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:  #include src/eps/epsimpl.h
 24:  #include slepcblaslapack.h

 28: PetscErrorCode EPSSetUp_KRYLOVSCHUR(EPS eps)
 29: {
 31:   PetscInt       N;

 34:   VecGetSize(eps->vec_initial,&N);
 35:   if (eps->ncv) {
 36:     if (eps->ncv<eps->nev+1) SETERRQ(1,"The value of ncv must be at least nev+1");
 37:   }
 38:   else eps->ncv = PetscMin(N,PetscMax(2*eps->nev,eps->nev+15));
 39:   if (!eps->max_it) eps->max_it = PetscMax(100,2*N/eps->ncv);
 40:   if (eps->ishermitian && (eps->which==EPS_LARGEST_IMAGINARY || eps->which==EPS_SMALLEST_IMAGINARY))
 41:     SETERRQ(1,"Wrong value of eps->which");

 43:   EPSAllocateSolution(eps);
 44:   PetscFree(eps->T);
 45:   PetscMalloc(eps->ncv*eps->ncv*sizeof(PetscScalar),&eps->T);
 46:   EPSDefaultGetWork(eps,1);
 47:   return(0);
 48: }

 52: PetscErrorCode EPSSolve_KRYLOVSCHUR(EPS eps)
 53: {
 55:   int            i,j,k,l,n,lwork,*perm;
 56:   Vec            u=eps->work[0];
 57:   PetscScalar    *S=eps->T,*Q,*work,*b;
 58:   PetscReal      beta,*ritz;
 59:   PetscTruth     breakdown;

 62:   PetscMemzero(S,eps->ncv*eps->ncv*sizeof(PetscScalar));
 63:   PetscMalloc(eps->ncv*eps->ncv*sizeof(PetscScalar),&Q);
 64:   PetscMalloc(eps->ncv*sizeof(PetscScalar),&b);
 65:   lwork = (eps->ncv+4)*eps->ncv;
 66:   if (!eps->ishermitian) {
 67:     PetscMalloc(lwork*sizeof(PetscScalar),&work);
 68:   } else {
 69:     PetscMalloc(eps->ncv*sizeof(PetscReal),&ritz);
 70:     PetscMalloc(eps->ncv*sizeof(int),&perm);
 71:   }

 73:   /* Get the starting Arnoldi vector */
 74:   EPSGetStartVector(eps,0,eps->V[0],PETSC_NULL);
 75:   l = 0;
 76: 
 77:   /* Restart loop */
 78:   while (eps->reason == EPS_CONVERGED_ITERATING) {
 79:     eps->its++;

 81:     /* Compute an nv-step Arnoldi factorization */
 82:     eps->nv = eps->ncv;
 83:     EPSBasicArnoldi(eps,PETSC_FALSE,S,eps->V,eps->nconv+l,&eps->nv,u,&beta,&breakdown);
 84:     VecScale(u,1.0/beta);

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

140:     /* Check convergence */
141:     k = eps->nconv;
142:     while (k<eps->nv && eps->errest[k]<eps->tol) k++;
143:     if (eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
144:     if (k >= eps->nev) eps->reason = EPS_CONVERGED_TOL;
145: 
146:     /* Update l */
147:     if (eps->reason != EPS_CONVERGED_ITERATING || breakdown) l = 0;
148:     else {
149:       l = (eps->nv-k)/2;
150: #if !defined(PETSC_USE_COMPLEX)
151:       if (S[(k+l-1)*(eps->ncv+1)+1] != 0.0) {
152:         if (k+l<eps->nv-1) l = l+1;
153:         else l = l-1;
154:       }
155: #endif
156:     }
157: 
158:     /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
159:     for (i=eps->nconv;i<k+l;i++) {
160:       VecSet(eps->AV[i],0.0);
161:       if (!eps->ishermitian) {
162:         VecMAXPY(eps->AV[i],n,Q+i*n,eps->V);
163:       } else {
164:         VecMAXPY(eps->AV[i],n,Q+i*n,eps->V+eps->nconv);
165:       }
166:     }
167:     for (i=eps->nconv;i<k+l;i++) {
168:       VecCopy(eps->AV[i],eps->V[i]);
169:     }
170:     eps->nconv = k;

172:     EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,eps->nv);
173: 
174:     if (eps->reason == EPS_CONVERGED_ITERATING) {
175:       if (breakdown) {
176:         /* start a new Arnoldi factorization */
177:         PetscInfo2(eps,"Breakdown in Krylov-Schur method (it=%i norm=%g)\n",eps->its,beta);
178:         EPSGetStartVector(eps,k,eps->V[k],&breakdown);
179:         if (breakdown) {
180:           eps->reason = EPS_DIVERGED_BREAKDOWN;
181:           PetscInfo(eps,"Unable to generate more start vectors\n");
182:         }
183:       } else {
184:         /* update the Arnoldi-Schur decomposition */
185:         for (i=k;i<k+l;i++) {
186:           S[i*eps->ncv+k+l] = Q[(i+1)*n-1]*beta;
187:         }
188:         VecCopy(u,eps->V[k+l]);
189:       }
190:     }
191:   }

193:   PetscFree(Q);
194:   PetscFree(b);
195:   if (!eps->ishermitian) {
196:     PetscFree(work);
197:   } else {
198:     PetscFree(ritz);
199:     PetscFree(perm);
200:   }
201:   return(0);
202: }

207: PetscErrorCode EPSCreate_KRYLOVSCHUR(EPS eps)
208: {
210:   eps->data                      = PETSC_NULL;
211:   eps->ops->solve                = EPSSolve_KRYLOVSCHUR;
212:   eps->ops->solvets              = PETSC_NULL;
213:   eps->ops->setup                = EPSSetUp_KRYLOVSCHUR;
214:   eps->ops->setfromoptions       = PETSC_NULL;
215:   eps->ops->destroy              = EPSDestroy_Default;
216:   eps->ops->view                 = PETSC_NULL;
217:   eps->ops->backtransform        = EPSBackTransform_Default;
218:   eps->ops->computevectors       = EPSComputeVectors_Schur;
219:   return(0);
220: }