update cross language results

Author: ChrisRackauckas

README.md

@@ -113,16 +113,17 @@ julia> @time MATLABDiffEq.eval_string("[t,u] = $(algstr)(f,tspan,u0,options);")
 The following benchmarks demonstrate a **100x performance advantage for the
 pure-Julia methods over the MATLAB ODE solvers** across a range of stiff and
 non-stiff ODEs. These were ran with Julia 1.2, MATLAB 2019B, deSolve 1.2.5,
-and SciPy 1.3.1 after verifying negligible overhead on interop.
+and SciPy 1.3.1 after verifying negligible overhead on interop. Note that the
+MATLAB solvers do outperform that of Python and R.
+
+#### Non-Stiff Problem 1: Lotka-Volterra
 
 ```julia
 using ParameterizedFunctions, MATLABDiffEq, OrdinaryDiffEq, ODEInterface,
-      ODEInterfaceDiffEq, Plots, Sundials
+      ODEInterfaceDiffEq, Plots, Sundials, SciPyDiffEq, deSolveDiffEq
 using DiffEqDevTools
 using LinearAlgebra
 
-## Non-Stiff Problem 1: Lotka-Volterra
-
 f = @ode_def_bare LotkaVolterra begin
   dx = a*x - b*x*y
   dy = -c*y + d*x*y
@@ -136,27 +137,48 @@ test_sol = TestSolution(sol)
 
 setups = [Dict(:alg=>DP5())
           Dict(:alg=>dopri5())
-          Dict(:alg=>BS5())
           Dict(:alg=>Tsit5())
-          Dict(:alg=>Vern6())
           Dict(:alg=>Vern7())
           Dict(:alg=>MATLABDiffEq.ode45())
           Dict(:alg=>MATLABDiffEq.ode113())
+          Dict(:alg=>SciPyDiffEq.RK45())
+          Dict(:alg=>SciPyDiffEq.LSODA())
+          Dict(:alg=>deSolveDiffEq.lsoda())
+          Dict(:alg=>deSolveDiffEq.ode45())
           Dict(:alg=>CVODE_Adams())
   ]
+
+names = [
+  "Julia: DP5"
+  "Hairer: dopri5"
+  "Julia: Tsit5"
+  "Julia: Vern7"
+  "MATLAB: ode45"
+  "MATLAB: ode113"
+  "SciPy: RK45"
+  "SciPy: LSODA"
+  "deSolve: lsoda"
+  "deSolve: ode45"
+  "Sundials: Adams"
+  ]
+
 abstols = 1.0 ./ 10.0 .^ (6:13)
 reltols = 1.0 ./ 10.0 .^ (3:10)
-wp = WorkPrecisionSet(prob,abstols,reltols,setups;appxsol=test_sol,dense=false,
+wp = WorkPrecisionSet(prob,abstols,reltols,setups;
+                      names = names,
+                      appxsol=test_sol,dense=false,
                       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/1814174/69478405-f9dac480-0dbf-11ea-8f8e-5572b86d2a97.png)
+![benchmark1](https://user-images.githubusercontent.com/1814174/69487806-157cb400-0e2e-11ea-876f-c519aed013c0.png)
+
+#### Non-Stiff Problem 2: Rigid Body
 
 ```julia
-## Non-Stiff Problem 2: Rigid Body
+
 
 f = @ode_def_bare RigidBodyBench begin
   dy1  = -2*y2*y3
@@ -169,61 +191,151 @@ test_sol = TestSolution(sol)
 
