Update README.md

Author: ChrisRackauckas

README.md

@@ -121,11 +121,6 @@ MATLAB solvers do outperform that of Python and R.
 #### Non-Stiff Problem 1: Lotka-Volterra
 
 ```julia
-using ParameterizedFunctions, MATLABDiffEq, OrdinaryDiffEq, ODEInterface,
-      ODEInterfaceDiffEq, Plots, Sundials, SciPyDiffEq, deSolveDiffEq
-using DiffEqDevTools
-using LinearAlgebra
-
 f = @ode_def_bare LotkaVolterra begin
   dx = a*x - b*x*y
   dy = -c*y + d*x*y
@@ -145,6 +140,7 @@ setups = [Dict(:alg=>DP5())
           Dict(:alg=>MATLABDiffEq.ode113())
           Dict(:alg=>SciPyDiffEq.RK45())
           Dict(:alg=>SciPyDiffEq.LSODA())
+          Dict(:alg=>SciPyDiffEq.odeint())
           Dict(:alg=>deSolveDiffEq.lsoda())
           Dict(:alg=>deSolveDiffEq.ode45())
           Dict(:alg=>CVODE_Adams())
@@ -159,6 +155,7 @@ names = [
   "MATLAB: ode113"
   "SciPy: RK45"
   "SciPy: LSODA"
+  "SciPy: odeint"
   "deSolve: lsoda"
   "deSolve: ode45"
   "Sundials: Adams"
@@ -172,10 +169,9 @@ wp = WorkPrecisionSet(prob,abstols,reltols,setups;
                       save_everystep=false,numruns=100,maxiters=10000000,
                       timeseries_errors=false,verbose=false)
 plot(wp,title="Non-stiff 1: Lotka-Volterra")
-savefig("benchmark1.png")
 ```
 
-![benchmark1](https://user-images.githubusercontent.com/1814174/69487806-157cb400-0e2e-11ea-876f-c519aed013c0.png)
+![](https://user-images.githubusercontent.com/1814174/71537082-ef42ac00-28e4-11ea-9acc-67dfd9990221.png)
 
 #### Non-Stiff Problem 2: Rigid Body
 
@@ -197,6 +193,7 @@ setups = [Dict(:alg=>DP5())
           Dict(:alg=>MATLABDiffEq.ode113())
           Dict(:alg=>SciPyDiffEq.RK45())
           Dict(:alg=>SciPyDiffEq.LSODA())
+          Dict(:alg=>SciPyDiffEq.odeint())
           Dict(:alg=>deSolveDiffEq.lsoda())
           Dict(:alg=>deSolveDiffEq.ode45())
           Dict(:alg=>CVODE_Adams())
@@ -211,6 +208,7 @@ names = [
   "MATLAB: ode113"
   "SciPy: RK45"
   "SciPy: LSODA"
+  "SciPy: odeint"
   "deSolve: lsoda"
   "deSolve: ode45"
   "Sundials: Adams"
@@ -224,20 +222,19 @@ wp = WorkPrecisionSet(prob,abstols,reltols,setups;
                       save_everystep=false,numruns=100,maxiters=10000000,
                       timeseries_errors=false,verbose=false)
 plot(wp,title="Non-stiff 2: Rigid-Body")
-savefig("benchmark2.png")
 ```
 
-![benchmark2](https://user-images.githubusercontent.com/1814174/69487808-17467780-0e2e-11ea-9db2-324d4e319d07.png)
+![](https://user-images.githubusercontent.com/1814174/71537083-ef42ac00-28e4-11ea-8dc7-a5dca0518baf.png)
 
-#### Stiff Problem 1: ROBER Shorter and Simpler for SciPy
+#### Stiff Problem 1: ROBER
 
 ```julia
 rober = @ode_def begin
   dy₁ = -k₁*y₁+k₃*y₂*y₃
   dy₂ =  k₁*y₁-k₂*y₂^2-k₃*y₂*y₃
   dy₃ =  k₂*y₂^2
 end k₁ k₂ k₃
-prob = ODEProblem(rober,[1.0,0.0,0.0],(0.0,1e3),[0.04,3e7,1e4])
+prob = ODEProblem(rober,[1.0,0.0,0.0],(0.0,1e5),[0.04,3e7,1e4])
 sol = solve(prob,CVODE_BDF(),abstol=1/10^14,reltol=1/10^14)
 test_sol = TestSolution(sol)
 
