src/Ganeti/Utils/Statistics.hs

{-# LANGUAGE BangPatterns #-}


{-| Utility functions for statistical accumulation. -}

{-

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module Ganeti.Utils.Statistics
  ( Statistics
  , TagTagMap
  , AggregateComponent(..)
  , getSumStatistics
  , getStdDevStatistics
  , getMapStatistics
  , getStatisticValue
  , updateStatistics
  ) where

import qualified Data.Foldable as Foldable
import Data.List (foldl')
import qualified Data.Map as Map

-- | Type to store the number of instances for each exclusion and location
-- pair. This is necessary to calculate second component of location score.
type TagTagMap = Map.Map (String, String) Int

-- | Abstract type of statistical accumulations. They behave as if the given
-- statistics were computed on the list of values, but they allow a potentially
-- more efficient update of a given value.
data Statistics = SumStatistics Double
                | StdDevStatistics Double Double Double
                  -- count, sum, and not the sum of squares---instead the
                  -- computed variance for better precission.
                | MapStatistics TagTagMap deriving Show

-- | Abstract type of per-node statistics measures. The SimpleNumber is used
-- to construct SumStatistics and StdDevStatistics while SpreadValues is used
-- to construct MapStatistics.
data AggregateComponent = SimpleNumber Double
                        | SpreadValues TagTagMap
-- Each function below depends on the contents of AggregateComponent but it's
-- necessary to define each function as a function processing both
-- SimpleNumber and SpreadValues instances (see Metrics.hs). That's why
-- pattern matches for invalid type defined as functions which change nothing.

-- | Get a statistics that sums up the values.
getSumStatistics :: [AggregateComponent] -> Statistics
getSumStatistics xs =
  let addComponent s (SimpleNumber x) =
        let !s' = s + x
        in s'
      addComponent s _ = s
      st = foldl' addComponent 0 xs
  in SumStatistics st

-- | Get a statistics for the standard deviation.
getStdDevStatistics :: [AggregateComponent] -> Statistics
getStdDevStatistics xs =
  let addComponent (n, s) (SimpleNumber x) =
        let !n' = n + 1
            !s' = s + x
        in (n', s')
      addComponent (n, s) _ = (n, s)
      (nt, st) = foldl' addComponent (0, 0) xs
      mean = st / nt
      center (SimpleNumber x) = x - mean
      center _ = 0
      nvar = foldl' (\v x -> let d = center x in v + d * d) 0 xs
  in StdDevStatistics nt st (nvar / nt)

-- | Get a statistics for the standard deviation.
getMapStatistics :: [AggregateComponent] -> Statistics
getMapStatistics xs =
  let addComponent m (SpreadValues x) =
        let !m' = Map.unionWith (+) m x
        in m'
      addComponent m _ = m
      mt = foldl' addComponent Map.empty xs
  in MapStatistics mt

-- | Obtain the value of a statistics.
getStatisticValue :: Statistics -> Double
getStatisticValue (SumStatistics s) = s
getStatisticValue (StdDevStatistics _ _ var) = sqrt var
getStatisticValue (MapStatistics m) = fromIntegral $ Foldable.sum m - Map.size m
-- Function above calculates sum (N_i - 1) over each map entry.

-- | In a given statistics replace on value by another. This
-- will only give meaningful results, if the original value
-- was actually part of the statistics.
updateStatistics :: Statistics -> (AggregateComponent, AggregateComponent) ->
                    Statistics
updateStatistics (SumStatistics s) (SimpleNumber x, SimpleNumber y) =
  SumStatistics $ s + (y - x)
updateStatistics (StdDevStatistics n s var) (SimpleNumber x, SimpleNumber y) =
  let !ds = y - x
      !dss = y * y - x * x
      !dnnvar = (n * dss - 2 * s * ds) - ds * ds
      !s' = s + ds
      !var' = max 0 $ var + dnnvar / (n * n)
  in StdDevStatistics n s' var'
updateStatistics (MapStatistics m) (SpreadValues x, SpreadValues y) =
  let nm = Map.unionWith (+) (Map.unionWith (-) m x) y
  in MapStatistics nm
updateStatistics s _ = s