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_tdcs_run(self, mock_fem, sampler_args):
mesh, poslist, fn_hdf5, roi = sampler_args
v = mesh.nodes.node_coord[:, 0]
v_roi = mesh.crop_mesh(roi).nodes.node_coord[:, 0]
mock_fem.tdcs.side_effect = [
mesh_io.NodeData(v, mesh=mesh),
mesh_io.NodeData(-v, mesh=mesh)]
S = simnibs_gpc.TDCSgPCSampler(
mesh, poslist, fn_hdf5, [1101, 1102], [-1, 1], roi)
S.qoi_function['rand'] = lambda v, rand: rand
E1 = S.run_simulation([1])
assert E1.shape == (3 * np.sum(mesh.elm.tag1 == 3), )
assert np.allclose(E1.reshape(-1, 3), [-1e3, 0, 0])
S.run_simulation([2])
with h5py.File(fn_hdf5) as f:
assert np.allclose(f['random_var_samples'][()], [[1], [2]])
assert np.allclose(f['mesh_roi/data_matrices/v_samples'][0, :], v_roi)
assert np.allclose(f['mesh_roi/data_matrices/v_samples'][1, :],-v_roi)
assert np.allclose(f['mesh_roi/data_matrices/E_samples'][0, :],[-1e3, 0., 0.])
assert np.allclose(f['mesh_roi/data_matrices/E_samples'][1, :],[1e3, 0., 0.])
assert np.allclose(f['mesh_roi/data_matrices/rand_samples'][:],[[1], [2]])
def test_calc_dadt(self, sphere3_msh):
phi = sphere3_msh.nodes.node_coord[:, 0] + \
2 * sphere3_msh.nodes.node_coord[:, 1] + \
-3 * sphere3_msh.nodes.node_coord[:, 2]
potential = mesh_io.NodeData(phi, mesh=sphere3_msh)
dadt = .2 * sphere3_msh.nodes.node_coord
dadt = mesh_io.NodeData(dadt, mesh=sphere3_msh)
E = np.zeros((sphere3_msh.elm.nr, 3))
E = [-1, -2, 3] - dadt.node_data2elm_data().value
E = mesh_io.ElementData(E, mesh=sphere3_msh)
E.assign_triangle_values()
cond = sphere3_msh.elm.tag1
cond = mesh_io.ElementData(cond, mesh=sphere3_msh)
m = fem.calc_fields(potential, 'vDJEgsej', cond, dadt=dadt,
units='m')
assert np.allclose(m.field['v'].value, potential.value)
assert np.allclose(m.field['D'].value, dadt.value)
assert np.allclose(m.field['g'].value, [1, 2, -3])
assert np.allclose(m.field['E'].value, E.value)
assert np.allclose(m.field['J'].value, cond.value[:, None] * E.value)
assert np.allclose(m.field['conductivity'].value, cond.value)
assert np.allclose(m.field['normE'].value, np.linalg.norm(E.value, axis=1))
assert np.allclose(m.field['normJ'].value,
np.linalg.norm(cond.value[:, None] * E.value, axis=1))
def test_solve_dirichlet_petsc(self, cube_msh):
m = cube_msh
cond = np.ones(m.elm.nr)
cond[m.elm.tag1 > 5] = 1e3
cond = mesh_io.ElementData(cond)
el_tags = [1100, 1101]
potentials = [1, -1]
S = fem.FEMSystem.tdcs(m, cond, el_tags, potentials)
x = S.solve()
sol = m.nodes.node_coord[:, 1]/50.
m.nodedata = [mesh_io.NodeData(x, 'FEM'), mesh_io.NodeData(sol, 'Analytical')]
#mesh_io.write_msh(m, '~/Tests/fem.msh')
assert rdm(sol, x.T) < .1
assert np.abs(mag(x, sol)) < np.log(1.1)
def test_solve_assemble_neumann_petsc(self, cube_msh):
m = cube_msh
cond = np.ones(m.elm.nr)
cond[m.elm.tag1 > 5] = 25
cond = mesh_io.ElementData(cond)
el_tags = [1100, 1101]
currents = [1, -1]
S = fem.FEMSystem.tdcs_neumann(m, cond, el_tags[0])
b = S.assemble_tdcs_neumann_rhs(el_tags[1:], currents[1:])
x = S.solve(b)
sol = (m.nodes.node_coord[:, 1] - 50) / 10
m.nodedata = [mesh_io.NodeData(x, 'FEM'), mesh_io.NodeData(sol, 'Analytical')]
#mesh_io.write_msh(m, '~/Tests/fem.msh')
assert rdm(sol, x.T) < .1
assert np.abs(mag(x, sol)) < np.log(1.5)
def test_solve_petsc(self, tms_sphere):
m, cond, dAdt, E_analytical = tms_sphere
S = fem.FEMSystem.tms(m, cond)
b = S.assemble_tms_rhs(dAdt)
x = S.solve(b)
v = mesh_io.NodeData(x, 'FEM', mesh=m)
E = -v.gradient().value * 1e3 - dAdt.node_data2elm_data().value
m.elmdata = [mesh_io.ElementData(E_analytical, 'analytical'),
mesh_io.ElementData(E, 'E_FEM'),
mesh_io.ElementData(E_analytical + dAdt.node_data2elm_data().value, 'grad_analytical'),
dAdt]
m.nodedata = [mesh_io.NodeData(x, 'FEM')]
#mesh_io.write_msh(m, '~/Tests/fem.msh')
assert rdm(E, E_analytical) < .2
assert np.abs(mag(E, E_analytical)) < np.log(1.1)
def test_avoid_mean_field_norm_node(self, sphere_surf):
a = opt_struct.TDCSavoid(tissues=[1003],
weight=1e4,
lf_type='node',
mesh=sphere_surf)
field = mesh_io.NodeData(np.ones((sphere_surf.nodes.nr, 3)))
assert np.isclose(a.mean_field_norm_in_region(field), np.sqrt(3))
def test_calc_vEJgs(self, sphere3_msh):
phi = sphere3_msh.nodes.node_coord[:, 0] + \
2 * sphere3_msh.nodes.node_coord[:, 1] + \
-3 * sphere3_msh.nodes.node_coord[:, 2]
potential = mesh_io.NodeData(phi, mesh=sphere3_msh)
E = np.zeros((sphere3_msh.elm.nr, 3))
E[:] = [-1., -2., 3.]
