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BlockArrays.jl

Block arrays in Julia

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A block array is a partition of an array into multiple blocks or subarrays, see wikipedia for a more extensive description. This package has two purposes. Firstly, it defines an interface for an AbstractBlockArray block arrays that can be shared among types representing different types of block arrays. The advantage to this is that it provides a consistent API for block arrays.

Secondly, it also implements two concrete types of block arrays that follow the AbstractBlockArray interface. The type BlockArray stores each single block contiguously, by wrapping an AbstractArray{<:AbstractArray{T,N},N} to concatenate all blocks – the complete array is thus not stored contiguously. Conversely, a BlockedArray stores the full matrix contiguously (by wrapping only one AbstractArray{T, N}) and only superimposes a block structure. This means that BlockArray supports fast non copying extraction and insertion of blocks, while BlockedArray supports fast access to the full matrix to use in, for example, a linear solver.

Terminology

We talk about an “a×b-blocked m×n block array”, if we have $m \times n$ values arranged in $a \times b$ blocks, like in the following example:

2×3-blocked 4×4 BlockMatrix{Float64}:
 0.56609   │  0.95429   │  0.0688403  0.980771 
 0.203829  │  0.138667  │  0.0200418  0.0515364
 ──────────┼────────────┼──────────────────────
 0.963832  │  0.391176  │  0.925799   0.148993 
 0.18693   │  0.838529  │  0.801236   0.793251

The dimension of arrays works the same as with standard Julia arrays; for example the following is a $2 \times 2$ block vector:

2-blocked 4-element BlockVector{Float64}:
 0.35609231970760424
 0.7732179994849591 
 ───────────────────
 0.8455294223894625 
 0.04250653797187476

A block array layout is specified its block sizes – a tuple of AbstractArray{Int}. The length of the tuple is equal to the dimension, the length of each block size array is the number of blocks in the corresponding dimension, and the sum of each block size is the scalar size in that dimension. For example, BlockArray{Int}(undef, [2,2,2], [2,2,2], [2,2,2]) will produce a blocked cube (an AbstractArray{Int, 3}, i.e., 3 dimensions), consisting of 27 2×2×2 blocks (3 in each dimension) and 216 values (6 in each dimension).

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