Date: 2022-11-02T11:46:05+00:00

Actual source code: fnrational.c
slepc-3.18.1 2022-11-02
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, 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:    Rational function  r(x) = p(x)/q(x), where p(x) and q(x) are polynomials
     12: */

     14: #include <slepc/private/fnimpl.h>

     16: typedef struct {
     17:   PetscScalar *pcoeff;    /* numerator coefficients */
     18:   PetscInt    np;         /* length of array pcoeff, p(x) has degree np-1 */
     19:   PetscScalar *qcoeff;    /* denominator coefficients */
     20:   PetscInt    nq;         /* length of array qcoeff, q(x) has degree nq-1 */
     21: } FN_RATIONAL;

     23: PetscErrorCode FNEvaluateFunction_Rational(FN fn,PetscScalar x,PetscScalar *y)
     24: {
     25:   FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data;
     26:   PetscInt    i;
     27:   PetscScalar p,q;

     29:   if (!ctx->np) p = 1.0;
     30:   else {
     31:     p = ctx->pcoeff[0];
     32:     for (i=1;i<ctx->np;i++)
     33:       p = ctx->pcoeff[i]+x*p;
     34:   }
     35:   if (!ctx->nq) *y = p;
     36:   else {
     37:     q = ctx->qcoeff[0];
     38:     for (i=1;i<ctx->nq;i++)
     39:       q = ctx->qcoeff[i]+x*q;
     41:     *y = p/q;
     42:   }
     43:   return 0;
     44: }

     46: /*
     47:    Horner evaluation of P=p(A)
     48:    d = degree of polynomial;   coeff = coefficients of polynomial;    W = workspace
     49: */
     50: static PetscErrorCode EvaluatePoly(Mat A,Mat P,Mat W,PetscInt d,PetscScalar *coeff)
     51: {
     52:   PetscInt j;

     54:   MatZeroEntries(P);
     55:   if (!d) MatShift(P,1.0);
     56:   else {
     57:     MatShift(P,coeff[0]);
     58:     for (j=1;j<d;j++) {
     59:       MatMatMult(P,A,MAT_REUSE_MATRIX,PETSC_DEFAULT,&W);
     60:       MatCopy(W,P,SAME_NONZERO_PATTERN);
     61:       MatShift(P,coeff[j]);
     62:     }
     63:   }
     64:   return 0;
     65: }

     67: PetscErrorCode FNEvaluateFunctionMat_Rational(FN fn,Mat A,Mat B)
     68: {
     69:   FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data;
     70:   Mat         P,Q,W,F;
     71:   PetscBool   iscuda;

     73:   if (A==B) MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&P);
     74:   else P = B;
     75:   MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&W);

     77:   EvaluatePoly(A,P,W,ctx->np,ctx->pcoeff);
     78:   if (ctx->nq) {
     79:     MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&Q);
     80:     EvaluatePoly(A,Q,W,ctx->nq,ctx->qcoeff);
     81:     PetscObjectTypeCompare((PetscObject)A,MATSEQDENSECUDA,&iscuda);
     82:     MatGetFactor(Q,iscuda?MATSOLVERCUDA:MATSOLVERPETSC,MAT_FACTOR_LU,&F);
     83:     MatLUFactorSymbolic(F,Q,NULL,NULL,NULL);
     84:     MatLUFactorNumeric(F,Q,NULL);
     85:     MatMatSolve(F,P,P);
     86:     MatDestroy(&F);
     87:     MatDestroy(&Q);
     88:   }

     90:   if (A==B) {
     91:     MatCopy(P,B,SAME_NONZERO_PATTERN);
     92:     MatDestroy(&P);
     93:   }
     94:   MatDestroy(&W);
     95:   return 0;
     96: }

     98: PetscErrorCode FNEvaluateFunctionMatVec_Rational(FN fn,Mat A,Vec v)
     99: {
    100:   FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data;
    101:   Mat         P,Q,W,F;
    102:   Vec         b;
    103:   PetscBool   iscuda;

    105:   MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&P);
    106:   MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&W);