@@ -253,7 +250,9 @@ setups = [Dict(:alg=>Rosenbrock23())
           Dict(:alg=>MATLABDiffEq.ode15s())
           Dict(:alg=>SciPyDiffEq.LSODA())
           Dict(:alg=>SciPyDiffEq.BDF())
+          Dict(:alg=>SciPyDiffEq.odeint())
           Dict(:alg=>deSolveDiffEq.lsoda())
+          Dict(:alg=>CVODE_BDF())
           ]
 
 names = [
@@ -266,68 +265,20 @@ names = [
   "MATLAB: ode15s"
   "SciPy: LSODA"
   "SciPy: BDF"
+  "SciPy: odeint"
   "deSolve: lsoda"
+  "Sundials: CVODE"
   ]
 
 wp = WorkPrecisionSet(prob,abstols,reltols,setups;
                       names = names,print_names = true,
                       dense=false,verbose = false,
                       save_everystep=false,appxsol=test_sol,
                       maxiters=Int(1e5))
-plot(wp,title="Stiff 1: ROBER Short")
-savefig("benchmark31.png")
-```
-
-![benchmark31](https://user-images.githubusercontent.com/1814174/69501071-4b25a980-0ecf-11ea-99d1-b7274491498e.png)
-
-#### Rober Standard length
-
-**SciPy Omitted due to failures at higher tolerances and because it's too slow to finish in a day!**
-See note below.
-
-```julia
-prob = ODEProblem(rober,[1.0,0.0,0.0],(0.0,1e5),[0.04,3e7,1e4])
-sol = solve(prob,CVODE_BDF(),abstol=1/10^14,reltol=1/10^14)
-test_sol = TestSolution(sol)
-
-abstols = 1.0 ./ 10.0 .^ (5:8)
-reltols = 1.0 ./ 10.0 .^ (1:4);
-
-setups = [Dict(:alg=>Rosenbrock23())
-          Dict(:alg=>TRBDF2())
-          Dict(:alg=>RadauIIA5())
-          Dict(:alg=>rodas())
-          Dict(:alg=>radau())
-          Dict(:alg=>MATLABDiffEq.ode23s())
-          Dict(:alg=>MATLABDiffEq.ode15s())
-          #Dict(:alg=>SciPyDiffEq.LSODA())
-          #Dict(:alg=>SciPyDiffEq.BDF())
-          Dict(:alg=>deSolveDiffEq.lsoda())
-          ]
-
-names = [
-  "Julia: Rosenbrock23"
-  "Julia: TRBDF2"
-  "Julia: radau"
-  "Hairer: rodas"
-  "Hairer: radau"
-  "MATLAB: ode23s"
-  "MATLAB: ode15s"
-  #"SciPy: LSODA"
-  #"SciPy: BDF"
-  "deSolve: lsoda"
-  ]
-
-wp = WorkPrecisionSet(prob,abstols,reltols,setups;
-                      names = names,print_names = true,
-                      dense=false,verbose = false,
-                      save_everystep=false,appxsol=test_sol,
-                      maxiters=Int(1e5))
-plot(wp,title="Stiff 1: ROBER Standard Length")
-savefig("benchmark32.png")
+plot(wp,title="Stiff 1: ROBER", legend=:topleft)
 ```
 
-![benchmark32](https://user-images.githubusercontent.com/1814174/69501072-4b25a980-0ecf-11ea-82dd-47aa566ecbc2.png)
+![](https://user-images.githubusercontent.com/1814174/71537080-ef42ac00-28e4-11ea-9abd-37631cd18ad9.png)
 
 #### Stiff Problem 2: HIRES
 
@@ -354,6 +305,7 @@ test_sol = TestSolution(sol)
 
 abstols = 1.0 ./ 10.0 .^ (5:8)
 reltols = 1.0 ./ 10.0 .^ (1:4);
+
 setups = [Dict(:alg=>Rosenbrock23())
           Dict(:alg=>TRBDF2())
           Dict(:alg=>RadauIIA5())
@@ -363,7 +315,9 @@ setups = [Dict(:alg=>Rosenbrock23())
           Dict(:alg=>MATLABDiffEq.ode15s())
           Dict(:alg=>SciPyDiffEq.LSODA())
           Dict(:alg=>SciPyDiffEq.BDF())
+          Dict(:alg=>SciPyDiffEq.odeint())
           Dict(:alg=>deSolveDiffEq.lsoda())
+          Dict(:alg=>CVODE_BDF())
           ]
 
 names = [
@@ -376,15 +330,16 @@ names = [
   "MATLAB: ode15s"
   "SciPy: LSODA"
   "SciPy: BDF"
+  "SciPy: odeint"
   "deSolve: lsoda"
+  "Sundials: CVODE"
   ]
 
 wp = WorkPrecisionSet(prob,abstols,reltols,setups;
                       names = names,print_names = true,
                       save_everystep=false,appxsol=test_sol,
                       maxiters=Int(1e5),numruns=100)
-plot(wp,title="Stiff 2: Hires")
-savefig("benchmark4.png")
+plot(wp,title="Stiff 2: Hires",legend=:topleft)
 ```
 
-![benchmark4](https://user-images.githubusercontent.com/1814174/69501114-bec7b680-0ecf-11ea-9095-7b7f2e98d514.png)
+![](https://user-images.githubusercontent.com/1814174/71537081-ef42ac00-28e4-11ea-950f-59c762ce9a69.png)