def test_pdf_rvs(self):
""" Check the Kullback-Leibler divergence between draws of random
samples form the distribution and the probability density function
of the distribution. This implementation only works for
one dimensional distriubtions.
"""
# set threshold for KL divergence
threshold = 0.1
# number of samples in random draw for test
n_samples = int(1e6)
# step size to take in PDF evaluation
step = 0.1
# loop over distributions
for dist in self.dists:
if dist.name in EXCLUDE_DIST_NAMES:
continue
for param in dist.params:
# get min and max
hist_min = dist.bounds[param][0]
hist_max = dist.bounds[param][1]
# generate some random draws
samples = dist.rvs(n_samples)[param]
# get the PDF
x = numpy.arange(hist_min, hist_max, step)
pdf = numpy.array([dist.pdf(**{param: xx}) for xx in x])
# compute the KL divergence and check if below threshold
kl_val = entropy.kl(samples,
pdf,
bins=pdf.size,
pdf2=True,
hist_min=hist_min,
hist_max=hist_max)
if not (kl_val < threshold):
raise ValueError("Class {} KL divergence is {} which is "
"greater than the threshold "
"of {}".format(dist.name, kl_val,
threshold))
def test_pdf_rvs(self):
""" Check the Kullback-Leibler divergence between draws of random
samples form the distribution and the probability density function
of the distribution. This implementation only works for
one dimensional distriubtions.
"""
# set threshold for KL divergence
threshold = 0.1
# number of samples in random draw for test
n_samples = int(1e6)
# step size to take in PDF evaluation
step = 0.1
# loop over distributions
for dist in self.dists:
if dist.name in EXCLUDE_DIST_NAMES:
continue
for param in dist.params:
# get min and max
hist_min = dist.bounds[param][0]
hist_max = dist.bounds[param][1]
# generate some random draws
samples = dist.rvs(n_samples)[param]
# get the PDF
x = numpy.arange(hist_min, hist_max, step)
pdf = numpy.array([dist.pdf(**{param : xx}) for xx in x])
# compute the KL divergence and check if below threshold
kl_val = entropy.kl(samples, pdf, bins=pdf.size, pdf2=True,
hist_min=hist_min, hist_max=hist_max)
if not (kl_val < threshold):
raise ValueError(
"Class {} KL divergence is {} which is "
"greater than the threshold "
"of {}".format(dist.name, kl_val, threshold))
def test_solid_angle(self):
""" The uniform solid angle and uniform sky position distributions
are two independent one-dimensional distributions. This tests checks
that the two indepdent one-dimensional distributions agree by comparing
the `rvs`, `pdf`, and `logpdf` functions' output.
"""
# set tolerance for comparing PDF and logPDF functions
tolerance = 0.01
# set threshold for KL divergence test
threshold = 0.1
# number of random draws for KL divergence test
n_samples = int(1e6)
# create generic angular distributions for test
sin_dist = distributions.SinAngle(theta=(0, 1))
cos_dist = distributions.CosAngle(theta=(-0.5, 0.5))
ang_dist = distributions.UniformAngle(theta=(0, 2))
# step size for PDF calculation
step = 0.1
# valid range of parameters
polar_sin = numpy.arange(0, numpy.pi, step)
polar_cos = numpy.arange(-numpy.pi, numpy.pi, step)
azimuthal = numpy.arange(0, 2 * numpy.pi, step)
# get Cartesian product to explore the two-dimensional space
cart_sin = cartesian([polar_sin, azimuthal])
# loop over distributions
for dist in self.dists:
if dist.name == distributions.UniformSolidAngle.name:
polar_vals = polar_sin
polar_dist = sin_dist
elif dist.name == distributions.UniformSky.name:
polar_vals = polar_cos
polar_dist = cos_dist
else:
continue
# check PDF equilvalent
pdf_1 = numpy.array([dist.pdf(**{dist.polar_angle : p,
dist.azimuthal_angle : a})
for p, a in cart_sin])
pdf_2 = numpy.array([polar_dist.pdf(**{"theta" : p})
* ang_dist.pdf(**{"theta" : a})
for p, a in cart_sin])
if not (numpy.all(numpy.nan_to_num(abs(1.0 - pdf_1 / pdf_2))
< tolerance)):
raise ValueError("The {} distribution PDF does not match its "
"component distriubtions.".format(dist.name))
# check logarithm of PDF equilvalent
pdf_1 = numpy.array([dist.logpdf(**{dist.polar_angle : p,
dist.azimuthal_angle : a})
for p, a in cart_sin])
pdf_2 = numpy.array([polar_dist.logpdf(**{"theta" : p})
+ ang_dist.logpdf(**{"theta" : a})
for p, a in cart_sin])
if not (numpy.all(numpy.nan_to_num(abs(1.0 - pdf_1 / pdf_2))
< tolerance)):
raise ValueError("The {} distribution PDF does not match its "
"component distriubtions.".format(dist.name))
# check random draws from polar angle equilvalent
ang_1 = dist.rvs(n_samples)[dist.polar_angle]
ang_2 = polar_dist.rvs(n_samples)["theta"]
kl_val = entropy.kl(ang_1, ang_2, bins=polar_vals.size,
hist_min=polar_vals.min(),
hist_max=polar_vals.max())
if not (kl_val < threshold):
raise ValueError(
"Class {} KL divergence is {} which is "
"greater than the threshold for polar angle"
"of {}".format(dist.name, kl_val, threshold))
# check random draws from azimuthal angle equilvalent
ang_1 = dist.rvs(n_samples)[dist.azimuthal_angle]
ang_2 = ang_dist.rvs(n_samples)["theta"]
kl_val = entropy.kl(ang_1, ang_2, bins=azimuthal.size,
hist_min=azimuthal.min(),
hist_max=azimuthal.max())
if not (kl_val < threshold):
raise ValueError(
"Class {} KL divergence is {} which is "
"greater than the threshold for azimuthal angle"
"of {}".format(dist.name, kl_val, threshold))
def test_solid_angle(self):
""" The uniform solid angle and uniform sky position distributions
are two independent one-dimensional distributions. This tests checks
that the two indepdent one-dimensional distributions agree by comparing
the `rvs`, `pdf`, and `logpdf` functions' output.
