/*******************************************************************************
* This file is part of SWIFT.
* Copyright (C) 2022 Filip Husko (filip.husko@durham.ac.uk).
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser 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 Lesser General Public License
* along with this program. If not, see .
*
******************************************************************************/
#include
/* System includes. */
#include
/* Local headers. */
#include "swift.h"
/* Number of different maximal opening angles to test between 0 and pi/2. */
const int N_cos = 20;
/* Number of random cones to draw for each opening angle. */
const int N_cos_cone = 30;
/* Cubical grid size when checking the cone function along axes of the Cartesian
* grid. Should be at least 2. */
const int N_cube = 5;
/**
* @brief Test to check whether the function that generates random directions
* within a cone actually generates vectors only within that cone. It also tests
* whether they are uniformly distributed in solid angle.
*
* @param id_bh The ID of a black hole particle around whose spin vector a given
* cone is drawn.
* @param ti_current Current time of the simulation.
* @param type Random number type used.
* @param opening_angle The opening angle of the cone (in radians).
* @param unit_vector The vector that defines where the cone is pointing.
* @param N_test How many random directions to draw within the cone.
* @param N_bins How many bins to distribute these directions into when testing
* the uniformity of the distribution.
* @param tolerance The tolerance of each bin relative to the expected value.
*/
float test_cone(int64_t id_bh, const integertime_t ti_current,
const enum random_number_type type, double opening_angle,
float unit_vector[3]) {
/* Compute cosine that corresponds to the maximum opening angle */
const double cos_theta_max = cos(opening_angle);
/* Initialize an array that will hold a random vector every step */
float rand_vector[3];
/* Generate a random unit vector within a cone around unit_vector */
random_direction_in_cone(id_bh, ti_current, type, opening_angle, unit_vector,
rand_vector);
/* Check that this vector is actually within the cone we want */
const double cos_rand_unit = rand_vector[0] * unit_vector[0] +
rand_vector[1] * unit_vector[1] +
rand_vector[2] * unit_vector[2];
if (cos_rand_unit < 0.99999 * cos_theta_max) {
printf("Cos_opening_angle is: %f, Random cos is: %f\n", cos_theta_max,
cos_rand_unit);
error("Generated random unit vector is outside cone.");
}
return cos_rand_unit;
}
int main(int argc, char *argv[]) {
/* Initialize CPU frequency, this also starts time. */
unsigned long long cpufreq = 0;
clocks_set_cpufreq(cpufreq);
/* Choke on FPEs */
#ifdef HAVE_FE_ENABLE_EXCEPT
feenableexcept(FE_DIVBYZERO | FE_INVALID | FE_OVERFLOW);
#endif
/* Get some randomness going */
const int seed = time(NULL);
message("Seed = %d", seed);
srand(seed);
/* Log the swift random seed */
message("SWIFT random seed = %d", SWIFT_RANDOM_SEED_XOR);
/* Test the random-vector-in-cone function, for different values of opening
* angle from 0 to pi/2 (in radians). For each of these opening angles we draw
* some number of cones, and test whether each of those has a uniform
* distribution of randomly drawn vectors within it.*/
for (int i = 1; i < N_cos; ++i) {
/* Opening angle to use */
const double opening_angle = 0.5 * M_PI * (double)i / (double)N_cos;
/* Do the test for N_cos_cone cones with this opening angle */
for (int l = 0; l < N_cos_cone; ++l) {
/* Generate an id for the bh and a time. We do this for every opening
* angle and every cone. */
const long long id_bh = rand() * (1LL << 31) + rand();
const integertime_t ti_current = rand() * (1LL << 31) + rand();
/* Generate a random unit vector that defines a cone, along with the
* opening angle. */
float unit_vector[3];
const double cos_unit =
random_unit_interval(id_bh, ti_current, random_number_BH_kick);
const double sin_unit = sqrtf(max(0., (1. - cos_unit) * (1. + cos_unit)));
const double phi_unit =
(2. * M_PI) * random_unit_interval(id_bh * id_bh, ti_current,
random_number_BH_kick);
unit_vector[0] = sin_unit * cos(phi_unit);
unit_vector[1] = sin_unit * sin(phi_unit);
unit_vector[2] = cos_unit;
/* Do the test. */
test_cone(id_bh, ti_current, random_number_BH_kick, opening_angle,
unit_vector);
}
}
