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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);
</* 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 "misc.h"
#include <math.h>
#include <stdlib.h> /* for size_t */
#include <gsl/gsl_sf_gamma.h>
#include "vector.h"
#include <stdio.h>
#include <stdlib.h>
static struct {
int n;
double f;
} ln_table[LN_MAX + 1] = {
{0,-INFINITY},
{1,0},
{2,0.69314718055994529},
{3,1.0986122886681098},
{4,1.3862943611198906},
{5,1.6094379124341003},
{6,1.791759469228055},
{7,1.9459101490553132},
{8,2.0794415416798357},
{9,2.1972245773362196},
{10,2.3025850929940459},
{11,2.3978952727983707},
{12,2.4849066497880004},
{13,2.5649493574615367},
{14,2.6390573296152584},
{15,2.7080502011022101},
{16,2.7725887222397811},
{17,2.8332133440562162},
{18,2.8903717578961645},
{19,2.9444389791664403},
{20,2.9957322735539909},
{21,3.044522437723423},
{22,3.0910424533583161},
{23,3.1354942159291497},
{24,3.1780538303479458},
{25,3.2188758248682006},
{26,3.2580965380214821},
{27,3.2958368660043291},
{28,3.3322045101752038},
{29,3.3672958299864741},
{30,3.4011973816621555},
{31,3.4339872044851463},
{32,3.4657359027997265},
{33,3.4965075614664802},
{34,3.5263605246161616},
{35,3.5553480614894135},
{36,3.5835189384561099},
{37,3.6109179126442243},
{38,3.6375861597263857},
{39,3.6635616461296463},
{40,3.6888794541139363},
{41,3.713572066704308},
{42,3.7376696182833684},
{43,3.7612001156935624},
{44,3.784189633918261},
{45,3.8066624897703196},
{46,3.8286413964890951},
{47,3.8501476017100584},
{48,3.8712010109078911},
{49,3.8918202981106265},
{50,3.912023005428146},
{51,3.9318256327243257},
{52,3.9512437185814275},
{53,3.970291913552122},
{54,3.9889840465642745},
{55,4.0073331852324712},
{56,4.0253516907351496},
{57,4.0430512678345503},
{58,4.0604430105464191},
{59,4.0775374439057197},
{60,4.0943445622221004},
{61,4.1108738641733114},
{62,4.1271343850450917},
{63,4.1431347263915326},
{64,4.1588830833596715},
{65,4.1743872698956368},
{66,4.1896547420264252},
{67,4.2046926193909657},
{68,4.219507705176107},
{69,4.2341065045972597},
{70,4.2484952420493594},
{71,4.2626798770413155},
{72,4.2766661190160553},
{73,4.290459441148391},
{74,4.3040650932041702},
{75,4.3174881135363101},
{76,4.3307333402863311},
{77,4.3438054218536841},
{78,4.3567088266895917},
{79,4.3694478524670215},
{80,4.3820266346738812},
{81,4.3944491546724391},
{82,4.4067192472642533},
{83,4.4188406077965983},
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