Date: 2015-10-02T22:20:42+00:00

Actual source code: eige.c
petsc-3.6.2 2015-10-02
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      2: #include <petsc/private/kspimpl.h>   /*I "petscksp.h" I*/
      3: #include <petscblaslapack.h>

      7: /*@
      8:     KSPComputeExplicitOperator - Computes the explicit preconditioned operator, including diagonal scaling and null
      9:     space removal if applicable.

     11:     Collective on KSP

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

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

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

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

     27:     Level: advanced

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

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

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

     49:   VecDuplicate(ksp->vec_sol,&in);
     50:   VecDuplicate(ksp->vec_sol,&out);
     51:   VecDuplicate(ksp->vec_sol,&work);
     52:   VecGetSize(in,&M);
     53:   VecGetLocalSize(in,&m);
     54:   VecGetOwnershipRange(in,&start,&end);
     55:   PetscMalloc1(m,&rows);
     56:   for (i=0; i<m; i++) rows[i] = start + i;

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

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

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

     78:     KSP_PCApplyBAorAB(ksp,in,out,work);

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

     84:   }
     85:   PetscFree(rows);
     86:   VecDestroy(&in);
     87:   VecDestroy(&out);
     88:   VecDestroy(&work);
     89:   MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);
     90:   MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);
     91:   return(0);
     92: }

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

    100:    Collective on KSP

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

    106:    Output Parameters:
    107: +  r - real part of computed eigenvalues, provided by user with a dimension at least of n
    108: -  c - complex part of computed eigenvalues, provided by user with a dimension at least of n

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

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

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

    124:    Level: advanced

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

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

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

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

    160:     MatGetOwnershipRange(BA,&row,&dummy);
    161:     MatGetLocalSize(BA,&m,&dummy);
    162:     for (i=0; i<m; i++) {
    163:       MatGetRow(BA,row,&nz,&cols,&vals);
    164:       MatSetValues(A,1,&row,nz,cols,vals,INSERT_VALUES);
    165:       MatRestoreRow(BA,row,&nz,&cols,&vals);
    166:       row++;
    167:     }

    169:     MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    170:     MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    171:     MatDenseGetArray(A,&array);
    172:   } else {
    173:     MatDenseGetArray(BA,&array);
    174:   }

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

    184: #if !defined(PETSC_USE_COMPLEX)
    185:     clen = n;
    186: #else
    187:     clen = 2*n;
    188: #endif
    189:     PetscMalloc1(clen,&cwork);
    190:     idummy = -1;                /* unused */
    191:     PetscBLASIntCast(n,&bn);
    192:     lwork  = 5*n;
    193:     PetscMalloc1(lwork,&work);
    194:     PetscMalloc1(n,&realpart);
    195:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    196:     PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_(&zero,array,&bn,cwork,&sdummy,&idummy,&idummy,&bn,work,&lwork));
    197:     PetscFPTrapPop();
    198:     PetscFree(work);

    200:     /* For now we stick with the convention of storing the real and imaginary
    201:        components of evalues separately.  But is this what we really want? */
    202:     PetscMalloc1(n,&perm);

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

    236:     idummy   = n;
    237:     lwork    = 5*n;
    238:     PetscMalloc2(n,&realpart,n,&imagpart);
    239:     PetscMalloc1(5*n,&work);
    240: #if defined(PETSC_MISSING_LAPACK_GEEV)
    241:     SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GEEV - Lapack routine is unavailable\nNot able to provide eigen values.");
    242: #else
    243:     {
    244:       PetscBLASInt lierr;
    245:       PetscScalar  sdummy;
    246:       PetscBLASInt bn;

    248:       PetscBLASIntCast(n,&bn);
    249:       PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    250:       PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_("N","N",&bn,array,&bn,realpart,imagpart,&sdummy,&idummy,&sdummy,&idummy,work,&lwork,&lierr));
    251:       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in LAPACK routine %d",(int)lierr);
    252:       PetscFPTrapPop();
    253:     }
    254: #endif
    255:     PetscFree(work);
    256:     PetscMalloc1(n,&perm);

    258:     for (i=0; i<n; i++)  perm[i] = i;
    259:     PetscSortRealWithPermutation(n,realpart,perm);
    260:     for (i=0; i<n; i++) {
    261:       r[i] = realpart[perm[i]];
    262:       c[i] = imagpart[perm[i]];
    263:     }
    264:     PetscFree(perm);
    265:     PetscFree2(realpart,imagpart);
    266:   }
    267: #else
    268:   if (!rank) {
    269:     PetscScalar  *work,*eigs;
    270:     PetscReal    *rwork;
    271:     PetscBLASInt idummy,lwork;
    272:     PetscInt     *perm;

