Date: 2015-09-03T15:03:50+00:00

Actual source code: fnrational.c
slepc-3.6.1 2015-09-03
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      1: /*
      2:    Rational function  r(x) = p(x)/q(x), where p(x) and q(x) are polynomials

      4:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      5:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      6:    Copyright (c) 2002-2015, Universitat Politecnica de Valencia, Spain

      8:    This file is part of SLEPc.

     10:    SLEPc is free software: you can redistribute it and/or modify it under  the
     11:    terms of version 3 of the GNU Lesser General Public License as published by
     12:    the Free Software Foundation.

     14:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     15:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     16:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     17:    more details.

     19:    You  should have received a copy of the GNU Lesser General  Public  License
     20:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     21:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     22: */

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

     27: typedef struct {
     28:   PetscScalar *pcoeff;    /* numerator coefficients */
     29:   PetscInt    np;         /* length of array pcoeff, p(x) has degree np-1 */
     30:   PetscScalar *qcoeff;    /* denominator coefficients */
     31:   PetscInt    nq;         /* length of array qcoeff, q(x) has degree nq-1 */
     32: } FN_RATIONAL;

     36: PetscErrorCode FNEvaluateFunction_Rational(FN fn,PetscScalar x,PetscScalar *y)
     37: {
     38:   FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data;
     39:   PetscInt    i;
     40:   PetscScalar p,q;

     43:   if (!ctx->np) p = 1.0;
     44:   else {
     45:     p = ctx->pcoeff[0];
     46:     for (i=1;i<ctx->np;i++)
     47:       p = ctx->pcoeff[i]+x*p;
     48:   }
     49:   if (!ctx->nq) *y = p;
     50:   else {
     51:     q = ctx->qcoeff[0];
     52:     for (i=1;i<ctx->nq;i++)
     53:       q = ctx->qcoeff[i]+x*q;
     54:     *y = p/q;
     55:   }
     56:   return(0);
     57: }

     61: PetscErrorCode FNEvaluateFunctionMat_Rational(FN fn,Mat A,Mat B)
     62: {
     63: #if defined(PETSC_MISSING_LAPACK_GESV)
     65:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GESV - Lapack routines are unavailable");
     66: #else
     68:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
     69:   PetscBLASInt   n,ld,*ipiv,info;
     70:   PetscInt       i,j,m;
     71:   PetscScalar    *Aa,*Ba,*W,*P,*Q,one=1.0,zero=0.0;

     74:   MatDenseGetArray(A,&Aa);
     75:   MatDenseGetArray(B,&Ba);
     76:   MatGetSize(A,&m,NULL);
     77:   PetscBLASIntCast(m,&n);
     78:   ld  = n;
     79:   P   = Ba;
     80:   PetscMalloc3(m*m,&Q,m*m,&W,ld,&ipiv);
     81:   PetscMemzero(P,m*m*sizeof(PetscScalar));
     82:   if (!ctx->np) {
     83:     for (i=0;i<m;i++) P[i+i*ld] = 1.0;
     84:   } else {
     85:     for (i=0;i<m;i++) P[i+i*ld] = ctx->pcoeff[0];
     86:     for (j=1;j<ctx->np;j++) {
     87:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,P,&ld,Aa,&ld,&zero,W,&ld));
     88:       PetscMemcpy(P,W,m*m*sizeof(PetscScalar));
     89:       for (i=0;i<m;i++) P[i+i*ld] += ctx->pcoeff[j];
     90:     }
     91:   }
     92:   if (ctx->nq) {
     93:     PetscMemzero(Q,m*m*sizeof(PetscScalar));
     94:     for (i=0;i<m;i++) Q[i+i*ld] = ctx->qcoeff[0];
     95:     for (j=1;j<ctx->nq;j++) {
     96:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,Q,&ld,Aa,&ld,&zero,W,&ld));
     97:       PetscMemcpy(Q,W,m*m*sizeof(PetscScalar));
     98:       for (i=0;i<m;i++) Q[i+i*ld] += ctx->qcoeff[j];
     99:     }
    100:     PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&n,&n,Q,&ld,ipiv,P,&ld,&info));
    101:     if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGESV %d",info);
    102:   }
    103:   PetscFree3(Q,W,ipiv);
    104:   MatDenseRestoreArray(A,&Aa);
    105:   MatDenseRestoreArray(B,&Ba);
    106:   return(0);
    107: #endif
    108: }