    108:   EvaluatePoly(A,P,W,ctx->np,ctx->pcoeff);
    109:   if (ctx->nq) {
    110:     MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&Q);
    111:     EvaluatePoly(A,Q,W,ctx->nq,ctx->qcoeff);
    112:     PetscObjectTypeCompare((PetscObject)A,MATSEQDENSECUDA,&iscuda);
    113:     MatGetFactor(Q,iscuda?MATSOLVERCUDA:MATSOLVERPETSC,MAT_FACTOR_LU,&F);
    114:     MatLUFactorSymbolic(F,Q,NULL,NULL,NULL);
    115:     MatLUFactorNumeric(F,Q,NULL);
    116:     MatCreateVecs(P,&b,NULL);
    117:     MatGetColumnVector(P,b,0);
    118:     MatSolve(F,b,v);
    119:     VecDestroy(&b);
    120:     MatDestroy(&F);
    121:     MatDestroy(&Q);
    122:   } else MatGetColumnVector(P,v,0);

    124:   MatDestroy(&P);
    125:   MatDestroy(&W);
    126:   return 0;
    127: }

    129: PetscErrorCode FNEvaluateDerivative_Rational(FN fn,PetscScalar x,PetscScalar *yp)
    130: {
    131:   FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data;
    132:   PetscInt    i;
    133:   PetscScalar p,q,pp,qp;

    135:   if (!ctx->np) {
    136:     p = 1.0;
    137:     pp = 0.0;
    138:   } else {
    139:     p = ctx->pcoeff[0];
    140:     pp = 0.0;
    141:     for (i=1;i<ctx->np;i++) {
    142:       pp = p+x*pp;
    143:       p = ctx->pcoeff[i]+x*p;
    144:     }
    145:   }
    146:   if (!ctx->nq) *yp = pp;
    147:   else {
    148:     q = ctx->qcoeff[0];
    149:     qp = 0.0;
    150:     for (i=1;i<ctx->nq;i++) {
    151:       qp = q+x*qp;
    152:       q = ctx->qcoeff[i]+x*q;
    153:     }
    155:     *yp = (pp*q-p*qp)/(q*q);
    156:   }
    157:   return 0;
    158: }

    160: PetscErrorCode FNView_Rational(FN fn,PetscViewer viewer)
    161: {
    162:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    163:   PetscBool      isascii;
    164:   PetscInt       i;
    165:   char           str[50];

    167:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    168:   if (isascii) {
    169:     if (fn->alpha!=(PetscScalar)1.0 || fn->beta!=(PetscScalar)1.0) {
    170:       SlepcSNPrintfScalar(str,sizeof(str),fn->alpha,PETSC_FALSE);
    171:       PetscViewerASCIIPrintf(viewer,"  scale factors: alpha=%s,",str);
    172:       PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
    173:       SlepcSNPrintfScalar(str,sizeof(str),fn->beta,PETSC_FALSE);
    174:       PetscViewerASCIIPrintf(viewer," beta=%s\n",str);
    175:       PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
    176:     }
    177:     if (!ctx->nq) {
    178:       if (!ctx->np) PetscViewerASCIIPrintf(viewer,"  constant: 1.0\n");
    179:       else if (ctx->np==1) {
    180:         SlepcSNPrintfScalar(str,sizeof(str),ctx->pcoeff[0],PETSC_FALSE);
    181:         PetscViewerASCIIPrintf(viewer,"  constant: %s\n",str);
    182:       } else {
    183:         PetscViewerASCIIPrintf(viewer,"  polynomial: ");
    184:         PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
    185:         for (i=0;i<ctx->np-1;i++) {
    186:           SlepcSNPrintfScalar(str,sizeof(str),ctx->pcoeff[i],PETSC_TRUE);
    187:           PetscViewerASCIIPrintf(viewer,"%s*x^%1" PetscInt_FMT,str,ctx->np-i-1);
    188:         }
    189:         SlepcSNPrintfScalar(str,sizeof(str),ctx->pcoeff[ctx->np-1],PETSC_TRUE);
    190:         PetscViewerASCIIPrintf(viewer,"%s\n",str);
    191:         PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
    192:       }
    193:     } else if (!ctx->np) {
    194:       PetscViewerASCIIPrintf(viewer,"  inverse polynomial: 1 / (");
    195:       PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
    196:       for (i=0;i<ctx->nq-1;i++) {
    197:         SlepcSNPrintfScalar(str,sizeof(str),ctx->qcoeff[i],PETSC_TRUE);
    198:         PetscViewerASCIIPrintf(viewer,"%s*x^%1" PetscInt_FMT,str,ctx->nq-i-1);
    199:       }
    200:       SlepcSNPrintfScalar(str,sizeof(str),ctx->qcoeff[ctx->nq-1],PETSC_TRUE);
    201:       PetscViewerASCIIPrintf(viewer,"%s)\n",str);
    202:       PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
    203:     } else {
    204:       PetscViewerASCIIPrintf(viewer,"  rational function: (");
    205:       PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
    206:       for (i=0;i<ctx->np-1;i++) {
    207:         SlepcSNPrintfScalar(str,sizeof(str),ctx->pcoeff[i],PETSC_TRUE);
    208:         PetscViewerASCIIPrintf(viewer,"%s*x^%1" PetscInt_FMT,str,ctx->np-i-1);
    209:       }
    210:       SlepcSNPrintfScalar(str,sizeof(str),ctx->pcoeff[ctx->np-1],PETSC_TRUE);
    211:       PetscViewerASCIIPrintf(viewer,"%s) / (",str);
    212:       for (i=0;i<ctx->nq-1;i++) {
    213:         SlepcSNPrintfScalar(str,sizeof(str),ctx->qcoeff[i],PETSC_TRUE);
    214:         PetscViewerASCIIPrintf(viewer,"%s*x^%1" PetscInt_FMT,str,ctx->nq-i-1);
    215:       }
    216:       SlepcSNPrintfScalar(str,sizeof(str),ctx->qcoeff[ctx->nq-1],PETSC_TRUE);
    217:       PetscViewerASCIIPrintf(viewer,"%s)\n",str);
    218:       PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
    219:     }
    220:   }
    221:   return 0;
    222: }

