Actual source code: ks-symm.c

  1: /*                       

  3:    SLEPc eigensolver: "krylovschur"

  5:    Method: Krylov-Schur for symmetric eigenproblems

  7:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  8:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  9:    Copyright (c) 2002-2011, Universitat Politecnica de Valencia, Spain

 11:    This file is part of SLEPc.
 12:       
 13:    SLEPc is free software: you can redistribute it and/or modify it under  the
 14:    terms of version 3 of the GNU Lesser General Public License as published by
 15:    the Free Software Foundation.

 17:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY 
 18:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS 
 19:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for 
 20:    more details.

 22:    You  should have received a copy of the GNU Lesser General  Public  License
 23:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 24:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 25: */

 27: #include <private/epsimpl.h>                /*I "slepceps.h" I*/
 28: #include <slepcblaslapack.h>

 32: /*
 33:    ArrowTridFlip - Solves the arrowhead-tridiagonal eigenproblem by flipping
 34:    the matrix and tridiagonalizing the bottom part.

 36:    On input:
 37:      l is the size of diagonal part
 38:      d contains diagonal elements (length n)
 39:      e contains offdiagonal elements (length n-1)

 41:    On output:
 42:      d contains the eigenvalues in ascending order
 43:      Q is the eigenvector matrix (order n)

 45:    Workspace:
 46:      S is workspace to store a copy of the full matrix (nxn reals)
 47: */
 48: PetscErrorCode ArrowTridFlip(PetscInt n_,PetscInt l,PetscReal *d,PetscReal *e,PetscReal *Q,PetscReal *S)
 49: {
 50: #if defined(SLEPC_MISSING_LAPACK_SYTRD) || defined(SLEPC_MISSING_LAPACK_ORGTR) || defined(SLEPC_MISSING_LAPACK_STEQR)
 52:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"SYTRD/ORGTR/STEQR - Lapack routine is unavailable.");
 53: #else
 55:   PetscInt       i,j;
 56:   PetscBLASInt   n,n1,n2,lwork,info;

 59:   PetscLogEventBegin(EPS_Dense,0,0,0,0);
 60:   n = PetscBLASIntCast(n_);
 61:   /* quick return */
 62:   if (n == 1) {
 63:     Q[0] = 1.0;
 64:     return(0);
 65:   }
 66:   n1 = PetscBLASIntCast(l+1);    /* size of leading block, including residuals */
 67:   n2 = PetscBLASIntCast(n-l-1);  /* size of trailing block */
 68:   PetscMemzero(S,n*n*sizeof(PetscReal));

 70:   /* Flip matrix S, copying the values saved in Q */
 71:   for (i=0;i<n;i++)
 72:     S[(n-1-i)+(n-1-i)*n] = d[i];
 73:   for (i=0;i<l;i++)
 74:     S[(n-1-i)+(n-1-l)*n] = e[i];
 75:   for (i=l;i<n-1;i++)
 76:     S[(n-1-i)+(n-1-i-1)*n] = e[i];

 78:   /* Reduce (2,2)-block of flipped S to tridiagonal form */
 79:   lwork = PetscBLASIntCast(n_*n_-n_);
 80:   LAPACKsytrd_("L",&n1,S+n2*(n+1),&n,d,e,Q,Q+n,&lwork,&info);
 81:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xSYTRD %d",info);

 83:   /* Flip back diag and subdiag, put them in d and e */
 84:   for (i=0;i<n-1;i++) {
 85:     d[n-i-1] = S[i+i*n];
 86:     e[n-i-2] = S[i+1+i*n];
 87:   }
 88:   d[0] = S[n-1+(n-1)*n];

 90:   /* Compute the orthogonal matrix used for tridiagonalization */
 91:   LAPACKorgtr_("L",&n1,S+n2*(n+1),&n,Q,Q+n,&lwork,&info);
 92:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xORGTR %d",info);

 94:   /* Create full-size Q, flipped back to original order */
 95:   for (i=0;i<n;i++)
 96:     for (j=0;j<n;j++)
 97:       Q[i+j*n] = 0.0;
 98:   for (i=n1;i<n;i++)
 99:     Q[i+i*n] = 1.0;
100:   for (i=0;i<n1;i++)
101:     for (j=0;j<n1;j++)
102:       Q[i+j*n] = S[n-i-1+(n-j-1)*n];

104:   /* Solve the tridiagonal eigenproblem */
105:   LAPACKsteqr_("V",&n,d,e,Q,&n,S,&info);
106:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xSTEQR %d",info);

108:   PetscLogEventEnd(EPS_Dense,0,0,0,0);
109:   return(0);
110: #endif
111: }

115: /*
116:    EPSProjectedKSSym - Solves the projected eigenproblem in the Krylov-Schur
117:    method (symmetric case).

