QuasiArrays.jl

A package for representing quasi-arrays

A quasi-array is an array with non-classical indexing, including possibly continuous indexing. This packages implements quasi-arrays. For example, we can create a quasi-array where the first index is float valued:

using QuasiArrays
A = QuasiArray(rand(5,4,3), (range(0,1; length=5), Base.OneTo(4), [2,3,6]))
A[0.25,2,6] # equivalent to parent(A)[2,2,3]

Analogues of many the base types are supported. For example, we can create a quasi-diagonal matrix

v = QuasiVector(rand(5), 0:0.5:2) # diagonal
D = QuasiDiagonal(v)
D[0.5,0.5] # equivalent to parent(D)[0.5] == parent(parent(D))[2]

We can take views of quasi-arrays:

view(A, 0:0.25:0.5, 2:3, [2,6])[2,1,2] # equivalent to A[0.25,2,6]

And we can also broadcast, which preserves axes:

exp.(v)[0.5] # equivalent to exp(v[0.5])

Finally, by combining with IntervalSets.jl we support continuous indexing:

using IntervalSets
x = Inclusion(0.0..1.0) # Inclusion is identity, e.g. x[0.2] == 0.2
D = QuasiDiagonal(x)
D[0.1,0.2] # 0.0
D[0.1,0.1] # 0.1

Full functionality for continuous quasi-arrays is in ContinuumArrays.jl.

There are other packages that allow non-standard indexing, such as NamedArrays and AxisArrays. QuasiArrays.jl focusses on linear algebra aspects, that is, the axes of a quasi-array encode the inner product. This forms the basis of ContinuumArrays.jl which is a fresh approach to finite element methods and spectral methods, where bases are represented as quasi-matrices and discretizations arise from linear algebra operations on quasi-matrices.