Actual source code: dsnep.c

slepc-3.18.2 2023-01-26
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  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: */

 11: #include <slepc/private/dsimpl.h>
 12: #include <slepcblaslapack.h>

 14: typedef struct {
 15:   PetscInt       nf;                 /* number of functions in f[] */
 16:   FN             f[DS_NUM_EXTRA];    /* functions defining the nonlinear operator */
 17:   PetscInt       max_mid;            /* maximum minimality index */
 18:   PetscInt       nnod;               /* number of nodes for quadrature rules */
 19:   PetscInt       spls;               /* number of sampling columns for quadrature rules */
 20:   PetscInt       Nit;                /* number of refinement iterations */
 21:   PetscReal      rtol;               /* tolerance of Newton refinement */
 22:   RG             rg;                 /* region for contour integral */
 23:   PetscLayout    map;                /* used to distribute work among MPI processes */
 24:   void           *computematrixctx;
 25:   PetscErrorCode (*computematrix)(DS,PetscScalar,PetscBool,DSMatType,void*);
 26: } DS_NEP;

 28: /*
 29:    DSNEPComputeMatrix - Build the matrix associated with a nonlinear operator
 30:    T(lambda) or its derivative T'(lambda), given the parameter lambda, where
 31:    T(lambda) = sum_i E_i*f_i(lambda). The result is written in mat.
 32: */
 33: static PetscErrorCode DSNEPComputeMatrix(DS ds,PetscScalar lambda,PetscBool deriv,DSMatType mat)
 34: {
 35:   DS_NEP            *ctx = (DS_NEP*)ds->data;
 36:   PetscScalar       *T,alpha;
 37:   const PetscScalar *E;
 38:   PetscInt          i,ld,n;
 39:   PetscBLASInt      k,inc=1;

 41:   PetscLogEventBegin(DS_Other,ds,0,0,0);
 42:   if (ctx->computematrix) (*ctx->computematrix)(ds,lambda,deriv,mat,ctx->computematrixctx);
 43:   else {
 44:     DSGetDimensions(ds,&n,NULL,NULL,NULL);
 45:     DSGetLeadingDimension(ds,&ld);
 46:     PetscBLASIntCast(ld*n,&k);
 47:     MatDenseGetArray(ds->omat[mat],&T);
 48:     PetscArrayzero(T,k);
 49:     for (i=0;i<ctx->nf;i++) {
 50:       if (deriv) FNEvaluateDerivative(ctx->f[i],lambda,&alpha);
 51:       else FNEvaluateFunction(ctx->f[i],lambda,&alpha);
 52:       MatDenseGetArrayRead(ds->omat[DSMatExtra[i]],&E);
 53:       PetscCallBLAS("BLASaxpy",BLASaxpy_(&k,&alpha,E,&inc,T,&inc));
 54:       MatDenseRestoreArrayRead(ds->omat[DSMatExtra[i]],&E);
 55:     }
 56:     MatDenseRestoreArray(ds->omat[mat],&T);
 57:   }
 58:   PetscLogEventEnd(DS_Other,ds,0,0,0);
 59:   return 0;
 60: }

 62: PetscErrorCode DSAllocate_NEP(DS ds,PetscInt ld)
 63: {
 64:   DS_NEP         *ctx = (DS_NEP*)ds->data;
 65:   PetscInt       i;

 67:   DSAllocateMat_Private(ds,DS_MAT_X);
 68:   for (i=0;i<ctx->nf;i++) DSAllocateMat_Private(ds,DSMatExtra[i]);
 69:   PetscFree(ds->perm);
 70:   PetscMalloc1(ld*ctx->max_mid,&ds->perm);
 71:   return 0;
 72: }

 74: PetscErrorCode DSView_NEP(DS ds,PetscViewer viewer)
 75: {
 76:   DS_NEP            *ctx = (DS_NEP*)ds->data;
 77:   PetscViewerFormat format;
 78:   PetscInt          i;
 79:   const char        *methodname[] = {
 80:                      "Successive Linear Problems",
 81:                      "Contour Integral"
 82:   };
 83:   const int         nmeth=PETSC_STATIC_ARRAY_LENGTH(methodname);

 85:   PetscViewerGetFormat(viewer,&format);
 86:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
 87:     if (ds->method<nmeth) PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method]);
 88: #if defined(PETSC_USE_COMPLEX)
 89:     if (ds->method==1) {  /* contour integral method */
 90:       PetscViewerASCIIPrintf(viewer,"number of integration points: %" PetscInt_FMT "\n",ctx->nnod);
 91:       PetscViewerASCIIPrintf(viewer,"maximum minimality index: %" PetscInt_FMT "\n",ctx->max_mid);
 92:       if (ctx->spls) PetscViewerASCIIPrintf(viewer,"number of sampling columns for quadrature: %" PetscInt_FMT "\n",ctx->spls);
 93:       if (ctx->Nit) PetscViewerASCIIPrintf(viewer,"doing iterative refinement (%" PetscInt_FMT " its, tolerance %g)\n",ctx->Nit,(double)ctx->rtol);
 94:       RGView(ctx->rg,viewer);
 95:     }
 96: #endif
 97:     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscViewerASCIIPrintf(viewer,"number of functions: %" PetscInt_FMT "\n",ctx->nf);
 98:     return 0;
 99:   }
100:   for (i=0;i<ctx->nf;i++) {
101:     FNView(ctx->f[i],viewer);
102:     DSViewMat(ds,viewer,DSMatExtra[i]);
103:   }
104:   if (ds->state>DS_STATE_INTERMEDIATE) DSViewMat(ds,viewer,DS_MAT_X);
105:   return 0;
106: }

108: PetscErrorCode DSVectors_NEP(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
109: {
111:   switch (mat) {
112:     case DS_MAT_X:
113:       break;
114:     case DS_MAT_Y:
115:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
116:     default:
117:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
118:   }
119:   return 0;
120: }

122: PetscErrorCode DSSort_NEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *dummy)
123: {
124:   DS_NEP         *ctx = (DS_NEP*)ds->data;
125:   PetscInt       n,l,i,*perm,lds;
126:   PetscScalar    *Q;

128:   if (!ds->sc) return 0;
129:   if (!ds->method) return 0;  /* SLP computes just one eigenvalue */
130:   n = ds->n*ctx->max_mid;
131:   lds = ds->ld*ctx->max_mid;
132:   l = ds->l;
133:   perm = ds->perm;
134:   for (i=0;i<n;i++) perm[i] = i;
135:   if (rr) DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_FALSE);
136:   else DSSortEigenvalues_Private(ds,wr,NULL,perm,PETSC_FALSE);
137:   MatDenseGetArray(ds->omat[DS_MAT_Q],&Q);
138:   for (i=l;i<ds->t;i++) Q[i+i*lds] = wr[perm[i]];
139:   for (i=l;i<ds->t;i++) wr[i] = Q[i+i*lds];
140:   MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q);
141:   /* n != ds->n */
142:   DSPermuteColumns_Private(ds,0,ds->t,ds->n,DS_MAT_X,perm);
143:   return 0;
144: }

