Date: 2013-07-02T14:47:55+00:00

Actual source code: eige.c
petsc-3.4.2 2013-07-02

      2: #include <petsc-private/kspimpl.h>   /*I "petscksp.h" I*/
      3: #include <petscblaslapack.h>

      7: /*@
      8:     KSPComputeExplicitOperator - Computes the explicit preconditioned operator.

     10:     Collective on KSP

     12:     Input Parameter:
     13: .   ksp - the Krylov subspace context

     15:     Output Parameter:
     16: .   mat - the explict preconditioned operator

     18:     Notes:
     19:     This computation is done by applying the operators to columns of the
     20:     identity matrix.

     22:     Currently, this routine uses a dense matrix format when 1 processor
     23:     is used and a sparse format otherwise.  This routine is costly in general,
     24:     and is recommended for use only with relatively small systems.

     26:     Level: advanced

     28: .keywords: KSP, compute, explicit, operator

     30: .seealso: KSPComputeEigenvaluesExplicitly(), PCComputeExplicitOperator()
     31: @*/
     32: PetscErrorCode  KSPComputeExplicitOperator(KSP ksp,Mat *mat)
     33: {
     34:   Vec            in,out;
     36:   PetscMPIInt    size;
     37:   PetscInt       i,M,m,*rows,start,end;
     38:   Mat            A;
     39:   MPI_Comm       comm;
     40:   PetscScalar    *array,one = 1.0;

     45:   PetscObjectGetComm((PetscObject)ksp,&comm);
     46:   MPI_Comm_size(comm,&size);

     48:   VecDuplicate(ksp->vec_sol,&in);
     49:   VecDuplicate(ksp->vec_sol,&out);
     50:   VecGetSize(in,&M);
     51:   VecGetLocalSize(in,&m);
     52:   VecGetOwnershipRange(in,&start,&end);
     53:   PetscMalloc(m*sizeof(PetscInt),&rows);
     54:   for (i=0; i<m; i++) rows[i] = start + i;

     56:   MatCreate(comm,mat);
     57:   MatSetSizes(*mat,m,m,M,M);
     58:   if (size == 1) {
     59:     MatSetType(*mat,MATSEQDENSE);
     60:     MatSeqDenseSetPreallocation(*mat,NULL);
     61:   } else {
     62:     MatSetType(*mat,MATMPIAIJ);
     63:     MatMPIAIJSetPreallocation(*mat,0,NULL,0,NULL);
     64:   }
     65:   MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
     66:   if (!ksp->pc) {KSPGetPC(ksp,&ksp->pc);}
     67:   PCGetOperators(ksp->pc,&A,NULL,NULL);

     69:   for (i=0; i<M; i++) {

     71:     VecSet(in,0.0);
     72:     VecSetValues(in,1,&i,&one,INSERT_VALUES);
     73:     VecAssemblyBegin(in);
     74:     VecAssemblyEnd(in);

     76:     KSP_MatMult(ksp,A,in,out);
     77:     KSP_PCApply(ksp,out,in);

     79:     VecGetArray(in,&array);
     80:     MatSetValues(*mat,m,rows,1,&i,array,INSERT_VALUES);
     81:     VecRestoreArray(in,&array);

     83:   }
     84:   PetscFree(rows);
     85:   VecDestroy(&in);
     86:   VecDestroy(&out);
     87:   MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);
     88:   MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);
     89:   return(0);
     90: }

     94: /*@
     95:    KSPComputeEigenvaluesExplicitly - Computes all of the eigenvalues of the
     96:    preconditioned operator using LAPACK.

     98:    Collective on KSP

    100:    Input Parameter:
    101: +  ksp - iterative context obtained from KSPCreate()
    102: -  n - size of arrays r and c

    104:    Output Parameters:
    105: +  r - real part of computed eigenvalues
    106: -  c - complex part of computed eigenvalues

    108:    Notes:
    109:    This approach is very slow but will generally provide accurate eigenvalue
    110:    estimates.  This routine explicitly forms a dense matrix representing
    111:    the preconditioned operator, and thus will run only for relatively small
    112:    problems, say n < 500.

    114:    Many users may just want to use the monitoring routine
    115:    KSPMonitorSingularValue() (which can be set with option -ksp_monitor_singular_value)
    116:    to print the singular values at each iteration of the linear solve.

