-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | Numerical spaces.
--
-- numhask-space provides support for spaces where space
-- is defined as a set of numbers with a lower and upper bound.
--
-- Usage
--
--
-- >>> {-# LANGUAGE RebindableSyntax #-}
--
-- >>> import NumHask.Prelude
--
-- >>> import NumHask.Space
--
@package numhask-space
@version 0.12.0.0
-- | A Space containing numerical elements
module NumHask.Space.Range
-- | A continuous range over type a
--
--
-- >>> let a = Range (-1) 1
--
-- >>> a
-- Range -1 1
--
--
--
-- >>> a + a
-- Range -2 2
--
--
--
-- >>> a * a
-- Range -2.0 2.0
--
--
--
-- >>> (+1) <$> (Range 1 2)
-- Range 2 3
--
--
-- Ranges are very useful in shifting a bunch of numbers from one Range
-- to another. eg project 0.5 from the range 0 to 1 to the range 1 to 4
--
--
-- >>> project (Range 0 1) (Range 1 4) 0.5
-- 2.5
--
--
-- Create an equally spaced grid including outer bounds over a Range
--
--
-- >>> grid OuterPos (Range 0.0 10.0) 5
-- [0.0,2.0,4.0,6.0,8.0,10.0]
--
--
-- divide up a Range into equal-sized sections
--
--
-- >>> gridSpace (Range 0.0 1.0) 4
-- [Range 0.0 0.25,Range 0.25 0.5,Range 0.5 0.75,Range 0.75 1.0]
--
data Range a
Range :: a -> a -> Range a
-- | a grid for five-digits per limb species
--
--
-- >>> gridSensible OuterPos False (Range (-12.0) 23.0) 6
-- [-15.0,-10.0,-5.0,0.0,5.0,10.0,15.0,20.0,25.0]
--
gridSensible :: Pos -> Bool -> Range Double -> Int -> [Double]
-- | Find a step that feels pleasent for a 10 digit species.
--
--
-- >>> stepSensible OuterPos 35 6
-- 5.0
--
stepSensible :: Pos -> Double -> Int -> Double
instance GHC.Generics.Generic (NumHask.Space.Range.Range a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (NumHask.Space.Range.Range a)
instance Data.Functor.Classes.Eq1 NumHask.Space.Range.Range
instance GHC.Show.Show a => GHC.Show.Show (NumHask.Space.Range.Range a)
instance GHC.Base.Functor NumHask.Space.Range.Range
instance Data.Functor.Bind.Class.Apply NumHask.Space.Range.Range
instance GHC.Base.Applicative NumHask.Space.Range.Range
instance Data.Foldable.Foldable NumHask.Space.Range.Range
instance Data.Traversable.Traversable NumHask.Space.Range.Range
instance Data.Distributive.Distributive NumHask.Space.Range.Range
instance Data.Functor.Rep.Representable NumHask.Space.Range.Range
instance GHC.Classes.Ord a => NumHask.Algebra.Lattice.JoinSemiLattice (NumHask.Space.Range.Range a)
instance GHC.Classes.Ord a => NumHask.Algebra.Lattice.MeetSemiLattice (NumHask.Space.Range.Range a)
instance GHC.Classes.Ord a => NumHask.Space.Types.Space (NumHask.Space.Range.Range a)
instance (NumHask.Algebra.Field.Field a, GHC.Classes.Ord a, NumHask.Data.Integral.FromIntegral a GHC.Types.Int) => NumHask.Space.Types.FieldSpace (NumHask.Space.Range.Range a)
instance GHC.Classes.Ord a => GHC.Base.Semigroup (NumHask.Space.Range.Range a)
instance (NumHask.Algebra.Additive.Additive a, GHC.Classes.Ord a) => NumHask.Algebra.Additive.Additive (NumHask.Space.Range.Range a)
instance (NumHask.Algebra.Additive.Subtractive a, GHC.Classes.Ord a) => NumHask.Algebra.Additive.Subtractive (NumHask.Space.Range.Range a)
instance (NumHask.Algebra.Field.Field a, GHC.Classes.Ord a) => NumHask.Algebra.Multiplicative.Multiplicative (NumHask.Space.Range.Range a)
instance (GHC.Classes.Ord a, NumHask.Algebra.Field.Field a) => NumHask.Algebra.Multiplicative.Divisive (NumHask.Space.Range.Range a)
instance (NumHask.Algebra.Field.Field a, GHC.Classes.Ord a) => NumHask.Algebra.Metric.Basis (NumHask.Space.Range.Range a)
-- | data algorithms related to time (as a Space)
