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

Actual source code: fnrational.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: */
     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,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(Aa,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: {
    102:   PetscInt       m;
    103:   PetscScalar    *Aa,*Ba;

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

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

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

    135: PetscErrorCode FNEvaluateDerivative_Rational(FN fn,PetscScalar x,PetscScalar *yp)
    136: {
    137:   FN_RATIONAL *ctx = (FN_RATIONAL*)fn->data;
    138:   PetscInt    i;
    139:   PetscScalar p,q,pp,qp;

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

    167: PetscErrorCode FNView_Rational(FN fn,PetscViewer viewer)
    168: {
    170:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    171:   PetscBool      isascii;
    172:   PetscInt       i;
    173:   char           str[50];

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

    234: static PetscErrorCode FNRationalSetNumerator_Rational(FN fn,PetscInt np,PetscScalar *pcoeff)
    235: {
    237:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    238:   PetscInt       i;

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

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

    256:    Logically Collective on fn

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

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

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

    272:    Level: intermediate

    274: .seealso: FNRationalSetDenominator(), FNRationalGetNumerator()
    275: @*/
    276: PetscErrorCode FNRationalSetNumerator(FN fn,PetscInt np,PetscScalar *pcoeff)
    277: {

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

    288: static PetscErrorCode FNRationalGetNumerator_Rational(FN fn,PetscInt *np,PetscScalar *pcoeff[])
    289: {
    291:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    292:   PetscInt       i;

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

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

    310:    Not Collective

    312:    Input Parameter:
    313: .  fn     - the math function context

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

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

    324:    Level: intermediate

    326: .seealso: FNRationalSetNumerator()
    327: @*/
    328: PetscErrorCode FNRationalGetNumerator(FN fn,PetscInt *np,PetscScalar *pcoeff[])
    329: {

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

    338: static PetscErrorCode FNRationalSetDenominator_Rational(FN fn,PetscInt nq,PetscScalar *qcoeff)
    339: {
    341:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    342:   PetscInt       i;

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

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

    360:    Logically Collective on fn

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

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

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

    376:    Level: intermediate

    378: .seealso: FNRationalSetNumerator(), FNRationalGetDenominator()
    379: @*/
    380: PetscErrorCode FNRationalSetDenominator(FN fn,PetscInt nq,PetscScalar *qcoeff)
    381: {

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

    392: static PetscErrorCode FNRationalGetDenominator_Rational(FN fn,PetscInt *nq,PetscScalar *qcoeff[])
    393: {
    395:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data;
    396:   PetscInt       i;

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

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

    414:    Not Collective

    416:    Input Parameter:
    417: .  fn     - the math function context

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

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

    428:    Level: intermediate

    430: .seealso: FNRationalSetDenominator()
    431: @*/
    432: PetscErrorCode FNRationalGetDenominator(FN fn,PetscInt *nq,PetscScalar *qcoeff[])
    433: {

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

    442: PetscErrorCode FNSetFromOptions_Rational(PetscOptionItems *PetscOptionsObject,FN fn)
    443: {
    445: #define PARMAX 10
    446:   PetscScalar    array[PARMAX];
    447:   PetscInt       i,k;
    448:   PetscBool      flg;

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

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

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

    463:   PetscOptionsTail();
    464:   return(0);
    465: }

    467: PetscErrorCode FNDuplicate_Rational(FN fn,MPI_Comm comm,FN *newfn)
    468: {
    470:   FN_RATIONAL    *ctx = (FN_RATIONAL*)fn->data,*ctx2 = (FN_RATIONAL*)(*newfn)->data;
    471:   PetscInt       i;

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

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

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

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