def test_rotate_by_angles():
before = np.array([1.,0.,0.])
theta = -np.pi/3. # upwards
phi = np.pi/3.
after = rotate_by_angles(before, theta, phi)
assert_almost_equal(after, np.array((0.25, np.sqrt(3)/4., np.sqrt(3)/2.)))
before = np.array([0., 1., 0.])
theta = np.pi/3.
phi = np.pi/4.
after = rotate_by_angles(before, theta, phi)
assert_almost_equal(after, np.array((-np.sqrt(2.)/2., np.sqrt(2)/2., 0.)))
# test stacking of vectors
before = np.array([[1., 0., 0.], [0., 0., 1.]]).T # shape (2, 3)
theta = -np.pi/3.
phi = np.pi/3.
after = rotate_by_angles(before, theta, phi)
assert_almost_equal(after,
np.array([[0.25, np.sqrt(3)/4., np.sqrt(3)/2.],
[np.sin(-np.pi/3.) * np.cos(np.pi/3.), -0.75, .5]]).T)
def vmf_rvs(mu, k, n_pts=1):
'''Simulate a Fisher distribution. From Statistical Analysis of
Spherical Data, 1987, section 3.6.2'''
size = (n_pts, 2)
R = np.random.uniform(size=size)
R_0 = R[...,0]
R_1 = R[...,1]
l = np.exp(-2 * k)
colat = 2 * np.arcsin(np.sqrt(-np.log(R_0 * (1 - l) + l) / (2 * k)))
longit = 2 * np.pi * R_1
pts = convert_polar_to_cartesian(colat, longit)
#print mean_dir(pts.T)
alpha, beta = convert_cartesian_to_polar(mu)
return rotate_by_angles(pts, alpha, beta).T