format markdown

Author: ArnoStrouwen

.JuliaFormatter.toml

@@ -1 +1,2 @@
-style = "sciml"
+style = "sciml"
+format_markdown = true

README.md

@@ -1,88 +1,87 @@
-# DataDrivenDiffEq.jl
-
-[![Join the chat at https://julialang.zulipchat.com #sciml-bridged](https://img.shields.io/static/v1?label=Zulip&message=chat&color=9558b2&labelColor=389826)](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)
-[![Global Docs](https://img.shields.io/badge/docs-SciML-blue.svg)](https://docs.sciml.ai/DataDrivenDiffEq/stable/)
-[![DOI](https://zenodo.org/badge/212827023.svg)](https://zenodo.org/badge/latestdoi/212827023)
-
-[![codecov](https://codecov.io/gh/SciML/DataDrivenDiffEq.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/SciML/DataDrivenDiffEq.jl)
-[![Build Status](https://github.com/SciML/DataDrivenDiffEq.jl/workflows/CI/badge.svg)](https://github.com/SciML/DataDrivenDiffEq.jl/actions?query=workflow%3ACI)
-
-[![ColPrac: Contributor's Guide on Collaborative Practices for Community Packages](https://img.shields.io/badge/ColPrac-Contributor's%20Guide-blueviolet)](https://github.com/SciML/ColPrac)
-[![SciML Code Style](https://img.shields.io/static/v1?label=code%20style&message=SciML&color=9558b2&labelColor=389826)](https://github.com/SciML/SciMLStyle)
-
-DataDrivenDiffEq.jl is a package in the SciML ecosystem for data-driven differential equation
-structural estimation and identification. These tools include automatically discovering equations
-from data and using this to simulate perturbed dynamics.
-
-For information on using the package,
-[see the stable documentation](https://docs.sciml.ai/DataDrivenDiffEq/stable/). Use the
-[in-development documentation](https://docs.sciml.ai/DataDrivenDiffEq/dev/) for the version of
-the documentation which contains the un-released features.
-
-## Quick Demonstration
-
-```julia
-## Generate some data by solving a differential equation
-########################################################
-using DataDrivenDiffEq
-using ModelingToolkit
-using OrdinaryDiffEq
-using DataDrivenSparse
-using LinearAlgebra
-
-# Create a test problem
-function lorenz(u,p,t)
-    x, y, z = u
-
-    ẋ = 10.0*(y - x)
-    ẏ = x*(28.0-z) - y
-    ż = x*y - (8/3)*z
-    return [ẋ, ẏ, ż]
-end
-
-u0 = [1.0;0.0;0.0]
-tspan = (0.0,100.0)
-dt = 0.1
-prob = ODEProblem(lorenz,u0,tspan)
-sol = solve(prob, Tsit5(), saveat = dt)
-
-
-## Start the automatic discovery
-ddprob = DataDrivenProblem(sol)
-
-@variables t x(t) y(t) z(t)
-u = [x;y;z]
-basis = Basis(polynomial_basis(u, 5), u, iv = t)
-opt = STLSQ(exp10.(-5:0.1:-1))
-ddsol = solve(ddprob, basis, opt, options = DataDrivenCommonOptions(digits = 1))
-println(get_basis(ddsol))
-```
-
-```
-Explicit Result
-Solution with 3 equations and 7 parameters.
-Returncode: success
-Sparsity: 7.0
-L2 Norm Error: 26.7343984476783
-AICC: 1.0013570199499398
-
-Model ##Basis#366 with 3 equations
-States : x(t) y(t) z(t)
-Parameters : 7
-Independent variable: t
-Equations
-Differential(t)(x(t)) = p₁*x(t) + p₂*y(t)
-Differential(t)(y(t)) = p₃*x(t) + p₄*y(t) + p₅*x(t)*z(t)
-Differential(t)(z(t)) = p₇*z(t) + p₆*x(t)*y(t)
-
-Parameters:
-   p₁ : -10.0
-   p₂ : 10.0
-   p₃ : 28.0
-   p₄ : -1.0
-   p₅ : -1.0
-   p₆ : 1.0
-   p₇ : -2.7
-```
-
-![](LorenzResult.png)
+# DataDrivenDiffEq.jl
+
