Date: 2021-02-01T14:41:44+00:00

Actual source code: dsnep.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */

     11: #include <slepc/private/dsimpl.h>
     12: #include <slepcblaslapack.h>

     14: typedef struct {
     15:   PetscInt       nf;                 /* number of functions in f[] */
     16:   FN             f[DS_NUM_EXTRA];    /* functions defining the nonlinear operator */
     17:   PetscInt       neig;               /* number of available eigenpairs */
     18:   void           *computematrixctx;
     19:   PetscErrorCode (*computematrix)(DS,PetscScalar,PetscBool,DSMatType,void*);
     20: } DS_NEP;

     22: /*
     23:    DSNEPComputeMatrix - Build the matrix associated with a nonlinear operator
     24:    T(lambda) or its derivative T'(lambda), given the parameter lambda, where
     25:    T(lambda) = sum_i E_i*f_i(lambda). The result is written in mat.
     26: */
     27: static PetscErrorCode DSNEPComputeMatrix(DS ds,PetscScalar lambda,PetscBool deriv,DSMatType mat)
     28: {
     30:   DS_NEP         *ctx = (DS_NEP*)ds->data;
     31:   PetscScalar    *T,*E,alpha;
     32:   PetscInt       i,ld,n;
     33:   PetscBLASInt   k,inc=1;

     36:   PetscLogEventBegin(DS_Other,ds,0,0,0);
     37:   if (ctx->computematrix) {
     38:     (*ctx->computematrix)(ds,lambda,deriv,mat,ctx->computematrixctx);
     39:   } else {
     40:     DSGetDimensions(ds,&n,NULL,NULL,NULL,NULL);
     41:     DSGetLeadingDimension(ds,&ld);
     42:     PetscBLASIntCast(ld*n,&k);
     43:     DSGetArray(ds,mat,&T);
     44:     PetscArrayzero(T,k);
     45:     for (i=0;i<ctx->nf;i++) {
     46:       if (deriv) {
     47:         FNEvaluateDerivative(ctx->f[i],lambda,&alpha);
     48:       } else {
     49:         FNEvaluateFunction(ctx->f[i],lambda,&alpha);
     50:       }
     51:       E = ds->mat[DSMatExtra[i]];
     52:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&k,&alpha,E,&inc,T,&inc));
     53:     }
     54:     DSRestoreArray(ds,mat,&T);
     55:   }
     56:   PetscLogEventEnd(DS_Other,ds,0,0,0);
     57:   return(0);
     58: }

     60: PetscErrorCode DSAllocate_NEP(DS ds,PetscInt ld)
     61: {
     63:   DS_NEP         *ctx = (DS_NEP*)ds->data;
     64:   PetscInt       i;

     67:   if (!ctx->nf) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_WRONGSTATE,"DSNEP requires passing some functions via DSSetFN()");
     68:   DSAllocateMat_Private(ds,DS_MAT_X);
     69:   for (i=0;i<ctx->nf;i++) {
     70:     DSAllocateMat_Private(ds,DSMatExtra[i]);
     71:   }
     72:   PetscFree(ds->perm);
     73:   PetscMalloc1(ld,&ds->perm);
     74:   PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
     75:   return(0);
     76: }

     78: PetscErrorCode DSView_NEP(DS ds,PetscViewer viewer)
     79: {
     80:   PetscErrorCode    ierr;
     81:   DS_NEP            *ctx = (DS_NEP*)ds->data;
     82:   PetscViewerFormat format;
     83:   PetscInt          i;

     86:   PetscViewerGetFormat(viewer,&format);
     87:   PetscViewerASCIIPrintf(viewer,"number of functions: %D\n",ctx->nf);
     88:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) return(0);
     89:   for (i=0;i<ctx->nf;i++) {
     90:     FNView(ctx->f[i],viewer);
     91:     DSViewMat(ds,viewer,DSMatExtra[i]);
     92:   }
     93:   if (ds->state>DS_STATE_INTERMEDIATE) { DSViewMat(ds,viewer,DS_MAT_X); }
     94:   return(0);
     95: }

     97: PetscErrorCode DSVectors_NEP(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
     98: {
    100:   if (rnorm) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
    101:   switch (mat) {
    102:     case DS_MAT_X:
    103:       break;
    104:     case DS_MAT_Y:
    105:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
    106:     default:
    107:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
    108:   }
    109:   return(0);
    110: }