"""
# set tolerance for comparing PDF and logPDF functions
tolerance = 0.01
# set threshold for KL divergence test
threshold = 0.1
# number of random draws for KL divergence test
n_samples = int(1e6)
# create generic angular distributions for test
sin_dist = distributions.SinAngle(theta=(0, 1))
cos_dist = distributions.CosAngle(theta=(-0.5, 0.5))
ang_dist = distributions.UniformAngle(theta=(0, 2))
# step size for PDF calculation
step = 0.1
# valid range of parameters
polar_sin = numpy.arange(0, numpy.pi, step)
polar_cos = numpy.arange(-numpy.pi, numpy.pi, step)
azimuthal = numpy.arange(0, 2 * numpy.pi, step)
# get Cartesian product to explore the two-dimensional space
cart_sin = cartesian([polar_sin, azimuthal])
# loop over distributions
for dist in self.dists:
if dist.name == distributions.UniformSolidAngle.name:
polar_vals = polar_sin
polar_dist = sin_dist
elif dist.name == distributions.UniformSky.name:
polar_vals = polar_cos
polar_dist = cos_dist
else:
continue
# check PDF equilvalent
pdf_1 = numpy.array([
dist.pdf(**{
dist.polar_angle: p,
dist.azimuthal_angle: a
}) for p, a in cart_sin
])
pdf_2 = numpy.array([
polar_dist.pdf(**{"theta": p}) * ang_dist.pdf(**{"theta": a})
for p, a in cart_sin
])
if not (numpy.all(
numpy.nan_to_num(abs(1.0 - pdf_1 / pdf_2)) < tolerance)):
raise ValueError("The {} distribution PDF does not match its "
"component distriubtions.".format(dist.name))
# check logarithm of PDF equilvalent
pdf_1 = numpy.array([
dist.logpdf(**{
dist.polar_angle: p,
dist.azimuthal_angle: a
}) for p, a in cart_sin
])
pdf_2 = numpy.array([
polar_dist.logpdf(**{"theta": p}) +
ang_dist.logpdf(**{"theta": a}) for p, a in cart_sin
])
if not (numpy.all(
numpy.nan_to_num(abs(1.0 - pdf_1 / pdf_2)) < tolerance)):
raise ValueError("The {} distribution PDF does not match its "
"component distriubtions.".format(dist.name))
# check random draws from polar angle equilvalent
ang_1 = dist.rvs(n_samples)[dist.polar_angle]
ang_2 = polar_dist.rvs(n_samples)["theta"]
kl_val = entropy.kl(ang_1,
ang_2,
bins=polar_vals.size,
hist_min=polar_vals.min(),
hist_max=polar_vals.max())
if not (kl_val < threshold):
raise ValueError("Class {} KL divergence is {} which is "
"greater than the threshold for polar angle"
"of {}".format(dist.name, kl_val, threshold))
# check random draws from azimuthal angle equilvalent
ang_1 = dist.rvs(n_samples)[dist.azimuthal_angle]
ang_2 = ang_dist.rvs(n_samples)["theta"]
kl_val = entropy.kl(ang_1,
ang_2,
bins=azimuthal.size,
hist_min=azimuthal.min(),
hist_max=azimuthal.max())
if not (kl_val < threshold):
raise ValueError(
"Class {} KL divergence is {} which is "
"greater than the threshold for azimuthal angle"
"of {}".format(dist.name, kl_val, threshold))