def test_01d_rand_fisher_vecs_shape(self):
shape = (5, 10)
v0 = coord.rand_vec(shape)
sigma = 0.1 * np.random.random(shape)
vecs = coord.rand_fisher_vec(v0, kappa=1. / sigma**2)
self.assertTrue(vecs.shape == (v0.shape))
self.assertTrue((coord.angle(vecs, v0) < 5 * sigma).all())
def test_09c_rotate_zaxis_to_x(self):
v = np.array([np.zeros(stat), np.zeros(stat), np.ones(stat)])
angle = np.deg2rad(5)
v_fisher = coord.rand_fisher_vec(v, kappa=1 / angle**2)
self.assertTrue(v_fisher.shape == (3, stat))
self.assertTrue(
np.abs(np.mean(coord.angle(v, v_fisher)) - angle) / angle < 0.5)
def test_01c_rand_fisher_vecs(self):
v0 = coord.rand_vec(stat)
sigma = 0.1
vecs = coord.rand_fisher_vec(v0, kappa=1. / sigma**2, n=stat)
angles = coord.angle(vecs, v0)
self.assertTrue((angles >= 0).all())
self.assertTrue((np.mean(angles) > 0.5 * sigma)
& (np.mean(angles) < 2. * sigma))
self.assertTrue((angles < 5 * sigma).all())
def test_01b_rand_fisher_vec(self):
vmean = np.array([0, 0, 1])
sigma = 0.25
vecs = coord.rand_fisher_vec(vmean, kappa=1. / sigma**2, n=stat)
angles = coord.angle(vecs, vmean)
self.assertTrue((angles >= 0).all())
self.assertTrue((np.mean(angles) > 0.5 * sigma)
& (np.mean(angles) < 2. * sigma))
self.assertTrue((angles < 5 * sigma).all())
def test_09a_rotate_zaxis_to_x(self):
zaxis = np.array([[0], [0], [1]])
v = coord.rand_fisher_vec(zaxis, kappa=1 / np.deg2rad(10)**2, n=100)
_scalar = np.sum(v * zaxis, axis=0)
# rotate to z-axis (no change)
x1 = zaxis
v1 = coord.rotate_zaxis_to_x(v, x1)
self.assertTrue(np.allclose(v, v1))
self.assertTrue(np.allclose(_scalar, np.sum(v1 * x1, axis=0)))
# rotate to negative z-axis
x2 = -zaxis
v2 = coord.rotate_zaxis_to_x(v, x2)
self.assertTrue(np.allclose(_scalar, np.sum(v2 * x2, axis=0)))
# rotate to arbitrary point on sphere
x3 = np.array([[1], [1], [1]]) / np.sqrt(3)
v3 = coord.rotate_zaxis_to_x(v, x3)
self.assertTrue(np.allclose(_scalar, np.sum(v3 * x3, axis=0)))
ncrs = 3000 # number of cosmic rays
log10e_min = 18.5 # minimum energy in log10(E / eV)
lons = coord.rand_phi(ncrs) # isotropic in phi (~Uniform(-pi, pi))
lats = coord.rand_theta(ncrs) # isotropic in theta (Uniform in cos(theta))
vecs = coord.ang2vec(lons, lats)
log10e = auger.rand_energy_from_auger(n=ncrs, log10e_min=log10e_min)
# Plot an example map with sampled energies. If you specify the opath keyword in
# the skymap function, the plot will be automatically saved and closed
skymap.scatter(vecs, c=log10e, opath='isotropic_sky.png')
# Creates an arrival map with a source located at v_src=(1, 0, 0) and apply a
# fisher distribution around it with gaussian spread sigma=10 degree
v_src = np.array([1, 0, 0])
kappa = 1. / np.radians(10.)**2
vecs = coord.rand_fisher_vec(v_src, kappa=kappa, n=ncrs)
# if you dont specify the opath you can use (fig, ax) to plot more stuff
fig, ax = skymap.scatter(vecs, c=log10e)
plt.scatter(0, 0, s=100, c='red', marker='*') # plot source in the center
plt.savefig('fisher_single_source_10deg.png', bbox_inches='tight')
plt.close()
# We can also use the coord.rand_fisher_vec() function to apply an angular uncertainty
# on simulated arrival directions by feeding a higher dimensional v_src in shape (3, ncrs).
# Each cosmic ray can also have a separate smearing angle, in the following code snippet
# increasing with the longitude.
lats = np.radians(np.array([-60, -30, -15, 0, 15, 30, 60]))
lons = np.radians(np.arange(-180, 180, 30))
lons, lats = np.meshgrid(lons, lats)
# vectors on this defined grid:
vecs = coord.ang2vec(lons.flatten(), lats.flatten())