+[![Join the chat at https://julialang.zulipchat.com #sciml-bridged](https://img.shields.io/static/v1?label=Zulip&message=chat&color=9558b2&labelColor=389826)](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)
+[![Global Docs](https://img.shields.io/badge/docs-SciML-blue.svg)](https://docs.sciml.ai/DataDrivenDiffEq/stable/)
+[![DOI](https://zenodo.org/badge/212827023.svg)](https://zenodo.org/badge/latestdoi/212827023)
+
+[![codecov](https://codecov.io/gh/SciML/DataDrivenDiffEq.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/SciML/DataDrivenDiffEq.jl)
+[![Build Status](https://github.com/SciML/DataDrivenDiffEq.jl/workflows/CI/badge.svg)](https://github.com/SciML/DataDrivenDiffEq.jl/actions?query=workflow%3ACI)
+
+[![ColPrac: Contributor's Guide on Collaborative Practices for Community Packages](https://img.shields.io/badge/ColPrac-Contributor%27s%20Guide-blueviolet)](https://github.com/SciML/ColPrac)
+[![SciML Code Style](https://img.shields.io/static/v1?label=code%20style&message=SciML&color=9558b2&labelColor=389826)](https://github.com/SciML/SciMLStyle)
+
+DataDrivenDiffEq.jl is a package in the SciML ecosystem for data-driven differential equation
+structural estimation and identification. These tools include automatically discovering equations
+from data and using this to simulate perturbed dynamics.
+
+For information on using the package,
+[see the stable documentation](https://docs.sciml.ai/DataDrivenDiffEq/stable/). Use the
+[in-development documentation](https://docs.sciml.ai/DataDrivenDiffEq/dev/) for the version of
+the documentation which contains the un-released features.
+
+## Quick Demonstration
+
+```julia
+## Generate some data by solving a differential equation
+########################################################
+using DataDrivenDiffEq
+using ModelingToolkit
+using OrdinaryDiffEq
+using DataDrivenSparse
+using LinearAlgebra
+
+# Create a test problem
+function lorenz(u, p, t)
+    x, y, z = u
+
+    ẋ = 10.0 * (y - x)
+    ẏ = x * (28.0 - z) - y
+    ż = x * y - (8 / 3) * z
+    return [ẋ, ẏ, ż]
+end
+
+u0 = [1.0; 0.0; 0.0]
+tspan = (0.0, 100.0)
+dt = 0.1
+prob = ODEProblem(lorenz, u0, tspan)
+sol = solve(prob, Tsit5(), saveat = dt)
+
+## Start the automatic discovery
+ddprob = DataDrivenProblem(sol)
+
+@variables t x(t) y(t) z(t)
+u = [x; y; z]
+basis = Basis(polynomial_basis(u, 5), u, iv = t)
+opt = STLSQ(exp10.(-5:0.1:-1))
+ddsol = solve(ddprob, basis, opt, options = DataDrivenCommonOptions(digits = 1))
+println(get_basis(ddsol))
+```
+
+```
+Explicit Result
+Solution with 3 equations and 7 parameters.
+Returncode: success
+Sparsity: 7.0
+L2 Norm Error: 26.7343984476783
+AICC: 1.0013570199499398
+
+Model ##Basis#366 with 3 equations
+States : x(t) y(t) z(t)
+Parameters : 7
+Independent variable: t
+Equations
+Differential(t)(x(t)) = p₁*x(t) + p₂*y(t)
+Differential(t)(y(t)) = p₃*x(t) + p₄*y(t) + p₅*x(t)*z(t)
+Differential(t)(z(t)) = p₇*z(t) + p₆*x(t)*y(t)
+
+Parameters:
+   p₁ : -10.0
+   p₂ : 10.0
+   p₃ : 28.0
+   p₄ : -1.0
+   p₅ : -1.0
+   p₆ : 1.0
+   p₇ : -2.7
+```
+
+![](LorenzResult.png)

docs/src/basis.md

@@ -4,7 +4,7 @@
 Basis
 ```
 
-## API 
+## API
 
 Next to [ModelingToolkits API](https://docs.sciml.ai/ModelingToolkit/stable/basics/AbstractSystem/) for `AbstractSystems`, a [`Basis`](@ref) can be called with the following methods:
 
@@ -15,7 +15,6 @@ get_parameter_values
 get_parameter_map
 ```
 