    112: PetscErrorCode FNEvaluateDerivative_Rational(FN fn,PetscScalar x,PetscScalar *yp)
    113: {
    114:   FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data;
    115:   PetscInt    i;
    116:   PetscScalar p,q,pp,qp;

    119:   if (!ctx->np) {
    120:     p = 1.0;
    121:     pp = 0.0;
    122:   } else {
    123:     p = ctx->pcoeff[0];
    124:     pp = 0.0;
    125:     for (i=1;i<ctx->np;i++) {
    126:       pp = p+x*pp;
    127:       p = ctx->pcoeff[i]+x*p;
    128:     }
    129:   }
    130:   if (!ctx->nq) *yp = pp;
    131:   else {
    132:     q = ctx->qcoeff[0];
    133:     qp = 0.0;
    134:     for (i=1;i<ctx->nq;i++) {
    135:       qp = q+x*qp;
    136:       q = ctx->qcoeff[i]+x*q;
    137:     }
    138:     *yp = (pp*q-p*qp)/(q*q);
    139:   }
    140:   return(0);
    141: }

    145: PetscErrorCode FNView_Rational(FN fn,PetscViewer viewer)
    146: {
    148:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    149:   PetscBool      isascii;
    150:   PetscInt       i;
    151:   char           str[50];

    154:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    155:   if (isascii) {
    156:     if (fn->alpha!=(PetscScalar)1.0 || fn->beta!=(PetscScalar)1.0) {
    157:       SlepcSNPrintfScalar(str,50,fn->alpha,PETSC_FALSE);
    158:       PetscViewerASCIIPrintf(viewer,"  Scale factors: alpha=%s,",str);
    159:       SlepcSNPrintfScalar(str,50,fn->beta,PETSC_FALSE);
    160:       PetscViewerASCIIPrintf(viewer," beta=%s\n",str);
    161:     }
    162:     if (!ctx->nq) {
    163:       if (!ctx->np) {
    164:         PetscViewerASCIIPrintf(viewer,"  Constant: 1.0\n");
    165:       } else if (ctx->np==1) {
    166:         SlepcSNPrintfScalar(str,50,ctx->pcoeff[0],PETSC_FALSE);
    167:         PetscViewerASCIIPrintf(viewer,"  Constant: %s\n",str);
    168:       } else {
    169:         PetscViewerASCIIPrintf(viewer,"  Polynomial: ");
    170:         for (i=0;i<ctx->np-1;i++) {
    171:           SlepcSNPrintfScalar(str,50,ctx->pcoeff[i],PETSC_TRUE);
    172:           PetscViewerASCIIPrintf(viewer,"%s*x^%1D",str,ctx->np-i-1);
    173:         }
    174:         SlepcSNPrintfScalar(str,50,ctx->pcoeff[ctx->np-1],PETSC_TRUE);
    175:         PetscViewerASCIIPrintf(viewer,"%s\n",str);
    176:       }
    177:     } else if (!ctx->np) {
    178:       PetscViewerASCIIPrintf(viewer,"  Inverse polinomial: 1 / (");
    179:       for (i=0;i<ctx->nq-1;i++) {
    180:         SlepcSNPrintfScalar(str,50,ctx->qcoeff[i],PETSC_TRUE);
    181:         PetscViewerASCIIPrintf(viewer,"%s*x^%1D",str,ctx->nq-i-1);
    182:       }
    183:       SlepcSNPrintfScalar(str,50,ctx->qcoeff[ctx->nq-1],PETSC_TRUE);
    184:       PetscViewerASCIIPrintf(viewer,"%s)\n",str);
    185:     } else {
    186:       PetscViewerASCIIPrintf(viewer,"  Rational function: (");
    187:       for (i=0;i<ctx->np-1;i++) {
    188:         SlepcSNPrintfScalar(str,50,ctx->pcoeff[i],PETSC_TRUE);
    189:         PetscViewerASCIIPrintf(viewer,"%s*x^%1D",str,ctx->np-i-1);
    190:       }
    191:         SlepcSNPrintfScalar(str,50,ctx->pcoeff[ctx->np-1],PETSC_TRUE);
    192:       PetscViewerASCIIPrintf(viewer,"%s) / (",str);
    193:       for (i=0;i<ctx->nq-1;i++) {
    194:         SlepcSNPrintfScalar(str,50,ctx->qcoeff[i],PETSC_TRUE);
    195:         PetscViewerASCIIPrintf(viewer,"%s*x^%1D",str,ctx->nq-i-1);
    196:       }
    197:       SlepcSNPrintfScalar(str,50,ctx->qcoeff[ctx->nq-1],PETSC_TRUE);
    198:       PetscViewerASCIIPrintf(viewer,"%s)\n",str);
    199:     }
    200:   }
    201:   return(0);
    202: }

