def exercise_variate_generators():
from scitbx.random \
import variate, normal_distribution, bernoulli_distribution, \
gamma_distribution, poisson_distribution
for i in range(10):
scitbx.random.set_random_seed(0)
g = variate(normal_distribution())
assert approx_equal(g(), -0.917787219374)
assert approx_equal(
g(10),
(1.21838707856, 1.732426915, 0.838038157555, -0.296895169923,
0.246451144946, -0.635474652255, -0.0980626986425, 0.36458295417,
0.534073780268, -0.665073136294))
stat = basic_statistics(flex.double(itertools.islice(g, 1000000)))
assert approx_equal(stat.mean, 0, eps=0.005)
assert approx_equal(stat.biased_variance, 1, eps=0.005)
assert approx_equal(stat.skew, 0, eps=0.005)
assert approx_equal(stat.kurtosis, 3, eps=0.005)
bernoulli_seq = variate(bernoulli_distribution(0.1))
for b in itertools.islice(bernoulli_seq, 10):
assert b in (True, False)
bernoulli_sample = flex.bool(itertools.islice(bernoulli_seq, 10000))
assert approx_equal(bernoulli_sample.count(True) / len(bernoulli_sample),
0.1,
eps=0.01)
# Boost 1.64 changes the exponential distribution to use Ziggurat algorithm
scitbx.random.set_random_seed(0)
g = variate(gamma_distribution())
if (boost_version < 106400):
assert approx_equal(g(), 0.79587450456577546)
assert approx_equal(g(2), (0.89856038848394115, 1.2559307580473893))
else:
assert approx_equal(g(), 0.864758191783)
assert approx_equal(g(2), (1.36660841837, 2.26740986094))
stat = basic_statistics(flex.double(itertools.islice(g, 1000000)))
assert approx_equal(stat.mean, 1, eps=0.005)
assert approx_equal(stat.skew, 2, eps=0.01)
assert approx_equal(stat.biased_variance, 1, eps=0.005)
scitbx.random.set_random_seed(0)
g = variate(gamma_distribution(alpha=2, beta=3))
assert approx_equal(g(), 16.670850592722729)
assert approx_equal(g(2), (10.03662877519449, 3.9357158398972873))
stat = basic_statistics(flex.double(itertools.islice(g, 1000000)))
assert approx_equal(stat.mean, 6, eps=0.005)
assert approx_equal(stat.skew, 2 / math.sqrt(2), eps=0.05)
assert approx_equal(stat.biased_variance, 18, eps=0.05)
mean = 10.0
pv = variate(poisson_distribution(mean))
draws = pv(1000000).as_double()
m = flex.mean(draws)
v = flex.mean(draws * draws) - m * m
assert approx_equal(m, mean, eps=0.05)
assert approx_equal(v, mean, eps=0.05)
def exercise_variate_generators():
from scitbx.random \
import variate, normal_distribution, bernoulli_distribution, \
gamma_distribution, poisson_distribution
for i in xrange(10):
scitbx.random.set_random_seed(0)
g = variate(normal_distribution())
assert approx_equal(g(), -1.2780081289048213)
assert approx_equal(g(10),
(-0.40474189234755492, -0.41845505596083288,
-1.8825790263067721, -1.5779112018107659,
-1.1888174422378859, -1.8619619179878537,
-0.53946818661388318, -1.2400941724410812,
0.64511959841907285, -0.59934120033270688))
stat = basic_statistics(flex.double(itertools.islice(g, 1000000)))
assert approx_equal(stat.mean, 0, eps=0.005)
assert approx_equal(stat.biased_variance, 1, eps=0.005)
assert approx_equal(stat.skew, 0, eps=0.005)
assert approx_equal(stat.kurtosis, 3, eps=0.005)
bernoulli_seq = variate(bernoulli_distribution(0.1))