146: PetscErrorCode DSSolve_NEP_SLP(DS ds,PetscScalar *wr,PetscScalar *wi)
147: {
148:   PetscScalar    *A,*B,*W,*X,*work,*alpha,*beta;
149:   PetscScalar    sigma,lambda,mu,re,re2,sone=1.0,szero=0.0;
150:   PetscBLASInt   info,n,ld,lrwork=0,lwork,one=1,zero=0;
151:   PetscInt       it,pos,j,maxit=100,result;
152:   PetscReal      norm,tol,done=1.0;
153: #if defined(PETSC_USE_COMPLEX)
154:   PetscReal      *rwork;
155: #else
156:   PetscReal      *alphai,im,im2;
157: #endif

159:   PetscBLASIntCast(ds->n,&n);
160:   PetscBLASIntCast(ds->ld,&ld);
161: #if defined(PETSC_USE_COMPLEX)
162:   PetscBLASIntCast(2*ds->n+2*ds->n,&lwork);
163:   PetscBLASIntCast(8*ds->n,&lrwork);
164: #else
165:   PetscBLASIntCast(3*ds->n+8*ds->n,&lwork);
166: #endif
167:   DSAllocateWork_Private(ds,lwork,lrwork,0);
168:   alpha = ds->work;
169:   beta = ds->work + ds->n;
170: #if defined(PETSC_USE_COMPLEX)
171:   work = ds->work + 2*ds->n;
172:   lwork -= 2*ds->n;
173: #else
174:   alphai = ds->work + 2*ds->n;
175:   work = ds->work + 3*ds->n;
176:   lwork -= 3*ds->n;
177: #endif
178:   DSAllocateMat_Private(ds,DS_MAT_A);
179:   DSAllocateMat_Private(ds,DS_MAT_B);
180:   DSAllocateMat_Private(ds,DS_MAT_W);
181:   MatDenseGetArray(ds->omat[DS_MAT_A],&A);
182:   MatDenseGetArray(ds->omat[DS_MAT_B],&B);
183:   MatDenseGetArray(ds->omat[DS_MAT_W],&W);
184:   MatDenseGetArray(ds->omat[DS_MAT_X],&X);

186:   sigma = 0.0;
187:   if (ds->sc->comparison==SlepcCompareTargetMagnitude || ds->sc->comparison==SlepcCompareTargetReal) sigma = *(PetscScalar*)ds->sc->comparisonctx;
188:   lambda = sigma;
189:   tol = n*PETSC_MACHINE_EPSILON/PetscSqrtReal(PETSC_SQRT_MACHINE_EPSILON);

191:   for (it=0;it<maxit;it++) {

193:     /* evaluate T and T' */
194:     DSNEPComputeMatrix(ds,lambda,PETSC_FALSE,DS_MAT_A);
195:     if (it) {
196:       PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,A,&ld,X,&one,&szero,X+ld,&one));
197:       norm = BLASnrm2_(&n,X+ld,&one);
198:       if (norm/PetscAbsScalar(lambda)<=tol) break;
199:     }
200:     DSNEPComputeMatrix(ds,lambda,PETSC_TRUE,DS_MAT_B);

202:     /* compute eigenvalue correction mu and eigenvector u */
203: #if defined(PETSC_USE_COMPLEX)
204:     rwork = ds->rwork;
205:     PetscCallBLAS("LAPACKggev",LAPACKggev_("N","V",&n,A,&ld,B,&ld,alpha,beta,NULL,&ld,W,&ld,work,&lwork,rwork,&info));
206: #else
207:     PetscCallBLAS("LAPACKggev",LAPACKggev_("N","V",&n,A,&ld,B,&ld,alpha,alphai,beta,NULL,&ld,W,&ld,work,&lwork,&info));
208: #endif
209:     SlepcCheckLapackInfo("ggev",info);

211:     /* find smallest eigenvalue */
212:     j = 0;
213:     if (beta[j]==0.0) re = (PetscRealPart(alpha[j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
214:     else re = alpha[j]/beta[j];
215: #if !defined(PETSC_USE_COMPLEX)
216:     if (beta[j]==0.0) im = (alphai[j]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
217:     else im = alphai[j]/beta[j];
218: #endif
219:     pos = 0;
220:     for (j=1;j<n;j++) {
221:       if (beta[j]==0.0) re2 = (PetscRealPart(alpha[j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
222:       else re2 = alpha[j]/beta[j];
223: #if !defined(PETSC_USE_COMPLEX)
224:       if (beta[j]==0.0) im2 = (alphai[j]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
225:       else im2 = alphai[j]/beta[j];
226:       SlepcCompareSmallestMagnitude(re,im,re2,im2,&result,NULL);
227: #else
228:       SlepcCompareSmallestMagnitude(re,0.0,re2,0.0,&result,NULL);
229: #endif
230:       if (result > 0) {
231:         re = re2;
232: #if !defined(PETSC_USE_COMPLEX)
233:         im = im2;
234: #endif
235:         pos = j;
236:       }
237:     }

239: #if !defined(PETSC_USE_COMPLEX)
241: #endif
242:     mu = alpha[pos]/beta[pos];
243:     PetscArraycpy(X,W+pos*ld,n);
244:     norm = BLASnrm2_(&n,X,&one);
245:     PetscCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&one,X,&n,&info));
246:     SlepcCheckLapackInfo("lascl",info);

248:     /* correct eigenvalue approximation */
249:     lambda = lambda - mu;
250:   }
251:   MatDenseRestoreArray(ds->omat[DS_MAT_A],&A);
252:   MatDenseRestoreArray(ds->omat[DS_MAT_B],&B);
253:   MatDenseRestoreArray(ds->omat[DS_MAT_W],&W);
254:   MatDenseRestoreArray(ds->omat[DS_MAT_X],&X);

257:   ds->t = 1;
258:   wr[0] = lambda;
259:   if (wi) wi[0] = 0.0;
260:   return 0;
261: }

263: #if defined(PETSC_USE_COMPLEX)
264: /*
265:   Newton refinement for eigenpairs computed with contour integral.
266:   k  - number of eigenpairs to refine
267:   wr - eigenvalues (eigenvectors are stored in DS_MAT_X)
268: */
269: static PetscErrorCode DSNEPNewtonRefine(DS ds,PetscInt k,PetscScalar *wr)
270: {
271:   DS_NEP         *ctx = (DS_NEP*)ds->data;
272:   PetscScalar    *X,*W,*U,*R,sone=1.0,szero=0.0;
273:   PetscReal      norm;
274:   PetscInt       i,j,ii,nwu=0,*p,jstart=0,jend=k;
275:   const PetscInt *range;
276:   PetscBLASInt   n,*perm,info,ld,one=1,n1;
277:   PetscMPIInt    len,size,root;
278:   PetscLayout    map;

