Module 3 - Inverse

class module3_inverse.InverseProblem(mesh, ele_pos, data, I_all, l, z=None, select_pot_method=0)

Inverse Object EIT 2D

Parameters

  • mesh (mesh) – Any mesh from Fenics module. We recommend from MyMesh()

  • ele_pos (electrodes_position()) – Object, list of arrays with position of electrodes.

  • z (array) – Vector of impedances in electrodes

  • data (array) – Vector with potencial in electrodes or any other vector.

  • I_all (current_method() or list of arrays) – Current density in each electrode for each measurement

  • l (int) – Measurements number.

Example

>>> InverseObject=InverseProblem(mesh_inverse, ele_pos, list_U0_noised, I_all, l, z)
>>> InverseObject.solve_inverse()
>>> gamma_k=InverseObject.gamma_k
solve_inverse()

Function that solves the inverse problem.

Example

>>> InverseObject=InverseProblem(mesh_inverse, ele_pos, list_U0_noised, I_all, l, z, select_pot_method=0)
>>> InverseObject.solve_inverse()
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, list_U0_noised, I_all, l, z)
>>> 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, list_U0_noised, I_all, l, z)
>>> 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, list_U0_noised, I_all, l, z)
>>> 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, list_U0_noised, I_all, l, z)
>>> 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, list_U0_noised, I_all, l, z)
>>> InverseObject.set_InnerParameters(inner_method='ME', ME_reg=5E-4)