Actual source code: epskrylov.c

slepc-3.18.1 2022-11-02
Report Typos and Errors
  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:    Common subroutines for all Krylov-type solvers
 12: */

 14: #include <slepc/private/epsimpl.h>
 15: #include <slepc/private/slepcimpl.h>
 16: #include <slepcblaslapack.h>

 18: /*
 19:    EPSDelayedArnoldi - This function is equivalent to BVMatArnoldi but
 20:    performs the computation in a different way. The main idea is that
 21:    reorthogonalization is delayed to the next Arnoldi step. This version is
 22:    more scalable but in some cases convergence may stagnate.
 23: */
 24: PetscErrorCode EPSDelayedArnoldi(EPS eps,PetscScalar *H,PetscInt ldh,PetscInt k,PetscInt *M,PetscReal *beta,PetscBool *breakdown)
 25: {
 26:   PetscInt       i,j,m=*M;
 27:   Vec            u,t;
 28:   PetscScalar    shh[100],*lhh,dot,dot2;
 29:   PetscReal      norm1=0.0,norm2=1.0;
 30:   Vec            vj,vj1,vj2=NULL;

 32:   if (m<=100) lhh = shh;
 33:   else PetscMalloc1(m,&lhh);
 34:   BVCreateVec(eps->V,&u);
 35:   BVCreateVec(eps->V,&t);

 37:   BVSetActiveColumns(eps->V,0,m);
 38:   for (j=k;j<m;j++) {
 39:     BVGetColumn(eps->V,j,&vj);
 40:     BVGetColumn(eps->V,j+1,&vj1);
 41:     STApply(eps->st,vj,vj1);
 42:     BVRestoreColumn(eps->V,j,&vj);
 43:     BVRestoreColumn(eps->V,j+1,&vj1);

 45:     BVDotColumnBegin(eps->V,j+1,H+ldh*j);
 46:     if (j>k) {
 47:       BVDotColumnBegin(eps->V,j,lhh);
 48:       BVGetColumn(eps->V,j,&vj);
 49:       VecDotBegin(vj,vj,&dot);
 50:       if (j>k+1) {
 51:         BVNormVecBegin(eps->V,u,NORM_2,&norm2);
 52:         BVGetColumn(eps->V,j-2,&vj2);
 53:         VecDotBegin(u,vj2,&dot2);
 54:       }
 55:       BVDotColumnEnd(eps->V,j+1,H+ldh*j);
 56:       BVDotColumnEnd(eps->V,j,lhh);
 57:       VecDotEnd(vj,vj,&dot);
 58:       BVRestoreColumn(eps->V,j,&vj);
 59:       if (j>k+1) {
 60:         BVNormVecEnd(eps->V,u,NORM_2,&norm2);
 61:         VecDotEnd(u,vj2,&dot2);
 62:         BVRestoreColumn(eps->V,j-2,&vj2);
 63:       }
 64:       norm1 = PetscSqrtReal(PetscRealPart(dot));
 65:       for (i=0;i<j;i++) H[ldh*j+i] = H[ldh*j+i]/norm1;
 66:       H[ldh*j+j] = H[ldh*j+j]/dot;
 67:       BVCopyVec(eps->V,j,t);
 68:       BVScaleColumn(eps->V,j,1.0/norm1);
 69:       BVScaleColumn(eps->V,j+1,1.0/norm1);
 70:     } else BVDotColumnEnd(eps->V,j+1,H+ldh*j); /* j==k */

 72:     BVMultColumn(eps->V,-1.0,1.0,j+1,H+ldh*j);

 74:     if (j>k) {
 75:       BVSetActiveColumns(eps->V,0,j);
 76:       BVMultVec(eps->V,-1.0,1.0,t,lhh);
 77:       BVSetActiveColumns(eps->V,0,m);
 78:       for (i=0;i<j;i++) H[ldh*(j-1)+i] += lhh[i];
 79:     }

 81:     if (j>k+1) {
 82:       BVGetColumn(eps->V,j-1,&vj1);
 83:       VecCopy(u,vj1);
 84:       BVRestoreColumn(eps->V,j-1,&vj1);
 85:       BVScaleColumn(eps->V,j-1,1.0/norm2);
 86:       H[ldh*(j-2)+j-1] = norm2;
 87:     }

