normaldistribution 1.0 → 1.1

raw patch · 2 files changed

+44/−40 lines, 2 files

Files

• Data/Random/Normal.hs +38/−36
• normaldistribution.cabal +6/−4

@@ -35,9 +35,11 @@ > sample    <- normalIO'  (mean,sigma) > samples   <- normalsIO' (mean,sigma) -Internally the library uses the Central Limit Theorem to approximate-normally distributed values from multiple uniformly distributed-random values.+Internally the library uses the Box-Muller method to generate+normally distributed values from uniformly distributed random values.+If more than one sample is needed taking samples off an infinite+list (created by e.g. 'normals') will be roughly twice as efficient+as repetedly generating individual samples with e.g. 'normal'.  -} @@ -69,51 +71,62 @@  -- Normal distribution approximation -- ------------------------------------ | Central limit theorem for approximating normally distributed--- sampling. Takes a list of no less than twelve random uniformly--- distributed samples in the range [0,1] and uses the first twelve--- samples to approximate a normally distributed random sample with--- mean 0 and standard deviation 1.-centralLimitTheorem :: Fractional a => [a] -> a-centralLimitTheorem ss = sum (take 12 ss) - 6+-- | Box-Muller method for generating two normally distributed+-- independent random values from two uniformly distributed+-- independent random values.+boxMuller :: Floating a => a -> a -> (a,a)+boxMuller u1 u2 = (r * cos t, r * sin t) where r = sqrt (-2 * log u1)+                                               t = 2 * pi * u2 +-- | Convert a list of uniformly distributed random values into a+-- list of normally distributed random values. The Box-Muller+-- algorithms converts values two at a time, so if the input list+-- has an uneven number of element the last one will be discarded.+boxMullers :: Floating a => [a] -> [a]+boxMullers (u1:u2:us) = n1:n2:boxMullers us where (n1,n2) = boxMuller u1 u2+boxMullers _          = [] + -- API -- === -- | Takes a random number generator g, and returns a random value -- normally distributed with mean 0 and standard deviation 1, -- together with a new generator. This function is ananalogous to -- 'Random.random'.-normal :: (RandomGen g, Random a, Fractional a) => g -> (a,g)-normal g = (centralLimitTheorem as, g')+normal :: (RandomGen g, Random a, Floating a) => g -> (a,g)+normal g0 = (fst $ boxMuller u1 u2, g2)   -- While The Haskell 98 report says "For fractional types, the   -- range is normally the semi-closed interval [0,1)" we will   -- specify the range explicitely just to be sure.-  where (g',as) = iterateN 12 (swap . randomR (0,1)) g+  where+     (u1,g1) = randomR (0,1) g0+     (u2,g2) = randomR (0,1) g1  -- | Plural variant of 'normal', producing an infinite list of -- random values instead of returning a new generator. This function -- is ananalogous to 'Random.randoms'.-normals :: (RandomGen g, Random a, Fractional a) => g -> [a]-normals g = x:normals g' where (x,g') = normal g+normals :: (RandomGen g, Random a, Floating a) => g -> [a]+normals = boxMullers . randoms  -- | Creates a infinite list of normally distributed random values -- from the provided random generator seed. (In the implementation -- the seed is fed to 'Random.mkStdGen' to produce the random -- number generator.)-mkNormals :: (Random a, Fractional a) => Int -> [a]+mkNormals :: (Random a, Floating a) => Int -> [a] mkNormals = normals . mkStdGen   -- | A variant of 'normal' that uses the global random number -- generator. This function is analogous to 'Random.randomIO'.-normalIO :: (Random a, Fractional a) => IO a-normalIO = fmap centralLimitTheorem $ mapM randomRIO $ repeat (0,1)+normalIO :: (Random a, Floating a) => IO a+normalIO = do u1 <- randomRIO (0,1)+              u2 <- randomRIO (0,1)+              return $ fst $ boxMuller u1 u2  -- | Creates a infinite list of normally distributed random values -- using the global random number generator. (In the implementation -- 'Random.newStdGen' is used.)-normalsIO :: (Random a, Fractional a) => IO [a]+normalsIO :: (Random a, Floating a) => IO [a] normalsIO = fmap normals newStdGen  @@ -121,37 +134,26 @@ -- -------------------------------- -- | Analogous to 'normal' but uses the supplied (mean, standard -- deviation).-normal' :: (RandomGen g, Random a, Fractional a) => (a,a) -> g -> (a,g)+normal' :: (RandomGen g, Random a, Floating a) => (a,a) -> g -> (a,g) normal' (mean, sigma) g = (x * sigma + mean, g') where (x, g') = normal g  -- | Analogous to 'normals' but uses the supplied (mean, standard -- deviation).-normals' :: (RandomGen g, Random a, Fractional a) => (a,a) -> g -> [a]+normals' :: (RandomGen g, Random a, Floating a) => (a,a) -> g -> [a] normals' (mean, sigma) g = map (\x -> x * sigma + mean) (normals g)  -- | Analogous to 'mkNormals' but uses the supplied (mean, standard -- deviation).-mkNormals' :: (Random a, Fractional a) => (a,a) -> Int -> [a]-mkNormals' ms= normals' ms . mkStdGen+mkNormals' :: (Random a, Floating a) => (a,a) -> Int -> [a]+mkNormals' ms = normals' ms . mkStdGen   -- | Analogous to 'normalIO' but uses the supplied (mean, standard -- deviation).-normalIO' ::(Random a, Fractional a) => (a,a) -> IO a+normalIO' ::(Random a, Floating a) => (a,a) -> IO a normalIO' (mean,sigma) = fmap (\x -> x * sigma + mean) normalIO  -- | Analogous to 'normalsIO' but uses the supplied (mean, standard -- deviation).-normalsIO' :: (Random a, Fractional a) => (a,a) -> IO [a]+normalsIO' :: (Random a, Floating a) => (a,a) -> IO [a] normalsIO' ms = fmap (normals' ms) newStdGen----- Helpers--- ---------- | Swap the elements in a tuple.-swap :: (a,b) -> (b,a)-swap (x,y) = (y,x)---- | Iterate on the accumulator a specified number of times.-iterateN :: Int -> (acc -> (acc, x)) -> acc -> (acc, [x])-iterateN n f a0 = mapAccumL (\a _ -> f a) a0 [1..n]

@@ -1,5 +1,5 @@ Name:                normaldistribution-Version:             1.0+Version:             1.1 License:             BSD3 License-File:        LICENSE Copyright:           Bjorn Buckwalter 2011@@ -43,9 +43,11 @@     > sample    <- normalIO'  (mean,sigma)     > samples   <- normalsIO' (mean,sigma)     .-    Internally the library uses the Central Limit Theorem to-    approximate normally distributed values from multiple uniformly-    distributed random values.+    Internally the library uses the Box-Muller method to generate+    normally distributed values from uniformly distributed random values.+    If more than one sample is needed taking samples off an infinite+    list (created by e.g. 'normals') will be roughly twice as efficient+    as repetedly generating individual samples with e.g. 'normal'.  Category:            Math, Statistics Build-Type:          Simple