    206: static PetscErrorCode FNRationalSetNumerator_Rational(FN fn,PetscInt np,PetscScalar *pcoeff)
    207: {
    209:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    210:   PetscInt       i;

    213:   ctx->np = np;
    214:   PetscFree(ctx->pcoeff);
    215:   if (np) {
    216:     PetscMalloc1(np,&ctx->pcoeff);
    217:     PetscLogObjectMemory((PetscObject)fn,np*sizeof(PetscScalar));
    218:     for (i=0;i<np;i++) ctx->pcoeff[i] = pcoeff[i];
    219:   }
    220:   return(0);
    221: }

    225: /*@
    226:    FNRationalSetNumerator - Sets the parameters defining the numerator of the
    227:    rational function.

    229:    Logically Collective on FN

    231:    Input Parameters:
    232: +  fn     - the math function context
    233: .  np     - number of coefficients
    234: -  pcoeff - coefficients (array of scalar values)

    236:    Notes:
    237:    Let the rational function r(x) = p(x)/q(x), where p(x) and q(x) are polynomials.
    238:    This function provides the coefficients of the numerator p(x).
    239:    Hence, p(x) is of degree np-1.
    240:    If np is zero, then the numerator is assumed to be p(x)=1.

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

    245:    Level: intermediate

    247: .seealso: FNRationalSetDenominator(), FNRationalGetNumerator()
    248: @*/
    249: PetscErrorCode FNRationalSetNumerator(FN fn,PetscInt np,PetscScalar *pcoeff)
    250: {

    256:   if (np<0) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"Argument np cannot be negative");
    258:   PetscTryMethod(fn,"FNRationalSetNumerator_C",(FN,PetscInt,PetscScalar*),(fn,np,pcoeff));
    259:   return(0);
    260: }

    264: static PetscErrorCode FNRationalGetNumerator_Rational(FN fn,PetscInt *np,PetscScalar *pcoeff[])
    265: {
    267:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    268:   PetscInt       i;

    271:   if (np) *np = ctx->np;
    272:   if (pcoeff) {
    273:     if (!ctx->np) *pcoeff = NULL;
    274:     else {
    275:       PetscMalloc1(ctx->np,pcoeff);
    276:       for (i=0;i<ctx->np;i++) (*pcoeff)[i] = ctx->pcoeff[i];
    277:     }
    278:   }
    279:   return(0);
    280: }

    284: /*@
    285:    FNRationalGetNumerator - Gets the parameters that define the numerator of the
    286:    rational function.

    288:    Not Collective

    290:    Input Parameter:
    291: .  fn     - the math function context

    293:    Output Parameters:
    294: +  np     - number of coefficients
    295: -  pcoeff - coefficients (array of scalar values, length nq)

    297:    Notes:
    298:    The values passed by user with FNRationalSetNumerator() are returned (or null
    299:    pointers otherwise).
    300:    The pcoeff array should be freed by the user when no longer needed.

