def test_interp_rbf():
from dipy.core.sphere import Sphere, interp_rbf
from dipy.core.subdivide_octahedron import create_unit_hemisphere
import numpy as np
s0 = create_unit_hemisphere(2)
s1 = create_unit_hemisphere(3)
data = np.cos(s0.theta) + np.sin(s0.phi)
expected = np.cos(s1.theta) + np.sin(s1.phi)
interp_data = interp_rbf(data, s0, s1)
nt.assert_(np.mean(np.abs(interp_data - expected)) < 0.1)
def test_interp_rbf():
from dipy.core.sphere import Sphere, interp_rbf
from dipy.core.subdivide_octahedron import create_unit_hemisphere
import numpy as np
s0 = create_unit_hemisphere(2)
s1 = create_unit_hemisphere(3)
data = np.cos(s0.theta) + np.sin(s0.phi)
expected = np.cos(s1.theta) + np.sin(s1.phi)
interp_data = interp_rbf(data, s0, s1)
nt.assert_(np.mean(np.abs(interp_data - expected)) < 0.1)
def odf_verts(self):
"""
The vertices on which to estimate the odf
"""
verts, edges, sides = create_unit_hemisphere(self.verts_level)
return verts, edges
def make_fake_signal():
hemisphere = create_unit_hemisphere(4)
v, e = hemisphere.vertices, hemisphere.edges
vecs_xy = v[np.flatnonzero(v[:, 2] < .001)]
evals = np.array([1.8, .2, .2])*10**-3*1.5
evecs_moveing = np.empty((len(vecs_xy), 3, 3))
evecs_moveing[:, :, 0] = vecs_xy
evecs_moveing[:, :, 1] = [0, 0, 1]
evecs_moveing[:, :, 2] = np.cross(evecs_moveing[:, :, 0],
evecs_moveing[:, :, 1])
assert ((evecs_moveing * evecs_moveing).sum(1) - 1 < .001).all()
assert ((evecs_moveing * evecs_moveing).sum(2) - 1 < .001).all()
gtab = np.empty((len(v) + 1, 3))
bval = np.empty(len(v) + 1)
bval[0] = 0
bval[1:] = 2000
gtab[0] = [0, 0, 0]
gtab[1:] = v
bvec = gtab.T
B = design_matrix(bvec, bval)
tensor_moveing = np.empty_like(evecs_moveing)
for ii in xrange(len(vecs_xy)):
tensor_moveing[ii] = np.dot(evecs_moveing[ii]*evals,
evecs_moveing[ii].T)
D_moveing = lower_triangular(tensor_moveing, 1)
tensor_fixed = np.diag(evals)
D_fixed = lower_triangular(tensor_fixed, 1)
sig = .45*np.exp(np.dot(D_moveing, B.T)) + .55*np.exp(np.dot(B, D_fixed))
print sig
assert sig.max() <= 1
assert sig.min() > 0
return hemisphere, vecs_xy, bval, bvec, sig
def odf_verts(self):
"""
The vertices on which to estimate the odf
"""
verts, edges, sides = create_unit_hemisphere(self.verts_level)
return verts, edges
def test_DiscreteDirectionFinder():
def discrete_eval(sphere):
X = np.zeros(len(sphere.phi))
X[0] = 1.
X[1] = .3
return X
sphere = create_unit_hemisphere(3)
ddf = DiscreteDirectionFinder()
ddf.config(sphere=sphere, relative_peak_threshold=.5, min_separation_angle=45)
direction = ddf(discrete_eval)
assert_array_almost_equal(direction, sphere.vertices[:1])
ddf.config(relative_peak_threshold=.2)
direction = ddf(discrete_eval)
assert_array_almost_equal(direction, sphere.vertices[:2])
def test_hat_and_lcr():
hemi = create_unit_hemisphere(6)
m, n = sph_harm_ind_list(8)
B = real_sph_harm(m, n, hemi.phi[:, None], hemi.theta[:, None])
H = hat(B)
B_hat = np.dot(H, B)
assert_array_almost_equal(B, B_hat)
R = lcr_matrix(H)
d = np.arange(len(hemi.theta))
r = d - np.dot(H, d)
lev = np.sqrt(1-H.diagonal())
r /= lev
r -= r.mean()
r2 = np.dot(R, d)
assert_array_almost_equal(r, r2)
r3 = np.dot(d, R.T)
assert_array_almost_equal(r, r3)
def test_smooth_pinv():
hemi = create_unit_hemisphere(3)
m, n = sph_harm_ind_list(4)
B = real_sph_harm(m, n, hemi.phi[:, None], hemi.theta[:, None])
L = np.zeros(len(m))
C = smooth_pinv(B, L)
D = np.dot(npl.inv(np.dot(B.T, B)), B.T)
assert_array_almost_equal(C, D)
L = n*(n+1)*.05
C = smooth_pinv(B, L)
L = np.diag(L)
D = np.dot(npl.inv(np.dot(B.T, B) + L*L), B.T)
assert_array_almost_equal(C, D)
L = np.arange(len(n))*.05
C = smooth_pinv(B, L)
L = np.diag(L)
D = np.dot(npl.inv(np.dot(B.T, B) + L*L), B.T)
assert_array_almost_equal(C, D)
x, y, z = sphere.vertices.T
B = (x * z > 0) + 2 * (y * z > 0)
return A * B
directions, values = peak_directions_nl(discrete_eval, 0.)
assert_equal(directions.shape, (3, 3))
directions, values = peak_directions_nl(discrete_eval, .6)
assert_equal(directions.shape, (2, 3))
directions, values = peak_directions_nl(discrete_eval, .8)
assert_equal(directions.shape, (1, 3))
assert_almost_equal(values, 3 * 3 / np.sqrt(3))
_sphere = create_unit_hemisphere(4)
_odf = (_sphere.vertices * [1, 2, 3]).sum(-1)
_gtab = GradientTable(np.ones((64, 3)))
class SimpleOdfModel(OdfModel):
sphere = _sphere
def fit(self, data):
fit = SimpleOdfFit(self, data)
fit.model = self
return fit
class SimpleOdfFit(OdfFit):
x, y, z = sphere.vertices.T
B = (x * z > 0) + 2 * (y * z > 0)
return A * B
directions, values = peak_directions_nl(discrete_eval, 0.)
assert_equal(directions.shape, (3, 3))
directions, values = peak_directions_nl(discrete_eval, .6)
assert_equal(directions.shape, (2, 3))
directions, values = peak_directions_nl(discrete_eval, .8)
assert_equal(directions.shape, (1, 3))
assert_almost_equal(values, 3 * 3 / np.sqrt(3))
_sphere = create_unit_hemisphere(4)
_odf = (_sphere.vertices * [1, 2, 3]).sum(-1)
_gtab = GradientTable(np.ones((64, 3)))
class SimpleOdfModel(OdfModel):
sphere = _sphere
def fit(self, data):
fit = SimpleOdfFit(self, data)
fit.model = self
return fit
class SimpleOdfFit(OdfFit):
def odf(self, sphere=None):