    118:    The preconditoner operator, rhs vector, solution vectors should be
    119:    set before this routine is called. i.e use KSPSetOperators(),KSPSolve() or
    120:    KSPSetOperators()

    122:    Level: advanced

    124: .keywords: KSP, compute, eigenvalues, explicitly

    126: .seealso: KSPComputeEigenvalues(), KSPMonitorSingularValue(), KSPComputeExtremeSingularValues(), KSPSetOperators(), KSPSolve()
    127: @*/
    128: PetscErrorCode  KSPComputeEigenvaluesExplicitly(KSP ksp,PetscInt nmax,PetscReal *r,PetscReal *c)
    129: {
    130:   Mat               BA;
    131:   PetscErrorCode    ierr;
    132:   PetscMPIInt       size,rank;
    133:   MPI_Comm          comm;
    134:   PetscScalar       *array;
    135:   Mat               A;
    136:   PetscInt          m,row,nz,i,n,dummy;
    137:   const PetscInt    *cols;
    138:   const PetscScalar *vals;

    141:   PetscObjectGetComm((PetscObject)ksp,&comm);
    142:   KSPComputeExplicitOperator(ksp,&BA);
    143:   MPI_Comm_size(comm,&size);
    144:   MPI_Comm_rank(comm,&rank);

    146:   MatGetSize(BA,&n,&n);
    147:   if (size > 1) { /* assemble matrix on first processor */
    148:     MatCreate(PetscObjectComm((PetscObject)ksp),&A);
    149:     if (!rank) {
    150:       MatSetSizes(A,n,n,n,n);
    151:     } else {
    152:       MatSetSizes(A,0,0,n,n);
    153:     }
    154:     MatSetType(A,MATMPIDENSE);
    155:     MatMPIDenseSetPreallocation(A,NULL);
    156:     PetscLogObjectParent(BA,A);

    158:     MatGetOwnershipRange(BA,&row,&dummy);
    159:     MatGetLocalSize(BA,&m,&dummy);
    160:     for (i=0; i<m; i++) {
    161:       MatGetRow(BA,row,&nz,&cols,&vals);
    162:       MatSetValues(A,1,&row,nz,cols,vals,INSERT_VALUES);
    163:       MatRestoreRow(BA,row,&nz,&cols,&vals);
    164:       row++;
    165:     }

    167:     MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    168:     MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    169:     MatDenseGetArray(A,&array);
    170:   } else {
    171:     MatDenseGetArray(BA,&array);
    172:   }

    174: #if defined(PETSC_HAVE_ESSL)
    175:   /* ESSL has a different calling sequence for dgeev() and zgeev() than standard LAPACK */
    176:   if (!rank) {
    177:     PetscScalar  sdummy,*cwork;
    178:     PetscReal    *work,*realpart;
    179:     PetscBLASInt clen,idummy,lwork,bn,zero = 0;
    180:     PetscInt     *perm;

    182: #if !defined(PETSC_USE_COMPLEX)
    183:     clen = n;
    184: #else
    185:     clen = 2*n;
    186: #endif
    187:     PetscMalloc(clen*sizeof(PetscScalar),&cwork);
    188:     idummy = -1;                /* unused */
    189:     PetscBLASIntCast(n,&bn);
    190:     lwork  = 5*n;
    191:     PetscMalloc(lwork*sizeof(PetscReal),&work);
    192:     PetscMalloc(n*sizeof(PetscReal),&realpart);
    193:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    194:     PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_(&zero,array,&bn,cwork,&sdummy,&idummy,&idummy,&bn,work,&lwork));
    195:     PetscFPTrapPop();
    196:     PetscFree(work);

    198:     /* For now we stick with the convention of storing the real and imaginary
    199:        components of evalues separately.  But is this what we really want? */
    200:     PetscMalloc(n*sizeof(PetscInt),&perm);

    202: #if !defined(PETSC_USE_COMPLEX)
    203:     for (i=0; i<n; i++) {
    204:       realpart[i] = cwork[2*i];
    205:       perm[i]     = i;
    206:     }
    207:     PetscSortRealWithPermutation(n,realpart,perm);
    208:     for (i=0; i<n; i++) {
    209:       r[i] = cwork[2*perm[i]];
    210:       c[i] = cwork[2*perm[i]+1];
    211:     }
    212: #else
    213:     for (i=0; i<n; i++) {
    214:       realpart[i] = PetscRealPart(cwork[i]);
    215:       perm[i]     = i;
    216:     }
    217:     PetscSortRealWithPermutation(n,realpart,perm);
    218:     for (i=0; i<n; i++) {
    219:       r[i] = PetscRealPart(cwork[perm[i]]);
    220:       c[i] = PetscImaginaryPart(cwork[perm[i]]);
    221:     }
    222: #endif
    223:     PetscFree(perm);
    224:     PetscFree(realpart);
    225:     PetscFree(cwork);
    226:   }
    227: #elif !defined(PETSC_USE_COMPLEX)
    228:   if (!rank) {
    229:     PetscScalar  *work;
    230:     PetscReal    *realpart,*imagpart;
    231:     PetscBLASInt idummy,lwork;
    232:     PetscInt     *perm;

