PetscErrorCode PetscViewerMathematicaPutMatrix(PetscViewer viewer, int m, int n, PetscReal *a) { PetscViewer_Mathematica *vmath = (PetscViewer_Mathematica*) viewer->data; MLINK link = vmath->link; /* The link to Mathematica */ char *name; PetscErrorCode ierr; PetscFunctionBegin; /* Determine the object name */ if (!vmath->objName) name = "mat"; else name = (char*) vmath->objName; /* Send the dense matrix object */ MLPutFunction(link, "EvaluatePacket", 1); MLPutFunction(link, "Set", 2); MLPutSymbol(link, name); MLPutFunction(link, "Transpose", 1); MLPutFunction(link, "Partition", 2); MLPutRealList(link, a, m*n); MLPutInteger(link, m); MLEndPacket(link); /* Skip packets until ReturnPacket */ ierr = PetscViewerMathematicaSkipPackets(viewer, RETURNPKT); CHKERRQ(ierr); /* Skip ReturnPacket */ MLNewPacket(link); PetscFunctionReturn(0); }
/*@C PetscViewerMathematicaPutVector - Send a vector to Mathematica Input Parameters: + viewer - The Mathematica viewer - v - The vector Level: intermediate .keywords PetscViewer, Mathematica, vector .seealso VecView(), PetscViewerMathematicaGetVector() @*/ PetscErrorCode PetscViewerMathematicaPutVector(PetscViewer viewer, Vec v) { PetscViewer_Mathematica *vmath = (PetscViewer_Mathematica*) viewer->data; MLINK link = vmath->link; /* The link to Mathematica */ char *name; PetscScalar *array; int n; PetscErrorCode ierr; PetscFunctionBegin; /* Determine the object name */ if (!vmath->objName) name = "vec"; else name = (char*) vmath->objName; ierr = VecGetLocalSize(v, &n); CHKERRQ(ierr); ierr = VecGetArray(v, &array); CHKERRQ(ierr); /* Send the Vector object */ MLPutFunction(link, "EvaluatePacket", 1); MLPutFunction(link, "Set", 2); MLPutSymbol(link, name); MLPutRealList(link, array, n); MLEndPacket(link); /* Skip packets until ReturnPacket */ ierr = PetscViewerMathematicaSkipPackets(viewer, RETURNPKT); CHKERRQ(ierr); /* Skip ReturnPacket */ MLNewPacket(link); ierr = VecRestoreArray(v, &array); CHKERRQ(ierr); PetscFunctionReturn(0); }
PetscErrorCode PetscViewerMathematicaPutCSRMatrix(PetscViewer viewer, int m, int n, int *i, int *j, PetscReal *a) { PetscViewer_Mathematica *vmath = (PetscViewer_Mathematica*) viewer->data; MLINK link = vmath->link; /* The link to Mathematica */ const char *symbol; char *name; PetscBool match; PetscErrorCode ierr; PetscFunctionBegin; /* Determine the object name */ if (!vmath->objName) name = "mat"; else name = (char*) vmath->objName; /* Make sure Mathematica recognizes sparse matrices */ MLPutFunction(link, "EvaluatePacket", 1); MLPutFunction(link, "Needs", 1); MLPutString(link, "LinearAlgebra`CSRMatrix`"); MLEndPacket(link); /* Skip packets until ReturnPacket */ ierr = PetscViewerMathematicaSkipPackets(viewer, RETURNPKT); CHKERRQ(ierr); /* Skip ReturnPacket */ MLNewPacket(link); /* Send the CSRMatrix object */ MLPutFunction(link, "EvaluatePacket", 1); MLPutFunction(link, "Set", 2); MLPutSymbol(link, name); MLPutFunction(link, "CSRMatrix", 5); MLPutInteger(link, m); MLPutInteger(link, n); MLPutFunction(link, "Plus", 2); MLPutIntegerList(link, i, m+1); MLPutInteger(link, 1); MLPutFunction(link, "Plus", 2); MLPutIntegerList(link, j, i[m]); MLPutInteger(link, 1); MLPutRealList(link, a, i[m]); MLEndPacket(link); /* Skip packets until ReturnPacket */ ierr = PetscViewerMathematicaSkipPackets(viewer, RETURNPKT); CHKERRQ(ierr); /* Skip ReturnPacket */ MLNewPacket(link); /* Check that matrix is valid */ MLPutFunction(link, "EvaluatePacket", 1); MLPutFunction(link, "ValidQ", 1); MLPutSymbol(link, name); MLEndPacket(link); ierr = PetscViewerMathematicaSkipPackets(viewer, RETURNPKT); CHKERRQ(ierr); MLGetSymbol(link, &symbol); ierr = PetscStrcmp("True", (char*) symbol, &match); CHKERRQ(ierr); if (!match) { MLDisownSymbol(link, symbol); SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB, "Invalid CSR matrix in Mathematica"); } MLDisownSymbol(link, symbol); /* Skip ReturnPacket */ MLNewPacket(link); PetscFunctionReturn(0); }
void pot( double cart[], int cartLength, double anuzero, int nulbl[], int nulblLength, int nflag[], int nflagLength, int nasurf[], int nasurfLength, int nder) { double output[10]; double buffer[3]; int i,j,k; i=0; for (j=0; j<cartLength/3; j++) { for (k=0; k<3; k++) { usricm_.CART[k][j]=cart[i]; i++; } } usricm_.ANUZERO=anuzero; for(i=0; i<nulblLength; i++) { usricm_.NULBL[i]=nulbl[i]; } /* //Set the option flags*/ /* usricm_.NFLAG[0]=1;*/ /* usricm_.NFLAG[1]=1;*/ /* usricm_.NFLAG[2]=0;*/ /* usricm_.NFLAG[3]=0;*/ /* usricm_.NFLAG[4]=0;*/ for(i=0; i<nflagLength; i++) { usricm_.NFLAG[i]=nflag[i]; } /* //clear out nasurf except the first*/ /* for(i=0; i<6; i++) {*/ /* for(j=0;j<6;j++) {*/ /* usricm_.NASURF[i][j]=0;*/ /* }*/ /* }*/ /* */ /* usricm_.NASURF[0][0]=1;*/ i=0; for(j=0; j<6; j++) { for(k=0; k<6; k++) { usricm_.NASURF[k][j]=nasurf[i]; i++; } } //Set the number of derivitaves to 1 (hopefully) usricm_.NDER=nder; pot_(); output[0]=usrocm_.PENGYGS; i=1; for (j=0; j<3; j++) { for (k=0; k<3; k++) { output[i]=usrocm_.DGSCART[k][j]; i++; } } MLPutRealList(stdlink, output, 10); }
