format markdown

Author: ArnoStrouwen

.JuliaFormatter.toml

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

README.md

@@ -6,7 +6,7 @@
 [![codecov](https://codecov.io/gh/SciML/SymbolicNumericIntegration.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/SciML/SymbolicNumericIntegration.jl)
 [![Build Status](https://github.com/SciML/SymbolicNumericIntegration.jl/workflows/CI/badge.svg)](https://github.com/SciML/SymbolicNumericIntegration.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)
+[![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)
 
 **SymbolicNumericIntegration.jl** is a hybrid symbolic/numerical integration package that works on the [Julia Symbolics](https://github.com/JuliaSymbolics/Symbolics.jl) expressions.
@@ -26,19 +26,29 @@ using SymbolicNumericIntegration
 
 @variables x
 
-julia> integrate(3x^3 + 2x - 5)
+integrate(3x^3 + 2x - 5)
+```
+
+```
 (x^2 + (3//4)*(x^4) - (5x), 0, 0)
 ```
 
 # Citation
+
 If you use SymbolicNumericIntegration.jl in your research, please cite [this paper](https://arxiv.org/abs/2201.12468):
+
 ```
-@article{Iravanian2022,   
-   author = {Shahriar Iravanian and Carl Julius Martensen and Alessandro Cheli and Shashi Gowda and Anand Jain and Julia Computing and Yingbo Ma and Chris Rackauckas},
-   doi = {10.48550/arxiv.2201.12468},
-   month = {1},
-   title = {Symbolic-Numeric Integration of Univariate Expressions based on Sparse Regression},
-   url = {https://arxiv.org/abs/2201.12468v2},
-   year = {2022},
+
+@article{Iravanian2022,
+author = {Shahriar Iravanian and Carl Julius Martensen and Alessandro Cheli and Shashi Gowda and Anand Jain and Julia Computing and Yingbo Ma and Chris Rackauckas},
+doi = {10.48550/arxiv.2201.12468},
+month = {1},
+title = {Symbolic-Numeric Integration of Univariate Expressions based on Sparse Regression},
+url = {https://arxiv.org/abs/2201.12468v2},
+year = {2022},
 }
+
+```
+
+```
 ```

docs/src/index.md

@@ -1,4 +1,5 @@
 # SymbolicNumericIntegration.jl
+
 **SymbolicNumericIntegration.jl** is a hybrid symbolic/numerical integration package that works on the [Julia Symbolics](https://docs.sciml.ai/Symbolics/stable/) expressions.
 
 **SymbolicNumericIntegration.jl** uses a randomized algorithm based on a hybrid of the *method of undetermined coefficients* and *sparse regression* and is able to solve a large subset of basic standard integrals (polynomials, exponential/logarithmic, trigonometric and hyperbolic, inverse trigonometric and hyperbolic, rational and square root).
@@ -11,7 +12,9 @@ using Symbolics
 using SymbolicNumericIntegration
 
 @variables x
+```
 
+```julia
 julia> integrate(3x^3 + 2x - 5)
 (x^2 + (3//4)*(x^4) - (5x), 0, 0)
 
@@ -21,37 +24,37 @@ julia> integrate((5 + 2x)^-1)
 julia> integrate(1 / (6 + x^2 - (5x)))
 (log(x - 3) - log(x - 2), 0, 3.339372764128952e-16)
 
-y = integrate(1 / (x^2 - 16))
+julia> integrate(1 / (x^2 - 16))
 ((1//8)*log(x - 4) - ((1//8)*log(4 + x)), 0, 1.546926788028958e-16)
 
-julia> integrate(x^2/(16 + x^2))
+julia> integrate(x^2 / (16 + x^2))
 (x + 4atan((-1//4)*x), 0, 1.3318788420751984e-16)
 
-julia> integrate(x^2/sqrt(4 + x^2))
+julia> integrate(x^2 / sqrt(4 + x^2))
 ((1//2)*x*((4 + x^2)^0.5) - ((2//1)*log(x + sqrt(4 + x^2))), 0, 8.702422633074313e-17)
 
-julia> integrate(x^2*log(x))
+julia> integrate(x^2 * log(x))
 ((1//3)*log(x)*(x^3) - ((1//9)*(x^3)), 0, 0)
 
-julia> integrate(x^2*exp(x))
+julia> integrate(x^2 * exp(x))
 (2exp(x) + exp(x)*(x^2) - (2x*exp(x)), 0, 0)
 
 julia> integrate(tan(2x))
 ((-1//2)*log(cos(2x)), 0, 0)
 
-julia> integrate(sec(x)*tan(x))
+julia> integrate(sec(x) * tan(x))
 (cos(x)^-1, 0, 0)
 
-julia> integrate(cosh(2x)*exp(x))
