def test_real_sym_sh_basis():
# This test should do for now
# The tournier07 basis should be the same as re-ordering and re-scaling the
# descoteaux07 basis
new_order = [0, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 9, 8, 7, 6]
sphere = hemi_icosahedron.subdivide(2)
basis, m, n = real_sym_sh_mrtrix(4, sphere.theta, sphere.phi)
expected = basis[:, new_order]
expected *= np.where(m == 0, 1., np.sqrt(2))
descoteaux07_basis, m, n = real_sym_sh_basis(4, sphere.theta, sphere.phi)
assert_array_almost_equal(descoteaux07_basis, expected)
def test_real_sym_sh_mrtrix():
coef, expected, sphere = mrtrix_spherical_functions()
basis, m, n = real_sym_sh_mrtrix(8, sphere.theta, sphere.phi)
func = np.dot(coef, basis.T)
assert_array_almost_equal(func, expected, 4)
def test_real_sym_sh_mrtrix():
coef, expected, sphere = mrtrix_spherical_functions()
basis, m, n = real_sym_sh_mrtrix(8, sphere.theta, sphere.phi)
func = np.dot(coef, basis.T)
assert_array_almost_equal(func, expected, 4)
def __init__(self, dmipy_acquisition_scheme, N_angular_samples=10):
self.Nsamples = N_angular_samples
scheme = dmipy_acquisition_scheme
thetas = np.linspace(0, np.pi / 2, N_angular_samples)
r = np.ones(N_angular_samples)
phis = np.zeros(N_angular_samples)
angles = np.c_[r, thetas, phis]
angles_cart = utils.sphere2cart(angles)
b_all_shells = []
Gdirs_all_shells = []
delta_all_shells = []
Delta_all_shells = []
shell_indices = []
for shell_index in scheme.unique_dwi_indices:
b = scheme.shell_bvalues[shell_index]
b_all_shells.append(np.tile(b, N_angular_samples))
if scheme.shell_delta is not None:
delta = scheme.shell_delta[shell_index]
delta_all_shells.append(np.tile(delta, N_angular_samples))
if scheme.shell_Delta is not None:
Delta = scheme.shell_Delta[shell_index]
Delta_all_shells.append(np.tile(Delta, N_angular_samples))
Gdirs_all_shells.append(angles_cart)
shell_indices.append(np.tile(shell_index, N_angular_samples))
self.shell_indices = np.hstack(shell_indices)
self.bvalues = np.hstack(b_all_shells)
self.gradient_directions = np.vstack(Gdirs_all_shells)
self.delta = None
if scheme.shell_delta is not None:
self.delta = np.hstack(delta_all_shells)
self.Delta = None
if scheme.shell_Delta is not None:
self.Delta = np.hstack(Delta_all_shells)
if self.delta is not None and self.Delta is not None:
self.gradient_strengths = g_from_b(self.bvalues, self.delta,
self.Delta)
self.qvalues = q_from_g(self.gradient_strengths, self.delta)
self.tau = self.Delta - self.delta / 3.0
else:
self.gradient_strengths = self.qvalues = self.tau = None
self.b0_mask = np.tile(False, len(self.bvalues))
self.shell_delta = scheme.shell_delta
self.shell_Delta = scheme.shell_Delta
self.unique_b0_indices = scheme.unique_b0_indices
self.unique_shell_indices = scheme.unique_shell_indices
self.unique_dwi_indices = scheme.unique_dwi_indices
self.N_b0_shells = len(self.unique_b0_indices)
self.N_dwi_shells = len(self.unique_dwi_indices)
self.N_shells = len(self.unique_shell_indices)
self.number_of_measurements = len(self.bvalues)
self.shell_sh_matrices = {}
self.shell_sh_orders = {}
for shell_index in scheme.unique_dwi_indices:
self.shell_sh_orders[shell_index] = int(
scheme.shell_sh_orders[shell_index])
self.shell_sh_matrices[shell_index] = real_sym_sh_mrtrix(
self.shell_sh_orders[shell_index], thetas, phis)[0]
self.inverse_rh_matrix = {
rh_order: np.linalg.pinv(real_sym_rh_basis(rh_order, thetas, phis))