280:   MatDenseGetArray(ds->omat[DS_MAT_X],&X);
281:   PetscBLASIntCast(ds->n,&n);
282:   PetscBLASIntCast(ds->ld,&ld);
283:   n1 = n+1;
284:   p  = ds->perm;
285:   PetscArrayzero(p,k);
286:   DSAllocateWork_Private(ds,(n+2)*(n+1),0,n+1);
287:   U    = ds->work+nwu;    nwu += (n+1)*(n+1);
288:   R    = ds->work+nwu;    /*nwu += n+1;*/
289:   perm = ds->iwork;
290:   if (ds->pmode==DS_PARALLEL_DISTRIBUTED) {
291:     PetscLayoutCreateFromSizes(PetscObjectComm((PetscObject)ds),PETSC_DECIDE,k,1,&map);
292:     PetscLayoutGetRange(map,&jstart,&jend);
293:   }
294:   for (ii=0;ii<ctx->Nit;ii++) {
295:     for (j=jstart;j<jend;j++) {
296:       if (p[j]<2) {
297:         DSNEPComputeMatrix(ds,wr[j],PETSC_FALSE,DS_MAT_W);
298:         MatDenseGetArray(ds->omat[DS_MAT_W],&W);
299:         PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,W,&ld,X+ld*j,&one,&szero,R,&one));
300:         MatDenseRestoreArray(ds->omat[DS_MAT_W],&W);
301:         norm = BLASnrm2_(&n,R,&one);
302:         if (norm/PetscAbsScalar(wr[j]) > ctx->rtol) {
303:           PetscInfo(NULL,"Refining eigenpair %" PetscInt_FMT ", residual=%g\n",j,(double)(norm/PetscAbsScalar(wr[j])));
304:           p[j] = 1;
305:           R[n] = 0.0;
306:           MatDenseGetArray(ds->omat[DS_MAT_W],&W);
307:           for (i=0;i<n;i++) {
308:             PetscArraycpy(U+i*n1,W+i*ld,n);
309:             U[n+i*n1] = PetscConj(X[j*ld+i]);
310:           }
311:           MatDenseRestoreArray(ds->omat[DS_MAT_W],&W);
312:           U[n+n*n1] = 0.0;
313:           DSNEPComputeMatrix(ds,wr[j],PETSC_TRUE,DS_MAT_W);
314:           MatDenseGetArray(ds->omat[DS_MAT_W],&W);
315:           PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,W,&ld,X+ld*j,&one,&szero,U+n*(n+1),&one));
316:           MatDenseRestoreArray(ds->omat[DS_MAT_W],&W);
317:           /* solve system  */
318:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
319:           PetscCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n1,&n1,U,&n1,perm,&info));
320:           SlepcCheckLapackInfo("getrf",info);
321:           PetscCallBLAS("LAPACKgetrs",LAPACKgetrs_("N",&n1,&one,U,&n1,perm,R,&n1,&info));
322:           SlepcCheckLapackInfo("getrs",info);
323:           PetscFPTrapPop();
324:           wr[j] -= R[n];
325:           for (i=0;i<n;i++) X[j*ld+i] -= R[i];
326:           /* normalization */
327:           norm = BLASnrm2_(&n,X+ld*j,&one);
328:           for (i=0;i<n;i++) X[ld*j+i] /= norm;
329:         } else p[j] = 2;
330:       }
331:     }
332:   }
333:   if (ds->pmode==DS_PARALLEL_DISTRIBUTED) {  /* communicate results */
334:     PetscMPIIntCast(k,&len);
335:     MPIU_Allreduce(MPI_IN_PLACE,p,len,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)ds));
336:     MPI_Comm_size(PetscObjectComm((PetscObject)ds),&size);
337:     PetscLayoutGetRanges(map,&range);
338:     for (j=0;j<k;j++) {
339:       if (p[j]) {  /* j-th eigenpair has been refined */
340:         for (root=0;root<size;root++) if (range[root+1]>j) break;
341:         PetscMPIIntCast(1,&len);
342:         MPI_Bcast(wr+j,len,MPIU_SCALAR,root,PetscObjectComm((PetscObject)ds));
343:         PetscMPIIntCast(n,&len);
344:         MPI_Bcast(X+ld*j,len,MPIU_SCALAR,root,PetscObjectComm((PetscObject)ds));
345:       }
346:     }
347:     PetscLayoutDestroy(&map);
348:   }
349:   MatDenseRestoreArray(ds->omat[DS_MAT_X],&X);
350:   return 0;
351: }

353: PetscErrorCode DSSolve_NEP_Contour(DS ds,PetscScalar *wr,PetscScalar *wi)
354: {
355:   DS_NEP         *ctx = (DS_NEP*)ds->data;
356:   PetscScalar    *alpha,*beta,*Q,*Z,*X,*U,*V,*W,*work,*Rc,*R,*w,*z,*zn,*S;
357:   PetscScalar    sone=1.0,szero=0.0,center;
358:   PetscReal      *rwork,norm,radius,vscale,rgscale,*sigma;
359:   PetscBLASInt   info,n,*perm,p,pp,ld,lwork,k_,rk_,colA,rowA,one=1;
360:   PetscInt       mid,lds,nnod=ctx->nnod,k,i,ii,jj,j,s,off,rk,nwu=0,nw,lrwork,*inside,kstart=0,kend=nnod;
361:   PetscMPIInt    len;
362:   PetscBool      isellipse;
363:   PetscRandom    rand;

366:   /* Contour parameters */
367:   PetscObjectTypeCompare((PetscObject)ctx->rg,RGELLIPSE,&isellipse);
369:   RGEllipseGetParameters(ctx->rg,&center,&radius,&vscale);
370:   RGGetScale(ctx->rg,&rgscale);
371:   if (ds->pmode==DS_PARALLEL_DISTRIBUTED) {
372:     if (!ctx->map) PetscLayoutCreateFromSizes(PetscObjectComm((PetscObject)ds),PETSC_DECIDE,ctx->nnod,1,&ctx->map);
373:     PetscLayoutGetRange(ctx->map,&kstart,&kend);
374:   }

376:   DSAllocateMat_Private(ds,DS_MAT_W); /* size n */
377:   DSAllocateMat_Private(ds,DS_MAT_Q); /* size mid*n */
378:   DSAllocateMat_Private(ds,DS_MAT_Z); /* size mid*n */
379:   DSAllocateMat_Private(ds,DS_MAT_U); /* size mid*n */
380:   DSAllocateMat_Private(ds,DS_MAT_V); /* size mid*n */
381:   MatDenseGetArray(ds->omat[DS_MAT_Q],&Q);
382:   MatDenseGetArray(ds->omat[DS_MAT_Z],&Z);
383:   MatDenseGetArray(ds->omat[DS_MAT_U],&U);
384:   MatDenseGetArray(ds->omat[DS_MAT_V],&V);
385:   mid  = ctx->max_mid;
386:   PetscBLASIntCast(ds->n,&n);
387:   p    = n;   /* maximum number of columns for the probing matrix */
388:   PetscBLASIntCast(ds->ld,&ld);
389:   PetscBLASIntCast(mid*n,&rowA);
390:   PetscBLASIntCast(5*rowA,&lwork);
391:   nw   = n*(2*p+7*mid)+3*nnod+2*mid*n*p;
392:   lrwork = mid*n*6+8*n;
393:   DSAllocateWork_Private(ds,nw,lrwork,n+1);

395:   sigma = ds->rwork;
396:   rwork = ds->rwork+mid*n;
397:   perm  = ds->iwork;
398:   z     = ds->work+nwu;    nwu += nnod;         /* quadrature points */
399:   zn    = ds->work+nwu;    nwu += nnod;         /* normalized quadrature points */
400:   w     = ds->work+nwu;    nwu += nnod;         /* quadrature weights */
401:   Rc    = ds->work+nwu;    nwu += n*p;
402:   R     = ds->work+nwu;    nwu += n*p;
403:   alpha = ds->work+nwu;    nwu += mid*n;
404:   beta  = ds->work+nwu;    nwu += mid*n;
405:   S     = ds->work+nwu;    nwu += 2*mid*n*p;
406:   work  = ds->work+nwu;    /*nwu += mid*n*5;*/