module NumHask.Space.Time
-- | a step in time
data TimeGrain
Years :: Int -> TimeGrain
Months :: Int -> TimeGrain
Days :: Int -> TimeGrain
Hours :: Int -> TimeGrain
Minutes :: Int -> TimeGrain
Seconds :: Double -> TimeGrain
-- | compute the floor UTCTime based on the timegrain
--
--
-- >>> floorGrain (Years 5) (UTCTime (fromGregorian 1999 1 1) (toDiffTime 0))
-- 1995-12-31 00:00:00 UTC
--
--
--
-- >>> floorGrain (Months 3) (UTCTime (fromGregorian 2016 12 30) (toDiffTime 0))
-- 2016-09-30 00:00:00 UTC
--
--
--
-- >>> floorGrain (Days 5) (UTCTime (fromGregorian 2016 12 30) (toDiffTime 1))
-- 2016-12-30 00:00:00 UTC
--
--
--
-- >>> floorGrain (Minutes 15) (UTCTime (fromGregorian 2016 12 30) (toDiffTime $ 15*60+1))
-- 2016-12-30 00:15:00 UTC
--
--
--
-- >>> floorGrain (Seconds 0.1) (UTCTime (fromGregorian 2016 12 30) ((toDiffTime 0.12)))
-- 2016-12-30 00:00:00.1 UTC
--
floorGrain :: TimeGrain -> UTCTime -> UTCTime
-- | compute the ceiling UTCTime based on the timegrain
--
--
-- >>> ceilingGrain (Years 5) (UTCTime (fromGregorian 1999 1 1) (toDiffTime 0))
-- 2000-12-31 00:00:00 UTC
--
--
--
-- >>> ceilingGrain (Months 3) (UTCTime (fromGregorian 2016 12 30) (toDiffTime 0))
-- 2016-12-31 00:00:00 UTC
--
--
--
-- >>> ceilingGrain (Days 5) (UTCTime (fromGregorian 2016 12 30) (toDiffTime 1))
-- 2016-12-31 00:00:00 UTC
--
--
--
-- >>> ceilingGrain (Minutes 15) (UTCTime (fromGregorian 2016 12 30) (toDiffTime $ 15*60+1))
-- 2016-12-30 00:30:00 UTC
--
--
--
-- >>> ceilingGrain (Seconds 0.1) (UTCTime (fromGregorian 2016 12 30) (toDiffTime 0.12))
-- 2016-12-30 00:00:00.2 UTC
--
ceilingGrain :: TimeGrain -> UTCTime -> UTCTime
-- | add a TimeGrain to a UTCTime
--
--
-- >>> addGrain (Years 1) 5 (UTCTime (fromGregorian 2015 2 28) (toDiffTime 0))
-- 2020-02-29 00:00:00 UTC
--
--
--
-- >>> addGrain (Months 1) 1 (UTCTime (fromGregorian 2015 2 28) (toDiffTime 0))
-- 2015-03-31 00:00:00 UTC
--
--
--
-- >>> addGrain (Hours 6) 5 (UTCTime (fromGregorian 2015 2 28) (toDiffTime 0))
-- 2015-03-01 06:00:00 UTC
--
--
--
-- >>> addGrain (Seconds 0.001) (60*1000+1) (UTCTime (fromGregorian 2015 2 28) (toDiffTime 0))
-- 2015-02-28 00:01:00.001 UTC
--
addGrain :: TimeGrain -> Int -> UTCTime -> UTCTime
-- | compute a sensible TimeGrain and list of UTCTimes
--
--
-- >>> sensibleTimeGrid InnerPos 2 (Range (UTCTime (fromGregorian 2016 12 31) (toDiffTime 0)) (UTCTime (fromGregorian 2017 12 31) (toDiffTime 0)))
-- (Months 6,[2016-12-31 00:00:00 UTC,2017-06-30 00:00:00 UTC,2017-12-31 00:00:00 UTC])
--
--
--
-- >>> sensibleTimeGrid InnerPos 2 (Range (UTCTime (fromGregorian 2017 1 1) (toDiffTime 0)) (UTCTime (fromGregorian 2017 12 30) (toDiffTime 0)))
-- (Months 6,[2017-06-30 00:00:00 UTC])
--
--
--
-- >>> sensibleTimeGrid UpperPos 2 (Range (UTCTime (fromGregorian 2017 1 1) (toDiffTime 0)) (UTCTime (fromGregorian 2017 12 30) (toDiffTime 0)))
-- (Months 6,[2017-06-30 00:00:00 UTC,2017-12-31 00:00:00 UTC])
--
--
--
-- >>> sensibleTimeGrid LowerPos 2 (Range (UTCTime (fromGregorian 2017 1 1) (toDiffTime 0)) (UTCTime (fromGregorian 2017 12 30) (toDiffTime 0)))
-- (Months 6,[2016-12-31 00:00:00 UTC,2017-06-30 00:00:00 UTC])
--
sensibleTimeGrid :: Pos -> Int -> Range UTCTime -> (TimeGrain, [UTCTime])
-- | whether to include lower and upper times
data PosDiscontinuous
PosInnerOnly :: PosDiscontinuous
PosIncludeBoundaries :: PosDiscontinuous
-- | Dates used for time series analysis or attached to charts are often
-- discontinuous, but we want to smooth that reality over and show a
-- continuous range on the axis.
