Faster normal cdf encoding (#399)

* Remove QuadGK, add StatsFuns instead

For computing normal cdf

* QuadGK is still needed for Schurmann estimator

Author: kahaaga

Project.toml

@@ -2,7 +2,7 @@ name = "ComplexityMeasures"
 uuid = "ab4b797d-85ee-42ba-b621-05d793b346a2"
 authors = "Kristian Agasøster Haaga <kahaaga@gmail.com>, George Datseries <datseris.george@gmail.com>"
 repo = "https://github.com/juliadynamics/ComplexityMeasures.jl.git"
-version = "3.4.2"
+version = "3.4.3"
 
 [deps]
 Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
@@ -20,6 +20,7 @@ StateSpaceSets = "40b095a5-5852-4c12-98c7-d43bf788e795"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
+StatsFuns = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
 Wavelets = "29a6e085-ba6d-5f35-a997-948ac2efa89a"
 
 [compat]
@@ -28,12 +29,13 @@ DelayEmbeddings = "2.6"
 Distances = "0.9, 0.10"
 FFTW = "1"
 Neighborhood = "0.2.4"
-QuadGK = "2"
+QuadGK = "2.9"
 Reexport = "1"
 SpecialFunctions = "0.10, 1.0, 2"
 StateSpaceSets = "1.0.4"
 StaticArrays = "0.12, 1.0"
 Statistics = "1"
 StatsBase = "0.33, 0.34"
+StatsFuns = "1.3"
 Wavelets = "0.10"
 julia = "1.5"

src/encoding_implementations/gaussian_cdf.jl

@@ -1,4 +1,5 @@
-using Statistics, QuadGK
+using Statistics
+using StatsFuns: normcdf
 
 export GaussianCDFEncoding
 
@@ -120,15 +121,9 @@ end
 gaussian(x, μ, σ) = exp((-(x - μ)^2)/(2σ^2))
 
 function encode(encoding::GaussianCDFEncoding, x::Real)
-    σ, μ = encoding.σ, encoding.μ
-    # We only need the value of the integral (not the error), so
-    # index first element returned from quadgk
-    k = 1/(σ*sqrt(2π))
-    y = k * first(quadgk(x -> gaussian(x, μ, σ), -Inf, x))
-    # The integral estimate sometime returns a value slightly above 1.0, so we need
-    # to adjust to be sure that all points fall within the FixedRectangularBinning.
-    y_corrected = min(y, 1.0)
-    return encode(encoding.binencoder, y_corrected)
+    binencoder, σ, μ = encoding.binencoder, encoding.σ, encoding.μ
+    
+    return encode(binencoder, normcdf(μ, σ, x))
 end
 
 function encode(encoding::GaussianCDFEncoding{m}, x::AbstractVector) where m