def test_apparent_kurtosis_coef():
""" Apparent kurtosis coeficients are tested for a spherical kurtosis
tensor """
sph = Sphere(xyz=gtab.bvecs[gtab.bvals > 0])
AKC = dki.apparent_kurtosis_coef(params_sph, sph)
# check all direction
for d in range(len(gtab.bvecs[gtab.bvals > 0])):
assert_array_almost_equal(AKC[d], Kref_sphere)
def test_apparent_kurtosis_coef():
""" Apparent kurtosis coeficients are tested for a spherical kurtosis
tensor """
sph = Sphere(xyz=gtab.bvecs[gtab.bvals > 0])
AKC = dki.apparent_kurtosis_coef(params_sph, sph)
# check all direction
for d in range(len(gtab.bvecs[gtab.bvals > 0])):
assert_array_almost_equal(AKC[d], Kref_sphere)
def test_MK_singularities():
# To test MK in case that analytical solution was a singularity not covered
# by other tests
dkiM = dki.DiffusionKurtosisModel(gtab_2s)
# test singularity L1 == L2 - this is the case of a prolate diffusion
# tensor for crossing fibers at 90 degrees
angles_all = np.array([[(90, 0), (90, 0), (0, 0), (0, 0)],
[(89.9, 0), (89.9, 0), (0, 0), (0, 0)]])
for angles_90 in angles_all:
s_90, dt_90, kt_90 = multi_tensor_dki(gtab_2s,
mevals_cross,
S0=100,
angles=angles_90,
fractions=frac_cross,
snr=None)
dkiF = dkiM.fit(s_90)
MK = dkiF.mk()
sph = Sphere(xyz=gtab.bvecs[gtab.bvals > 0])
MK_nm = np.mean(dkiF.akc(sph))
assert_almost_equal(MK, MK_nm, decimal=2)
# test singularity L1 == L3 and L1 != L2
# since L1 is defined as the larger eigenvalue and L3 the smallest
# eigenvalue, this singularity teoretically will never be called,
# because for L1 == L3, L2 have also to be = L1 and L2.
# Nevertheless, I decided to include this test since this singularity
# is revelant for cases that eigenvalues are not ordered
# artificially revert the eigenvalue and eigenvector order
dki_params = dkiF.model_params.copy()
dki_params[1] = dkiF.model_params[2]
dki_params[2] = dkiF.model_params[1]
dki_params[4] = dkiF.model_params[5]
dki_params[5] = dkiF.model_params[4]
dki_params[7] = dkiF.model_params[8]
dki_params[8] = dkiF.model_params[7]
dki_params[10] = dkiF.model_params[11]
dki_params[11] = dkiF.model_params[10]
MK = dki.mean_kurtosis(dki_params)
MK_nm = np.mean(dki.apparent_kurtosis_coef(dki_params, sph))
assert_almost_equal(MK, MK_nm, decimal=2)
def test_compare_MK_method():
# tests if analytical solution of MK is equal to the average of directional
# kurtosis sampled from a sphere
# DKI Model fitting
dkiM = dki.DiffusionKurtosisModel(gtab_2s)
dkiF = dkiM.fit(signal_cross)
# MK analytical solution
MK_as = dkiF.mk()
# MK numerical method
sph = Sphere(xyz=gtab.bvecs[gtab.bvals > 0])
MK_nm = np.mean(dki.apparent_kurtosis_coef(dkiF.model_params, sph), axis=-1)
assert_array_almost_equal(MK_as, MK_nm, decimal=1)
def test_compare_MK_method():
# tests if analytical solution of MK is equal to the average of directional
# kurtosis sampled from a sphere
# DKI Model fitting
dkiM = dki.DiffusionKurtosisModel(gtab_2s)
dkiF = dkiM.fit(signal_cross)
# MK analytical solution
MK_as = dkiF.mk()
# MK numerical method
sph = Sphere(xyz=gtab.bvecs[gtab.bvals > 0])
MK_nm = np.mean(dki.apparent_kurtosis_coef(dkiF.model_params, sph),
axis=-1)
assert_array_almost_equal(MK_as, MK_nm, decimal=1)
def test_MK_singularities():
# To test MK in case that analytical solution was a singularity not covered
# by other tests
dkiM = dki.DiffusionKurtosisModel(gtab_2s)
# test singularity L1 == L2 - this is the case of a prolate diffusion
# tensor for crossing fibers at 90 degrees
angles_all = np.array([[(90, 0), (90, 0), (0, 0), (0, 0)],
[(89.9, 0), (89.9, 0), (0, 0), (0, 0)]])
for angles_90 in angles_all:
s_90, dt_90, kt_90 = multi_tensor_dki(gtab_2s, mevals_cross, S0=100,
angles=angles_90,
fractions=frac_cross, snr=None)
dkiF = dkiM.fit(s_90)
MK = dkiF.mk()
sph = Sphere(xyz=gtab.bvecs[gtab.bvals > 0])
MK_nm = np.mean(dkiF.akc(sph))
assert_almost_equal(MK, MK_nm, decimal=2)
# test singularity L1 == L3 and L1 != L2
# since L1 is defined as the larger eigenvalue and L3 the smallest
# eigenvalue, this singularity teoretically will never be called,
# because for L1 == L3, L2 have also to be = L1 and L2.
# Nevertheless, I decided to include this test since this singularity
# is revelant for cases that eigenvalues are not ordered
# artificially revert the eigenvalue and eigenvector order
dki_params = dkiF.model_params.copy()
dki_params[1] = dkiF.model_params[2]
dki_params[2] = dkiF.model_params[1]
dki_params[4] = dkiF.model_params[5]
dki_params[5] = dkiF.model_params[4]
dki_params[7] = dkiF.model_params[8]
dki_params[8] = dkiF.model_params[7]
dki_params[10] = dkiF.model_params[11]
dki_params[11] = dkiF.model_params[10]
MK = dki.mean_kurtosis(dki_params)
MK_nm = np.mean(dki.apparent_kurtosis_coef(dki_params, sph))
assert_almost_equal(MK, MK_nm, decimal=2)
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)