    234:     idummy   = n;
    235:     lwork    = 5*n;
    236:     PetscMalloc(2*n*sizeof(PetscReal),&realpart);
    237:     imagpart = realpart + n;
    238:     PetscMalloc(5*n*sizeof(PetscReal),&work);
    239: #if defined(PETSC_MISSING_LAPACK_GEEV)
    240:     SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GEEV - Lapack routine is unavailable\nNot able to provide eigen values.");
    241: #else
    242:     {
    243:       PetscBLASInt lierr;
    244:       PetscScalar  sdummy;
    245:       PetscBLASInt bn;

    247:       PetscBLASIntCast(n,&bn);
    248:       PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    249:       PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_("N","N",&bn,array,&bn,realpart,imagpart,&sdummy,&idummy,&sdummy,&idummy,work,&lwork,&lierr));
    250:       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in LAPACK routine %d",(int)lierr);
    251:       PetscFPTrapPop();
    252:     }
    253: #endif
    254:     PetscFree(work);
    255:     PetscMalloc(n*sizeof(PetscInt),&perm);

    257:     for (i=0; i<n; i++)  perm[i] = i;
    258:     PetscSortRealWithPermutation(n,realpart,perm);
    259:     for (i=0; i<n; i++) {
    260:       r[i] = realpart[perm[i]];
    261:       c[i] = imagpart[perm[i]];
    262:     }
    263:     PetscFree(perm);
    264:     PetscFree(realpart);
    265:   }
    266: #else
    267:   if (!rank) {
    268:     PetscScalar  *work,*eigs;
    269:     PetscReal    *rwork;
    270:     PetscBLASInt idummy,lwork;
    271:     PetscInt     *perm;

    273:     idummy = n;
    274:     lwork  = 5*n;
    275:     PetscMalloc(5*n*sizeof(PetscScalar),&work);
    276:     PetscMalloc(2*n*sizeof(PetscReal),&rwork);
    277:     PetscMalloc(n*sizeof(PetscScalar),&eigs);
    278: #if defined(PETSC_MISSING_LAPACK_GEEV)
    279:     SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GEEV - Lapack routine is unavailable\nNot able to provide eigen values.");
    280: #else
    281:     {
    282:       PetscBLASInt lierr;
    283:       PetscScalar  sdummy;
    284:       PetscBLASInt nb;
    285:       PetscBLASIntCast(n,&nb);
    286:       PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    287:       PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_("N","N",&nb,array,&nb,eigs,&sdummy,&idummy,&sdummy,&idummy,work,&lwork,rwork,&lierr));
    288:       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in LAPACK routine %d",(int)lierr);
    289:       PetscFPTrapPop();
    290:     }
    291: #endif
    292:     PetscFree(work);
    293:     PetscFree(rwork);
    294:     PetscMalloc(n*sizeof(PetscInt),&perm);
    295:     for (i=0; i<n; i++) perm[i] = i;
    296:     for (i=0; i<n; i++) r[i]    = PetscRealPart(eigs[i]);
    297:     PetscSortRealWithPermutation(n,r,perm);
    298:     for (i=0; i<n; i++) {
    299:       r[i] = PetscRealPart(eigs[perm[i]]);
    300:       c[i] = PetscImaginaryPart(eigs[perm[i]]);
    301:     }
    302:     PetscFree(perm);
    303:     PetscFree(eigs);
    304:   }
    305: #endif
    306:   if (size > 1) {
    307:     MatDenseRestoreArray(A,&array);
    308:     MatDestroy(&A);
    309:   } else {
    310:     MatDenseRestoreArray(BA,&array);
    311:   }
    312:   MatDestroy(&BA);
    313:   return(0);
    314: }

