Merge pull request #100 from SciML/ChrisRackauckas-patch-1

Update the README to point to the new docs

Author: AlCap23

README.md

@@ -5,11 +5,84 @@
 [![Coverage Status](https://coveralls.io/repos/JuliaDiffEq/DataDrivenDiffEq.jl/badge.svg?branch=master&service=github)](https://coveralls.io/github/JuliaDiffEq/DataDrivenDiffEq.jl?branch=master)
 [![codecov.io](http://codecov.io/github/JuliaDiffEq/DataDrivenDiffEq.jl/coverage.svg?branch=master)](http://codecov.io/github/JuliaDiffEq/DataDrivenDiffEq.jl?branch=master)
 
-DataDrivenDiffEq.jl is a component package in the DifferentialEquations ecosystem.
-It holds the tools for data-driven differential equation structural estimation and identification.
-Users interested in using this functionality should check out 
-[DifferentialEquations.jl](https://github.com/JuliaDiffEq/DifferentialEquations.jl).
+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.
 
-## Documentation
+For information on using the package,
+[see the stable documentation](https://datadriven.sciml.ai/stable/). Use the
+[in-development documentation](https://datadriven.sciml.ai/dev/) for the version of
+the documentation which contains the un-released features.
 
-Extensive documentation of this functionality is on the [Structural Estimation page](http://docs.juliadiffeq.org/dev/analysis/structural_estimation.html).
+## Quick Demonstration
+
+```julia
+## Generate some data by solving a differential equation
+########################################################
+
+using DataDrivenDiffEq
+using ModelingToolkit
+using OrdinaryDiffEq
+
+using LinearAlgebra
+using Plots
+gr()
+
+# 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 = [-8.0; 7.0; 27.0]
+p = [10.0; -10.0; 28.0; -1.0; -1.0; 1.0; -8/3]
+tspan = (0.0,100.0)
+dt = 0.001
+problem = ODEProblem(lorenz,u0,tspan)
+solution = solve(problem, Tsit5(), saveat = dt, atol = 1e-7, rtol = 1e-8)
+
+X = Array(solution)
+DX = similar(X)
+for (i, xi) in enumerate(eachcol(X))
+    DX[:,i] = lorenz(xi, [], 0.0)
+end
+
+## Now automatically discover the system that generated the data
+################################################################
+
+@variables x y z
+u = Operation[x; y; z]
+polys = Operation[]
+for i ∈ 0:4
+    for j ∈ 0:i
+        for k ∈ 0:j
+            push!(polys, u[1]^i*u[2]^j*u[3]^k)
+            push!(polys, u[2]^i*u[3]^j*u[1]^k)
+            push!(polys, u[3]^i*u[1]^j*u[2]^k)
+        end
+    end
+end
+
+basis = Basis(polys, u)
+
+opt = STRRidge(0.1)
+Ψ = SInDy(X, DX, basis, maxiter = 100, opt = opt, normalize = true)
+print_equations(Ψ)
+get_error(Ψ)
+```
+
+```
+3 dimensional basis in ["x", "y", "z"]
+dx = p₁ * x + p₂ * y
+dy = p₃ * x + p₄ * y + z * x * p₅
+dz = p₆ * z + x * y * p₇
+
+# Error
+3-element Array{Float64,1}:
+ 6.7202639134663155e-12
+ 3.505423292198665e-11
+ 1.2876598297504605e-11
+```