Various fixes (#72)

- Fix intervals in `sqrt`
- Fix derivatives for `sigmoid` and `bisigmoid`
- Add more `MC` constructors

Author: DimitriAlston

Project.toml

@@ -1,7 +1,7 @@
 name = "McCormick"
 uuid = "53c679d3-6890-5091-8386-c291e8c8aaa1"
 authors = ["Matthew Wilhelm <[email protected]>"]
-version = "0.13.10"
+version = "0.13.11"
 
 [deps]
 DiffRules = "b552c78f-8df3-52c6-915a-8e097449b14b"

src/McCormick.jl

@@ -363,6 +363,7 @@ function MC{N,T}(cv::Float64, cc::Float64) where {N, T <: RelaxTag}
     MC{N,T}(cv, cc, Interval{Float64}(cv, cc), zero(SVector{N,Float64}),
                                                zero(SVector{N,Float64}), true)
 end
+MC{N,T}(cv::Q, cc::R) where {N, T <: RelaxTag, Q <: NumberNotRelax, R <: NumberNotRelax} = MC{N,T}(Float64(cv), Float64(cc))
 
 """
 MC{N,T}(cv::Float64, cc::Float64, Intv::Interval{Float64})
@@ -374,6 +375,7 @@ function MC{N,T}(cv::Float64, cc::Float64, Intv::Interval{Float64}) where {N, T
     MC{N,T}(cv, cc, Intv, zero(SVector{N,Float64}),
                           zero(SVector{N,Float64}), true)
 end
+MC{N,T}(cv::Q, cc::R, Intv::Interval{Float64}) where {N, T <: RelaxTag, Q <: NumberNotRelax, R <: NumberNotRelax} = MC{N,T}(Float64(cv), Float64(cc), Intv)
 
 """
 MC{N,T}(val::Float64, Intv::Interval{Float64}, i::Int64)
@@ -385,6 +387,7 @@ with a nonzero ith dimension of length N.
 function MC{N,T}(val::Float64, Intv::Interval{Float64}, i::Int64) where {N, T <: RelaxTag}
     MC{N,T}(val, val, Intv, seed_gradient(i, Val{N}()), seed_gradient(i, Val{N}()), false)
 end
+MC{N,T}(val::Q, Intv::Interval{Float64}, i::Int64) where {N, T <: RelaxTag, Q <: NumberNotRelax} = MC{N,T}(Float64(val), Intv, i)
 function MC{N,T}(x::MC{N,T}) where {N, T <: RelaxTag}
     MC{N,T}(x.cv, x.cc, x.Intv, x.cv_grad, x.cc_grad, x.cnst)
 end

src/forward_operators/activation_functions.jl

@@ -298,7 +298,13 @@ sigmoid
 The `sigmoid` activation function `sigmoid(x) = 1.0/(1.0 + exp(-x))`.
 =#
 @inline sigmoid(x::Interval{Float64}) = 1.0/(1.0 + exp(-x))
-@inline sigmoid_deriv(x::Float64) = exp(-x)/(1.0 + exp(-x))^2
+@inline function sigmoid_deriv(x::Float64)
+    if isinf(exp(-x))
+        return 0.0
+    else
+        return exp(-x)/(1.0 + exp(-x))^2
+    end
+end
 @inline sigmoid_deriv2(x::Float64) = -exp(x)*(exp(x) - 1.0)/(exp(x) + 1.0)^3
 @inline function sigmoid_env(x::Float64, y::Float64, z::Float64)
     (x - y)*sigmoid_deriv(x) - (sigmoid(x) - sigmoid(y))
@@ -338,7 +344,13 @@ The `bisigmoid` activation function `bisigmoid(x) = (1.0 - exp(-x))/(1.0 + exp(-
     xUc = (1.0 - exp(-xUintv))/(1.0 + exp(-xUintv))
     return Interval(xLc.hi, xUc.hi)
 end
-@inline bisigmoid_deriv(x::Float64) = 2.0*exp(x)/(exp(x) + 1.0)^2
+@inline function bisigmoid_deriv(x::Float64)
+    if isinf(exp(-x))
+        return 0.0
+    else
+        return 2.0*exp(x)/(exp(x) + 1.0)^2
+    end
+end
 @inline function bisigmoid_deriv2(x::Float64)
     term1 = exp(-x)/(exp(-x) + 1.0)
     term2 = 2.0*exp(-2.0*x)/(exp(-x) + 1.0)^2

src/forward_operators/concave_increasing.jl

@@ -97,14 +97,14 @@ end
 
 @inline function sqrt_kernel(x::MC{N, T}, z::Interval{Float64}) where {N, T<:Union{NS, MV}}
      isempty(x) && (return empty(x))
-     (x.Intv.lo < 0.0 || x.Intv.hi < 0.0) && (return nan(MC{N,T}))
+     (x.Intv.lo < 0.0 || x.Intv.hi < 0.0) && (return MC{N,T}(NaN, NaN, z, fill(0, SVector{N,Float64}), fill(0, SVector{N,Float64}), x.cnst))
      xLc = z.lo
      xUc = z.hi
      xL = x.Intv.lo
      xU = x.Intv.hi
      midcc, cc_id = mid3(x.cc, x.cv, xU)
      midcv, cv_id = mid3(x.cc, x.cv, xL)
-     dcv = (xUc > xLc) ? (xUc - xLc)/(xU - xL) : 0.0
+     dcv = (xUc > xLc && !isinf(xUc)) ? (xUc - xLc)/(xU - xL) : 0.0
      convex = dcv*(midcv - xL) + xLc
      concave = NaNMath.sqrt(midcc)
      concave_grad = mid_grad(x.cc_grad, x.cv_grad, cc_id)*(0.5/NaNMath.sqrt(x.cv))