def test_OneSphereVolumeConductor_01(self):
"""test case where sigma_i == sigma_o which
should be identical to the standard point-source potential in
infinite homogeneous media
"""
# current magnitude
I = np.ones(10)
# conductivity
sigma = 0.3
# sphere radius
R = 1000
# source location (along x-axis)
rs = 800
# sphere coordinates of observation points
radius = np.r_[np.arange(0, rs), np.arange(rs + 1, rs * 2)]
theta = np.zeros(radius.shape)
phi = np.zeros(radius.shape)
r = np.array([radius, theta, phi])
# predict potential
sphere = LFPy.OneSphereVolumeConductor(r=r,
R=R,
sigma_i=sigma,
sigma_o=sigma)
phi = sphere.calc_potential(rs=rs, I=I)
# ground truth
phi_gt = I[0] / (4 * np.pi * sigma * abs(radius - rs))
# test
np.testing.assert_almost_equal(phi, np.array([phi_gt] * I.size).T)
def test_OneSphereVolumeConductor_02(self):
"""test case where sigma_i == sigma_o which
should be identical to the standard point-source potential in
infinite homogeneous media
"""
# current magnitude
current = 1.
# conductivity
sigma = 0.3
# sphere radius
R = 10000
# cell body position
xs = 8000.
# sphere coordinates of observation points
radius = np.r_[np.arange(0, xs), np.arange(xs + 1, xs * 2)][::10]
theta = np.zeros(radius.shape) + np.pi / 2
phi = np.zeros(radius.shape)
r = np.array([radius, theta, phi])
# set up cell
cell = LFPy.Cell(
morphology=os.path.join(LFPy.__path__[0], 'test', 'stick.hoc'))
cell.set_pos(x=xs, y=0, z=0)
cell.set_rotation(y=np.pi / 2)
# predict potential
sphere = LFPy.OneSphereVolumeConductor(cell=cell,
r=r,
R=R,
sigma_i=sigma,
sigma_o=sigma)
M = sphere.get_transformation_matrix(n_max=100)
# ground truth and tests
for i, x in enumerate(cell.x.mean(axis=-1)):
dist = radius - x
dist[abs(dist) < cell.d[i]] = cell.d[i]
phi_gt = current / (4 * np.pi * sigma * abs(dist))
np.testing.assert_almost_equal(M[:, i], phi_gt)
