NumHask.Space.Histogram

A histogram, if you squint, is a series of contiguous Ranges, annotated with values.

Documentation

data Histogram

This Histogram is a list of contiguous boundaries (a boundary being the lower edge of one bucket and the upper edge of another), and a value (usually a count) for each bucket, represented here as a map

Overs and Unders are contained in key = 0 and key = length cuts Intervals are defined as (l,u]

Constructors

Histogram

Fields

• cuts :: Vector Double
• values :: Map Int Double

Instances

Show Histogram

Defined in NumHask.Space.Histogram

Methods

showsPrec :: Int -> Histogram -> ShowS

show :: Histogram -> String

showList :: [Histogram] -> ShowS

Eq Histogram

Defined in NumHask.Space.Histogram

Methods

(==) :: Histogram -> Histogram -> Bool

(/=) :: Histogram -> Histogram -> Bool

emptyHistogram :: Histogram

A histogram with no cuts nor data.

data DealOvers

Whether or not to ignore unders and overs. If overs and unders are dealt with, IncludeOvers supplies an assumed width for the outer buckets.

Constructors

IgnoreOvers

IncludeOvers Double

fill :: Foldable f => [Double] -> f Double -> Histogram

Fill a Histogram using pre-specified cuts

>>> fill [0,50,100] [0..99]
Histogram {cuts = [0.0,50.0,100.0], values = fromList [(1,50.0),(2,50.0)]}

cutI :: Ord a => Vector a -> a -> Int

find the index of the bucket the value is contained in.

regular :: Int -> [Double] -> Histogram

Make a histogram using n equally spaced cuts over the entire range of the data

>>> regular 4 [0..100]
Histogram {cuts = [0.0,25.0,50.0,75.0,100.0], values = fromList [(1,25.0),(2,25.0),(3,25.0),(4,25.0),(5,1.0)]}

makeRects :: DealOvers -> Histogram -> [Rect Double]

Transform a Histogram to Rects

>>> makeRects IgnoreOvers (regular 4 [0..100])
[Rect 0.0 25.0 0.0 0.25,Rect 25.0 50.0 0.0 0.25,Rect 50.0 75.0 0.0 0.25,Rect 75.0 100.0 0.0 0.25]

regularQuantiles :: Double -> [Double] -> [Double]

approx regular n-quantiles

>>> regularQuantiles 4 [0..100]
[0.0,24.75,50.0,75.25,100.0]

quantileFold :: [Double] -> [Double] -> [Double]

one-pass approximate quantiles fold

freq :: Histogram -> Histogram

normalize a histogram

\h -> sum (values $ freq h) == one

>>> freq $ fill [0,50,100] [0..99]
Histogram {cuts = [0.0,50.0,100.0], values = fromList [(1,0.5),(2,0.5)]}

average :: Foldable f => f Double -> Double

average

>>> average [0..1000]
500.0

quantiles :: Foldable f => Int -> f Double -> [Double]

Regularly spaced (approx) quantiles

>>> quantiles 5 [1..1000]
[1.0,200.5,400.5,600.5000000000001,800.5,1000.0]

quantile :: Foldable f => Double -> f Double -> Double

single (approx) quantile

>>> quantile 0.1 [1..1000]
100.5