Simulation.Aivika.Trans.Transform

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.

The Transform Arrow

newtype Transform m a b

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 m a -> Simulation m (Dynamics m b)

  Run the transform.

Instances

MonadSD m => Arrow (Transform m)

Methods

arr :: (b -> c) -> Transform m b c

first :: Transform m b c -> Transform m (b, d) (c, d)

second :: Transform m b c -> Transform m (d, b) (d, c)

(***) :: Transform m b c -> Transform m b' c' -> Transform m (b, b') (c, c')

(&&&) :: Transform m b c -> Transform m b c' -> Transform m b (c, c')

Monad m => Category * (Transform m)

Methods

id :: cat a a

(.) :: cat b c -> cat a b -> cat a c

Delaying the Transform

delayTransform

Arguments

:: MonadSD m

=> Dynamics m Double

the lag time

-> Dynamics m a

the initial value

-> Transform m 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 :: Monad m => Transform m a Double

A transform that returns the current modeling time.

Differential and Difference Equations

integTransform

Arguments

:: (MonadSD m, MonadFix m)

=> Dynamics m Double

the initial value

-> Transform m 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

Arguments

:: (MonadSD m, MonadFix m)

=> Dynamics m Double

the initial value

-> Transform m (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

Arguments

:: (MonadSD m, MonadFix m, Num a, MonadMemo m a)

=> Dynamics m a

the initial value

-> Transform m 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

Arguments

:: (MonadSD m, MonadFix m, Num a, MonadMemo m a)

=> Dynamics m a

the initial value

-> Transform m (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.