 setups = [Dict(:alg=>DP5())
           Dict(:alg=>dopri5())
-          Dict(:alg=>BS5())
           Dict(:alg=>Tsit5())
-          Dict(:alg=>Vern6())
           Dict(:alg=>Vern7())
           Dict(:alg=>MATLABDiffEq.ode45())
           Dict(:alg=>MATLABDiffEq.ode113())
+          Dict(:alg=>SciPyDiffEq.RK45())
+          Dict(:alg=>SciPyDiffEq.LSODA())
+          Dict(:alg=>deSolveDiffEq.lsoda())
+          Dict(:alg=>deSolveDiffEq.ode45())
           Dict(:alg=>CVODE_Adams())
   ]
+
+names = [
+  "Julia: DP5"
+  "Hairer: dopri5"
+  "Julia: Tsit5"
+  "Julia: Vern7"
+  "MATLAB: ode45"
+  "MATLAB: ode113"
+  "SciPy: RK45"
+  "SciPy: LSODA"
+  "deSolve: lsoda"
+  "deSolve: ode45"
+  "Sundials: Adams"
+  ]
+
 abstols = 1.0 ./ 10.0 .^ (6:13)
 reltols = 1.0 ./ 10.0 .^ (3:10)
-wp = WorkPrecisionSet(prob,abstols,reltols,setups;appxsol=test_sol,dense=false,
+wp = WorkPrecisionSet(prob,abstols,reltols,setups;
+                      names = names,
+                      appxsol=test_sol,dense=false,
                       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/1814174/69478406-fe9f7880-0dbf-11ea-8f15-a0a0f3e8717f.png)
+![benchmark2](https://user-images.githubusercontent.com/1814174/69487808-17467780-0e2e-11ea-9db2-324d4e319d07.png)
 
+#### Stiff Problem 1: ROBER Shorter and Simpler for SciPy
 
 ```julia
-## Stiff Problem 1: ROBER
+
 
 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])
+sol = solve(prob,CVODE_BDF(),abstol=1/10^14,reltol=1/10^14)
+test_sol = TestSolution(sol)
+
+abstols = 1.0 ./ 10.0 .^ (7:8)
+reltols = 1.0 ./ 10.0 .^ (3:4);
+
+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 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=>rodas()),
-          Dict(:alg=>radau()),
-          Dict(:alg=>RadauIIA5()),
-          Dict(:alg=>MATLABDiffEq.ode23s()),
+
+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;
-                      save_everystep=false,appxsol=test_sol,maxiters=Int(1e5),numruns=100)
-plot(wp,title="Stiff 1: ROBER")
-savefig("benchmark3.png")
+                      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")
 ```
 
-![benchmark3](https://user-images.githubusercontent.com/1814174/69478407-ffd0a580-0dbf-11ea-9311-909bd3938b42.png)
+![benchmark32](https://user-images.githubusercontent.com/1814174/69501072-4b25a980-0ecf-11ea-82dd-47aa566ecbc2.png)
 
+#### Stiff Problem 2: HIRES
 
 ```julia
-## Stiff Problem 2: HIRES
-
 f = @ode_def Hires begin
   dy1 = -1.71*y1 + 0.43*y2 + 8.32*y3 + 0.0007
   dy2 = 1.71*y1 - 8.75*y2
@@ -246,26 +358,37 @@ 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=>rodas()),
-          Dict(:alg=>radau()),
-          Dict(:alg=>RadauIIA5()),
-          Dict(:alg=>MATLABDiffEq.ode23s()),
+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;
-                      save_everystep=false,appxsol=test_sol,maxiters=Int(1e5),numruns=100)
+                      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")
 ```
 
-![benchmark4](https://user-images.githubusercontent.com/1814174/69478409-019a6900-0dc0-11ea-9fce-c11a5e4de9a4.png)
-
-
-Together this demonstrates that the algorithms like `ode45` and `ode15s` are
-not competitive performance-wise against the Fortran and Julia methods.
-This shows that being able to run MATLAB ODE algorithms with MATLAB functions
-is cute, but does not really have a practical use due to MATLAB's lack of
-performance (and its [pass by copy](https://www.mathworks.com/matlabcentral/answers/152-can-matlab-pass-by-reference) for functions).
+![benchmark4](https://user-images.githubusercontent.com/1814174/69501114-bec7b680-0ecf-11ea-9095-7b7f2e98d514.png)