-
 ## Generators
 
 ```@docs
@@ -25,4 +24,4 @@ sin_basis
 cos_basis
 fourier_basis
 chebyshev_basis
-```
+```

docs/src/index.md

@@ -5,8 +5,9 @@ DataDrivenDiffEq.jl is a package for finding systems of equations automatically
 The methods in this package take in data and return the model which generated the data. A known model is not required as input. These methods can estimate equation-free and equation-based models for discrete, continuous differential equations or direct mappings.
 
 There are two main types of estimation, depending on if you need the result to be human-understandable:
-+ Structural identification - returns a human-readable result in symbolic form.
-+ Structural estimation - returns a function that predicts the derivative and generates a correct time series, but is not necessarily human-readable.
+
+  - Structural identification - returns a human-readable result in symbolic form.
+  - Structural estimation - returns a function that predicts the derivative and generates a correct time series, but is not necessarily human-readable.
 
 A quick-start example:
 
@@ -18,27 +19,26 @@ using DataDrivenSparse
 using LinearAlgebra
 
 # Create a test problem
-function lorenz(u,p,t)
+function lorenz(u, p, t)
     x, y, z = u
 
-    ẋ = 10.0*(y - x)
-    ẏ = x*(28.0-z) - y
-    ż = x*y - (8/3)*z
+    ẋ = 10.0 * (y - x)
+    ẏ = x * (28.0 - z) - y
+    ż = x * y - (8 / 3) * z
     return [ẋ, ẏ, ż]
 end
 
-u0 = [1.0;0.0;0.0]
-tspan = (0.0,100.0)
+u0 = [1.0; 0.0; 0.0]
+tspan = (0.0, 100.0)
 dt = 0.1
-prob = ODEProblem(lorenz,u0,tspan)
+prob = ODEProblem(lorenz, u0, tspan)
 sol = solve(prob, Tsit5(), saveat = dt)
 
-
 ## Start the automatic discovery
 ddprob = DataDrivenProblem(sol)
 
 @variables t x(t) y(t) z(t)
-u = [x;y;z]
+u = [x; y; z]
 basis = Basis(polynomial_basis(u, 5), u, iv = t)
 opt = STLSQ(exp10.(-5:0.1:-1))
 ddsol = solve(ddprob, basis, opt, options = DataDrivenCommonOptions(digits = 1))
@@ -53,6 +53,7 @@ To use [DataDrivenDiffEq.jl](https://github.com/SciML/DataDrivenDiffEq.jl), inst
 using Pkg
 Pkg.add("DataDrivenDiffEq")
 ```
+
 ## Package Overview
 
 Several algorithms for structural estimation and identification are implemented in the following subpackages.
@@ -70,18 +71,18 @@ Pkg.add("DataDrivenDMD")
 
 ### Sparse Regression
 
-Uses Sparse Regression algorithms to find a suitable and sparse combination of basis functions to approximate a system of (differential) equations. 
+Uses Sparse Regression algorithms to find a suitable and sparse combination of basis functions to approximate a system of (differential) equations.
 
