Safe Haskell	None
Language	Haskell2010

NumHask.Space

Description

A Space represents an abstract continuous range class for a type. The interval package is an alternative approach.

Synopsis

class (Eq (Element s), Ord (Element s), Field (Element s)) => Space s where
- type Element s :: *
- type Grid s :: *
data Pos
- = OuterPos
- | InnerPos
- | LowerPos
- | UpperPos
- | MidPos

Documentation

class (Eq (Element s), Ord (Element s), Field (Element s)) => Space s where #

space laws

a `union` nul == a
a `union` a == a
project o n (lower o) == lower n
project o n (upper o) == upper n
project a a == id

Minimal complete definition

lower, upper, singleton, union, nul, grid, gridSpace

Associated Types

type Element s :: * #

type Grid s :: * #

Methods

lower :: s -> Element s #

lower boundary of space

upper :: s -> Element s #

upper boundary of space

mid :: s -> Element s #

mid-point of the space

width :: s -> Element s #

distance between boundaries

singleton :: Element s -> s #

singleton space

singular :: s -> Bool #

zero-width test

element :: Element s -> s -> Bool #

determine whether an a is in the space

contains :: s -> s -> Bool #

is a space contained within another?

disjoint :: s -> s -> Bool #

do two spaces intersect?

intersects :: s -> s -> Bool #

do two spaces intersect?

union :: s -> s -> s #

convex hull

nul :: s #

null space, which can be interpreted as mempty

space :: Foldable f => f (Element s) -> s #

the containing space of a Foldable

project :: s -> s -> Element s -> Element s #

project a data point from an old range to a new range

grid :: Pos -> s -> Grid s -> [Element s] #

create equally-spaced as from a space

gridSpace :: s -> Grid s -> [s] #

create equally-spaced `Space a`s from a space

Instances

(FromInteger a, Ord a, BoundedField a) => Space (Range a) #
Instance details Defined in NumHask.Range Associated Types type Element (Range a) :: * # type Grid (Range a) :: * # Methods lower :: Range a -> Element (Range a) # upper :: Range a -> Element (Range a) # mid :: Range a -> Element (Range a) # width :: Range a -> Element (Range a) # singleton :: Element (Range a) -> Range a # singular :: Range a -> Bool # element :: Element (Range a) -> Range a -> Bool # contains :: Range a -> Range a -> Bool # disjoint :: Range a -> Range a -> Bool # intersects :: Range a -> Range a -> Bool # union :: Range a -> Range a -> Range a # nul :: Range a # space :: Foldable f => f (Element (Range a)) -> Range a # project :: Range a -> Range a -> Element (Range a) -> Element (Range a) # grid :: Pos -> Range a -> Grid (Range a) -> [Element (Range a)] # gridSpace :: Range a -> Grid (Range a) -> [Range a] #
(FromInteger a, Signed a, Ord a, BoundedField a) => Space (Rect a) #
Instance details Defined in NumHask.Rect Associated Types type Element (Rect a) :: * # type Grid (Rect a) :: * # Methods lower :: Rect a -> Element (Rect a) # upper :: Rect a -> Element (Rect a) # mid :: Rect a -> Element (Rect a) # width :: Rect a -> Element (Rect a) # singleton :: Element (Rect a) -> Rect a # singular :: Rect a -> Bool # element :: Element (Rect a) -> Rect a -> Bool # contains :: Rect a -> Rect a -> Bool # disjoint :: Rect a -> Rect a -> Bool # intersects :: Rect a -> Rect a -> Bool # union :: Rect a -> Rect a -> Rect a # nul :: Rect a # space :: Foldable f => f (Element (Rect a)) -> Rect a # project :: Rect a -> Rect a -> Element (Rect a) -> Element (Rect a) # grid :: Pos -> Rect a -> Grid (Rect a) -> [Element (Rect a)] # gridSpace :: Rect a -> Grid (Rect a) -> [Rect a] #

data Pos #

Pos suggests where data points are placed on a grid across a range. Pos can also be thought about as whether the lower and upper points on the range are open or closed (plus the mid-point as an extra option).

Constructors

OuterPos
InnerPos
LowerPos
UpperPos
MidPos

Instances

Eq Pos #
Instance details Defined in NumHask.Space Methods (==) :: Pos -> Pos -> Bool # (/=) :: Pos -> Pos -> Bool #
Show Pos #
Instance details Defined in NumHask.Space Methods showsPrec :: Int -> Pos -> ShowS # show :: Pos -> String # showList :: [Pos] -> ShowS #
Generic Pos #
Instance details Defined in NumHask.Space Associated Types type Rep Pos :: * -> * # Methods from :: Pos -> Rep Pos x # to :: Rep Pos x -> Pos #
type Rep Pos #
Instance details Defined in NumHask.Space type Rep Pos = D1 (MetaData "Pos" "NumHask.Space" "numhask-range-0.2.3.1-J89sQYUYBLeKCiE9B8m0BR" False) ((C1 (MetaCons "OuterPos" PrefixI False) (U1 :: * -> ) :+: C1 (MetaCons "InnerPos" PrefixI False) (U1 :: -> )) :+: (C1 (MetaCons "LowerPos" PrefixI False) (U1 :: -> ) :+: (C1 (MetaCons "UpperPos" PrefixI False) (U1 :: -> ) :+: C1 (MetaCons "MidPos" PrefixI False) (U1 :: -> *))))