This package provides a collection of utilities for working with n-dimensional array-like data structures that do have considerable overhead for single read operations. Most important examples are arrays that represent data on hard disk that are accessed through a C library or that are compressed in chunks. It can be inadvisable to make these arrays a direct subtype of AbstractArray many functions working with AbstractArrays assume fast random access into single values (including basic things like getindex, show, reduce, etc...).

Currently supported features are:

• getindex/setindex with the same rules as base (trailing or singleton dimensions etc)
• views into DiskArrays
• a fallback Base.show method that does not call getindex repeatedly
• implementations for mapreduce and mapreducedim, that respect the chunking of the underlying dataset. This greatly increases performance of higher-level reductions like sum(a,dims=d)
• an iterator over the values of a DiskArray that caches a chunk of data and returns the values within. This allows efficient usage of e.g. using DataStructures; counter(a)
• customization of broadcast when there is a DiskArray on the LHS. This at least makes things like a.=5 possible and relatively fast

Package authors who want to use this library to make their disk-based array an AbstractDiskArray should at least implement methods for the following functions:

Base.size(A::CustomDiskArray)
readblock!(A::CustomDiskArray{T,N},aout,r::Vararg{AbstractUnitRange,N})
writeblock!(A::CustomDiskArray{T,N},ain,r::Vararg{AbstractUnitRange,N})

Here readblock! will read a subset of array A in a hyper-rectangle defined by the unit ranges r. The results shall be written into aout. writeblock! should write the data given by ain into the (hyper-)rectangle of A defined by r When defining the functions it can be safely assumed that length(r) == ndims(A) as well as size(ain) == length.(r). However, bounds checking is not performed by the DiskArray machinery and currently should be done by the implementation.

If the data on disk has rectangular chunks as underlying storage units, you should addtionally implement the following methods to optimize some operations like broadcast, reductions and sparse indexing:

DiskArrays.haschunks(A::CustomDiskArray) = DiskArrays.Chunked()
DiskArrays.eachchunk(A::CustomDiskArray) = DiskArrays.GridChunks(A, chunksize)

where chunksize is a int-tuple of chunk lengths. If the array does not have an internal chunking structure, one should define

DiskArrays.haschunks(A::CustomDiskArray) = DiskArrays.Unchunked()

Implementing only these methods makes all kinds of strange indexing patterns work (Colons, StepRanges, Integer vectors, Boolean masks, CartesianIndices, Arrays of CartesianIndex, and mixtures of all these) while making sure that as few readblock! or writeblock! calls as possible are performed by reading a rectangular bounding box of the required array values and re-arranging the resulting values into the output array.

In addition, DiskArrays.jl provides a few optimizations for sparse indexing patterns to avoid reading and discarding too much unnecessary data from disk, for example for indices like A[:,:,[1,1500]].

Here we define a new array type that wraps a normal AbstractArray. The only access method that we define is a readblock! function where indices are strictly given as unit ranges along every dimension of the array. This is a very common API used in libraries like HDF5, NetCDF and Zarr. We also define a chunking, which will control the way iteration and reductions are computed. In order to understand how exactly data is accessed, we added the additional print statements in the readblock! and writeblock! functions.

using DiskArrays

struct PseudoDiskArray{T,N,A<:AbstractArray{T,N}} <: AbstractDiskArray{T,N}
  parent::A
  chunksize::NTuple{N,Int}
end
PseudoDiskArray(a;chunksize=size(a)) = PseudoDiskArray(a,chunksize)
haschunks(a::PseudoDiskArray) = Chunked()
eachchunk(a::PseudoDiskArray) = GridChunks(a,a.chunksize)
Base.size(a::PseudoDiskArray) = size(a.parent)
function DiskArrays.readblock!(a::PseudoDiskArray,aout,i::AbstractUnitRange...)
  ndims(a) == length(i) || error("Number of indices is not correct")
  all(r->isa(r,AbstractUnitRange),i) || error("Not all indices are unit ranges")
  println("Reading at index ", join(string.(i)," "))
  aout .= a.parent[i...]
end
function DiskArrays.writeblock!(a::PseudoDiskArray,v,i::AbstractUnitRange...)
  ndims(a) == length(i) || error("Number of indices is not correct")
  all(r->isa(r,AbstractUnitRange),i) || error("Not all indices are unit ranges")
  println("Writing to indices ", join(string.(i)," "))
  view(a.parent,i...) .= v
end
a = PseudoDiskArray(rand(4,5,1))