    302:    Level: intermediate

    304: .seealso: FNRationalSetNumerator()
    305: @*/
    306: PetscErrorCode FNRationalGetNumerator(FN fn,PetscInt *np,PetscScalar *pcoeff[])
    307: {

    312:   PetscTryMethod(fn,"FNRationalGetNumerator_C",(FN,PetscInt*,PetscScalar**),(fn,np,pcoeff));
    313:   return(0);
    314: }

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

    325:   ctx->nq = nq;
    326:   PetscFree(ctx->qcoeff);
    327:   if (nq) {
    328:     PetscMalloc1(nq,&ctx->qcoeff);
    329:     PetscLogObjectMemory((PetscObject)fn,nq*sizeof(PetscScalar));
    330:     for (i=0;i<nq;i++) ctx->qcoeff[i] = qcoeff[i];
    331:   }
    332:   return(0);
    333: }

    337: /*@
    338:    FNRationalSetDenominator - Sets the parameters defining the denominator of the
    339:    rational function.

    341:    Logically Collective on FN

    343:    Input Parameters:
    344: +  fn     - the math function context
    345: .  nq     - number of coefficients
    346: -  qcoeff - coefficients (array of scalar values)

    348:    Notes:
    349:    Let the rational function r(x) = p(x)/q(x), where p(x) and q(x) are polynomials.
    350:    This function provides the coefficients of the denominator q(x).
    351:    Hence, q(x) is of degree nq-1.
    352:    If nq is zero, then the function is assumed to be polynomial, r(x) = p(x).

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

    357:    Level: intermediate

    359: .seealso: FNRationalSetNumerator(), FNRationalGetDenominator()
    360: @*/
    361: PetscErrorCode FNRationalSetDenominator(FN fn,PetscInt nq,PetscScalar *qcoeff)
    362: {

    368:   if (nq<0) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"Argument nq cannot be negative");
    370:   PetscTryMethod(fn,"FNRationalSetDenominator_C",(FN,PetscInt,PetscScalar*),(fn,nq,qcoeff));
    371:   return(0);
    372: }

    376: static PetscErrorCode FNRationalGetDenominator_Rational(FN fn,PetscInt *nq,PetscScalar *qcoeff[])
    377: {
    379:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    380:   PetscInt       i;

    383:   if (nq) *nq = ctx->nq;
    384:   if (qcoeff) {
    385:     if (!ctx->nq) *qcoeff = NULL;
    386:     else {
    387:       PetscMalloc1(ctx->nq,qcoeff);
    388:       for (i=0;i<ctx->nq;i++) (*qcoeff)[i] = ctx->qcoeff[i];
    389:     }
    390:   }
    391:   return(0);
    392: }

    396: /*@
    397:    FNRationalGetDenominator - Gets the parameters that define the denominator of the
    398:    rational function.

    400:    Not Collective

    402:    Input Parameter:
    403: .  fn     - the math function context

    405:    Output Parameters:
    406: +  nq     - number of coefficients
    407: -  qcoeff - coefficients (array of scalar values, length nq)

    409:    Notes:
    410:    The values passed by user with FNRationalSetDenominator() are returned (or null
    411:    pointers otherwise).
    412:    The qcoeff array should be freed by the user when no longer needed.

