Sound.SC3.Lang.Random.Lorrain_1980

Denis Lorrain. "A Panoply of Stochastic 'Cannons'". Computer Music Journal, 4(1):53-81, Spring 1980.

Documentation

linear :: Floating a => a -> a -> a

§4.3.1 (g=1)

import System.Random
let r = take 32768 (randomRs (0.0,1.0) (mkStdGen 12345))

import Sound.SC3.Plot
import Sound.SC3.Plot.Histogram
let h = plotHistogram . map (histogram 512)

h [map (linear 1.0) r]

exponential :: Floating a => a -> a -> a

§4.3.2 (δ=[0.5,1,2])

h (map (\d -> map (exponential d) r) [0.5,1,2])

cauchy :: Floating a => a -> a -> a

§4.3.5 (τ=1)

h [map (cauchy 1.0) r]

import Data.Maybe
let narrow z n = if n < -z || n > z then Nothing else Just n
h [mapMaybe (narrow 10 . cauchy 1.0) r]

cauchy' :: Floating a => Bool -> a -> a -> a

§4.3.5 (iopt=False,τ=1) (Algorithm 10)

h [mapMaybe (narrow 20 . cauchy' False 1.0) r]
h [mapMaybe (narrow 20 . cauchy' True 1.0) r]

hyperbolic_cosine :: Floating a => a -> a

§4.3.6

h [map hyperbolic_cosine r]

logistic :: Floating a => a -> a -> a -> a

§4.3.7 (β=0,α=1)

h [map (logistic 0.0 1.0) r]

arc_sine :: Floating a => a -> a

§4.3.8

h [map arc_sine r]

beta :: (Floating a, Ord a) => a -> a -> (a, a) -> Maybe a

§4.4.2 (Algorithm 15)

let adj l = case l of {[] -> []; p:q:l' -> (p,q) : adj l'}
let r' = adj r
h [mapMaybe (beta 0.45 0.45) r'
  ,mapMaybe (beta 0.65 0.45) r'
  ,mapMaybe (beta 0.45 0.65) r']

h [mapMaybe (beta 0.35 0.5) r'
  ,mapMaybe (beta 0.5 0.65) r']