static int Integrate(This *t, real *integral, real *error, real *prob) { TYPEDEFREGION; typedef struct pool { struct pool *next; Region region[POOLSIZE]; } Pool; count dim, comp, ncur, ipool, npool; int fail; Totals totals[NCOMP]; Pool *cur = NULL, *pool; Region *region; if( VERBOSE > 1 ) { char s[256]; sprintf(s, "Cuhre input parameters:\n" " ndim " COUNT "\n ncomp " COUNT "\n" " epsrel " REAL "\n epsabs " REAL "\n" " flags %d\n mineval " NUMBER "\n maxeval " NUMBER "\n" " key " COUNT, t->ndim, t->ncomp, t->epsrel, t->epsabs, t->flags, t->mineval, t->maxeval, t->key); Print(s); } if( BadComponent(t) ) return -2; if( BadDimension(t) ) return -1; t->epsabs = Max(t->epsabs, NOTZERO); RuleAlloc(t); t->mineval = IMax(t->mineval, t->rule.n + 1); FrameAlloc(t, ShmRm(t)); ForkCores(t); if( (fail = setjmp(t->abort)) ) goto abort; Alloc(cur, 1); cur->next = NULL; ncur = 1; region = cur->region; region->div = 0; for( dim = 0; dim < t->ndim; ++dim ) { Bounds *b = ®ion->bounds[dim]; b->lower = 0; b->upper = 1; } Sample(t, region); for( comp = 0; comp < t->ncomp; ++comp ) { Totals *tot = &totals[comp]; Result *r = ®ion->result[comp]; tot->avg = tot->lastavg = tot->guess = r->avg; tot->err = tot->lasterr = r->err; tot->weightsum = 1/Max(Sq(r->err), NOTZERO); tot->avgsum = tot->weightsum*r->avg; tot->chisq = tot->chisqsum = tot->chisum = 0; } for( t->nregions = 1; ; ++t->nregions ) { count maxcomp, bisectdim; real maxratio, maxerr; Result result[NCOMP]; Region *regionL, *regionR; Bounds *bL, *bR; if( VERBOSE ) { char s[128 + 128*NCOMP], *p = s; p += sprintf(p, "\n" "Iteration " COUNT ": " NUMBER " integrand evaluations so far", t->nregions, t->neval); for( comp = 0; comp < t->ncomp; ++comp ) { cTotals *tot = &totals[comp]; p += sprintf(p, "\n[" COUNT "] " REAL " +- " REAL " \tchisq " REAL " (" COUNT " df)", comp + 1, tot->avg, tot->err, tot->chisq, t->nregions - 1); } Print(s); } maxratio = -INFTY; maxcomp = 0; for( comp = 0; comp < t->ncomp; ++comp ) { creal ratio = totals[comp].err/MaxErr(totals[comp].avg); if( ratio > maxratio ) { maxratio = ratio; maxcomp = comp; } } if( maxratio <= 1 && t->neval >= t->mineval ) break; if( t->neval >= t->maxeval ) { fail = 1; break; } maxerr = -INFTY; regionL = cur->region; npool = ncur; for( pool = cur; pool; npool = POOLSIZE, pool = pool->next ) for( ipool = 0; ipool < npool; ++ipool ) { Region *region = &pool->region[ipool]; creal err = region->result[maxcomp].err; if( err > maxerr ) { maxerr = err; regionL = region; } } if( ncur == POOLSIZE ) { Pool *prev = cur; Alloc(cur, 1); cur->next = prev; ncur = 0; } regionR = &cur->region[ncur++]; regionR->div = ++regionL->div; FCopy(result, regionL->result); XCopy(regionR->bounds, regionL->bounds); bisectdim = result[maxcomp].bisectdim; bL = ®ionL->bounds[bisectdim]; bR = ®ionR->bounds[bisectdim]; bL->upper = bR->lower = .5*(bL->upper + bL->lower); Sample(t, regionL); Sample(t, regionR); for( comp = 0; comp < t->ncomp; ++comp ) { cResult *r = &result[comp]; Result *rL = ®ionL->result[comp]; Result *rR = ®ionR->result[comp]; Totals *tot = &totals[comp]; real diff, err, w, avg, sigsq; tot->lastavg += diff = rL->avg + rR->avg - r->avg; diff = fabs(.25*diff); err = rL->err + rR->err; if( err > 0 ) { creal c = 1 + 2*diff/err; rL->err *= c; rR->err *= c; } rL->err += diff; rR->err += diff; tot->lasterr += rL->err + rR->err - r->err; tot->weightsum += w = 1/Max(Sq(tot->lasterr), NOTZERO); sigsq = 1/tot->weightsum; tot->avgsum += w*tot->lastavg; avg = sigsq*tot->avgsum; tot->chisum += w *= tot->lastavg - tot->guess; tot->chisqsum += w*tot->lastavg; tot->chisq = tot->chisqsum - avg*tot->chisum; if( LAST ) { tot->avg = tot->lastavg; tot->err = tot->lasterr; } else { tot->avg = avg; tot->err = sqrt(sigsq); } } } for( comp = 0; comp < t->ncomp; ++comp ) { cTotals *tot = &totals[comp]; integral[comp] = tot->avg; error[comp] = tot->err; prob[comp] = ChiSquare(tot->chisq, t->nregions - 1); } #ifdef MLVERSION if( REGIONS ) { MLPutFunction(stdlink, "List", 2); MLPutFunction(stdlink, "List", t->nregions); npool = ncur; for( pool = cur; pool; npool = POOLSIZE, pool = pool->next ) for( ipool = 0; ipool < npool; ++ipool ) { Region const *region = &pool->region[ipool]; real lower[NDIM], upper[NDIM]; for( dim = 0; dim < t->ndim; ++dim ) { cBounds *b = ®ion->bounds[dim]; lower[dim] = b->lower; upper[dim] = b->upper; } MLPutFunction(stdlink, "Cuba`Cuhre`region", 3); MLPutRealList(stdlink, lower, t->ndim); MLPutRealList(stdlink, upper, t->ndim); MLPutFunction(stdlink, "List", t->ncomp); for( comp = 0; comp < t->ncomp; ++comp ) { cResult *r = ®ion->result[comp]; real res[] = {r->avg, r->err}; MLPutRealList(stdlink, res, Elements(res)); } } } #endif abort: while( (pool = cur) ) { cur = cur->next; free(pool); } WaitCores(t); FrameFree(t); RuleFree(t); return fail; }