--
-- The assumption with getSensibleTimeGrid is that there is a list of
-- discountinuous UTCTimes rather than a continuous range. Output is a
-- list of index points for the original [UTCTime] and label tuples, and
-- a list of unused list elements.
--
--
-- >>> placedTimeLabelDiscontinuous PosIncludeBoundaries (Just (pack "%d %b")) 2 [UTCTime (fromGregorian 2017 12 6) (toDiffTime 0), UTCTime (fromGregorian 2017 12 29) (toDiffTime 0), UTCTime (fromGregorian 2018 1 31) (toDiffTime 0), UTCTime (fromGregorian 2018 3 3) (toDiffTime 0)]
-- ([(0,"06 Dec"),(1,"31 Dec"),(2,"28 Feb"),(3,"03 Mar")],[])
--
placedTimeLabelDiscontinuous :: PosDiscontinuous -> Maybe Text -> Int -> [UTCTime] -> ([(Int, Text)], [UTCTime])
-- | A sensible time grid between two dates, projected onto (0,1) with no
-- attempt to get finnicky.
--
--
-- >>> placedTimeLabelContinuous PosIncludeBoundaries (Just (pack "%d %b")) 2 (Range (UTCTime (fromGregorian 2017 12 6) (toDiffTime 0)) (UTCTime (fromGregorian 2017 12 29) (toDiffTime 0)))
-- [(0.0,"06 Dec"),(0.4347826086956521,"16 Dec"),(0.8695652173913042,"26 Dec"),(0.9999999999999999,"29 Dec")]
--
placedTimeLabelContinuous :: PosDiscontinuous -> Maybe Text -> Int -> Range UTCTime -> [(Double, Text)]
-- | convenience conversion to Double
fromNominalDiffTime :: NominalDiffTime -> Double
-- | convenience conversion from Double
toNominalDiffTime :: Double -> NominalDiffTime
-- | Convert from DiffTime to seconds (as a Double)
--
--
-- >>> fromDiffTime $ toDiffTime 1
-- 1.0
--
fromDiffTime :: DiffTime -> Double
-- | Convert from seconds (as a Double) to DiffTime >>>
-- toDiffTime 1 1s
toDiffTime :: Double -> DiffTime
instance GHC.Generics.Generic NumHask.Space.Time.TimeGrain
instance GHC.Classes.Eq NumHask.Space.Time.TimeGrain
instance GHC.Show.Show NumHask.Space.Time.TimeGrain
-- | A 2-dimensional point.
module NumHask.Space.Point
-- | A 2-dimensional Point of a's
--
-- In contrast with a tuple, a Point is functorial over both arguments.
--
--
-- >>> let p = Point 1 1
--
-- >>> p + p
-- Point 2 2
--
-- >>> (2*) <$> p
-- Point 2 2
--
--
-- A major reason for this bespoke treatment (compared to just using
-- linear, say) is that Points do not have maximums and minimums but they
-- do form a lattice, and this is useful for folding sets of points to
-- find out the (rectangular) Space they occupy.
--
--
-- >>> Point 0 1 /\ Point 1 0
-- Point 0 0
--
-- >>> Point 0 1 \/ Point 1 0
-- Point 1 1
--
--
-- This is used extensively in chart-svg to ergonomically obtain
-- chart areas.
--
--
-- unsafeSpace1 [Point 1 0, Point 0 1] :: Rect Double
--
--
-- Rect 0.0 1.0 0.0 1.0
data Point a
Point :: a -> a -> Point a
[_x] :: Point a -> a
[_y] :: Point a -> a
-- | rotate a point by x relative to the origin
--
--
-- >>> rotateP (pi/2) (Point 1 0)
-- Point 6.123233995736766e-17 1.0
--
rotateP :: TrigField a => a -> Point a -> Point a
-- | Create Points for a formulae y = f(x) across an x range
--
--
-- >>> gridP (^^2) (Range 0 4) 4
-- [Point 0.0 0.0,Point 1.0 1.0,Point 2.0 4.0,Point 3.0 9.0,Point 4.0 16.0]
--
gridP :: FieldSpace (Range a) => (a -> a) -> Range a -> Grid (Range a) -> [Point a]
-- | dot product
dotP :: (Multiplicative a, Additive a) => Point a -> Point a -> a
-- | dot product operator
(<.>) :: (Multiplicative a, Additive a) => Point a -> Point a -> a
infix 4 <.>
-- | cross product
crossP :: (Multiplicative a, Subtractive a) => Point a -> Point a -> a
-- | reflect on x-axis
flipY :: Subtractive a => Point a -> Point a
-- | A line is a composed of 2 Points
data Line a
Line :: Point a -> Point a -> Line a
[lineStart] :: Line a -> Point a
[lineEnd] :: Line a -> Point a
-- | Return the parameters (a, b, c) for the line equation a*x + b*y +
-- c = 0.
