Actual source code: fnbasic.c
slepc-3.10.1 2018-10-23
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2018, 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: */
     10: /*
     11:    Basic FN routines
     12: */

     14: #include <slepc/private/fnimpl.h>      /*I "slepcfn.h" I*/
     15: #include <slepcblaslapack.h>

     17: PetscFunctionList FNList = 0;
     18: PetscBool         FNRegisterAllCalled = PETSC_FALSE;
     19: PetscClassId      FN_CLASSID = 0;
     20: PetscLogEvent     FN_Evaluate = 0;
     21: static PetscBool  FNPackageInitialized = PETSC_FALSE;

     23: const char *FNParallelTypes[] = {"REDUNDANT","SYNCHRONIZED","FNParallelType","FN_PARALLEL_",0};

     25: /*@C
     26:    FNFinalizePackage - This function destroys everything in the Slepc interface
     27:    to the FN package. It is called from SlepcFinalize().

     29:    Level: developer

     31: .seealso: SlepcFinalize()
     32: @*/
     33: PetscErrorCode FNFinalizePackage(void)
     34: {

     38:   PetscFunctionListDestroy(&FNList);
     39:   FNPackageInitialized = PETSC_FALSE;
     40:   FNRegisterAllCalled  = PETSC_FALSE;
     41:   return(0);
     42: }

     44: /*@C
     45:   FNInitializePackage - This function initializes everything in the FN package.
     46:   It is called from PetscDLLibraryRegister() when using dynamic libraries, and
     47:   on the first call to FNCreate() when using static libraries.

     49:   Level: developer

     51: .seealso: SlepcInitialize()
     52: @*/
     53: PetscErrorCode FNInitializePackage(void)
     54: {
     55:   char           logList[256];
     56:   PetscBool      opt,pkg;

     60:   if (FNPackageInitialized) return(0);
     61:   FNPackageInitialized = PETSC_TRUE;
     62:   /* Register Classes */
     63:   PetscClassIdRegister("Math Function",&FN_CLASSID);
     64:   /* Register Constructors */
     65:   FNRegisterAll();
     66:   /* Register Events */
     67:   PetscLogEventRegister("FNEvaluate",FN_CLASSID,&FN_Evaluate);
     68:   /* Process info exclusions */
     69:   PetscOptionsGetString(NULL,NULL,"-info_exclude",logList,sizeof(logList),&opt);
     70:   if (opt) {
     71:     PetscStrInList("fn",logList,',',&pkg);
     72:     if (pkg) { PetscInfoDeactivateClass(FN_CLASSID); }
     73:   }
     74:   /* Process summary exclusions */
     75:   PetscOptionsGetString(NULL,NULL,"-log_exclude",logList,sizeof(logList),&opt);
     76:   if (opt) {
     77:     PetscStrInList("fn",logList,',',&pkg);
     78:     if (pkg) { PetscLogEventDeactivateClass(FN_CLASSID); }
     79:   }
     80:   /* Register package finalizer */
     81:   PetscRegisterFinalize(FNFinalizePackage);
     82:   return(0);
     83: }

     85: /*@
     86:    FNCreate - Creates an FN context.

     88:    Collective on MPI_Comm

     90:    Input Parameter:
     91: .  comm - MPI communicator

     93:    Output Parameter:
     94: .  newfn - location to put the FN context

     96:    Level: beginner

     98: .seealso: FNDestroy(), FN
     99: @*/
    100: PetscErrorCode FNCreate(MPI_Comm comm,FN *newfn)
    101: {
    102:   FN             fn;

    107:   *newfn = 0;
    108:   FNInitializePackage();
    109:   SlepcHeaderCreate(fn,FN_CLASSID,"FN","Math Function","FN",comm,FNDestroy,FNView);

    111:   fn->alpha    = 1.0;
    112:   fn->beta     = 1.0;
    113:   fn->method   = 0;

    115:   fn->nw       = 0;
    116:   fn->cw       = 0;
    117:   fn->data     = NULL;

    119:   *newfn = fn;
    120:   return(0);
    121: }

    123: /*@C
    124:    FNSetOptionsPrefix - Sets the prefix used for searching for all
    125:    FN options in the database.

    127:    Logically Collective on FN

    129:    Input Parameters:
    130: +  fn - the math function context
    131: -  prefix - the prefix string to prepend to all FN option requests

    133:    Notes:
    134:    A hyphen (-) must NOT be given at the beginning of the prefix name.
    135:    The first character of all runtime options is AUTOMATICALLY the
    136:    hyphen.

    138:    Level: advanced

    140: .seealso: FNAppendOptionsPrefix()
    141: @*/
    142: PetscErrorCode FNSetOptionsPrefix(FN fn,const char *prefix)
    143: {

    148:   PetscObjectSetOptionsPrefix((PetscObject)fn,prefix);
    149:   return(0);
    150: }

    152: /*@C
    153:    FNAppendOptionsPrefix - Appends to the prefix used for searching for all
    154:    FN options in the database.

