Copyright	Copyright (c) 2009-2017 David Sorokin <david.sorokin@gmail.com>
License	BSD3
Maintainer	David Sorokin <david.sorokin@gmail.com>
Stability	experimental
Safe Haskell	None
Language	Haskell2010

Simulation.Aivika.Transform

Contents

The Transform Arrow
Delaying the Transform
The Time Transform
Differential and Difference Equations

Description

Tested with: GHC 8.0.1

The module defines something which is most close to the notion of analogous circuit as an opposite to the digital one.

Synopsis

newtype Transform a b = Transform {
- runTransform :: Dynamics a -> Simulation (Dynamics b)
}
delayTransform :: Dynamics Double -> Dynamics a -> Transform a a
timeTransform :: Transform a Double
integTransform :: Dynamics Double -> Transform Double Double
integTransformEither :: Dynamics Double -> Transform (Either Double Double) Double
sumTransform :: (Num a, Unboxed a) => Dynamics a -> Transform a a
sumTransformEither :: (Num a, Unboxed a) => Dynamics a -> Transform (Either a a) a

The Transform Arrow

newtype Transform a b Source #

It allows representing an analogous circuit as an opposite to the digital one.

This is a transform of one time varying function to another usually specified in the integration time points and then interpolated in other time points with help of one of the memoization functions like memo0Dynamics.

Constructors

Transform
Fields runTransform :: Dynamics a -> Simulation (Dynamics b) Run the transform.

Instances

Arrow Transform Source #
Instance details Defined in Simulation.Aivika.Transform Methods arr :: (b -> c) -> Transform b c # first :: Transform b c -> Transform (b, d) (c, d) # second :: Transform b c -> Transform (d, b) (d, c) # (***) :: Transform b c -> Transform b' c' -> Transform (b, b') (c, c') # (&&&) :: Transform b c -> Transform b c' -> Transform b (c, c') #
Category Transform Source #
Instance details Defined in Simulation.Aivika.Transform Methods id :: Transform a a # (.) :: Transform b c -> Transform a b -> Transform a c #

Delaying the Transform

delayTransform Source #

Arguments

:: Dynamics Double	the lag time
-> Dynamics a	the initial value
-> Transform a a	the delayed transform

Return a delayed transform by the specified lag time and initial value.

This is actually the delayI function wrapped in the Transform type.

The Time Transform

timeTransform :: Transform a Double Source #

A transform that returns the current modeling time.

Differential and Difference Equations

integTransform Source #

Arguments

:: Dynamics Double	the initial value
-> Transform Double Double	map the derivative to an integral

Return a transform that maps the derivative to an integral by the specified initial value.

This is actually the integ function wrapped in the Transform type.

integTransformEither Source #

Arguments

:: Dynamics Double	the initial value
-> Transform (Either Double Double) Double	map either a new `Left` value or the `Right` derivative to an integral

Like integTransform but allows either setting a new Left value of the integral, or updating it by the specified Right derivative.

sumTransform Source #

Arguments

:: (Num a, Unboxed a)
=> Dynamics a	the initial value
-> Transform a a	map the difference to a sum

Return a transform that maps the difference to a sum by the specified initial value.

This is actually the diffsum function wrapped in the Transform type.

sumTransformEither Source #

Arguments

:: (Num a, Unboxed a)
=> Dynamics a	the initial value
-> Transform (Either a a) a	map either a new `Left` value or the `Right` difference to a sum

Like sumTransform but allows either setting a new Left value of the sum, or updating it by the specified Right difference.