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https://github.com/mschauer/DynamicIterators.jl

Iterators with message passing and feedback loops
https://github.com/mschauer/DynamicIterators.jl

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Iterators with message passing and feedback loops

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# DynamicIterators.jl



## `DynamicIterator`

Iterators combine to a tree of iterators, but dynamic iterators combine to a network of interacting entities.



Dynamic iterators subtype `<:DynamicIterator`. They extend the iteration protocol and define

```julia

    dyniterate(iter, somemessage(state))

```

or

```julia

    dyniterate(iter, othermessage(state), arg)

```

where message wraps a state or other relevant information.

For example the definition

```julia

struct Start{T} <: Message

    value::T

end

dyniterate(iter, Start(value))

```

communicates that `iter` should start at `value` (if this is implemented).

This is similar to `iterate(iter)` communicating that `iter` should start at a predefined

value. In fact a fallback

```julia

dyniterate(iter, ::Nothing) = iterate(iter)

```

is in place.



Some messages make the iterator accept a third argument.

A simple example using `bind` to bind an iterator to an iterator using the three-argument form of `dyniterate`:

```julia

using DynamicIterators

import DynamicIterators: dyniterate



struct Summed <: DynamicIterator

end



function dyniterate(::Summed, ::Nothing, y)

    y, y

end



function dyniterate(::Summed, i, y)

    i + y, i + y

end



@show collect(bind(1:5, Summed()))

```



A more in-depth example showing the power of the approach is https://github.com/mschauer/DynamicIterators.jl/blob/master/example/ressourcemanagement.jl, showing how to extend the iterator protocol

to allow resource management (e.g. closing of files of child iterators) at the end of iteration of the parent.



A preliminary list of supported messages:



Message (and third argument) | Meaning

----------------------------|--------------------

`state` or `State(state)`   | ordinary iteration

`Start(noting)`             | start the iterator at its default

`Start(x)`                  | start the iterate from the state corresponding to value `x`

`Value(x, state)`           | continue to iterate from the state corresponding to iterate `x`

`NextKey(state, nextkey)`   | advance an iterator over pairs of `key=>values` to `nextkey`

`Steps(state, n)`           | advance the iterator `n` steps or possibly rewind if `n` negative

`Control(state), control`   | control term as in the Kalman filter provided as third argument to dyniterate⋆

`Sample(state[,rng])`       | sample from iterates⋆

`NextKeys(state), key`      | advance iterator to the keys provided as third argument to dyniterate⋆



⋆persistent messages: `dyniterate` returns a state again wrapped by the message



## `Evolution`: Evolution-type dynamic iterators

Typically, the state of an iterator is opaque. But for some iterators

the iterates *are* the states:



```julia

julia> value, state = iterate('A':'Z')

('A', 'A')



julia> value, state = iterate('A':'Z', 'X')

('Y', 'Y')

```



This means that the states/iterates of an iterator can be modified in a

transparent way. This allows iterators not only to depend on each other, but to

*interact*.



`DynamicIterators.jl` embeds a constrained iterator protocol for

iterators subtyping `<:Evolution`, which define

```julia

evolve(iterator, x) -> y

dub(x) = x === nothing ? nothing : (x,x)

iterate(iterator::Evolution, x) = dub(evolve(iterator, x))

```

which guarantees `value == state` and introduces a powerful set of combinators

for such iterators.



## Combinators



As a simple example take a Metropolis-Hastings chain



It can be described as a simple Evolution.

```julia

function evolve(MH::MetropolisHastings, (t,x)::Pair)

    P = MH.P

    Q = MH.proposal(x)

    xᵒ = rand(Q)

    Qᵒ = MH.proposal(xᵒ)

    if log(rand(MH.rng)) < MH.logpdf(P, xᵒ) - MH.logpdf(P, x) + MH.logpdf(Qᵒ, x) - MH.logpdf(Q, xᵒ)

        x = xᵒ

    end

    (t+1 => x)

end

```



The following example shows that the `Mixture` iterator combinator can be used to combine two Metropolis-Hastings chains into a component wise MetropolisHastings sampler:



```julia

using DynamicIterators

using Distributions



D = MvNormal([1.0, 0.5], [1.0 0.5; 0.5 1.5] )

struct Move{T}

    x::T

    σ::Float64

    i::Int

end

m1(x) = Move(x, 0.1, 1)

m2(x) = Move(x, 0.1, 2)

Base.rand(M::Move) = M.x + M.σ*randn()*[M.i-1, 2-M.i]

Distributions.logpdf(M::Move, x) = logpdf(Normal(M.x[M.i], M.σ), x[M.i])

MH1 = MetropolisHastings(D, m1, logpdf)

MH2 = MetropolisHastings(D, m2, logpdf)



I = Evolve(i->rand(1:2))



MH = mixture(I, (MH1, MH2))



X = values(trace(MH, 1=>(1, [0.0, 0.0]), endtime(2000)))

```



![img](https://raw.githubusercontent.com/mschauer/DynamicIterators.jl/master/asset/mh.png)



## Lifting time



Letting

```julia

evolve(E, (i, x)::Pair) = i + 1 => evolve(E, x)

```

constitutes a "lifting" of discrete time. This corresponds to enumerating the iterates of an evolution `x = f(x)` as `(1 => x1, 2 => x2, ...)`.



`DynamicIterators` control keywords treat `Pair`s as pair of key and value in concordance with the package `Trajectories` and somewhat in line with Julia's general convention.



## Traces



## Controlled Dynamic Iterators



## Examples



To illustrates the range of this I have picked some examples of very diverse nature.