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Diffstat (limited to 'src/samball/samball.py')
-rw-r--r-- | src/samball/samball.py | 100 |
1 files changed, 0 insertions, 100 deletions
diff --git a/src/samball/samball.py b/src/samball/samball.py deleted file mode 100644 index e5d84ad..0000000 --- a/src/samball/samball.py +++ /dev/null @@ -1,100 +0,0 @@ -# samball --- Sample n-dimensional balls -# Copyright © 2021 Arun I <arunisaac@systemreboot.net> -# Copyright © 2021 Murugesan Venkatapathi <murugesh@iisc.ac.in> -# -# 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/>. - -from numpy import arcsin, cos, dot, empty, log, ones, sin, sqrt, pi, where -from numpy.random import randn, random -from numpy.linalg import norm -from scipy.special import betainc, betaincinv - -def random_vector_on_sphere(dim): - """Return a random vector uniformly distributed on the unit sphere.""" - x = randn(dim) - return x / norm(x) - -def planar_angle2solid_angle_fraction(planar_angle, dim): - """Return the solid angle fraction for a given planar angle.""" - alpha = (dim - 1) / 2 - beta = 1/2 - return where(planar_angle < pi/2, - 0.5*betainc(alpha, beta, sin(planar_angle)**2), - 1 - 0.5*betainc(alpha, beta, sin(planar_angle)**2)) - -def solid_angle_fraction2planar_angle(solid_angle_fraction, dim): - """Return the planar angle for a given solid angle fraction.""" - alpha = (dim - 1) / 2 - beta = 1/2 - return where(solid_angle_fraction < 1/2, - arcsin(sqrt(betaincinv(alpha, beta, 2*solid_angle_fraction))), - pi - arcsin(sqrt(betaincinv(alpha, beta, 2*(1-solid_angle_fraction))))) - -def rotate_from_nth_canonical(x, axis): - """Rotate vector from around the nth canonical axis to the given axis. - """ - xn = x[-1] - axisn = axis[-1] - if axisn != 1: - b = norm(axis[:-1]) - a = (dot(x, axis) - xn*axisn) / b - s = sqrt(1 - axisn**2) - x = x + (xn*s + a*(axisn - 1))/b * axis - x[-1] = x[-1] + xn*(axisn - 1) - a*s \ - - axisn*(xn*s + a*(axisn - 1))/b - return x - -def random_planar_angle_cdf(maximum_planar_angle, dim): - """Return a random planar angle using inverse transform sampling.""" - return solid_angle_fraction2planar_angle( - planar_angle2solid_angle_fraction(maximum_planar_angle, dim)*random(), - dim) - -def random_planar_angle_pdf(maximum_planar_angle, dim): - """Return a random planar angle using rejection sampling.""" - # We apply the log function just to prevent the floats from - # underflowing. - box_height = (dim-2)*log(sin(min(maximum_planar_angle, pi/2))) - while True: - theta = maximum_planar_angle*random() - f = box_height + log(random()) - if f < (dim-2)*log(sin(theta)): - return theta - -def random_vector_on_disk(axis, planar_angle): - """Return a random vector uniformly distributed on the periphery of a -disk.""" - dim = axis.size - x = empty(dim) - x[:-1] = sin(planar_angle) * random_vector_on_sphere(dim - 1) - x[-1] = cos(planar_angle) - return rotate_from_nth_canonical(x, axis) - -def random_vector_on_spherical_cap_cdf(axis, maximum_planar_angle): - """Return a random vector uniformly distributed on a spherical -cap. The random planar angle is generated using inverse transform -sampling.""" - return random_vector_on_disk(axis, random_planar_angle_cdf(maximum_planar_angle, axis.size)) - -def random_vector_on_spherical_cap_pdf(axis, maximum_planar_angle): - """Return a random vector uniformly distributed on a spherical -cap. The random planar angle is generated using rejection sampling. - -This function is more numerically stable than -random_vector_on_spherical_cap_cdf for large dimensions and small -angles. - - """ - return random_vector_on_disk(axis, random_planar_angle_pdf(maximum_planar_angle, axis.size)) |