/* Copyright (c) 2019, Anthony Latorre * * 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 . */ #include "muon.h" #include "random.h" #include "optics.h" #include "quantum_efficiency.h" #include #include #include "sno.h" #include "pdg.h" #include "vector.h" #include "solid_angle.h" #include /* for atoi() and strtod() */ #include /* for exit() */ #include "scattering.h" #include /* for errno */ #include /* 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; double sin_theta = sqrt(1-cos_theta*cos_theta); h->bin[i] = get_probability(beta, cos_theta, sin_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; } 32'>132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297