lmax = 4
alm = np.zeros((lmax * (lmax + 2), ))
blm = np.zeros((lmax * (lmax + 2), ))
# Set one specific component to one
blm[16] += 1
sphfield = sphtools.field(target_points, alm, blm, lmax)
target_field = sphfield / np.max(sphfield[:, 0])
coil.plot_mesh(opacity=0.2)
mlab.quiver3d(*target_points.T, *sphfield.T)
target_spec = {
"coupling": coil.B_coupling(target_points),
"abs_error": 0.1,
"target": target_field,
}
#%%
# Run QP solver
import mosek
coil.s, prob = optimize_streamfunctions(
coil,
[target_spec],
objective="minimum_inductive_energy",
solver="MOSEK",
solver_opts={"mosek_params": {
mosek.iparam.num_threads: 8
figure=f,
magnification=4,
)
mlab.close()
#%%
# Create bfield specifications used when optimizing the coil geometry
# The absolute target field amplitude is not of importance,
# and it is scaled to match the C matrix in the optimization function
target_field = np.zeros(target_points.shape)
target_field[:, 0] += 1 # Homogeneous field on X-axis
target_spec = {
"coupling": coil.B_coupling(target_points),
"abs_error": 0.005,
"target": target_field,
}
stray_spec = {
"coupling": coil.B_coupling(stray_points),
"abs_error": 0.01,
"target": np.zeros((n_stray_points, 3)),
}
bfield_specification = [target_spec, stray_spec]
#%%
# Run QP solver
import mosek
fgcolor=(0.5, 0.5, 0.5),
size=(800, 800))
coil.s.plot(figure=f, contours=20)
shieldcoil.s.plot(figure=f, contours=20)
#%%
# Compute the field and scalar potential on an XY-plane
x = y = np.linspace(-8, 8, 150)
X, Y = np.meshgrid(x, y, indexing="ij")
points = np.zeros((X.flatten().shape[0], 3))
points[:, 0] = X.flatten()
points[:, 1] = Y.flatten()
CB1 = coil.B_coupling(points)
CB2 = shieldcoil.B_coupling(points)
CU1 = coil.U_coupling(points)
CU2 = shieldcoil.U_coupling(points)
B1 = CB1 @ coil.s
B2 = CB2 @ shieldcoil.s
U1 = CU1 @ coil.s
U2 = CU2 @ shieldcoil.s
#%%
# Now, plot the field streamlines and scalar potential
from bfieldtools.contour import scalar_contour
mesh = data["mesh"]
p = data["p"]
n = data["n"]
mesh = trimesh.Trimesh(vertices=data["vertices"], faces=data["faces"])
evoked = mne.Evoked(SAVE_DIR + "left_auditory-ave.fif")
#%%
# Fit the surface current for the auditory evoked response
c = MeshConductor(mesh_obj=mesh, basis_name="suh", N_suh=150)
M = c.mass
sensor_coupling = np.einsum("ijk,ij->ik", c.B_coupling(p), n)
# a = np.linalg.pinv(sensor_coupling, rcond=1e-15) @ field
ss = np.linalg.svd(sensor_coupling @ sensor_coupling.T, False, False)
# reg_exps = [0.5, 1, 2, 3, 4, 5, 6, 7, 8]
reg_exps = [1]
rel_errors = []
for reg_exp in reg_exps:
_lambda = np.max(ss) * (10 ** (-reg_exp))
# Laplacian in the suh basis is diagonal
BB = sensor_coupling.T @ sensor_coupling + _lambda * (-c.laplacian) / np.max(
abs(c.laplacian)
)
a = np.linalg.solve(BB, sensor_coupling.T @ field)
s = StreamFunction(a, c)