    414:    Level: intermediate

    416: .seealso: FNRationalSetDenominator()
    417: @*/
    418: PetscErrorCode FNRationalGetDenominator(FN fn,PetscInt *nq,PetscScalar *qcoeff[])
    419: {

    424:   PetscTryMethod(fn,"FNRationalGetDenominator_C",(FN,PetscInt*,PetscScalar**),(fn,nq,qcoeff));
    425:   return(0);
    426: }

    430: PetscErrorCode FNSetFromOptions_Rational(PetscOptions *PetscOptionsObject,FN fn)
    431: {
    433: #define PARMAX 10
    434:   PetscScalar    array[PARMAX];
    435:   PetscInt       i,k;
    436:   PetscBool      flg;

    439:   PetscOptionsHead(PetscOptionsObject,"FN Rational Options");

    441:   k = PARMAX;
    442:   for (i=0;i<k;i++) array[i] = 0;
    443:   PetscOptionsScalarArray("-fn_rational_numerator","Numerator coefficients (one or more scalar values separated with a comma without spaces)","FNRationalSetNumerator",array,&k,&flg);
    444:   if (flg) {
    445:     FNRationalSetNumerator(fn,k,array);
    446:   }

    448:   k = PARMAX;
    449:   for (i=0;i<k;i++) array[i] = 0;
    450:   PetscOptionsScalarArray("-fn_rational_denominator","Denominator coefficients (one or more scalar values separated with a comma without spaces)","FNRationalSetDenominator",array,&k,&flg);
    451:   if (flg) {
    452:     FNRationalSetDenominator(fn,k,array);
    453:   }

    455:   PetscOptionsTail();
    456:   return(0);
    457: }

    461: PetscErrorCode FNDuplicate_Rational(FN fn,MPI_Comm comm,FN *newfn)
    462: {
    464:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data,*ctx2;
    465:   PetscInt       i;

    468:   PetscNewLog(*newfn,&ctx2);
    469:   (*newfn)->data = (void*)ctx2;
    470:   ctx2->np = ctx->np;
    471:   if (ctx->np) {
    472:     PetscMalloc1(ctx->np,&ctx2->pcoeff);
    473:     PetscLogObjectMemory((PetscObject)(*newfn),ctx->np*sizeof(PetscScalar));
    474:     for (i=0;i<ctx->np;i++) ctx2->pcoeff[i] = ctx->pcoeff[i];
    475:   }
    476:   ctx2->nq = ctx->nq;
    477:   if (ctx->nq) {
    478:     PetscMalloc1(ctx->nq,&ctx2->qcoeff);
    479:     PetscLogObjectMemory((PetscObject)(*newfn),ctx->nq*sizeof(PetscScalar));
    480:     for (i=0;i<ctx->nq;i++) ctx2->qcoeff[i] = ctx->qcoeff[i];
    481:   }
    482:   return(0);
    483: }

    487: PetscErrorCode FNDestroy_Rational(FN fn)
    488: {
    490:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;

    493:   PetscFree(ctx->pcoeff);
    494:   PetscFree(ctx->qcoeff);
    495:   PetscFree(fn->data);
    496:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalSetNumerator_C",NULL);
    497:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalGetNumerator_C",NULL);
    498:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalSetDenominator_C",NULL);
    499:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalGetDenominator_C",NULL);
    500:   return(0);
    501: }

    505: PETSC_EXTERN PetscErrorCode FNCreate_Rational(FN fn)
    506: {
    508:   FN_RATIONAL    *ctx;

    511:   PetscNewLog(fn,&ctx);
    512:   fn->data = (void*)ctx;

    514:   fn->ops->evaluatefunction    = FNEvaluateFunction_Rational;
    515:   fn->ops->evaluatederivative  = FNEvaluateDerivative_Rational;
    516:   fn->ops->evaluatefunctionmat = FNEvaluateFunctionMat_Rational;
    517:   fn->ops->setfromoptions      = FNSetFromOptions_Rational;
    518:   fn->ops->view                = FNView_Rational;
    519:   fn->ops->duplicate           = FNDuplicate_Rational;
    520:   fn->ops->destroy             = FNDestroy_Rational;
    521:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalSetNumerator_C",FNRationalSetNumerator_Rational);
    522:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalGetNumerator_C",FNRationalGetNumerator_Rational);
    523:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalSetDenominator_C",FNRationalSetDenominator_Rational);
    524:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalGetDenominator_C",FNRationalGetDenominator_Rational);
    525:   return(0);
    526: }