/* Perform sky localization based on TDOAs alone. Returns log probability; not normalized. */
double bayestar_log_posterior_toa(
double theta,
double phi,
double gmst,
int nifos, /* Input: number of detectors. */
const double **locs, /* Input: array of detector positions. */
const double *toas, /* Input: array of times of arrival. */
const double *w_toas /* Input: sum-of-squares weights, (1/TOA variance)^2. */
) {
double dt[nifos];
toa_errors(dt, theta, phi, gmst, nifos, locs, toas);
return -0.5 * gsl_stats_wtss(w_toas, 1, dt, 1, nifos);
}
int
main (void)
{
const size_t n = N;
const size_t ncoeffs = NCOEFFS;
const size_t nbreak = NBREAK;
size_t i, j;
gsl_bspline_workspace *bw;
gsl_vector *B;
double dy;
gsl_rng *r;
gsl_vector *c, *w;
gsl_vector *x, *y;
gsl_matrix *X, *cov;
gsl_multifit_linear_workspace *mw;
double chisq;
double Rsq;
double dof;
gsl_rng_env_setup();
r = gsl_rng_alloc(gsl_rng_default);
/* allocate a cubic bspline workspace (k = 4) */
bw = gsl_bspline_alloc(4, nbreak);
B = gsl_vector_alloc(ncoeffs);
x = gsl_vector_alloc(n);
y = gsl_vector_alloc(n);
X = gsl_matrix_alloc(n, ncoeffs);
c = gsl_vector_alloc(ncoeffs);
w = gsl_vector_alloc(n);
cov = gsl_matrix_alloc(ncoeffs, ncoeffs);
mw = gsl_multifit_linear_alloc(n, ncoeffs);
printf("#m=0,S=0\n");
/* this is the data to be fitted */
for (i = 0; i < n; ++i)
{
double sigma;
double xi = (15.0 / (N - 1)) * i;
double yi = cos(xi) * exp(-0.1 * xi);
sigma = 0.1 * yi;
dy = gsl_ran_gaussian(r, sigma);
yi += dy;
gsl_vector_set(x, i, xi);
gsl_vector_set(y, i, yi);
gsl_vector_set(w, i, 1.0 / (sigma * sigma));
printf("%f %f\n", xi, yi);
}
/* use uniform breakpoints on [0, 15] */
gsl_bspline_knots_uniform(0.0, 15.0, bw);
/* construct the fit matrix X */
for (i = 0; i < n; ++i)
{
double xi = gsl_vector_get(x, i);
/* compute B_j(xi) for all j */
gsl_bspline_eval(xi, B, bw);
/* fill in row i of X */
for (j = 0; j < ncoeffs; ++j)
{
double Bj = gsl_vector_get(B, j);
gsl_matrix_set(X, i, j, Bj);
}
}
/* do the fit */
gsl_multifit_wlinear(X, w, y, c, cov, &chisq, mw);
dof = n - ncoeffs;
Rsq = 1.0 - chisq / gsl_stats_wtss(w->data, 1, y->data, 1, y->size);
fprintf(stderr, "chisq/dof = %e, Rsq = %f\n", chisq / dof, Rsq);
/* output the smoothed curve */
{
double xi, yi, yerr;
printf("#m=1,S=0\n");
for (xi = 0.0; xi < 15.0; xi += 0.1)
{
gsl_bspline_eval(xi, B, bw);
gsl_multifit_linear_est(B, c, cov, &yi, &yerr);
printf("%f %f\n", xi, yi);
}
}
gsl_rng_free(r);
gsl_bspline_free(bw);
gsl_vector_free(B);
gsl_vector_free(x);
gsl_vector_free(y);
gsl_matrix_free(X);
gsl_vector_free(c);
gsl_vector_free(w);
gsl_matrix_free(cov);
gsl_multifit_linear_free(mw);
return 0;
} /* main() */
void bSplineGSLOriginalDemo ()
