{-# LANGUAGE BangPatterns #-} {-| Utility functions for statistical accumulation. -} {- Copyright (C) 2014 Google Inc. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -} module Ganeti.Utils.Statistics ( Statistics , getSumStatistics , getStdDevStatistics , getStatisticValue , updateStatistics ) where import Data.List (foldl') -- | 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 deriving Show -- count, sum, and not the sum of squares---instead the -- computed variance for better precission. -- | Get a statistics that sums up the values. getSumStatistics :: [Double] -> Statistics getSumStatistics = SumStatistics . sum -- | Get a statistics for the standard deviation. getStdDevStatistics :: [Double] -> Statistics getStdDevStatistics xs = let (nt, st) = foldl' (\(n, s) x -> let !n' = n + 1 !s' = s + x in (n', s')) (0, 0) xs mean = st / nt nvar = foldl' (\v x -> let d = x - mean in v + d * d) 0 xs in StdDevStatistics nt st (nvar / nt) -- | Obtain the value of a statistics. getStatisticValue :: Statistics -> Double getStatisticValue (SumStatistics s) = s getStatisticValue (StdDevStatistics _ _ var) = sqrt var -- | 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 -> (Double, Double) -> Statistics updateStatistics (SumStatistics s) (x, y) = SumStatistics $ s + (y - x) updateStatistics (StdDevStatistics n s var) (x, 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'