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Commit 28f5af3f authored by MALOU THIBAULT's avatar MALOU THIBAULT
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improve the documentation of the source_localization package

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source\_localization package
============================
Submodules
----------
.. automodule:: source_localization
:members:
:undoc-members:
:show-inheritance:
.. toctree::
:maxdepth: 4
./source_localization/adjoint_convection_diffusion_2D
./source_localization/control
./source_localization/cost
./source_localization/gradient_descent
./source_localization/obs
./source_localization/population_dynamique
./source_localization/proximal_gradient
The main feature of the package :mod:`source_localization` is to estimate the quantity of pheromone emitted by the insects :math:`s_a` by solving the following optimization problem:
.. math::
s_a(x,y,t)=\underset{s(x,y,t)}{\arg\text{min}}~j(s)\text{ with } j(s)=j_{obs}(s)+j_{reg}(s)
Module contents
---------------
with the cost function :math:`j` of the following form:
.. automodule:: source_localization
:members:
:undoc-members:
:show-inheritance:
.. math::
j(s)=\|m\left(c(s)\right)-m^{obs}\|_{\mathbf{R}^{-1}}^2 + \sum_{i} \alpha_{reg,i} j_{reg,i}(s)
with :math:`\|m\left(c(s)\right)-m^{obs}\|_{\mathbf{R}^{-1}}^2` the term of discrepancy between the data :math:`m^{obs}`
and the estimate computed using the pheromone propagation model :math:`m\left(c(s)\right)`,
:math:`j_{reg,i}` some regularization terms based on biological information and
:math:`\alpha_{reg,i}` the associated weight coefficient.
To solve such optimization problems, the package includes:
- a submodule :mod:`~source_localization.cost` that contains the cost function :math:`j`, tools to construct the cost function and to minimize it;
- a submodule :mod:`~source_localization.obs` that contains all the features related to the sensors and the observations, including the observations :math:`m^{obs}` and the observation operator :math:`c\mapsto m(c)`;
- a submodule :mod:`~source_localization.control` containing the control variable to optimize :math:`s(x,y,t)` and all its prior known features;
- a submodule :mod:`~source_localization.population_dynamique` containing population dynamic models used as prior knowledge of the control variable and their implementation;
- a submodule :mod:`~source_localization.adjoint_convection_diffusion_2D` that contains the adjoint model used to compute the gradient of the cost function;
- submodules :mod:`~source_localization.gradient_descent` and :mod:`~source_localization.proximal_gradient` that contain algorithms to solve the optimization problem.
.. toctree::
:maxdepth: 4
The cost function and its related tools <./source_localization/cost>
The sensors, its observations and its features <./source_localization/obs>
The control variable and all its prior known features <./source_localization/control>
The population dynamic models and its implementation <./source_localization/population_dynamique>
The adjoint model, its implementation and its solvers <./source_localization/adjoint_convection_diffusion_2D>
The implementation of the gradient descent algorithm <./source_localization/gradient_descent>
The implementation of the proximal gradient algorithm <./source_localization/proximal_gradient>
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