    274:     idummy = n;
    275:     lwork  = 5*n;
    276:     PetscMalloc1(5*n,&work);
    277:     PetscMalloc1(2*n,&rwork);
    278:     PetscMalloc1(n,&eigs);
    279: #if defined(PETSC_MISSING_LAPACK_GEEV)
    280:     SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GEEV - Lapack routine is unavailable\nNot able to provide eigen values.");
    281: #else
    282:     {
    283:       PetscBLASInt lierr;
    284:       PetscScalar  sdummy;
    285:       PetscBLASInt nb;
    286:       PetscBLASIntCast(n,&nb);
    287:       PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    288:       PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_("N","N",&nb,array,&nb,eigs,&sdummy,&idummy,&sdummy,&idummy,work,&lwork,rwork,&lierr));
    289:       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in LAPACK routine %d",(int)lierr);
    290:       PetscFPTrapPop();
    291:     }
    292: #endif
    293:     PetscFree(work);
    294:     PetscFree(rwork);
    295:     PetscMalloc1(n,&perm);
    296:     for (i=0; i<n; i++) perm[i] = i;
    297:     for (i=0; i<n; i++) r[i]    = PetscRealPart(eigs[i]);
    298:     PetscSortRealWithPermutation(n,r,perm);
    299:     for (i=0; i<n; i++) {
    300:       r[i] = PetscRealPart(eigs[perm[i]]);
    301:       c[i] = PetscImaginaryPart(eigs[perm[i]]);
    302:     }
    303:     PetscFree(perm);
    304:     PetscFree(eigs);
    305:   }
    306: #endif
    307:   if (size > 1) {
    308:     MatDenseRestoreArray(A,&array);
    309:     MatDestroy(&A);
    310:   } else {
    311:     MatDenseRestoreArray(BA,&array);
    312:   }
    313:   MatDestroy(&BA);
    314:   return(0);
    315: }

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

    325:   for (i=0; i<nroots; i++) {
    326:     PetscReal rnew = rprod*(x - r[i]) - iprod*(y - c[i]);
    327:     PetscReal inew = rprod*(y - c[i]) + iprod*(x - r[i]);
    328:     rprod = rnew;
    329:     iprod = inew;
    330:   }
    331:   *px = rprod;
    332:   *py = iprod;
    333:   return(0);
    334: }

    336: #include <petscdraw.h>
    339: /* collective on KSP */
    340: PetscErrorCode KSPPlotEigenContours_Private(KSP ksp,PetscInt neig,const PetscReal *r,const PetscReal *c)
    341: {
    343:   PetscReal      xmin,xmax,ymin,ymax,*xloc,*yloc,*value,px0,py0,rscale,iscale;
    344:   PetscInt       M,N,i,j;
    345:   PetscMPIInt    rank;
    346:   PetscViewer    viewer;
    347:   PetscDraw      draw;
    348:   PetscDrawAxis  drawaxis;

    351:   MPI_Comm_rank(PetscObjectComm((PetscObject)ksp),&rank);
    352:   if (rank) return(0);
    353:   M    = 80;
    354:   N    = 80;
    355:   xmin = r[0]; xmax = r[0];
    356:   ymin = c[0]; ymax = c[0];
    357:   for (i=1; i<neig; i++) {
    358:     xmin = PetscMin(xmin,r[i]);
    359:     xmax = PetscMax(xmax,r[i]);
    360:     ymin = PetscMin(ymin,c[i]);
    361:     ymax = PetscMax(ymax,c[i]);
    362:   }
    363:   PetscMalloc3(M,&xloc,N,&yloc,M*N,&value);
    364:   for (i=0; i<M; i++) xloc[i] = xmin - 0.1*(xmax-xmin) + 1.2*(xmax-xmin)*i/(M-1);
    365:   for (i=0; i<N; i++) yloc[i] = ymin - 0.1*(ymax-ymin) + 1.2*(ymax-ymin)*i/(N-1);
    366:   PolyEval(neig,r,c,0,0,&px0,&py0);
    367:   rscale = px0/(PetscSqr(px0)+PetscSqr(py0));
    368:   iscale = -py0/(PetscSqr(px0)+PetscSqr(py0));
    369:   for (j=0; j<N; j++) {
    370:     for (i=0; i<M; i++) {
    371:       PetscReal px,py,tx,ty,tmod;
    372:       PolyEval(neig,r,c,xloc[i],yloc[j],&px,&py);
    373:       tx   = px*rscale - py*iscale;
    374:       ty   = py*rscale + px*iscale;
    375:       tmod = PetscSqr(tx) + PetscSqr(ty); /* modulus of the complex polynomial */
    376:       if (tmod > 1) tmod = 1.0;
    377:       if (tmod > 0.5 && tmod < 1) tmod = 0.5;
    378:       if (tmod > 0.2 && tmod < 0.5) tmod = 0.2;
    379:       if (tmod > 0.05 && tmod < 0.2) tmod = 0.05;
    380:       if (tmod < 1e-3) tmod = 1e-3;
    381:       value[i+j*M] = PetscLogReal(tmod) / PetscLogReal(10.0);
    382:     }
    383:   }
    384:   PetscViewerDrawOpen(PETSC_COMM_SELF,0,"Iteratively Computed Eigen-contours",PETSC_DECIDE,PETSC_DECIDE,450,450,&viewer);
    385:   PetscViewerDrawGetDraw(viewer,0,&draw);
    386:   PetscDrawTensorContour(draw,M,N,NULL,NULL,value);
    387:   if (0) {
    388:     PetscDrawAxisCreate(draw,&drawaxis);
    389:     PetscDrawAxisSetLimits(drawaxis,xmin,xmax,ymin,ymax);
    390:     PetscDrawAxisSetLabels(drawaxis,"Eigen-counters","real","imag");
    391:     PetscDrawAxisDraw(drawaxis);
    392:     PetscDrawAxisDestroy(&drawaxis);
    393:   }
    394:   PetscViewerDestroy(&viewer);
    395:   PetscFree3(xloc,yloc,value);
    396:   return(0);
    397: }