    112: PetscErrorCode DSSort_NEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *dummy)
    113: {
    115:   DS_NEP         *ctx = (DS_NEP*)ds->data;
    116:   PetscInt       n,l,i,j,k,p,*perm,told,ld=ds->ld;
    117:   PetscScalar    *A,*X,rtmp;

    120:   if (!ds->sc) return(0);
    121:   n = ds->n;
    122:   l = ds->l;
    123:   A  = ds->mat[DS_MAT_A];
    124:   perm = ds->perm;
    125:   for (i=0;i<ctx->neig;i++) perm[i] = i;
    126:   told = ds->t;
    127:   ds->t = ctx->neig;  /* force the sorting routines to consider ctx->neig eigenvalues */
    128:   if (rr) {
    129:     DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_FALSE);
    130:   } else {
    131:     DSSortEigenvalues_Private(ds,wr,NULL,perm,PETSC_FALSE);
    132:   }
    133:   ds->t = told;  /* restore value of t */
    134:   for (i=l;i<n;i++) A[i+i*ld] = wr[perm[i]];
    135:   for (i=l;i<n;i++) wr[i] = A[i+i*ld];
    136:   /* cannot use DSPermuteColumns_Private() since not all columns are filled */
    137:   X  = ds->mat[DS_MAT_X];
    138:   for (i=0;i<ctx->neig;i++) {
    139:     p = perm[i];
    140:     if (p != i) {
    141:       j = i + 1;
    142:       while (perm[j] != i) j++;
    143:       perm[j] = p; perm[i] = i;
    144:       /* swap columns i and j */
    145:       for (k=0;k<n;k++) {
    146:         rtmp  = X[k+p*ld]; X[k+p*ld] = X[k+i*ld]; X[k+i*ld] = rtmp;
    147:       }
    148:     }
    149:   }
    150:   return(0);
    151: }

    153: PetscErrorCode DSSolve_NEP_SLP(DS ds,PetscScalar *wr,PetscScalar *wi)
    154: {
    156:   DS_NEP         *ctx = (DS_NEP*)ds->data;
    157:   PetscScalar    *A,*B,*W,*X,*work,*alpha,*beta;
    158:   PetscScalar    norm,sigma,lambda,mu,re,re2,sone=1.0,zero=0.0;
    159:   PetscBLASInt   info,n,ld,lrwork=0,lwork,one=1;
    160:   PetscInt       it,pos,j,maxit=100,result;
    161:   PetscReal      tol;
    162: #if defined(PETSC_USE_COMPLEX)
    163:   PetscReal      *rwork;
    164: #else
    165:   PetscReal      *alphai,im,im2;
    166: #endif

    169:   if (!ds->mat[DS_MAT_A]) {
    170:     DSAllocateMat_Private(ds,DS_MAT_A);
    171:   }
    172:   if (!ds->mat[DS_MAT_B]) {
    173:     DSAllocateMat_Private(ds,DS_MAT_B);
    174:   }
    175:   if (!ds->mat[DS_MAT_W]) {
    176:     DSAllocateMat_Private(ds,DS_MAT_W);
    177:   }
    178:   PetscBLASIntCast(ds->n,&n);
    179:   PetscBLASIntCast(ds->ld,&ld);
    180: #if defined(PETSC_USE_COMPLEX)
    181:   PetscBLASIntCast(2*ds->n+2*ds->n,&lwork);
    182:   PetscBLASIntCast(8*ds->n,&lrwork);
    183: #else
    184:   PetscBLASIntCast(3*ds->n+8*ds->n,&lwork);
    185: #endif
    186:   DSAllocateWork_Private(ds,lwork,lrwork,0);
    187:   alpha = ds->work;
    188:   beta = ds->work + ds->n;
    189: #if defined(PETSC_USE_COMPLEX)
    190:   work = ds->work + 2*ds->n;
    191:   lwork -= 2*ds->n;
    192: #else
    193:   alphai = ds->work + 2*ds->n;
    194:   work = ds->work + 3*ds->n;
    195:   lwork -= 3*ds->n;
    196: #endif
    197:   A = ds->mat[DS_MAT_A];
    198:   B = ds->mat[DS_MAT_B];
    199:   W = ds->mat[DS_MAT_W];
    200:   X = ds->mat[DS_MAT_X];