    156:    Logically Collective on FN

    158:    Input Parameters:
    159: +  fn - the math function context
    160: -  prefix - the prefix string to prepend to all FN option requests

    162:    Notes:
    163:    A hyphen (-) must NOT be given at the beginning of the prefix name.
    164:    The first character of all runtime options is AUTOMATICALLY the hyphen.

    166:    Level: advanced

    168: .seealso: FNSetOptionsPrefix()
    169: @*/
    170: PetscErrorCode FNAppendOptionsPrefix(FN fn,const char *prefix)
    171: {

    176:   PetscObjectAppendOptionsPrefix((PetscObject)fn,prefix);
    177:   return(0);
    178: }

    180: /*@C
    181:    FNGetOptionsPrefix - Gets the prefix used for searching for all
    182:    FN options in the database.

    184:    Not Collective

    186:    Input Parameters:
    187: .  fn - the math function context

    189:    Output Parameters:
    190: .  prefix - pointer to the prefix string used is returned

    192:    Note:
    193:    On the Fortran side, the user should pass in a string 'prefix' of
    194:    sufficient length to hold the prefix.

    196:    Level: advanced

    198: .seealso: FNSetOptionsPrefix(), FNAppendOptionsPrefix()
    199: @*/
    200: PetscErrorCode FNGetOptionsPrefix(FN fn,const char *prefix[])
    201: {

    207:   PetscObjectGetOptionsPrefix((PetscObject)fn,prefix);
    208:   return(0);
    209: }

    211: /*@C
    212:    FNSetType - Selects the type for the FN object.

    214:    Logically Collective on FN

    216:    Input Parameter:
    217: +  fn   - the math function context
    218: -  type - a known type

    220:    Notes:
    221:    The default is FNRATIONAL, which includes polynomials as a particular
    222:    case as well as simple functions such as f(x)=x and f(x)=constant.

    224:    Level: intermediate

    226: .seealso: FNGetType()
    227: @*/
    228: PetscErrorCode FNSetType(FN fn,FNType type)
    229: {
    230:   PetscErrorCode ierr,(*r)(FN);
    231:   PetscBool      match;

    237:   PetscObjectTypeCompare((PetscObject)fn,type,&match);
    238:   if (match) return(0);

    240:    PetscFunctionListFind(FNList,type,&r);
    241:   if (!r) SETERRQ1(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_UNKNOWN_TYPE,"Unable to find requested FN type %s",type);

    243:   if (fn->ops->destroy) { (*fn->ops->destroy)(fn); }
    244:   PetscMemzero(fn->ops,sizeof(struct _FNOps));

    246:   PetscObjectChangeTypeName((PetscObject)fn,type);
    247:   (*r)(fn);
    248:   return(0);
    249: }

    251: /*@C
    252:    FNGetType - Gets the FN type name (as a string) from the FN context.

    254:    Not Collective

    256:    Input Parameter:
    257: .  fn - the math function context

    259:    Output Parameter:
    260: .  name - name of the math function

    262:    Level: intermediate

    264: .seealso: FNSetType()
    265: @*/
    266: PetscErrorCode FNGetType(FN fn,FNType *type)
    267: {
    271:   *type = ((PetscObject)fn)->type_name;
    272:   return(0);
    273: }

    275: /*@
    276:    FNSetScale - Sets the scaling parameters that define the matematical function.

    278:    Logically Collective on FN

    280:    Input Parameters:
    281: +  fn    - the math function context
    282: .  alpha - inner scaling (argument)
    283: -  beta  - outer scaling (result)

    285:    Notes:
    286:    Given a function f(x) specified by the FN type, the scaling parameters can
    287:    be used to realize the function beta*f(alpha*x). So when these values are given,
    288:    the procedure for function evaluation will first multiply the argument by alpha,
    289:    then evaluate the function itself, and finally scale the result by beta.
    290:    Likewise, these values are also considered when evaluating the derivative.

    292:    If you want to provide only one of the two scaling factors, set the other
    293:    one to 1.0.

    295:    Level: intermediate

    297: .seealso: FNGetScale(), FNEvaluateFunction()
    298: @*/
    299: PetscErrorCode FNSetScale(FN fn,PetscScalar alpha,PetscScalar beta)
    300: {
    305:   fn->alpha = alpha;
    306:   fn->beta  = beta;
    307:   return(0);
    308: }

    310: /*@
    311:    FNGetScale - Gets the scaling parameters that define the matematical function.

