add Compat and list

Author: Dutto

docs/Project.toml

@@ -7,5 +7,10 @@ OptimalControl = "5f98b655-cc9a-415a-b60e-744165666948"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 
 [compat]
-MINPACK = "1.3"
+DifferentialEquations = "7.13.0"
+Documenter = "1.5.0"
+ForwardDiff = "0.10.36"
+MINPACK = "1.3.0"
+OptimalControl = "0.11.0"
+Plots = "1.40.5"
 julia = "1.10"

docs/src/2D-preconditioner.md

@@ -194,8 +194,13 @@ where $r$ and $s$ correspond respectively to the rotation and the scale matrix,
 
 and where $\beta_0 = \arctan \left(\frac{a \sin(\theta)}{b \cos(\theta)} \right)$. 
 
-```@example main 
-function fit_ellipse(x, y)
+```@raw html
+<article class="docstring">
+<header>
+    <a class="docstring-article-toggle-button fa-solid fa-chevron-right" href="javascript:;" title="Expand docstring"> </a>
+    <code>fit_ellipse</code> — <span class="docstring-category">Function</span>
+</header>
+<section style="display: none;"><div><pre><code class="language-julia hljs">function fit_ellipse(x, y)
     M = hcat(x.^2, x.*y, y.^2, x, y)                            # quadratic form of ellipse
     p = M\ones(length(x))                                       # fit parameters for the ellipse
     A, B, C, D, E = p
@@ -208,9 +213,28 @@ function fit_ellipse(x, y)
     θ = atan(-B, C-A)/2
     c = [(2*C*D - B*E)/Δ, (2*A*E - B*D)/Δ]
     return a, b, -θ+Base.π/2, c
-end
+end</code><button class="copy-button fa-solid fa-copy" aria-label="Copy this code ;opblock" title="Copy"></button></pre></div>
+</section>
+</article>
+```
+
+```@example main
+function fit_ellipse(x, y) # hide
+    M = hcat(x.^2, x.*y, y.^2, x, y) # hide
+    p = M\ones(length(x)) # hide
+    A, B, C, D, E = p # hide
+    F = -1.0 # hide
+    Δ = B^2 - 4*A*C # hide
+    Λ = (A-C)^2 + B^2 # hide
+    b, a = [-sqrt(clamp( 2*(A*E^2 + C*D^2 - B*D*E + Δ*F) * ( (A+C) + op(sqrt(Λ)) ), 0, Inf)) / Δ   for op in (+, -)] # hide
+    θ = atan(-B, C-A)/2 # hide
+    c = [(2*C*D - B*E)/Δ, (2*A*E - B*D)/Δ] # hide
+    return a, b, -θ+Base.π/2, c # hide
+end # hide
+nothing # hide
 ```
 
+
 ```@example main
 n = 15                                                          # number of points for fit : 2n
 n_ = 100                                                        # number of points for plot: 2n_

docs/src/index.md

@@ -12,3 +12,13 @@ We consider the following optimal control problem
 ```
 
 with $x_0$, $t_0$, $x_f$ and $t_f$ fixed. This problem is simple, and can be analytically solve without the use of numerical method. However, the goal is to solve this problem by indirect shooting.  
+
+# Dependencies
+
+All the numerical simulations to generate this documentation from `MRI.jl` are performed with 
+the following packages.
+
+```@example
+using Pkg
+Pkg.status()
+```