    202:   sigma = 0.0;
    203:   if (ds->sc->comparison==SlepcCompareTargetMagnitude || ds->sc->comparison==SlepcCompareTargetReal) sigma = *(PetscScalar*)ds->sc->comparisonctx;
    204:   lambda = sigma;
    205:   tol = 1000*n*PETSC_MACHINE_EPSILON;

    207:   for (it=0;it<maxit;it++) {

    209:     /* evaluate T and T' */
    210:     DSNEPComputeMatrix(ds,lambda,PETSC_FALSE,DS_MAT_A);
    211:     if (it) {
    212:       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,A,&ld,X,&one,&zero,X+ld,&one));
    213:       norm = BLASnrm2_(&n,X+ld,&one);
    214:       if (PetscRealPart(norm)/PetscAbsScalar(lambda)<=tol) break;
    215:     }
    216:     DSNEPComputeMatrix(ds,lambda,PETSC_TRUE,DS_MAT_B);

    218:     /* compute eigenvalue correction mu and eigenvector u */
    219: #if defined(PETSC_USE_COMPLEX)
    220:     rwork = ds->rwork;
    221:     PetscStackCallBLAS("LAPACKggev",LAPACKggev_("N","V",&n,A,&ld,B,&ld,alpha,beta,NULL,&ld,W,&ld,work,&lwork,rwork,&info));
    222: #else
    223:     PetscStackCallBLAS("LAPACKggev",LAPACKggev_("N","V",&n,A,&ld,B,&ld,alpha,alphai,beta,NULL,&ld,W,&ld,work,&lwork,&info));
    224: #endif
    225:     SlepcCheckLapackInfo("ggev",info);

    227:     /* find smallest eigenvalue */
    228:     j = 0;
    229:     if (beta[j]==0.0) re = (PetscRealPart(alpha[j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
    230:     else re = alpha[j]/beta[j];
    231: #if !defined(PETSC_USE_COMPLEX)
    232:     if (beta[j]==0.0) im = (alphai[j]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
    233:     else im = alphai[j]/beta[j];
    234: #endif
    235:     pos = 0;
    236:     for (j=1;j<n;j++) {
    237:       if (beta[j]==0.0) re2 = (PetscRealPart(alpha[j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
    238:       else re2 = alpha[j]/beta[j];
    239: #if !defined(PETSC_USE_COMPLEX)
    240:       if (beta[j]==0.0) im2 = (alphai[j]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
    241:       else im2 = alphai[j]/beta[j];
    242:       SlepcCompareSmallestMagnitude(re,im,re2,im2,&result,NULL);
    243: #else
    244:       SlepcCompareSmallestMagnitude(re,0.0,re2,0.0,&result,NULL);
    245: #endif
    246:       if (result > 0) {
    247:         re = re2;
    248: #if !defined(PETSC_USE_COMPLEX)
    249:         im = im2;
    250: #endif
    251:         pos = j;
    252:       }
    253:     }

    255: #if !defined(PETSC_USE_COMPLEX)
    256:     if (im!=0.0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"DSNEP found a complex eigenvalue; try rerunning with complex scalars");
    257: #endif
    258:     mu = alpha[pos]/beta[pos];
    259:     PetscArraycpy(X,W+pos*ld,n);
    260:     norm = BLASnrm2_(&n,X,&one);
    261:     norm = 1.0/norm;
    262:     PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,X,&one));

    264:     /* correct eigenvalue approximation */
    265:     lambda = lambda - mu;
    266:   }

    268:   if (it==maxit) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_CONV_FAILED,"DSNEP did not converge");
    269:   ctx->neig = 1;
    270:   wr[0] = lambda;
    271:   if (wi) wi[0] = 0.0;
    272:   return(0);
    273: }

    275: PetscErrorCode DSSynchronize_NEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
    276: {
    278:   PetscInt       k=0;
    279:   PetscMPIInt    n,rank,size,off=0;