    313:    Not Collective

    315:    Input Parameter:
    316: .  fn    - the math function context

    318:    Output Parameters:
    319: +  alpha - inner scaling (argument)
    320: -  beta  - outer scaling (result)

    322:    Level: intermediate

    324: .seealso: FNSetScale()
    325: @*/
    326: PetscErrorCode FNGetScale(FN fn,PetscScalar *alpha,PetscScalar *beta)
    327: {
    330:   if (alpha) *alpha = fn->alpha;
    331:   if (beta)  *beta  = fn->beta;
    332:   return(0);
    333: }

    335: /*@
    336:    FNSetMethod - Selects the method to be used to evaluate functions of matrices.

    338:    Logically Collective on FN

    340:    Input Parameter:
    341: +  fn   - the math function context
    342: -  meth - an index indentifying the method

    344:    Options Database Key:
    345: .  -fn_method <meth> - Sets the method

    347:    Notes:
    348:    In some FN types there are more than one algorithms available for computing
    349:    matrix functions. In that case, this function allows choosing the wanted method.

    351:    If meth is currently set to 0 (the default) and the input argument A of
    352:    FNEvaluateFunctionMat() is a symmetric/Hermitian matrix, then the computation
    353:    is done via the eigendecomposition of A, rather than with the general algorithm.

    355:    Level: intermediate

    357: .seealso: FNGetMethod(), FNEvaluateFunctionMat()
    358: @*/
    359: PetscErrorCode FNSetMethod(FN fn,PetscInt meth)
    360: {
    364:   if (meth<0) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"The method must be a non-negative integer");
    365:   if (meth>FN_MAX_SOLVE) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"Too large value for the method");
    366:   fn->method = meth;
    367:   return(0);
    368: }

    370: /*@
    371:    FNGetMethod - Gets the method currently used in the FN.

    373:    Not Collective

    375:    Input Parameter:
    376: .  fn - the math function context

    378:    Output Parameter:
    379: .  meth - identifier of the method

    381:    Level: intermediate

    383: .seealso: FNSetMethod()
    384: @*/
    385: PetscErrorCode FNGetMethod(FN fn,PetscInt *meth)
    386: {
    390:   *meth = fn->method;
    391:   return(0);
    392: }

    394: /*@
    395:    FNSetParallel - Selects the mode of operation in parallel runs.

    397:    Logically Collective on FN

    399:    Input Parameter:
    400: +  fn    - the math function context
    401: -  pmode - the parallel mode

    403:    Options Database Key:
    404: .  -fn_parallel <mode> - Sets the parallel mode, either 'redundant' or 'synchronized'

    406:    Notes:
    407:    This is relevant only when the function is evaluated on a matrix, with
    408:    either FNEvaluateFunctionMat() or FNEvaluateFunctionMatVec().

    410:    In the 'redundant' parallel mode, all processes will make the computation
    411:    redundantly, starting from the same data, and producing the same result.
    412:    This result may be slightly different in the different processes if using a
    413:    multithreaded BLAS library, which may cause issues in ill-conditioned problems.

    415:    In the 'synchronized' parallel mode, only the first MPI process performs the
    416:    computation and then the computed matrix is broadcast to the other
    417:    processes in the communicator. This communication is done automatically at
    418:    the end of FNEvaluateFunctionMat() or FNEvaluateFunctionMatVec().

    420:    Level: advanced

    422: .seealso: FNEvaluateFunctionMat() or FNEvaluateFunctionMatVec(), FNGetParallel()
    423: @*/
    424: PetscErrorCode FNSetParallel(FN fn,FNParallelType pmode)
    425: {
    429:   fn->pmode = pmode;
    430:   return(0);
    431: }

    433: /*@
    434:    FNGetParallel - Gets the mode of operation in parallel runs.

    436:    Not Collective

    438:    Input Parameter:
    439: .  fn - the math function context

    441:    Output Parameter:
    442: .  pmode - the parallel mode

    444:    Level: advanced

    446: .seealso: FNSetParallel()
    447: @*/
    448: PetscErrorCode FNGetParallel(FN fn,FNParallelType *pmode)
    449: {
    453:   *pmode = fn->pmode;
    454:   return(0);
    455: }

    457: /*@
    458:    FNEvaluateFunction - Computes the value of the function f(x) for a given x.

    460:    Not collective

    462:    Input Parameters:
    463: +  fn - the math function context
    464: -  x  - the value where the function must be evaluated

    466:    Output Parameter:
    467: .  y  - the result of f(x)

    469:    Note:
    470:    Scaling factors are taken into account, so the actual function evaluation
    471:    will return beta*f(alpha*x).