for b in itertools.islice(bernoulli_seq, 10):
assert b in (True, False)
bernoulli_sample = flex.bool(itertools.islice(bernoulli_seq, 10000))
assert approx_equal(
bernoulli_sample.count(True)/len(bernoulli_sample),
0.1,
eps = 0.01)
scitbx.random.set_random_seed(0)
g = variate(gamma_distribution())
assert approx_equal(g(), 0.79587450456577546)
assert approx_equal(g(2), (0.89856038848394115, 1.2559307580473893))
stat = basic_statistics(flex.double(itertools.islice(g, 1000000)))
assert approx_equal(stat.mean, 1, eps=0.005)
assert approx_equal(stat.skew, 2, eps=0.005)
assert approx_equal(stat.biased_variance, 1, eps=0.005)
scitbx.random.set_random_seed(0)
g = variate(gamma_distribution(alpha=2, beta=3))
assert approx_equal(g(), 16.670850592722729)
assert approx_equal(g(2), (10.03662877519449, 3.9357158398972873))
stat = basic_statistics(flex.double(itertools.islice(g, 1000000)))
assert approx_equal(stat.mean, 6, eps=0.005)
assert approx_equal(stat.skew, 2/math.sqrt(2), eps=0.05)
assert approx_equal(stat.biased_variance, 18, eps=0.05)
mean = 10.0
pv = variate(poisson_distribution(mean))
draws = pv(1000000).as_double()
m = flex.mean(draws)
v = flex.mean(draws*draws) - m*m
assert approx_equal(m,mean,eps=0.05)
assert approx_equal(v,mean,eps=0.05)
def exercise_variate_generators():
from scitbx.random \
import variate, normal_distribution, bernoulli_distribution, \
gamma_distribution, poisson_distribution
for i in xrange(10):
scitbx.random.set_random_seed(0)
g = variate(normal_distribution())
assert approx_equal(g(), -1.2780081289048213)
assert approx_equal(
g(10),
(-0.40474189234755492, -0.41845505596083288, -1.8825790263067721,
-1.5779112018107659, -1.1888174422378859, -1.8619619179878537,
-0.53946818661388318, -1.2400941724410812, 0.64511959841907285,
-0.59934120033270688))
stat = basic_statistics(flex.double(itertools.islice(g, 1000000)))
assert approx_equal(stat.mean, 0, eps=0.005)
assert approx_equal(stat.biased_variance, 1, eps=0.005)
assert approx_equal(stat.skew, 0, eps=0.005)
assert approx_equal(stat.kurtosis, 3, eps=0.005)
bernoulli_seq = variate(bernoulli_distribution(0.1))
for b in itertools.islice(bernoulli_seq, 10):
assert b in (True, False)
bernoulli_sample = flex.bool(itertools.islice(bernoulli_seq, 10000))
assert approx_equal(bernoulli_sample.count(True) / len(bernoulli_sample),
0.1,
eps=0.01)
scitbx.random.set_random_seed(0)
g = variate(gamma_distribution())
assert approx_equal(g(), 0.79587450456577546)
assert approx_equal(g(2), (0.89856038848394115, 1.2559307580473893))
stat = basic_statistics(flex.double(itertools.islice(g, 1000000)))
assert approx_equal(stat.mean, 1, eps=0.005)
assert approx_equal(stat.skew, 2, eps=0.005)
assert approx_equal(stat.biased_variance, 1, eps=0.005)
scitbx.random.set_random_seed(0)
g = variate(gamma_distribution(alpha=2, beta=3))
assert approx_equal(g(), 16.670850592722729)
assert approx_equal(g(2), (10.03662877519449, 3.9357158398972873))
stat = basic_statistics(flex.double(itertools.islice(g, 1000000)))
assert approx_equal(stat.mean, 6, eps=0.005)
assert approx_equal(stat.skew, 2 / math.sqrt(2), eps=0.05)
