Module 4 - Auxiliar

module4_auxiliar.plot_figure(function, name, save=False, map='inferno')

Plot a given function with an optional color map and save the plot if specified.

Parameters:

  • function (dolfin.function.Function) – The function to plot.

  • name (str) – The title of the plot.

  • save (bool, optional) – If True, save the plot with the title as the filename.

  • colormap (str, optional) – The name of the colormap to use for the plot.

Returns:

None

Example:

>>> plot_figure(u, "Potential Field", save=True, colormap='viridis')
module4_auxiliar.getBoundaryVertex(mesh, u)

Get the values of a function u at the boundary vertices of a given mesh.

Parameters:

  • mesh (Mesh) – The input mesh.

  • u (Function) – The function to evaluate at the boundary vertices.

Returns:

A list of function values at the boundary vertices.

Return type:

list

module4_auxiliar.plot_boundary(mesh, data, name='boundary', line=2, data2=1, save=False, plot=True)

Plot the boundary of a mesh along with data.

Parameters:

  • mesh (Mesh) – The mesh to plot.

  • data (numpy.ndarray) – The data to plot on the boundary.

  • name (str) – The name of the plot (default ‘boundary’).

  • line (int) – The line width for plotting (default 2).

  • data2 (int or numpy.ndarray) – Additional data to plot (default 1).

  • save (bool) – Whether to save the plot (default False).

  • plot (bool) – Whether to display the plot (default True).

Returns:

The boundary plot as a numpy array.

Return type:

numpy.ndarray

module4_auxiliar.plot_electrodes(mesh, linewidth_mesh=1, linewidth_elec=5, figsize=(5, 5), fontsize=20, elec_num=True, axis=False)

Plot the electrodes on a mesh.

Parameters:

  • mesh (Mesh) – A mesh object.

  • linewidth_mesh (int) – The width of the mesh lines (default 1).

  • linewidth_elec (int) – The width of the electrode lines (default 5).

  • figsize (tuple) – The size of the figure (default (5,5)).

  • fontsize (int) – The font size of the electrode numbers (default 20).

  • elec_num (bool) – Whether to show electrode numbers (default True).

  • axis (bool) – Whether to show the axis (default False).

Returns:

The figure object.

Return type:

matplotlib.figure.Figure

module4_auxiliar.EstimateDelta(list_U_noised: ndarray, I: ndarray) → float

Estimate the noise level in potential measurements obtained from a grounded electrode system. The method was based on

Robert Winkler work: A model-aware inexact Newton scheme for electrical impedance tomography, 2016.

Parameters:

  • list_U_noised (numpy.ndarray) – Noisy potential measurements with shape (l, L).

  • I (numpy.ndarray) – Current pattern matrix with shape (l, L).

Returns:

A scalar value representing the estimated noise level in the potential measurements.

Return type:

float

Notes:

The data must be measured through a grounded electrode, i.e., the sum of potential of each of the electrodes must be zero.

This function estimates the noise level in potential measurements obtained from a grounded electrode system. It takes two arguments as inputs: list_U_noised and I.

module4_auxiliar.ConvertingData(U, method)

Convert data from different measurement patterns to the ground pattern.

Parameters:

  • U (numpy.ndarray) – The data to be converted.

  • method (str) – The measurement pattern to be converted to. Currently only “KIT4” is supported.

Returns:

The converted data.

Return type:

numpy.ndarray

module4_auxiliar.EstimateCond(list_U0, I, mesh, z, method='CONT')

Estimate the conductivity of the background based on noisy voltage measurements.

Parameters:

  • list_U0 (list) – A list of noisy voltage measurements.

  • I (numpy.ndarray) – A current pattern matrix.

  • mesh (Mesh) – A mesh object.

  • z (numpy.ndarray) – The background impedance (default 1E-5).

  • method (str) – The method used for estimating conductivity. Options: “CONT”, “SHUNT”, “CEM1”, “CEM2”.

Returns:

A tuple containing the estimated conductivity and minimum potential.

Return type:

tuple(float, float)

module4_auxiliar.EstimateCondIterative(list_U0, I, mesh, z, zmin=1e-05)

Estimate the conductivity of the background based on noisy voltage measurements using an iterative approach.

Parameters:

  • list_U0 (list) – A list of noisy voltage measurements.

  • I (numpy.ndarray) – A current pattern matrix.

  • mesh (Mesh) – A mesh object.

  • z (numpy.ndarray) – The background impedance (default 1E-5).

  • zmin (float) – The minimum background impedance value (default 1E-5).

Returns:

A tuple containing the estimated conductivity and impedance.

Return type:

tuple(float, float)