Disk Array with size 10 x 9 x 1

Now all the Base indexing behaviors work for our array, while minimizing the number of reads that have to be done:

a[:,3]

Reading at index Base.OneTo(10) 3:3 1:1

10-element Array{Float64,1}:
 0.8821177068878834
 0.6220977650963209
 0.22676949571723437
 0.3177934541451004
 0.08014908894614026
 0.9989838001681182
 0.5865160181790519
 0.27931778627456216
 0.449108677620097  
 0.22886146620923808

As can be seen from the read message, only a single call to readblock is performed, which will map to a single call into the underlying C library.

mask = falses(4,5,1)
mask[3,2:4,1] .= true
a[mask]

3-element Array{Int64,1}:
 6
 7
 8

One can check in a similar way, that reductions respect the chunks defined by the data type:

sum(a,dims=(1,3))

Reading at index 1:5 1:3 1:1
Reading at index 6:10 1:3 1:1
Reading at index 1:5 4:6 1:1
Reading at index 6:10 4:6 1:1
Reading at index 1:5 7:9 1:1
Reading at index 6:10 7:9 1:1

1×9×1 Array{Float64,3}:
[:, :, 1] =
 6.33221  4.91877  3.98709  4.18658  …  6.01844  5.03799  3.91565  6.06882

When a DiskArray is on the LHS of a broadcasting expression, the results with be written chunk by chunk:

va = view(a,5:10,5:8,1)
va .= 2.0
a[:,:,1]

Writing to indices 5:5 5:6 1:1
Writing to indices 6:10 5:6 1:1
Writing to indices 5:5 7:8 1:1
Writing to indices 6:10 7:8 1:1
Reading at index Base.OneTo(10) Base.OneTo(9) 1:1

10×9 Array{Float64,2}:
 0.929979   0.664717  0.617594  0.720272   …  0.564644  0.430036  0.791838
 0.392748   0.508902  0.941583  0.854843      0.682924  0.323496  0.389914
 0.761131   0.937071  0.805167  0.951293      0.630261  0.290144  0.534721
 0.332388   0.914568  0.497409  0.471007      0.470808  0.726594  0.97107
 0.251657   0.24236   0.866905  0.669599      2.0       2.0       0.427387
 0.388476   0.121011  0.738621  0.304039   …  2.0       2.0       0.687802
 0.991391   0.621701  0.210167  0.129159      2.0       2.0       0.733581
 0.371857   0.549601  0.289447  0.509249      2.0       2.0       0.920333
 0.76309    0.648815  0.632453  0.623295      2.0       2.0       0.387723
 0.0882056  0.842403  0.147516  0.0562536     2.0       2.0       0.107673

There are situations where one wants to read every other value along a certain axis or provide arbitrary strides. Some DiskArray backends may want to provide optimized methods to read these strided arrays. In this case a backend can define readblock!(a,aout,r::OrdinalRange...) and the respective writeblock method which will overwrite the fallback behavior that would read the whol block of data and only return the desired range.

There are arrays that live on disk but which are not split into rectangular chunks, so that the haschunks trait returns Unchunked(). In order to still enable broadcasting and reductions for these arrays, a chunk size will be estimated in a way that a certain memory limit per chunk is not exceeded. This memory limit defaults to 100MB and can be modified by changing DiskArrays.default_chunk_size[]. Then a chunk size is computed based on the element size of the array. However, there are cases where the size of the element type is undefined, e.g. for Strings or variable-length vectors. In these cases one can overload the DiskArrays.element_size function for certain container types which returns an approximate element size (in bytes). Otherwise the size of an element will simply be assumed to equal the value stored in DiskArrays.fallback_element_size which defaults to 100 bytes.