+julia> integrate(cosh(2x) * exp(x))
 ((2//3)*exp(x)*sinh(2x) - ((1//3)*exp(x)*cosh(2x)), 0, 7.073930088880992e-8)
 
-julia> integrate(cosh(x)*sin(x))
+julia> integrate(cosh(x) * sin(x))
 ((1//2)*sin(x)*sinh(x) - ((1//2)*cos(x)*cosh(x)), 0, 4.8956233716268386e-17)
 
-julia> integrate(cosh(2x)*sin(3x))
+julia> integrate(cosh(2x) * sin(3x))
 (0.153845sinh(2x)*sin(3x) - (0.23077cosh(2x)*cos(3x)), 0, 4.9807620877373405e-6)
 
-julia> integrate(log(log(x))*(x^-1))
+julia> integrate(log(log(x)) * (x^-1))
 (log(x)*log(log(x)) - log(x), 0, 0)
 
 julia> integrate(exp(x^2))
@@ -60,18 +63,18 @@ julia> integrate(exp(x^2))
 
 `integrate` has the form `integrate(y; kw...)` or `integrate(y, x; kw...)`, where `y` is the integrand and the optional `x` is the variable of integration. The keyword parameters are:
 
-* `abstol` (default `1e-6`): the error tolerance to accept a solution.
-* `symbolic` (default `true`): if true, pure symbolic integration is attempted first.
-* `bypass` (default `false`): if true, the whole expression is considered at once and not per term.
-* `num_steps` (default `2`): one plus the number of expanded basis to check (if `num_steps` is 1, only the main basis is checked).
-* `num_trials` (default `5`): the number of attempts to solve the integration numerically for each basis set.
-* `show_basis` (default `false`): print the basis set, useful for debugging. Only works if `verbose` is also set.
-* `homotopy` (default: `true` as of version 0.7.0): uses the continuous Homotopy operators to generate the integration candidates.
-* `verbose` (default `false`): if true, prints extra (and voluminous!) debugging information.
-* `radius` (default `1.0`): the starting radius to generate random test points.
-* `opt` (default `STLSQ(exp.(-10:1:0))`): the optimizer passed to `sparse_regression!`.
-* `max_basis` (default `110`): the maximum number of expression in the basis.
-* `complex_plane` (default `true`): random test points are generated on the complex plane (only over the real axis if `complex_plane` is `false`).
+  - `abstol` (default `1e-6`): the error tolerance to accept a solution.
+  - `symbolic` (default `true`): if true, pure symbolic integration is attempted first.
+  - `bypass` (default `false`): if true, the whole expression is considered at once and not per term.
+  - `num_steps` (default `2`): one plus the number of expanded basis to check (if `num_steps` is 1, only the main basis is checked).
+  - `num_trials` (default `5`): the number of attempts to solve the integration numerically for each basis set.
+  - `show_basis` (default `false`): print the basis set, useful for debugging. Only works if `verbose` is also set.
+  - `homotopy` (default: `true` as of version 0.7.0): uses the continuous Homotopy operators to generate the integration candidates.
+  - `verbose` (default `false`): if true, prints extra (and voluminous!) debugging information.
+  - `radius` (default `1.0`): the starting radius to generate random test points.
+  - `opt` (default `STLSQ(exp.(-10:1:0))`): the optimizer passed to `sparse_regression!`.
+  - `max_basis` (default `110`): the maximum number of expression in the basis.
+  - `complex_plane` (default `true`): random test points are generated on the complex plane (only over the real axis if `complex_plane` is `false`).
 
 ## Testing
 
@@ -80,29 +83,29 @@ julia> integrate(exp(x^2))
 Additionally, 12 test suites from the *Rule-based Integrator* ([Rubi](https://rulebasedintegration.org/)) are included in the `/test` directory. For example, we can test the first one as below ([Axiom](http://www.axiom-developer.org/) refers to the format of the test files)
 