408:   /* Compute quadrature parameters */
409:   RGComputeQuadrature(ctx->rg,RG_QUADRULE_TRAPEZOIDAL,nnod,z,zn,w);

411:   /* Set random matrix */
412:   PetscRandomCreate(PetscObjectComm((PetscObject)ds),&rand);
413:   PetscRandomSetSeed(rand,0x12345678);
414:   PetscRandomSeed(rand);
415:   for (j=0;j<p;j++)
416:     for (i=0;i<n;i++) PetscRandomGetValue(rand,Rc+i+j*n);
417:   PetscArrayzero(S,2*mid*n*p);
418:   /* Loop of integration points */
419:   for (k=kstart;k<kend;k++) {
420:     PetscInfo(NULL,"Solving integration point %" PetscInt_FMT "\n",k);
421:     PetscArraycpy(R,Rc,p*n);
422:     DSNEPComputeMatrix(ds,z[k],PETSC_FALSE,DS_MAT_W);

424:     /* LU factorization */
425:     MatDenseGetArray(ds->omat[DS_MAT_W],&W);
426:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
427:     PetscCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,W,&ld,perm,&info));
428:     SlepcCheckLapackInfo("getrf",info);
429:     PetscCallBLAS("LAPACKgetrs",LAPACKgetrs_("N",&n,&p,W,&ld,perm,R,&n,&info));
430:     SlepcCheckLapackInfo("getrs",info);
431:     PetscFPTrapPop();
432:     MatDenseRestoreArray(ds->omat[DS_MAT_W],&W);

434:     /* Moments computation */
435:     for (s=0;s<2*ctx->max_mid;s++) {
436:       off = s*n*p;
437:       for (j=0;j<p;j++)
438:         for (i=0;i<n;i++) S[off+i+j*n] += w[k]*R[j*n+i];
439:       w[k] *= zn[k];
440:     }
441:   }

443:   if (ds->pmode==DS_PARALLEL_DISTRIBUTED) {  /* compute final S via reduction */
444:     PetscMPIIntCast(2*mid*n*p,&len);
445:     MPIU_Allreduce(MPI_IN_PLACE,S,len,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)ds));
446:   }
447:   p = ctx->spls?PetscMin(ctx->spls,n):n;
448:   pp = p;
449:   do {
450:     p = pp;
451:     PetscBLASIntCast(mid*p,&colA);

453:     PetscInfo(ds,"Computing SVD of size %" PetscBLASInt_FMT "x%" PetscBLASInt_FMT "\n",rowA,colA);
454:     for (jj=0;jj<mid;jj++) {
455:       for (ii=0;ii<mid;ii++) {
456:         off = jj*p*rowA+ii*n;
457:         for (j=0;j<p;j++)
458:           for (i=0;i<n;i++) Q[off+j*rowA+i] = S[((jj+ii)*n+j)*n+i];
459:       }
460:     }
461:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
462:     PetscCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&rowA,&colA,Q,&rowA,sigma,U,&rowA,V,&colA,work,&lwork,rwork,&info));
463:     SlepcCheckLapackInfo("gesvd",info);
464:     PetscFPTrapPop();

466:     rk = colA;
467:     for (i=1;i<colA;i++) if (sigma[i]/sigma[0]<PETSC_MACHINE_EPSILON*1e4) {rk = i; break;}
468:     if (rk<colA || p==n) break;
469:     pp *= 2;
470:   } while (pp<=n);
471:   PetscInfo(ds,"Solving generalized eigenproblem of size %" PetscInt_FMT "\n",rk);
472:   for (jj=0;jj<mid;jj++) {
473:     for (ii=0;ii<mid;ii++) {
474:       off = jj*p*rowA+ii*n;
475:       for (j=0;j<p;j++)
476:         for (i=0;i<n;i++) Q[off+j*rowA+i] = S[((jj+ii+1)*n+j)*n+i];
477:     }
478:   }
479:   PetscBLASIntCast(rk,&rk_);
480:   PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&rowA,&rk_,&colA,&sone,Q,&rowA,V,&colA,&szero,Z,&rowA));
481:   PetscCallBLAS("BLASgemm",BLASgemm_("C","N",&rk_,&rk_,&rowA,&sone,U,&rowA,Z,&rowA,&szero,Q,&rk_));
482:   PetscArrayzero(Z,n*mid*n*mid);
483:   for (j=0;j<rk;j++) Z[j+j*rk_] = sigma[j];
484:   PetscCallBLAS("LAPACKggev",LAPACKggev_("N","V",&rk_,Q,&rk_,Z,&rk_,alpha,beta,NULL,&ld,V,&rk_,work,&lwork,rwork,&info));
485:   for (i=0;i<rk;i++) wr[i] = (center+radius*alpha[i]/beta[i])*rgscale;
486:   PetscMalloc1(rk,&inside);
487:   RGCheckInside(ctx->rg,rk,wr,wi,inside);
488:   k=0;
489:   for (i=0;i<rk;i++)
490:     if (inside[i]==1) inside[k++] = i;
491:   /* Discard values outside region */
492:   lds = ld*mid;
493:   PetscArrayzero(Q,lds*lds);
494:   PetscArrayzero(Z,lds*lds);
495:   for (i=0;i<k;i++) Q[i+i*lds] = (center*beta[inside[i]]+radius*alpha[inside[i]])*rgscale;
496:   for (i=0;i<k;i++) Z[i+i*lds] = beta[inside[i]];
497:   for (i=0;i<k;i++) wr[i] = Q[i+i*lds]/Z[i+i*lds];
498:   for (j=0;j<k;j++) for (i=0;i<rk;i++) V[j*rk+i] = sigma[i]*V[inside[j]*rk+i];
499:   PetscBLASIntCast(k,&k_);
500:   MatDenseGetArray(ds->omat[DS_MAT_X],&X);
501:   PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&k_,&rk_,&sone,U,&rowA,V,&rk_,&szero,X,&ld));
502:   /* Normalize */
503:   for (j=0;j<k;j++) {
504:     norm = BLASnrm2_(&n,X+ld*j,&one);
505:     for (i=0;i<n;i++) X[ld*j+i] /= norm;
506:   }
507:   PetscFree(inside);
508:   MatDenseRestoreArray(ds->omat[DS_MAT_X],&X);
509:   MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q);
510:   MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z);
511:   MatDenseRestoreArray(ds->omat[DS_MAT_U],&U);
512:   MatDenseRestoreArray(ds->omat[DS_MAT_V],&V);

514:   /* Newton refinement */
515:   if (ctx->Nit) DSNEPNewtonRefine(ds,k,wr);
516:   ds->t = k;
517:   PetscRandomDestroy(&rand);
518:   return 0;
519: }
520: #endif

