def _setup_eit(self):
mesh_t = self._mesh # ms, el_pos
el_dist, step = 1, 1
ex_mat = eit_scan_lines(16, el_dist)
# Reconstruction step
eit_obj = greit.GREIT(mesh_t[0], mesh_t[1], ex_mat=ex_mat, step=step, perm=0.8,
parser='std') # prem default value eq = 1.
eit_obj.setup(p=0.45, lamb=1e-3, n=96, s=10.0, ratio=0.05) # n - wielkość siatki, domyślna wartość 32
return eit_obj
def current_matrix_generator(n_el: int, ex_mat_length: int, ex_pair_mode='adj', spaced: bool=False):
"""
This function generates an excitation matrix of current pairs using the adj method, opposite method, all
possible pairs or custom step. It can iterate and build the matrix contiguously, assigning electrodes in
turn around the perimeter or 'spaced' can be set to True, which spaces out the measurements slightly.
I.e. for the adj method, spaced=True might give [(1,2),(5,6),(10,11)] as opposed to [(1,2),(2,3),(3,4)].
To Do:
- Add in a randomly assigned current pairs method
Parameters
----------
n_el : int
The number of electrodes.
ex_mat_length : int
The desired length of the excitation matrix, if none will generate maximum number of measurements
for the given ex_pair_mode.
ex_pair_mode : int or string
The default is 'adj' or step of 1, but can be 'opp' step of n_el/2 or 'all'. Also accepts a
custom step value.
spaced : bool, optional
If True, this will activate orderedExMat which spaces out measurements around the perimeter.
Returns
-------
ex_mat : ndarray (N, 2)
List of the current pairs (Source, sink).
"""
if (ex_pair_mode == 1 or ex_pair_mode == 'adj'):
print("Adjacent current pairs mode")
dist = 1
elif (ex_pair_mode == n_el//2 or ex_pair_mode == 'opp'):
print("Opposite current pairs mode")
dist = n_el//2
elif (ex_pair_mode == 'all'):
print("All current pairs mode")
elif (ex_pair_mode != 1 and ex_pair_mode != n_el//2 and (1 < ex_pair_mode < n_el-1)):
print("Custom distance between current pairs. Dist:", ex_pair_mode)
dist = ex_pair_mode
else:
print("Incorrect current pair mode selected. Function returning 0.")
return 0
if (ex_pair_mode == 'all'):
ex_mat = train.generateExMat(ne=n_el)
elif spaced == True:
ex_mat = train.orderedExMat(n_el=n_el, el_dist=dist)
elif spaced == False:
ex_mat = eit_scan_lines(ne=n_el, dist=dist)
else:
print("Something went wrong ...")
if ex_mat_length is not None:
ex_mat = ex_mat[0:ex_mat_length]
return ex_mat
def set_pde(self):
# construct mesh
self.mesh_obj,self.el_pos=mesh.create(self.n_el, bbox=self.bbox, h0=self.meshsz)
# extract node, element
self.pts=self.mesh_obj['node']
self.tri=self.mesh_obj['element']
# initialize forward solver using the unstructured mesh object and the positions of electrodes
self.fwd=Forward(self.mesh_obj, self.el_pos)
# boundary condition
self.ex_mat=eit_scan_lines(self.n_el,self.el_dist)
# count PDE solving times
self.soln_count = np.zeros(2)
# build tetrahedron
# 3D tetrahedron must have a bbox
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)
# 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,
no2xy = ms['node']
el2no = ms['element']
alpha = ms1['alpha'] - ms['alpha']
# show alpha
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 """
no2xy = ms['node']
el2no = ms['element']
alpha = ms1['alpha'] - ms['alpha']
# show alpha
fig = plt.figure()
plt.tripcolor(no2xy[:, 0], no2xy[:, 1], el2no,
np.real(alpha), shading='flat')
plt.colorbar()
plt.title(r'$\Delta$ Permitivity')
fig.set_size_inches(6, 4.5)
""" 2. calculate simulated data using stack exMtx """
elDist, step = 7, 1
numEl = len(elPos)
exMtx1 = eit_scan_lines(numEl, elDist)
exMtx2 = eit_scan_lines(numEl, 1)
exMtx = np.vstack([exMtx1, exMtx2])
# forward solver
fwd = forward(ms, elPos)
f0 = fwd.solve(exMtx, step, perm=ms['alpha'])
f1 = fwd.solve(exMtx, step, perm=ms1['alpha'])
""" 3. solving using dynamic EIT """
# number of excitation lines & excitation patterns
eit = jac.JAC(ms, elPos, exMtx=exMtx, step=step,
