Merge pull request #84 from JuliaDiffEq/hg/fix/82

Reduce potential for nontermination in Derivative

Author: ChrisRackauckas

README.md

@@ -234,7 +234,8 @@ to better scale to larger systems. You can define derivatives for your own
 function via the dispatch:
 
 ```julia
-ModelingToolkit.Derivative(::typeof(my_function),args,::Val{i})
+# `N` arguments are accepted by the relevant method of `my_function`
+ModelingToolkit.Derivative(::typeof(my_function), args::NTuple{N,Any}, ::Val{i})
 ```
 
 where `i` means that it's the derivative of the `i`th argument. `args` is the
@@ -244,7 +245,7 @@ You should return an `Operation` for the derivative of your function.
 For example, `sin(t)`'s derivative (by `t`) is given by the following:
 
 ```julia
-ModelingToolkit.Derivative(::typeof(sin),args,::Val{1}) = cos(args[1])
+ModelingToolkit.Derivative(::typeof(sin), args::NTuple{1,Any}, ::Val{1}) = cos(args[1])
 ```
 
 ### Macro-free Usage

src/differentials.jl

@@ -7,7 +7,6 @@ Differential(x) = Differential(x,1)
 Base.show(io::IO, D::Differential) = print(io,"($(D.x),$(D.order))")
 Base.convert(::Type{Expr}, D::Differential) = D
 
-function Derivative end
 (D::Differential)(x::Operation) = Operation(D, Expression[x])
 function (D::Differential)(x::Variable)
     D.x === x             && return Constant(1)
@@ -33,11 +32,7 @@ end
 expand_derivatives(x) = x
 
 # Don't specialize on the function here
-function Derivative(O::Operation,idx)
-    # This calls the Derivative dispatch from the user or pre-defined code
-    Derivative(O.op, O.args, Val(idx))
-end
-Derivative(op, args, idx) = Derivative(op, (args...,), idx)
+Derivative(O::Operation, idx) = Derivative(O.op, (O.args...,), Val(idx))
 
 # Pre-defined derivatives
 import DiffRules, SpecialFunctions, NaNMath

test/derivatives.jl

@@ -17,8 +17,8 @@ dcsch = D(csch(t))
 dsinsin = D(sin(sin(t)))
 @test expand_derivatives(dsinsin) == cos(sin(t))*cos(t)
 # Binary
-dpow1 = Derivative(^,[x, y],Val(1))
-dpow2 = Derivative(^,[x, y],Val(2))
+dpow1 = Derivative(^, (x, y), Val(1))
+dpow2 = Derivative(^, (x, y), Val(2))
 @test dpow1 == y*x^(y-1)
 @test dpow2 == x^y*log(x)