    282:   if (ds->state>=DS_STATE_CONDENSED) k += ds->n;
    283:   if (eigr) k += 1;
    284:   if (eigi) k += 1;
    285:   DSAllocateWork_Private(ds,k,0,0);
    286:   PetscMPIIntCast(k*sizeof(PetscScalar),&size);
    287:   PetscMPIIntCast(ds->n,&n);
    288:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
    289:   if (!rank) {
    290:     if (ds->state>=DS_STATE_CONDENSED) {
    291:       MPI_Pack(ds->mat[DS_MAT_X],n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    292:     }
    293:     if (eigr) {
    294:       MPI_Pack(eigr,1,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    295:     }
    296:     if (eigi) {
    297:       MPI_Pack(eigi,1,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    298:     }
    299:   }
    300:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
    301:   if (rank) {
    302:     if (ds->state>=DS_STATE_CONDENSED) {
    303:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_X],n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    304:     }
    305:     if (eigr) {
    306:       MPI_Unpack(ds->work,size,&off,eigr,1,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    307:     }
    308:     if (eigi) {
    309:       MPI_Unpack(ds->work,size,&off,eigi,1,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    310:     }
    311:   }
    312:   return(0);
    313: }

    315: static PetscErrorCode DSNEPSetFN_NEP(DS ds,PetscInt n,FN fn[])
    316: {
    318:   DS_NEP         *ctx = (DS_NEP*)ds->data;
    319:   PetscInt       i;

    322:   if (n<=0) SETERRQ1(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Must have one or more functions, you have %D",n);
    323:   if (n>DS_NUM_EXTRA) SETERRQ2(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Too many functions, you specified %D but the limit is %D",n,DS_NUM_EXTRA);
    324:   if (ds->ld) { PetscInfo(ds,"DSNEPSetFN() called after DSAllocate()\n"); }
    325:   for (i=0;i<n;i++) {
    326:     PetscObjectReference((PetscObject)fn[i]);
    327:   }
    328:   for (i=0;i<ctx->nf;i++) {
    329:     FNDestroy(&ctx->f[i]);
    330:   }
    331:   for (i=0;i<n;i++) ctx->f[i] = fn[i];
    332:   ctx->nf = n;
    333:   return(0);
    334: }

    336: /*@
    337:    DSNEPSetFN - Sets a number of functions that define the nonlinear
    338:    eigenproblem.

    340:    Collective on ds

    342:    Input Parameters:
    343: +  ds - the direct solver context
    344: .  n  - number of functions
    345: -  fn - array of functions

    347:    Notes:
    348:    The nonlinear eigenproblem is defined in terms of the split nonlinear
    349:    operator T(lambda) = sum_i A_i*f_i(lambda).

    351:    This function must be called before DSAllocate(). Then DSAllocate()
    352:    will allocate an extra matrix A_i per each function, that can be
    353:    filled in the usual way.

    355:    Level: advanced

    357: .seealso: DSNEPGetFN(), DSAllocate()
    358:  @*/
    359: PetscErrorCode DSNEPSetFN(DS ds,PetscInt n,FN fn[])
    360: {
    361:   PetscInt       i;

    368:   for (i=0;i<n;i++) {
    371:   }
    372:   PetscTryMethod(ds,"DSNEPSetFN_C",(DS,PetscInt,FN[]),(ds,n,fn));
    373:   return(0);
    374: }

    376: static PetscErrorCode DSNEPGetFN_NEP(DS ds,PetscInt k,FN *fn)
    377: {
    378:   DS_NEP *ctx = (DS_NEP*)ds->data;

    381:   if (k<0 || k>=ctx->nf) SETERRQ1(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"k must be between 0 and %D",ctx->nf-1);
    382:   *fn = ctx->f[k];
    383:   return(0);
    384: }

    386: /*@
    387:    DSNEPGetFN - Gets the functions associated with the nonlinear DS.

    389:    Not collective, though parallel FNs are returned if the DS is parallel

    391:    Input Parameter:
    392: +  ds - the direct solver context
    393: -  k  - the index of the requested function (starting in 0)

    395:    Output Parameter:
    396: .  fn - the function

    398:    Level: advanced

    400: .seealso: DSNEPSetFN()
    401: @*/
    402: PetscErrorCode DSNEPGetFN(DS ds,PetscInt k,FN *fn)
    403: {

    409:   PetscUseMethod(ds,"DSNEPGetFN_C",(DS,PetscInt,FN*),(ds,k,fn));
    410:   return(0);
    411: }

    413: static PetscErrorCode DSNEPGetNumFN_NEP(DS ds,PetscInt *n)
    414: {
    415:   DS_NEP *ctx = (DS_NEP*)ds->data;

    418:   *n = ctx->nf;
    419:   return(0);
    420: }

    422: /*@
    423:    DSNEPGetNumFN - Returns the number of functions stored internally by
    424:    the DS.