119:    On input:
120:      n is the matrix dimension
121:      l is the number of vectors kept in previous restart
122:      a contains diagonal elements (length n)
123:      b contains offdiagonal elements (length n-1)

125:    On output:
126:      eig is the sorted list of eigenvalues
127:      Q is the eigenvector matrix (order n, leading dimension n)

129:    Workspace:
130:      work is workspace to store a real square matrix of order n
131:      perm is workspace to store 2n integers
132: */
133: PetscErrorCode EPSProjectedKSSym(EPS eps,PetscInt n,PetscInt l,PetscReal *a,PetscReal *b,PetscScalar *eig,PetscScalar *Q,PetscReal *work,PetscInt *perm)
134: {
136:   PetscInt       i,j,k,p;
137:   PetscReal      rtmp,*Qreal = (PetscReal*)Q;

140:   /* Compute eigendecomposition of projected matrix */
141:   ArrowTridFlip(n,l,a,b,Qreal,work);

143:   /* Sort eigendecomposition according to eps->which */
144:   EPSSortEigenvaluesReal(eps,n,a,perm);
145:   for (i=0;i<n;i++)
146:     eig[i] = a[perm[i]];
147:   for (i=0;i<n;i++) {
148:     p = perm[i];
149:     if (p != i) {
150:       j = i + 1;
151:       while (perm[j] != i) j++;
152:       perm[j] = p; perm[i] = i;
153:       /* swap eigenvectors i and j */
154:       for (k=0;k<n;k++) {
155:         rtmp = Qreal[k+p*n]; Qreal[k+p*n] = Qreal[k+i*n]; Qreal[k+i*n] = rtmp;
156:       }
157:     }
158:   }

160: #if defined(PETSC_USE_COMPLEX)
161:   for (j=n-1;j>=0;j--)
162:     for (i=n-1;i>=0;i--)
163:       Q[i+j*n] = Qreal[i+j*n];
164: #endif
165:   return(0);
166: }

170: PetscErrorCode EPSSolve_KrylovSchur_Symm(EPS eps)
171: {
173:   PetscInt       i,k,l,lds,lt,nv,m,*iwork;
174:   Vec            u=eps->work[0];
175:   PetscScalar    *Q;
176:   PetscReal      *a,*b,*work,beta;
177:   PetscBool      breakdown;

180:   lds = PetscMin(eps->mpd,eps->ncv);
181:   PetscMalloc(lds*lds*sizeof(PetscReal),&work);
182:   PetscMalloc(lds*lds*sizeof(PetscScalar),&Q);
183:   PetscMalloc(2*lds*sizeof(PetscInt),&iwork);
184:   lt = PetscMin(eps->nev+eps->mpd,eps->ncv);
185:   PetscMalloc(lt*sizeof(PetscReal),&a);
186:   PetscMalloc(lt*sizeof(PetscReal),&b);

188:   /* Get the starting Lanczos vector */
189:   EPSGetStartVector(eps,0,eps->V[0],PETSC_NULL);
190:   l = 0;
191: 
192:   /* Restart loop */
193:   while (eps->reason == EPS_CONVERGED_ITERATING) {
194:     eps->its++;

196:     /* Compute an nv-step Lanczos factorization */
197:     m = PetscMin(eps->nconv+eps->mpd,eps->ncv);
198:     EPSFullLanczos(eps,a+l,b+l,eps->V,eps->nconv+l,&m,u,&breakdown);
199:     nv = m - eps->nconv;
200:     beta = b[nv-1];

202:     /* Solve projected problem and compute residual norm estimates */
203:     EPSProjectedKSSym(eps,nv,l,a,b,eps->eigr+eps->nconv,Q,work,iwork);

205:     /* Check convergence */
206:     EPSKrylovConvergence(eps,PETSC_TRUE,eps->trackall,eps->nconv,nv,PETSC_NULL,nv,Q,eps->V+eps->nconv,nv,beta,1.0,&k,PETSC_NULL);
207:     if (eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
208:     if (k >= eps->nev) eps->reason = EPS_CONVERGED_TOL;
209: 
210:     /* Update l */
211:     if (eps->reason != EPS_CONVERGED_ITERATING || breakdown) l = 0;
212:     else l = (eps->nconv+nv-k)/2;

214:     if (eps->reason == EPS_CONVERGED_ITERATING) {
215:       if (breakdown) {
216:         /* Start a new Lanczos factorization */
217:         PetscInfo2(eps,"Breakdown in Krylov-Schur method (it=%D norm=%G)\n",eps->its,beta);
218:         EPSGetStartVector(eps,k,eps->V[k],&breakdown);
219:         if (breakdown) {
220:           eps->reason = EPS_DIVERGED_BREAKDOWN;
221:           PetscInfo(eps,"Unable to generate more start vectors\n");
222:         }
223:       } else {
224:         /* Prepare the Rayleigh quotient for restart */
225:         for (i=0;i<l;i++) {
226:           a[i] = PetscRealPart(eps->eigr[i+k]);
227:           b[i] = PetscRealPart(Q[nv-1+(i+k-eps->nconv)*nv]*beta);
228:         }
229:       }
230:     }
231:     /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
232:     SlepcUpdateVectors(nv,eps->V+eps->nconv,0,k+l-eps->nconv,Q,nv,PETSC_FALSE);
233:     /* Normalize u and append it to V */
234:     if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
235:       VecAXPBY(eps->V[k+l],1.0/beta,0.0,u);
236:     }

238:     EPSMonitor(eps,eps->its,k,eps->eigr,eps->eigi,eps->errest,nv+eps->nconv);
239:     eps->nconv = k;
240:   }
241:   PetscFree(Q);
242:   PetscFree(a);
243:   PetscFree(b);
244:   PetscFree(work);
245:   PetscFree(iwork);
246:   return(0);
247: }