NumHask.Space

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

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?

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)

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

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]

(Signed a, FromInteger a, Ord a, BoundedField a) => Space (Rect a)

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

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

Methods

(==) :: Pos -> Pos -> Bool

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