_));
420: for (j=0;j<ncu;j++) {
421: PetscMemcpy(S+lds*(s+j),work+j*sr,sr*sizeof(PetscScalar));
422: }
423: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&sr_,&ncu_,&qr_,&a,S+ld,&lds_,Q,&ldq_,&b,work,&sr_));
424: for (j=0;j<ncu;j++) {
425: PetscMemcpy(S+lds*(s+j)+ld,work+j*sr,sr*sizeof(PetscScalar));
426: }
427: return(0);
428: }
430: #if 0
433: static PetscErrorCode PEPSTOARpreKConvergence(PEP pep,PetscInt nv,PetscReal *norm,Vec *w)
434: {
436: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
437: PetscBLASInt n_,one=1;
438: PetscInt lds=2*ctx->ld;
439: PetscReal t1,t2;
440: PetscScalar *S=ctx->S;
443: PetscBLASIntCast(nv+2,&n_);
444: t1 = BLASnrm2_(&n_,S+nv*2*ctx->ld,&one);
445: t2 = BLASnrm2_(&n_,S+(nv*2+1)*ctx->ld,&one);
446: *norm = SlepcAbs(t1,t2);
447: BVSetActiveColumns(pep->V,0,nv+2);
448: BVMultVec(pep->V,1.0,0.0,w[1],S+nv*lds);
449: STMatMult(pep->st,0,w[1],w[2]);
450: VecNorm(w[2],NORM_2,&t1);
451: BVMultVec(pep->V,1.0,0.0,w[1],S+ctx->ld+nv*lds);
452: STMatMult(pep->st,2,w[1],w[2]);
453: VecNorm(w[2],NORM_2,&t2);
454: t2 *= pep->sfactor*pep->sfactor;
455: *norm = PetscMax(*norm,SlepcAbs(t1,t2));
456: return(0);
457: }
458: #endif
462: PetscErrorCode PEPSolve_STOAR(PEP pep)
463: {
465: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
466: PetscInt j,k,l,nv=0,ld=ctx->ld,lds=ctx->d*ctx->ld,off,ldds,t;
467: PetscInt lwa,lrwa,nwu=0,nrwu=0,nconv=0;
468: PetscScalar *S=ctx->S,*Q,*work;
469: PetscReal beta,norm=1.0,*omega,*a,*b,*r,*rwork;
470: PetscBool breakdown,symmlost=PETSC_FALSE,sinv;
473: PetscCitationsRegister(citation,&cited);
474: BVSetMatrix(pep->V,NULL,PETSC_FALSE);
475: lwa = 9*ld*ld+5*ld;
476: lrwa = 8*ld;
477: PetscMalloc2(lwa,&work,lrwa,&rwork); /* REVIEW */
478: PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
479: RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor);
480: STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor);
482: /* Restart loop */
483: l = 0;
484: DSGetLeadingDimension(pep->ds,&ldds);
485: while (pep->reason == PEP_CONVERGED_ITERATING) {
486: pep->its++;
487: DSGetArrayReal(pep->ds,DS_MAT_T,&a);
488: b = a+ldds;
489: DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
491: /* Compute an nv-step Lanczos factorization */
492: nv = PetscMin(pep->nconv+pep->mpd,pep->ncv);
493: PEPSTOARrun(pep,a,b,omega,pep->nconv+l,&nv,&breakdown,&symmlost,work+nwu,pep->work);
494: beta = b[nv-1];
495: if (symmlost) {
496: pep->reason = PEP_DIVERGED_SYMMETRY_LOST;
497: if (nv==pep->nconv+l+1) { pep->nconv = nconv; break; }
498: }
499: DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
500: DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
501: DSSetDimensions(pep->ds,nv,0,pep->nconv,pep->nconv+l);
502: if (l==0) {
503: DSSetState(pep->ds,DS_STATE_INTERMEDIATE);
504: } else {
505: DSSetState(pep->ds,DS_STATE_RAW);
506: }
508: /* Solve projected problem */
509: DSSolve(pep->ds,pep->eigr,pep->eigi);
510: DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
512: /* Check convergence */
513: /* PEPSTOARpreKConvergence(pep,nv,&norm,pep->work);*/
514: norm = 1.0;
515: DSGetDimensions(pep->ds,NULL,NULL,NULL,NULL,&t);
516: PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,t-pep->nconv,PetscAbsReal(beta)*norm,&k);
517: nconv = k;
518: (*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx);
520: /* Update l */
