def test_tms_getdp_aniso(self, sphere3_msh):
dipole_pos = np.array([0., 0., 200])
dipole_moment = np.array([0., 1., 0.])
didt = 1e6
r = (sphere3_msh.nodes.node_coord - dipole_pos) * 1e-3
dAdt = 1e-7 * didt * np.cross(dipole_moment, r) / (np.linalg.norm(r, axis=1)[:, None] ** 3)
dAdt = gmsh.NodeData(dAdt, mesh=sphere3_msh)
cond = gmsh.ElementData(np.ones((sphere3_msh.elm.nr, 9)), mesh=sphere3_msh)
cond.value[:] = [1, 0, 0, 0, 1, 0, 0, 0, 1]
phi_sim = fem.tms_getdp(sphere3_msh, cond, dAdt)
m = fem.calc_fields(phi_sim, 'vE', dadt=dAdt)
m = m.crop_mesh(elm_type=4)
E_fem = m.field['E'].value
pos = m.elements_baricenters().value
E_analytical = analytical_solutions.tms_E_field(dipole_pos * 1e-3,
dipole_moment, didt,
pos * 1e-3)
rdm = np.linalg.norm(
E_fem.reshape(-1)/np.linalg.norm(E_fem) -
E_analytical.reshape(-1)/np.linalg.norm(E_analytical))
mag = np.log(np.linalg.norm(E_fem)/np.linalg.norm(E_analytical))
assert rdm < .2
assert np.abs(mag) < np.log(1.1)
def test_reciprocal(self, get_opt_grid_mock, target_direction, sphere_msh,
simple_coil_ccd):
tms_opt = opt_struct.TMSoptimize()
tms_opt.fnamecoil = simple_coil_ccd
tms_opt.mesh = sphere_msh
tms_opt.didt = 1e6
tms_opt.target_direction = target_direction
coil_centers = [
[150., 0., 0.],
[-150., 0., 0.],
[0., 150., 0.],
[0., -150., 0.],
[0., 0, 150.],
[0., 0, -150.],
]
center_matrices = []
for cc in coil_centers:
z_dir = -np.array(cc) / np.linalg.norm(cc)
y_dir = np.array([0., 1., 0.])
if np.isclose(np.abs(z_dir.dot(y_dir)), 1):
y_dir = np.array([1., 0., 0.])
p = np.eye(4)
p[:3, 0] = np.cross(y_dir, z_dir)
p[:3, 1] = y_dir
p[:3, 2] = z_dir
p[:3, 3] = cc
center_matrices.append(p)
coil_dir = []
for angle in np.linspace(-np.pi / 2, np.pi / 2, 7):
coil_dir.append([-np.sin(angle), np.cos(angle), 0])
coil_dir = np.array(coil_dir)
get_opt_grid_mock.return_value = (np.array(center_matrices).transpose(
1, 2, 0), coil_dir.T)
target_pos, target_region = sphere_msh.find_closest_element(
[85, 0, 0],
elements_of_interest=sphere_msh.elm.tetrahedra,
return_index=True)
cond_field = sim_struct.SimuList.cond2elmdata(tms_opt)
E_recp, pos_matrices = tms_opt._ADM_optimize(cond_field, target_region)
dipole_pos, dipole_moment = simple_coil()
E_analytical = []
for p in pos_matrices:
dp = p[:3, :3].dot(dipole_pos.T).T + p[:3, 3]
dm = p[:3, :3].dot(dipole_moment.T).T
E = analytical_solutions.tms_E_field(
dp * 1e-3, dm, tms_opt.didt,
np.atleast_2d(target_pos) * 1e-3)
if target_direction is None:
E_analytical.append(np.linalg.norm(E))
else:
E_analytical.append(E[0, 1])
assert np.allclose(E_analytical, E_recp, rtol=0.1, atol=1)
def test_radial_source(self, quadrant_points):
""" The field of a radial source is given by a 3.10 (Heller and Hulsteyn) """
