Module 2 - Forward

module2_forward_cont.current_method(n_g, value=1, method=1)

This function an expression that represent the current in the vertex.

Parameters

n_g (int) – Measurements number.
value (float) – value in the vertex.
method (int) – Current pattern.

Returns

Expression – Return list of expressions.

Method Values:

1 and -1 in opposite direction, where 50% of the boundary is always 0.

Example

"Current"
 n_g=2
 list_gs=current_method(n_g, value=1, method=1)

 for i in range(n_g):
     mesh=mesh_direct
     VD=FiniteElement('CG',mesh.ufl_cell(),1) 
     g_u=interpolate(list_gs[i], FunctionSpace(mesh,VD))
     g_u=getBoundaryVertex(mesh, g_u)
     bond=plot_boundary(mesh, data=g_u, name='boundary g'+str(i))

module2_forward_cont.fn_addnoise(data, level, noise_type='uniform', seed=42)

Function receives a vector which represents the data in the electrodes and returns a noised vector with the chosen noise level and the type of noise. We use it in ForwardProblem.add_noise().

Parameters

data (array) – Vector with potencial in electrodes or any other vector.
level (float) – Noise level (%), expect values between 0 and 1.
noise_type – Noise type, uniform or cauchy.
seed (int.) – Seed for random function.

Returns

Array – Return noised vector.

Example

>>> print(np.ones(8))
>>> print(fn_addnoise(data=np.ones(8), level=0.01, noise_type='cauchy', seed=32))
    [1. 1. 1. 1. 1. 1. 1. 1.]
    array([0.99905327, 1.02206251, 1.00356633, 1.00236212, 1.00101231, 0.99904405, 1.0105611 , 0.98656216])

module2_forward_cont.GammaCircle(mesh, in_v, out_v, radius, centerx, centery)

Function to create a circle in the mesh with some proprieties

Parameters

mesh (dolfin.cpp.mesh.Mesh) – Mesh.
in_v (float) – Value inside circle
out_v (float) – Value outside circle
radius (float) – Circle radius
centerx (float) – Circle center position x
centery (float) – Circle center position y

Returns

Array – Return a vector where each position correspond de value of the function in that element.

Example

>>> ValuesCells0=GammaCircle(mesh=mesh_direct, in_v=3.0, out_v=1.0, radius=0.50, centerx=0.25, centery=0.25)
>>> print(ValuesCells0)
[1. 1. 1. ... 1. 1. 1.]

>>> "Plot"
>>> gamma0=CellFunction(mesh_direct, values=ValuesCells0);   
>>> V_DG=FiniteElement('DG',mesh_direct.ufl_cell(),0)
>>> plot_figure(mesh_direct, V_DG, gamma0, name="Resposta gamma");

class module2_forward_cont.CellFunction(mesh, values, **kwargs)

Auxiliar function to transform an array to a Function We use it with GammaCircle()

Parameters

mesh (dolfin.cpp.mesh.Mesh) – Mesh.
values (array) – Array with values of the function in the cell.

Example

>>> ValuesCells0=np.zeros(mesh_inverse.num_cells())        #Define a vector of zeros
>>> ValuesCells0[5]=1                                      #Cell 5 has value 1
>>> gamma0=CellFunction(mesh_inverse, values=ValuesCells0);#Get vector and transform in a function cell

If you want plot the function:

>>> V_DG=FiniteElement('DG',mesh_inverse.ufl_cell(),0)     #Space of Finite Elemente descontinuous garlekin degree 0
>>> Q=FunctionSpace(mesh_inverse,V_DG)                     #Functionspace to interpolate gamma
>>> gamma0=interpolate(gamma0, Q)                          #Interpolation gamma to generate a function
>>> p=plot(gamma0)                                         #plot gamma0
>>> plot(mesh_inverse)                                     #plot mesh
>>> plt.colorbar(p)                                        #set colorbar.

class module2_forward_cont.ForwardProblem(mesh)

Object Forward Problem EIT 2D Continous Model.

Parameters: mesh (dolfin.cpp.mesh.Mesh) – Mesh. We recommend from MyMesh()
Example

"Basic Definitions"
VD=FiniteElement('CG',mesh_direct.ufl_cell(),1) 
F_Problem=ForwardProblem(mesh_direct)

"Solver"
list_u0=F_Problem.solve_forward(VD, gamma0, I_all)
u0_boundary=F_Problem.boundary_array(mesh_inverse)

If you need it, see GammaCircle() and CellFunction().

solve_forward(V, gamma, I_all)

Solver Forward Problem EIT 2D

Parameters

V (FiniteElement) – FiniteElement Fenics object
gamma (CellFunction()) – Finite Element Function
I_all (current_method() or list of arrays) – Current density in each electrode for each measurement

Returns

(Array) – Return function that is solution from variational problem.

Example

>>> F_Problem=ForwardProblem(mesh_direct)
>>> list_u0=F_Problem.solve_forward(VD, gamma0, list_gs)

boundary_array(mesh_inverse=None, concatenate=True)

Get’s the boundary values of function solution and returns array. If you set a coarse mesh you will get the values in the vertices that are commum. If you set conccatenate=False, will receive a array with separeted results, is usefull if you used more than one current.

Parameters

mesh (dolfin.cpp.mesh.Mesh) – Corse Mesh. We recommend from MyMesh()
concatenate (bool) – Default True

Returns

(Array) – Vertex values of the function.

Example

>>> u0_boundary=F_Problem.boundary_array(mesh_inverse)

plot_boundary(mesh_inverse=None, index=0)

Get’s the boundary values of function solution and returns a graph. If you set a coarse mesh you will get the values in the vertices that are commum and plot it.

Parameters

mesh (dolfin.cpp.mesh.Mesh) – Corse Mesh. We recommend from MyMesh()
index (int) – Index of solution, if you need it.

Example

>>> data_u0=F_Problem.plot_boundary(mesh_inverse, index=1)

add_noise(noise_level=0, noise_type='uniform', seed=42, mesh=None)

Function that add noise in the potential values.

Parameters

data (array) – Vector with potencial in electrodes or any other vector.
level (float) – Noise level (%), expect values between 0 and 1.
noise_type (str.) – Noise type, uniform or cauchy.
mesh (dolfin.cpp.mesh.Mesh) – Corse Mesh. We recommend from MyMesh()

Returns

Array – Return a vector with potentials values concatenated.

Example

"Noise Parameters"
noise_level=0.01
noise_type='uniform'
seed=1
u0_boundary=F_Problem.add_noise(noise_level noise_type, seed, mesh_inverse)