# Efficient iterated discrete dynamics in Flux

**URL:** <https://discourse.julialang.org/t/efficient-iterated-discrete-dynamics-in-flux/73837>\
**Category:** General Usage\
**Tags:** flux\
**Created:** [December 30, 2021, 9:16pm UTC](https://discourse.julialang.org/t/efficient-iterated-discrete-dynamics-in-flux/73837 "2021-12-30T21:16:04Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![GlenHenshaw](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/glenhenshaw/32/5269_2.png) [@GlenHenshaw](https://discourse.julialang.org/u/GlenHenshaw)\
**Post date:** [December 30, 2021, 9:16pm UTC](https://discourse.julialang.org/t/efficient-iterated-discrete-dynamics-in-flux/73837/1 "2021-12-30T21:16:04Z")

</div>

I’m trying to implement a Koopman operator layer in Flux. This is the operation of starting with a vector, x, and iteratively multiplying it by a dynamics matrix, K, for n steps, e.g.

x1 = x  
x2 = K \* x1  
x3 = K \* x2  
etc etc

where n is typically a couple of thousand steps, so you end up with an array with a small number of rows and a lot of columns: [x x1 x2 x3…]

One easy way to do this is to calculate all the matrix powers, e.g. K, K^2, K^3, etc, and then do the matrix-vector multiply and combine everything:

```
hcat(map(i->(K^i)*x, 1:n)...)

```

but this is slow as molasses. As best I can determine, the most efficient way to do it in Julia would be to preallocate the array you need and just do a for loop:

```
xi = Array{Float32}(undef, size(K,1), n)
xi[:,1]=x
for i=2:n
    xi[:,i] = K*xi[:, i-1]
end

```

but Flux throws a “Mutating arrays is not supported” error when I do this.

What the Julia Way to do this that’s compatible with Flux?