assert approx_equal(stat.biased_variance, 18, eps=0.05)
mean = 10.0
pv = variate(poisson_distribution(mean))
draws = pv(1000000).as_double()
m = flex.mean(draws)
v = flex.mean(draws * draws) - m * m
assert approx_equal(m, mean, eps=0.05)
assert approx_equal(v, mean, eps=0.05)
def __init__(self, space_group_info, **kwds):
libtbx.adopt_optional_init_args(self, kwds)
self.space_group_info = space_group_info
self.structure = random_structure.xray_structure(
space_group_info,
elements=self.elements,
volume_per_atom=20.,
min_distance=1.5,
general_positions_only=True,
use_u_aniso=False,
u_iso=adptbx.b_as_u(10),
)
self.structure.set_inelastic_form_factors(1.54, "sasaki")
self.scale_factor = 0.05 + 10 * flex.random_double()
fc = self.structure.structure_factors(anomalous_flag=True,
d_min=self.d_min,
algorithm="direct").f_calc()
fo = fc.as_amplitude_array()
fo.set_observation_type_xray_amplitude()
if self.use_students_t_errors:
nu = random.uniform(1, 10)
normal_g = variate(normal_distribution())
gamma_g = variate(gamma_distribution(0.5 * nu, 2))
errors = normal_g(fc.size()) / flex.sqrt(2 * gamma_g(fc.size()))
else:
# use gaussian errors
g = variate(normal_distribution())
errors = g(fc.size())
fo2 = fo.as_intensity_array()
self.fo2 = fo2.customized_copy(
data=(fo2.data() + errors) * self.scale_factor,
sigmas=flex.double(fc.size(), 1),
)
self.fc = fc
xs_i = self.structure.inverse_hand()
self.fc_i = xs_i.structure_factors(anomalous_flag=True,
d_min=self.d_min,
algorithm="direct").f_calc()
fo2_twin = self.fc.customized_copy(
data=self.fc.data() + self.fc_i.data()).as_intensity_array()
self.fo2_twin = fo2_twin.customized_copy(
data=(errors + fo2_twin.data()) * self.scale_factor,
sigmas=self.fo2.sigmas())
def __init__(self, space_group_info, **kwds):
libtbx.adopt_optional_init_args(self, kwds)
self.space_group_info = space_group_info
self.structure = random_structure.xray_structure(
space_group_info,
elements=self.elements,
volume_per_atom=20.,
min_distance=1.5,
general_positions_only=True,
use_u_aniso=False,
u_iso=adptbx.b_as_u(10),
)
self.structure.set_inelastic_form_factors(1.54, "sasaki")
self.scale_factor = 0.05 + 10 * flex.random_double()
fc = self.structure.structure_factors(
anomalous_flag=True, d_min=self.d_min, algorithm="direct").f_calc()
fo = fc.as_amplitude_array()
fo.set_observation_type_xray_amplitude()
if self.use_students_t_errors:
nu = random.uniform(1, 10)
normal_g = variate(normal_distribution())
gamma_g = variate(gamma_distribution(0.5*nu, 2))
errors = normal_g(fc.size())/flex.sqrt(2*gamma_g(fc.size()))
else:
# use gaussian errors
g = variate(normal_distribution())
errors = g(fc.size())
fo2 = fo.as_intensity_array()
self.fo2 = fo2.customized_copy(
data=(fo2.data()+errors)*self.scale_factor,
sigmas=flex.double(fc.size(), 1),
)
self.fc = fc
xs_i = self.structure.inverse_hand()
self.fc_i = xs_i.structure_factors(
anomalous_flag=True, d_min=self.d_min, algorithm="direct").f_calc()
fo2_twin = self.fc.customized_copy(
data=self.fc.data()+self.fc_i.data()).as_intensity_array()
self.fo2_twin = fo2_twin.customized_copy(
data=(errors + fo2_twin.data()) * self.scale_factor,
sigmas=self.fo2.sigmas())
