Add support to calculate analytical derivative of ifelse function (assuming it was used to define piecewise functions).

Use inline expression instead of parse for differentiation of ifelse funtion

Author: Alejandro Morales Sierra

src/differentiate.jl

@@ -242,6 +242,11 @@ end
 ## hypot 
 ## beta, lbeta, eta, zeta, digamma
 
+## Differentiate for piecewise functions defined using ifelse
+function differentiate(::SymbolParameter{:ifelse}, args, wrt)
+	:(ifelse($(args[1]), $(differentiate(args[2],wrt)),$(differentiate(args[3],wrt))))
+end
+
 function differentiate(ex::Expr, targets::Vector{Symbol})
     n = length(targets)
     exprs = Array(Any, n)

test/symbolic.jl

@@ -91,3 +91,10 @@ end
 @test isequal(simplify(:(x*3)), :(*(3,x)))
 @test isequal(simplify(:(x*3*4)), :(*(12,x)))
 @test isequal(simplify(:(2*y*x*3)), :(*(6,y,x)))
+
+#
+# Tests with ifelse
+#
+@test isequal(differentiate(:(ifelse(x < 1, exp(x^2), 1/x)), :x), :(ifelse(x < 1,2x * exp(x^2), -1/x^2)))
+@test isequal(differentiate(:(ifelse(x <= 0, 0, ifelse(x > 1, 1, x))), : x), 
+														:(ifelse(x <= 0, 0, ifelse(x > 1, 0, 1))))