    473:    Level: intermediate

    475: .seealso: FNEvaluateDerivative(), FNEvaluateFunctionMat(), FNSetScale()
    476: @*/
    477: PetscErrorCode FNEvaluateFunction(FN fn,PetscScalar x,PetscScalar *y)
    478: {
    480:   PetscScalar    xf,yf;

    486:   PetscLogEventBegin(FN_Evaluate,fn,0,0,0);
    487:   xf = fn->alpha*x;
    488:   (*fn->ops->evaluatefunction)(fn,xf,&yf);
    489:   *y = fn->beta*yf;
    490:   PetscLogEventEnd(FN_Evaluate,fn,0,0,0);
    491:   return(0);
    492: }

    494: /*@
    495:    FNEvaluateDerivative - Computes the value of the derivative f'(x) for a given x.

    497:    Not Collective

    499:    Input Parameters:
    500: +  fn - the math function context
    501: -  x  - the value where the derivative must be evaluated

    503:    Output Parameter:
    504: .  y  - the result of f'(x)

    506:    Note:
    507:    Scaling factors are taken into account, so the actual derivative evaluation will
    508:    return alpha*beta*f'(alpha*x).

    510:    Level: intermediate

    512: .seealso: FNEvaluateFunction()
    513: @*/
    514: PetscErrorCode FNEvaluateDerivative(FN fn,PetscScalar x,PetscScalar *y)
    515: {
    517:   PetscScalar    xf,yf;

    523:   PetscLogEventBegin(FN_Evaluate,fn,0,0,0);
    524:   xf = fn->alpha*x;
    525:   (*fn->ops->evaluatederivative)(fn,xf,&yf);
    526:   *y = fn->alpha*fn->beta*yf;
    527:   PetscLogEventEnd(FN_Evaluate,fn,0,0,0);
    528:   return(0);
    529: }

    531: static PetscErrorCode FNEvaluateFunctionMat_Sym_Private(FN fn,PetscScalar *As,PetscScalar *Bs,PetscInt m,PetscBool firstonly)
    532: {
    533: #if defined(PETSC_MISSING_LAPACK_SYEV) || defined(SLEPC_MISSING_LAPACK_LACPY)
    535:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"SYEV/LACPY - Lapack routines are unavailable");
    536: #else
    538:   PetscInt       i,j;
    539:   PetscBLASInt   n,k,ld,lwork,info;
    540:   PetscScalar    *Q,*W,*work,a,x,y,one=1.0,zero=0.0;
    541:   PetscReal      *eig,dummy;
    542: #if defined(PETSC_USE_COMPLEX)
    543:   PetscReal      *rwork,rdummy;
    544: #endif

    547:   PetscBLASIntCast(m,&n);
    548:   ld = n;
    549:   k = firstonly? 1: n;

    551:   /* workspace query and memory allocation */
    552:   lwork = -1;
    553: #if defined(PETSC_USE_COMPLEX)
    554:   PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","L",&n,As,&ld,&dummy,&a,&lwork,&rdummy,&info));
    555:   PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork);
    556:   PetscMalloc5(m,&eig,m*m,&Q,m*k,&W,lwork,&work,PetscMax(1,3*m-2),&rwork);
    557: #else
    558:   PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","L",&n,As,&ld,&dummy,&a,&lwork,&info));
    559:   PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork);
    560:   PetscMalloc4(m,&eig,m*m,&Q,m*k,&W,lwork,&work);
    561: #endif

    563:   /* compute eigendecomposition */
    564:   PetscStackCallBLAS("LAPACKlacpy",LAPACKlacpy_("L",&n,&n,As,&ld,Q,&ld));
    565: #if defined(PETSC_USE_COMPLEX)
    566:   PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","L",&n,Q,&ld,eig,work,&lwork,rwork,&info));
    567: #else
    568:   PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","L",&n,Q,&ld,eig,work,&lwork,&info));
    569: #endif
    570:   SlepcCheckLapackInfo("syev",info);

    572:   /* W = f(Lambda)*Q' */
    573:   for (i=0;i<n;i++) {
    574:     x = fn->alpha*eig[i];
    575:     (*fn->ops->evaluatefunction)(fn,x,&y);  /* y = f(x) */
    576:     for (j=0;j<k;j++) W[i+j*ld] = PetscConj(Q[j+i*ld])*fn->beta*y;
    577:   }
    578:   /* Bs = Q*W */
    579:   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&k,&n,&one,Q,&ld,W,&ld,&zero,Bs,&ld));
    580: #if defined(PETSC_USE_COMPLEX)
    581:   PetscFree5(eig,Q,W,work,rwork);
    582: #else
    583:   PetscFree4(eig,Q,W,work);
    584: #endif
    585:   PetscLogFlops(9.0*n*n*n+2.0*n*n*n);
    586:   return(0);
    587: #endif
    588: }

    590: /*
    591:    FNEvaluateFunctionMat_Sym_Default - given a symmetric matrix A,
    592:    compute the matrix function as f(A)=Q*f(D)*Q' where the spectral
    593:    decomposition of A is A=Q*D*Q'
    594: */
    595: static PetscErrorCode FNEvaluateFunctionMat_Sym_Default(FN fn,Mat A,Mat B)
    596: {
    598:   PetscInt       m;
    599:   PetscScalar    *As,*Bs;

