shading='flat',
cmap=plt.cm.viridis)
ax.set_title(r'$\Delta$ Conductivities')
fig.colorbar(im)
ax.axis('equal')
fig.set_size_inches(6, 4)
# fig.savefig('demo_bp_0.png', dpi=96)
plt.show()
""" 2. FEM forward simulations """
# setup EIT scan conditions
# adjacent stimulation (el_dist=1), adjacent measures (step=1)
el_dist, step = 1, 1
ex_mat = eit_scan_lines(16, el_dist)
# calculate simulated data
fwd = Forward(mesh_obj, el_pos)
f0 = fwd.solve_eit(ex_mat, step=step, perm=mesh_obj['perm'])
f1 = fwd.solve_eit(ex_mat, step=step, perm=mesh_new['perm'])
"""
3. naive inverse solver using back-projection
"""
eit = bp.BP(mesh_obj, el_pos, ex_mat=ex_mat, step=1, parser='std')
eit.setup(weight='none')
ds = 192.0 * eit.solve(f1.v, f0.v)
# plot
fig = plt.figure()
ax1 = fig.add_subplot(111)
im = ax1.tripcolor(pts[:, 0], pts[:, 1], tri, ds, cmap=plt.cm.viridis)
ax1.set_title(r'$\Delta$ Conductivities')
ax1.axis('equal')
bbox = [[-1, -1, -1], [1, 1, 1]]
# save calling convention as distmesh 2D
ms, el_pos = mesh.create(h0=0.15, bbox=bbox)
no2xy = ms['node']
el2no = ms['element']
# report the status of the 2D mesh
quality.stats(no2xy, el2no)
""" 1. FEM forward simulations """
# setup EIT scan conditions
el_dist, step = 7, 1
ex_mat = eit_scan_lines(16, el_dist)
# calculate simulated data
fwd = Forward(ms, el_pos)
# in python, index start from 0
ex_line = ex_mat[1].ravel()
# change alpha
anomaly = [{'x': 0.40, 'y': 0.40, 'z': 0.0, 'd': 0.30, 'alpha': 100.0}]
ms_test = mesh.set_alpha(ms, anomaly=anomaly, background=1.0)
tri_perm = ms_test['alpha']
node_perm = pdeprtni(no2xy, el2no, np.real(tri_perm))
# solving once using fem
f, _ = fwd.solve_once(ex_line, tri_perm)
f = np.real(f)
# mplot.tetplot(p, t, edge_color=(0.2, 0.2, 1.0, 1.0), alpha=0.01)
# save calling convention as distmesh 2D
mesh_obj, el_pos = mesh.create(h0=0.15, bbox=bbox)
pts = mesh_obj['node']
tri = mesh_obj['element']
# report the status of the 2D mesh
quality.stats(pts, tri)
""" 1. FEM forward simulations """
# setup EIT scan conditions
el_dist, step = 7, 1
ex_mat = eit_scan_lines(16, el_dist)
# calculate simulated data
fwd = Forward(mesh_obj, el_pos)
# in python, index start from 0
ex_line = ex_mat[1].ravel()
# change alpha
anomaly = [{'x': 0.40, 'y': 0.40, 'z': 0.0, 'd': 0.30, 'perm': 100.0}]
mesh_new = mesh.set_perm(mesh_obj, anomaly=anomaly, background=1.0)
tri_perm = mesh_new['perm']
node_perm = sim2pts(pts, tri, np.real(tri_perm))
# solving once using fem
f, _ = fwd.solve(ex_line, perm=tri_perm)
f = np.real(f)
# mplot.tetplot(p, t, edge_color=(0.2, 0.2, 1.0, 1.0), alpha=0.01)
# show
fig, ax = plt.subplots(figsize=(6, 4))
im = ax.tripcolor(pts[:, 0],
pts[:, 1],
tri,
np.real(perm),
shading="flat",
cmap=plt.cm.viridis)
fig.colorbar(im)
ax.axis("equal")
ax.set_title(r"$\Delta$ Conductivities")
plt.show()
""" 2. calculate simulated data """
el_dist, step = 1, 1
ex_mat = eit_scan_lines(n_el, el_dist)
fwd = Forward(mesh_obj, el_pos)
f1 = fwd.solve_eit(ex_mat, step, perm=mesh_new["perm"], parser="std")
""" 3. solve_eit using gaussian-newton (with regularization) """
# number of stimulation lines/patterns
eit = jac.JAC(mesh_obj, el_pos, ex_mat, step, perm=1.0, parser="std")
eit.setup(p=0.25, lamb=1.0, method="lm")
# lamb = lamb * lamb_decay
ds = eit.gn(f1.v, lamb_decay=0.1, lamb_min=1e-5, maxiter=20, verbose=True)
# plot
fig, ax = plt.subplots(figsize=(6, 4))
im = ax.tripcolor(
pts[:, 0],
pts[:, 1],
tri,
np.real(ds),
tri = mesh_obj['element']
perm = mesh_new['perm']
# show
fig, ax = plt.subplots(figsize=(6, 4))
im = ax.tripcolor(pts[:, 0], pts[:, 1], tri,
np.real(perm), shading='flat', cmap=plt.cm.viridis)
fig.colorbar(im)
ax.axis('equal')
ax.set_title(r'$\Delta$ Conductivities')
plt.show()
""" 2. calculate simulated data """
el_dist, step = 1, 1
ex_mat = eit_scan_lines(n_el, el_dist)
fwd = Forward(mesh_obj, el_pos)
f1 = fwd.solve_eit(ex_mat, step, perm=mesh_new['perm'], parser='std')
""" 3. solve_eit using gaussian-newton (with regularization) """