 89:     if (j<m-1) VecCopy(t,u);
 90:   }

 92:   BVNormVec(eps->V,t,NORM_2,&norm2);
 93:   VecScale(t,1.0/norm2);
 94:   BVGetColumn(eps->V,m-1,&vj1);
 95:   VecCopy(t,vj1);
 96:   BVRestoreColumn(eps->V,m-1,&vj1);
 97:   H[ldh*(m-2)+m-1] = norm2;

 99:   BVDotColumn(eps->V,m,lhh);

101:   BVMultColumn(eps->V,-1.0,1.0,m,lhh);
102:   for (i=0;i<m;i++)
103:     H[ldh*(m-1)+i] += lhh[i];

105:   BVNormColumn(eps->V,m,NORM_2,beta);
106:   BVScaleColumn(eps->V,m,1.0 / *beta);
107:   *breakdown = PETSC_FALSE;

109:   if (m>100) PetscFree(lhh);
110:   VecDestroy(&u);
111:   VecDestroy(&t);
112:   return 0;
113: }

115: /*
116:    EPSDelayedArnoldi1 - This function is similar to EPSDelayedArnoldi,
117:    but without reorthogonalization (only delayed normalization).
118: */
119: PetscErrorCode EPSDelayedArnoldi1(EPS eps,PetscScalar *H,PetscInt ldh,PetscInt k,PetscInt *M,PetscReal *beta,PetscBool *breakdown)
120: {
121:   PetscInt       i,j,m=*M;
122:   PetscScalar    dot;
123:   PetscReal      norm=0.0;
124:   Vec            vj,vj1;

126:   BVSetActiveColumns(eps->V,0,m);
127:   for (j=k;j<m;j++) {
128:     BVGetColumn(eps->V,j,&vj);
129:     BVGetColumn(eps->V,j+1,&vj1);
130:     STApply(eps->st,vj,vj1);
131:     BVRestoreColumn(eps->V,j+1,&vj1);
132:     if (j>k) {
133:       BVDotColumnBegin(eps->V,j+1,H+ldh*j);
134:       VecDotBegin(vj,vj,&dot);
135:       BVDotColumnEnd(eps->V,j+1,H+ldh*j);
136:       VecDotEnd(vj,vj,&dot);
137:       norm = PetscSqrtReal(PetscRealPart(dot));
138:       BVScaleColumn(eps->V,j,1.0/norm);
139:       H[ldh*(j-1)+j] = norm;
140:       for (i=0;i<j;i++) H[ldh*j+i] = H[ldh*j+i]/norm;
141:       H[ldh*j+j] = H[ldh*j+j]/dot;
142:       BVScaleColumn(eps->V,j+1,1.0/norm);
143:       *beta = norm;
144:     } else {  /* j==k */
145:       BVDotColumn(eps->V,j+1,H+ldh*j);
146:     }
147:     BVRestoreColumn(eps->V,j,&vj);
148:     BVMultColumn(eps->V,-1.0,1.0,j+1,H+ldh*j);
149:   }

151:   *breakdown = PETSC_FALSE;
152:   return 0;
153: }

155: /*
156:    EPSKrylovConvergence_Filter - Specialized version for STFILTER.
157: */
158: PetscErrorCode EPSKrylovConvergence_Filter(EPS eps,PetscBool getall,PetscInt kini,PetscInt nits,PetscReal beta,PetscReal gamma,PetscInt *kout)
159: {
160:   PetscInt       k,ninside,nconv;
161:   PetscScalar    re,im;
162:   PetscReal      resnorm;

164:   ninside = 0;   /* count how many eigenvalues are located in the interval */
165:   for (k=kini;k<kini+nits;k++) {
166:     if (PetscRealPart(eps->eigr[k]) < gamma) break;
167:     ninside++;
168:   }
169:   eps->nev = ninside+kini;  /* adjust eigenvalue count */
170:   nconv = 0;   /* count how many eigenvalues satisfy the convergence criterion */
171:   for (k=kini;k<kini+ninside;k++) {
172:     /* eigenvalue */
173:     re = eps->eigr[k];
174:     im = eps->eigi[k];
175:     DSVectors(eps->ds,DS_MAT_X,&k,&resnorm);
176:     resnorm *= beta;
177:     /* error estimate */
178:     (*eps->converged)(eps,re,im,resnorm,&eps->errest[k],eps->convergedctx);
179:     if (eps->errest[k] < eps->tol) nconv++;
180:     else break;
181:   }
182:   *kout = kini+nconv;
183:   PetscInfo(eps,"Found %" PetscInt_FMT " eigenvalue approximations inside the interval (gamma=%g), k=%" PetscInt_FMT " nconv=%" PetscInt_FMT "\n",ninside,(double)gamma,k,nconv);
184:   return 0;
185: }

187: /*
188:    EPSKrylovConvergence - Implements the loop that checks for convergence
189:    in Krylov methods.

