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: }