    224: static PetscErrorCode FNRationalSetNumerator_Rational(FN fn,PetscInt np,PetscScalar *pcoeff)
    225: {
    226:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    227:   PetscInt       i;

    230:   ctx->np = np;
    231:   PetscFree(ctx->pcoeff);
    232:   if (np) {
    233:     PetscMalloc1(np,&ctx->pcoeff);
    234:     for (i=0;i<np;i++) ctx->pcoeff[i] = pcoeff[i];
    235:   }
    236:   return 0;
    237: }

    239: /*@C
    240:    FNRationalSetNumerator - Sets the parameters defining the numerator of the
    241:    rational function.

    243:    Logically Collective on fn

    245:    Input Parameters:
    246: +  fn     - the math function context
    247: .  np     - number of coefficients
    248: -  pcoeff - coefficients (array of scalar values)

    250:    Notes:
    251:    Let the rational function r(x) = p(x)/q(x), where p(x) and q(x) are polynomials.
    252:    This function provides the coefficients of the numerator p(x).
    253:    Hence, p(x) is of degree np-1.
    254:    If np is zero, then the numerator is assumed to be p(x)=1.

    256:    In polynomials, high order coefficients are stored in the first positions
    257:    of the array, e.g. to represent x^2-3 use {1,0,-3}.

    259:    Level: intermediate

    261: .seealso: FNRationalSetDenominator(), FNRationalGetNumerator()
    262: @*/
    263: PetscErrorCode FNRationalSetNumerator(FN fn,PetscInt np,PetscScalar *pcoeff)
    264: {
    268:   PetscTryMethod(fn,"FNRationalSetNumerator_C",(FN,PetscInt,PetscScalar*),(fn,np,pcoeff));
    269:   return 0;
    270: }

    272: static PetscErrorCode FNRationalGetNumerator_Rational(FN fn,PetscInt *np,PetscScalar *pcoeff[])
    273: {
    274:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    275:   PetscInt       i;

    277:   if (np) *np = ctx->np;
    278:   if (pcoeff) {
    279:     if (!ctx->np) *pcoeff = NULL;
    280:     else {
    281:       PetscMalloc1(ctx->np,pcoeff);
    282:       for (i=0;i<ctx->np;i++) (*pcoeff)[i] = ctx->pcoeff[i];
    283:     }
    284:   }
    285:   return 0;
    286: }

    288: /*@C
    289:    FNRationalGetNumerator - Gets the parameters that define the numerator of the
    290:    rational function.

