TrajectoryIndexingUtils.jl

This is a super lightweight package that exports two functions: index and slice. These functions have helped to ease the burden of handling messy indexing into trajectory data vectors of the form

$$\vec Z = \text{vec}\left(z_1, z_2, \ldots, z_T\right) \in \mathbf{R}^{T \cdot d}$$

where each element $z_t$ is referred to as a knot point and normally contains state variables and control variables. In a simple situation we might have $z_t = \text{vec} (x_t, u_t) \in \mathbf{R}^{d = n+m}$, for the state $x_t \in \mathbf{R}^n$ and control $u_t \in \mathbf{R}^m$. In this case, with dim = n + m, we can use slice and index, to extract what we want from $\vec Z$ in the following way:

extract $z_t$:
```
zₜ = Z⃗[slice(t, dim)]
```
extract $x_t$:
```
xₜ = Z⃗[slice(t, 1:n, dim)]
```
extract $u_t$:
```
uₜ = Z⃗[slice(t, (1:m) .+ n, dim)]
```
extract $i$-th component of $x_t$:
```
xₜⁱ = Z⃗[index(t, i, dim)]
```
extract $j$-th component of $u_t$:
```
uₜʲ = Z⃗[index(t, j + n, dim)]
```

With this, the user is still responsible for keeping track of the component indices for $x$ and $u$, and possibly other variables. To alleviate this nuisance, the package NamedTrajectories.jl provides a richer alternative for handling trajectory data with arbitrarily named components, please check it out!

Installation

This package is not yet registered. To install, use the following command:

using Pkg
Pkg.add(url="https://github.com/aarontrowbridge/TrajectoryIndexingUtils.jl", rev="main")

Methods

The `index` function

index(t::Int, dim::Int) -> zₜ[dim]
index(t::Int, pos::Int, dim::Int) -> zₜ[pos]

The `slice` function

slice(t::Int, dim::Int; stretch=0) -> zₜ[1:dim + stretch] # can be used to extract, e.g., [xₜ; xₜ₊₁], with stretch = dim
slice(t::Int, pos::Int, dim::Int) -> zₜ[1:pos]
slice(t::Int, pos1::Int, pos2::Int, dim::Int) -> zₜ[pos1:pos2]
slice(t::Int, indices::AbstractVector{Int}, dim::Int) -> zₜ[indices]
slice(ts::UnitRange{Int}, dim::Int) -> vec(zₜ for t ∈ ts)

TODO

Add tests
Add examples
Add documentation
Add methods that take in trajectory vector as the first argument
Add block function for accessing blocks of matrices with trajectory structure, e.g. jacobians & hessians

kestrelquantum / trajectoryindexingutils.jl Goto Github PK