522: #if !defined(PETSC_HAVE_MPIUNI)
523: PetscErrorCode DSSynchronize_NEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
524: {
525:   DS_NEP         *ctx = (DS_NEP*)ds->data;
526:   PetscInt       ld=ds->ld,k=0;
527:   PetscMPIInt    n,n2,rank,size,off=0;
528:   PetscScalar    *X;

530:   if (!ds->method) { /* SLP */
531:     if (ds->state>=DS_STATE_CONDENSED) k += ds->n;
532:     if (eigr) k += 1;
533:     if (eigi) k += 1;
534:     PetscMPIIntCast(1,&n);
535:     PetscMPIIntCast(ds->n,&n2);
536:   } else { /* Contour */
537:     if (ds->state>=DS_STATE_CONDENSED) k += ctx->max_mid*ds->n*ld;
538:     if (eigr) k += ctx->max_mid*ds->n;
539:     if (eigi) k += ctx->max_mid*ds->n;
540:     PetscMPIIntCast(ctx->max_mid*ds->n,&n);
541:     PetscMPIIntCast(ctx->max_mid*ds->n*ld,&n2);
542:   }
543:   DSAllocateWork_Private(ds,k,0,0);
544:   PetscMPIIntCast(k*sizeof(PetscScalar),&size);
545:   if (ds->state>=DS_STATE_CONDENSED) MatDenseGetArray(ds->omat[DS_MAT_X],&X);
546:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
547:   if (!rank) {
548:     if (ds->state>=DS_STATE_CONDENSED) MPI_Pack(X,n2,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
549:     if (eigr) MPI_Pack(eigr,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
550: #if !defined(PETSC_USE_COMPLEX)
551:     if (eigi) MPI_Pack(eigi,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
552: #endif
553:   }
554:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
555:   if (rank) {
556:     if (ds->state>=DS_STATE_CONDENSED) MPI_Unpack(ds->work,size,&off,X,n2,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
557:     if (eigr) MPI_Unpack(ds->work,size,&off,eigr,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
558: #if !defined(PETSC_USE_COMPLEX)
559:     if (eigi) MPI_Unpack(ds->work,size,&off,eigi,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
560: #endif
561:   }
562:   if (ds->state>=DS_STATE_CONDENSED) MatDenseRestoreArray(ds->omat[DS_MAT_X],&X);
563:   return 0;
564: }
565: #endif

567: static PetscErrorCode DSNEPSetFN_NEP(DS ds,PetscInt n,FN fn[])
568: {
569:   DS_NEP         *ctx = (DS_NEP*)ds->data;
570:   PetscInt       i;

574:   if (ds->ld) PetscInfo(ds,"DSNEPSetFN() called after DSAllocate()\n");
575:   for (i=0;i<n;i++) PetscObjectReference((PetscObject)fn[i]);
576:   for (i=0;i<ctx->nf;i++) FNDestroy(&ctx->f[i]);
577:   for (i=0;i<n;i++) ctx->f[i] = fn[i];
578:   ctx->nf = n;
579:   return 0;
580: }

582: /*@
583:    DSNEPSetFN - Sets a number of functions that define the nonlinear
584:    eigenproblem.

586:    Collective on ds

588:    Input Parameters:
589: +  ds - the direct solver context
590: .  n  - number of functions
591: -  fn - array of functions

593:    Notes:
594:    The nonlinear eigenproblem is defined in terms of the split nonlinear
595:    operator T(lambda) = sum_i A_i*f_i(lambda).

597:    This function must be called before DSAllocate(). Then DSAllocate()
598:    will allocate an extra matrix A_i per each function, that can be
599:    filled in the usual way.

601:    Level: advanced

603: .seealso: DSNEPGetFN(), DSAllocate()
604: @*/
605: PetscErrorCode DSNEPSetFN(DS ds,PetscInt n,FN fn[])
606: {
607:   PetscInt       i;

612:   for (i=0;i<n;i++) {
615:   }
616:   PetscTryMethod(ds,"DSNEPSetFN_C",(DS,PetscInt,FN[]),(ds,n,fn));
617:   return 0;
618: }

620: static PetscErrorCode DSNEPGetFN_NEP(DS ds,PetscInt k,FN *fn)
621: {
622:   DS_NEP *ctx = (DS_NEP*)ds->data;

625:   *fn = ctx->f[k];
626:   return 0;
627: }

629: /*@
630:    DSNEPGetFN - Gets the functions associated with the nonlinear DS.

632:    Not collective, though parallel FNs are returned if the DS is parallel

634:    Input Parameters:
635: +  ds - the direct solver context
636: -  k  - the index of the requested function (starting in 0)

638:    Output Parameter:
639: .  fn - the function

641:    Level: advanced

643: .seealso: DSNEPSetFN()
644: @*/
645: PetscErrorCode DSNEPGetFN(DS ds,PetscInt k,FN *fn)
646: {
649:   PetscUseMethod(ds,"DSNEPGetFN_C",(DS,PetscInt,FN*),(ds,k,fn));
650:   return 0;
651: }

653: static PetscErrorCode DSNEPGetNumFN_NEP(DS ds,PetscInt *n)
654: {
655:   DS_NEP *ctx = (DS_NEP*)ds->data;

657:   *n = ctx->nf;
658:   return 0;
659: }

661: /*@
662:    DSNEPGetNumFN - Returns the number of functions stored internally by
663:    the DS.

665:    Not collective

667:    Input Parameter:
668: .  ds - the direct solver context

670:    Output Parameters:
671: .  n - the number of functions passed in DSNEPSetFN()

673:    Level: advanced

675: .seealso: DSNEPSetFN()
676: @*/
677: PetscErrorCode DSNEPGetNumFN(DS ds,PetscInt *n)
678: {
681:   PetscUseMethod(ds,"DSNEPGetNumFN_C",(DS,PetscInt*),(ds,n));
682:   return 0;
683: }

685: static PetscErrorCode DSNEPSetMinimality_NEP(DS ds,PetscInt n)
686: {
687:   DS_NEP *ctx = (DS_NEP*)ds->data;

689:   if (n == PETSC_DECIDE || n == PETSC_DEFAULT) ctx->max_mid = 4;
690:   else {
692:     ctx->max_mid = n;
693:   }
694:   return 0;
695: }

697: /*@
698:    DSNEPSetMinimality - Sets the maximum minimality index used internally by
699:    the DSNEP.

701:    Logically Collective on ds

703:    Input Parameters:
704: +  ds - the direct solver context
705: -  n  - the maximum minimality index

707:    Options Database Key:
708: .  -ds_nep_minimality <n> - sets the maximum minimality index

710:    Notes:
711:    The maximum minimality index is used only in the contour integral method,
712:    and is related to the highest momemts used in the method. The default
713:    value is 1, an larger value might give better accuracy in some cases, but
714:    at a higher cost.

716:    Level: advanced

718: .seealso: DSNEPGetMinimality()
719: @*/
720: PetscErrorCode DSNEPSetMinimality(DS ds,PetscInt n)
721: {
724:   PetscTryMethod(ds,"DSNEPSetMinimality_C",(DS,PetscInt),(ds,n));
725:   return 0;
726: }

728: static PetscErrorCode DSNEPGetMinimality_NEP(DS ds,PetscInt *n)
729: {
730:   DS_NEP *ctx = (DS_NEP*)ds->data;

732:   *n = ctx->max_mid;
733:   return 0;
734: }

736: /*@
737:    DSNEPGetMinimality - Returns the maximum minimality index used internally by
738:    the DSNEP.