    292:    Not Collective

    294:    Input Parameter:
    295: .  fn     - the math function context

    297:    Output Parameters:
    298: +  np     - number of coefficients
    299: -  pcoeff - coefficients (array of scalar values, length nq)

    301:    Notes:
    302:    The values passed by user with FNRationalSetNumerator() are returned (or null
    303:    pointers otherwise).
    304:    The pcoeff array should be freed by the user when no longer needed.

    306:    Level: intermediate

    308: .seealso: FNRationalSetNumerator()
    309: @*/
    310: PetscErrorCode FNRationalGetNumerator(FN fn,PetscInt *np,PetscScalar *pcoeff[])
    311: {
    313:   PetscUseMethod(fn,"FNRationalGetNumerator_C",(FN,PetscInt*,PetscScalar**),(fn,np,pcoeff));
    314:   return 0;
    315: }

    317: static PetscErrorCode FNRationalSetDenominator_Rational(FN fn,PetscInt nq,PetscScalar *qcoeff)
    318: {
    319:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    320:   PetscInt       i;

    323:   ctx->nq = nq;
    324:   PetscFree(ctx->qcoeff);
    325:   if (nq) {
    326:     PetscMalloc1(nq,&ctx->qcoeff);
    327:     for (i=0;i<nq;i++) ctx->qcoeff[i] = qcoeff[i];
    328:   }
    329:   return 0;
    330: }

    332: /*@C
    333:    FNRationalSetDenominator - Sets the parameters defining the denominator of the
    334:    rational function.

    336:    Logically Collective on fn

    338:    Input Parameters:
    339: +  fn     - the math function context
    340: .  nq     - number of coefficients
    341: -  qcoeff - coefficients (array of scalar values)

    343:    Notes:
    344:    Let the rational function r(x) = p(x)/q(x), where p(x) and q(x) are polynomials.
    345:    This function provides the coefficients of the denominator q(x).
    346:    Hence, q(x) is of degree nq-1.
    347:    If nq is zero, then the function is assumed to be polynomial, r(x) = p(x).

    349:    In polynomials, high order coefficients are stored in the first positions
    350:    of the array, e.g. to represent x^2-3 use {1,0,-3}.

    352:    Level: intermediate

    354: .seealso: FNRationalSetNumerator(), FNRationalGetDenominator()
    355: @*/
    356: PetscErrorCode FNRationalSetDenominator(FN fn,PetscInt nq,PetscScalar *qcoeff)
    357: {
    361:   PetscTryMethod(fn,"FNRationalSetDenominator_C",(FN,PetscInt,PetscScalar*),(fn,nq,qcoeff));
    362:   return 0;
    363: }

    365: static PetscErrorCode FNRationalGetDenominator_Rational(FN fn,PetscInt *nq,PetscScalar *qcoeff[])
    366: {
    367:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    368:   PetscInt       i;

    370:   if (nq) *nq = ctx->nq;
    371:   if (qcoeff) {
    372:     if (!ctx->nq) *qcoeff = NULL;
    373:     else {
    374:       PetscMalloc1(ctx->nq,qcoeff);
    375:       for (i=0;i<ctx->nq;i++) (*qcoeff)[i] = ctx->qcoeff[i];
    376:     }
    377:   }
    378:   return 0;
    379: }

    381: /*@C
    382:    FNRationalGetDenominator - Gets the parameters that define the denominator of the
    383:    rational function.

    385:    Not Collective

    387:    Input Parameter:
    388: .  fn     - the math function context

    390:    Output Parameters:
    391: +  nq     - number of coefficients
    392: -  qcoeff - coefficients (array of scalar values, length nq)

    394:    Notes:
    395:    The values passed by user with FNRationalSetDenominator() are returned (or a null
    396:    pointer otherwise).
    397:    The qcoeff array should be freed by the user when no longer needed.

