Date: 2021-09-20T09:43:37+00:00

Actual source code: fnrational.c
slepc-3.15.2 2021-09-20
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2021, 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>
     15: #include <slepcblaslapack.h>

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

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

     31:   if (!ctx->np) p = 1.0;
     32:   else {
     33:     p = ctx->pcoeff[0];
     34:     for (i=1;i<ctx->np;i++)
     35:       p = ctx->pcoeff[i]+x*p;
     36:   }
     37:   if (!ctx->nq) *y = p;
     38:   else {
     39:     q = ctx->qcoeff[0];
     40:     for (i=1;i<ctx->nq;i++)
     41:       q = ctx->qcoeff[i]+x*q;
     42:     if (q==0.0) SETERRQ(PETSC_COMM_SELF,1,"Function not defined in the requested value");
     43:     *y = p/q;
     44:   }
     45:   return(0);
     46: }

     48: static PetscErrorCode FNEvaluateFunctionMat_Rational_Private(FN fn,const PetscScalar *Aa,PetscScalar *Ba,PetscInt m,PetscBool firstonly)
     49: {
     51:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
     52:   PetscBLASInt   n,k,ld,*ipiv,info;
     53:   PetscInt       i,j;
     54:   PetscScalar    *W,*P,*Q,one=1.0,zero=0.0;

     57:   PetscBLASIntCast(m,&n);
     58:   ld = n;
     59:   k  = firstonly? 1: n;
     60:   if (Aa==Ba) {
     61:     PetscMalloc4(m*m,&P,m*m,&Q,m*m,&W,ld,&ipiv);
     62:   } else {
     63:     P = Ba;
     64:     PetscMalloc3(m*m,&Q,m*m,&W,ld,&ipiv);
     65:   }
     66:   PetscArrayzero(P,m*m);
     67:   if (!ctx->np) {
     68:     for (i=0;i<m;i++) P[i+i*ld] = 1.0;
     69:   } else {
     70:     for (i=0;i<m;i++) P[i+i*ld] = ctx->pcoeff[0];
     71:     for (j=1;j<ctx->np;j++) {
     72:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,P,&ld,Aa,&ld,&zero,W,&ld));
     73:       PetscArraycpy(P,W,m*m);
     74:       for (i=0;i<m;i++) P[i+i*ld] += ctx->pcoeff[j];
     75:     }
     76:     PetscLogFlops(2.0*n*n*n*(ctx->np-1));
     77:   }
     78:   if (ctx->nq) {
     79:     PetscArrayzero(Q,m*m);
     80:     for (i=0;i<m;i++) Q[i+i*ld] = ctx->qcoeff[0];
     81:     for (j=1;j<ctx->nq;j++) {
     82:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,Q,&ld,Aa,&ld,&zero,W,&ld));
     83:       PetscArraycpy(Q,W,m*m);
     84:       for (i=0;i<m;i++) Q[i+i*ld] += ctx->qcoeff[j];
     85:     }
     86:     PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&n,&k,Q,&ld,ipiv,P,&ld,&info));
     87:     SlepcCheckLapackInfo("gesv",info);
     88:     PetscLogFlops(2.0*n*n*n*(ctx->nq-1)+2.0*n*n*n/3.0+2.0*n*n*k);
     89:   }
     90:   if (Aa==Ba) {
     91:     PetscArraycpy(Ba,P,m*k);
     92:     PetscFree4(P,Q,W,ipiv);
     93:   } else {
     94:     PetscFree3(Q,W,ipiv);
     95:   }
     96:   return(0);
     97: }

     99: PetscErrorCode FNEvaluateFunctionMat_Rational(FN fn,Mat A,Mat B)
    100: {
    101:   PetscErrorCode    ierr;
    102:   PetscInt          m;
    103:   const PetscScalar *Aa;
    104:   PetscScalar       *Ba;

    107:   MatDenseGetArrayRead(A,&Aa);
    108:   MatDenseGetArray(B,&Ba);
    109:   MatGetSize(A,&m,NULL);
    110:   FNEvaluateFunctionMat_Rational_Private(fn,Aa,Ba,m,PETSC_FALSE);
    111:   MatDenseRestoreArrayRead(A,&Aa);
    112:   MatDenseRestoreArray(B,&Ba);
    113:   return(0);
    114: }