void sload(const char *fn, int *SZ, long SZlen) { uint16_t numberChannels; size_t k=0; size_t numberSamples; double samplerate; double *t; char *str = NULL; #ifdef _WIN32 long int sz[2]; #else size_t sz[2]; #endif biosig_data_type *data; #ifdef __LIBBIOSIG2_H__ size_t rowcol[2]; #endif HDRTYPE *hdr = constructHDR(0,0); if (VERBOSE_LEVEL > 5) fprintf(stdout,"=== start sload ===\n"); /* contains [experiment,series,sweep,trace] numbers for selecting data. */ while ((k < SZlen) && (k < 5)) { #ifdef __LIBBIOSIG2_H__ biosig_set_segment_selection(hdr, k+1, SZ[k]); #else hdr->AS.SegSel[k] = (uint32_t)SZ[k]; #endif k++; } // ********* open file and read header ************ hdr = sopen(fn, "r", hdr); if (serror2(hdr)) { destructHDR(hdr); fprintf(stdout,"Cannot open file <%s>\n", fn); return; } #ifdef __LIBBIOSIG2_H__ numberChannels = biosig_get_number_of_channels(hdr); numberSamples = biosig_get_number_of_samples(hdr); samplerate = biosig_get_samplerate(hdr); biosig_reset_flag(hdr, BIOSIG_FLAG_ROW_BASED_CHANNELS); #else numberChannels = hdr->NS; numberSamples = hdr->NRec * hdr->SPR samplerate = hdr->SampleRate; hdr->FLAG.ROW_BASED_CHANNELS = 0; #endif if (VERBOSE_LEVEL > 5) fprintf(stdout,"open filename <%s>NoOfChans=%i\n", fn, numberChannels); // ********** read data ******************** sread(NULL, 0, numberSamples, hdr); if (serror2(hdr)) { destructHDR(hdr); fprintf(stdout,"Error reading data from file <%s>\n", fn); return; } #ifdef __LIBBIOSIG2_H__ biosig_get_datablock(hdr, &data, &rowcol[0], &rowcol[1]); sz[0] = rowcol[1]; sz[1] = rowcol[0]; #else sz[0] = hdr->data.size[1]; sz[1] = hdr->data.size[0]; data = hdr->data.block; #endif MLPutFunction(stdlink, "List", 3); // write data matrix MLPutRealArray(stdlink, data, sz, NULL, 2); // generate and write time axis t = (double*)malloc(numberSamples * sizeof(double)); for (k=0; k < numberSamples;) { t[k] = (++k)/samplerate; } MLPutRealList(stdlink, t, numberSamples); free(t); // generate and write header information in JSON format asprintf_hdr2json(&str, hdr); MLPutString(stdlink, str); free(str); if (VERBOSE_LEVEL > 5) { for (k=0; k<numberChannels; k++) fprintf(stdout,"%f ",data[k]); fprintf(stdout,"\n\nopen filename <%s>@%p sz=[%i,%i]\n", fn, data, sz[1],sz[0]); } // *********** close file ********************* sclose(hdr); destructHDR(hdr); return; }
static int Integrate(This *t, real *integral, real *error, real *prob) { TYPEDEFREGION; Totals totals[NCOMP]; real nneed, weight; count dim, comp, iter, pass = 0, err, iregion; number nwant, nmin = INT_MAX; int fail; if( VERBOSE > 1 ) { char s[512]; sprintf(s, "Divonne input parameters:\n" " ndim " COUNT "\n ncomp " COUNT "\n" " epsrel " REAL "\n epsabs " REAL "\n" " flags %d\n seed %d\n" " mineval " NUMBER "\n maxeval " NUMBER "\n" " key1 %d\n key2 %d\n key3 %d\n maxpass " COUNT "\n" " border " REAL "\n maxchisq " REAL "\n mindeviation " REAL "\n" " ngiven " NUMBER "\n nextra " NUMBER, t->ndim, t->ncomp, t->epsrel, t->epsabs, t->flags, t->seed, t->mineval, t->maxeval, t->key1, t->key2, t->key3, t->maxpass, t->border.lower, t->maxchisq, t->mindeviation, t->ngiven, t->nextra); Print(s); } if( BadComponent(t) ) return -2; if( BadDimension(t, t->key1) || BadDimension(t, t->key2) || ((t->key3 & -2) && BadDimension(t, t->key3)) ) return -1; t->neval_opt = t->neval_cut = 0; t->size = CHUNKSIZE; MemAlloc(t->voidregion, t->size*sizeof(Region)); for( dim = 0; dim < t->ndim; ++dim ) { Bounds *b = &RegionPtr(0)->bounds[dim]; b->lower = 0; b->upper = 1; } RuleIni(&t->rule7); RuleIni(&t->rule9); RuleIni(&t->rule11); RuleIni(&t->rule13); SamplesIni(&t->samples[0]); SamplesIni(&t->samples[1]); SamplesIni(&t->samples[2]); if( (fail = setjmp(t->abort)) ) goto abort; t->epsabs = Max(t->epsabs, NOTZERO); /* Step 1: partition the integration region */ if( VERBOSE ) Print("Partitioning phase:"); if( IsSobol(t->key1) || IsSobol(t->key2) || IsSobol(t->key3) ) IniRandom(t); SamplesLookup(t, &t->samples[0], t->key1, (number)47, (number)INT_MAX, (number)0); SamplesAlloc(t, &t->samples[0]); t->totals = totals; Zap(totals); t->phase = 1; Explore(t, 0, &t->samples[0], INIDEPTH, 1); for( iter = 1; ; ++iter ) { Totals *maxtot; count valid; for( comp = 