def test_shpere_pot_rotation_x(self, sensor_setup):
""" V should be invariant to rotations """
tx = np.pi / 3
Mx = np.array(((1, 0, 0),
(0, np.cos(tx), -np.sin(tx)),
(0, np.sin(tx), np.cos(tx))), dtype=float)
ty = np.pi / 2
My = np.array(((np.cos(ty), 0, np.sin(ty)),
(0, 1, 0),
(-np.sin(ty), 0, np.cos(ty))), dtype=float)
tz = np.pi / 3
Mz = np.array(((np.cos(tz), -np.sin(tz), 0),
(np.sin(tz), np.cos(tz), 0),
(0, 0, 1)), dtype=float)
R = Mx.dot(My.dot(Mz))
cathode = [1, 0, 0]
anode = [-1, 0, 0]
cond = [1.0, 0.5, 1]
radii = [0.4, 0.5, 1]
pot1 = sphere.potential_3layers_surface_electrodes(
radii, cond, anode, cathode, sensor_setup)
cathode = R.dot(cathode)
anode = R.dot(anode)
sensors = np.array([R.dot(p) for p in sensor_setup])
pot2 = sphere.potential_3layers_surface_electrodes(
radii, cond, anode, cathode, sensors)
np.testing.assert_allclose(pot1, pot2, rtol=1e-3, atol=1e-5)
def test_sphere_homogeneous_cond(self, sensor_setup):
""" The potential should be the same, independent of the radii """
cathode = [1, 0, 0]
anode = [-1, 0, 0]
cond = [1, 1, 1]
radii = [0.7, 0.85, 1]
pot1 = sphere.potential_3layers_surface_electrodes(
radii, cond, anode, cathode, sensor_setup)
radii = [0.1, 0.2, 1]
pot2 = sphere.potential_3layers_surface_electrodes(
radii, cond, anode, cathode, sensor_setup)
np.testing.assert_allclose(pot1, pot2)
def test_dirichlet_problem_sphere(self, sphere3_msh):
m = sphere3_msh.crop_mesh(elm_type=4)
cond = np.ones(len(m.elm.tetrahedra))
cond[m.elm.tag1 == 4] = .01
anode = m.nodes.node_number[m.nodes.node_coord[:, 2].argmax()]
cathode = m.nodes.node_number[m.nodes.node_coord[:, 2].argmin()]
bcs = [fem.DirichletBC([anode], [1]),
fem.DirichletBC([cathode], [-1])]
S = fem.FEMSystem(m, cond)
A = S.A
b = np.zeros(m.nodes.nr)
dof_map = S.dof_map
for bc in bcs:
A, b, dof_map = bc.apply(A, b, dof_map)
x = spalg.spsolve(A, b)
for bc in bcs:
x, dof_map = bc.apply_to_solution(x, dof_map)
order = dof_map.inverse.argsort()
x = x[order].squeeze()
v_analytical = analytical_solutions.potential_3layers_surface_electrodes(
[85, 90, 95], [1., .01, 1.], [0, 0, -95], [0, 0, 95], m.nodes.node_coord)
v_analytical /= v_analytical[anode - 1]
v_analytical -= v_analytical[0]
x -= x[0]
m.nodedata = [mesh_io.NodeData(v_analytical, 'Analytical'),
mesh_io.NodeData(x, 'FEM')]
#mesh_io.write_msh(m, '~/Tests/fem.msh')
m = m.crop_mesh(3)
assert rdm(m.nodedata[0].value, m.nodedata[1].value) < .1
def test_sphere_pot_symmetry_xz(self, sensor_setup):
""" V should be symmetric to a reflection along the XY plane """
cathode = [1, 0, 0]
anode = [1 / np.sqrt(2), 0, 1 / np.sqrt(2)]
cond = [1.0, 0.5, 1]
radii = [0.4, 0.5, 1]
pot1 = sphere.potential_3layers_surface_electrodes(
radii, cond, anode, cathode, sensor_setup)
anode = [1 / np.sqrt(2), 0, -1 / np.sqrt(2)]
p2 = sensor_setup
p2[:, 2] *= -1
pot2 = sphere.potential_3layers_surface_electrodes(
radii, cond, anode, cathode, p2)
np.testing.assert_array_almost_equal(pot1, pot2)
def test_sphere_pot_continuity(self):
""" V should be continuous across interfaces """
cathode = [1, 0, 0]
anode = [-1, 0, 0]
cond = [1.0, 0.5, 1]
radii = [0.4, 0.5, 1]
sensor = np.array(((0.5000001, 0, 0), (0.4999999, 0, 0)), dtype=float)
pot = sphere.potential_3layers_surface_electrodes(
radii, cond, anode, cathode, sensor)
np.testing.assert_allclose(pot[0], pot[1], rtol=1e-3)
def test_tdcs_getdp_sphere(self, sphere_el_msh):
surface_tags = [1100, 1101]
currents = [-1, 1]
cond = gmsh.ElementData(np.ones(sphere_el_msh.elm.nr), mesh=cube_msh)
cond.value[sphere_el_msh.elm.tag1 == 4] = .01
v = fem.tdcs_getdp(sphere_el_msh, cond, currents, surface_tags)
m = copy.deepcopy(sphere_el_msh)
m.nodedata = [v]
m = m.crop_mesh(3)
v_fem = m.nodedata[0].value - m.nodedata[0].value[0]
v_analytical = analytical_solutions.potential_3layers_surface_electrodes(
[85, 90, 95], [1., .01, 1.], [0, 0, 95], [0, 0, -95], m.nodes.node_coord)
v_analytical -= v_analytical[0]
rdm = np.linalg.norm(
v_fem/np.linalg.norm(v_fem) -
v_analytical/np.linalg.norm(v_analytical))
#m.nodedata.append(gmsh.NodeData(v_analytical))
#gmsh.write_msh(m, '~/Tests/tdcs.msh')
assert rdm < .2
def test_reciprocity():
cond = [1, 1, 1]
radii = [0.7, 0.85, 1]
electrodes = np.array(((1, 0, 0), (-1, 0, 0)), dtype=float)
dipole_pos = np.array(
((0.5, 0, 0), (0.5 + 1e-10, 0., 0), (0.5, 1e-10, 0), (0.5, 0, 1e-10),
(0.5 - 1e-10, 0., 0), (0.5, -1e-10, 0), (0.5, 0, -1e-10)),
dtype=float)
dipole_moment = np.array((1, 1, 1), dtype=float)
pot = sphere.potential_3layers_surface_electrodes(radii, cond,
electrodes[0, :],
electrodes[1, :],
dipole_pos)
E_field = (pot[1:4] - pot[4:7]) / 2e-13
dipole_pot = sphere.potential_homogeneous_dipole(1., 1., dipole_pos[0],
dipole_moment, electrodes)
np.testing.assert_allclose(dipole_pot[0] - dipole_pot[1],
-E_field.dot(dipole_moment),
rtol=1e-4)