{
const size_t n = N;
const size_t ncoeffs = NCOEFFS;
const size_t nbreak = NBREAK;
size_t i, j;
gsl_bspline_workspace *bw;
gsl_vector *B;
double dy;
gsl_rng *r;
gsl_vector *c, *w;
gsl_vector *x, *y;
gsl_matrix *X, *cov;
gsl_multifit_linear_workspace *mw;
double chisq, Rsq, dof, tss;
vector<double> xControl, yControl, xFit, yFit;
gsl_rng_env_setup();
r = gsl_rng_alloc(gsl_rng_default);
/* allocate a cubic bspline workspace (k = 4) */
bw = gsl_bspline_alloc(4, nbreak);
B = gsl_vector_alloc(ncoeffs);
x = gsl_vector_alloc(n);
y = gsl_vector_alloc(n);
X = gsl_matrix_alloc(n, ncoeffs);
c = gsl_vector_alloc(ncoeffs);
w = gsl_vector_alloc(n);
cov = gsl_matrix_alloc(ncoeffs, ncoeffs);
mw = gsl_multifit_linear_alloc(n, ncoeffs);
printf("#m=0,S=0\n");
/* this is the data to be fitted */
for (i = 0; i < n; ++i)
{
double sigma;
double xi = (15.0 / (N - 1)) * i;
double yi = cos(xi) * exp(-0.1 * xi);
sigma = 0.1 * yi;
dy = gsl_ran_gaussian(r, sigma);
yi += dy;
gsl_vector_set(x, i, xi);
xControl.push_back(xi);
gsl_vector_set(y, i, yi);
yControl.push_back(yi);
gsl_vector_set(w, i, 1.0 / (sigma * sigma));
printf("%f %f\n", xi, yi);
}
/* use uniform breakpoints on [0, 15] */
gsl_bspline_knots_uniform(0.0, 15.0, bw);
/* construct the fit matrix X */
for (i = 0; i < n; ++i)
{
double xi = gsl_vector_get(x, i);
/* compute B_j(xi) for all j */
gsl_bspline_eval(xi, B, bw);
/* fill in row i of X */
for (j = 0; j < ncoeffs; ++j)
{
double Bj = gsl_vector_get(B, j);
gsl_matrix_set(X, i, j, Bj);
}
}
/* do the fit */
gsl_multifit_wlinear(X, w, y, c, cov, &chisq, mw);
dof = n - ncoeffs;
tss = gsl_stats_wtss(w->data, 1, y->data, 1, y->size);
Rsq = 1.0 - chisq / tss;
fprintf(stderr, "chisq/dof = %e, Rsq = %f\n",
chisq / dof, Rsq);
/* output the smoothed curve */
{
double xi, yi, yerr;
printf("#m=1,S=0\n");
for (xi = 0.0; xi < 15.0; xi += 0.1)
{
gsl_bspline_eval(xi, B, bw);
gsl_multifit_linear_est(B, c, cov, &yi, &yerr);
xFit.push_back(xi);
yFit.push_back(yi);
printf("%f %f\n", xi, yi);
}
}
gsl_rng_free(r);
gsl_bspline_free(bw);
gsl_vector_free(B);
gsl_vector_free(x);
gsl_vector_free(y);
gsl_matrix_free(X);
gsl_vector_free(c);
gsl_vector_free(w);
gsl_matrix_free(cov);
gsl_multifit_linear_free(mw);
TGraph *gr = LoadGraphFromVectors(xControl, yControl);
TGraph *grFit = LoadGraphFromVectors(xFit, yFit);
gr->SetMarkerColor(kRed);
TCanvas *c1 = new TCanvas("c1", "Graph", 200, 10, 700, 500);
gr->Draw("apz");
grFit->Draw("SAME");
c1->Update();
}
// [[Rcpp::export]]
Rcpp::List fitData(Rcpp::DataFrame ds) {
const size_t ncoeffs = NCOEFFS;
const size_t nbreak = NBREAK;
const size_t n = N;
size_t i, j;
Rcpp::DataFrame D(ds); // construct the data.frame object