 ```julia
-  using SymbolicNumericIntegration
-  include("test/axiom.jl")  # note, you may need to use the correct path
+using SymbolicNumericIntegration
+include("test/axiom.jl")  # note, you may need to use the correct path
 
-  L = convert_axiom(:Apostle)   # can also use L = convert_axiom(1)  
-  test_axiom(L, false; bypass=false, verbose=false, homotopy=true)
+L = convert_axiom(:Apostle)   # can also use L = convert_axiom(1)  
+test_axiom(L, false; bypass = false, verbose = false, homotopy = true)
 ```
 
 The test suites description based on the header of the files in the Rubi directory are
 
-| name        | id | comment                                  |
-|-------------|----|------------------------------------------|
-|:Apostle     | 1  | Tom M. Apostol - Calculus, Volume I, Second Edition (1967) |
-|:Bondarenko  | 2  | Vladimir Bondarenko Integration Problems |
-|:Bronstein   | 3  | Manuel Bronstein - Symbolic Integration Tutorial (1998) |
-|:Charlwood   | 4  | Kevin Charlwood - Integration on Computer Algebra Systems (2008) |
-|:Hearn       | 5  | Anthony Hearn - Reduce Integration Test Package |
-|:Hebisch     | 6  | Waldek Hebisch - email May 2013 |
-|:Jeffrey     | 7  | David Jeffrey - Rectifying Transformations for Trig Integration (1997) |
-|:Moses       | 8  | Joel Moses - Symbolic Integration Ph.D. Thesis (1967) |
-|:Stewart     | 9  | James Stewart - Calculus (1987) |
-|:Timofeev    | 10 | A. F. Timofeev - Integration of Functions (1948) |
-|:Welz        | 11 | Martin Welz - posts on Sci.Math.Symbolic |
-|:Webster     | 12 | Michael Wester |
+| name        | id | comment                                                                |
+|:----------- |:-- |:---------------------------------------------------------------------- |
+| :Apostle    | 1  | Tom M. Apostol - Calculus, Volume I, Second Edition (1967)             |
+| :Bondarenko | 2  | Vladimir Bondarenko Integration Problems                               |
+| :Bronstein  | 3  | Manuel Bronstein - Symbolic Integration Tutorial (1998)                |
+| :Charlwood  | 4  | Kevin Charlwood - Integration on Computer Algebra Systems (2008)       |
+| :Hearn      | 5  | Anthony Hearn - Reduce Integration Test Package                        |
+| :Hebisch    | 6  | Waldek Hebisch - email May 2013                                        |
+| :Jeffrey    | 7  | David Jeffrey - Rectifying Transformations for Trig Integration (1997) |
+| :Moses      | 8  | Joel Moses - Symbolic Integration Ph.D. Thesis (1967)                  |
+| :Stewart    | 9  | James Stewart - Calculus (1987)                                        |
+| :Timofeev   | 10 | A. F. Timofeev - Integration of Functions (1948)                       |
+| :Welz       | 11 | Martin Welz - posts on Sci.Math.Symbolic                               |
+| :Webster    | 12 | Michael Wester                                                         |
 
 ## Citation
 
@@ -120,56 +123,72 @@ If you use **SymbolicNumericIntegration.jl**, please cite [Symbolic-Numeric Inte
 ```
 
 ## 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.
-```
+```

src/integral.jl

@@ -335,7 +335,7 @@ function sparse_fit(T, A, x, basis, Δbasis, opt; abstol = 1e-6)
         if sum(iscomplex.(q)) > 2
             return nothing, Inf
         end   # eliminating complex coefficients
-        return sum(q[i] * basis[i] for i = 1:length(basis) if q[i] != 0; init = zero(x)),
+        return sum(q[i] * basis[i] for i in 1:length(basis) if q[i] != 0; init = zero(x)),
                abs(ϵ)
     catch e
         println("Error from sparse_fit", e)

src/rules.jl

@@ -220,7 +220,7 @@ function decompose_rational(eq)
 
     q₀ = A \ b
     q = nice_parameter.(q₀)
-    p = sum(F[i] * q[i] for i = 1:n if q[i] != 0; init = zero(x))
+    p = sum(F[i] * q[i] for i in 1:n if q[i] != 0; init = zero(x))
     return p
 end