lineSolve :: (ExpField a, Eq a) => Line a -> (a, a, a)
-- | Return the signed distance from a point to the line. If the distance
-- is negative, the point lies to the right of the line
lineDistance :: ExpField a => Line a -> Point a -> a
-- | Return the point on the line closest to the given point.
closestPoint :: Field a => Line a -> Point a -> Point a
-- | Calculate the intersection of two lines. If the determinant is less
-- than tolerance (parallel or coincident lines), return Nothing.
lineIntersect :: (Ord a, Epsilon a, Absolute a, Field a) => Line a -> Line a -> Maybe (Point a)
-- | move an Affinity by a Point
translate :: TrigField a => Point a -> Transform a
-- | scale an Affinity by a Point
scaleT :: TrigField a => Point a -> Transform a
-- | Skew transform
--
-- x-axis skew
--
--
-- skew (Point x 0)
--
skew :: TrigField a => Point a -> Transform a
instance GHC.Generics.Generic (NumHask.Space.Point.Point a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (NumHask.Space.Point.Point a)
instance Data.Traversable.Traversable NumHask.Space.Point.Line
instance Data.Foldable.Foldable NumHask.Space.Point.Line
instance GHC.Base.Functor NumHask.Space.Point.Line
instance GHC.Classes.Eq a => GHC.Classes.Eq (NumHask.Space.Point.Line a)
instance (GHC.Classes.Ord a, NumHask.Algebra.Additive.Additive a, GHC.Show.Show a) => GHC.Show.Show (NumHask.Space.Point.Line a)
instance (NumHask.Algebra.Multiplicative.Multiplicative a, NumHask.Algebra.Additive.Additive a) => NumHask.Space.Types.Affinity (NumHask.Space.Point.Line a) a
instance Data.Functor.Classes.Eq1 NumHask.Space.Point.Point
instance (GHC.Classes.Ord a, NumHask.Algebra.Additive.Additive a, GHC.Show.Show a) => GHC.Show.Show (NumHask.Space.Point.Point a)
instance GHC.Base.Functor NumHask.Space.Point.Point
instance GHC.Base.Applicative NumHask.Space.Point.Point
instance GHC.Base.Monad NumHask.Space.Point.Point
instance Data.Foldable.Foldable NumHask.Space.Point.Point
instance Data.Traversable.Traversable NumHask.Space.Point.Point
instance GHC.Base.Semigroup a => GHC.Base.Semigroup (NumHask.Space.Point.Point a)
instance GHC.Base.Monoid a => GHC.Base.Monoid (NumHask.Space.Point.Point a)
instance GHC.Enum.Bounded a => GHC.Enum.Bounded (NumHask.Space.Point.Point a)
instance NumHask.Algebra.Additive.Additive a => NumHask.Algebra.Additive.Additive (NumHask.Space.Point.Point a)
instance NumHask.Algebra.Additive.Subtractive a => NumHask.Algebra.Additive.Subtractive (NumHask.Space.Point.Point a)
instance NumHask.Algebra.Multiplicative.Multiplicative a => NumHask.Algebra.Multiplicative.Multiplicative (NumHask.Space.Point.Point a)
instance NumHask.Algebra.Multiplicative.Divisive a => NumHask.Algebra.Multiplicative.Divisive (NumHask.Space.Point.Point a)
instance Data.Distributive.Distributive NumHask.Space.Point.Point
instance NumHask.Algebra.Additive.Additive a => NumHask.Algebra.Action.AdditiveAction (NumHask.Space.Point.Point a)
instance NumHask.Algebra.Additive.Subtractive a => NumHask.Algebra.Action.SubtractiveAction (NumHask.Space.Point.Point a)
instance NumHask.Algebra.Multiplicative.Multiplicative a => NumHask.Algebra.Action.MultiplicativeAction (NumHask.Space.Point.Point a)
instance NumHask.Algebra.Multiplicative.Divisive a => NumHask.Algebra.Action.DivisiveAction (NumHask.Space.Point.Point a)
instance Data.Functor.Rep.Representable NumHask.Space.Point.Point
instance GHC.Classes.Ord a => NumHask.Algebra.Lattice.JoinSemiLattice (NumHask.Space.Point.Point a)
instance GHC.Classes.Ord a => NumHask.Algebra.Lattice.MeetSemiLattice (NumHask.Space.Point.Point a)
instance (NumHask.Algebra.Field.ExpField a, GHC.Classes.Eq a) => NumHask.Algebra.Metric.Basis (NumHask.Space.Point.Point a)
instance NumHask.Algebra.Field.TrigField a => NumHask.Algebra.Metric.Direction (NumHask.Space.Point.Point a)
instance System.Random.Internal.UniformRange a => System.Random.Internal.UniformRange (NumHask.Space.Point.Point a)
instance (NumHask.Algebra.Multiplicative.Multiplicative a, NumHask.Algebra.Additive.Additive a) => NumHask.Space.Types.Affinity (NumHask.Space.Point.Point a) a
-- | A (finite) two-dimensional plane, implemented as a composite of a
-- Point of Ranges.
module NumHask.Space.Rect
-- | a rectangular space often representing a finite 2-dimensional or XY
-- plane.