RcppGSL::vector<double> y = D["y"]; // access columns by name,
RcppGSL::vector<double> x = D["x"]; // assigning to GSL vectors
RcppGSL::vector<double> w = D["w"];
gsl_bspline_workspace *bw;
gsl_vector *B;
gsl_vector *c;
gsl_matrix *X, *cov;
gsl_multifit_linear_workspace *mw;
double chisq, Rsq, dof, tss;
bw = gsl_bspline_alloc(4, nbreak); // allocate a cubic bspline workspace (k = 4)
B = gsl_vector_alloc(ncoeffs);
X = gsl_matrix_alloc(n, ncoeffs);
c = gsl_vector_alloc(ncoeffs);
cov = gsl_matrix_alloc(ncoeffs, ncoeffs);
mw = gsl_multifit_linear_alloc(n, ncoeffs);
gsl_bspline_knots_uniform(0.0, 15.0, bw); // use uniform breakpoints on [0, 15]
for (i = 0; i < n; ++i) { // construct the fit matrix X
double xi = gsl_vector_get(x, i);
gsl_bspline_eval(xi, B, bw); // compute B_j(xi) for all j
for (j = 0; j < ncoeffs; ++j) { // fill in row i of X
double Bj = gsl_vector_get(B, j);
gsl_matrix_set(X, i, j, Bj);
}
}
gsl_multifit_wlinear(X, w, y, c, cov, &chisq, mw); // do the fit
dof = n - ncoeffs;
tss = gsl_stats_wtss(w->data, 1, y->data, 1, y->size);
Rsq = 1.0 - chisq / tss;
Rcpp::NumericVector FX(151), FY(151); // output the smoothed curve
double xi, yi, yerr;
for (xi = 0.0, i=0; xi < 15.0; xi += 0.1, i++) {
gsl_bspline_eval(xi, B, bw);
gsl_multifit_linear_est(B, c, cov, &yi, &yerr);
FX[i] = xi;
FY[i] = yi;
}
Rcpp::List res =
Rcpp::List::create(Rcpp::Named("X")=FX,
Rcpp::Named("Y")=FY,
Rcpp::Named("chisqdof")=Rcpp::wrap(chisq/dof),
Rcpp::Named("rsq")=Rcpp::wrap(Rsq));
gsl_bspline_free(bw);
gsl_vector_free(B);
gsl_matrix_free(X);
gsl_vector_free(c);
gsl_matrix_free(cov);
gsl_multifit_linear_free(mw);
y.free();
x.free();
w.free();
return(res);
}
/*=============================================================================
* FITTING CODE
*=============================================================================*/
int find_best_alpha(){
//double alpha_2pcf[num_alpha][nr], trials_2pcf[num_alpha][ntrials][total_nr], alpha_err[num_alpha][nr];
double **alpha_2pcf, ***trials_2pcf, **alpha_err;
double low, high, da;
long i,nend,k,j,ir,jk;
double chi2;
double yi,yerr,xi,minerr;
int nbreak, iii,ind,min_ind,max_ind;
long thisseed[Nalpha*num_alpha*ntrials];
#ifdef ALLOUT
char Output2PCF[LINELENGTH];
char ThisFile[15];
#endif
ncoeffs = num_alpha-1;
nbreak =ncoeffs-2;
// Allocate alphavec, which is our result
//alphavec = (double *) calloc(Nalpha,sizeof(double));
//betavec = (double *) calloc(Nalpha,sizeof(double));
alpha_2pcf = (double **) calloc(num_alpha,sizeof(double *));
alpha_err = (double **) calloc(num_alpha,sizeof(double *));
trials_2pcf = (double ***) calloc(num_alpha,sizeof(double **));
for (i=0;i<num_alpha;i++){
alpha_2pcf[i] = (double *) calloc(nr,sizeof(double));
