more examples

Author: ArnoStrouwen

docs/src/basics/Validation.md

@@ -78,8 +78,8 @@ In order to validate user-defined types and `register`ed functions, specialize `
 expect an object type, while two-parameter calls expect a function type as the first argument, and a vector of arguments as the 
 second argument.
 
-```julia
-using ModelingToolkit
+```@example validation2
+using ModelingToolkit, Unitful
 # Composite type parameter in registered function
 @parameters t
 D = Differential(t)
@@ -90,10 +90,10 @@ end
 dummycomplex(complex, scalar) = complex.f - scalar
 
 c = NewType(1)
-MT.get_unit(x::NewType) = MT.get_unit(x.f)
-function MT.get_unit(op::typeof(dummycomplex),args)
-    argunits = MT.get_unit.(args)
-    MT.get_unit(-,args)
+ModelingToolkit.get_unit(x::NewType) = ModelingToolkit.get_unit(x.f)
+function ModelingToolkit.get_unit(op::typeof(dummycomplex),args)
+    argunits = ModelingToolkit.get_unit.(args)
+    ModelingToolkit.get_unit(-,args)
 end
 
 sts = @variables a(t)=0 [unit = u"cm"]
@@ -121,14 +121,15 @@ ModelingToolkit.validate(eqs) #Returns false while displaying a warning message
 
 Instead, they should be parameterized:
 
-```julia
+```@example validation3
 using ModelingToolkit, Unitful
 @parameters τ [unit = u"ms"]
 @variables t [unit = u"ms"] E(t) [unit = u"kJ"] P(t) [unit = u"MW"]
 D = Differential(t)
 eqs = [D(E) ~ P - E/τ]
 ModelingToolkit.validate(eqs) #Returns true
-
+```
+```@example validation3
 myfunc(E,τ) = E/τ 
 eqs = [D(E) ~ P - myfunc(E,τ)]
 ModelingToolkit.validate(eqs) #Returns true

docs/src/examples/sparse_jacobians.md

@@ -63,17 +63,22 @@ sparseprob = ODEProblem(sys,Pair[],(0.,11.5),jac=true,sparse=true)
 
 Hard? No! How much did that help?
 
-```julia
+```@example sparsejac
 using BenchmarkTools
-@btime solve(prob,save_everystep=false) # 51.714 s (7317 allocations: 70.12 MiB)
-@btime solve(sparseprob,save_everystep=false) # 2.880 s (55533 allocations: 885.09 MiB)
+@btime solve(prob,save_everystep=false);
+return nothing # hide
+```
+```@example sparsejac
+@btime solve(sparseprob,save_everystep=false);
+return nothing # hide
 ```
 
 Notice though that the analytical solution to the Jacobian can be quite expensive.
 Thus in some cases we may only want to get the sparsity pattern. In this case,
 we can simply do:
 
-```julia
+```@example sparsejac
 sparsepatternprob = ODEProblem(sys,Pair[],(0.,11.5),sparse=true)
-@btime solve(sparsepatternprob,save_everystep=false) # 2.880 s (55533 allocations: 885.09 MiB)
+@btime solve(sparsepatternprob,save_everystep=false);
+return nothing # hide
 ```