740:    Not collective

742:    Input Parameter:
743: .  ds - the direct solver context

745:    Output Parameters:
746: .  n - the maximum minimality index passed in DSNEPSetMinimality()

748:    Level: advanced

750: .seealso: DSNEPSetMinimality()
751: @*/
752: PetscErrorCode DSNEPGetMinimality(DS ds,PetscInt *n)
753: {
756:   PetscUseMethod(ds,"DSNEPGetMinimality_C",(DS,PetscInt*),(ds,n));
757:   return 0;
758: }

760: static PetscErrorCode DSNEPSetRefine_NEP(DS ds,PetscReal tol,PetscInt its)
761: {
762:   DS_NEP *ctx = (DS_NEP*)ds->data;

764:   if (tol == PETSC_DEFAULT) ctx->rtol = PETSC_MACHINE_EPSILON/PetscSqrtReal(PETSC_SQRT_MACHINE_EPSILON);
765:   else {
767:     ctx->rtol = tol;
768:   }
769:   if (its == PETSC_DECIDE || its == PETSC_DEFAULT) ctx->Nit = 3;
770:   else {
772:     ctx->Nit = its;
773:   }
774:   return 0;
775: }

777: /*@
778:    DSNEPSetRefine - Sets the tolerance and the number of iterations of Newton iterative
779:    refinement for eigenpairs.

781:    Logically Collective on ds

783:    Input Parameters:
784: +  ds  - the direct solver context
785: .  tol - the tolerance
786: -  its - the number of iterations

788:    Options Database Key:
789: +  -ds_nep_refine_tol <tol> - sets the tolerance
790: -  -ds_nep_refine_its <its> - sets the number of Newton iterations

792:    Notes:
793:    Iterative refinement of eigenpairs is currently used only in the contour
794:    integral method.

796:    Level: advanced

798: .seealso: DSNEPGetRefine()
799: @*/
800: PetscErrorCode DSNEPSetRefine(DS ds,PetscReal tol,PetscInt its)
801: {
805:   PetscTryMethod(ds,"DSNEPSetRefine_C",(DS,PetscReal,PetscInt),(ds,tol,its));
806:   return 0;
807: }

809: static PetscErrorCode DSNEPGetRefine_NEP(DS ds,PetscReal *tol,PetscInt *its)
810: {
811:   DS_NEP *ctx = (DS_NEP*)ds->data;

813:   if (tol) *tol = ctx->rtol;
814:   if (its) *its = ctx->Nit;
815:   return 0;
816: }

818: /*@
819:    DSNEPGetRefine - Returns the tolerance and the number of iterations of Newton iterative
820:    refinement for eigenpairs.

822:    Not collective

824:    Input Parameter:
825: .  ds - the direct solver context

827:    Output Parameters:
828: +  tol - the tolerance
829: -  its - the number of iterations

831:    Level: advanced

833: .seealso: DSNEPSetRefine()
834: @*/
835: PetscErrorCode DSNEPGetRefine(DS ds,PetscReal *tol,PetscInt *its)
836: {
838:   PetscUseMethod(ds,"DSNEPGetRefine_C",(DS,PetscReal*,PetscInt*),(ds,tol,its));
839:   return 0;
840: }

842: static PetscErrorCode DSNEPSetIntegrationPoints_NEP(DS ds,PetscInt ip)
843: {
844:   DS_NEP         *ctx = (DS_NEP*)ds->data;

846:   if (ip == PETSC_DECIDE || ip == PETSC_DEFAULT) ctx->nnod = 64;
847:   else {
849:     ctx->nnod = ip;
850:   }
851:   PetscLayoutDestroy(&ctx->map);  /* need to redistribute at next solve */
852:   return 0;
853: }

855: /*@
856:    DSNEPSetIntegrationPoints - Sets the number of integration points to be
857:    used in the contour integral method.

859:    Logically Collective on ds

861:    Input Parameters:
862: +  ds - the direct solver context
863: -  ip - the number of integration points

865:    Options Database Key:
866: .  -ds_nep_integration_points <ip> - sets the number of integration points

868:    Notes:
869:    This parameter is relevant only in the contour integral method.

871:    Level: advanced

873: .seealso: DSNEPGetIntegrationPoints()
874: @*/
875: PetscErrorCode DSNEPSetIntegrationPoints(DS ds,PetscInt ip)
876: {
879:   PetscTryMethod(ds,"DSNEPSetIntegrationPoints_C",(DS,PetscInt),(ds,ip));
880:   return 0;
881: }

883: static PetscErrorCode DSNEPGetIntegrationPoints_NEP(DS ds,PetscInt *ip)
884: {
885:   DS_NEP *ctx = (DS_NEP*)ds->data;

887:   *ip = ctx->nnod;
888:   return 0;
889: }

891: /*@
892:    DSNEPGetIntegrationPoints - Returns the number of integration points used
893:    in the contour integral method.

895:    Not collective

897:    Input Parameter:
898: .  ds - the direct solver context

900:    Output Parameters:
901: .  ip - the number of integration points

903:    Level: advanced

905: .seealso: DSNEPSetIntegrationPoints()
906: @*/
907: PetscErrorCode DSNEPGetIntegrationPoints(DS ds,PetscInt *ip)
908: {
911:   PetscUseMethod(ds,"DSNEPGetIntegrationPoints_C",(DS,PetscInt*),(ds,ip));
912:   return 0;
913: }

915: static PetscErrorCode DSNEPSetSamplingSize_NEP(DS ds,PetscInt p)
916: {
917:   DS_NEP *ctx = (DS_NEP*)ds->data;

919:   if (p == PETSC_DECIDE || p == PETSC_DEFAULT) ctx->spls = 0;
920:   else {
922:     ctx->spls = p;
923:   }
924:   return 0;
925: }

927: /*@
928:    DSNEPSetSamplingSize - Sets the number of sampling columns to be
929:    used in the contour integral method.

931:    Logically Collective on ds

933:    Input Parameters:
934: +  ds - the direct solver context
935: -  p - the number of columns for the sampling matrix

937:    Options Database Key:
938: .  -ds_nep_sampling_size <p> - sets the number of sampling columns

940:    Notes:
941:    This parameter is relevant only in the contour integral method.

943:    Level: advanced

945: .seealso: DSNEPGetSamplingSize()
946: @*/
947: PetscErrorCode DSNEPSetSamplingSize(DS ds,PetscInt p)
948: {
951:   PetscTryMethod(ds,"DSNEPSetSamplingSize_C",(DS,PetscInt),(ds,p));
952:   return 0;
953: }

955: static PetscErrorCode DSNEPGetSamplingSize_NEP(DS ds,PetscInt *p)
956: {
957:   DS_NEP *ctx = (DS_NEP*)ds->data;

959:   *p = ctx->spls;
960:   return 0;
961: }

963: /*@
964:    DSNEPGetSamplingSize - Returns the number of sampling columns used
965:    in the contour integral method.

