Data.StepFunction

Functions for dealing with step functions.

Documentation

data Transition x y

A Transition, for a certain value on the x axis, there is a new y value.

Constructors

Transition

Fields

• x_val :: x

  The x value where the transition happens.

• y_val :: y

  The new y value.

• left_closed :: Bool

  If True, y_val is for all x >= x_val, otherwise for all x > x_val.

Instances

Functor (Transition x)

Methods

fmap :: (a -> b) -> Transition x a -> Transition x b

(<$) :: a -> Transition x b -> Transition x a

(Eq y, Eq x) => Eq (Transition x y)

Methods

(==) :: Transition x y -> Transition x y -> Bool

(/=) :: Transition x y -> Transition x y -> Bool

(Ord x, Eq y) => Ord (Transition x y)

Methods

compare :: Transition x y -> Transition x y -> Ordering

(<) :: Transition x y -> Transition x y -> Bool

(<=) :: Transition x y -> Transition x y -> Bool

(>) :: Transition x y -> Transition x y -> Bool

(>=) :: Transition x y -> Transition x y -> Bool

max :: Transition x y -> Transition x y -> Transition x y

min :: Transition x y -> Transition x y -> Transition x y

(Show y, Show x) => Show (Transition x y)

Methods

showsPrec :: Int -> Transition x y -> ShowS

show :: Transition x y -> String

showList :: [Transition x y] -> ShowS

data StepFunction x y

A StepFunction is implemented as a default value and a sorted list of Transitions.

Instances

Functor (StepFunction x)

Methods

fmap :: (a -> b) -> StepFunction x a -> StepFunction x b

(<$) :: a -> StepFunction x b -> StepFunction x a

(Eq x, Eq y) => Eq (StepFunction x y)

Methods

(==) :: StepFunction x y -> StepFunction x y -> Bool

(/=) :: StepFunction x y -> StepFunction x y -> Bool

(Show x, Show y) => Show (StepFunction x y)

Methods

showsPrec :: Int -> StepFunction x y -> ShowS

show :: StepFunction x y -> String

showList :: [StepFunction x y] -> ShowS

mkStepFunction :: (Ord x, Eq y) => y -> [Transition x y] -> StepFunction x y

Smart constructor sorts and simplifies the list of transitions.

valAt :: Ord x => x -> StepFunction x y -> y

Get the y value for a given x.

transitions :: StepFunction x y -> [Transition x y]

The transitions.

merge :: (Ord x, Eq c) => (a -> b -> c) -> StepFunction x a -> StepFunction x b -> StepFunction x c

Merge two step function, such that the following should be true:

valAt x (merge f sf1 sf2) == f (valAt x sf1) (valAt x sf2)

The resulting step function will be simplified, transitions that don't change the y value will be eliminated, and transitions that happen on the same x position will be eliminated.