191:    Input Parameters:
192:      eps   - the eigensolver; some error estimates are updated in eps->errest
193:      getall - whether all residuals must be computed
194:      kini  - initial value of k (the loop variable)
195:      nits  - number of iterations of the loop
196:      V     - set of basis vectors (used only if trueresidual is activated)
197:      nv    - number of vectors to process (dimension of Q, columns of V)
198:      beta  - norm of f (the residual vector of the Arnoldi/Lanczos factorization)
199:      corrf - correction factor for residual estimates (only in harmonic KS)

201:    Output Parameters:
202:      kout  - the first index where the convergence test failed
203: */
204: PetscErrorCode EPSKrylovConvergence(EPS eps,PetscBool getall,PetscInt kini,PetscInt nits,PetscReal beta,PetscReal betat,PetscReal corrf,PetscInt *kout)
205: {
206:   PetscInt       k,newk,newk2,marker,ld,inside;
207:   PetscScalar    re,im,*Zr,*Zi,*X;
208:   PetscReal      resnorm,gamma,lerrest;
209:   PetscBool      isshift,isfilter,refined,istrivial;
210:   Vec            x=NULL,y=NULL,w[3];

212:   if (PetscUnlikely(eps->which == EPS_ALL)) {
213:     PetscObjectTypeCompare((PetscObject)eps->st,STFILTER,&isfilter);
214:     if (isfilter) {
215:       STFilterGetThreshold(eps->st,&gamma);
216:       EPSKrylovConvergence_Filter(eps,getall,kini,nits,beta,gamma,kout);
217:       return 0;
218:     }
219:   }
220:   RGIsTrivial(eps->rg,&istrivial);
221:   if (PetscUnlikely(eps->trueres)) {
222:     BVCreateVec(eps->V,&x);
223:     BVCreateVec(eps->V,&y);
224:     BVCreateVec(eps->V,&w[0]);
225:     BVCreateVec(eps->V,&w[2]);
226: #if !defined(PETSC_USE_COMPLEX)
227:     BVCreateVec(eps->V,&w[1]);
228: #else
229:     w[1] = NULL;
230: #endif
231:   }
232:   DSGetLeadingDimension(eps->ds,&ld);
233:   DSGetRefined(eps->ds,&refined);
234:   PetscObjectTypeCompare((PetscObject)eps->st,STSHIFT,&isshift);
235:   marker = -1;
236:   if (eps->trackall) getall = PETSC_TRUE;
237:   for (k=kini;k<kini+nits;k++) {
238:     /* eigenvalue */
239:     re = eps->eigr[k];
240:     im = eps->eigi[k];
241:     if (!istrivial || eps->trueres || isshift || eps->conv==EPS_CONV_NORM) STBackTransform(eps->st,1,&re,&im);
242:     if (PetscUnlikely(!istrivial)) {
243:       RGCheckInside(eps->rg,1,&re,&im,&inside);
244:       if (marker==-1 && inside<0) marker = k;
245:       if (!(eps->trueres || isshift || eps->conv==EPS_CONV_NORM)) {  /* make sure eps->converged below uses the right value */
246:         re = eps->eigr[k];
247:         im = eps->eigi[k];
248:       }
249:     }
250:     newk = k;
251:     DSVectors(eps->ds,DS_MAT_X,&newk,&resnorm);
252:     if (PetscUnlikely(eps->trueres)) {
253:       DSGetArray(eps->ds,DS_MAT_X,&X);
254:       Zr = X+k*ld;
255:       if (newk==k+1) Zi = X+newk*ld;
256:       else Zi = NULL;
257:       EPSComputeRitzVector(eps,Zr,Zi,eps->V,x,y);
258:       DSRestoreArray(eps->ds,DS_MAT_X,&X);
259:       EPSComputeResidualNorm_Private(eps,PETSC_FALSE,re,im,x,y,w,&resnorm);
260:     }
261:     else if (!refined) resnorm *= beta*corrf;
262:     /* error estimate */
263:     (*eps->converged)(eps,re,im,resnorm,&eps->errest[k],eps->convergedctx);
264:     if (marker==-1 && eps->errest[k] >= eps->tol) marker = k;
265:     if (PetscUnlikely(eps->twosided)) {
266:       newk2 = k;
267:       DSVectors(eps->ds,DS_MAT_Y,&newk2,&resnorm);
268:       resnorm *= betat;
269:       (*eps->converged)(eps,re,im,resnorm,&lerrest,eps->convergedctx);
270:       eps->errest[k] = PetscMax(eps->errest[k],lerrest);
271:       if (marker==-1 && lerrest >= eps->tol) marker = k;
272:     }
273:     if (PetscUnlikely(newk==k+1)) {
274:       eps->errest[k+1] = eps->errest[k];
275:       k++;
276:     }
277:     if (marker!=-1 && !getall) break;
278:   }
279:   if (marker!=-1) k = marker;
280:   *kout = k;
281:   if (PetscUnlikely(eps->trueres)) {
282:     VecDestroy(&x);
283:     VecDestroy(&y);
284:     VecDestroy(&w[0]);
285:     VecDestroy(&w[2]);
286: #if !defined(PETSC_USE_COMPLEX)
287:     VecDestroy(&w[1]);
288: #endif
289:   }
290:   return 0;
291: }