# number of stimulation lines/patterns
eit = jac.JAC(mesh_obj, el_pos, ex_mat, step, perm=1.0, parser='std')
eit.setup(p=0.25, lamb=1.0, method='lm')
# lamb = lamb * lamb_decay
ds = eit.gn(f1.v, lamb_decay=0.1, lamb_min=1e-5, maxiter=20, verbose=True)
# plot
fig, ax = plt.subplots(figsize=(6, 4))
im = ax.tripcolor(pts[:, 0], pts[:, 1], tri, np.real(ds),
shading='flat', alpha=1.0, cmap=plt.cm.viridis)
fig.colorbar(im)
ax.axis('equal')
fig, ax = plt.subplots(figsize=(6, 4))
im = ax.tripcolor(no2xy[:, 0], no2xy[:, 1], el2no,
np.real(alpha), shading='flat')
fig.colorbar(im)
ax.axis('tight')
ax.set_title(r'$\Delta$ Permitivity')
""" 2. calculate simulated data using stack ex_mat """
el_dist, step = 7, 1
n_el = len(el_pos)
ex_mat1 = eit_scan_lines(n_el, el_dist)
ex_mat2 = eit_scan_lines(n_el, 1)
ex_mat = np.vstack([ex_mat1, ex_mat2])
# forward solver
fwd = Forward(ms, el_pos)
f0 = fwd.solve(ex_mat, step, perm=ms['alpha'])
f1 = fwd.solve(ex_mat, step, perm=ms1['alpha'])
""" 3. solving using dynamic EIT """
# number of stimulation lines/patterns
eit = jac.JAC(ms, el_pos, ex_mat=ex_mat, step=step, parser='std')
eit.setup(p=0.40, lamb=1e-3, method='kotre')
ds = eit.solve(f1.v, f0.v)
""" 4. plot """
fig, ax = plt.subplots(figsize=(6, 4))
im = ax.tripcolor(no2xy[:, 0], no2xy[:, 1], el2no, np.real(ds),
shading='flat', alpha=0.90, cmap=plt.cm.viridis)
fig.colorbar(im)
ax.axis('tight')
'alpha': 0.1
}, {
'x': 0,
'y': -0.5,
'd': 0.1,
'alpha': 0.1
}]
ms1 = mesh.set_alpha(ms, anomaly=anomaly, background=1.0)
alpha = np.real(ms1['alpha'] - ms0['alpha'])
""" ax1. FEM forward simulations """
# setup EIT scan conditions
el_dist, step = 1, 1
ex_mat = eit_scan_lines(16, el_dist)
# calculate simulated data
fwd = Forward(ms, el_pos)
f0 = fwd.solve(ex_mat, step=step, perm=ms0['alpha'])
f1 = fwd.solve(ex_mat, step=step, perm=ms1['alpha'])
""" ax2. BP """
eit = bp.BP(ms, el_pos, ex_mat=ex_mat, step=1, parser='std')
ds = eit.solve(f1.v, f0.v, normalize=True)
ds_bp = ds
""" ax3. JAC """
eit = jac.JAC(ms, el_pos, ex_mat=ex_mat, step=step, perm=1., parser='std')
eit.setup(p=0.2, lamb=0.001, method='kotre')
# parameter tuning is needed for better display
ds = eit.solve(f1.v, f0.v)
ds_jac = pdeprtni(no2xy, el2no, ds)
""" ax4. GREIT """
eit = greit.GREIT(ms, el_pos, ex_mat=ex_mat, step=step, parser='std')
ds = eit.solve(f1.v, f0.v)
# show
fig, ax = plt.subplots(figsize=(6, 4))
im = ax.tripcolor(no2xy[:, 0],
no2xy[:, 1],
el2no,
np.real(alpha),
shading='flat',
cmap=plt.cm.viridis)
fig.colorbar(im)
ax.axis('equal')
ax.set_title(r'$\Delta$ Conductivities')
plt.show()
""" 2. calculate simulated data """
el_dist, step = 1, 1
ex_mat = eit_scan_lines(n_el, el_dist)
fwd = Forward(ms, el_pos)
f1 = fwd.solve(ex_mat, step, perm=ms1['alpha'], parser='std')
""" 3. solve using gaussian-newton """
# number of stimulation lines/patterns
eit = jac.JAC(ms, el_pos, ex_mat, step, perm=1.0, parser='std')
eit.setup(p=0.25, lamb=1.0, method='lm')
ds = eit.gn(f1.v, lamb_decay=0.1, lamb_min=1e-4, maxiter=20, verbose=True)
# plot
fig, ax = plt.subplots(figsize=(6, 4))
im = ax.tripcolor(no2xy[:, 0],
no2xy[:, 1],
el2no,
np.real(ds),
shading='flat',
alpha=1.0,
v0 = v0[:, np.newaxis]
jac = p.jac / v0
# calculate sensitivity matrix
s = np.linalg.norm(jac, axis=0)
ae = tri_area(pts, tri)
s = np.sqrt(s) / ae
assert (any(s >= 0))
se = np.log10(s)
sn = sim2pts(pts, tri, se)
return sn
""" 1. FEM forward setup """
# calculate simulated data using FEM
fwd = Forward(mesh_obj, el_pos)
# loop over EIT scan settings: vary the distance of stimulation nodes, AB
ex_list = [1, 2, 4, 8]
N = len(ex_list)
s = []
for ex_dist in ex_list:
ex_mat = eit_scan_lines(16, ex_dist)
# TODO: ex_mat can also be stacked, see demo_dynamic_stack.py
s0 = calc_sens(fwd, ex_mat)
s.append(s0)
""" 2. Plot (elements) sensitivity """
vmin = np.min(s)
vmax = np.max(s)
fig = plt.figure(figsize=(12, 2.5))
gs = gridspec.GridSpec(1, N)
for ix in range(N):