    602:   MatDenseGetArray(A,&As);
    603:   MatDenseGetArray(B,&Bs);
    604:   MatGetSize(A,&m,NULL);
    605:   FNEvaluateFunctionMat_Sym_Private(fn,As,Bs,m,PETSC_FALSE);
    606:   MatDenseRestoreArray(A,&As);
    607:   MatDenseRestoreArray(B,&Bs);
    608:   return(0);
    609: }

    611: PetscErrorCode FNEvaluateFunctionMat_Private(FN fn,Mat A,Mat B,PetscBool sync)
    612: {
    614:   PetscBool      set,flg,symm=PETSC_FALSE;
    615:   PetscInt       m,n;
    616:   PetscMPIInt    size,rank;
    617:   PetscScalar    *pF;
    618:   Mat            M,F;

    621:   /* destination matrix */
    622:   F = B?B:A;

    624:   /* check symmetry of A */
    625:   MatIsHermitianKnown(A,&set,&flg);
    626:   symm = set? flg: PETSC_FALSE;

    628:   MPI_Comm_size(PetscObjectComm((PetscObject)fn),&size);
    629:   MPI_Comm_rank(PetscObjectComm((PetscObject)fn),&rank);
    630:   if (size==1 || fn->pmode==FN_PARALLEL_REDUNDANT || (fn->pmode==FN_PARALLEL_SYNCHRONIZED && !rank)) {
    631:
    632:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    633:     if (symm && !fn->method) {  /* prefer diagonalization */
    634:       PetscInfo(fn,"Computing matrix function via diagonalization\n");
    635:       FNEvaluateFunctionMat_Sym_Default(fn,A,F);
    636:     } else {
    637:       /* scale argument */
    638:       if (fn->alpha!=(PetscScalar)1.0) {
    639:         FN_AllocateWorkMat(fn,A,&M);
    640:         MatScale(M,fn->alpha);
    641:       } else M = A;
    642:       if (fn->ops->evaluatefunctionmat[fn->method]) {
    643:         (*fn->ops->evaluatefunctionmat[fn->method])(fn,M,F);
    644:       } else if (!fn->method) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_SUP,"Matrix functions not implemented in this FN type");
    645:       else SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"The specified method number does not exist for this FN type");
    646:       if (fn->alpha!=(PetscScalar)1.0) {
    647:         FN_FreeWorkMat(fn,&M);
    648:       }
    649:       /* scale result */
    650:       MatScale(F,fn->beta);
    651:     }
    652:     PetscFPTrapPop();
    653:   }
    654:   if (size>1 && fn->pmode==FN_PARALLEL_SYNCHRONIZED && sync) {  /* synchronize */
    655:     MatGetSize(A,&m,&n);
    656:     MatDenseGetArray(F,&pF);
    657:     MPI_Bcast(pF,n*n,MPIU_SCALAR,0,PetscObjectComm((PetscObject)fn));
    658:     MatDenseRestoreArray(F,&pF);
    659:   }
    660:   return(0);
    661: }

    663: /*@
    664:    FNEvaluateFunctionMat - Computes the value of the function f(A) for a given
    665:    matrix A, where the result is also a matrix.

    667:    Logically Collective on FN

    669:    Input Parameters:
    670: +  fn - the math function context
    671: -  A  - matrix on which the function must be evaluated

    673:    Output Parameter:
    674: .  B  - (optional) matrix resulting from evaluating f(A)

    676:    Notes:
    677:    Matrix A must be a square sequential dense Mat, with all entries equal on
    678:    all processes (otherwise each process will compute different results).
    679:    If matrix B is provided, it must also be a square sequential dense Mat, and
    680:    both matrices must have the same dimensions. If B is NULL (or B=A) then the
    681:    function will perform an in-place computation, overwriting A with f(A).

    683:    If A is known to be real symmetric or complex Hermitian then it is
    684:    recommended to set the appropriate flag with MatSetOption(), because
    685:    symmetry can sometimes be exploited by the algorithm.

    687:    Scaling factors are taken into account, so the actual function evaluation
    688:    will return beta*f(alpha*A).