E = mesh_io.ElementData(E, mesh=sphere3_msh)
cond = sphere3_msh.elm.tag1
cond = mesh_io.ElementData(cond, mesh=sphere3_msh)
m = fem.calc_fields(potential, 'vJEgsej', cond)
assert np.allclose(m.field['v'].value, potential.value)
assert np.allclose(m.field['E'].value, E.value * 1e3)
assert np.allclose(m.field['J'].value,
cond.value[:, None] * E.value * 1e3)
assert np.allclose(m.field['g'].value, -E.value * 1e3)
assert np.allclose(m.field['conductivity'].value, cond.value)
assert np.allclose(m.field['normE'].value,
np.linalg.norm(E.value, axis=1) * 1e3)
assert np.allclose(
m.field['normJ'].value,
np.linalg.norm(cond.value[:, None] * E.value, axis=1) * 1e3)
def test_solve_assemble_aniso(self, cube_msh):
m = cube_msh
cond = np.tile(np.eye(3), (m.elm.nr, 1, 1))
cond[m.elm.tag1 > 5] *= 100
cond[m.elm.tag1 < 5, 0, :] = 0.01
cond[m.elm.tag1 < 5, 1, :] = 0.1
cond = mesh_io.ElementData(cond.reshape(-1, 9))
el_tags = [1100, 1101]
currents = [1, -1]
S = fem.FEMSystem.tdcs_neumann(m, cond, el_tags[0])
b = S.assemble_tdcs_neumann_rhs(el_tags[1:], currents[1:])
x = S.solve(b)
sol = (m.nodes.node_coord[:, 1] - 50) / 10
m.nodedata = [mesh_io.NodeData(x, 'FEM'), mesh_io.NodeData(sol, 'Analytical')]
#mesh_io.write_msh(m, '~/Tests/fem.msh')
assert rdm(sol, x.T) < .1
assert np.abs(mag(x, sol)) < np.log(1.5)
def test_solve_assemble_neumann_nodes(self, cube_msh):
m = cube_msh
cond = np.ones(m.elm.nr)
cond[m.elm.tag1 > 5] = 25
cond = mesh_io.ElementData(cond)
currents = [1, -1]
nodes_top = np.unique(m.elm[m.elm.tag1 == 1100, :3])
nodes_bottom = np.unique(m.elm[m.elm.tag1 == 1101, :3])
S = fem.FEMSystem.tdcs_neumann(m, cond, nodes_top, input_type='node')
b = S.assemble_tdcs_neumann_rhs(nodes_bottom,
currents[1:],
input_type='node')
x = S.solve(b)
sol = (m.nodes.node_coord[:, 1] - 50) / 10
m.nodedata = [
mesh_io.NodeData(x, 'FEM'),
mesh_io.NodeData(sol, 'Analytical')
]
#mesh_io.write_msh(m, '~/Tests/fem.msh')
assert rdm(sol, x.T) < .1
assert np.abs(mag(x, sol)) < np.log(1.5)
def test_tdcs_neumann_3_el(self, cube_msh):
m = cube_msh
cond = np.ones(m.elm.nr)
cond[m.elm.tag1 > 5] = 1e3
cond = mesh_io.ElementData(cond)
el_tags = [1100, 1101, 1101]
currents = [.5, -1.5, 1.]
x = fem.tdcs_neumann(m, cond, currents, el_tags)
sol = (m.nodes.node_coord[:, 1] - 50) / 20
m.nodedata = [x, mesh_io.NodeData(sol, 'Analytical')]
#mesh_io.write_msh(m, '~/Tests/fem.msh')
assert rdm(sol, x.value) < .1
assert np.abs(mag(x.value, sol)) < np.log(1.1)
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_calc_tensor(self, sphere3_msh):
phi = sphere3_msh.nodes.node_coord[:, 0] + \
2 * sphere3_msh.nodes.node_coord[:, 1] + \
-3 * sphere3_msh.nodes.node_coord[:, 2]
potential = mesh_io.NodeData(phi, mesh=sphere3_msh)
o = np.ones(sphere3_msh.elm.nr)
z = np.zeros(sphere3_msh.elm.nr)
cond = np.reshape(np.eye(3) * np.array([1, 2, 3]), -1)
cond = np.tile(cond, [sphere3_msh.elm.nr, 1])
cond = mesh_io.ElementData(cond, mesh=sphere3_msh)
m = fem.calc_fields(potential, 'vJEgsej', cond, units='m')
assert np.allclose(m.field['v'].value, potential.value)
assert np.allclose(m.field['g'].value, [1, 2, -3])
assert np.allclose(m.field['E'].value, [-1, -2, 3])
assert np.allclose(m.field['J'].value, [-1, -4, 9])
def test_calc_E(self, sampler_args):
mesh, poslist, fn_hdf5, roi = sampler_args
S = simnibs_gpc.gPCSampler(mesh, poslist, fn_hdf5, roi)
v = mesh_io.NodeData(mesh.nodes.node_coord[:, 0], mesh=mesh)
E = S._calc_E(v, None)
assert np.allclose(E, [-1e3, 0, 0])