for rh_order in np.arange(0, 15, 2)
}
def __init__(self, bvalues, gradient_directions, qvalues,
gradient_strengths, delta, Delta, TE, min_b_shell_distance,
b0_threshold):
self.min_b_shell_distance = float(min_b_shell_distance)
self.b0_threshold = float(b0_threshold)
self.bvalues = bvalues.astype(float)
self.b0_mask = self.bvalues <= b0_threshold
self.number_of_b0s = np.sum(self.b0_mask)
self.number_of_measurements = len(self.bvalues)
self.gradient_directions = gradient_directions.astype(float)
self.qvalues = None
if qvalues is not None:
self.qvalues = qvalues.astype(float)
self.gradient_strengths = None
if gradient_strengths is not None:
self.gradient_strengths = gradient_strengths.astype(float)
self.delta = None
if delta is not None:
self.delta = delta.astype(float)
self.Delta = None
if Delta is not None:
self.Delta = Delta.astype(float)
self.TE = None
self.N_TE = 1 # default if not given
if TE is not None:
self.TE = TE.astype(float)
self.tau = None
if self.delta is not None and self.Delta is not None:
self.tau = Delta - delta / 3.
# if there are more then 1 measurement
if self.number_of_measurements > 1:
# we check if there are multiple unique delta-Delta combinations
if self.TE is not None:
deltas = np.c_[self.delta, self.Delta, self.TE]
elif self.delta is not None and self.Delta is not None:
deltas = np.c_[self.delta, self.Delta]
elif self.delta is None and self.Delta is not None:
deltas = np.c_[self.Delta]
elif self.delta is not None and self.Delta is None:
deltas = np.c_[self.delta]
else:
deltas = []
if deltas == []:
deltas = np.c_[np.zeros(len(self.bvalues))]
unique_deltas = np.unique(deltas, axis=0)
self.shell_indices = np.zeros(len(bvalues), dtype=int)
self.shell_bvalues = []
max_index = 0
# for every unique combination we separate shells based on bvalue
# reason for separation is that different combinations of
# delta and Delta can result in the same b-value, which could
# result in wrong classification of DWIs to unique shells.
for unique_deltas_ in unique_deltas:
delta_mask = np.all(deltas == unique_deltas_, axis=1)
masked_bvals = bvalues[delta_mask]
if len(masked_bvals) > 1:
shell_indices_, shell_bvalues_ = (
calculate_shell_bvalues_and_indices(
masked_bvals, min_b_shell_distance))
else:
shell_indices_, shell_bvalues_ = np.array(0), masked_bvals
self.shell_indices[delta_mask] = shell_indices_ + max_index
self.shell_bvalues.append(shell_bvalues_)
max_index = max(self.shell_indices + 1)
self.shell_bvalues = np.hstack(self.shell_bvalues)
self.shell_b0_mask = self.shell_bvalues <= b0_threshold
first_indices = [
np.argmax(self.shell_indices == ind)
for ind in np.arange(self.shell_indices.max() + 1)
]
self.shell_qvalues = None
if self.qvalues is not None:
self.shell_qvalues = self.qvalues[first_indices]
self.shell_gradient_strengths = None
if self.gradient_strengths is not None:
self.shell_gradient_strengths = (
self.gradient_strengths[first_indices])
self.shell_delta = None
if self.delta is not None:
self.shell_delta = self.delta[first_indices]
self.shell_Delta = None
if self.Delta is not None:
self.shell_Delta = self.Delta[first_indices]
self.shell_TE = None
if self.TE is not None:
self.shell_TE = self.TE[first_indices]
if (len(np.unique(self.TE)) != len(
np.unique(self.TE[self.b0_mask]))):
msg = "Not every TE shell has b0 measurements.\n"
msg += "This is required to properly normalize the signal."
