Actual source code: gmreig.c

      2: #include <../src/ksp/ksp/impls/gmres/gmresimpl.h>
      3: #include <petscblaslapack.h>

      5: PetscErrorCode KSPComputeExtremeSingularValues_GMRES(KSP ksp,PetscReal *emax,PetscReal *emin)
      6: {
      7:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
      8:   PetscInt       n = gmres->it + 1,i,N = gmres->max_k + 2;
      9:   PetscBLASInt   bn, bN,lwork, idummy,lierr;
     10:   PetscScalar    *R        = gmres->Rsvd,*work = R + N*N,sdummy = 0;
     11:   PetscReal      *realpart = gmres->Dsvd;

     13:   PetscBLASIntCast(n,&bn);
     14:   PetscBLASIntCast(N,&bN);
     15:   PetscBLASIntCast(5*N,&lwork);
     16:   PetscBLASIntCast(N,&idummy);
     17:   if (n <= 0) {
     18:     *emax = *emin = 1.0;
     19:     return 0;
     20:   }
     21:   /* copy R matrix to work space */
     22:   PetscArraycpy(R,gmres->hh_origin,(gmres->max_k+2)*(gmres->max_k+1));

     24:   /* zero below diagonal garbage */
     25:   for (i=0; i<n; i++) R[i*N+i+1] = 0.0;

     27:   /* compute Singular Values */
     28:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
     29: #if !defined(PETSC_USE_COMPLEX)
     30:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","N",&bn,&bn,R,&bN,realpart,&sdummy,&idummy,&sdummy,&idummy,work,&lwork,&lierr));
     31: #else
     32:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","N",&bn,&bn,R,&bN,realpart,&sdummy,&idummy,&sdummy,&idummy,work,&lwork,realpart+N,&lierr));
     33: #endif
     35:   PetscFPTrapPop();

     37:   *emin = realpart[n-1];
     38:   *emax = realpart[0];
     39:   return 0;
     40: }

     42: PetscErrorCode KSPComputeEigenvalues_GMRES(KSP ksp,PetscInt nmax,PetscReal *r,PetscReal *c,PetscInt *neig)
     43: {
     44: #if !defined(PETSC_USE_COMPLEX)
     45:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
     46:   PetscInt       n = gmres->it + 1,N = gmres->max_k + 1,i,*perm;
     47:   PetscBLASInt   bn, bN, lwork, idummy, l-1;
     48:   PetscScalar    *R        = gmres->Rsvd,*work = R + N*N;
     49:   PetscScalar    *realpart = gmres->Dsvd,*imagpart = realpart + N,sdummy = 0;

     51:   PetscBLASIntCast(n,&bn);
     52:   PetscBLASIntCast(N,&bN);
     53:   PetscBLASIntCast(5*N,&lwork);
     54:   PetscBLASIntCast(N,&idummy);
     56:   *neig = n;

     58:   if (!n) return 0;

     60:   /* copy R matrix to work space */
     61:   PetscArraycpy(R,gmres->hes_origin,N*N);

     63:   /* compute eigenvalues */
     64:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
     65:   PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_("N","N",&bn,R,&bN,realpart,imagpart,&sdummy,&idummy,&sdummy,&idummy,work,&lwork,&lierr));
     67:   PetscFPTrapPop();
     68:   PetscMalloc1(n,&perm);
     69:   for (i=0; i<n; i++) perm[i] = i;
     70:   PetscSortRealWithPermutation(n,realpart,perm);
     71:   for (i=0; i<n; i++) {
     72:     r[i] = realpart[perm[i]];
     73:     c[i] = imagpart[perm[i]];
     74:   }
     75:   PetscFree(perm);
     76: #else
     77:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
     78:   PetscInt       n  = gmres->it + 1,N = gmres->max_k + 1,i,*perm;
     79:   PetscScalar    *R = gmres->Rsvd,*work = R + N*N,*eigs = work + 5*N,sdummy;
     80:   PetscBLASInt   bn,bN,lwork,idummy,l-1;