/* Repeat the same test but with a larger number of random directions and
* bins, but for just one opening angle and one randomly generated cone */
const double opening_angle_0 = 0.2;
/* Compute cosine that corresponds to the maximum opening angle */
const double cos_theta_max = cos(opening_angle_0);
/* Generate a random unit vector that defines a cone, along with the
* opening angle. */
const long long id_bh_0 = rand() * (1LL << 31) + rand();
const integertime_t ti_current_0 = rand() * (1LL << 31) + rand();
float unit_vector_0[3];
const double cos_unit =
random_unit_interval(id_bh_0, ti_current_0, random_number_BH_kick);
const double sin_unit = sqrtf(max(0., (1. - cos_unit) * (1. + cos_unit)));
const double phi_unit =
(2. * M_PI) * random_unit_interval(id_bh_0 * id_bh_0, ti_current_0,
random_number_BH_kick);
unit_vector_0[0] = sin_unit * cos(phi_unit);
unit_vector_0[1] = sin_unit * sin(phi_unit);
unit_vector_0[2] = cos_unit;
/* Some parameters to test the uniformity of drawn vectors */
int N_test = 10000000;
int N_bins = 100;
float tolerance = 0.05;
/* Initialize an array that will hold the binned number of drawn cosines,
i.e. this is the probability density function that we wish to test. */
double binned_cosines[N_bins];
for (int j = 0; j < N_bins; ++j) {
binned_cosines[j] = 0.;
}
/* Draw N_test vectors and bin them to test uniformity */
for (int k = 0; k < N_test; ++k) {
const long long id_bh = rand() * (1LL << 31) + rand();
const integertime_t ti_current = rand() * (1LL << 31) + rand();
/* Do the test, with a newly generated BH id and time */
const float cos_rand_unit =
test_cone(id_bh, ti_current, random_number_BH_kick, opening_angle_0,
unit_vector_0);
/* Add the unit vector to the probability density function array. The solid
* angle subtended by some angle theta grows as (1-cos(theta)). Furthermore,
* we are limited to the spherical cap defined by the angles [0, theta_max].
* Therefore the variable which we expect to be uniformly distributed is (1
* - cos(theta)) / (1 - cos(theta_max)). */
double uniform_variable = (1. - cos_rand_unit) / (1 - cos_theta_max);
for (int j = 0; j < N_bins; ++j) {
if ((uniform_variable > (double)j / (double)N_bins) &&
(uniform_variable < (double)(j + 1) / (double)N_bins)) {
binned_cosines[j] = binned_cosines[j] + 1. / (double)N_test;
}
}
}
/* Check whether the binned quantity is really uniformly distributed. If it
* is, the density (value) of each bin should be 1/N_bin. */
for (int j = 0; j < N_bins; ++j) {
if ((binned_cosines[j] < (1. - tolerance) / (double)N_bins) ||
(binned_cosines[j] > (1. + tolerance) / (double)N_bins)) {
error(
"Generated distribution of random unit vectors within a cone exceeds "
"the limit imposed by the tolerance.");
}
}
/* We now repeat the same process, but we do not generate random unit vectors
* to define the cones. Instead, we sample unit vectors along the grid
* [-N_cube, -N_cube + 1, ..., N_cube -1, N_cube] ^ 3. This can be, e.g. [-2,
* -1, 0, 1, 2] ^ 3 (N_cube should be at least 2). This makes sure that the
* function that generates random unit vectors is well-defined if the unit
* vectors that define the cones point along any of the Cartesian axes, or if
* any of their components are equal. Here we use a fixed opening angle of
* 0.1, since we assume that the earlier test passing means that the function
* correctly does what it should for all opening angles. */
const double opening_angle = 0.1;
for (int x = -N_cube; x < N_cube + 1; ++x) {
for (int y = -N_cube; y < N_cube + 1; ++y) {
for (int z = -N_cube; z < N_cube + 1; ++z) {
/* Create our unit vector on this point of the grid */
float unit_vector[3] = {(float)x, (float)y, (float)z};
float unit_vector_norm =
sqrtf((float)(x * x) + (float)(y * y) + (float)(z * z));
/* Only do the test if the norm is >0, i.e. if we are not at the origin
* of the coordinate frame. */
if (unit_vector_norm > 0) {
/* Generate an id for the bh and a time. We do this for every opening
* angle and every cone. */
const long long id_bh = rand() * (1LL << 31) + rand();
const integertime_t ti_current = rand() * (1LL << 31) + rand();
/* Normalize the unit vector. */
unit_vector[0] = unit_vector[0] / unit_vector_norm;
unit_vector[1] = unit_vector[1] / unit_vector_norm;
unit_vector[2] = unit_vector[2] / unit_vector_norm;
/* Do the test. */
test_cone(id_bh, ti_current, random_number_BH_kick, opening_angle,
unit_vector);
}
}
}
}
return 0;
}