Actual source code: arpack.c

  1: /*
  2:        This file implements a wrapper to the ARPACK package

  4:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  5:       SLEPc - Scalable Library for Eigenvalue Problem Computations
  6:       Copyright (c) 2002-2007, Universidad Politecnica de Valencia, Spain

  8:       This file is part of SLEPc. See the README file for conditions of use
  9:       and additional information.
 10:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 11: */

 13:  #include src/eps/impls/arpack/arpackp.h

 17: PetscErrorCode EPSSetUp_ARPACK(EPS eps)
 18: {
 20:   PetscInt       N, n;
 21:   int            ncv;
 22:   EPS_ARPACK     *ar = (EPS_ARPACK *)eps->data;

 25:   VecGetSize(eps->vec_initial,&N);
 26:   if (eps->ncv) {
 27:     if (eps->ncv<eps->nev+2) SETERRQ(1,"The value of ncv must be at least nev+2");
 28:   } else /* set default value of ncv */
 29:     eps->ncv = PetscMin(PetscMax(20,2*eps->nev+1),N);
 30:   if (!eps->max_it) eps->max_it = PetscMax(300,(int)(2*N/eps->ncv));

 32:   ncv = eps->ncv;
 33: #if defined(PETSC_USE_COMPLEX)
 34:   PetscFree(ar->rwork);
 35:   PetscMalloc(ncv*sizeof(PetscReal),&ar->rwork);
 36:   ar->lworkl = 3*ncv*ncv+5*ncv;
 37:   PetscFree(ar->workev);
 38:   PetscMalloc(3*ncv*sizeof(PetscScalar),&ar->workev);
 39: #else
 40:   if( eps->ishermitian ) {
 41:     ar->lworkl = ncv*(ncv+8);
 42:   } else {
 43:     ar->lworkl = 3*ncv*ncv+6*ncv;
 44:     PetscFree(ar->workev);
 45:     PetscMalloc(3*ncv*sizeof(PetscScalar),&ar->workev);
 46:   }
 47: #endif
 48:   PetscFree(ar->workl);
 49:   PetscMalloc(ar->lworkl*sizeof(PetscScalar),&ar->workl);
 50:   PetscFree(ar->select);
 51:   PetscMalloc(ncv*sizeof(PetscTruth),&ar->select);
 52:   VecGetLocalSize(eps->vec_initial,&n);
 53:   PetscFree(ar->workd);
 54:   PetscMalloc(3*n*sizeof(PetscScalar),&ar->workd);

 56:   EPSDefaultGetWork(eps,2);
 57:   EPSAllocateSolutionContiguous(eps);

 59:   return(0);
 60: }

 64: PetscErrorCode EPSSolve_ARPACK(EPS eps)
 65: {
 67:   EPS_ARPACK           *ar = (EPS_ARPACK *)eps->data;
 68:   char                 bmat[1], howmny[] = "A";
 69:   const char           *which;
 70:   PetscInt             nn;
 71:   int                  n, iparam[11], ipntr[14], ido, info;
 72:   PetscScalar          sigmar, *pV, *resid;
 73:   Vec                  x, y, w = eps->work[0];
 74:   Mat                  A;
 75:   PetscTruth           isSinv, isShift, rvec;
 76:   MPI_Fint             fcomm;
 77: #if !defined(PETSC_USE_COMPLEX)
 78:   PetscScalar    sigmai = 0.0;
 79: #endif

 82:   fcomm = MPI_Comm_c2f(eps->comm);
 83:   VecGetLocalSize(eps->vec_initial,&nn);
 84:   n = nn;
 85:   VecCreateMPIWithArray(eps->comm,n,PETSC_DECIDE,PETSC_NULL,&x);
 86:   VecCreateMPIWithArray(eps->comm,n,PETSC_DECIDE,PETSC_NULL,&y);
 87:   VecGetArray(eps->V[0],&pV);
 88:   VecCopy(eps->vec_initial,eps->work[1]);
 89:   VecGetArray(eps->work[1],&resid);
 90: 
 91:   ido  = 0;            /* first call to reverse communication interface */
 92:   info = 1;            /* indicates a initial vector is provided */
 93:   iparam[0] = 1;       /* use exact shifts */
 94:   iparam[2] = eps->max_it;  /* maximum number of Arnoldi update iterations */
 95:   iparam[3] = 1;       /* blocksize */
 96:   iparam[4] = 0;       /* number of converged Ritz values */
 97: 
 98:   /*
 99:      Computational modes ([]=not supported):
100:             symmetric    non-symmetric    complex
101:         1     1  'I'        1  'I'         1  'I'
102:         2     3  'I'        3  'I'         3  'I'
103:         3     2  'G'        2  'G'         2  'G'
104:         4     3  'G'        3  'G'         3  'G'
105:         5   [ 4  'G' ]    [ 3  'G' ]
106:         6   [ 5  'G' ]    [ 4  'G' ]
107:    */
108:   PetscTypeCompare((PetscObject)eps->OP,STSINV,&isSinv);
109:   PetscTypeCompare((PetscObject)eps->OP,STSHIFT,&isShift);
110:   STGetShift(eps->OP,&sigmar);
111:   STGetOperators(eps->OP,&A,PETSC_NULL);