     82:   PetscBLASIntCast(n,&bn);
     83:   PetscBLASIntCast(N,&bN);
     84:   PetscBLASIntCast(5*N,&lwork);
     85:   PetscBLASIntCast(N,&idummy);
     87:   *neig = n;

     89:   if (!n) return 0;

     91:   /* copy R matrix to work space */
     92:   PetscArraycpy(R,gmres->hes_origin,N*N);

     94:   /* compute eigenvalues */
     95:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
     96:   PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_("N","N",&bn,R,&bN,eigs,&sdummy,&idummy,&sdummy,&idummy,work,&lwork,gmres->Dsvd,&lierr));
     98:   PetscFPTrapPop();
     99:   PetscMalloc1(n,&perm);
    100:   for (i=0; i<n; i++) perm[i] = i;
    101:   for (i=0; i<n; i++) r[i] = PetscRealPart(eigs[i]);
    102:   PetscSortRealWithPermutation(n,r,perm);
    103:   for (i=0; i<n; i++) {
    104:     r[i] = PetscRealPart(eigs[perm[i]]);
    105:     c[i] = PetscImaginaryPart(eigs[perm[i]]);
    106:   }
    107:   PetscFree(perm);
    108: #endif
    109:   return 0;
    110: }

    112: #if !defined(PETSC_USE_COMPLEX)
    113: PetscErrorCode KSPComputeRitz_GMRES(KSP ksp,PetscBool ritz,PetscBool small,PetscInt *nrit,Vec S[],PetscReal *tetar,PetscReal *tetai)
    114: {
    115:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    116:   PetscInt       n = gmres->it + 1,N = gmres->max_k + 1,NbrRitz,nb=0;
    117:   PetscInt       i,j,*perm;
    118:   PetscReal      *H,*Q,*Ht;              /* H Hessenberg Matrix and Q matrix of eigenvectors of H*/
    119:   PetscReal      *wr,*wi,*modul;       /* Real and imaginary part and modul of the Ritz values*/
    120:   PetscReal      *SR,*work;
    121:   PetscBLASInt   bn,bN,lwork,idummy;
    122:   PetscScalar    *t,sdummy = 0;

    124:   /* n: size of the Hessenberg matrix */
    125:   if (gmres->fullcycle) n = N-1;
    126:   /* NbrRitz: number of (harmonic) Ritz pairs to extract */
    127:   NbrRitz = PetscMin(*nrit,n);

    129:   /* Definition of PetscBLASInt for lapack routines*/
    130:   PetscBLASIntCast(n,&bn);
    131:   PetscBLASIntCast(N,&bN);
    132:   PetscBLASIntCast(N,&idummy);
    133:   PetscBLASIntCast(5*N,&lwork);
    134:   /* Memory allocation */
    135:   PetscMalloc1(bN*bN,&H);
    136:   PetscMalloc1(bn*bn,&Q);
    137:   PetscMalloc1(lwork,&work);
    138:   PetscMalloc1(n,&wr);
    139:   PetscMalloc1(n,&wi);

    141:   /* copy H matrix to work space */
    142:   if (gmres->fullcycle) {
    143:     PetscArraycpy(H,gmres->hes_ritz,bN*bN);
    144:   } else {
    145:     PetscArraycpy(H,gmres->hes_origin,bN*bN);
    146:   }