--
--
-- >>> one :: Rect Double
-- Rect (-0.5) 0.5 (-0.5) 0.5
--
--
--
-- >>> zero :: Rect Double
-- Rect 0.0 0.0 0.0 0.0
--
--
--
-- >>> one + one :: Rect Double
-- Rect (-1.0) 1.0 (-1.0) 1.0
--
--
--
-- >>> let a = Rect (-1.0) 1.0 (-2.0) 4.0
--
-- >>> a
-- Rect (-1.0) 1.0 (-2.0) 4.0
--
--
--
-- >>> a * one
-- Rect (-1.0) 1.0 (-2.0) 4.0
--
--
--
-- >>> let (Ranges x y) = a
--
-- >>> x
-- Range -1.0 1.0
--
-- >>> y
-- Range -2.0 4.0
--
-- >>> fmap (+1) (Rect 1 2 3 4)
-- Rect 2 3 4 5
--
--
-- as a Space instance with Points as Elements
--
--
-- >>> project (Rect 0.0 1.0 (-1.0) 0.0) (Rect 1.0 4.0 10.0 0.0) (Point 0.5 1.0)
-- Point 2.5 (-10.0)
--
-- >>> gridSpace (Rect 0.0 10.0 0.0 1.0) (Point (2::Int) (2::Int))
-- [Rect 0.0 5.0 0.0 0.5,Rect 0.0 5.0 0.5 1.0,Rect 5.0 10.0 0.0 0.5,Rect 5.0 10.0 0.5 1.0]
--
-- >>> grid MidPos (Rect 0.0 10.0 0.0 1.0) (Point (2::Int) (2::Int))
-- [Point 2.5 0.25,Point 2.5 0.75,Point 7.5 0.25,Point 7.5 0.75]
--
newtype Rect a
Rect' :: Compose Point Range a -> Rect a
-- | pattern of Rect lowerx upperx lowery uppery
pattern Rect :: a -> a -> a -> a -> Rect a
-- | pattern of Ranges xrange yrange
pattern Ranges :: Range a -> Range a -> Rect a
-- | The first X coordinate of a Rect
--
--
-- >>> rx one
-- -0.5
--
rx :: Rect a -> a
-- | The second X coordinate of a Rect
--
--
-- >>> rz one
-- 0.5
--
rz :: Rect a -> a
-- | The first Y coordinate of a Rect
--
--
-- >>> ry one
-- -0.5
--
ry :: Rect a -> a
-- | The second Y coordinate of a Rect
--
--
-- >>> rw one
-- 0.5
--
rw :: Rect a -> a
-- | flip axes
--
--
-- >>> flipAxes (Rect 1 2 3 4)
-- Rect 3 4 1 2
--
flipAxes :: Rect a -> Rect a
-- | create a list of points representing the lower left and upper right
-- corners of a rectangle.
--
--
-- >>> corners one
-- [Point (-0.5) (-0.5),Point 0.5 0.5]
--
corners :: Ord a => Rect a -> [Point a]
-- | the 4 corners
--
--
-- >>> corners4 one
-- [Point (-0.5) (-0.5),Point (-0.5) 0.5,Point 0.5 (-0.5),Point 0.5 0.5]
--
corners4 :: Rect a -> [Point a]
-- | project a Rect from an old Space (Rect) to a new one.
--
-- The Space instance of Rect uses Points as Elements, but a Rect can
-- also be a Space over Rects.
--
--
-- >>> projectRect (Rect 0 1 (-1) 0) (Rect 0 4 0 8) (Rect 0.25 0.75 (-0.75) (-0.25))
-- Rect 1.0 3.0 2.0 6.0
--
projectRect :: (Field a, Ord a) => Rect a -> Rect a -> Rect a -> Rect a
-- | convex hull union of Rect's
--
--
-- >>> foldRect [Rect 0 1 0 1, one]
-- Just Rect (-0.5) 1.0 (-0.5) 1.0
--
foldRect :: Ord a => [Rect a] -> Maybe (Rect a)
-- | convex hull union of Rect's applied to a non-empty structure
--
--
-- >>> foldRectUnsafe [Rect 0 1 0 1, one]
-- Rect (-0.5) 1.0 (-0.5) 1.0
--
foldRectUnsafe :: (Foldable f, Ord a) => f (Rect a) -> Rect a
-- | add a Point to a Rect
--
--
-- >>> addPoint (Point 0 1) one
-- Rect (-0.5) 0.5 0.5 1.5
--
addPoint :: Additive a => Point a -> Rect a -> Rect a
-- | rotate the corners of a Rect by x degrees relative to the origin, and
-- fold to a new Rect
--
--
-- >>> rotationBound (pi/4) one
-- Rect (-0.7071067811865475) 0.7071067811865475 (-0.7071067811865475) 0.7071067811865475
--
rotationBound :: (TrigField a, Ord a) => a -> Rect a -> Rect a
-- | Create Rects for a formulae y = f(x) across an x range where the y
-- range is Range 0 y
--
--
-- >>> gridR (^2) (Range 0 4) 4
-- [Rect 0.0 1.0 0.0 0.25,Rect 1.0 2.0 0.0 2.25,Rect 2.0 3.0 0.0 6.25,Rect 3.0 4.0 0.0 12.25]
--
gridR :: (Field a, FromIntegral a Int, Ord a) => (a -> a) -> Range a -> Int -> [Rect a]
-- | Create values c for Rects data for a formulae c = f(x,y)
--
--
-- >>> gridF (\(Point x y) -> x * y) (Rect 0 4 0 4) (Point 2 2)
-- [(Rect 0.0 2.0 0.0 2.0,1.0),(Rect 0.0 2.0 2.0 4.0,3.0),(Rect 2.0 4.0 0.0 2.0,3.0),(Rect 2.0 4.0 2.0 4.0,9.0)]
--
gridF :: (Point Double -> b) -> Rect Double -> Grid (Rect Double) -> [(Rect Double, b)]
-- | convert a ratio (eg x:1) to a Rect with a height of one.