113:   if (isSinv) {
114:     /* shift-and-invert mode */
115:     iparam[6] = 3;
116:     if (eps->ispositive) bmat[0] = 'G';
117:     else bmat[0] = 'I';
118:   } else if (isShift && eps->ispositive) {
119:     /* generalized shift mode with B positive definite */
120:     iparam[6] = 2;
121:     bmat[0] = 'G';
122:   } else {
123:     /* regular mode */
124:     if (eps->ishermitian && eps->isgeneralized)
125:       SETERRQ(PETSC_ERR_SUP,"Spectral transformation not supported by ARPACK hermitian solver");
126:     iparam[6] = 1;
127:     bmat[0] = 'I';
128:   }
129: 
130: #if !defined(PETSC_USE_COMPLEX)
131:     if (eps->ishermitian) {
132:       switch(eps->which) {
133:         case EPS_LARGEST_MAGNITUDE:  which = "LM"; break;
134:         case EPS_SMALLEST_MAGNITUDE: which = "SM"; break;
135:         case EPS_LARGEST_REAL:       which = "LA"; break;
136:         case EPS_SMALLEST_REAL:      which = "SA"; break;
137:         default: SETERRQ(1,"Wrong value of eps->which");
138:       }
139:     } else {
140: #endif
141:       switch(eps->which) {
142:         case EPS_LARGEST_MAGNITUDE:  which = "LM"; break;
143:         case EPS_SMALLEST_MAGNITUDE: which = "SM"; break;
144:         case EPS_LARGEST_REAL:       which = "LR"; break;
145:         case EPS_SMALLEST_REAL:      which = "SR"; break;
146:         case EPS_LARGEST_IMAGINARY:  which = "LI"; break;
147:         case EPS_SMALLEST_IMAGINARY: which = "SI"; break;
148:         default: SETERRQ(1,"Wrong value of eps->which");
149:       }
150: #if !defined(PETSC_USE_COMPLEX)
151:     }
152: #endif

154:   do {

156: #if !defined(PETSC_USE_COMPLEX)
157:     if (eps->ishermitian) {
158:       ARsaupd_( &fcomm, &ido, bmat, &n, which, &eps->nev, &eps->tol,
159:                 resid, &eps->ncv, pV, &n, iparam, ipntr, ar->workd,
160:                 ar->workl, &ar->lworkl, &info, 1, 2 );
161:     }
162:     else {
163:       ARnaupd_( &fcomm, &ido, bmat, &n, which, &eps->nev, &eps->tol,
164:                 resid, &eps->ncv, pV, &n, iparam, ipntr, ar->workd,
165:                 ar->workl, &ar->lworkl, &info, 1, 2 );
166:     }
167: #else
168:     ARnaupd_( &fcomm, &ido, bmat, &n, which, &eps->nev, &eps->tol,
169:               resid, &eps->ncv, pV, &n, iparam, ipntr, ar->workd,
170:               ar->workl, &ar->lworkl, ar->rwork, &info, 1, 2 );
171: #endif
172: 
173:     if (ido == -1 || ido == 1 || ido == 2) {
174:       if (ido == 1 && iparam[6] == 3 && bmat[0] == 'G') {
175:         /* special case for shift-and-invert with B semi-positive definite*/
176:         VecPlaceArray(x,&ar->workd[ipntr[2]-1]);
177:       } else {
178:         VecPlaceArray(x,&ar->workd[ipntr[0]-1]);
179:       }
180:       VecPlaceArray(y,&ar->workd[ipntr[1]-1]);
181: 
182:       if (ido == -1) {
183:         /* Y = OP * X for for the initialization phase to 
184:            force the starting vector into the range of OP */
185:         STApply(eps->OP,x,y);
186:       } else if (ido == 2) {
187:         /* Y = B * X */
188:         IPApplyMatrix(eps->ip,x,y);
189:       } else { /* ido == 1 */
190:         if (iparam[6] == 3 && bmat[0] == 'G') {
191:           /* Y = OP * X for shift-and-invert with B semi-positive definite */
192:           STAssociatedKSPSolve(eps->OP,x,y);
193:         } else if (iparam[6] == 2) {
194:           /* X=A*X Y=B^-1*X for shift with B positive definite */
195:           MatMult(A,x,y);
196:           if (sigmar != 0.0) {
197:             IPApplyMatrix(eps->ip,x,w);
198:             VecAXPY(y,sigmar,w);
199:           }
200:           VecCopy(y,x);
201:           STAssociatedKSPSolve(eps->OP,x,y);
202:         } else  {
203:           /* Y = OP * X */
204:           STApply(eps->OP,x,y);
205:         }
206:         IPOrthogonalize(eps->ip,eps->nds,PETSC_NULL,eps->DS,y,PETSC_NULL,PETSC_NULL,PETSC_NULL,w);
207:       }
208: 
209:       VecResetArray(x);
210:       VecResetArray(y);
211:     } else if (ido != 99) {
212:       SETERRQ1(1,"Internal error in ARPACK reverse comunication interface (ido=%i)\n",ido);
213:     }
214: 
215:   } while (ido != 99);