alpha_err[i] = (double *) calloc(nr,sizeof(double));
trials_2pcf[i] = (double **) calloc(ntrials,sizeof(double*));
for (j=0;j<ntrials;j++)
trials_2pcf[i][j] = (double *) calloc(total_nr,sizeof(double));
}
// allocate a cubic bspline workspace (k = 4)
bw = gsl_bspline_alloc(4, nbreak);
B = gsl_vector_alloc(ncoeffs);
alpha_grid = gsl_vector_alloc(num_alpha);
chi2_alpha = gsl_vector_alloc(num_alpha);
X = gsl_matrix_alloc(num_alpha,ncoeffs);
c = gsl_vector_alloc(ncoeffs);
weights = gsl_vector_alloc(num_alpha);
cov = gsl_matrix_alloc(ncoeffs, ncoeffs);
mw = gsl_multifit_linear_alloc(num_alpha, ncoeffs);
// Loop through each mass bin
nend = 0;
iii = 0;
seed = time(NULL);
for (i=0;i<Nalpha;i++){
for(j=0;j<num_alpha;j++){
for(k=0;k<ntrials;k++){
thisseed[iii] = seed + iii;
iii++;
}
}
}
fprintf(stderr,"STARTING LOOPS...\n");
iii = 0;
for (i=0;i<Nalpha;i++){
// Get where to place halos to
nend += ncuts[i];
// Calculate a more optimum alpha_grid for this bin
if (i < 2)
low = alpha_ratio_1*best_alpha;
else{
low = alpha_ratio*best_alpha;
}
high = 1.05*best_alpha;
da = (high-low)/(num_alpha-1);
fprintf(stderr,"STARTING THREADS\n");
#ifndef NO_PAR_FIT
#pragma omp parallel for num_threads(nthreads) private(jk,j,k) \
shared(num_alpha,ntrials,i,alpha_grid,low,da,stderr,Nalpha,alphavec,iii,mcuts,ListOfParticles,\
NPartPerCell,x,y,z,Lbox,Npart,Nlin,HaloMass,nend,mpart,recalc_frac,betavec,thisseed,trials_2pcf,rho,maxr,\
total_nr,Nhalos) default(none)
#endif
for(jk=0;jk<num_alpha*ntrials;jk++){
fprintf(stderr,"Thread %d/%d\n",omp_get_thread_num(),omp_get_num_threads());
float *hx,*hy,*hz,*hR;
double *thisalphavec;
double *ercorr;
unsigned long long *DD;
hx = (float *) calloc(Nhalos,sizeof(float));
hy = (float *) calloc(Nhalos,sizeof(float));
hz = (float *) calloc(Nhalos,sizeof(float));
hR = (float *) calloc(Nhalos,sizeof(float));
thisalphavec = (double *) calloc(Nalpha,sizeof(double));
DD = (unsigned long long *) calloc(total_nr,sizeof(unsigned long long));
ercorr = (double *) calloc(total_nr,sizeof(double));
k=jk%ntrials;
j=jk/ntrials;
fprintf(stderr,"MOVED MEMORY\n");
fprintf(stderr,"GOT k,j: %ld, %ld\n",k,j);
fprintf(stderr,"sizeof M : %f MB\n",(Nlin*Nlin*Nlin*sizeof(double)/1024./1024.));
//define the alpha grid for this mass bin
gsl_vector_set(alpha_grid,j,low+j*da);
// create a local alphavec, to which we add the current gridded alpha
int itemp;
for (itemp=0;itemp<Nalpha;itemp++)
thisalphavec[itemp] = alphavec[itemp];
//fprintf(stderr,"mem copied\n");
thisalphavec[i] = gsl_vector_get(alpha_grid,j);
// Place the halos
#ifdef NO_PAR_FIT
place_halos(nend,HaloMass, Nlin, Npart, x, y, z, NULL,NULL,NULL,Lbox,
rho,thisseed[jk+i*num_alpha*ntrials],
