Cumulative standard deviation: Difference between revisions

Or as a map-accumulation:

<lang applescript>-------------- CUMULATIVE STANDARD DEVIATION -------------

-- cumulativeStdDevns :: [Float] -> [Float]

on cumulativeStdDevns(xs)

script go

on |λ|(sq, x, i)

set {s, q} to sq

set _s to x + s

set _q to q + (x ^ 2)

{{_s, _q}, ((_q / i) - ((_s / i) ^ 2)) ^ 0.5}

end |λ|

end script

item 2 of mapAccumL(go, {0, 0}, xs)

end cumulativeStdDevns

--------------------------- TEST -------------------------

on run

cumulativeStdDevns({2, 4, 4, 4, 5, 5, 7, 9})

end run

------------------------- GENERIC ------------------------

-- foldl :: (a -> b -> a) -> a -> [b] -> a

on foldl(f, startValue, xs)

tell mReturn(f)

set v to startValue

set lng to length of xs

repeat with i from 1 to lng

set v to |λ|(v, item i of xs, i, xs)

end repeat

return v

end tell

end foldl

-- mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])

on mapAccumL(f, acc, xs)

-- 'The mapAccumL function behaves like a combination of map and foldl;

-- it applies a function to each element of a list, passing an

-- accumulating parameter from |Left| to |Right|, and returning a final

-- value of this accumulator together with the new list.' (see Hoogle)

script

on |λ|(a, x, i)

tell mReturn(f) to set pair to |λ|(item 1 of a, x, i)

{item 1 of pair, (item 2 of a) & {item 2 of pair}}

end |λ|

end script

foldl(result, {acc, []}, xs)

end mapAccumL

-- mReturn :: First-class m => (a -> b) -> m (a -> b)

on mReturn(f)

-- 2nd class handler function lifted into 1st class script wrapper.

if script is class of f then

f

else

script

property |λ| : f

end script

end if

end mReturn</lang>

{{Out}}

<pre>{0.0, 1.0, 0.942809041582, 0.866025403784, 0.979795897113, 1.0, 1.399708424448, 2.0}</pre>