    690:    Level: advanced

    692: .seealso: FNEvaluateFunction(), FNEvaluateFunctionMatVec(), FNSetMethod()
    693: @*/
    694: PetscErrorCode FNEvaluateFunctionMat(FN fn,Mat A,Mat B)
    695: {
    697:   PetscBool      match,inplace=PETSC_FALSE;
    698:   PetscInt       m,n,n1;

    705:   if (B) {
    708:   } else inplace = PETSC_TRUE;
    709:   PetscObjectTypeCompare((PetscObject)A,MATSEQDENSE,&match);
    710:   if (!match) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_SUP,"Mat A must be of type seqdense");
    711:   MatGetSize(A,&m,&n);
    712:   if (m!=n) SETERRQ2(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_SIZ,"Mat A is not square (has %D rows, %D cols)",m,n);
    713:   if (!inplace) {
    714:     PetscObjectTypeCompare((PetscObject)B,MATSEQDENSE,&match);
    715:     if (!match) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_SUP,"Mat B must be of type seqdense");
    716:     n1 = n;
    717:     MatGetSize(B,&m,&n);
    718:     if (m!=n) SETERRQ2(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_SIZ,"Mat B is not square (has %D rows, %D cols)",m,n);
    719:     if (n1!=n) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_SIZ,"Matrices A and B must have the same dimension");
    720:   }

    722:   /* evaluate matrix function */
    723:   PetscLogEventBegin(FN_Evaluate,fn,0,0,0);
    724:   FNEvaluateFunctionMat_Private(fn,A,B,PETSC_TRUE);
    725:   PetscLogEventEnd(FN_Evaluate,fn,0,0,0);
    726:   return(0);
    727: }

    729: /*
    730:    FNEvaluateFunctionMatVec_Default - computes the full matrix f(A)
    731:    and then copies the first column.
    732: */
    733: static PetscErrorCode FNEvaluateFunctionMatVec_Default(FN fn,Mat A,Vec v)
    734: {
    736:   Mat            F;

    739:   FN_AllocateWorkMat(fn,A,&F);
    740:   if (fn->ops->evaluatefunctionmat[fn->method]) {
    741:     (*fn->ops->evaluatefunctionmat[fn->method])(fn,A,F);
    742:   } else if (!fn->method) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_SUP,"Matrix functions not implemented in this FN type");
    743:   else SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"The specified method number does not exist for this FN type");
    744:   MatGetColumnVector(F,v,0);
    745:   FN_FreeWorkMat(fn,&F);
    746:   return(0);
    747: }

    749: /*
    750:    FNEvaluateFunctionMatVec_Sym_Default - given a symmetric matrix A,
    751:    compute the matrix function as f(A)=Q*f(D)*Q' where the spectral
    752:    decomposition of A is A=Q*D*Q'. Only the first column is computed.
    753: */
    754: static PetscErrorCode FNEvaluateFunctionMatVec_Sym_Default(FN fn,Mat A,Vec v)
    755: {
    757:   PetscInt       m;
    758:   PetscScalar    *As,*vs;

    761:   MatDenseGetArray(A,&As);
    762:   VecGetArray(v,&vs);
    763:   MatGetSize(A,&m,NULL);
    764:   FNEvaluateFunctionMat_Sym_Private(fn,As,vs,m,PETSC_TRUE);
    765:   MatDenseRestoreArray(A,&As);
    766:   VecRestoreArray(v,&vs);
    767:   return(0);
    768: }

    770: PetscErrorCode FNEvaluateFunctionMatVec_Private(FN fn,Mat A,Vec v,PetscBool sync)
    771: {
    773:   PetscBool      set,flg,symm=PETSC_FALSE;
    774:   PetscInt       m,n;
    775:   Mat            M;
    776:   PetscMPIInt    size,rank;
    777:   PetscScalar    *pv;

    780:   /* check symmetry of A */
    781:   MatIsHermitianKnown(A,&set,&flg);
    782:   symm = set? flg: PETSC_FALSE;

    784:   /* evaluate matrix function */
    785:   MPI_Comm_size(PetscObjectComm((PetscObject)fn),&size);
    786:   MPI_Comm_rank(PetscObjectComm((PetscObject)fn),&rank);
    787:   if (size==1 || fn->pmode==FN_PARALLEL_REDUNDANT || (fn->pmode==FN_PARALLEL_SYNCHRONIZED && !rank)) {
    788:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    789:     if (symm && !fn->method) {  /* prefer diagonalization */
    790:       PetscInfo(fn,"Computing matrix function via diagonalization\n");
    791:       FNEvaluateFunctionMatVec_Sym_Default(fn,A,v);
    792:     } else {
    793:       /* scale argument */
    794:       if (fn->alpha!=(PetscScalar)1.0) {
    795:         FN_AllocateWorkMat(fn,A,&M);
    796:         MatScale(M,fn->alpha);
    797:       } else M = A;
    798:       if (fn->ops->evaluatefunctionmatvec[fn->method]) {
    799:         (*fn->ops->evaluatefunctionmatvec[fn->method])(fn,M,v);
    800:       } else {
    801:         FNEvaluateFunctionMatVec_Default(fn,M,v);
    802:       }
    803:       if (fn->alpha!=(PetscScalar)1.0) {
    804:         FN_FreeWorkMat(fn,&M);
    805:       }
    806:       /* scale result */
    807:       VecScale(v,fn->beta);
    808:     }
    809:     PetscFPTrapPop();
    810:   }