mpart,nthreads,thisalphavec, betavec, mcuts, Nalpha, recalc_frac,hx, hy, hz,
NULL,NULL,NULL,hR,ListOfParticles,NPartPerCell);
#else
place_halos(nend,HaloMass, Nlin, Npart, x, y, z, NULL,NULL,NULL,Lbox,
rho,thisseed[jk+i*num_alpha*ntrials],
mpart,1,thisalphavec, betavec, mcuts, Nalpha, recalc_frac,hx, hy, hz,
NULL,NULL,NULL,hR,ListOfParticles,NPartPerCell);
#endif
fprintf(stderr,"correlating...\n");
//Get the 2PCF
correlate(nend, Lbox,hx,hy,hz,trials_2pcf[j][k], ercorr, DD,total_nr,maxr,1);
fprintf(stderr,"...correlated\n");
free(hx);
free(hy);
free(hz);
free(hR);
free(thisalphavec);
free(ercorr);
free(DD);
}
for (jk=0;jk<num_alpha*ntrials;jk++){
k=jk%ntrials;
j=jk/ntrials;
fprintf(stderr,"RAWCORR %ld, %ld: %e\n",j,k,trials_2pcf[j][k][0]);
}
// #pragma omp parallel for private(ir,j,chi2,k) shared(num_alpha,stderr,i,nr,alpha_2pcf) default(none)
fprintf(stderr,"GOT CORRELATIONS , GETTING CHI2...\n");
for(j=0;j<num_alpha;j++){
//Get mean and stdev of trials_2pcf
chi2 = 0.0;
for (ir=0;ir<nr;ir++){
alpha_2pcf[j][ir] = 0.0;
for(k=0;k<ntrials;k++){
alpha_2pcf[j][ir] += trials_2pcf[j][k][ir+total_nr-nr-2];
}
alpha_2pcf[j][ir] = alpha_2pcf[j][ir]/ntrials;
alpha_err[j][ir] = 0.0;
for(k=0;k<ntrials;k++){
alpha_err[j][ir] += pow((trials_2pcf[j][k][ir+total_nr-nr-2]-alpha_2pcf[j][ir]),2);
}
alpha_err[j][ir] = pow((alpha_err[j][ir]/(ntrials-1)),0.5);
// Now get chi^2 values
#ifdef REL_CHI2
chi2 += pow(((alpha_2pcf[j][ir]-nbody_2pcf[i][ir+total_nr-nr-2])/nbody_2pcf[i][ir+total_nr-nr-2]),2);
#else
chi2 += pow(((alpha_2pcf[j][ir]-nbody_2pcf[i][ir+total_nr-nr-2])/alpha_err[j][ir]),2);
#endif
fprintf(stderr,"%ld, %ld, %e, %e, %e, %e\n",j,ir,alpha_2pcf[j][ir],nbody_2pcf[i][ir+total_nr-nr-2],alpha_err[j][ir],chi2);
}
gsl_vector_set(chi2_alpha,j,chi2/nr);
gsl_vector_set(weights,j,nr/chi2);
}
// #endif //NO_PARALLEL_FIT
//*/
#ifdef ALLOUT
//OUTPUT SOME THINGS FOR CHECKING
sprintf(ThisFile,"/raw.2pcf.%ld",i);
strcpy(Output2PCF,OutputDir);
strcat(Output2PCF,ThisFile);
FILE* output_2pcf;
output_2pcf = fopen(Output2PCF,"w");
//header
fprintf(output_2pcf,"# r, ");
for (k=0;k<num_alpha;k++){
fprintf(output_2pcf,"%e\t",gsl_vector_get(alpha_grid,k));
}
fprintf(output_2pcf,"\n");
//table
for (ir=0;ir<nr;ir++){
fprintf(output_2pcf,"%e\t",(ir+total_nr-nr+0.5)*maxr/total_nr);
for(k=0;k<num_alpha-1;k++){
fprintf(output_2pcf,"%e\t",alpha_2pcf[k][ir]);
}
fprintf(output_2pcf,"%e\n",alpha_2pcf[num_alpha-1][ir]);
}
fclose(output_2pcf);
sprintf(ThisFile,"/raw.err.%ld",i);
strcpy(Output2PCF,OutputDir);
strcat(Output2PCF,ThisFile);
FILE* output_err;
output_err = fopen(Output2PCF,"w");
//header
fprintf(output_err,"# r, ");
for (k=0;k<num_alpha;k++){
