def test_perpendicular_directions():
num = 35
vectors_v = np.zeros((4, 3))
for v in range(4):
theta = random.uniform(0, np.pi)
phi = random.uniform(0, 2*np.pi)
vectors_v[v] = sphere2cart(1., theta, phi)
vectors_v[3] = [1, 0, 0]
for vector_v in vectors_v:
pd = perpendicular_directions(vector_v, num=num, half=False)
# see if length of pd is equal to the number of intendend samples
assert_equal(num, len(pd))
# check if all directions are perpendicular to vector v
for d in pd:
cos_angle = np.dot(d, vector_v)
assert_almost_equal(cos_angle, 0)
# check if directions are sampled by multiples of 2*pi / num
delta_a = 2. * np.pi / num
for d in pd[1:]:
angle = np.arccos(np.dot(pd[0], d))
rest = angle % delta_a
if rest > delta_a * 0.99: # To correct cases of negative error
rest = rest - delta_a
assert_almost_equal(rest, 0)
def test_compare_RK_methods():
# tests if analytical solution of RK is equal to the perpendicular kurtosis
# relative to the first diffusion axis
# DKI Model fitting
dkiM = dki.DiffusionKurtosisModel(gtab_2s)
dkiF = dkiM.fit(signal_cross)
# MK analytical solution
RK_as = dkiF.rk()
# MK numerical method
evecs = dkiF.evecs
p_dir = perpendicular_directions(evecs[:, 0], num=30, half=True)
ver = Sphere(xyz=p_dir)
RK_nm = np.mean(dki.apparent_kurtosis_coef(dkiF.model_params, ver), axis=-1)
assert_array_almost_equal(RK_as, RK_nm)
def test_compare_RK_methods():
# tests if analytical solution of RK is equal to the perpendicular kurtosis
# relative to the first diffusion axis
# DKI Model fitting
dkiM = dki.DiffusionKurtosisModel(gtab_2s)
dkiF = dkiM.fit(signal_cross)
# MK analytical solution
RK_as = dkiF.rk()
# MK numerical method
evecs = dkiF.evecs
p_dir = perpendicular_directions(evecs[:, 0], num=30, half=True)
ver = Sphere(xyz=p_dir)
RK_nm = np.mean(dki.apparent_kurtosis_coef(dkiF.model_params, ver),
axis=-1)
assert_array_almost_equal(RK_as, RK_nm)
