{-# LANGUAGE FlexibleContexts #-}
-- |
-- Module : Statistics.Sample.Normalize
-- Copyright : (c) 2017 Gregory W. Schwartz
-- License : BSD3
--
-- Maintainer : gsch@mail.med.upenn.edu
-- Stability : experimental
-- Portability : portable
--
-- Functions for normalizing samples.
module Statistics.Sample.Normalize
(
standardize
) where
import Statistics.Sample
import qualified Data.Vector.Generic as G
import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Storable as S
-- | /O(n)/ Normalize a sample using standard scores:
--
-- \[ z = \frac{x - \mu}{\sigma} \]
--
-- Where μ is sample mean and σ is standard deviation computed from
-- unbiased variance estimation. If sample to small to compute σ or
-- it's equal to 0 @Nothing@ is returned.
standardize :: (G.Vector v Double) => v Double -> Maybe (v Double)
standardize xs
| G.length xs < 2 = Nothing
| sigma == 0 = Nothing
| otherwise = Just $ G.map (\x -> (x - mu) / sigma) xs
where
mu = mean xs
sigma = stdDev xs
{-# INLINABLE standardize #-}
{-# SPECIALIZE standardize :: V.Vector Double -> Maybe (V.Vector Double) #-}
{-# SPECIALIZE standardize :: U.Vector Double -> Maybe (U.Vector Double) #-}
{-# SPECIALIZE standardize :: S.Vector Double -> Maybe (S.Vector Double) #-}