Actual source code: krylovschur.c

  1: /*                       

  3:    SLEPc eigensolver: "krylovschur"

  5:    Method: Krylov-Schur

  7:    Algorithm:

  9:        Single-vector Krylov-Schur method for both symmetric and non-symmetric
 10:        problems.

 12:    References:

 14:        [1] "Krylov-Schur Methods in SLEPc", SLEPc Technical Report STR-7, 
 15:            available at http://www.grycap.upv.es/slepc.

 17:        [2] G.W. Stewart, "A Krylov-Schur Algorithm for Large Eigenproblems",
 18:            SIAM J. Matrix Analysis and App., 23(3), pp. 601-614, 2001. 

 20:    Last update: Oct 2006

 22:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 23:       SLEPc - Scalable Library for Eigenvalue Problem Computations
 24:       Copyright (c) 2002-2007, Universidad Politecnica de Valencia, Spain

 26:       This file is part of SLEPc. See the README file for conditions of use
 27:       and additional information.
 28:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 29: */

 31:  #include src/eps/epsimpl.h
 32:  #include slepcblaslapack.h

 36: PetscErrorCode EPSSetUp_KRYLOVSCHUR(EPS eps)
 37: {
 39:   PetscInt       N;

 42:   VecGetSize(eps->vec_initial,&N);
 43:   if (eps->ncv) {
 44:     if (eps->ncv<eps->nev+1) SETERRQ(1,"The value of ncv must be at least nev+1");
 45:   }
 46:   else eps->ncv = PetscMin(N,PetscMax(2*eps->nev,eps->nev+15));
 47:   if (!eps->max_it) eps->max_it = PetscMax(100,2*N/eps->ncv);
 48:   if (eps->ishermitian && (eps->which==EPS_LARGEST_IMAGINARY || eps->which==EPS_SMALLEST_IMAGINARY))
 49:     SETERRQ(1,"Wrong value of eps->which");

 51:   EPSAllocateSolution(eps);
 52:   PetscFree(eps->T);
 53:   PetscMalloc(eps->ncv*eps->ncv*sizeof(PetscScalar),&eps->T);
 54:   EPSDefaultGetWork(eps,2);
 55:   return(0);
 56: }

 60: PetscErrorCode EPSSolve_KRYLOVSCHUR(EPS eps)
 61: {
 63:   int            i,j,k,l,n,lwork,*perm;
 64:   Vec            u=eps->work[1];
 65:   PetscScalar    *S=eps->T,*Q,*work,*b;
 66:   PetscReal      beta,*ritz;
 67:   PetscTruth     breakdown;

 70:   PetscMemzero(S,eps->ncv*eps->ncv*sizeof(PetscScalar));
 71:   PetscMalloc(eps->ncv*eps->ncv*sizeof(PetscScalar),&Q);
 72:   PetscMalloc(eps->ncv*sizeof(PetscScalar),&b);
 73:   lwork = (eps->ncv+4)*eps->ncv;
 74:   if (!eps->ishermitian) {
 75:     PetscMalloc(lwork*sizeof(PetscScalar),&work);
 76:   } else {
 77:     PetscMalloc(eps->ncv*sizeof(PetscReal),&ritz);
 78:     PetscMalloc(eps->ncv*sizeof(int),&perm);
 79:   }

 81:   /* Get the starting Arnoldi vector */
 82:   EPSGetStartVector(eps,0,eps->V[0],PETSC_NULL);
 83:   l = 0;
 84: 
 85:   /* Restart loop */
 86:   while (eps->reason == EPS_CONVERGED_ITERATING) {
 87:     eps->its++;

 89:     /* Compute an nv-step Arnoldi factorization */
 90:     eps->nv = eps->ncv;
 91:     EPSBasicArnoldi(eps,PETSC_FALSE,S,eps->V,eps->nconv+l,&eps->nv,u,&beta,&breakdown);
 92:     VecScale(u,1.0/beta);