msg += " Make sure the TE values for b0-measurements have "
msg += "not defaulted to 0 for example."
raise ValueError(msg)
self.N_TE = len(self.shell_TE)
# if for some reason only one measurement is given (for testing)
else:
self.shell_bvalues = self.bvalues
self.shell_indices = np.r_[int(0)]
if self.shell_bvalues > b0_threshold:
self.shell_b0_mask = np.r_[False]
else:
self.shell_b0_mask = np.r_[True]
self.shell_qvalues = self.qvalues
self.shell_gradient_strengths = self.gradient_strengths
self.shell_delta = self.delta
self.shell_Delta = self.Delta
self.shell_TE = TE
# calculates observation matrices to convert spherical harmonic
# coefficients to the positions on the sphere for every shell
self.unique_b0_indices = np.unique(self.shell_indices[self.b0_mask])
self.unique_dwi_indices = np.unique(self.shell_indices[~self.b0_mask])
self.unique_shell_indices = np.unique(self.shell_indices)
self.N_b0_shells = len(self.unique_b0_indices)
self.N_dwi_shells = len(self.unique_dwi_indices)
self.N_shells = len(self.unique_shell_indices)
self.shell_sh_matrices = {}
self.shell_sh_orders = {}
for shell_index in self.unique_b0_indices:
self.shell_sh_orders[shell_index] = 0
for shell_index in self.unique_dwi_indices:
shell_mask = self.shell_indices == shell_index
bvecs_shell = self.gradient_directions[shell_mask]
_, theta_, phi_ = utils.cart2sphere(bvecs_shell).T
self.shell_sh_orders[shell_index] = get_sh_order_from_bval(
self.shell_bvalues[shell_index])
self.shell_sh_matrices[shell_index] = real_sym_sh_mrtrix(
self.shell_sh_orders[shell_index], theta_, phi_)[0]
# warning in case there are no b0 measurements
if sum(self.b0_mask) == 0:
msg = "No b0 measurements were detected. Check if the b0_threshold"
msg += " option is high enough, or if there is a mistake in the "
msg += "acquisition design."
warn(msg)
self.spherical_mean_scheme = SphericalMeanAcquisitionScheme(
self.shell_bvalues, self.shell_qvalues,
self.shell_gradient_strengths, self.shell_Delta, self.shell_delta)
if len(self.unique_dwi_indices) > 0:
self.rotational_harmonics_scheme = (
RotationalHarmonicsAcquisitionScheme(self))
numba, have_numba, _ = optional_package("numba")
GRADIENT_TABLES_PATH = pkg_resources.resource_filename('dmipy',
'data/gradient_tables')
SIGNAL_MODELS_PATH = pkg_resources.resource_filename('dmipy', 'signal_models')
DATA_PATH = pkg_resources.resource_filename('dmipy', 'data')
SPHERE_CARTESIAN = np.loadtxt(join(GRADIENT_TABLES_PATH,
'sphere_with_cap.txt'))
SPHERE_SPHERICAL = utils.cart2sphere(SPHERE_CARTESIAN)
log_bingham_normalization_splinefit = np.load(join(
DATA_PATH, "bingham_normalization_splinefit.npz"),
encoding='bytes')['arr_0']
inverse_sh_matrix_kernel = {
sh_order: np.linalg.pinv(
real_sym_sh_mrtrix(sh_order, hemisphere.theta, hemisphere.phi)[0])
for sh_order in np.arange(0, 15, 2)
}
BETA_SCALING = 1e-6
__all__ = [
'get_sh_order_from_odi', 'SD1Watson', 'SD2Bingham', 'DD1Gamma',
'odi2kappa', 'kappa2odi'
]
def get_sh_order_from_odi(odi):
"Returns minimum sh_order to estimate spherical harmonics for given odi."
odis = np.array([
0.80606061, 0.46666667, 0.25333333, 0.15636364, 0.09818182, 0.06909091,
0.
