def test_UniformCausticSampling_simple():
"""
Tests only very basic usage of UniformCausticSampling.
"""
sampling = mm.UniformCausticSampling(s=1.5, q=0.9, n_points=10)
assert sampling.s == 1.5
assert sampling.q == 0.9
assert sampling.n_caustics == 1
def test_get_uniform_sampling():
"""
Basic test for get_uniform_sampling() - only if the shape of output is
correct
"""
n = 50
sampling = mm.UniformCausticSampling(s=1.1, q=0.5, n_points=100)
(x_caustic_in, x_caustic_out) = sampling.get_uniform_sampling(n_points=n)
assert x_caustic_in.shape == (n,)
assert x_caustic_out.shape == (n,)
def test_UniformCausticSampling():
"""
Test if the main functions of work correctly, namely:
- get_standard_parameters(),
- get_x_in_x_out(),
- check_valid_trajectory(),
- caustic_point(),
- n_caustics,
- which_caustic().
Most tests are run for each of the three topologies.
"""
s_ = [1.1, 0.5, 2]
q_ = [0.1, 0.001, 0.01]
n_points = 1000
# Expected results:
n_c = [1, 3, 2]
p_ = [0.01401270+0.22985537j, -1.49730846-0.11183662j,
1.49051495+0.03108463j]
checks = [False, False, True]
for (s, q, nc, p, c) in zip(s_, q_, n_c, p_, checks):
sampling = mm.UniformCausticSampling(s=s, q=q, n_points=n_points)
standard = sampling.get_standard_parameters(0.2, 0.499, 0., 10.)
x_list = sampling.get_x_in_x_out(standard['u_0'], standard['alpha'])
assert np.min(np.abs(np.array(x_list) - 0.2)) < 1.e-6
assert np.min(np.abs(np.array(x_list) - 0.499)) < 2.e-6
assert sampling.check_valid_trajectory(0.2, 0.5) == c
np.testing.assert_almost_equal(sampling.caustic_point(0.3), p)
assert sampling.n_caustics == nc
assert sampling.which_caustic(0.95) == sampling.n_caustics
np.testing.assert_almost_equal(standard['t_0'], 216.3783662)
np.testing.assert_almost_equal(standard['u_0'], 0.0076099741)
np.testing.assert_almost_equal(standard['t_E'], 142.7154375)
np.testing.assert_almost_equal(standard['alpha'], 180.54305134)
# For the last (s, q) we also check alpha = 90 or 270:
x_1 = 0.1885475223517683
x_2 = 0.9504818975429649
u_0 = s - 1. / s + s * q / (1. + q)
standard = sampling.get_standard_parameters(x_1, x_2, -10., 0.)
np.testing.assert_almost_equal(standard['alpha'], 270.)
np.testing.assert_almost_equal(standard['u_0'], u_0)
standard = sampling.get_standard_parameters(x_2, x_1, -10., 0.)
np.testing.assert_almost_equal(standard['alpha'], 90.)
np.testing.assert_almost_equal(standard['u_0'], -u_0)
def generate_random_parameters(parameters, starting, n, s=None, q=None):
"""
Generate *n* vectors of values of *parameters* according to distributions
specified in *starting*.
"""
values = []
for param in parameters:
settings = starting[param]
if settings[0] == 'gauss':
v = settings[2] * np.random.randn(n)
v += settings[1]
elif settings[0] == 'uniform':
v = np.random.uniform(low=settings[1], high=settings[2], size=n)
elif settings[0] == 'log-uniform':
beg = np.log(settings[1])
end = np.log(settings[2])
v = np.exp(np.random.uniform(beg, end, n))
values.append(v)
if 'x_caustic_in' in parameters and 'x_caustic_out' in parameters:
sampling = mm.UniformCausticSampling(s=s, q=q)
(x_in, x_out) = sampling.get_uniform_sampling(n)
values[parameters.index('x_caustic_in')] = x_in
values[parameters.index('x_caustic_out')] = x_out
return np.array(values).T.tolist()
s = 1.2
q = 0.5
n_points = 200
color = np.linspace(0., 1., n_points)
# First, we use standard procedure to plot the caustic. You will see that
# the points are distributed non-uniformly, i.e., the density is higher
# near cusps. We also add color to indicate order of plotting.
# It turns out to be a complicated shape.
caustic = mm.Caustics(s=s, q=q)
caustic.plot(c=color, n_points=n_points)
plt.axis('equal')
plt.colorbar()
plt.title('standard plotting')
# Second, we use uniform sampling. The density of points is constant.
# Here the color scale indicates x_caustic values.
plt.figure()
sampling = mm.UniformCausticSampling(s=s, q=q)
points = [sampling.caustic_point(c) for c in color]
x = [p.real for p in points]
y = [p.imag for p in points]
plt.scatter(x, y, c=color)
plt.axis('equal')
plt.colorbar()
plt.title('uniform sampling plotting')
plt.show()