521: if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
522: else {
523: l = PetscMax(1,(PetscInt)((nv-k)/2));
524: l = PetscMin(l,t);
525: DSGetArrayReal(pep->ds,DS_MAT_T,&a);
526: if (*(a+ldds+k+l-1)!=0) {
527: if (k+l<nv-1) l = l+1;
528: else l = l-1;
529: }
530: DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
531: }
532: if (!ctx->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
534: /* Update S */
535: off = pep->nconv*ldds;
536: DSGetArray(pep->ds,DS_MAT_Q,&Q);
537: PEPSTOARSupdate(S,ld,nv+2,pep->nconv,k+l-pep->nconv,nv,Q+off,ldds,work+nwu);
538: DSRestoreArray(pep->ds,DS_MAT_Q,&Q);
540: /* Copy last column of S */
541: PetscMemcpy(S+lds*(k+l),S+lds*nv,lds*sizeof(PetscScalar));
543: if (pep->reason == PEP_CONVERGED_ITERATING) {
544: if (breakdown) {
545: /* Stop if breakdown */
546: PetscInfo2(pep,"Breakdown STOAR method (it=%D norm=%g)\n",pep->its,(double)beta);
547: pep->reason = PEP_DIVERGED_BREAKDOWN;
548: } else {
549: /* Prepare the Rayleigh quotient for restart */
550: DSGetArray(pep->ds,DS_MAT_Q,&Q);
551: DSGetArrayReal(pep->ds,DS_MAT_T,&a);
552: DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
553: r = a + 2*ldds;
554: for (j=k;j<k+l;j++) {
555: r[j] = PetscRealPart(Q[nv-1+j*ldds]*beta);
556: }
557: b = a+ldds;
558: b[k+l-1] = r[k+l-1];
559: omega[k+l] = omega[nv];
560: DSRestoreArray(pep->ds,DS_MAT_Q,&Q);
561: DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
562: DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
563: /* Truncate S */
564: DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
565: PEPSTOARTrunc(pep,nv+2,k+l+1,work+nwu,rwork+nrwu);
566: DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
567: }
568: }
571: pep->nconv = k;
572: PEPMonitor(pep,pep->its,pep->nconv,pep->eigr,pep->eigi,pep->errest,nv);
573: }
575: if (pep->nconv>0) {
576: /* Truncate S */
577: DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
578: PEPSTOARTrunc(pep,nv+2,pep->nconv,work+nwu,rwork+nrwu);
579: DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
581: /* Extraction */
582: DSSetDimensions(pep->ds,pep->nconv,0,0,0);
583: DSSetState(pep->ds,DS_STATE_RAW);
585: for (j=0;j<pep->nconv;j++) {
586: pep->eigr[j] *= pep->sfactor;
587: pep->eigi[j] *= pep->sfactor;
588: }
589: }
590: STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor);
591: RGPopScale(pep->rg);
593: /* truncate Schur decomposition and change the state to raw so that
594: DSVectors() computes eigenvectors from scratch */
595: DSSetDimensions(pep->ds,pep->nconv,0,0,0);
596: DSSetState(pep->ds,DS_STATE_RAW);
597: PetscFree2(work,rwork);
598: return(0);
599: }
603: PetscErrorCode PEPSetFromOptions_STOAR(PetscOptionItems *PetscOptionsObject,PEP pep)
604: {
606: PetscBool flg,lock;
609: PetscOptionsHead(PetscOptionsObject,"PEP STOAR Options");
610: PetscOptionsBool("-pep_stoar_locking","Choose between locking and non-locking variants","PEPSTOARSetLocking",PETSC_FALSE,&lock,&flg);
611: if (flg) {
612: PEPSTOARSetLocking(pep,lock);
613: }
614: PetscOptionsTail();
615: return(0);
616: }
620: static PetscErrorCode PEPSTOARSetLocking_STOAR(PEP pep,PetscBool lock)
621: {
622: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
625: ctx->lock = lock;
626: return(0);
627: }
631: /*@
632: PEPSTOARSetLocking - Choose between locking and non-locking variants of
633: the STOAR method.
