Bordered Arrays

Advanced usage

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Here are some informations on a composite type which is used all over the package to hold a couple (array, array) or (array, scalar) while implementing the methods described in Requested methods for Custom State.

x = BorderedArray(vec1, vec2)

This defines an array (although not <: AbstractArray) to hold two arrays or an array and a scalar. This is useful when one wants to add constraints (phase, ...) to a functional for example. It is used throughout the package for the Pseudo Arc Length Continuation, for the continuation of Fold / Hopf points, for periodic orbits... It is also used to define periodic orbits as (orbit, period). As such, it is a convenient alternative to cat, vcat and friends. We chose not to make it a subtype of AbstractArray as we wish to apply the current package to general "arrays", see Requested methods for Custom State. Finally, it proves useful for the GPU where the operation x[end] can be slow.