def test_coordinate_transformation():
# test for a vector of size 3
cartesian_vector = np.random.rand(3)
spherical_vector = utils.cart2sphere(cartesian_vector)
recovered_cartesian_vector = utils.sphere2cart(spherical_vector)
assert_almost_equal(cartesian_vector, recovered_cartesian_vector)
# test for a vector of size N x 3
cartesian_vector = np.random.rand(10, 3)
spherical_vector = utils.cart2sphere(cartesian_vector)
recovered_cartesian_vector = utils.sphere2cart(spherical_vector)
assert_almost_equal(cartesian_vector, recovered_cartesian_vector)
def test_orienting_stick():
# test for orienting the axis of the Stick along mu
# first test to see if Estick equals Gaussian with lambda_par along mu
random_n_mu_vector = np.random.rand(2) * np.pi
n = utils.sphere2cart(np.r_[1, random_n_mu_vector])
random_bval = np.r_[np.random.rand() * 1e9]
random_lambda_par = np.random.rand() * 3e-9
scheme = acquisition_scheme_from_bvalues(
random_bval, np.atleast_2d(n), delta, Delta)
# initialize model
stick = cylinder_models.C1Stick(mu=random_n_mu_vector,
lambda_par=random_lambda_par)
# test if parallel direction attenuation as a Gaussian
E_stick = stick(scheme)
E_check = np.exp(-random_bval * (random_lambda_par))
assert_almost_equal(E_stick, E_check)
# test if perpendicular direction does not attenuate
n_perp = perpendicular_vector(n)
scheme = acquisition_scheme_from_bvalues(
random_bval, np.atleast_2d(n_perp), delta, Delta)
E_stick_perp = stick(scheme)
assert_almost_equal(E_stick_perp, 1.)
def test_watson_kappa():
# test for Wn(k2) > Wn(k1) when k2>k1 along mu
random_mu = np.random.rand(2)
random_mu_cart = utils.sphere2cart(np.r_[1., random_mu])
odi1 = .8
odi2 = .6
watson = distributions.SD1Watson(mu=random_mu)
Wn1 = watson(n=random_mu_cart, odi=odi1)
Wn2 = watson(n=random_mu_cart, odi=odi2)
assert_equal(Wn2 > Wn1, True)
def test_bingham_equal_to_watson(beta_fraction=0):
# test if bingham with beta=0 equals watson distribution
mu_ = np.random.rand(2)
n_cart = utils.sphere2cart(np.r_[1., mu_])
psi_ = np.random.rand() * np.pi
odi_ = np.random.rand()
bingham = distributions.SD2Bingham(mu=mu_,
psi=psi_,
odi=odi_,
beta_fraction=beta_fraction)
watson = distributions.SD1Watson(mu=mu_, odi=odi_)
Bn = bingham(n=n_cart)
Wn = watson(n=n_cart)
assert_almost_equal(Bn, Wn, 3)
def test_orienting_zeppelin():
# test for orienting the axis of the Zeppelin along mu
# first test to see if Ezeppelin equals Gaussian with lambda_par along mu
random_mu = np.random.rand(2) * np.pi
n = np.array([utils.sphere2cart(np.r_[1, random_mu])])
random_bval = np.r_[np.random.rand() * 1e9]
scheme = acquisition_scheme_from_bvalues(random_bval, n, delta, Delta)
random_lambda_par = np.random.rand() * 3 * 1e-9
random_lambda_perp = random_lambda_par / 2.
zeppelin = gaussian_models.G2Zeppelin(
mu=random_mu, lambda_par=random_lambda_par,
lambda_perp=random_lambda_perp)
E_zep_par = zeppelin(scheme)
E_check_par = np.exp(-random_bval * random_lambda_par)
assert_almost_equal(E_zep_par, E_check_par)
# second test to see if Ezeppelin equals Gaussian with lambda_perp
# perpendicular to mu
n_perp = np.array([perpendicular_vector(n[0])])
scheme = acquisition_scheme_from_bvalues(random_bval, n_perp, delta, Delta)
E_zep_perp = zeppelin(scheme)
E_check_perp = np.exp(-random_bval * random_lambda_perp)
assert_almost_equal(E_zep_perp, E_check_perp)