def test_calling_cartesian_laplacian_with_precomputed_matrices(
radial_order=4, time_order=2, ut=2e-3, us=np.r_[1e-3, 2e-3, 3e-3]):
ind_mat = qtdmri.qtdmri_index_matrix(radial_order, time_order)
part4_reg_mat_tau = qtdmri.part4_reg_matrix_tau(ind_mat, 1.)
part23_reg_mat_tau = qtdmri.part23_reg_matrix_tau(ind_mat, 1.)
part1_reg_mat_tau = qtdmri.part1_reg_matrix_tau(ind_mat, 1.)
S_mat, T_mat, U_mat = mapmri.mapmri_STU_reg_matrices(radial_order)
laplacian_matrix_precomputed = qtdmri.qtdmri_laplacian_reg_matrix(
ind_mat, us, ut, S_mat, T_mat, U_mat, part1_reg_mat_tau,
part23_reg_mat_tau, part4_reg_mat_tau)
laplacian_matrix_regular = qtdmri.qtdmri_laplacian_reg_matrix(
ind_mat, us, ut)
assert_array_almost_equal(laplacian_matrix_precomputed,
laplacian_matrix_regular)
def test_calling_cartesian_laplacian_with_precomputed_matrices(
radial_order=4, time_order=2, ut=2e-3, us=np.r_[1e-3, 2e-3, 3e-3]):
ind_mat = qtdmri.qtdmri_index_matrix(radial_order, time_order)
part4_reg_mat_tau = qtdmri.part4_reg_matrix_tau(ind_mat, 1.)
part23_reg_mat_tau = qtdmri.part23_reg_matrix_tau(ind_mat, 1.)
part1_reg_mat_tau = qtdmri.part1_reg_matrix_tau(ind_mat, 1.)
S_mat, T_mat, U_mat = mapmri.mapmri_STU_reg_matrices(radial_order)
laplacian_matrix_precomputed = qtdmri.qtdmri_laplacian_reg_matrix(
ind_mat, us, ut, S_mat, T_mat, U_mat,
part1_reg_mat_tau, part23_reg_mat_tau, part4_reg_mat_tau
)
laplacian_matrix_regular = qtdmri.qtdmri_laplacian_reg_matrix(
ind_mat, us, ut)
assert_array_almost_equal(laplacian_matrix_precomputed,
laplacian_matrix_regular)
def test_signal_fitting_equality_anisotropic_isotropic(radial_order=6):
gtab = get_gtab_taiwan_dsi()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S, _ = generate_signal_crossing(gtab, l1, l2, l3, angle2=60)
gridsize = 17
radius_max = 0.02
r_points = mapmri.create_rspace(gridsize, radius_max)
tenmodel = dti.TensorModel(gtab)
evals = tenmodel.fit(S).evals
tau = 1 / (4 * np.pi**2)
# estimate isotropic scale factor
u0 = mapmri.isotropic_scale_factor(evals * 2 * tau)
mu = np.array([u0, u0, u0])
qvals = np.sqrt(gtab.bvals / tau) / (2 * np.pi)
q = gtab.bvecs * qvals[:, None]
M_aniso = mapmri.mapmri_phi_matrix(radial_order, mu, q)
K_aniso = mapmri.mapmri_psi_matrix(radial_order, mu, r_points)
M_iso = mapmri.mapmri_isotropic_phi_matrix(radial_order, u0, q)
K_iso = mapmri.mapmri_isotropic_psi_matrix(radial_order, u0, r_points)
coef_aniso = np.dot(np.linalg.pinv(M_aniso), S)
coef_iso = np.dot(np.linalg.pinv(M_iso), S)
# test if anisotropic and isotropic implementation produce equal results
# if the same isotropic scale factors are used
s_fitted_aniso = np.dot(M_aniso, coef_aniso)
s_fitted_iso = np.dot(M_iso, coef_iso)
assert_array_almost_equal(s_fitted_aniso, s_fitted_iso)
# the same test for the PDF
pdf_fitted_aniso = np.dot(K_aniso, coef_aniso)
pdf_fitted_iso = np.dot(K_iso, coef_iso)
assert_array_almost_equal(pdf_fitted_aniso / pdf_fitted_iso,
np.ones_like(pdf_fitted_aniso), 3)
# test if the implemented version also produces the same result
mapm = MapmriModel(gtab,
radial_order=radial_order,
laplacian_regularization=False,
anisotropic_scaling=False)