 To use this functionality, install [DataDrivenSparse](@ref) via:
 
 ```julia
 using Pkg
 Pkg.add("DataDrivenSparse")
-``` 
+```
 
 ### Symbolic Regression
 
-Uses SymbolicRegression.jl to find a suitable set of equations to match the data. 
+Uses SymbolicRegression.jl to find a suitable set of equations to match the data.
 
 To use this functionality, install [DataDrivenSR](@ref) via:
 
@@ -90,73 +91,90 @@ using Pkg
 Pkg.add("DataDrivenSR")
 ```
 
-
 ## Contributing
 
-- Please refer to the
-  [SciML ColPrac: Contributor's Guide on Collaborative Practices for Community Packages](https://github.com/SciML/ColPrac/blob/master/README.md)
-  for guidance on PRs, issues, and other matters relating to contributing to SciML.
-- See the [SciML Style Guide](https://github.com/SciML/SciMLStyle) for common coding practices and other style decisions.
-- There are a few community forums:
-    - The #diffeq-bridged and #sciml-bridged channels in the
-      [Julia Slack](https://julialang.org/slack/),
-      you can message @AlCap23 to start a discussion.
-    - The #diffeq-bridged and #sciml-bridged channels in the
-      [Julia Zulip](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)
-    - On the [Julia Discourse forums](https://discourse.julialang.org)
-    - See also [SciML Community page](https://sciml.ai/community/)
+  - Please refer to the
+    [SciML ColPrac: Contributor's Guide on Collaborative Practices for Community Packages](https://github.com/SciML/ColPrac/blob/master/README.md)
+    for guidance on PRs, issues, and other matters relating to contributing to SciML.
+
+  - See the [SciML Style Guide](https://github.com/SciML/SciMLStyle) for common coding practices and other style decisions.
+  - There are a few community forums:
+    
+      + The #diffeq-bridged and #sciml-bridged channels in the
+        [Julia Slack](https://julialang.org/slack/),
+        you can message @AlCap23 to start a discussion.
+      + The #diffeq-bridged and #sciml-bridged channels in the
+        [Julia Zulip](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)
+      + On the [Julia Discourse forums](https://discourse.julialang.org)
+      + See also [SciML Community page](https://sciml.ai/community/)
 
 ## Reproducibility
+
 ```@raw html
 <details><summary>The documentation of this SciML package was built using these direct dependencies,</summary>
 ```
+
 ```@example
 using Pkg # hide
 Pkg.status() # hide
 ```
+
 ```@raw html
 </details>
 ```
+
 ```@raw html
 <details><summary>and using this machine and Julia version.</summary>
 ```
+
 ```@example
 using InteractiveUtils # hide
 versioninfo() # hide
 ```
+
 ```@raw html
 </details>
 ```
+
 ```@raw html
 <details><summary>A more complete overview of all dependencies and their versions is also provided.</summary>
 ```
+
 ```@example
 using Pkg # hide
-Pkg.status(;mode = PKGMODE_MANIFEST) # hide
+Pkg.status(; mode = PKGMODE_MANIFEST) # hide
 ```
+
 ```@raw html
 </details>
 ```
+
 ```@raw html
 You can also download the 
 <a href="
 ```
+
 ```@eval
 using TOML
-version = TOML.parse(read("../../Project.toml",String))["version"]
-name = TOML.parse(read("../../Project.toml",String))["name"]
-link = "https://github.com/SciML/"*name*".jl/tree/gh-pages/v"*version*"/assets/Manifest.toml"
+version = TOML.parse(read("../../Project.toml", String))["version"]
+name = TOML.parse(read("../../Project.toml", String))["name"]
+link = "https://github.com/SciML/" * name * ".jl/tree/gh-pages/v" * version *
+       "/assets/Manifest.toml"
 ```
+
 ```@raw html
 ">manifest</a> file and the
 <a href="
 ```
+
 ```@eval
 using TOML
-version = TOML.parse(read("../../Project.toml",String))["version"]
-name = TOML.parse(read("../../Project.toml",String))["name"]
-link = "https://github.com/SciML/"*name*".jl/tree/gh-pages/v"*version*"/assets/Project.toml"
+version = TOML.parse(read("../../Project.toml", String))["version"]
+name = TOML.parse(read("../../Project.toml", String))["name"]
+link = "https://github.com/SciML/" * name * ".jl/tree/gh-pages/v" * version *
+       "/assets/Project.toml"
 ```
+
 ```@raw html
 ">project</a> file.
 ```