293: PetscErrorCode EPSPseudoLanczos(EPS eps,PetscReal *alpha,PetscReal *beta,PetscReal *omega,PetscInt k,PetscInt *M,PetscBool *breakdown,PetscBool *symmlost,PetscReal *cos,Vec w)
294: {
295:   PetscInt       j,m = *M,i,ld,l;
296:   Vec            vj,vj1;
297:   PetscScalar    *hwork,lhwork[100];
298:   PetscReal      norm,norm1,norm2,t,sym=0.0,fro=0.0;
299:   PetscBLASInt   j_,one=1;

301:   DSGetLeadingDimension(eps->ds,&ld);
302:   DSGetDimensions(eps->ds,NULL,&l,NULL,NULL);
303:   if (cos) *cos = 1.0;
304:   if (m > 100) PetscMalloc1(m,&hwork);
305:   else hwork = lhwork;

307:   BVSetActiveColumns(eps->V,0,m);
308:   for (j=k;j<m;j++) {
309:     BVGetColumn(eps->V,j,&vj);
310:     BVGetColumn(eps->V,j+1,&vj1);
311:     STApply(eps->st,vj,vj1);
312:     BVRestoreColumn(eps->V,j,&vj);
313:     BVRestoreColumn(eps->V,j+1,&vj1);
314:     BVOrthogonalizeColumn(eps->V,j+1,hwork,&norm,breakdown);
315:     alpha[j] = PetscRealPart(hwork[j]);
316:     beta[j] = PetscAbsReal(norm);
317:     if (j==k) {
318:       PetscReal *f;

320:       DSGetArrayReal(eps->ds,DS_MAT_T,&f);
321:       for (i=0;i<l;i++) hwork[i]  = 0.0;
322:       for (;i<j-1;i++)  hwork[i] -= f[2*ld+i];
323:       DSRestoreArrayReal(eps->ds,DS_MAT_T,&f);
324:     }
325:     if (j>0) {
326:       hwork[j-1] -= beta[j-1];
327:       PetscBLASIntCast(j,&j_);
328:       sym = SlepcAbs(BLASnrm2_(&j_,hwork,&one),sym);
329:     }
330:     fro = SlepcAbs(fro,SlepcAbs(alpha[j],beta[j]));
331:     if (j>0) fro = SlepcAbs(fro,beta[j-1]);
332:     if (sym/fro>PetscMax(PETSC_SQRT_MACHINE_EPSILON,10*eps->tol)) { *symmlost = PETSC_TRUE; *M=j+1; break; }
333:     omega[j+1] = (norm<0.0)? -1.0: 1.0;
334:     BVScaleColumn(eps->V,j+1,1.0/norm);
335:     /* */
336:     if (cos) {
337:       BVGetColumn(eps->V,j+1,&vj1);
338:       VecNorm(vj1,NORM_2,&norm1);
339:       BVApplyMatrix(eps->V,vj1,w);
340:       BVRestoreColumn(eps->V,j+1,&vj1);
341:       VecNorm(w,NORM_2,&norm2);
342:       t = 1.0/(norm1*norm2);
343:       if (*cos>t) *cos = t;
344:     }
345:   }
346:   if (m > 100) PetscFree(hwork);
347:   return 0;
348: }