## InfiniteArrays.jl

A Julia package for representing infinite-dimensional arrays
Popularity
67 Stars
Updated Last
10 Months Ago
Started In
March 2018

# InfiniteArrays.jl

A Julia package for representing arrays with infinite dimension sizes, designed to work with other array types. Infinite arrays are by necessity lazy, and so this package is closely linked to LazyArrays.jl.

The package currently supports construction, but future versions will include support for linear algebra operations like matrix multiplication, LU decompositions, and QR decompositions.

Here are some examples of current functionality:

```julia> using InfiniteArrays, LinearAlgebra

julia> x = Ones(∞) # infinite vector of all ones
Ones{Float64,1,Tuple{InfiniteArrays.OneToInf{Int64}}} with indices OneToInf():
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
⋮

julia> cumsum(x) # infinite sum
1.0:1.0:+∞

julia> exp.(-(1:∞)) .+ 2 # broadcasting supported
2.3678794411714423
2.135335283236613
2.049787068367864
2.018315638888734
2.0067379469990856
2.0024787521766663
2.0009118819655547
2.0003354626279024
2.0001234098040865
2.0000453999297623
2.0000167017007904
2.000006144212353
2.000002260329407
2.000000831528719
2.0000003059023204
2.0000001125351745
2.0000000413993773
2.00000001522998
2.0000000056027964
2.0000000020611535
2.000000000758256
2.0000000002789466
2.000000000102619
2.000000000037751
2.000000000013888
2.0000000000051092
⋮

julia> Diagonal(1:∞) # combines well with Base arrays
Diagonal{Int64,InfiniteArrays.InfUnitRange{Int64}} with indices OneToInf()×OneToInf():
1  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅   ⋅   ⋅   ⋅   ⋅   ⋅   ⋅  …
⋅  2  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅   ⋅   ⋅   ⋅   ⋅   ⋅   ⋅
⋅  ⋅  3  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅   ⋅   ⋅   ⋅   ⋅   ⋅   ⋅
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⋅  ⋅  ⋅  ⋅  ⋅  6  ⋅  ⋅  ⋅   ⋅   ⋅   ⋅   ⋅   ⋅   ⋅  …
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⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅   ⋅   ⋅   ⋅   ⋅   ⋅  15
⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅   ⋅   ⋅   ⋅   ⋅   ⋅   ⋅  …
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⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅   ⋅   ⋅   ⋅   ⋅   ⋅   ⋅  …
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⋮              ⋮                ⋮                  ⋱

julia> C = cache(Ones(∞)); C[1] = 3; C # Use cache to make mutable
LazyArrays.CachedArray{Float64,1,Array{Float64,1},Ones{Float64,1,Tuple{InfiniteArrays.InfiniteCardinal{0}}}} with indices OneToInf():
3.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
⋮```