--
--
-- >>> aspect 2
-- Rect (-1.0) 1.0 (-0.5) 0.5
--
aspect :: Double -> Rect Double
-- | convert a Rect to a ratio
--
--
-- >>> :set -XNegativeLiterals
--
-- >>> ratio (Rect (-1) 1 (-0.5) 0.5)
-- 2.0
--
ratio :: Field a => Rect a -> a
-- | project a Rect from one Rect to another, preserving relative position,
-- with guards for singleton Rects.
--
--
-- >>> projectOnR one (Rect 0 1 0 1) (Rect 0 0.5 0 0.5)
-- Rect (-0.5) 0.0 (-0.5) 0.0
--
projectOnR :: Rect Double -> Rect Double -> Rect Double -> Rect Double
-- | project a Point from one Rect to another, preserving relative
-- position, with guards for singleton Rects.
--
--
-- >>> projectOnP one (Rect 0 1 0 1) zero
-- Point (-0.5) (-0.5)
--
projectOnP :: Rect Double -> Rect Double -> Point Double -> Point Double
instance GHC.Generics.Generic (NumHask.Space.Rect.Rect a)
instance Data.Traversable.Traversable NumHask.Space.Rect.Rect
instance Data.Foldable.Foldable NumHask.Space.Rect.Rect
instance GHC.Base.Applicative NumHask.Space.Rect.Rect
instance GHC.Base.Functor NumHask.Space.Rect.Rect
instance GHC.Classes.Eq a => GHC.Classes.Eq (NumHask.Space.Rect.Rect a)
instance (GHC.Classes.Ord a, NumHask.Algebra.Additive.Additive a, GHC.Show.Show a) => GHC.Show.Show (NumHask.Space.Rect.Rect a)
instance Data.Distributive.Distributive NumHask.Space.Rect.Rect
instance Data.Functor.Rep.Representable NumHask.Space.Rect.Rect
instance GHC.Classes.Ord a => GHC.Base.Semigroup (NumHask.Space.Rect.Rect a)
instance GHC.Classes.Ord a => NumHask.Space.Types.Space (NumHask.Space.Rect.Rect a)
instance (NumHask.Data.Integral.FromIntegral a GHC.Types.Int, NumHask.Algebra.Field.Field a, GHC.Classes.Ord a) => NumHask.Space.Types.FieldSpace (NumHask.Space.Rect.Rect a)
instance NumHask.Algebra.Additive.Additive a => NumHask.Algebra.Additive.Additive (NumHask.Space.Rect.Rect a)
instance NumHask.Algebra.Additive.Subtractive a => NumHask.Algebra.Additive.Subtractive (NumHask.Space.Rect.Rect a)
instance (GHC.Classes.Ord a, NumHask.Algebra.Field.Field a) => NumHask.Algebra.Multiplicative.Multiplicative (NumHask.Space.Rect.Rect a)
instance (GHC.Classes.Ord a, NumHask.Algebra.Field.Field a) => NumHask.Algebra.Multiplicative.Divisive (NumHask.Space.Rect.Rect a)
instance (GHC.Classes.Ord a, NumHask.Algebra.Field.Field a) => NumHask.Algebra.Metric.Basis (NumHask.Space.Rect.Rect a)
-- | A histogram, if you squint, is a series of contiguous Ranges,
-- annotated with values.
module NumHask.Space.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]
data Histogram
Histogram :: Vector Double -> Map Int Double -> Histogram
[cuts] :: Histogram -> Vector Double
[values] :: Histogram -> Map Int Double
-- | A histogram with no cuts nor data.
emptyHistogram :: Histogram
-- | Whether or not to ignore unders and overs. If overs and unders are
-- dealt with, IncludeOvers supplies an assumed width for the outer
-- buckets.
