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Repository Structure

In this section, we describe the structure of the repository. Note that the description of the functions used for running the algorithm itself are defined in the next section.

Root

The root of the repository contains five files.

  • .gitignore: This file tells git which files to ignore when committing changes.
  • LICENSE: This file contains the license for the repository. The license for this package is an MIT license.
  • README.md: This file contains the basic description of the repository, primarily for linking to the documentation.
  • Project.toml: This file contains the dependencies for the package.
  • Manifest.toml: This file contains the exact versions of the dependencies for the package. This together with Project.toml makes the paper results exactly reproducible.

.github/workflows

This folder just contains some basic workflows for testing the package and producing its documentation. These are standard files you'll see in almost any Julia package.

docs

The docs folder is what produces the documentation, and produces the paper results. Within this folder, what actually produces the documentation is the make.jl file, which uses Documenter.jl and Literate.jl to run the scripts and launch the documentation. The src folders contains all the scripts for each section, which you can inspect yourself - just read the documentation and, if you do want to see the source file, either see the link at the top-right or at the bottom of the page.

src

The src folder is where all the code for the algorithm lives. The folder is broken into other folders, and the only file inside this folder directly is:

  • StepwiseEQL.jl: This is the module that defines the package and loads in all the dependencies and the files.

src/structs

The src/structs folder contains the definitions for all the structs used in the package:

  • eql_model.jl: The definition of an EQLModel, used for producing the stepwise learning results. This struct would have a very similar definition if you were to extend to other types of problems.
  • eql_solution.jl: The definition of an EQLSolution, giving the results for the stepwise learning procedure.
  • ensemble_eql_solution.jl: If running the stepwise learning procedure for multiple initial sets of active coefficients, you obtain an EnsembleEQLSolution defined here.
  • averaged_ode_solution.jl: For proliferation we average the solution over each simulation, leading to a single set of results. This average is defined as an AveragedODESolution, defined here.

src/function_evaluation

The src/function_evaluation folder contains the files used for defining how we evaluate basis functions, and for how we compute densities and their derivatives:

  • basis_functions.jl: Defines the structs for a basis function, specifically as a BasisSet or a PolynomialBasis.
  • density_computations.jl: This contains all the functions that are used to compute densities, their derivatives, and similarly for leading edges.

src/problem_building

The src/problem_building folder contains the main functions used for building up the EQLModels:

  • matrix_construction.jl: The main component of the algorithm is the construction of the matrix system $\boldsymbol A\boldsymbol\theta = \boldsymbol b$. The code in this file constructs the matrix $\boldsymbol A$ and the vector $\boldsymbol b$.
  • pde_construction.jl: This script automatically detects the type of PDE to be built (fixed boundary, moving boundary, proliferation, etc.) and constructs it.

src/individual_steps

The src/individual_steps folder is used for performing the individual steps in our procedure:

  • cross_validation.jl: This script contains the code used for creating the training and test sets if cross-validation is used for the algorithm.
  • density_loss.jl: This script contains the functions used for evaluating the density component, and the leading edge component, of the loss function.
  • evaluate_loss.jl: This script contains the functions used for evaluating the loss function completely.
  • model_voting.jl: This script contains the functions used for incorporating and removing each term one at a time during an individual step of the algorithm, and for then making a vote on which model to step to in the next iteration.
  • penalty.jl: This file contains the functions used for penalising model complexity, and also for enforcing constraints on $D(q)$ and $E(q)$.
  • regression_loss.jl: This file contains the functions used for evaluating the regression component of the loss function.

src/algorithm

The src/algorithm folder is used for actually running the algorithm, with the main script being stepwise.jl:

  • stepwise.jl: This script contains the main entry point for running our stepwise procedure, defining the stepwise_selection function (described in more detail in the next section).
  • run_stepwise.jl: The stepwise_selection function from the previous point constructs an EQLModel and then runs the main internal method of stepwise_selection that actually runs all the results. This is defined in this file.
  • model_sampling.jl: This file contains the internal function that is used for running the procedure for multiple initial conditions efficiently.

test

This folder is just for testing the algorithm's implementation itself. It is a bit lengthy and unlikely to be very readable, so you should not be overly concerned about it. If you did want to test the function, you can run 

julia> ] test

assuming the StepwiseEQL package is activated; you can tell if it is by seeing if, after typing ] test inside the Julia REPL without executing it, you see

(StepwiseEQL) pkg> test