967:    Not collective

969:    Input Parameter:
970: .  ds - the direct solver context

972:    Output Parameters:
973: .  p -  the number of columns for the sampling matrix

975:    Level: advanced

977: .seealso: DSNEPSetSamplingSize()
978: @*/
979: PetscErrorCode DSNEPGetSamplingSize(DS ds,PetscInt *p)
980: {
983:   PetscUseMethod(ds,"DSNEPGetSamplingSize_C",(DS,PetscInt*),(ds,p));
984:   return 0;
985: }

987: static PetscErrorCode DSNEPSetComputeMatrixFunction_NEP(DS ds,PetscErrorCode (*fun)(DS,PetscScalar,PetscBool,DSMatType,void*),void *ctx)
988: {
989:   DS_NEP *dsctx = (DS_NEP*)ds->data;

991:   dsctx->computematrix    = fun;
992:   dsctx->computematrixctx = ctx;
993:   return 0;
994: }

996: /*@C
997:    DSNEPSetComputeMatrixFunction - Sets a user-provided subroutine to compute
998:    the matrices T(lambda) or T'(lambda).

1000:    Logically Collective on ds

1002:    Input Parameters:
1003: +  ds  - the direct solver context
1004: .  fun - a pointer to the user function
1005: -  ctx - a context pointer (the last parameter to the user function)

1007:    Calling Sequence of fun:
1008: $   fun(DS ds,PetscScalar lambda,PetscBool deriv,DSMatType mat,void *ctx)

1010: +   ds     - the direct solver object
1011: .   lambda - point where T(lambda) or T'(lambda) must be evaluated
1012: .   deriv  - if true compute T'(lambda), otherwise compute T(lambda)
1013: .   mat    - the DS matrix where the result must be stored
1014: -   ctx    - optional context, as set by DSNEPSetComputeMatrixFunction()

1016:    Note:
1017:    The result is computed as T(lambda) = sum_i E_i*f_i(lambda), and similarly
1018:    for the derivative.

1020:    Level: developer

1022: .seealso: DSNEPGetComputeMatrixFunction()
1023: @*/
1024: PetscErrorCode DSNEPSetComputeMatrixFunction(DS ds,PetscErrorCode (*fun)(DS,PetscScalar,PetscBool,DSMatType,void*),void *ctx)
1025: {
1027:   PetscTryMethod(ds,"DSNEPSetComputeMatrixFunction_C",(DS,PetscErrorCode (*)(DS,PetscScalar,PetscBool,DSMatType,void*),void*),(ds,fun,ctx));
1028:   return 0;
1029: }

1031: static PetscErrorCode DSNEPGetComputeMatrixFunction_NEP(DS ds,PetscErrorCode (**fun)(DS,PetscScalar,PetscBool,DSMatType,void*),void **ctx)
1032: {
1033:   DS_NEP *dsctx = (DS_NEP*)ds->data;

1035:   if (fun) *fun = dsctx->computematrix;
1036:   if (ctx) *ctx = dsctx->computematrixctx;
1037:   return 0;
1038: }

1040: /*@C
1041:    DSNEPGetComputeMatrixFunction - Returns the user-provided callback function
1042:    set in DSNEPSetComputeMatrixFunction().

1044:    Not Collective

1046:    Input Parameter:
1047: .  ds  - the direct solver context

1049:    Output Parameters:
1050: +  fun - the pointer to the user function
1051: -  ctx - the context pointer

1053:    Level: developer

1055: .seealso: DSNEPSetComputeMatrixFunction()
1056: @*/
1057: PetscErrorCode DSNEPGetComputeMatrixFunction(DS ds,PetscErrorCode (**fun)(DS,PetscScalar,PetscBool,DSMatType,void*),void **ctx)
1058: {
1060:   PetscUseMethod(ds,"DSNEPGetComputeMatrixFunction_C",(DS,PetscErrorCode (**)(DS,PetscScalar,PetscBool,DSMatType,void*),void**),(ds,fun,ctx));
1061:   return 0;
1062: }

1064: static PetscErrorCode DSNEPSetRG_NEP(DS ds,RG rg)
1065: {
1066:   DS_NEP         *dsctx = (DS_NEP*)ds->data;

1068:   PetscObjectReference((PetscObject)rg);
1069:   RGDestroy(&dsctx->rg);
1070:   dsctx->rg = rg;
1071:   return 0;
1072: }

1074: /*@
1075:    DSNEPSetRG - Associates a region object to the DSNEP solver.

1077:    Logically Collective on ds

1079:    Input Parameters:
1080: +  ds  - the direct solver context
1081: -  rg  - the region context

1083:    Notes:
1084:    The region is used only in the contour integral method, and
1085:    should enclose the wanted eigenvalues.

1087:    Level: developer

1089: .seealso: DSNEPGetRG()
1090: @*/
1091: PetscErrorCode DSNEPSetRG(DS ds,RG rg)
1092: {
1094:   if (rg) {
1097:   }
1098:   PetscTryMethod(ds,"DSNEPSetRG_C",(DS,RG),(ds,rg));
1099:   return 0;
1100: }

1102: static PetscErrorCode DSNEPGetRG_NEP(DS ds,RG *rg)
1103: {
1104:   DS_NEP         *ctx = (DS_NEP*)ds->data;

1106:   if (!ctx->rg) {
1107:     RGCreate(PetscObjectComm((PetscObject)ds),&ctx->rg);
1108:     PetscObjectIncrementTabLevel((PetscObject)ctx->rg,(PetscObject)ds,1);
1109:     RGSetOptionsPrefix(ctx->rg,((PetscObject)ds)->prefix);
1110:     RGAppendOptionsPrefix(ctx->rg,"ds_nep_");
1111:     PetscObjectSetOptions((PetscObject)ctx->rg,((PetscObject)ds)->options);
1112:   }
1113:   *rg = ctx->rg;
1114:   return 0;
1115: }

1117: /*@
1118:    DSNEPGetRG - Obtain the region object associated to the DSNEP solver.

1120:    Not Collective

1122:    Input Parameter:
1123: .  ds  - the direct solver context

1125:    Output Parameter:
1126: .  rg  - the region context

1128:    Level: developer

1130: .seealso: DSNEPSetRG()
1131: @*/
1132: PetscErrorCode DSNEPGetRG(DS ds,RG *rg)
1133: {
1136:   PetscUseMethod(ds,"DSNEPGetRG_C",(DS,RG*),(ds,rg));
1137:   return 0;
1138: }

1140: PetscErrorCode DSSetFromOptions_NEP(DS ds,PetscOptionItems *PetscOptionsObject)
1141: {
1142:   PetscInt       k;
1143:   PetscBool      flg;
1144: #if defined(PETSC_USE_COMPLEX)
1145:   PetscReal      r;
1146:   PetscBool      flg1;
1147:   DS_NEP         *ctx = (DS_NEP*)ds->data;
1148: #endif

1150:   PetscOptionsHeadBegin(PetscOptionsObject,"DS NEP Options");

1152:     PetscOptionsInt("-ds_nep_minimality","Maximum minimality index","DSNEPSetMinimality",4,&k,&flg);
1153:     if (flg) DSNEPSetMinimality(ds,k);

1155:     PetscOptionsInt("-ds_nep_integration_points","Number of integration points","DSNEPSetIntegrationPoints",64,&k,&flg);
1156:     if (flg) DSNEPSetIntegrationPoints(ds,k);

