BlockArrays.jl

A block array is a partition of an array into 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 different type of block arrays that follow the AbstractBlockArray interface. The type BlockArray stores each block contiguously while the type BlockedArray stores the full matrix contiguously. 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.

A simple way to produce BlockArrays is via mortar, which combines an array of arrays into a BlockArray:

julia> using BlockArrays

julia> mortar([randn(3), randn(4)])
2-blocked 7-element BlockVector{Float64}:
 -0.19808699390960527
  0.04711385377738941
 -0.6308529482215658
 ─────────────────────
 -0.021279626465135287
 -1.0991149020591062
  1.0817971931026398
 -0.012442892450142308

julia> mortar(reshape([randn(2,2), randn(1,2), randn(2,3), randn(1,3)],2,2))
2×2-blocked 3×5 BlockMatrix{Float64}:
 -1.17797    0.359738   │   0.87676    -2.06495    1.74256
  1.54787    1.64133    │  -0.0416484  -2.00241   -0.522441
 ───────────────────────┼──────────────────────────────────
  0.430093  -0.0263753  │  -1.31275     0.278447  -0.139579

Alternatively, one can add block structure on top of an existing array by wrapping the array in BlockedArray, where the extra arguments give the sizes of the blocks:

julia> BlockedArray(randn(7), [3,4])
2-blocked 7-element BlockedVector{Float64}:
 -0.17348560551451797
 -0.5680124317024628
  1.699007590285868
 ─────────────────────
 -0.7437814954416642
 -0.018198226033108045
  1.3335354818213445
 -0.03512135185007728

julia> BlockedArray(randn(3,5), [2,1], [2,3])
2×2-blocked 3×5 BlockedMatrix{Float64}:
  0.444186   0.788823  │   0.743428  -0.815026   0.715779
 -0.721074  -0.43783   │   1.07413   -0.336926   0.539873
 ──────────────────────┼─────────────────────────────────
  0.128836  -0.350202  │  -2.71365    1.67605   -0.25611

Documentation

• STABLE — most recently tagged version of the documentation.
• LATEST — in-development version of the documentation.

Changes in v1.0

We are excited to release v1.0! There are some important breaking changes from previous versions of BlockArrays.jl:

• BlockedArray replaces PseudoBlockArray.
• Axes are now typically BlockedOneTo instead of BlockUnitRange.
• Support for some simple block-banded matrices has been moved here from BlockBandedMatrices.jl.
• The definition of blocksizes(array::AbstractArray) is changed from blocklengths.(axes(array)) to an iterator of size blocksize(array) over the sizes of each block of array.
• BlockedUnitRange is now parametrized by the element type instead of hardcoded to Int.

Contributing

Possible ways of contributing to this package include:

• Implement the fusing broadcasting interface for blocked arrays.
• Make different Linear Algebra function (like matrix / vector multiplications) with blocked arrays work.
• Implement different reductions functionalities, (sum and co.).
• Audit the performance and make improvements as needed.