 94:     if (!eps->ishermitian) {
 95:       n = eps->nv; /* size of Q */
 96:       if (l==0) {
 97:         PetscMemzero(Q,n*n*sizeof(PetscScalar));
 98:         for (i=0;i<n;i++)
 99:           Q[i*(n+1)] = 1.0;
100:       } else {
101:         /* Reduce S to Hessenberg form, S <- Q S Q' */
102:         EPSDenseHessenberg(n,eps->nconv,S,eps->ncv,Q);
103:       }
104:       /* Reduce S to (quasi-)triangular form, S <- Q S Q' */
105:       EPSDenseSchur(n,eps->nconv,S,eps->ncv,Q,eps->eigr,eps->eigi);
106:       /* Sort the remaining columns of the Schur form */
107:       EPSSortDenseSchur(n,eps->nconv,S,eps->ncv,Q,eps->eigr,eps->eigi,eps->which);
108:       /* Compute residual norm estimates */
109:       ArnoldiResiduals(S,eps->ncv,Q,beta,eps->nconv,n,eps->eigr,eps->eigi,eps->errest,work);
110:    } else {
111:       n = eps->nv-eps->nconv; /* size of Q */
112:       /* Reduce S to diagonal form, S <- Q S Q' */
113:       if (l==0) {
114:         EPSDenseTridiagonal(n,S+eps->nconv*(eps->ncv+1),eps->ncv,ritz,Q+eps->nconv*n);
115:       } else {
116:         EPSDenseHEP(n,S+eps->nconv*(eps->ncv+1),eps->ncv,ritz,Q+eps->nconv*n);
117:       }
118:       /* Sort the remaining columns of the Schur form */
119:       if (eps->which == EPS_SMALLEST_REAL) {
120:         for (i=0;i<n;i++)
121:           eps->eigr[i+eps->nconv] = ritz[i];
122:       } else {
123: #ifdef PETSC_USE_COMPLEX
124:         for (i=0;i<n;i++)
125:           eps->eigr[i+eps->nconv] = ritz[i];
126:         EPSSortEigenvalues(n,eps->eigr+eps->nconv,eps->eigi,eps->which,n,perm);
127: #else
128:         EPSSortEigenvalues(n,ritz,eps->eigi+eps->nconv,eps->which,n,perm);
129: #endif
130:         for (i=0;i<n;i++)
131:           eps->eigr[i+eps->nconv] = ritz[perm[i]];
132:         PetscMemcpy(S,Q+eps->nconv*n,n*n*sizeof(PetscScalar));
133:         for (j=0;j<n;j++)
134:           for (i=0;i<n;i++)
135:             Q[(j+eps->nconv)*n+i] = S[perm[j]*n+i];
136:       }
137:       /* rebuild S from eigr */
138:       for (i=eps->nconv;i<eps->nv;i++) {
139:         S[i*(eps->ncv+1)] = eps->eigr[i];
140:         for (j=i+1;j<eps->ncv;j++)
141:           S[i*eps->ncv+j] = 0.0;
142:       }
143:       /* Compute residual norm estimates */
144:       for (i=eps->nconv;i<eps->nv;i++)
145:         eps->errest[i] = beta*PetscAbsScalar(Q[(i+1)*n-1]) / PetscAbsScalar(eps->eigr[i]);
146:     }

148:     /* Check convergence */
149:     k = eps->nconv;
150:     while (k<eps->nv && eps->errest[k]<eps->tol) k++;
151:     if (eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
152:     if (k >= eps->nev) eps->reason = EPS_CONVERGED_TOL;
153: 
154:     /* Update l */
155:     if (eps->reason != EPS_CONVERGED_ITERATING || breakdown) l = 0;
156:     else {
157:       l = (eps->nv-k)/2;
158: #if !defined(PETSC_USE_COMPLEX)
159:       if (S[(k+l-1)*(eps->ncv+1)+1] != 0.0) {
160:         if (k+l<eps->nv-1) l = l+1;
161:         else l = l-1;
162:       }
163: #endif
164:     }
165: 
166:     /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
167:     for (i=eps->nconv;i<k+l;i++) {
168:       VecSet(eps->AV[i],0.0);
169:       if (!eps->ishermitian) {
170:         VecMAXPY(eps->AV[i],n,Q+i*n,eps->V);
171:       } else {
172:         VecMAXPY(eps->AV[i],n,Q+i*n,eps->V+eps->nconv);
173:       }
174:     }
175:     for (i=eps->nconv;i<k+l;i++) {
176:       VecCopy(eps->AV[i],eps->V[i]);
177:     }
178:     eps->nconv = k;

180:     EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,eps->nv);
181: 
182:     if (eps->reason == EPS_CONVERGED_ITERATING) {
183:       if (breakdown) {
184:         /* start a new Arnoldi factorization */
185:         PetscInfo2(eps,"Breakdown in Krylov-Schur method (it=%i norm=%g)\n",eps->its,beta);
186:         EPSGetStartVector(eps,k,eps->V[k],&breakdown);
187:         if (breakdown) {
188:           eps->reason = EPS_DIVERGED_BREAKDOWN;
189:           PetscInfo(eps,"Unable to generate more start vectors\n");
190:         }
191:       } else {
192:         /* update the Arnoldi-Schur decomposition */
193:         for (i=k;i<k+l;i++) {
194:           S[i*eps->ncv+k+l] = Q[(i+1)*n-1]*beta;
195:         }
196:         VecCopy(u,eps->V[k+l]);
197:       }
198:     }
199:   }

201:   PetscFree(Q);
202:   PetscFree(b);
203:   if (!eps->ishermitian) {
204:     PetscFree(work);
205:   } else {
206:     PetscFree(ritz);
207:     PetscFree(perm);
208:   }
209:   return(0);
210: }

215: PetscErrorCode EPSCreate_KRYLOVSCHUR(EPS eps)
216: {
218:   eps->data                      = PETSC_NULL;
219:   eps->ops->solve                = EPSSolve_KRYLOVSCHUR;
220:   eps->ops->solvets              = PETSC_NULL;
221:   eps->ops->setup                = EPSSetUp_KRYLOVSCHUR;
222:   eps->ops->setfromoptions       = PETSC_NULL;
223:   eps->ops->destroy              = EPSDestroy_Default;
224:   eps->ops->view                 = PETSC_NULL;
225:   eps->ops->backtransform        = EPSBackTransform_Default;
226:   eps->ops->computevectors       = EPSComputeVectors_Schur;
227:   return(0);
228: }