217:   eps->nconv = iparam[4];
218:   eps->its = iparam[2];
219: 
220:   if (info==3) { SETERRQ(1,"No shift could be applied in xxAUPD.\n"
221:                            "Try increasing the size of NCV relative to NEV."); }
222:   else if (info!=0 && info!=1) { SETERRQ1(PETSC_ERR_LIB,"Error reported by ARPACK subroutine xxAUPD (%d)",info);}

224:   rvec = PETSC_TRUE;

226:   if (eps->nconv > 0) {
227: #if !defined(PETSC_USE_COMPLEX)
228:     if (eps->ishermitian) {
229:       EPSMonitor(eps,iparam[2],iparam[4],&ar->workl[ipntr[5]-1],eps->eigi,&ar->workl[ipntr[6]-1],eps->ncv);
230:       ARseupd_ ( &fcomm, &rvec, howmny, ar->select, eps->eigr,
231:                  pV, &n, &sigmar,
232:                  bmat, &n, which, &eps->nev, &eps->tol,
233:                  resid, &eps->ncv, pV, &n, iparam, ipntr, ar->workd,
234:                  ar->workl, &ar->lworkl, &info, 1, 1, 2 );
235:     }
236:     else {
237:       EPSMonitor(eps,iparam[2],iparam[4],&ar->workl[ipntr[5]-1],&ar->workl[ipntr[6]-1],&ar->workl[ipntr[7]-1],eps->ncv);
238:       ARneupd_ ( &fcomm, &rvec, howmny, ar->select, eps->eigr, eps->eigi,
239:                  pV, &n, &sigmar, &sigmai, ar->workev,
240:                  bmat, &n, which, &eps->nev, &eps->tol,
241:                  resid, &eps->ncv, pV, &n, iparam, ipntr, ar->workd,
242:                  ar->workl, &ar->lworkl, &info, 1, 1, 2 );
243:     }
244: #else
245:     EPSMonitor(eps,eps->its,iparam[4],&ar->workl[ipntr[5]-1],eps->eigi,(PetscReal*)&ar->workl[ipntr[7]-1],eps->ncv);
246:     ARneupd_ ( &fcomm, &rvec, howmny, ar->select, eps->eigr,
247:                pV, &n, &sigmar, ar->workev,
248:                bmat, &n, which, &eps->nev, &eps->tol,
249:                resid, &eps->ncv, pV, &n, iparam, ipntr, ar->workd,
250:                ar->workl, &ar->lworkl, ar->rwork, &info, 1, 1, 2 );
251: #endif
252:     if (info!=0) { SETERRQ1(PETSC_ERR_LIB,"Error reported by ARPACK subroutine xxEUPD (%d)",info); }
253:   }

255:   VecRestoreArray( eps->V[0], &pV );
256:   VecRestoreArray( eps->work[1], &resid );
257:   if( eps->nconv >= eps->nev ) eps->reason = EPS_CONVERGED_TOL;
258:   else eps->reason = EPS_DIVERGED_ITS;

260:   if (eps->ishermitian) {
261:     PetscMemcpy(eps->errest,&ar->workl[ipntr[8]-1],eps->nconv);
262:   } else {
263:     PetscMemcpy(eps->errest,&ar->workl[ipntr[10]-1],eps->nconv);
264:   }

266:   VecDestroy(x);
267:   VecDestroy(y);

269:   return(0);
270: }

274: PetscErrorCode EPSBackTransform_ARPACK(EPS eps)
275: {
277:   PetscTruth     isSinv;

280:   PetscTypeCompare((PetscObject)eps->OP,STSINV,&isSinv);
281:   if (!isSinv) {
282:     EPSBackTransform_Default(eps);
283:   }
284:   return(0);
285: }

289: PetscErrorCode EPSDestroy_ARPACK(EPS eps)
290: {
292:   EPS_ARPACK     *ar = (EPS_ARPACK *)eps->data;

296:   PetscFree(ar->workev);
297:   PetscFree(ar->workl);
298:   PetscFree(ar->select);
299:   PetscFree(ar->workd);
300: #if defined(PETSC_USE_COMPLEX)
301:   PetscFree(ar->rwork);
302: #endif
303:   PetscFree(eps->data);
304:   EPSDefaultFreeWork(eps);
305:   EPSFreeSolutionContiguous(eps);
306:   return(0);
307: }

312: PetscErrorCode EPSCreate_ARPACK(EPS eps)
313: {
315:   EPS_ARPACK     *arpack;

318:   PetscNew(EPS_ARPACK,&arpack);
319:   PetscLogObjectMemory(eps,sizeof(EPS_ARPACK));
320:   eps->data                      = (void *) arpack;
321:   eps->ops->solve                = EPSSolve_ARPACK;
322:   eps->ops->setup                = EPSSetUp_ARPACK;
323:   eps->ops->destroy              = EPSDestroy_ARPACK;
324:   eps->ops->backtransform        = EPSBackTransform_ARPACK;
325:   eps->ops->computevectors       = EPSComputeVectors_Default;
326:   return(0);
327: }