    399:    Level: intermediate

    401: .seealso: FNRationalSetDenominator()
    402: @*/
    403: PetscErrorCode FNRationalGetDenominator(FN fn,PetscInt *nq,PetscScalar *qcoeff[])
    404: {
    406:   PetscUseMethod(fn,"FNRationalGetDenominator_C",(FN,PetscInt*,PetscScalar**),(fn,nq,qcoeff));
    407:   return 0;
    408: }

    410: PetscErrorCode FNSetFromOptions_Rational(FN fn,PetscOptionItems *PetscOptionsObject)
    411: {
    412: #define PARMAX 10
    413:   PetscScalar    array[PARMAX];
    414:   PetscInt       i,k;
    415:   PetscBool      flg;

    417:   PetscOptionsHeadBegin(PetscOptionsObject,"FN Rational Options");

    419:     k = PARMAX;
    420:     for (i=0;i<k;i++) array[i] = 0;
    421:     PetscOptionsScalarArray("-fn_rational_numerator","Numerator coefficients (one or more scalar values separated with a comma without spaces)","FNRationalSetNumerator",array,&k,&flg);
    422:     if (flg) FNRationalSetNumerator(fn,k,array);

    424:     k = PARMAX;
    425:     for (i=0;i<k;i++) array[i] = 0;
    426:     PetscOptionsScalarArray("-fn_rational_denominator","Denominator coefficients (one or more scalar values separated with a comma without spaces)","FNRationalSetDenominator",array,&k,&flg);
    427:     if (flg) FNRationalSetDenominator(fn,k,array);

    429:   PetscOptionsHeadEnd();
    430:   return 0;
    431: }

    433: PetscErrorCode FNDuplicate_Rational(FN fn,MPI_Comm comm,FN *newfn)
    434: {
    435:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data,*ctx2 = (FN_RATIONAL*)(*newfn)->data;
    436:   PetscInt       i;

    438:   ctx2->np = ctx->np;
    439:   if (ctx->np) {
    440:     PetscMalloc1(ctx->np,&ctx2->pcoeff);
    441:     for (i=0;i<ctx->np;i++) ctx2->pcoeff[i] = ctx->pcoeff[i];
    442:   }
    443:   ctx2->nq = ctx->nq;
    444:   if (ctx->nq) {
    445:     PetscMalloc1(ctx->nq,&ctx2->qcoeff);
    446:     for (i=0;i<ctx->nq;i++) ctx2->qcoeff[i] = ctx->qcoeff[i];
    447:   }
    448:   return 0;
    449: }

    451: PetscErrorCode FNDestroy_Rational(FN fn)
    452: {
    453:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;

    455:   PetscFree(ctx->pcoeff);
    456:   PetscFree(ctx->qcoeff);
    457:   PetscFree(fn->data);
    458:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalSetNumerator_C",NULL);
    459:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalGetNumerator_C",NULL);
    460:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalSetDenominator_C",NULL);
    461:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalGetDenominator_C",NULL);
    462:   return 0;
    463: }

    465: SLEPC_EXTERN PetscErrorCode FNCreate_Rational(FN fn)
    466: {
    467:   FN_RATIONAL    *ctx;

    469:   PetscNew(&ctx);
    470:   fn->data = (void*)ctx;

    472:   fn->ops->evaluatefunction          = FNEvaluateFunction_Rational;
    473:   fn->ops->evaluatederivative        = FNEvaluateDerivative_Rational;
    474:   fn->ops->evaluatefunctionmat[0]    = FNEvaluateFunctionMat_Rational;
    475:   fn->ops->evaluatefunctionmatvec[0] = FNEvaluateFunctionMatVec_Rational;
    476: #if defined(PETSC_HAVE_CUDA)
    477:   fn->ops->evaluatefunctionmatcuda[0]    = FNEvaluateFunctionMat_Rational;
    478:   fn->ops->evaluatefunctionmatveccuda[0] = FNEvaluateFunctionMatVec_Rational;
    479: #endif
    480:   fn->ops->setfromoptions            = FNSetFromOptions_Rational;
    481:   fn->ops->view                      = FNView_Rational;
    482:   fn->ops->duplicate                 = FNDuplicate_Rational;
    483:   fn->ops->destroy                   = FNDestroy_Rational;
    484:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalSetNumerator_C",FNRationalSetNumerator_Rational);
    485:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalGetNumerator_C",FNRationalGetNumerator_Rational);
    486:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalSetDenominator_C",FNRationalSetDenominator_Rational);
    487:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalGetDenominator_C",FNRationalGetDenominator_Rational);
    488:   return 0;
    489: }