0; comp < t->ncomp; ++comp ) { Totals *tot = &totals[comp]; tot->avg = tot->spreadsq = 0; tot->spread = tot->secondspread = -INFTY; } for( iregion = 0; iregion < t->nregions; ++iregion ) { Region *region = RegionPtr(iregion); for( comp = 0; comp < t->ncomp; ++comp ) { cResult *r = ®ion->result[comp]; Totals *tot = &totals[comp]; tot->avg += r->avg; tot->spreadsq += Sq(r->spread); if( r->spread > tot->spread ) { tot->secondspread = tot->spread; tot->spread = r->spread; tot->iregion = iregion; } else if( r->spread > tot->secondspread ) tot->secondspread = r->spread; } } maxtot = totals; valid = 0; for( comp = 0; comp < t->ncomp; ++comp ) { Totals *tot = &totals[comp]; integral[comp] = tot->avg; valid += tot->avg == tot->avg; if( tot->spreadsq > maxtot->spreadsq ) maxtot = tot; tot->spread = sqrt(tot->spreadsq); error[comp] = tot->spread*t->samples[0].weight; } if( VERBOSE ) { char s[128 + 64*NCOMP], *p = s; p += sprintf(p, "\n" "Iteration " COUNT " (pass " COUNT "): " COUNT " regions\n" NUMBER7 " integrand evaluations so far,\n" NUMBER7 " in optimizing regions,\n" NUMBER7 " in finding cuts", iter, pass, t->nregions, t->neval, t->neval_opt, t->neval_cut); for( comp = 0; comp < t->ncomp; ++comp ) p += sprintf(p, "\n[" COUNT "] " REAL " +- " REAL, comp + 1, integral[comp], error[comp]); Print(s); } if( valid == 0 ) goto abort; /* all NaNs */ if( t->neval > t->maxeval ) break; nneed = maxtot->spread/MaxErr(maxtot->avg); if( nneed < MAXPRIME ) { cnumber n = t->neval + t->nregions*(number)ceil(nneed); if( n < nmin ) { nmin = n; pass = 0; } else if( ++pass > t->maxpass && n >= t->mineval ) break; } Split(t, maxtot->iregion, DEPTH); } /* Step 2: do a "full" integration on each region */ /* nneed = t->samples[0].neff + 1; */ nneed = 2*t->samples[0].neff; for( comp = 0; comp < t->ncomp; ++comp ) { Totals *tot = &totals[comp]; creal maxerr = MaxErr(tot->avg); tot->nneed = tot->spread/maxerr; nneed = Max(nneed, tot->nneed); tot->maxerrsq = Sq(maxerr); tot->mindevsq = tot->maxerrsq*Sq(t->mindeviation); } nwant = (number)Min(ceil(nneed), MARKMASK/40.); err = SamplesLookup(t, &t->samples[1], t->key2, nwant, (t->maxeval - t->neval)/t->nregions + 1, t->samples[0].n + 1); /* the number of points needed to reach the desired accuracy */ fail = Unmark(err)*t->nregions; if( Marked(err) ) { if( VERBOSE ) Print("\nNot enough samples left for main integration."); for( comp = 0; comp < t->ncomp; ++comp ) prob[comp] = -999; weight = t->samples[0].weight; } else { bool can_adjust = (t->key3 == 1 && t->samples[1].sampler != SampleRule && (t->key2 < 0 || t->samples[1].neff < MAXPRIME)); count df, nlimit; SamplesAlloc(t, &t->samples[1]); if( VERBOSE ) { char s[128]; sprintf(s, "\nMain integration on " COUNT " regions with " NUMBER " samples per region.", t->nregions, t->samples[1].neff); Print(s); } ResClear(integral); ResClear(error); ResClear(prob); nlimit = t->maxeval - t->nregions*t->samples[1].n; df = 0; for( iregion = 0; iregion < t->nregions; ++iregion ) { Region *region = RegionPtr(iregion); char s[64*NDIM + 256*NCOMP], *p = s; int todo; refine: t->phase = 2; t->samples[1].sampler(t, &t->samples[1], region->bounds, region->vol); if( can_adjust ) for( comp = 0; comp < t->ncomp; ++comp ) totals[comp].spreadsq -= Sq(region->result[comp].spread); nlimit += t->samples[1].n; todo = 0; for( comp = 0; comp < t->ncomp; ++comp ) { cResult *r = ®ion->result[comp]; Totals *tot = &totals[comp]; t->samples[0].avg[comp] = r->avg; t->samples[0].err[comp] = r->err; if( t->neval < nlimit ) { creal avg2 = t->samples[1].avg[comp]; creal err2 = t->samples[1].err[comp]; creal diffsq = Sq(avg2 - r->avg); #define Var(s) Sq((s.err[comp] == 0) ? r->spread*s.weight : s.err[comp]) if( err2*tot->nneed > r->spread || diffsq > Max(t->maxchisq*(Var(t->samples[0]) + Var(t->samples[1])), EPS*Sq(avg2)) ) { if( t->key3 && diffsq > tot->mindevsq ) { if( t->key3 == 1 ) { ccount xregion = t->nregions; if( VERBOSE > 2 ) Print("\nSplit"); t->phase = 1; Explore(t, iregion, &t->samples[1], POSTDEPTH, 2); if( can_adjust ) { number nnew; count ireg, xreg; for( ireg = iregion, xreg = xregion; ireg < t->nregions; ireg = xreg++ ) { cResult *result = RegionPtr(ireg)->result; count c; for( c = 0; c < t->ncomp; ++c ) totals[c].spreadsq += Sq(result[c].spread); } nnew = (tot->spreadsq/Sq(MARKMASK) > tot->maxerrsq) ? MARKMASK : (number)ceil(sqrt(tot->spreadsq/tot->maxerrsq)); if( nnew > nwant + nwant/64 ) { ccount err = SamplesLookup(t, &t->samples[1], t->key2, nnew, (t->maxeval - t->neval)/t->nregions + 1, t->samples[1].n); fail += Unmark(err)*t->nregions; nwant = nnew; SamplesFree(&t->samples[1]); SamplesAlloc(t, &t->samples[1]); if( t->key2 > 0 && t->samples[1].neff >= MAXPRIME ) can_adjust = false; if( VERBOSE > 2 ) { char s[128]; sprintf(s, "Sampling remaining " COUNT " regions with " NUMBER " points per region.", t->nregions, t->samples[1].neff); Print(s); } } } goto refine; } todo |= 3; } todo |= 1; } } } if( can_adjust ) { for( comp = 0; comp < t->ncomp; ++comp ) totals[comp].maxerrsq -= Sq(region->result[comp].spread*t->samples[1].weight); } switch( todo ) { case 1: /* get spread right */ Explore(t, iregion, &t->samples[1], 0, 2); break; case 3: /* sample region again with more points */ if( SamplesIniQ(&t->samples[2]) ) { SamplesLookup(t, &t->samples[2], t->key3, nwant, (number)INT_MAX, (number)0); SamplesAlloc(t, &t->samples[2]); } t->phase = 3; t->samples[2].sampler(t, &t->samples[2], region->bounds, region->vol); Explore(t, iregion, &t->samples[2], 0, 2); ++region->depth; /* misused for df here */ ++df; } ++region->depth; /* misused for df here */ if( VERBOSE > 2 ) { for( dim = 0; dim < t->ndim; ++dim ) { cBounds *b = ®ion->bounds[dim]; p += sprintf(p, (dim == 0) ? "\nRegion (" REALF ") - (" REALF ")" : "\n (" REALF ") - (" REALF ")", b->lower, b->upper); } } for( comp = 0; comp < t->ncomp; ++comp ) { Result *r = ®ion->result[comp]; creal x1 = t->samples[0].avg[comp]; creal s1 = Var(t->samples[0]); creal x2 = t->samples[1].avg[comp]; creal s2 = Var(t->samples[1]); creal r2 = (s1 == 0) ? Sq(t->samples[1].neff*t->samples[0].weight) : s2/s1; real norm = 1 + r2; real avg = x2 + r2*x1; real sigsq = s2; real chisq = Sq(x2 - x1); real chiden = s1 + s2; if( todo == 3 ) { creal x3 = t->samples[2].avg[comp]; creal s3 = Var(t->samples[2]); creal r3 = (s2 == 0) ? Sq(t->samples[2].neff*t->samples[1].weight) : s3/s2; norm = 1 + r3*norm; avg = x3 + r3*avg; sigsq = s3; chisq = s1*Sq(x3 - x2) + s2*Sq(x3 - x1) + s3*chisq; chiden = s1*s2 + s3*chiden; } avg = LAST ? r->avg : (sigsq *= norm = 1/norm, avg*norm); if( chisq > EPS ) chisq /= Max(chiden, NOTZERO); #define Out(s) s.avg[comp], r->spread*s.weight, s.err[comp] if( VERBOSE > 2 ) { p += sprintf(p, "\n[" COUNT "] " REAL " +- " REAL "(" REAL ")\n " REAL " +- " REAL "(" REAL ")", comp + 1, Out(t->samples[0]), Out(t->samples[1])); if( todo == 3 ) p += sprintf(p, "\n " REAL " +- " REAL "(" REAL ")", Out(t->samples[2])); p += sprintf(p, " \tchisq " REAL, chisq); } integral[comp] += avg; error[comp] += sigsq; prob[comp] += chisq; r->avg = avg; r->spread = sqrt(sigsq); r->chisq = chisq; } if( VERBOSE > 2 ) Print(s); } for( comp = 0; comp < t->ncomp; ++comp ) error[comp] = sqrt(error[comp]); df += t->nregions; if( VERBOSE > 2 ) { char s[16 + 128*NCOMP], *p = s; p += sprintf(p, "\nTotals:"); for( comp = 0; comp < t->ncomp; ++comp ) p += sprintf(p, "\n[" COUNT "] " REAL " +- " REAL " \tchisq " REAL " (" COUNT " df)", comp + 1, integral[comp], error[comp], prob[comp], df); Print(s); } for( comp = 0; comp < t->ncomp; ++comp ) prob[comp] = ChiSquare(prob[comp], df); weight = 1; } #ifdef MLVERSION if( REGIONS ) { MLPutFunction(stdlink, "List", 2); MLPutFunction(stdlink, "List", t->nregions); for( iregion = 0; iregion < t->nregions; ++iregion ) { Region *region = RegionPtr(iregion); cBounds *b = region->bounds; real lower[NDIM], upper[NDIM]; for( dim = 0; dim < t->ndim; ++dim ) { lower[dim] = b[dim].lower; upper[dim] = b[dim].upper; } MLPutFunction(stdlink, "Cuba`Divonne`region", 4); MLPutRealList(stdlink, lower, t->ndim); MLPutRealList(stdlink, upper, t->ndim); MLPutFunction(stdlink, "List", t->ncomp); for( comp = 0; comp < t->ncomp; ++comp ) { cResult *r = ®ion->result[comp]; real res[] = {r->avg, r->spread*weight, r->chisq}; MLPutRealList(stdlink, res, Elements(res)); } MLPutInteger(stdlink, region->depth); /* misused for df */ } } #endif abort: SamplesFree(&t->samples[2]); SamplesFree(&t->samples[1]); SamplesFree(&t->samples[0]); RuleFree(&t->rule13); RuleFree(&t->rule11); RuleFree(&t->rule9); RuleFree(&t->rule7); free(t->voidregion); return fail; }
static int Integrate(creal epsrel, creal epsabs, cint flags, number mineval, cnumber maxeval, ccount key, real *integral, real *error, real *prob) { TYPEDEFREGION; count dim, comp; int fail = 1; Rule rule; Totals totals[NCOMP]; Region *anchor = NULL, *region = NULL; if( VERBOSE > 1 ) { char s[256]; sprintf(s, "Cuhre input parameters:\n" " ndim " COUNT "\n ncomp " COUNT "\n" " epsrel " REAL "\n epsabs " REAL "\n" " flags %d\n mineval " NUMBER "\n maxeval " NUMBER "\n" " key " COUNT, ndim_, ncomp_, epsrel, epsabs, flags, mineval, maxeval, key); Print(s); } #ifdef MLVERSION if( setjmp(abort_) ) goto abort; #endif if( key == 13 && ndim_ == 2 ) Rule13Alloc(&rule); else if( key == 11 && ndim_ == 3 ) Rule11Alloc(&rule); else if( key == 9 ) Rule9Alloc(&rule); else if( key == 7 ) Rule7Alloc(&rule); else { if( ndim_ == 2 ) Rule13Alloc(&rule); else if( ndim_ == 3 ) Rule11Alloc(&rule); else Rule9Alloc(&rule); } Alloc(rule.x, rule.n*(ndim_ + ncomp_)); rule.f = rule.x + rule.n*ndim_; mineval = IMax(mineval, rule.n + 1); Alloc(anchor, 1); anchor->next = NULL; anchor->div = 0; for( dim = 0; dim < ndim_; ++dim ) { Bounds *b = &anchor->bounds[dim]; b->lower = 0; b->upper = 1; } Sample(&rule, anchor, flags); for( comp = 0; comp < ncomp_; ++comp ) { Totals *tot = &totals[comp]; Result *r = &anchor->result[comp]; tot->avg = tot->lastavg = tot->guess = r->avg; tot->err = tot->lasterr = r->err; tot->weightsum = 1/Max(Sq(r->err), NOTZERO); tot->avgsum = tot->weightsum*r->avg; tot->chisq = tot->chisqsum = tot->chisum = 0; } for( nregions_ = 1; ; ++nregions_ ) { count maxcomp, bisectdim; real maxratio, maxerr; Region *regionL, *regionR, *reg, **parent, **par; Bounds *bL, *bR; if( VERBOSE ) { char s[128 + 128*NCOMP], *p = s; p += sprintf(p, "\n" "Iteration " COUNT ": " NUMBER " integrand evaluations so far", nregions_, neval_); for( comp = 0; comp < ncomp_; ++comp ) { cTotals *tot = &totals[comp]; p += sprintf(p, "\n[" COUNT "] " REAL " +- " REAL " \tchisq " REAL " (" COUNT " df)", comp + 1, tot->avg, tot->err, tot->chisq, nregions_ - 1); } Print(s); } maxratio = -INFTY; maxcomp = 0; for( comp = 0; comp < ncomp_; ++comp ) { creal ratio = totals[comp].err/MaxErr(totals[comp].avg); if( ratio > maxratio ) { maxratio = ratio; maxcomp = comp; } } if( maxratio <= 1 && neval_ >= mineval ) { fail = 0; break; } if( neval_ >= maxeval ) break; maxerr = -INFTY; parent = &anchor; region = anchor; for( par = &anchor; (reg = *par); par = ®->next ) { creal err = reg->result[maxcomp].err; if( err > maxerr ) { maxerr = err; parent = par; region = reg; } } Alloc(regionL, 1); Alloc(regionR, 1); *parent = regionL; regionL->next = regionR; regionR->next = region->next; regionL->div = regionR->div = region->div + 1; VecCopy(regionL->bounds, region->bounds); VecCopy(regionR->bounds, region->bounds); bisectdim = region->result[maxcomp].bisectdim; bL = ®ionL->bounds[bisectdim]; bR = ®ionR->bounds[bisectdim]; bL->upper = bR->lower = .5*(bL->upper + bL->lower); Sample(&rule, regionL, flags); Sample(&rule, regionR, flags); for( comp = 0; comp < ncomp_; ++comp ) { cResult *r = ®ion->result[comp]; Result *rL = ®ionL->result[comp]; Result *rR = ®ionR->result[comp]; Totals *tot = &totals[comp]; real diff, err, w, avg, sigsq; tot->lastavg += diff = rL->avg + rR->avg - r->avg; diff = fabs(.25*diff); err = rL->err + rR->err; if( err > 0 ) { creal c = 1 + 2*diff/err; rL->err *= c; rR->err *= c; } rL->err += diff; rR->err += diff; tot->lasterr += rL->err + rR->err - r->err; tot->weightsum += w = 1/Max(Sq(tot->lasterr), NOTZERO); sigsq = 1/tot->weightsum; tot->avgsum += w*tot->lastavg; avg = sigsq*tot->avgsum; tot->chisum += w *= tot->lastavg - tot->guess; tot->chisqsum += w*tot->lastavg; tot->chisq = tot->chisqsum - avg*tot->chisum; if( LAST ) { tot->avg = tot->lastavg; tot->err = tot->lasterr; } else { tot->avg = avg; tot->err = sqrt(sigsq); } } free(region); region = NULL; } for( comp = 0; comp < ncomp_; ++comp ) { cTotals *tot = &totals[comp]; integral[comp] = tot->avg; error[comp] = tot->err; prob[comp] = ChiSquare(tot->chisq, nregions_ - 1); } #ifdef MLVERSION if( REGIONS ) { MLPutFunction(stdlink, "List", 2); MLPutFunction(stdlink, "List", nregions_); for( region = anchor; region; region = region->next ) { real lower[NDIM], upper[NDIM]; for( dim = 0; dim < ndim_; ++dim ) { cBounds *b = ®ion->bounds[dim]; lower[dim] = b->lower; upper[dim] = b->upper; } MLPutFunction(stdlink, "Cuba`Cuhre`region", 3); MLPutRealList(stdlink, lower, ndim_); MLPutRealList(stdlink, upper, ndim_); MLPutFunction(stdlink, "List", ncomp_); for( comp = 0; comp < ncomp_; ++comp ) { cResult *r = ®ion->result[comp]; real res[] = {r->avg, r->err}; MLPutRealList(stdlink, res, Elements(res)); } } } #endif #ifdef MLVERSION abort: #endif if( region ) free(region); while( (region = anchor) ) { anchor = anchor->next; free(region); } free(rule.x); RuleFree(&rule); return fail; }
