Numeric.DDE.Types

Documentation

newtype RHS state

DDE right-hand side.

Parameter state is and abstraction of a dynamical system's state, i.e. it can be a vector of any length (x(t), y(t), ...).

Constructors

RHS

Fields

• _state :: (state, HistorySnapshot state, InputSnapshot) -> state

newtype HistorySnapshot state

Contains only the required snapshot of history to make steppers (e.g. Heun) work. There could be several delay variables

Constructors

Hist

Fields

• _histsnap :: state

newtype Input

Vector of input data points

Constructors

Input

Fields

• _input :: Vector Double

newtype InputSnapshot

Input u(t) is one-dimensional

Constructors

Inp

Fields

• _insnap :: Double

type Stepper = forall state. (Functor state, VectorSpace (state Double), Num (Scalar (state Double))) => Scalar (state Double) -> RHS (state Double) -> state Double -> (HistorySnapshot (state Double), HistorySnapshot (state Double)) -> (Double, Double) -> state Double

DDE stepper (all delays are equal).

Stepper is a function of the following arguments:

• Integration step
• DDE right-hand side
• Current state vector (x(t), y(t), ...)
• Two subsequent history snapshots
• Two subsequent inputs

The result (step) is a new state vector.