    116: PetscErrorCode FNEvaluateFunctionMatVec_Rational(FN fn,Mat A,Vec v)
    117: {
    118:   PetscErrorCode    ierr;
    119:   PetscInt          m;
    120:   const PetscScalar *Aa;
    121:   PetscScalar       *Ba;
    122:   Mat               B;

    125:   FN_AllocateWorkMat(fn,A,&B);
    126:   MatDenseGetArrayRead(A,&Aa);
    127:   MatDenseGetArray(B,&Ba);
    128:   MatGetSize(A,&m,NULL);
    129:   FNEvaluateFunctionMat_Rational_Private(fn,Aa,Ba,m,PETSC_TRUE);
    130:   MatDenseRestoreArrayRead(A,&Aa);
    131:   MatDenseRestoreArray(B,&Ba);
    132:   MatGetColumnVector(B,v,0);
    133:   FN_FreeWorkMat(fn,&B);
    134:   return(0);
    135: }

    137: PetscErrorCode FNEvaluateDerivative_Rational(FN fn,PetscScalar x,PetscScalar *yp)
    138: {
    139:   FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data;
    140:   PetscInt    i;
    141:   PetscScalar p,q,pp,qp;

    144:   if (!ctx->np) {
    145:     p = 1.0;
    146:     pp = 0.0;
    147:   } else {
    148:     p = ctx->pcoeff[0];
    149:     pp = 0.0;
    150:     for (i=1;i<ctx->np;i++) {
    151:       pp = p+x*pp;
    152:       p = ctx->pcoeff[i]+x*p;
    153:     }
    154:   }
    155:   if (!ctx->nq) *yp = pp;
    156:   else {
    157:     q = ctx->qcoeff[0];
    158:     qp = 0.0;
    159:     for (i=1;i<ctx->nq;i++) {
    160:       qp = q+x*qp;
    161:       q = ctx->qcoeff[i]+x*q;
    162:     }
    163:     if (q==0.0) SETERRQ(PETSC_COMM_SELF,1,"Derivative not defined in the requested value");
    164:     *yp = (pp*q-p*qp)/(q*q);
    165:   }
    166:   return(0);
    167: }

    169: PetscErrorCode FNView_Rational(FN fn,PetscViewer viewer)
    170: {
    172:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    173:   PetscBool      isascii;
    174:   PetscInt       i;
    175:   char           str[50];

