Module 3 - Inverse

class module3_inverse_cont.InverseProblem(mesh, V, data, I_all)

Inverse Object EIT 2D

Parameters:

mesh (mesh) – Any mesh from Fenics module. We recommend from MyMesh()
V (FiniteElement) – FiniteElement Fenics object
data (array) – Vector with potencial in each vertex.
I_all (current_method()) – Current for each measurement

Example:

VI=FiniteElement('CG',mesh_inverse.ufl_cell(),1) 
InverseObject=InverseProblem(mesh_inverse, VI, u0_boundary, I_all)
InverseObject.solve_inverse()
gamma_k=InverseObject.gamma_k

solve_inverse()

Function that solves the inverse problem.

Example:

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

set_answer(gamma0, mesh0)

“Get and set the answer if we have it. It is usefull to determine the best solution reached. error_gamma() will return you the percentual error in L2.

Parameters:

mesh0 (mesh) – Any mesh from Fenics module. We recommend from MyMesh()
gamma0 – Finite Element Function

set_NewtonParameters(**kwargs)

Newton Parameters

Kwargs:

mu_i (float): Mu initial (0,1]
mumax (float): mumax (0,1]
nu (float): Decrease last mu_n
R (float): Minimal value for mu_n

Default Parameters:

>>> self.mu_i=0.9      
>>> self.mumax=0.999   
>>> self.nu=0.99       
>>> self.R=0.9         

Example:

>>> InverseObject=InverseProblem(mesh_inverse,  ele_pos,  z, list_U0_noised, I_all, l)
>>> InverseObject.set_NewtonParameters(mu_i=0.90, mumax=0.999, nu=0.985, R=0.90)

set_NoiseParameters(tau, noise_level)

Noise Parameters to stop with Discrepancy Principle.

Parameters:

tau (float) – Tau for disprance principle [0, infty)
noise_level (float) – Noise_level(%) from data [0,1)

Default Parameters:

>>> self.tau=0      
>>> self.noise_level=0   

Example:

>>> InverseObject=InverseProblem(mesh_inverse,  ele_pos,  z, list_U0_noised, I_all, l)
>>> InverseObject.set_NoiseParameters(tau=5, noise_level=0.01)

set_firstguess(Cellsgamma_k)

Default parameters for first guess in external step newton.

Parameters:: Cellsgamma_k (array) – We expect a vector that represents the value of gamma in your cell.

Default Parameters:

>>> self.Cellsgamma_k=np.ones(self.mesh.num_cells())*0.9      

Example:

>>> InverseObject=InverseProblem(mesh_inverse,  ele_pos,  z, list_U0_noised, I_all, l)
>>> InverseObject.set_firstguess(np.ones(mesh_inverse.num_cells())*5)

set_solverconfig(**kwargs)

Solver config.

Kwargs:

weight_value (bool): Weight function in Jacobian matrix
step_limit (float): Step limit while solve
min_v (float): Minimal value in element for gamma_k

Default Parameters:

>>> self.weight_value=True  
>>> self.step_limit=5       
>>> self.min_v=0.05         

Example:

>>> InverseObject=InverseProblem(mesh_inverse,  ele_pos,  z, list_U0_noised, I_all, l)
>>> InverseObject.set_solverconfig(weight_value=True, step_limit=200, min_v=0.01)

set_InnerParameters(**kwargs)

Inner-step Newton Parameters

Kwargs:

inner_method (str): Method to solver inner step newton. Options: ‘Landweber’, ‘CG’, ‘ME’, ‘LM’, ‘Tikhonov’
land_a (int): Step-size Landweber
ME_reg (float): Minimal value in element for gamma_k
Tik_c0 (float): Regularization parameter Iterative Tikhonov
Tik_q (float): Regularization parameter Iterative Tikhonov
LM_c0 (float): Regularization parameter Levenberg-Marquadt
LM_q (float): Regularization parameter Levenberg-Marquadt

Default Parameters:

>>> self.inner_method='Landweber'
>>> self.land_a=1    
>>> self.ME_reg=5E-4 
>>> self.Tik_c0=1    
>>> self.Tik_q=0.95  
>>> self.LM_c0=1     
>>> self.LM_q=0.95   

Example:

>>> InverseObject=InverseProblem(mesh_inverse,  ele_pos,  z, list_U0_noised, I_all, l)
>>> InverseObject.set_InnerParameters(inner_method='ME', ME_reg=5E-4)