    812:   /* synchronize */
    813:   if (size>1 && fn->pmode==FN_PARALLEL_SYNCHRONIZED && sync) {
    814:     MatGetSize(A,&m,&n);
    815:     VecGetArray(v,&pv);
    816:     MPI_Bcast(pv,n,MPIU_SCALAR,0,PetscObjectComm((PetscObject)fn));
    817:     VecRestoreArray(v,&pv);
    818:   }
    819:   return(0);
    820: }

    822: /*@
    823:    FNEvaluateFunctionMatVec - Computes the first column of the matrix f(A)
    824:    for a given matrix A.

    826:    Logically Collective on FN

    828:    Input Parameters:
    829: +  fn - the math function context
    830: -  A  - matrix on which the function must be evaluated

    832:    Output Parameter:
    833: .  v  - vector to hold the first column of f(A)

    835:    Notes:
    836:    This operation is similar to FNEvaluateFunctionMat() but returns only
    837:    the first column of f(A), hence saving computations in most cases.

    839:    Level: advanced

    841: .seealso: FNEvaluateFunction(), FNEvaluateFunctionMat(), FNSetMethod()
    842: @*/
    843: PetscErrorCode FNEvaluateFunctionMatVec(FN fn,Mat A,Vec v)
    844: {
    846:   PetscBool      match;
    847:   PetscInt       m,n;

    856:   PetscObjectTypeCompare((PetscObject)A,MATSEQDENSE,&match);
    857:   if (!match) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_SUP,"Mat A must be of type seqdense");
    858:   MatGetSize(A,&m,&n);
    859:   if (m!=n) SETERRQ2(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_SIZ,"Mat A is not square (has %D rows, %D cols)",m,n);
    860:   VecGetSize(v,&m);
    861:   if (m!=n) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_SIZ,"Matrix A and vector v must have the same size");
    862:   PetscLogEventBegin(FN_Evaluate,fn,0,0,0);
    863:   FNEvaluateFunctionMatVec_Private(fn,A,v,PETSC_TRUE);
    864:   PetscLogEventEnd(FN_Evaluate,fn,0,0,0);
    865:   return(0);
    866: }

    868: /*@
    869:    FNSetFromOptions - Sets FN options from the options database.

    871:    Collective on FN

    873:    Input Parameters:
    874: .  fn - the math function context

    876:    Notes:
    877:    To see all options, run your program with the -help option.

    879:    Level: beginner
    880: @*/
    881: PetscErrorCode FNSetFromOptions(FN fn)
    882: {
    884:   char           type[256];
    885:   PetscScalar    array[2];
    886:   PetscInt       k,meth;
    887:   PetscBool      flg;
    888:   FNParallelType pmode;

    892:   FNRegisterAll();
    893:   PetscObjectOptionsBegin((PetscObject)fn);
    894:     PetscOptionsFList("-fn_type","Math function type","FNSetType",FNList,(char*)(((PetscObject)fn)->type_name?((PetscObject)fn)->type_name:FNRATIONAL),type,256,&flg);
    895:     if (flg) {
    896:       FNSetType(fn,type);
    897:     } else if (!((PetscObject)fn)->type_name) {
    898:       FNSetType(fn,FNRATIONAL);
    899:     }

    901:     k = 2;
    902:     array[0] = 0.0; array[1] = 0.0;
    903:     PetscOptionsScalarArray("-fn_scale","Scale factors (one or two scalar values separated with a comma without spaces)","FNSetScale",array,&k,&flg);
    904:     if (flg) {
    905:       if (k<2) array[1] = 1.0;
    906:       FNSetScale(fn,array[0],array[1]);
    907:     }

    909:     PetscOptionsInt("-fn_method","Method to be used for computing matrix functions","FNSetMethod",fn->method,&meth,&flg);
    910:     if (flg) { FNSetMethod(fn,meth); }

    912:     PetscOptionsEnum("-fn_parallel","Operation mode in parallel runs","FNSetParallel",FNParallelTypes,(PetscEnum)fn->pmode,(PetscEnum*)&pmode,&flg);
    913:     if (flg) { FNSetParallel(fn,pmode); }

    915:     if (fn->ops->setfromoptions) {
    916:       (*fn->ops->setfromoptions)(PetscOptionsObject,fn);
    917:     }
    918:     PetscObjectProcessOptionsHandlers(PetscOptionsObject,(PetscObject)fn);
    919:   PetscOptionsEnd();
    920:   return(0);
    921: }

    923: /*@C
    924:    FNView - Prints the FN data structure.