# Use lines below to get coulings with different normalization # from bfieldtools.sphtools import compute_sphcoeffs_mesh # A1, Beta1 = compute_sphcoeffs_mesh(mesh1, 5, normalization='energy', R=1) # A2, Beta2 = compute_sphcoeffs_mesh(mesh2, 5, normalization='energy', R=1) # Beta1 = Beta1[:, coil1.inner_vertices] # Beta2 = Beta2[:, coil2.inner_vertices] x = y = np.linspace(-0.8, 0.8, 50) # 150) X, Y = np.meshgrid(x, y, indexing="ij") points = np.zeros((X.flatten().shape[0], 3)) points[:, 0] = X.flatten() points[:, 1] = Y.flatten() CB1 = coil1.B_coupling(points) CB2 = coil2.B_coupling(points) CU1 = coil1.U_coupling(points) CU2 = coil2.U_coupling(points) #%% Precalculations for the solution # alpha[15] = 1 # Minimization of magnetic energy with spherical harmonic constraint C = Beta1 + Beta2 @ P M = M11 + M21.T @ P from scipy.linalg import eigvalsh ssmax = eigvalsh(C.T @ C, M, eigvals=[M.shape[1] - 1, M.shape[1] - 1])
# c = MeshConductor(mesh_obj=mesh, basis_name="suh", N_suh=35)
# M = c.mass
# B_sensors = np.einsum("ijk,ij->ik", c.B_coupling(p), n)
#
#
# asuh = np.linalg.pinv(B_sensors, rcond=1e-15) @ field
#
# s = StreamFunction(asuh, c)
# b_filt = B_sensors @ s
#%% Suh fit
c = MeshConductor(mesh_obj=mesh, basis_name="suh", N_suh=150)
M = c.mass
B_sensors = np.einsum("ijk,ij->ik", c.B_coupling(p), n)
ss = np.linalg.svd(B_sensors @ B_sensors.T, False, False)
reg_exp = 1
plot_this = True
rel_errors = []
_lambda = np.max(ss) * (10**(-reg_exp))
# Laplacian in the suh basis is diagonal
BB = B_sensors.T @ B_sensors + _lambda * (-c.laplacian) / np.max(
abs(c.laplacian))
a = np.linalg.solve(BB, B_sensors.T @ field)
s = StreamFunction(a, c)
reco_suh = B_sensors @ s
fgcolor=(0.5, 0.5, 0.5),
size=(800, 800))
coil.plot_mesh(figure=f, opacity=0.2)
shield.plot_mesh(figure=f, opacity=0.2)
mlab.points3d(*target_points.T)
#%%
# Compute C matrices that are used to compute the generated magnetic field
mutual_inductance = coil.mutual_inductance(shield)
# Take into account the field produced by currents induced into the shield
# NB! This expression is for instantaneous step-function switching of coil current, see Eq. 18 in G.N. Peeren, 2003.
shield.M_coupling = np.linalg.solve(-shield.inductance, mutual_inductance.T)
secondary_C = shield.B_coupling(target_points) @ -shield.M_coupling
#%%
# Create bfield specifications used when optimizing the coil geometry
# The absolute target field amplitude is not of importance,
# and it is scaled to match the C matrix in the optimization function
target_field = np.zeros(target_points.shape)
target_field[:, 1] = target_field[:, 1] + 1
target_spec = {
"coupling": coil.B_coupling(target_points),
"abs_error": 0.01,
"target": target_field,
}
f.scene.camera.zoom(1.1)
#%%
# Let's design a coil without taking the magnetic shield into account
# The absolute target field amplitude is not of importance,
# and it is scaled to match the C matrix in the optimization function
target_field = np.zeros(target_points.shape)
target_field[:, 0] = target_field[:, 0] + 1 # Homogeneous Y-field
target_abs_error = np.zeros_like(target_field)
target_abs_error[:, 0] += 0.005
target_abs_error[:, 1:3] += 0.01
target_spec = {
"coupling": coil.B_coupling(target_points),
"rel_error": 0,
"abs_error": target_abs_error,
"target": target_field,
}
import mosek
coil.s, coil.prob = optimize_streamfunctions(
coil,
[target_spec],
objective="minimum_inductive_energy",
solver="MOSEK",
solver_opts={"mosek_params": {
mosek.iparam.num_threads: 8
}},