    426:    Not collective

    428:    Input Parameter:
    429: .  ds - the direct solver context

    431:    Output Parameters:
    432: .  n - the number of functions passed in DSNEPSetFN()

    434:    Level: advanced

    436: .seealso: DSNEPSetFN()
    437: @*/
    438: PetscErrorCode DSNEPGetNumFN(DS ds,PetscInt *n)
    439: {

    445:   PetscUseMethod(ds,"DSNEPGetNumFN_C",(DS,PetscInt*),(ds,n));
    446:   return(0);
    447: }

    449: static PetscErrorCode DSNEPSetComputeMatrixFunction_NEP(DS ds,PetscErrorCode (*fun)(DS,PetscScalar,PetscBool,DSMatType,void*),void *ctx)
    450: {
    451:   DS_NEP *dsctx = (DS_NEP*)ds->data;

    454:   dsctx->computematrix    = fun;
    455:   dsctx->computematrixctx = ctx;
    456:   return(0);
    457: }

    459: /*@
    460:    DSNEPSetComputeMatrixFunction - Sets a user-provided subroutine to compute
    461:    the matrices T(lambda) or T'(lambda).

    463:    Logically Collective on ds

    465:    Input Parameters:
    466: +  ds  - the direct solver context
    467: .  fun - a pointer to the user function
    468: -  ctx - a context pointer (the last parameter to the user function)

    470:    Calling Sequence of fun:
    471: $   fun(DS ds,PetscScalar lambda,PetscBool deriv,DSMatType mat,void *ctx)

    473: +   ds     - the direct solver object
    474: .   lambda - point where T(lambda) or T'(lambda) must be evaluated
    475: .   deriv  - if true compute T'(lambda), otherwise compute T(lambda)
    476: .   mat    - the DS matrix where the result must be stored
    477: -   ctx    - optional context, as set by DSNEPSetComputeMatrixFunction()

    479:    Note:
    480:    The result is computed as T(lambda) = sum_i E_i*f_i(lambda), and similarly
    481:    for the derivative.

    483:    Level: developer
    484: @*/
    485: PetscErrorCode DSNEPSetComputeMatrixFunction(DS ds,PetscErrorCode (*fun)(DS,PetscScalar,PetscBool,DSMatType,void*),void *ctx)
    486: {

    491:   PetscTryMethod(ds,"DSNEPSetComputeMatrixFunction_C",(DS,PetscErrorCode (*)(DS,PetscScalar,PetscBool,DSMatType,void*),void*),(ds,fun,ctx));
    492:   return(0);
    493: }

    495: PetscErrorCode DSDestroy_NEP(DS ds)
    496: {
    498:   DS_NEP         *ctx = (DS_NEP*)ds->data;
    499:   PetscInt       i;

    502:   for (i=0;i<ctx->nf;i++) {
    503:     FNDestroy(&ctx->f[i]);
    504:   }
    505:   PetscFree(ds->data);
    506:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetFN_C",NULL);
    507:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetFN_C",NULL);
    508:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetNumFN_C",NULL);
    509:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetComputeMatrixFunction_C",NULL);
    510:   return(0);
    511: }

    513: SLEPC_EXTERN PetscErrorCode DSCreate_NEP(DS ds)
    514: {
    515:   DS_NEP         *ctx;

    519:   PetscNewLog(ds,&ctx);
    520:   ds->data = (void*)ctx;

    522:   ds->ops->allocate      = DSAllocate_NEP;
    523:   ds->ops->view          = DSView_NEP;
    524:   ds->ops->vectors       = DSVectors_NEP;
    525:   ds->ops->solve[0]      = DSSolve_NEP_SLP;
    526:   ds->ops->sort          = DSSort_NEP;
    527:   ds->ops->synchronize   = DSSynchronize_NEP;
    528:   ds->ops->destroy       = DSDestroy_NEP;
    529:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetFN_C",DSNEPSetFN_NEP);
    530:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetFN_C",DSNEPGetFN_NEP);
    531:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetNumFN_C",DSNEPGetNumFN_NEP);
    532:   PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetComputeMatrixFunction_C",DSNEPSetComputeMatrixFunction_NEP);
    533:   return(0);
    534: }