    926:    Collective on FN

    928:    Input Parameters:
    929: +  fn - the math function context
    930: -  viewer - optional visualization context

    932:    Note:
    933:    The available visualization contexts include
    934: +     PETSC_VIEWER_STDOUT_SELF - standard output (default)
    935: -     PETSC_VIEWER_STDOUT_WORLD - synchronized standard
    936:          output where only the first processor opens
    937:          the file.  All other processors send their
    938:          data to the first processor to print.

    940:    The user can open an alternative visualization context with
    941:    PetscViewerASCIIOpen() - output to a specified file.

    943:    Level: beginner
    944: @*/
    945: PetscErrorCode FNView(FN fn,PetscViewer viewer)
    946: {
    947:   PetscBool      isascii;
    948:   PetscInt       tabs;
    950:   PetscMPIInt    size;

    954:   if (!viewer) viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)fn));
    957:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    958:   if (isascii) {
    959:     PetscViewerASCIIGetTab(viewer,&tabs);
    960:     PetscViewerASCIISetTab(viewer,((PetscObject)fn)->tablevel);
    961:     PetscObjectPrintClassNamePrefixType((PetscObject)fn,viewer);
    962:     MPI_Comm_size(PetscObjectComm((PetscObject)fn),&size);
    963:     if (size>1) {
    964:       PetscViewerASCIIPrintf(viewer,"  parallel operation mode: %s\n",FNParallelTypes[fn->pmode]);
    965:     }
    966:     if (fn->ops->view) {
    967:       PetscViewerASCIIPushTab(viewer);
    968:       (*fn->ops->view)(fn,viewer);
    969:       PetscViewerASCIIPopTab(viewer);
    970:     }
    971:     PetscViewerASCIISetTab(viewer,tabs);
    972:   }
    973:   return(0);
    974: }

    976: /*@
    977:    FNDuplicate - Duplicates a math function, copying all parameters, possibly with a
    978:    different communicator.

    980:    Collective on FN

    982:    Input Parameters:
    983: +  fn   - the math function context
    984: -  comm - MPI communicator

    986:    Output Parameter:
    987: .  newfn - location to put the new FN context

    989:    Note:
    990:    In order to use the same MPI communicator as in the original object,
    991:    use PetscObjectComm((PetscObject)fn).

    993:    Level: developer

    995: .seealso: FNCreate()
    996: @*/
    997: PetscErrorCode FNDuplicate(FN fn,MPI_Comm comm,FN *newfn)
    998: {
    1000:   FNType         type;
    1001:   PetscScalar    alpha,beta;
    1002:   PetscInt       meth;
    1003:   FNParallelType ptype;

    1009:   FNCreate(comm,newfn);
    1010:   FNGetType(fn,&type);
    1011:   FNSetType(*newfn,type);
    1012:   FNGetScale(fn,&alpha,&beta);
    1013:   FNSetScale(*newfn,alpha,beta);
    1014:   FNGetMethod(fn,&meth);
    1015:   FNSetMethod(*newfn,meth);
    1016:   FNGetParallel(fn,&ptype);
    1017:   FNSetParallel(*newfn,ptype);
    1018:   if (fn->ops->duplicate) {
    1019:     (*fn->ops->duplicate)(fn,comm,newfn);
    1020:   }
    1021:   return(0);
    1022: }

    1024: /*@
    1025:    FNDestroy - Destroys FN context that was created with FNCreate().

    1027:    Collective on FN

    1029:    Input Parameter:
    1030: .  fn - the math function context

    1032:    Level: beginner

    1034: .seealso: FNCreate()
    1035: @*/
    1036: PetscErrorCode FNDestroy(FN *fn)
    1037: {
    1039:   PetscInt       i;

    1042:   if (!*fn) return(0);
    1044:   if (--((PetscObject)(*fn))->refct > 0) { *fn = 0; return(0); }
    1045:   if ((*fn)->ops->destroy) { (*(*fn)->ops->destroy)(*fn); }
    1046:   for (i=0;i<(*fn)->nw;i++) {
    1047:     MatDestroy(&(*fn)->W[i]);
    1048:   }
    1049:   PetscHeaderDestroy(fn);
    1050:   return(0);
    1051: }

    1053: /*@C
    1054:    FNRegister - Adds a mathematical function to the FN package.

    1056:    Not collective

    1058:    Input Parameters:
    1059: +  name - name of a new user-defined FN
    1060: -  function - routine to create context

    1062:    Notes:
    1063:    FNRegister() may be called multiple times to add several user-defined functions.

    1065:    Level: advanced

    1067: .seealso: FNRegisterAll()
    1068: @*/
    1069: PetscErrorCode FNRegister(const char *name,PetscErrorCode (*function)(FN))
    1070: {

    1074:   FNInitializePackage();
    1075:   PetscFunctionListAdd(&FNList,name,function);
    1076:   return(0);
    1077: }