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