    178:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    179:   if (isascii) {
    180:     if (fn->alpha!=(PetscScalar)1.0 || fn->beta!=(PetscScalar)1.0) {
    181:       SlepcSNPrintfScalar(str,sizeof(str),fn->alpha,PETSC_FALSE);
    182:       PetscViewerASCIIPrintf(viewer,"  Scale factors: alpha=%s,",str);
    183:       PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
    184:       SlepcSNPrintfScalar(str,sizeof(str),fn->beta,PETSC_FALSE);
    185:       PetscViewerASCIIPrintf(viewer," beta=%s\n",str);
    186:       PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
    187:     }
    188:     if (!ctx->nq) {
    189:       if (!ctx->np) {
    190:         PetscViewerASCIIPrintf(viewer,"  Constant: 1.0\n");
    191:       } else if (ctx->np==1) {
    192:         SlepcSNPrintfScalar(str,sizeof(str),ctx->pcoeff[0],PETSC_FALSE);
    193:         PetscViewerASCIIPrintf(viewer,"  Constant: %s\n",str);
    194:       } else {
    195:         PetscViewerASCIIPrintf(viewer,"  Polynomial: ");
    196:         PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
    197:         for (i=0;i<ctx->np-1;i++) {
    198:           SlepcSNPrintfScalar(str,sizeof(str),ctx->pcoeff[i],PETSC_TRUE);
    199:           PetscViewerASCIIPrintf(viewer,"%s*x^%1D",str,ctx->np-i-1);
    200:         }
    201:         SlepcSNPrintfScalar(str,sizeof(str),ctx->pcoeff[ctx->np-1],PETSC_TRUE);
    202:         PetscViewerASCIIPrintf(viewer,"%s\n",str);
    203:         PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
    204:       }
    205:     } else if (!ctx->np) {
    206:       PetscViewerASCIIPrintf(viewer,"  Inverse polinomial: 1 / (");
    207:       PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
    208:       for (i=0;i<ctx->nq-1;i++) {
    209:         SlepcSNPrintfScalar(str,sizeof(str),ctx->qcoeff[i],PETSC_TRUE);
    210:         PetscViewerASCIIPrintf(viewer,"%s*x^%1D",str,ctx->nq-i-1);
    211:       }
    212:       SlepcSNPrintfScalar(str,sizeof(str),ctx->qcoeff[ctx->nq-1],PETSC_TRUE);
    213:       PetscViewerASCIIPrintf(viewer,"%s)\n",str);
    214:       PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
    215:     } else {
    216:       PetscViewerASCIIPrintf(viewer,"  Rational function: (");
    217:       PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
    218:       for (i=0;i<ctx->np-1;i++) {
    219:         SlepcSNPrintfScalar(str,sizeof(str),ctx->pcoeff[i],PETSC_TRUE);
    220:         PetscViewerASCIIPrintf(viewer,"%s*x^%1D",str,ctx->np-i-1);
    221:       }
    222:       SlepcSNPrintfScalar(str,sizeof(str),ctx->pcoeff[ctx->np-1],PETSC_TRUE);
    223:       PetscViewerASCIIPrintf(viewer,"%s) / (",str);
    224:       for (i=0;i<ctx->nq-1;i++) {
    225:         SlepcSNPrintfScalar(str,sizeof(str),ctx->qcoeff[i],PETSC_TRUE);
    226:         PetscViewerASCIIPrintf(viewer,"%s*x^%1D",str,ctx->nq-i-1);
    227:       }
    228:       SlepcSNPrintfScalar(str,sizeof(str),ctx->qcoeff[ctx->nq-1],PETSC_TRUE);
    229:       PetscViewerASCIIPrintf(viewer,"%s)\n",str);
    230:       PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
    231:     }
    232:   }
    233:   return(0);
    234: }

    236: static PetscErrorCode FNRationalSetNumerator_Rational(FN fn,PetscInt np,PetscScalar *pcoeff)
    237: {
    239:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    240:   PetscInt       i;

    243:   if (np<0) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"Argument np cannot be negative");
    244:   ctx->np = np;
    245:   PetscFree(ctx->pcoeff);
    246:   if (np) {
    247:     PetscMalloc1(np,&ctx->pcoeff);
    248:     PetscLogObjectMemory((PetscObject)fn,np*sizeof(PetscScalar));
    249:     for (i=0;i<np;i++) ctx->pcoeff[i] = pcoeff[i];
    250:   }
    251:   return(0);
    252: }

    254: /*@C
    255:    FNRationalSetNumerator - Sets the parameters defining the numerator of the
    256:    rational function.

    258:    Logically Collective on fn

    260:    Input Parameters:
    261: +  fn     - the math function context
    262: .  np     - number of coefficients
    263: -  pcoeff - coefficients (array of scalar values)

    265:    Notes:
    266:    Let the rational function r(x) = p(x)/q(x), where p(x) and q(x) are polynomials.
    267:    This function provides the coefficients of the numerator p(x).
    268:    Hence, p(x) is of degree np-1.
    269:    If np is zero, then the numerator is assumed to be p(x)=1.