    318: static PetscErrorCode PolyEval(PetscInt nroots,const PetscReal *r,const PetscReal *c,PetscReal x,PetscReal y,PetscReal *px,PetscReal *py)
    319: {
    320:   PetscInt  i;
    321:   PetscReal rprod = 1,iprod = 0;

    324:   for (i=0; i<nroots; i++) {
    325:     PetscReal rnew = rprod*(x - r[i]) - iprod*(y - c[i]);
    326:     PetscReal inew = rprod*(y - c[i]) + iprod*(x - r[i]);
    327:     rprod = rnew;
    328:     iprod = inew;
    329:   }
    330:   *px = rprod;
    331:   *py = iprod;
    332:   return(0);
    333: }

    335: #include <petscdraw.h>
    338: /* collective on KSP */
    339: PetscErrorCode KSPPlotEigenContours_Private(KSP ksp,PetscInt neig,const PetscReal *r,const PetscReal *c)
    340: {
    342:   PetscReal      xmin,xmax,ymin,ymax,*xloc,*yloc,*value,px0,py0,rscale,iscale;
    343:   PetscInt       M,N,i,j;
    344:   PetscMPIInt    rank;
    345:   PetscViewer    viewer;
    346:   PetscDraw      draw;
    347:   PetscDrawAxis  drawaxis;

    350:   MPI_Comm_rank(PetscObjectComm((PetscObject)ksp),&rank);
    351:   if (rank) return(0);
    352:   M    = 80;
    353:   N    = 80;
    354:   xmin = r[0]; xmax = r[0];
    355:   ymin = c[0]; ymax = c[0];
    356:   for (i=1; i<neig; i++) {
    357:     xmin = PetscMin(xmin,r[i]);
    358:     xmax = PetscMax(xmax,r[i]);
    359:     ymin = PetscMin(ymin,c[i]);
    360:     ymax = PetscMax(ymax,c[i]);
    361:   }
    362:   PetscMalloc3(M,PetscReal,&xloc,N,PetscReal,&yloc,M*N,PetscReal,&value);
    363:   for (i=0; i<M; i++) xloc[i] = xmin - 0.1*(xmax-xmin) + 1.2*(xmax-xmin)*i/(M-1);
    364:   for (i=0; i<N; i++) yloc[i] = ymin - 0.1*(ymax-ymin) + 1.2*(ymax-ymin)*i/(N-1);
    365:   PolyEval(neig,r,c,0,0,&px0,&py0);
    366:   rscale = px0/(PetscSqr(px0)+PetscSqr(py0));
    367:   iscale = -py0/(PetscSqr(px0)+PetscSqr(py0));
    368:   for (j=0; j<N; j++) {
    369:     for (i=0; i<M; i++) {
    370:       PetscReal px,py,tx,ty,tmod;
    371:       PolyEval(neig,r,c,xloc[i],yloc[j],&px,&py);
    372:       tx   = px*rscale - py*iscale;
    373:       ty   = py*rscale + px*iscale;
    374:       tmod = PetscSqr(tx) + PetscSqr(ty); /* modulus of the complex polynomial */
    375:       if (tmod > 1) tmod = 1.0;
    376:       if (tmod > 0.5 && tmod < 1) tmod = 0.5;
    377:       if (tmod > 0.2 && tmod < 0.5) tmod = 0.2;
    378:       if (tmod > 0.05 && tmod < 0.2) tmod = 0.05;
    379:       if (tmod < 1e-3) tmod = 1e-3;
    380:       value[i+j*M] = PetscLogReal(tmod) / PetscLogReal(10.0);
    381:     }
    382:   }
    383:   PetscViewerDrawOpen(PETSC_COMM_SELF,0,"Iteratively Computed Eigen-contours",PETSC_DECIDE,PETSC_DECIDE,450,450,&viewer);
    384:   PetscViewerDrawGetDraw(viewer,0,&draw);
    385:   PetscDrawTensorContour(draw,M,N,NULL,NULL,value);
    386:   if (0) {
    387:     PetscDrawAxisCreate(draw,&drawaxis);
    388:     PetscDrawAxisSetLimits(drawaxis,xmin,xmax,ymin,ymax);
    389:     PetscDrawAxisSetLabels(drawaxis,"Eigen-counters","real","imag");
    390:     PetscDrawAxisDraw(drawaxis);
    391:     PetscDrawAxisDestroy(&drawaxis);
    392:   }
    393:   PetscViewerDestroy(&viewer);
    394:   PetscFree3(xloc,yloc,value);
    395:   return(0);
    396: }