Minor fixes

Author: eeshan9815

src/slopes.jl

@@ -4,19 +4,13 @@ import Base: +, -, *, /, ^, sqrt, exp, log, sin, cos, tan, asin, acos, atan
 import IntervalArithmetic: mid, interval
 
 function slope(f::Function, x::Interval, c::Number)
-    try
-        f(slope_var(x, c)).s
-    catch y
-        if isa(y, MethodError)
-            ForwardDiff.derivative(f, x)
-        end
-    end
+    f(slope_var(x, c)).s
 end
 
 struct Slope{T}
-    x::Interval{T}
-    c::Interval{T}
-    s::Interval{T}
+    x::Interval{T}  # Interval on which slope is evaluated
+    c::Interval{T}  # Point about which slope is evaluated (Interval to get bounded rounding errors)
+    s::Interval{T}  # Variable which propogates the slope information
 end
 
 Slope(c) = Slope(c, c, 0)

test/slopes.jl

@@ -12,19 +12,19 @@ end
 @testset "Automatic slope expansion" begin
     for T in [Float64, BigFloat]
         s = interval(T(0.75), T(1.75))
-        rts = Slopes{T}[]
-        push!(rts, Slopes(x->((x + sin(x)) * exp(-x^2)), s, mid(s), interval(T(-2.8), T(0.1))))
-        push!(rts, Slopes(x->(x^4 - 10x^3 + 35x^2 - 50x + 24), s, mid(s), interval(T(-44), T(38.5))))
-        push!(rts, Slopes(x->((log(x + 1.25) - 0.84x) ^ 2), s, mid(s), interval(T(-0.16), T(0.44))))
-        push!(rts, Slopes(x->(0.02x^2 - 0.03exp(-(20(x - 0.875))^2)), s, mid(s), interval(T(0.03), T(0.33))))
-        push!(rts, Slopes(x->(exp(x^2)), s, mid(s), interval(T(6.03), T(33.23))))
-        push!(rts, Slopes(x->(x^4 - 12x^3 + 47x^2 - 60x - 20exp(-x)), s, mid(s), interval(T(-39), T(65.56))))
-        push!(rts, Slopes(x->(x^6 - 15x^4 + 27x^2 + 250), s, mid(s), interval(T(-146.9), T(67.1))))
-        push!(rts, Slopes(x->(atan(cos(tan(x)))), s, mid(s), interval(T(1), T(2))))
-        push!(rts, Slopes(x->(asin(cos(acos(sin(x))))), s, mid(s), interval(T(1.36), T(∞))))
+        example = Slopes{T}[]
+        push!(example, Slopes(x->((x + sin(x)) * exp(-x^2)), s, mid(s), interval(T(-2.8), T(0.1))))
+        push!(example, Slopes(x->(x^4 - 10x^3 + 35x^2 - 50x + 24), s, mid(s), interval(T(-44), T(38.5))))
+        push!(example, Slopes(x->((log(x + 1.25) - 0.84x) ^ 2), s, mid(s), interval(T(-0.16), T(0.44))))
+        push!(example, Slopes(x->(0.02x^2 - 0.03exp(-(20(x - 0.875))^2)), s, mid(s), interval(T(0.03), T(0.33))))
+        push!(example, Slopes(x->(exp(x^2)), s, mid(s), interval(T(6.03), T(33.23))))
+        push!(example, Slopes(x->(x^4 - 12x^3 + 47x^2 - 60x - 20exp(-x)), s, mid(s), interval(T(-39), T(65.56))))
+        push!(example, Slopes(x->(x^6 - 15x^4 + 27x^2 + 250), s, mid(s), interval(T(-146.9), T(67.1))))
+        push!(example, Slopes(x->(atan(cos(tan(x)))), s, mid(s), interval(T(1), T(2))))
+        push!(example, Slopes(x->(asin(cos(acos(sin(x))))), s, mid(s), interval(T(1.36), T(∞))))
 
-        for i in 1:length(rts)
-                @test slope(rts[i].f, rts[i].x, rts[i].c) ⊆ rts[i].sol
+        for i in 1:length(example)
+            @test slope(example[i].f, example[i].x, example[i].c) ⊆ example[i].sol
         end
     end
 end