static int Integrate(creal epsrel, creal epsabs, cint flags, cnumber mineval, cnumber maxeval, int key1, int key2, int key3, ccount maxpass, creal maxchisq, creal mindeviation, real *integral, real *error, real *prob) { TYPEDEFREGION; Region anchor, *region; Totals totals[NCOMP]; real nneed, weight; count dim, comp, iter, nregions, pass = 0, err; number nwant, nmin = INT_MAX; int fail = -1; if( VERBOSE > 1 ) { char s[512]; sprintf(s, "Divonne input parameters:\n" " ndim " COUNT "\n ncomp " COUNT "\n" " epsrel " REAL "\n epsabs " REAL "\n" " flags %d\n mineval " NUMBER "\n maxeval " NUMBER "\n" " key1 %d\n key2 %d\n key3 %d\n maxpass " COUNT "\n" " border " REAL "\n maxchisq " REAL "\n mindeviation " REAL "\n" " ngiven " NUMBER "\n nextra " NUMBER "\n", ndim_, ncomp_, epsrel, epsabs, flags, mineval, maxeval, key1, key2, key3, maxpass, border_.lower, maxchisq, mindeviation, ngiven_, nextra_); Print(s); } anchor.next = NULL; for( dim = 0; dim < ndim_; ++dim ) { Bounds *b = &anchor.bounds[dim]; b->lower = 0; b->upper = 1; } RuleIni(&rule7_); RuleIni(&rule9_); RuleIni(&rule11_); RuleIni(&rule13_); SamplesIni(&samples_[0]); SamplesIni(&samples_[1]); SamplesIni(&samples_[2]); #ifdef MLVERSION if( setjmp(abort_) ) goto abort; #endif /* Step 1: partition the integration region */ if( VERBOSE ) Print("Partitioning phase:"); if( IsSobol(key1) || IsSobol(key2) || IsSobol(key3) ) IniRandom(2*maxeval, flags); SamplesLookup(&samples_[0], key1, (number)47, (number)INT_MAX, (number)0); SamplesAlloc(&samples_[0]); totals_ = totals; Zap(totals); phase_ = 1; Explore(&anchor, &samples_[0], INIDEPTH, 1); for( iter = 1; ; ++iter ) { Totals *maxtot; for( comp = 0; comp < ncomp_; ++comp ) { Totals *tot = &totals[comp]; tot->avg = tot->spreadsq = 0; tot->spread = tot->secondspread = -INFTY; } nregions = 0; for( region = anchor.next; region; region = region->next ) { ++nregions; for( comp = 0; comp < ncomp_; ++comp ) { cResult *r = ®ion->result[comp]; Totals *tot = &totals[comp]; tot->avg += r->avg; tot->spreadsq += Sq(r->spread); if( r->spread > tot->spread ) { tot->secondspread = tot->spread; tot->spread = r->spread; tot->region = region; } else if( r->spread > tot->secondspread ) tot->secondspread = r->spread; } } maxtot = totals; for( comp = 0; comp < ncomp_; ++comp ) { Totals *tot = &totals[comp]; integral[comp] = tot->avg; if( tot->spreadsq > maxtot->spreadsq ) maxtot = tot; tot->spread = sqrt(tot->spreadsq); error[comp] = tot->spread*samples_[0].weight; } if( VERBOSE ) { char s[128 + 64*NCOMP], *p = s; p += sprintf(p, "\n" "Iteration " COUNT " (pass " COUNT "): " COUNT " regions\n" NUMBER7 " integrand evaluations so far,\n" NUMBER7 " in optimizing regions,\n" NUMBER7 " in finding cuts", iter, pass, nregions, neval_, neval_opt_, neval_cut_); for( comp = 0; comp < ncomp_; ++comp ) p += sprintf(p, "\n[" COUNT "] " REAL " +- " REAL, comp + 1, integral[comp], error[comp]); Print(s); } if( neval_ > maxeval ) break; nneed = maxtot->spread/MaxErr(maxtot->avg); if( nneed < MAXPRIME ) { cnumber n = neval_ + nregions*(number)ceil(nneed); if( n < nmin ) { nmin = n; pass = 0; } else if( ++pass > maxpass && n >= mineval ) break; } Split(maxtot->region, DEPTH); } /* Step 2: do a "full" integration on each region */ /* nneed = samples_[0].neff + 1; */ nneed = 2*samples_[0].neff; for( comp = 0; comp < ncomp_; ++comp ) { Totals *tot = &totals[comp]; creal maxerr = MaxErr(tot->avg); tot->nneed = tot->spread/maxerr; nneed = Max(nneed, tot->nneed); tot->maxerrsq = Sq(maxerr); tot->mindevsq = tot->maxerrsq*Sq(mindeviation); } nwant = (number)Min(ceil(nneed), MARKMASK/40.); err = SamplesLookup(&samples_[1], key2, nwant, (maxeval - neval_)/nregions + 1, samples_[0].n + 1); /* the number of points needed to reach the desired accuracy */ fail = Unmark(err)*nregions; if( Marked(err) ) { if( VERBOSE ) Print("\nNot enough samples left for main integration."); for( comp = 0; comp < ncomp_; ++comp ) prob[comp] = -999; weight = samples_[0].weight; nregions_ = nregions; } else { bool can_adjust = (key3 == 1 && samples_[1].sampler != SampleRule && (key2 < 0 || samples_[1].neff < MAXPRIME)); count df, nlimit; SamplesAlloc(&samples_[1]); if( VERBOSE ) { char s[128]; sprintf(s, "\nMain integration on " COUNT " regions with " NUMBER " samples per region.", nregions, samples_[1].neff); Print(s); } ResClear(integral); ResClear(error); ResClear(prob); nlimit = maxeval - nregions*samples_[1].n; df = nregions_ = 0; for( region = anchor.next; region; region = region->next ) { char s[64*NDIM + 256*NCOMP], *p = s; int todo; refine: phase_ = 2; samples_[1].sampler(&samples_[1], region->bounds, region->vol); if( can_adjust ) { --nregions; for( comp = 0; comp < ncomp_; ++comp ) totals[comp].spreadsq -= Sq(region->result[comp].spread); } nlimit += samples_[1].n; todo = 0; for( comp = 0; comp < ncomp_; ++comp ) { cResult *r = ®ion->result[comp]; Totals *tot = &totals[comp]; samples_[0].avg[comp] = r->avg; samples_[0].err[comp] = r->err; if( neval_ < nlimit ) { creal avg2 = samples_[1].avg[comp]; creal err2 = samples_[1].err[comp]; creal diffsq = Sq(avg2 - r->avg); #define Var(s) Sq((s.err[comp] == 0) ? r->spread*s.weight : s.err[comp]) if( err2*tot->nneed > r->spread || diffsq > Max(maxchisq*(Var(samples_[0]) + Var(samples_[1])), EPS*Sq(avg2)) ) { if( key3 && diffsq > tot->mindevsq ) { if( key3 == 1 ) { const Region *next = region->next; if( VERBOSE > 2 ) Print("\nSplit"); phase_ = 1; Explore(region, &samples_[1], POSTDEPTH, 2); if( can_adjust ) { number nnew; Region *child; for( child = region; child != next; child = child->next ) { count c; for( c = 0; c < ncomp_; ++c ) totals[c].spreadsq += Sq(child->result[c].spread); ++nregions; } nnew = (tot->spreadsq/Sq(MARKMASK) > tot->maxerrsq) ? MARKMASK : (number)ceil(sqrt(tot->spreadsq/tot->maxerrsq)); if( nnew > nwant + nwant/64 ) { ccount err = SamplesLookup(&samples_[1], key2, nnew, (maxeval - neval_)/nregions + 1, samples_[1].n); fail += Unmark(err)*nregions; nwant = nnew; SamplesFree(&samples_[1]); SamplesAlloc(&samples_[1]); if( key2 > 0 && samples_[1].neff >= MAXPRIME ) can_adjust = false; if( VERBOSE > 2 ) { char s[128]; sprintf(s, "Sampling remaining " COUNT " regions with " NUMBER " points per region.", nregions, samples_[1].neff); Print(s); } } } goto refine; } todo |= 3; } todo |= 1; } } } if( can_adjust ) { for( comp = 0; comp < ncomp_; ++comp ) totals[comp].maxerrsq -= Sq(region->result[comp].spread*samples_[1].weight); } switch( todo ) { case 1: /* get spread right */ Explore(region, &samples_[1], 0, 2); break; case 3: /* sample region again with more points */ if( MEM(&samples_[2]) == NULL ) { SamplesLookup(&samples_[2], key3, nwant, (number)INT_MAX, (number)0); SamplesAlloc(&samples_[2]); } phase_ = 3; samples_[2].sampler(&samples_[2], region->bounds, region->vol); Explore(region, &samples_[2], 0, 2); ++region->depth; /* misused for df here */ ++df; } ++region->depth; /* misused for df here */ ++nregions_; if( VERBOSE > 2 ) { for( dim = 0; dim < ndim_; ++dim ) { cBounds *b = ®ion->bounds[dim]; p += sprintf(p, (dim == 0) ? "\nRegion (" REALF ") - (" REALF ")" : "\n (" REALF ") - (" REALF ")", b->lower, b->upper); } } for( comp = 0; comp < ncomp_; ++comp ) { Result *r = ®ion->result[comp]; creal x1 = samples_[0].avg[comp]; creal s1 = Var(samples_[0]); creal x2 = samples_[1].avg[comp]; creal s2 = Var(samples_[1]); creal r2 = (s1 == 0) ? Sq(samples_[1].neff*samples_[0].weight) : s2/s1; real norm = 1 + r2; real avg = x2 + r2*x1; real sigsq = s2; real chisq = Sq(x2 - x1); real chiden = s1 + s2; if( todo == 3 ) { creal x3 = samples_[2].avg[comp]; creal s3 = Var(samples_[2]); creal r3 = (s2 == 0) ? Sq(samples_[2].neff*samples_[1].weight) : s3/s2; norm = 1 + r3*norm; avg = x3 + r3*avg; sigsq = s3; chisq = s1*Sq(x3 - x2) + s2*Sq(x3 - x1) + s3*chisq; chiden = s1*s2 + s3*chiden; } avg = LAST ? r->avg : (sigsq *= norm = 1/norm, avg*norm); if( chisq > EPS ) chisq /= Max(chiden, NOTZERO); #define Out(s) s.avg[comp], r->spread*s.weight, s.err[comp] if( VERBOSE > 2 ) { p += sprintf(p, "\n[" COUNT "] " REAL " +- " REAL "(" REAL ")\n " REAL " +- " REAL "(" REAL ")", comp + 1, Out(samples_[0]), Out(samples_[1])); if( todo == 3 ) p += sprintf(p, "\n " REAL " +- " REAL "(" REAL ")", Out(samples_[2])); p += sprintf(p, " \tchisq " REAL, chisq); } integral[comp] += avg; error[comp] += sigsq; prob[comp] += chisq; r->avg = avg; r->spread = sqrt(sigsq); r->chisq = chisq; } if( VERBOSE > 2 ) Print(s); } for( comp = 0; comp < ncomp_; ++comp ) error[comp] = sqrt(error[comp]); df += nregions_; if( VERBOSE > 2 ) { char s[16 + 128*NCOMP], *p = s; p += sprintf(p, "\nTotals:"); for( comp = 0; comp < ncomp_; ++comp ) p += sprintf(p, "\n[" COUNT "] " REAL " +- " REAL " \tchisq " REAL " (" COUNT " df)", comp + 1, integral[comp], error[comp], prob[comp], df); Print(s); } for( comp = 0; comp < ncomp_; ++comp ) prob[comp] = ChiSquare(prob[comp], df); weight = 1; } #ifdef MLVERSION if( REGIONS ) { MLPutFunction(stdlink, "List", 2); MLPutFunction(stdlink, "List", nregions_); for( region = anchor.next; region; region = region->next ) { cBounds *b = region->bounds; real lower[NDIM], upper[NDIM]; for( dim = 0; dim < ndim_; ++dim ) { lower[dim] = b[dim].lower; upper[dim] = b[dim].upper; } MLPutFunction(stdlink, "Cuba`Divonne`region", 4); MLPutRealList(stdlink, lower, ndim_); MLPutRealList(stdlink, upper, ndim_); MLPutFunction(stdlink, "List", ncomp_); for( comp = 0; comp < ncomp_; ++comp ) { cResult *r = ®ion->result[comp]; real res[] = {r->avg, r->spread*weight, r->chisq}; MLPutRealList(stdlink, res, Elements(res)); } MLPutInteger(stdlink, region->depth); /* misused for df */ } } #endif #ifdef MLVERSION abort: #endif SamplesFree(&samples_[2]); SamplesFree(&samples_[1]); SamplesFree(&samples_[0]); RuleFree(&rule13_); RuleFree(&rule11_); RuleFree(&rule9_); RuleFree(&rule7_); for( region = anchor.next; region; ) { Region *next = region->next; free(region); region = next; } return fail; }