NumHask.Range

A Range a is a tuple representing an interval of a number space. A Range can be thought of as consisting of a low and high value, though low<high isn't strictly enforced, allowing a negative space so to speak. The library uses the NumHask classes and thus most of the usual arithmetic operators can be used.

Documentation

newtype Range a

a newtype wrapped (a, a) tuple

Constructors

Range

Fields

• range_ :: (a, a)

Instances

Functor Range

Methods

fmap :: (a -> b) -> Range a -> Range b

(<$) :: a -> Range b -> Range a

Ord a => AdditiveHomomorphic a (Range a)

natural interpretation of an a as a `Range a` is a singular Range

Methods

plushom :: a -> Range a

Eq a => Eq (Range a)

Methods

(==) :: Range a -> Range a -> Bool

(/=) :: Range a -> Range a -> Bool

Ord a => Ord (Range a)

Methods

compare :: Range a -> Range a -> Ordering

(<) :: Range a -> Range a -> Bool

(<=) :: Range a -> Range a -> Bool

(>) :: Range a -> Range a -> Bool

(>=) :: Range a -> Range a -> Bool

max :: Range a -> Range a -> Range a

min :: Range a -> Range a -> Range a

Show a => Show (Range a)

Methods

showsPrec :: Int -> Range a -> ShowS

show :: Range a -> String

showList :: [Range a] -> ShowS

Ord a => Semigroup (Range a)

Methods

(<>) :: Range a -> Range a -> Range a

sconcat :: NonEmpty (Range a) -> Range a

stimes :: Integral b => b -> Range a -> Range a

(AdditiveUnital (Range a), Semigroup (Range a)) => Monoid (Range a)

Methods

mempty :: Range a

mappend :: Range a -> Range a -> Range a

mconcat :: [Range a] -> Range a

Arbitrary a => Arbitrary (Range a)

Methods

arbitrary :: Gen (Range a)

shrink :: Range a -> [Range a]

(BoundedField a, Ord a) => Signed (Range a)

Methods

sign :: Range a -> Range a

abs :: Range a -> Range a

BoundedField a => MultiplicativeMagma (Range a)

times may well be some sort of affine projection lurking under the hood

Methods

times :: Range a -> Range a -> Range a

BoundedField a => MultiplicativeUnital (Range a)

The unital object derives from:

view range one = one view mid zero = zero ie (-0.5,0.5)

Methods

one :: Range a

BoundedField a => MultiplicativeAssociative (Range a)

(Ord a, BoundedField a) => MultiplicativeInvertible (Range a)

Methods

recip :: Range a -> Range a

(Ord a, BoundedField a) => MultiplicativeLeftCancellative (Range a)

Methods

(~/) :: Range a -> Range a -> Range a

(Ord a, BoundedField a) => MultiplicativeRightCancellative (Range a)

Methods

(/~) :: Range a -> Range a -> Range a

Ord a => AdditiveMagma (Range a)

choosing the convex hull as plus seems like a natural choice, given the cute zero definition.

Methods

plus :: Range a -> Range a -> Range a

(Ord a, BoundedField a) => AdditiveUnital (Range a)

Methods

zero :: Range a

Ord a => AdditiveAssociative (Range a)

Ord a => AdditiveCommutative (Range a)

Ord a => AdditiveInvertible (Range a)

Methods

negate :: Range a -> Range a

(Ord a, BoundedField a) => Additive (Range a)

Methods

(+) :: Range a -> Range a -> Range a

(BoundedField a, Ord a) => AdditiveGroup (Range a)

Methods

(-) :: Range a -> Range a -> Range a

AdditiveGroup a => Normed (Range a) a

Methods

size :: Range a -> a

(Ord a, AdditiveGroup a) => Metric (Range a) a

Methods

distance :: Range a -> Range a -> a

BoundedField a => AdditiveHomomorphic (Range a) a

natural interpretation of a `Range a` as an a is the mid-point

Methods

plushom :: Range a -> a

(...) :: Ord a => a -> a -> Range a

alternative constructor

low :: Lens' (Range a) a

lens for the fst of the tuple

high :: Lens' (Range a) a

lens for the snd of the tuple

mid :: BoundedField a => Lens' (Range a) a

mid-value lens

width :: BoundedField a => Lens' (Range a) a

range width lens

element :: Ord a => a -> Range a -> Bool

determine whether a point is within the range

singleton :: a -> Range a

singular :: Eq a => Range a -> Bool

is the range a singleton point

intersection :: Ord a => Range a -> Range a -> Range a

contains :: Ord a => Range a -> Range a -> Bool

range :: (Foldable f, Ord a, BoundedField a) => f a -> Range a

range of a foldable

project :: Field b => Range b -> Range b -> b -> b

project a data point from an old range to a new range project o n (view low o) == view low n project o n (view high o) == view high n project a a == id

data LinearPos

overns where data points go on the range

Constructors

OuterPos

InnerPos

LowerPos

UpperPos

MidPos

Instances

Eq LinearPos

Methods

(==) :: LinearPos -> LinearPos -> Bool

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

linearSpace :: (Field a, FromInteger a) => LinearPos -> Range a -> Int -> [a]

turn a range into a list of n equally-spaced as

linearSpaceSensible :: (Fractional a, Ord a, FromInteger a, QuotientField a, ExpField a) => LinearPos -> Range a -> Int -> [a]

turn a range into n as pleasing to human sense and sensibility the as may well lie outside the original range as a result

fromLinearSpace :: [a] -> [Range a]

take a list of (ascending) as and make some (ascending) ranges based on OuterPos fromLinearSpace . linearSpace OuterPos == id linearSpace OuterPos . fromLinearSpace == id