s_fitted_implemented_isotropic = mapm.fit(S).fitted_signal()
# normalize non-implemented fitted signal with b0 value
s_fitted_aniso_norm = s_fitted_aniso / s_fitted_aniso.max()
assert_array_almost_equal(s_fitted_aniso_norm,
s_fitted_implemented_isotropic)
# test if norm of signal laplacians are the same
laplacian_matrix_iso = mapmri.mapmri_isotropic_laplacian_reg_matrix(
radial_order, mu[0])
ind_mat = mapmri.mapmri_index_matrix(radial_order)
S_mat, T_mat, U_mat = mapmri.mapmri_STU_reg_matrices(radial_order)
laplacian_matrix_aniso = mapmri.mapmri_laplacian_reg_matrix(
ind_mat, mu, S_mat, T_mat, U_mat)
norm_aniso = np.dot(coef_aniso, np.dot(coef_aniso, laplacian_matrix_aniso))
norm_iso = np.dot(coef_iso, np.dot(coef_iso, laplacian_matrix_iso))
assert_almost_equal(norm_iso, norm_aniso)
def test_signal_fitting_equality_anisotropic_isotropic(radial_order=6):
gtab = get_gtab_taiwan_dsi()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S, _ = generate_signal_crossing(gtab, l1, l2, l3, angle2=60)
gridsize = 17
radius_max = 0.02
r_points = mapmri.create_rspace(gridsize, radius_max)
tenmodel = dti.TensorModel(gtab)
evals = tenmodel.fit(S).evals
tau = 1 / (4 * np.pi ** 2)
# estimate isotropic scale factor
u0 = mapmri.isotropic_scale_factor(evals * 2 * tau)
mu = np.array([u0, u0, u0])
qvals = np.sqrt(gtab.bvals / tau) / (2 * np.pi)
q = gtab.bvecs * qvals[:, None]
M_aniso = mapmri.mapmri_phi_matrix(radial_order, mu, q)
K_aniso = mapmri.mapmri_psi_matrix(radial_order, mu, r_points)
M_iso = mapmri.mapmri_isotropic_phi_matrix(radial_order, u0, q)
K_iso = mapmri.mapmri_isotropic_psi_matrix(radial_order, u0, r_points)
coef_aniso = np.dot(np.linalg.pinv(M_aniso), S)
coef_iso = np.dot(np.linalg.pinv(M_iso), S)
# test if anisotropic and isotropic implementation produce equal results
# if the same isotropic scale factors are used
s_fitted_aniso = np.dot(M_aniso, coef_aniso)
s_fitted_iso = np.dot(M_iso, coef_iso)
assert_array_almost_equal(s_fitted_aniso, s_fitted_iso)
# the same test for the PDF
pdf_fitted_aniso = np.dot(K_aniso, coef_aniso)
pdf_fitted_iso = np.dot(K_iso, coef_iso)
assert_array_almost_equal(pdf_fitted_aniso / pdf_fitted_iso,
np.ones_like(pdf_fitted_aniso), 3)
# test if the implemented version also produces the same result
mapm = MapmriModel(gtab, radial_order=radial_order,
laplacian_regularization=False,
anisotropic_scaling=False)
s_fitted_implemented_isotropic = mapm.fit(S).fitted_signal()
# normalize non-implemented fitted signal with b0 value
s_fitted_aniso_norm = s_fitted_aniso / s_fitted_aniso.max()
assert_array_almost_equal(s_fitted_aniso_norm,
s_fitted_implemented_isotropic)
# test if norm of signal laplacians are the same
laplacian_matrix_iso = mapmri.mapmri_isotropic_laplacian_reg_matrix(
radial_order, mu[0])
ind_mat = mapmri.mapmri_index_matrix(radial_order)
S_mat, T_mat, U_mat = mapmri.mapmri_STU_reg_matrices(radial_order)
laplacian_matrix_aniso = mapmri.mapmri_laplacian_reg_matrix(
ind_mat, mu, S_mat, T_mat, U_mat)
norm_aniso = np.dot(coef_aniso, np.dot(coef_aniso, laplacian_matrix_aniso))
norm_iso = np.dot(coef_iso, np.dot(coef_iso, laplacian_matrix_iso))
assert_almost_equal(norm_iso, norm_aniso)