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

    274:    Level: intermediate

    276: .seealso: FNRationalSetDenominator(), FNRationalGetNumerator()
    277: @*/
    278: PetscErrorCode FNRationalSetNumerator(FN fn,PetscInt np,PetscScalar *pcoeff)
    279: {

    286:   PetscTryMethod(fn,"FNRationalSetNumerator_C",(FN,PetscInt,PetscScalar*),(fn,np,pcoeff));
    287:   return(0);
    288: }

    290: static PetscErrorCode FNRationalGetNumerator_Rational(FN fn,PetscInt *np,PetscScalar *pcoeff[])
    291: {
    293:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    294:   PetscInt       i;

    297:   if (np) *np = ctx->np;
    298:   if (pcoeff) {
    299:     if (!ctx->np) *pcoeff = NULL;
    300:     else {
    301:       PetscMalloc1(ctx->np,pcoeff);
    302:       for (i=0;i<ctx->np;i++) (*pcoeff)[i] = ctx->pcoeff[i];
    303:     }
    304:   }
    305:   return(0);
    306: }

    308: /*@C
    309:    FNRationalGetNumerator - Gets the parameters that define the numerator of the
    310:    rational function.

    312:    Not Collective

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

    317:    Output Parameters:
    318: +  np     - number of coefficients
    319: -  pcoeff - coefficients (array of scalar values, length nq)

    321:    Notes:
    322:    The values passed by user with FNRationalSetNumerator() are returned (or null
    323:    pointers otherwise).
    324:    The pcoeff array should be freed by the user when no longer needed.

    326:    Level: intermediate

    328: .seealso: FNRationalSetNumerator()
    329: @*/
    330: PetscErrorCode FNRationalGetNumerator(FN fn,PetscInt *np,PetscScalar *pcoeff[])
    331: {

    336:   PetscUseMethod(fn,"FNRationalGetNumerator_C",(FN,PetscInt*,PetscScalar**),(fn,np,pcoeff));
    337:   return(0);
    338: }

    340: static PetscErrorCode FNRationalSetDenominator_Rational(FN fn,PetscInt nq,PetscScalar *qcoeff)
    341: {
    343:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    344:   PetscInt       i;

    347:   if (nq<0) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"Argument nq cannot be negative");
    348:   ctx->nq = nq;
    349:   PetscFree(ctx->qcoeff);
    350:   if (nq) {
    351:     PetscMalloc1(nq,&ctx->qcoeff);
    352:     PetscLogObjectMemory((PetscObject)fn,nq*sizeof(PetscScalar));
    353:     for (i=0;i<nq;i++) ctx->qcoeff[i] = qcoeff[i];
    354:   }
    355:   return(0);
    356: }

    358: /*@C
    359:    FNRationalSetDenominator - Sets the parameters defining the denominator of the
    360:    rational function.

    362:    Logically Collective on fn

    364:    Input Parameters:
    365: +  fn     - the math function context
    366: .  nq     - number of coefficients
    367: -  qcoeff - coefficients (array of scalar values)

    369:    Notes:
    370:    Let the rational function r(x) = p(x)/q(x), where p(x) and q(x) are polynomials.
    371:    This function provides the coefficients of the denominator q(x).
    372:    Hence, q(x) is of degree nq-1.
    373:    If nq is zero, then the function is assumed to be polynomial, r(x) = p(x).

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

    378:    Level: intermediate

    380: .seealso: FNRationalSetNumerator(), FNRationalGetDenominator()
    381: @*/
    382: PetscErrorCode FNRationalSetDenominator(FN fn,PetscInt nq,PetscScalar *qcoeff)
    383: {

    390:   PetscTryMethod(fn,"FNRationalSetDenominator_C",(FN,PetscInt,PetscScalar*),(fn,nq,qcoeff));
    391:   return(0);
    392: }

    394: static PetscErrorCode FNRationalGetDenominator_Rational(FN fn,PetscInt *nq,PetscScalar *qcoeff[])
    395: {
    397:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    398:   PetscInt       i;

    401:   if (nq) *nq = ctx->nq;
    402:   if (qcoeff) {
    403:     if (!ctx->nq) *qcoeff = NULL;
    404:     else {
    405:       PetscMalloc1(ctx->nq,qcoeff);
    406:       for (i=0;i<ctx->nq;i++) (*qcoeff)[i] = ctx->qcoeff[i];
    407:     }
    408:   }
    409:   return(0);
    410: }

    412: /*@C
    413:    FNRationalGetDenominator - Gets the parameters that define the denominator of the
    414:    rational function.