1158:     PetscOptionsInt("-ds_nep_sampling_size","Number of sampling columns","DSNEPSetSamplingSize",0,&k,&flg);
1159:     if (flg) DSNEPSetSamplingSize(ds,k);

1161: #if defined(PETSC_USE_COMPLEX)
1162:     r = ctx->rtol;
1163:     PetscOptionsReal("-ds_nep_refine_tol","Refinement tolerance","DSNEPSetRefine",ctx->rtol,&r,&flg1);
1164:     k = ctx->Nit;
1165:     PetscOptionsInt("-ds_nep_refine_its","Number of iterative refinement iterations","DSNEPSetRefine",ctx->Nit,&k,&flg);
1166:     if (flg1||flg) DSNEPSetRefine(ds,r,k);

1168:     if (ds->method==1) {
1169:       if (!ctx->rg) DSNEPGetRG(ds,&ctx->rg);
1170:       RGSetFromOptions(ctx->rg);
1171:     }
1172: #endif

1174:   PetscOptionsHeadEnd();
1175:   return 0;
1176: }

1178: PetscErrorCode DSDestroy_NEP(DS ds)
1179: {
1180:   DS_NEP         *ctx = (DS_NEP*)ds->data;
1181:   PetscInt       i;

1183:   for (i=0;i<ctx->nf;i++) FNDestroy(&ctx->f[i]);
1184:   RGDestroy(&ctx->rg);
1185:   PetscLayoutDestroy(&ctx->map);
1186:   PetscFree(ds->data);
1187:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetFN_C",NULL);
1188:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetFN_C",NULL);
1189:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetNumFN_C",NULL);
1190:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetMinimality_C",NULL);
1191:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetMinimality_C",NULL);
1192:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetRefine_C",NULL);
1193:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetRefine_C",NULL);
1194:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetIntegrationPoints_C",NULL);
1195:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetIntegrationPoints_C",NULL);
1196:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetSamplingSize_C",NULL);
1197:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetSamplingSize_C",NULL);
1198:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetRG_C",NULL);
1199:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetRG_C",NULL);
1200:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetComputeMatrixFunction_C",NULL);
1201:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetComputeMatrixFunction_C",NULL);
1202:   return 0;
1203: }

1205: PetscErrorCode DSMatGetSize_NEP(DS ds,DSMatType t,PetscInt *rows,PetscInt *cols)
1206: {
1207:   DS_NEP *ctx = (DS_NEP*)ds->data;

1209:   *rows = ds->n;
1210:   if (t==DS_MAT_Q || t==DS_MAT_Z || t==DS_MAT_U || t==DS_MAT_V) *rows *= ctx->max_mid;
1211:   *cols = ds->n;
1212:   if (t==DS_MAT_Q || t==DS_MAT_Z || t==DS_MAT_U || t==DS_MAT_V || t==DS_MAT_X || t==DS_MAT_Y) *cols *= ctx->max_mid;
1213:   return 0;
1214: }

1216: /*MC
1217:    DSNEP - Dense Nonlinear Eigenvalue Problem.

1219:    Level: beginner

1221:    Notes:
1222:    The problem is expressed as T(lambda)*x = 0, where T(lambda) is a
1223:    parameter-dependent matrix written as T(lambda) = sum_i E_i*f_i(lambda).
1224:    The eigenvalues lambda are the arguments returned by DSSolve()..

1226:    The coefficient matrices E_i are the extra matrices of the DS, and
1227:    the scalar functions f_i are passed via DSNEPSetFN(). Optionally, a
1228:    callback function to fill the E_i matrices can be set with
1229:    DSNEPSetComputeMatrixFunction().

1231:    Used DS matrices:
1232: +  DS_MAT_Ex - coefficient matrices of the split form of T(lambda)
1233: .  DS_MAT_A  - (workspace) T(lambda) evaluated at a given lambda (SLP only)
1234: .  DS_MAT_B  - (workspace) T'(lambda) evaluated at a given lambda (SLP only)
1235: .  DS_MAT_Q  - (workspace) left Hankel matrix (contour only)
1236: .  DS_MAT_Z  - (workspace) right Hankel matrix (contour only)
1237: .  DS_MAT_U  - (workspace) left singular vectors (contour only)
1238: .  DS_MAT_V  - (workspace) right singular vectors (contour only)
1239: -  DS_MAT_W  - (workspace) auxiliary matrix of size nxn

1241:    Implemented methods:
1242: +  0 - Successive Linear Problems (SLP), computes just one eigenpair
1243: -  1 - Contour integral, computes all eigenvalues inside a region

1245: .seealso: DSCreate(), DSSetType(), DSType, DSNEPSetFN(), DSNEPSetComputeMatrixFunction()
1246: M*/
1247: SLEPC_EXTERN PetscErrorCode DSCreate_NEP(DS ds)
1248: {
1249:   DS_NEP         *ctx;

1251:   PetscNew(&ctx);
1252:   ds->data = (void*)ctx;
1253:   ctx->max_mid = 4;
1254:   ctx->nnod    = 64;
1255:   ctx->Nit     = 3;
1256:   ctx->rtol    = PETSC_MACHINE_EPSILON/PetscSqrtReal(PETSC_SQRT_MACHINE_EPSILON);

1258:   ds->ops->allocate       = DSAllocate_NEP;
1259:   ds->ops->setfromoptions = DSSetFromOptions_NEP;
1260:   ds->ops->view           = DSView_NEP;
1261:   ds->ops->vectors        = DSVectors_NEP;
1262:   ds->ops->solve[0]       = DSSolve_NEP_SLP;
1263: #if defined(PETSC_USE_COMPLEX)
1264:   ds->ops->solve[1]       = DSSolve_NEP_Contour;
1265: #endif
1266:   ds->ops->sort           = DSSort_NEP;
1267: #if !defined(PETSC_HAVE_MPIUNI)
1268:   ds->ops->synchronize    = DSSynchronize_NEP;
1269: #endif
1270:   ds->ops->destroy        = DSDestroy_NEP;
1271:   ds->ops->matgetsize     = DSMatGetSize_NEP;

1273:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetFN_C",DSNEPSetFN_NEP);
1274:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetFN_C",DSNEPGetFN_NEP);
1275:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetNumFN_C",DSNEPGetNumFN_NEP);
1276:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetMinimality_C",DSNEPGetMinimality_NEP);
1277:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetMinimality_C",DSNEPSetMinimality_NEP);
1278:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetRefine_C",DSNEPGetRefine_NEP);
1279:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetRefine_C",DSNEPSetRefine_NEP);
1280:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetIntegrationPoints_C",DSNEPGetIntegrationPoints_NEP);
1281:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetIntegrationPoints_C",DSNEPSetIntegrationPoints_NEP);
1282:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetSamplingSize_C",DSNEPGetSamplingSize_NEP);
1283:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetSamplingSize_C",DSNEPSetSamplingSize_NEP);
1284:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetRG_C",DSNEPSetRG_NEP);
1285:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetRG_C",DSNEPGetRG_NEP);
1286:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetComputeMatrixFunction_C",DSNEPSetComputeMatrixFunction_NEP);
1287:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetComputeMatrixFunction_C",DSNEPGetComputeMatrixFunction_NEP);
1288:   return 0;
1289: }