data DealOvers
IgnoreOvers :: DealOvers
IncludeOvers :: Double -> DealOvers
-- | 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)]}
--
fill :: Foldable f => [Double] -> f Double -> Histogram
-- | find the index of the bucket the value is contained in.
cutI :: Ord a => Vector a -> a -> Int
-- | 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)]}
--
regular :: Int -> [Double] -> Histogram
-- | 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]
--
makeRects :: DealOvers -> Histogram -> [Rect Double]
-- | approx regular n-quantiles
--
--
-- >>> regularQuantiles 4 [0..100]
-- [0.0,24.75,50.0,75.25,100.0]
--
regularQuantiles :: Double -> [Double] -> [Double]
-- | one-pass approximate quantiles fold
quantileFold :: [Double] -> [Double] -> [Double]
-- | 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)]}
--
freq :: Histogram -> Histogram
-- | average
--
--
-- >>> average [0..1000]
-- 500.0
--
average :: Foldable f => f Double -> Double
-- | Regularly spaced (approx) quantiles
--
--
-- >>> quantiles 5 [1..1000]
-- [1.0,200.5,400.5,600.5000000000001,800.5,1000.0]
--
quantiles :: Foldable f => Int -> f Double -> [Double]
-- | single (approx) quantile
--
--
-- >>> quantile 0.1 [1..1000]
-- 100.5
--
quantile :: Foldable f => Double -> f Double -> Double
instance GHC.Classes.Eq NumHask.Space.Histogram.Histogram
instance GHC.Show.Show NumHask.Space.Histogram.Histogram
-- | Mathematics does not rigorously define a space, leaving library
-- devs free to explore.
--
-- “But who can quantify the algebra of space, or weigh those worlds that
-- swim each in its place? Who can outdo the dark? And what computer
-- knows how beauty comes to birth - shell star and rose?
--
-- ~ Technicians by Jean Kenward” ~ John Foster
module NumHask.Space
-- | A Space is a continuous set of numbers. Continuous here means
-- that the set has an upper and lower bound, and an element that is
-- between these two bounds is a member of the Space.
--
--
-- a `union` b == b `union` a
-- a `intersection` b == b `intersection` a
-- (a `union` b) `intersection` c == (a `intersection` b) `union` (a `intersection` c)
-- (a `intersection` b) `union` c == (a `union` b) `intersection` (a `union` c)
-- norm (norm a) = norm a
-- a |>| b == b |<| a
-- a |.| singleton a
--
class Space s where {
-- | the underlying element in the space
type Element s :: Type;
}
-- | lower boundary
lower :: Space s => s -> Element s
-- | upper boundary
upper :: Space s => s -> Element s
-- | space containing a single element
singleton :: Space s => Element s -> s
-- | the intersection of two spaces
intersection :: Space s => s -> s -> s
-- | the intersection of two spaces
intersection :: (Space s, Ord (Element s)) => s -> s -> s
-- | the union of two spaces
union :: Space s => s -> s -> s
-- | the union of two spaces
union :: (Space s, Ord (Element s)) => s -> s -> s
-- | Normalise a space so that
--
--
-- lower a \/ upper a == lower a
-- lower a /\ upper a == upper a
--
normalise :: Space s => s -> s
-- | create a normalised space from two elements
(...) :: Space s => Element s -> Element s -> s
-- | create a normalised space from two elements
(...) :: (Space s, Ord (Element s)) => Element s -> Element s -> s
-- | create a space from two elements without normalising
(>.<) :: Space s => Element s -> Element s -> s
-- | is an element in the space
(|.|) :: Space s => Element s -> s -> Bool
-- | is an element in the space
(|.|) :: (Space s, Ord (Element s)) => Element s -> s -> Bool
-- | is one space completely above the other
(|>|) :: Space s => s -> s -> Bool
-- | is one space completely above the other
(|>|) :: (Space s, Ord (Element s)) => s -> s -> Bool
-- | is one space completely below the other
(|<|) :: Space s => s -> s -> Bool
-- | is one space completely below the other
(|<|) :: (Space s, Ord (Element s)) => s -> s -> Bool
infix 3 ...
infix 3 >.<
infixl 7 |.|
infixl 7 |>|
infixl 7 |<|
-- | a convex hull
newtype Union a
Union :: a -> Union a
[getUnion] :: Union a -> a
-- | https://en.wikipedia.org/wiki/Intersection_(set_theory)
newtype Intersection a
Intersection :: a -> Intersection a
[getIntersection] :: Intersection a -> a
-- | a space that can be divided neatly
--
--
-- unsafeSpace1 (grid OuterPos s g) == s
-- getUnion (sconcat (Union <$> (gridSpace s g))) == s
--
class (Space s, Field (Element s)) => FieldSpace s where {
-- | the type that divides or quotients the space
type Grid s :: Type;
}
-- | create equally-spaced elements across a space
grid :: FieldSpace s => Pos -> s -> Grid s -> [Element s]
-- | create equally-spaced spaces from a space
gridSpace :: FieldSpace s => s -> Grid s -> [s]
-- | middle element of the space
mid :: (Space s, Field (Element s)) => s -> Element s
-- | interpolate a space
--
--
-- interpolate s x == project s (zero ... one) x
--
interpolate :: (Space s, Ring (Element s)) => s -> Element s -> Element s
-- | project an element from one space to another, preserving relative
-- position.
