Cumulative standard deviation: Difference between revisions

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+Or, as a map-accumulation over an indexed list
-Or, simply accumulating across a fold:
-{{Trans|AppleScript}}
-<lang Haskell>type Index = Int
+<lang Haskell>import Data.List (mapAccumL)
-type DataPoint = Float
+-------------- CUMULATIVE STANDARD DEVIATION -------------
-type Sum = Float
+cumulativeStdDevns :: [Float] -> [Float]
-type SumOfSquares = Float
+cumulativeStdDevns xs = snd $ mapAccumL go (0, 0) $ zip [1 ..] xs
-type Deviations = [Float]
-type Accumulator = (Sum, SumOfSquares, Deviations)
-stdDevInc :: Accumulator -> (DataPoint, Index) -> Accumulator
-stdDevInc (s, q, ds) (x, i) = (_s, _q, _ds)
   where
-    _s = s + x
+    go (s, q) (i, x) =
-    _q = q + (x ^ 2)
+      let _s = s + x
-    _i = fromIntegral i
+          _q = q + (x ^ 2)
-    _ds = ds ++ [sqrt ((_q / _i) - ((_s / _i) ^ 2))]
+          _i = fromIntegral i
+      in ((_s, _q), sqrt ((_q / _i) - ((_s / _i) ^ 2)))
-sample :: [DataPoint]
-sample = [2, 4, 4, 4, 5, 5, 7, 9]
--- The Prelude definition of foldl' --'
+--------------------------- TEST -------------------------
--- adjusted to avoid wiki formatting glitches.
-foldl_ :: Foldable t => (b -> a -> b) -> b -> t a -> b
-foldl_ f z0 xs = foldr f_ id xs z0
-  where f_ x k z = k $! f z x
 main :: IO ()
-main = mapM_ print devns
+main = mapM_ print $ cumulativeStdDevns [2, 4, 4, 4, 5, 5, 7, 9]</lang>
-  where
-    (_, _, devns) = foldl_ stdDevInc (0, 0, []) $ zip sample [1 .. ]</lang>
 {{Out}}
 <pre>0.0