p=0.40, lamb=1e-3,
parser='std', method='kotre')
ds = eit.solve(f1.v, f0.v)
ms1 = mesh.set_alpha(ms, anom=anomaly, background=1.0)
alpha = np.real(ms1['alpha'] - ms0['alpha'])
# show alpha
fig = plt.figure()
plt.tripcolor(no2xy[:, 0], no2xy[:, 1], el2no, alpha,
shading='flat', cmap=plt.cm.viridis)
plt.colorbar()
plt.title(r'$\Delta$ Conductivity')
fig.set_size_inches(6, 4)
plt.axis('equal')
""" 2. FEM forward simulations """
# setup EIT scan conditions
elDist, step = 1, 1
exMtx = eit_scan_lines(16, elDist)
# calculate simulated data
fwd = forward(ms, elPos)
f0 = fwd.solve(exMtx, step=step, perm=ms0['alpha'])
f1 = fwd.solve(exMtx, step=step, perm=ms1['alpha'])
""" 3. Construct using GREIT
"""
eit = greit.GREIT(ms, elPos, exMtx=exMtx, step=step, parser='std',
p=0.50, lamb=1e-4)
ds = eit.solve(f1.v, f0.v)
x, y, ds = eit.mask_value(ds, mask_value=np.NAN)
# plot
fig = plt.figure()
el2no = ms['element']
alpha = ms1['alpha']
# show
fig = plt.figure()
plt.tripcolor(no2xy[:, 0], no2xy[:, 1], el2no,
np.real(alpha), shading='flat')
plt.colorbar()
plt.axis('equal')
plt.title(r'$\Delta$ Conductivities')
fig.set_size_inches((6, 4))
plt.show()
""" 2. calculate simulated data """
elDist, step = 1, 1
exMtx = eit_scan_lines(numEl, elDist)
fwd = forward(ms, elPos)
f1 = fwd.solve(exMtx, step, perm=ms1['alpha'])
""" 3. solve using gaussian-newton """
# number of excitation lines & excitation patterns
eit = jac.JAC(ms, elPos, exMtx, step,
perm=1.0, parser='std',
p=0.25, lamb=1e-4, method='kotre')
ds = eit.gn_solve(f1.v, maxiter=6, verbose=True)
# plot
fig = plt.figure()
plt.tripcolor(no2xy[:, 0], no2xy[:, 1], el2no, np.real(ds),
shading='flat', alpha=1.0, cmap=plt.cm.viridis)
plt.colorbar()
def solve_eit(self,
ex_mat=None,
step=1,
perm=None,
parser=None,
skip_jac=False):
"""
EIT simulation, generate perturbation matrix and forward v
Parameters
----------
ex_mat: NDArray
numLines x n_el array, stimulation matrix
step: int
the configuration of measurement electrodes (default: adjacent)
perm: NDArray
Mx1 array, initial x0. must be the same size with self.tri_perm
parser: str
if parser is 'fmmu', within each stimulation pattern, diff_pairs
or boundary measurements are re-indexed and started
from the positive stimulus electrode
if parser is 'std', subtract_row start from the 1st electrode
Returns
-------
jac: NDArray
number of measures x n_E complex array, the Jacobian
v: NDArray
number of measures x 1 array, simulated boundary measures
b_matrix: NDArray
back-projection mappings (smear matrix)
"""
# initialize/extract the scan lines (default: apposition)
if ex_mat is None:
ex_mat = eit_scan_lines(16, 8)
# initialize the permittivity on element
if perm is None:
perm0 = self.tri_perm
elif np.isscalar(perm):
perm0 = np.ones(self.n_tri, dtype=np.float)
else:
assert perm.shape == (self.n_tri, )
perm0 = perm
# calculate f and Jacobian iteratively over all stimulation lines
jac, v, b_matrix = [], [], []
n_lines = ex_mat.shape[0]
for i in range(n_lines):
# FEM solver of one stimulation pattern, a row in ex_mat
ex_line = ex_mat[i]
f, jac_i = self.solve(ex_line, perm0, skip_jac)
f_el = f[self.el_pos]
# boundary measurements, subtract_row-voltages on electrodes
diff_op = voltage_meter(ex_line,
n_el=self.ne,
step=step,
parser=parser)
v_diff = subtract_row(f_el, diff_op)
if not skip_jac: jac_diff = subtract_row(jac_i, diff_op)
# build bp projection matrix
# 1. we can either smear at the center of elements, using
# >> fe = np.mean(f[self.tri], axis=1)
# 2. or, simply smear at the nodes using f
b = smear(f, f_el, diff_op)
# append
v.append(v_diff)
if not skip_jac: jac.append(jac_diff)
b_matrix.append(b)
# update output, now you can call p.jac, p.v, p.b_matrix
pde_result = namedtuple("pde_result", ['jac', 'v', 'b_matrix'])
p = pde_result(jac=np.vstack(jac) if jac else jac,
v=np.hstack(v),
b_matrix=np.vstack(b_matrix))
return p