--
--
-- project o n (lower o) = lower n
-- project o n (upper o) = upper n
-- project o n (mid o) = mid n
-- project a a x = x
--
project :: (Space s, Field (Element s)) => s -> s -> Element s -> Element s
-- | Pos suggests where points should be placed in forming a grid across a
-- field space.
data Pos
-- | include boundaries
OuterPos :: Pos
-- | don't include boundaries
InnerPos :: Pos
-- | include the lower boundary
LowerPos :: Pos
-- | include the upper boundary
UpperPos :: Pos
-- | use the mid-point of the space
MidPos :: Pos
-- | Maybe containing space of a traversable.
space1 :: (Space s, Traversable f) => f (Element s) -> Maybe s
-- | the containing space of a non-empty Traversable.
--
-- partial function.
--
--
-- all $ unsafeSpace1 a `contains` <$> a
--
unsafeSpace1 :: (Space s, Traversable f) => f (Element s) -> s
-- | supply a random element within a Space
--
--
-- >>> randomS (one :: Range Double) g
-- (0.43085240252163404,StdGen {unStdGen = SMGen 4530528345362647137 13679457532755275413})
--
randomS :: (Space s, RandomGen g, UniformRange (Element s)) => s -> g -> (Element s, g)
-- | StatefulGen version of randomS
--
--
-- >>> import Control.Monad
--
-- >>> runStateGen_ g (randomSM (one :: Range Double))
-- 0.43085240252163404
--
randomSM :: (UniformRange (Element s), StatefulGen g m, Space s) => s -> g -> m (Element s)
-- | list of n random elements within a Space
--
--
-- >>> let g = mkStdGen 42
--
-- >>> fst (randomSs 3 (one :: Range Double) g)
-- [0.43085240252163404,-6.472345419562497e-2,0.3854692674681801]
--
--
--
-- >>> fst (randomSs 3 (Rect 0 10 0 10 :: Rect Int) g)
-- [Point 0 7,Point 0 2,Point 1 7]
--
randomSs :: (Space s, RandomGen g, UniformRange (Element s)) => Int -> s -> g -> ([Element s], g)
-- | is an element contained within a space
memberOf :: Space s => Element s -> s -> Bool
-- | is a space contained within another?
--
--
-- (a `union` b) `contains` a
-- (a `union` b) `contains` b
--
contains :: Space s => s -> s -> Bool
-- | are two spaces disjoint?
disjoint :: Space s => s -> s -> Bool
-- | distance between boundaries
width :: (Space s, Subtractive (Element s)) => s -> Element s
-- | create a space centered on a plus or minus b
(+/-) :: (Space s, Subtractive (Element s)) => Element s -> Element s -> s
infixl 6 +/-
-- | lift a monotone function (increasing or decreasing) over a given space
monotone :: (Space a, Space b) => (Element a -> Element b) -> a -> b
-- | a small space
eps :: (Space s, FromRational (Element s), Field (Element s)) => Element s -> Element s -> s
-- | widen a space
widen :: (Space s, Ring (Element s)) => Element s -> s -> s
-- | widen by a small amount
widenEps :: (Space s, FromRational (Element s), Ring (Element s)) => Element s -> s -> s
-- | Scale a Space. (scalar multiplication)
scale :: (Multiplicative (Element s), Space s) => Element s -> s -> s
-- | Move a Space. (scalar addition)
move :: (Additive (Element s), Space s) => Element s -> s -> s
-- | linear transform + translate of a point-like number
--
--
-- (x, y) -> (ax + by + c, dx + ey + d)
--
--
-- or
--
-- <math>
data Transform a
Transform :: !a -> !a -> !a -> !a -> !a -> !a -> Transform a
[ta] :: Transform a -> !a
[tb] :: Transform a -> !a
[tc] :: Transform a -> !a
[td] :: Transform a -> !a
[te] :: Transform a -> !a
[tf] :: Transform a -> !a
-- | Calculate the inverse of a transformation.
inverseTransform :: (Eq a, Field a) => Transform a -> Maybe (Transform a)
-- | An Affinity is something that can be subjected to an affine
-- transformation in 2-dimensional space, where affine means a linear
-- matrix operation or a translation (+).
--
-- https://en.wikipedia.org/wiki/Affine_transformation
class Affinity a b | a -> b
transform :: Affinity a b => Transform b -> a -> a
-- | Apply a Transform to an Affinity
(|.) :: Affinity a b => Transform b -> a -> a
infix 3 |.
-- | Rotate an Affinity (counter-clockwise)
rotate :: TrigField a => a -> Transform a