    416:    Not Collective

    418:    Input Parameter:
    419: .  fn     - the math function context

    421:    Output Parameters:
    422: +  nq     - number of coefficients
    423: -  qcoeff - coefficients (array of scalar values, length nq)

    425:    Notes:
    426:    The values passed by user with FNRationalSetDenominator() are returned (or a null
    427:    pointer otherwise).
    428:    The qcoeff array should be freed by the user when no longer needed.

    430:    Level: intermediate

    432: .seealso: FNRationalSetDenominator()
    433: @*/
    434: PetscErrorCode FNRationalGetDenominator(FN fn,PetscInt *nq,PetscScalar *qcoeff[])
    435: {

    440:   PetscUseMethod(fn,"FNRationalGetDenominator_C",(FN,PetscInt*,PetscScalar**),(fn,nq,qcoeff));
    441:   return(0);
    442: }

    444: PetscErrorCode FNSetFromOptions_Rational(PetscOptionItems *PetscOptionsObject,FN fn)
    445: {
    447: #define PARMAX 10
    448:   PetscScalar    array[PARMAX];
    449:   PetscInt       i,k;
    450:   PetscBool      flg;

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

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

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

    465:   PetscOptionsTail();
    466:   return(0);
    467: }

    469: PetscErrorCode FNDuplicate_Rational(FN fn,MPI_Comm comm,FN *newfn)
    470: {
    472:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data,*ctx2 = (FN_RATIONAL*)(*newfn)->data;
    473:   PetscInt       i;

    476:   ctx2->np = ctx->np;
    477:   if (ctx->np) {
    478:     PetscMalloc1(ctx->np,&ctx2->pcoeff);
    479:     PetscLogObjectMemory((PetscObject)(*newfn),ctx->np*sizeof(PetscScalar));
    480:     for (i=0;i<ctx->np;i++) ctx2->pcoeff[i] = ctx->pcoeff[i];
    481:   }
    482:   ctx2->nq = ctx->nq;
    483:   if (ctx->nq) {
    484:     PetscMalloc1(ctx->nq,&ctx2->qcoeff);
    485:     PetscLogObjectMemory((PetscObject)(*newfn),ctx->nq*sizeof(PetscScalar));
    486:     for (i=0;i<ctx->nq;i++) ctx2->qcoeff[i] = ctx->qcoeff[i];
    487:   }
    488:   return(0);
    489: }

    491: PetscErrorCode FNDestroy_Rational(FN fn)
    492: {
    494:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;

    497:   PetscFree(ctx->pcoeff);
    498:   PetscFree(ctx->qcoeff);
    499:   PetscFree(fn->data);
    500:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalSetNumerator_C",NULL);
    501:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalGetNumerator_C",NULL);
    502:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalSetDenominator_C",NULL);
    503:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalGetDenominator_C",NULL);
    504:   return(0);
    505: }

    507: SLEPC_EXTERN PetscErrorCode FNCreate_Rational(FN fn)
    508: {
    510:   FN_RATIONAL    *ctx;

    513:   PetscNewLog(fn,&ctx);
    514:   fn->data = (void*)ctx;

    516:   fn->ops->evaluatefunction          = FNEvaluateFunction_Rational;
    517:   fn->ops->evaluatederivative        = FNEvaluateDerivative_Rational;
    518:   fn->ops->evaluatefunctionmat[0]    = FNEvaluateFunctionMat_Rational;
    519:   fn->ops->evaluatefunctionmatvec[0] = FNEvaluateFunctionMatVec_Rational;
    520:   fn->ops->setfromoptions            = FNSetFromOptions_Rational;
    521:   fn->ops->view                      = FNView_Rational;
    522:   fn->ops->duplicate                 = FNDuplicate_Rational;
    523:   fn->ops->destroy                   = FNDestroy_Rational;
    524:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalSetNumerator_C",FNRationalSetNumerator_Rational);
    525:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalGetNumerator_C",FNRationalGetNumerator_Rational);
    526:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalSetDenominator_C",FNRationalSetDenominator_Rational);
    527:   PetscObjectComposeFunction((PetscObject)fn,"FNRationalGetDenominator_C",FNRationalGetDenominator_Rational);
    528:   return(0);
    529: }