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/* Copyright (c) 2019, Anthony Latorre <tlatorre at uchicago>
*
* This program is free software: you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option)
* any later version.
* This program is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
* more details.
* You should have received a copy of the GNU General Public License along with
* this program. If not, see <https://www.gnu.org/licenses/>.
*/
#include "muon.h"
#include "random.h"
#include "optics.h"
#include "quantum_efficiency.h"
#include <math.h>
#include <gsl/gsl_histogram.h>
#include "sno.h"
#include "pdg.h"
#include "vector.h"
#include "solid_angle.h"
#include <stdlib.h> /* for atoi() and strtod() */
#include <unistd.h> /* for exit() */
#include "scattering.h"
#include <errno.h> /* for errno */
#include <string.h> /* for strerror() */
void simulate_cos_theta_distribution(int N, gsl_histogram *h, double T, double theta0)
{
/* Simulate the cos(theta) distribution around the original track direction
* for a muon with kinetic energy T. The angle from the original track
* distribution is simulated as a gaussian distribution with standard
* deviation `theta0`. */
int i;
double theta, phi, wavelength, u, qe, index, cerenkov_angle, dir[3], n[3], dest[3], E, p, beta, cos_theta, thetax, thetay;
i = 0;
while (i < N) {
/* Generate a random wavelength in the range 300-600 nm from the
* distribution of Cerenkov light. */
u = genrand_real2();
wavelength = 300.0*600.0/(u*(300.0-600.0) + 600.0);
qe = get_quantum_efficiency(wavelength);
/* Check to see if the photon was detected. */
if (genrand_real2() > qe) continue;
index = get_index_snoman_d2o(wavelength);
/* Calculate total energy */
E = T + MUON_MASS;
p = sqrt(E*E - MUON_MASS*MUON_MASS);
beta = p/E;
cerenkov_angle = acos(1/(index*beta));
/* Assuming the muon track is dominated by small angle scattering, the
* angular distribution looks like the product of two uncorrelated
* Gaussian distributions with a standard deviation of `theta0` in the
* plane perpendicular to the track direction. Here, we draw two random
* angles and then compute the polar and azimuthal angle for the track
* direction. */
thetax = randn()*theta0;
thetay = randn()*theta0;
theta = sqrt(thetax*thetax + thetay*thetay);
phi = atan2(thetay,thetax);
n[0] = sin(theta)*cos(phi);
n[1] = sin(theta)*sin(phi);
n[2] = cos(theta);
/* To compute the direction of the photon, we start with a vector which
* has the same azimuthal angle as the track direction but is offset
* from the track direction in the polar angle by the Cerenkov angle
* and then rotate it around the track direction by a random angle
* `phi`. */
dir[0] = sin(cerenkov_angle + theta)*cos(phi);
dir[1] = sin(cerenkov_angle + theta)*sin(phi);
dir[2] = cos(cerenkov_angle + theta);
phi = genrand_real2()*2*M_PI;
rotate(dest,dir,n,phi);
cos_theta = dest[2];
gsl_histogram_increment(h, cos_theta);
i += 1;
}
}
void usage(void)
{
fprintf(stderr,"Usage: ./test-likelihood [options]\n");
fprintf(stderr," -n number of events\n");
fprintf(stderr," -T kinetic energy of muon (MeV)\n");
fprintf(stderr," -t standard deviation of angular distribution\n");
fprintf(stderr," -b number of bins\n");
fprintf(stderr," --xmin lowest value of cos(theta)\n");
fprintf(stderr," --xmax highest value of cos(theta)\n");
fprintf(stderr," -h display this help message\n");
exit(1);
}
int main(int argc, char **argv)
{
size_t i, N, bins;
double T, theta0;
double E, p, beta;
double xmin, xmax;
N = 100000;
bins = 1000;
T = 1000.0;
theta0 = 0.1;
xmin = -1.0;
xmax = 1.0;
for (i = 1; i < argc; i++) {
if (!strncmp(argv[i], "--", 2)) {
if (!strcmp(argv[i]+2,"xmin")) {
xmin = strtod(argv[++i],NULL);
continue;
} else if (!strcmp(argv[i]+2,"xmax")) {
xmax = strtod(argv[++i],NULL);
continue;
}
} else if (argv[i][0] == '-') {
switch (argv[i][1]) {
case 'n':
N = atoi(argv[++i]);
break;
case 'b':
bins = atoi(argv[++i]);
break;
case 'T':
T = strtod(argv[++i],NULL);
break;
case 't':
theta0 = strtod(argv[++i],NULL);
break;
case 'h':
usage();
default:
fprintf(stderr, "unrecognized option '%s'\n", argv[i]);
exit(1);
}
}
}
gsl_histogram *h = gsl_histogram_alloc(bins);
gsl_histogram_set_ranges_uniform(h,xmin,xmax);
simulate_cos_theta_distribution(N, h, T, theta0);
gsl_histogram_scale(h, 1.0/gsl_histogram_sum(h));
FILE *pipe = popen("graph -T X --bitmap-size 2000x2000 -X 'Cos(theta)' -Y Probability", "w");
if (!pipe) {
fprintf(stderr, "error running graph command: %s\n", strerror(errno));
exit(1);
}
for (i = 0; i < h->n; i++) {
fprintf(pipe, "%g %g\n", h->range[i], h->bin[i]);
fprintf(pipe, "%g %g\n", h->range[i+1], h->bin[i]);
}
fprintf(pipe, "\n\n");
gsl_histogram_reset(h);
init_interpolation();
/* Calculate total energy */
E = T + MUON_MASS;
p = sqrt(E*E - MUON_MASS*MUON_MASS);
beta = p/E;
for (i = 0; i < bins; i++) {
double lo, hi;
gsl_histogram_get_range(h, i, &lo, &hi);
double cos_theta = (lo+hi)/2.0;
h->bin[i] = get_probability(beta, cos_theta, theta0);
}
free_interpolation();
printf("\n\n");
gsl_histogram_scale(h, 1.0/gsl_histogram_sum(h));
for (i = 0; i < h->n; i++) {
fprintf(pipe, "%g %g\n", h->range[i], h->bin[i]);
fprintf(pipe, "%g %g\n", h->range[i+1], h->bin[i]);
}
fprintf(pipe, "\n\n");
if (pclose(pipe)) {
fprintf(stderr, "error closing graph command: %s\n", strerror(errno));
exit(1);
}
gsl_histogram_free(h);
return 0;
}
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