635: Logically Collective on PEP
637: Input Parameters:
638: + pep - the eigenproblem solver context
639: - lock - true if the locking variant must be selected
641: Options Database Key:
642: . -pep_stoar_locking - Sets the locking flag
644: Notes:
645: The default is to lock converged eigenpairs when the method restarts.
646: This behaviour can be changed so that all directions are kept in the
647: working subspace even if already converged to working accuracy (the
648: non-locking variant).
650: Level: advanced
652: .seealso: PEPSTOARGetLocking()
653: @*/
654: PetscErrorCode PEPSTOARSetLocking(PEP pep,PetscBool lock)
655: {
661: PetscTryMethod(pep,"PEPSTOARSetLocking_C",(PEP,PetscBool),(pep,lock));
662: return(0);
663: }
667: static PetscErrorCode PEPSTOARGetLocking_STOAR(PEP pep,PetscBool *lock)
668: {
669: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
672: *lock = ctx->lock;
673: return(0);
674: }
678: /*@
679: PEPSTOARGetLocking - Gets the locking flag used in the STOAR method.
681: Not Collective
683: Input Parameter:
684: . pep - the eigenproblem solver context
686: Output Parameter:
687: . lock - the locking flag
689: Level: advanced
691: .seealso: PEPSTOARSetLocking()
692: @*/
693: PetscErrorCode PEPSTOARGetLocking(PEP pep,PetscBool *lock)
694: {
700: PetscUseMethod(pep,"PEPSTOARGetLocking_C",(PEP,PetscBool*),(pep,lock));
701: return(0);
702: }
706: PetscErrorCode PEPView_STOAR(PEP pep,PetscViewer viewer)
707: {
709: PEP_TOAR *ctx = (PEP_TOAR*)pep->data;
710: PetscBool isascii;
713: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
714: if (isascii) {
715: PetscViewerASCIIPrintf(viewer," STOAR: using the %slocking variant\n",ctx->lock?"":"non-");
716: }
717: return(0);
718: }
722: PetscErrorCode PEPDestroy_STOAR(PEP pep)
723: {
727: PetscFree(pep->data);
728: PetscObjectComposeFunction((PetscObject)pep,"PEPSTOARSetLocking_C",NULL);
729: PetscObjectComposeFunction((PetscObject)pep,"PEPSTOARGetLocking_C",NULL);
730: return(0);
731: }
735: PETSC_EXTERN PetscErrorCode PEPCreate_STOAR(PEP pep)
736: {
738: PEP_TOAR *ctx;
741: PetscNewLog(pep,&ctx);
742: pep->data = (void*)ctx;
743: ctx->lock = PETSC_TRUE;
745: pep->ops->solve = PEPSolve_STOAR;
746: pep->ops->setup = PEPSetUp_STOAR;
747: pep->ops->setfromoptions = PEPSetFromOptions_STOAR;
748: pep->ops->view = PEPView_STOAR;
749: pep->ops->destroy = PEPDestroy_STOAR;
750: pep->ops->backtransform = PEPBackTransform_Default;
751: pep->ops->computevectors = PEPComputeVectors_Default;
752: pep->ops->extractvectors = PEPExtractVectors_TOAR;
753: pep->ops->reset = PEPReset_TOAR;
754: PetscObjectComposeFunction((PetscObject)pep,"PEPSTOARSetLocking_C",PEPSTOARSetLocking_STOAR);
755: PetscObjectComposeFunction((PetscObject)pep,"PEPSTOARGetLocking_C",PEPSTOARGetLocking_STOAR);
756: return(0);
757: }