September 2017 Update

Task/Numeric-error-propagation/Julia/numeric-error-propagation.julia

@@ -0,0 +1,59 @@
+module NumericError
+
+import Base: convert, promote_rule, +, -, *, /, ^
+
+export Measure
+
+type Measure <: Number
+  x::Float64
+  σ::Float64
+  Measure(x::Real) = new(Float64(x), 0)
+  Measure(x::Real, σ::Real) = new(Float64(x), σ)
+end
+
+Base.show(io::IO, x::Measure) = print(io, string(x.x, " ± ", x.σ))
+
+Base.convert(::Type{Measure}, x::Real) = Measure(Float64(x), 0.0)
+Base.promote_rule(::Type{Float64}, ::Type{Measure}) = Measure
+Base.promote_rule(::Type{Int64}, ::Type{Measure}) = Measure
+
++(a::Measure, b::Measure) = Measure(a.x + b.x, sqrt(a.σ ^ 2 + b.σ ^ 2))
+-(a::Measure, b::Measure) = Measure(a.x - b.x, sqrt(a.σ ^ 2 + b.σ ^ 2))
+-(a::Measure) = Measure(-a.x, a.σ)
+
+*(a::Measure, b::Measure) = begin
+  x = a.x * b.x
+  σ = sqrt(x ^ 2 * ((a.σ / a.x) ^ 2 + (b.σ / b.x) ^ 2))
+  Measure(x, σ)
+end
+/(a::Measure, b::Measure) = begin
+  x = a.x / b.x
+  σ = sqrt(x ^ 2 * ((a.σ / a.x) ^ 2 + (b.σ / b.x) ^ 2))
+  Measure(x, σ)
+end
+
+^(a::Measure, b::Float64) = begin
+  x = a.x ^ b
+  σ = abs(x * b * a.σ / a.x)
+  Measure(x, σ)
+end
+
+Base.sqrt(a::Measure) = a ^ .5
+
+end  # module NumericError
+
+using NumericError
+
+# x1 = 100 ± 1.1
+# y1 = 50 ± 1.2
+# x2 = 200 ± 2.2
+# y2 = 100 ± 2.3
+
+x1 = Measure(100, 1.1)
+y1 = Measure(50,  1.2)
+x2 = Measure(200, 2.2)
+y2 = Measure(100, 2.3)
+
+d = sqrt((x1 - x2) ^ 2 + (y1 - y2) ^ 2)
+
+@show x1 y1 x2 y2 sqrt((x1 - x2) ^ 2 + (y1 - y2) ^ 2)