fprintf(output_err,"%e\t",gsl_vector_get(alpha_grid,k));
}
fprintf(output_err,"\n");
//table
for (ir=0;ir<nr;ir++){
fprintf(output_err,"%e\t",(ir+total_nr-nr+0.5)*maxr/total_nr);
for(k=0;k<num_alpha-1;k++){
fprintf(output_err,"%e\t",alpha_err[k][ir]);
}
fprintf(output_err,"%e\n",alpha_err[num_alpha-1][ir]);
}
fclose(output_err);
sprintf(ThisFile,"/chi2.%ld",i);
strcpy(Output2PCF,OutputDir);
strcat(Output2PCF,ThisFile);
FILE* chifile;
chifile = fopen(Output2PCF,"w");
fprintf(chifile,"# alpha, chi2, weight\n");
for (k=0;k<num_alpha;k++){
fprintf(chifile,"%e\t%e\t%e\n",gsl_vector_get(alpha_grid,k),gsl_vector_get(chi2_alpha,k),
gsl_vector_get(weights,k));
}
fclose(chifile);
#endif
// Check if final value or initial value is the smallest
minerr = gsl_vector_get(chi2_alpha,0);
ind = 0;
for(k=1;k<num_alpha;k++){
if(minerr>gsl_vector_get(chi2_alpha,k)){
minerr = gsl_vector_get(chi2_alpha,k);
ind = k;
}
}
if(ind==0){
fprintf(stderr,"ERROR: alpha_grid doesn't extend low enough, set alpha_ratio lower");
}
if(ind==num_alpha-1){
fprintf(stderr,"ERROR: alpha_grid doesn't extend high enough, set best_alpha higher");
}
if (ind>=2){
min_ind = ind-2;
}else{
min_ind = 0;
}
if (ind<=num_alpha-3){
max_ind = ind+2;
}else{
max_ind = num_alpha-1;
}
/* use uniform breakpoints on interval */
gsl_bspline_knots_uniform(gsl_vector_get(alpha_grid,0), gsl_vector_get(alpha_grid,num_alpha-1), bw);
/* construct the fit matrix X */
for (k = 0; k < num_alpha; ++k){
double xi = gsl_vector_get(alpha_grid, k);
/* compute B_j(xi) for all j */
gsl_bspline_eval(xi, B, bw);
/* fill in row i of X */
for (j = 0; j < ncoeffs; ++j){
double Bj = gsl_vector_get(B, j);
gsl_matrix_set(X, k, j, Bj);
}
}
fprintf(stderr,"Got to the fit part\n");
/* do the fit */
gsl_multifit_wlinear(X, weights, chi2_alpha, c, cov, &chisq, mw);
// PRINT OUT EVERYTHING WE HAVE SO FAR
fprintf(stderr,"alpha\tchi2_alpha\t\n");
for (k=0;k<num_alpha;k++){
fprintf(stderr,"%e\t%e\t\n",gsl_vector_get(alpha_grid,k),
gsl_vector_get(chi2_alpha,k));
}
#ifdef VERB
dof = num_alpha - ncoeffs;
tss = gsl_stats_wtss(weights->data, 1, chi2_alpha->data, 1, chi2_alpha->size);
Rsq = 1.0 - chisq / tss;
fprintf(stderr, "chisq/dof = %e, Rsq = %f\n",chisq / dof, Rsq);
#endif
for (xi=gsl_vector_get(alpha_grid,0);xi<gsl_vector_get(alpha_grid,num_alpha-1);xi+=0.01){
gsl_bspline_eval(xi, B, bw);
gsl_multifit_linear_est(B, c, cov, &yi, &yerr);
fprintf(stderr,"%e\t%e\t%e\n",xi,yi,gsl_vector_get(B,0));
}
//DO THE MINIMIZATION
alphavec[i] = minimize(gsl_vector_get(alpha_grid,min_ind), gsl_vector_get(alpha_grid,max_ind),
gsl_vector_get(alpha_grid,ind));
best_alpha = alphavec[i];
fprintf(stderr,"\n Best alpha: %f\n\n",best_alpha);
}
return 0;
}
