Revert "move example to a file (#110)" (#111)

This reverts commit 399d655.

README.md

@@ -29,4 +29,44 @@ using Pkg
 Pkg.add(url="https://github.com/impICNF/ICNF.jl")
 ```
 
-See [`simple_example.jl`](examples/simple_example.jl) for a simple example of using this package.
+To use this package, here is an example:
+
+```julia
+using ICNF
+using Distributions, Flux
+using DifferentialEquations, SciMLSensitivity
+
+# Parameters
+nvars = 1
+n = 1024
+
+# Data
+data_dist = Beta(2.0, 4.0)
+r = rand(data_dist, nvars, n)
+
+# Model
+nn = Chain(
+    Dense(nvars => 4*nvars, tanh),
+    Dense(4*nvars => nvars, tanh),
+) |> f64
+icnf = RNODE{Float64, Array}(nn, nvars; tspan=(0.0, 4.0))
+
+# Training
+using DataFrames, MLJBase
+df = DataFrame(transpose(r), :auto)
+model = ICNFModel(icnf; opt_app=SciMLOptApp())
+mach = machine(model, df)
+fit!(mach)
+
+# Use It
+d = ICNFDist(icnf)
+actual_pdf = pdf.(data_dist, vec(r))
+estimated_pdf = pdf(d, r)
+new_data = rand(d, n)
+
+# Evaluation
+using LinearAlgebra, Distances
+n1 = norm(estimated_pdf - actual_pdf, 1) / n
+n2 = norm(estimated_pdf - actual_pdf, 2) / n
+tv_dis = totalvariation(estimated_pdf, actual_pdf) / n
+```