    148:   /* Modify H to compute Harmonic Ritz pairs H = H + H^{-T}*h^2_{m+1,m}e_m*e_m^T */
    149:   if (!ritz) {
    150:     /* Transpose the Hessenberg matrix => Ht */
    151:     PetscMalloc1(bn*bn,&Ht);
    152:     for (i=0; i<bn; i++) {
    153:       for (j=0; j<bn; j++) {
    154:         Ht[i*bn+j] = H[j*bN+i];
    155:       }
    156:     }
    157:     /* Solve the system H^T*t = h^2_{m+1,m}e_m */
    158:     PetscCalloc1(bn,&t);
    159:     /* t = h^2_{m+1,m}e_m */
    160:     if (gmres->fullcycle) {
    161:       t[bn-1] = PetscSqr(gmres->hes_ritz[(bn-1)*bN+bn]);
    162:     } else {
    163:       t[bn-1] = PetscSqr(gmres->hes_origin[(bn-1)*bN+bn]);
    164:     }
    165:     /* Call the LAPACK routine dgesv to compute t = H^{-T}*t */
    166:     {
    167:       PetscBLASInt info;
    168:       PetscBLASInt nrhs = 1;
    169:       PetscBLASInt *ipiv;
    170:       PetscMalloc1(bn,&ipiv);
    171:       PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&bn,&nrhs,Ht,&bn,ipiv,t,&bn,&info));
    173:       PetscFree(ipiv);
    174:       PetscFree(Ht);
    175:     }
    176:     /* Now form H + H^{-T}*h^2_{m+1,m}e_m*e_m^T */
    177:     for (i=0; i<bn; i++) H[(bn-1)*bn+i] += t[i];
    178:     PetscFree(t);
    179:   }

    181:   /* Compute (harmonic) Ritz pairs */
    182:   {
    183:     PetscBLASInt info;
    184:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    185:     PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_("N","V",&bn,H,&bN,wr,wi,&sdummy,&idummy,Q,&bn,work,&lwork,&info));
    187:   }
    188:   /* sort the (harmonic) Ritz values */
    189:   PetscMalloc1(n,&modul);
    190:   PetscMalloc1(n,&perm);
    191:   for (i=0; i<n; i++) modul[i] = PetscSqrtReal(wr[i]*wr[i]+wi[i]*wi[i]);
    192:   for (i=0; i<n; i++) perm[i] = i;
    193:   PetscSortRealWithPermutation(n,modul,perm);
    194:   /* count the number of extracted Ritz or Harmonic Ritz pairs (with complex conjugates) */
    195:   if (small) {
    196:     while (nb < NbrRitz) {
    197:       if (!wi[perm[nb]]) nb += 1;
    198:       else nb += 2;
    199:     }
    200:     PetscMalloc1(nb*n,&SR);
    201:     for (i=0; i<nb; i++) {
    202:       tetar[i] = wr[perm[i]];
    203:       tetai[i] = wi[perm[i]];
    204:       PetscArraycpy(&SR[i*n],&(Q[perm[i]*bn]),n);
    205:     }
    206:   } else {
    207:     while (nb < NbrRitz) {
    208:       if (wi[perm[n-nb-1]] == 0) nb += 1;
    209:       else nb += 2;
    210:     }
    211:     PetscMalloc1(nb*n,&SR);
    212:     for (i=0; i<nb; i++) {
    213:       tetar[i] = wr[perm[n-nb+i]];
    214:       tetai[i] = wi[perm[n-nb+i]];
    215:       PetscArraycpy(&SR[i*n], &(Q[perm[n-nb+i]*bn]), n);
    216:     }
    217:   }
    218:   PetscFree(modul);
    219:   PetscFree(perm);

    221:   /* Form the Ritz or Harmonic Ritz vectors S=VV*Sr,
    222:     where the columns of VV correspond to the basis of the Krylov subspace */
    223:   if (gmres->fullcycle) {
    224:     for (j=0; j<nb; j++) {
    225:       VecZeroEntries(S[j]);
    226:       VecMAXPY(S[j],n,&SR[j*n],gmres->vecb);
    227:     }
    228:   } else {
    229:     for (j=0; j<nb; j++) {
    230:       VecZeroEntries(S[j]);
    231:       VecMAXPY(S[j],n,&SR[j*n],&VEC_VV(0));
    232:     }
    233:   }
    234:   *nrit = nb;
    235:   PetscFree(H);
    236:   PetscFree(Q);
    237:   PetscFree(SR);
    238:   PetscFree(wr);
    239:   PetscFree(wi);
    240:   return 0;
    241: }
    242: #endif