def odf(self, vertices=None, cache=None):
"""Predict the ODF at the given vertices.
"""
if vertices is None:
self._odf_kernel_matrix = cache._odf_kernel_matrix
else:
odf_theta, odf_phi = cart2sphere(*vertices.T)[1:]
X = kernel_matrix(odf_theta, odf_phi,
self.model.kernel_theta,
self.model.kernel_phi,
kernel=even_kernel,
N=self.model.sh_order)
#attempt to append iso col and spherical harmonic cols to X:
append = sh(odf_theta, odf_phi, np.size(odf_theta))
X = np.hstack((X, append))
self._odf_kernel_matrix = X
#return np.dot(self._odf_kernel_matrix, self.beta) + \
# self.intercept
return self._odf_kernel_matrix, self.beta, self.intercept
def __init__(self, bvals, gradients, sh_order=8, qp=132,
loglog_tf=True):
"""Sparse kernel model.
Parameters
----------
bvals : 1-D ndarray
B-values.
gradients : (N, 3) ndarray
Gradient directions, xyz.
sh_order : int
Highest order of spherical harmonic fit.
qp : {72, 132, 492}
Number of kernels used to represent the signal.
loglog_tf : bool
Whether to perform ``log(-log(.))`` on the signal before fitting.
In theory, this gives a better representation of the ODF (but does
predict back the original signal). Also, it seems not to work well
for low b-values (<= 1500).
"""
where_dwi = bvals > 0
self.qp = qp
self.sh_order = sh_order
self.loglog_tf = loglog_tf
self.gradient_theta, self.gradient_phi = \
cart2sphere(*gradients[where_dwi].T)[1:]
self.kernel_theta, self.kernel_phi, _ = quadrature_points(N=qp)
self.X = np.asfortranarray(
kernel_matrix(self.gradient_theta, self.gradient_phi,
self.kernel_theta, self.kernel_phi,
kernel=inv_funk_radon_even_kernel,
N=self.sh_order))
#attempt to append iso col and spherical harmonic cols to X:
P2 = sp.special.legendre(2)
append = sh(self.gradient_theta, self.gradient_phi, np.size(self.gradient_theta))
append[:,1:] = append[:,1:]/(-12*np.pi*P2(0))
#print append, "append"
self.X = np.hstack((self.X, append))
