Current Examples

This demo is implemented in a single Python file. Download here: tutorial_current.ipynb

This demo illustrates how to:

  • Define currents in the electrodes.

from module1_mesh import*
from module2_forward import*
from module3_inverse import*
from module4_auxiliar import*
import matplotlib.pyplot as plt
%matplotlib inline

Mesh

"Electrodes and Mesh"
  ele_pos=electrodes_position(L=6, per_cober=0.5, rotate=0)
  mesh_direct=MyMesh(r=1, n=20, n_in=40, n_out=8, electrodes_obj=ele_pos)
  plot(mesh_direct);
../../_images/mesh2.png

Defining Gamma function

"Gamma function"
ValuesCells0=GammaCircle(mesh_direct,3.0,1.0,0.50, 0.25, 0.25);
gamma0=CellFunction(mesh_direct, values=ValuesCells0)

"Plot"
V_DG=FiniteElement('DG',mesh_direct.ufl_cell(),0)
gamma_direct=plot_figure(mesh_direct, V_DG, gamma0, name="Gamma");
../../_images/gamma6.png

Forward Problem

"Forward Problem"
VD=FiniteElement('CG',mesh_direct.ufl_cell(),1) #Lagrange pol. degree 1
L=ele_pos.L
l=int(L)                                        #Measurements number.
z=np.ones(L)*0.025                              #Impedance

#Solver
ForwardObject=ForwardProblem(mesh_direct, z)

Current Examples

Method 1

>>> I_all=current_method(L,l, method=1)
>>> list_u0, list_U0 = ForwardObject.solve_forward(VD, I_all, gamma0)

This method only accept until L/2 currents, returning L/2 currents.

>>> print(np.array(I_all))
[[ 1.  0.  0. -1.  0.  0.]
 [ 0.  1.  0.  0. -1.  0.]
 [ 0.  0.  1.  0.  0. -1.]]

plt.figure(figsize=(10, 10))
for i in range(0, int(l/2)):
    plt.subplot(4,4,i+1)
    plot(list_u0[i])
../../_images/method1.png

Method 2

>>> I_all=current_method(L,l, method=2)
>>> list_u0, list_U0 = ForwardObject.solve_forward(VD, I_all, gamma0)

>>> print(np.array(I_all))
[[ 1. -1.  0.  0.  0.  0.]
 [ 0.  1. -1.  0.  0.  0.]
 [ 0.  0.  1. -1.  0.  0.]
 [ 0.  0.  0.  1. -1.  0.]
 [ 0.  0.  0.  0.  1. -1.]
 [ 1.  0.  0.  0.  0. -1.]]

plt.figure(figsize=(10, 10))
for i in range(0, int(l)):
    plt.subplot(4,4,i+1)
    plot(list_u0[i])
../../_images/method2.png

Method 3

>>> I_all=current_method(L,l, method=3)
>>> list_u0, list_U0 = ForwardObject.solve_forward(VD, I_all, gamma0)

>>> np.set_printoptions(precision=5)
>>> print(np.array(I_all))
[[ 1.  -0.2 -0.2 -0.2 -0.2 -0.2]
 [-0.2  1.  -0.2 -0.2 -0.2 -0.2]
 [-0.2 -0.2  1.  -0.2 -0.2 -0.2]
 [-0.2 -0.2 -0.2  1.  -0.2 -0.2]
 [-0.2 -0.2 -0.2 -0.2  1.  -0.2]
 [-0.2 -0.2 -0.2 -0.2 -0.2  1. ]]

plt.figure(figsize=(10, 10))
for i in range(0, int(l)):
    plt.subplot(4,4,i+1)
    plot(list_u0[i])
../../_images/method3.png

Method 4

>>> I_all=current_method(L,l, method=4)
>>> list_u0, list_U0 = ForwardObject.solve_forward(VD, I_all, gamma0)

>>> np.set_printoptions(precision=1)
>>> print(np.array(I_all))
[[ 8.7e-01  8.7e-01  1.2e-16 -8.7e-01 -8.7e-01 -2.4e-16]
 [ 8.7e-01 -8.7e-01 -2.4e-16  8.7e-01 -8.7e-01 -4.9e-16]
 [ 1.2e-16 -2.4e-16  3.7e-16 -4.9e-16  2.4e-15 -7.3e-16]
 [-8.7e-01  8.7e-01 -4.9e-16 -8.7e-01  8.7e-01 -9.8e-16]
 [-8.7e-01 -8.7e-01  2.4e-15  8.7e-01  8.7e-01 -4.8e-15]
 [-2.4e-16 -4.9e-16 -7.3e-16 -9.8e-16 -4.8e-15 -1.5e-15]]

plt.figure(figsize=(10, 10))
for i in range(0, int(l)):
    plt.subplot(4,4,i+1)
    plot(list_u0[i])
../../_images/method4.png

Setting Diffent Values

I_all=current_method(L,l, method=2, value=1.337)
np.set_printoptions(precision=4)

>>> print(np.array(I_all))
[[ 1.337 -1.337  0.     0.     0.     0.   ]
 [ 0.     1.337 -1.337  0.     0.     0.   ]
 [ 0.     0.     1.337 -1.337  0.     0.   ]
 [ 0.     0.     0.     1.337 -1.337  0.   ]
 [ 0.     0.     0.     0.     1.337 -1.337]
 [ 1.337  0.     0.     0.     0.    -1.337]]

I_all=current_method(L,l, method=3, value=1.337)
np.set_printoptions(precision=4)

>>> print(np.array(I_all))
[[ 1.337  -0.2674 -0.2674 -0.2674 -0.2674 -0.2674]
 [-0.2674  1.337  -0.2674 -0.2674 -0.2674 -0.2674]
 [-0.2674 -0.2674  1.337  -0.2674 -0.2674 -0.2674]
 [-0.2674 -0.2674 -0.2674  1.337  -0.2674 -0.2674]
 [-0.2674 -0.2674 -0.2674 -0.2674  1.337  -0.2674]
 [-0.2674 -0.2674 -0.2674 -0.2674 -0.2674  1.337 ]]

My Current

I_all= [ [5, -3, -1, 1, -2, 0],
         [1, 1, -1, -1, 0, 0],
         [8.5, 0, -3.5,0 ,0, -3]]
l=len(I_all)

list_u0, list_U0 = ForwardObject.solve_forward(VD, I_all, gamma0)

plt.figure(figsize=(10, 10))
for i in range(0, l):
    plt.subplot(4,4,i+1)
    plot(list_u0[i])
../../_images/mycurrent.png