dipole_pos = np.array([3, 0, 0])
dipole_moment = np.array([1, 0, 0])
E = sphere.tms_E_field(dipole_pos, dipole_moment, 1, quadrant_points)
E_simple = -1e-7 * np.cross(dipole_pos - quadrant_points, dipole_moment) \
/ np.linalg.norm(quadrant_points - dipole_pos, axis=1)[:, None]**3
# Explanation for the minus: see appendix 1 in Heller and Hulsteyn
assert np.allclose(E, E_simple)
def test_direct(self, target_direction, sphere_msh, simple_coil_ccd):
tms_opt = opt_struct.TMSoptimize()
tms_opt.fnamecoil = simple_coil_ccd
tms_opt.mesh = sphere_msh
tms_opt.didt = 1e6
tms_opt.target_direction = target_direction
fn_hdf5 = tempfile.mktemp(".hdf5")
tms_opt._name_hdf5 = MagicMock(return_value=fn_hdf5)
coil_centers = [
[150., 0., 0.],
[-150., 0., 0.],
[0., 150., 0.],
[0., -150., 0.],
[0., 0, 150.],
[0., 0, -150.],
]
pos_matrices = []
for cc in coil_centers:
z_dir = -np.array(cc) / np.linalg.norm(cc)
y_dir = np.array([0., 1., 0.])
if np.isclose(np.abs(z_dir.dot(y_dir)), 1):
y_dir = np.array([1., 0., 0.])
p = np.eye(4)
p[:3, 0] = np.cross(y_dir, z_dir)
p[:3, 1] = y_dir
p[:3, 2] = z_dir
p[:3, 3] = cc
pos_matrices.append(p)
target_pos, target_region = sphere_msh.find_closest_element(
[85, 0, 0],
elements_of_interest=sphere_msh.elm.tetrahedra,
return_index=True)
cond_field = sim_struct.SimuList.cond2elmdata(tms_opt)
E_fem = tms_opt._direct_optimize(cond_field,
np.atleast_1d(target_region),
pos_matrices, 1)
dipole_pos, dipole_moment = simple_coil()
E_analytical = []
for p in pos_matrices:
dp = p[:3, :3].dot(dipole_pos.T).T + p[:3, 3]
dm = p[:3, :3].dot(dipole_moment.T).T
E = analytical_solutions.tms_E_field(
dp * 1e-3, dm, tms_opt.didt,
np.atleast_2d(target_pos) * 1e-3)
if target_direction is None:
E_analytical.append(np.linalg.norm(E))
else:
E_analytical.append(E[0, 1])
assert np.allclose(E_analytical, E_fem, rtol=0.1, atol=1)
def tms_sphere(sphere3_msh):
m = sphere3_msh.crop_mesh(elm_type=4)
dipole_pos = np.array([0., 0., 300])
dipole_moment = np.array([1., 0., 0.])
didt = 1e6
r = (m.nodes.node_coord - dipole_pos) * 1e-3
dAdt = 1e-7 * didt * np.cross(dipole_moment, r) / (np.linalg.norm(r, axis=1)[:, None] ** 3)
dAdt = mesh_io.NodeData(dAdt, mesh=m)
dAdt.field_name = 'dAdt'
dAdt.mesh = m
pos = m.elements_baricenters().value
E_analytical = analytical_solutions.tms_E_field(dipole_pos * 1e-3,
dipole_moment, didt,
pos * 1e-3)
cond = mesh_io.ElementData(np.ones(m.elm.nr))
cond.mesh = m
return m, cond, dAdt, E_analytical
def test_2_dipoles(self, quadrant_points):
dipole_pos = np.array([[3, 0, 0], [3, 0, 0]])
dipole_moment = np.array([[1, 0, 0], [-1, 0, 0]])
E = sphere.tms_E_field(dipole_pos, dipole_moment, 1, quadrant_points)
assert np.allclose(E, 0)