# Recursive Array Types

The Recursive Array types are types which implement an AbstractArray interface so that recursive arrays can be handled with standard array functionality. For example, wrapped arrays will automatically do things like recurse broadcast, define optimized mapping and iteration functions, and more.

## Concrete Types

RecursiveArrayTools.VectorOfArrayType
VectorOfArray(u::AbstractVector)

A VectorOfArray is an array which has the underlying data structure Vector{AbstractArray{T}} (but, hopefully, concretely typed!). This wrapper over such data structures allows one to lazily act like it's a higher-dimensional vector, and easily convert to different forms. The indexing structure is:

A[i] # Returns the ith array in the vector of arrays
A[j,i] # Returns the jth component in the ith array
A[j1,...,jN,i] # Returns the (j1,...,jN) component of the ith array

which presents itself as a column-major matrix with the columns being the arrays from the vector. The AbstractArray interface is implemented, giving access to copy, push, append!, etc. functions, which act appropriately. Points to note are:

• The length is the number of vectors, or length(A.u) where u is the vector of arrays.
• Iteration follows the linear index and goes over the vectors

Additionally, the convert(Array,VA::AbstractVectorOfArray) function is provided, which transforms the VectorOfArray into a matrix/tensor. Also, vecarr_to_vectors(VA::AbstractVectorOfArray) returns a vector of the series for each component, that is, A[i,:] for each i. A plot recipe is provided, which plots the A[i,:] series.

RecursiveArrayTools.DiffEqArrayType
DiffEqArray(u::AbstractVector,t::AbstractVector)

This is a VectorOfArray, which stores A.t that matches A.u. This will plot (A.t[i],A[i,:]). The function tuples(diffeq_arr) returns tuples of (t,u).

To construct a DiffEqArray

t = 0.0:0.1:10.0
f(t) = t - 1
f2(t) = t^2
vals = [[f(tval) f2(tval)] for tval in t]
A = DiffEqArray(vals, t)
A[1,:]  # all time periods for f(t)
A.t
RecursiveArrayTools.ArrayPartitionType
ArrayPartition(x::AbstractArray...)

An ArrayPartition A is an array, which is made up of different arrays A.x. These index like a single array, but each subarray may have a different type. However, broadcast is overloaded to loop in an efficient manner, meaning that A .+= 2.+B is type-stable in its computations, even if A.x[i] and A.x[j] do not match types. A full array interface is included for completeness, which allows this array type to be used in place of a standard array where such a type stable broadcast may be needed. One example is in heterogeneous differential equations for DifferentialEquations.jl.

An ArrayPartition acts like a single array. A[i] indexes through the first array, then the second, etc., all linearly. But A.x is where the arrays are stored. Thus, for:

using RecursiveArrayTools
A = ArrayPartition(y,z)

we would have A.x[1]==y and A.x[2]==z. Broadcasting like f.(A) is efficient.