Julia package for defining infinite random arrays using InfRandVector and InfRandMatrix. Simple examples using these types are given below, and the full list of functions available is:
InfRandBidiagonal
InfRandDiagonal
InfRandLowerTriangular
InfRandMatrix
InfRandSymTridiagonal
InfRandSymmetric
InfRandTridiagonal
InfRandUnitLowerTriangular
InfRandUnitUpperTriangular
InfRandUpperTriangular
InfRandVector
julia> using InfiniteRandomArrays, Random
julia> seq = InfRandVector()
ℵ₀-element InfRandVector{Float64, Type{Float64}, Xoshiro} with indices 1:∞:
0.45212042137198805
0.9647238362580713
0.6462526785368201
0.6070361635715884
0.10222222882722942
⋮
julia> using Distributions
julia> seq = InfRandVector(Xoshiro(); dist = Normal()) # you can provide your own RNG objects and probability distributions
ℵ₀-element InfRandVector{Float64, Normal{Float64}, Xoshiro} with indices 1:∞:
-0.2504330818050723
0.5311482824138374
-0.44943761206068344
-0.05495674359736308
-1.3213053212880623
⋮
julia> mat = InfRandMatrix() # ∞ × ∞ by default
ℵ₀×ℵ₀ InfRandMatrix{Float64, InfRandVector{Float64, Type{Float64}, Xoshiro}, Infinities.Infinity, Infinities.Infinity} with indices OneToInf()×OneToInf():
0.984449 0.203976 0.898197 0.84345 0.745756 0.368674 0.351961 0.461869 …
0.585687 0.610724 0.267032 0.495627 0.697247 0.873579 0.44229 0.301071
0.534054 0.557934 0.478424 0.843203 0.723205 0.339773 0.731446 0.18291
0.0206029 0.0462717 0.160456 0.76735 0.869515 0.365665 0.476832 0.565982
0.49287 0.616739 0.637889 0.870164 0.770499 0.616812 0.580221 0.370818
⋮ ⋮ ⋱
julia> mat = InfRandMatrix(3, ∞) # wide random matrix
3×ℵ₀ InfRandMatrix{Float64, InfRandVector{Float64, Type{Float64}, Xoshiro}, Int64, Infinities.Infinity} with indices Base.OneTo(3)×OneToInf():
0.900203 0.261395 0.222175 0.429518 0.732901 0.820293 0.972021 0.0544778 …
0.914717 0.538762 0.46626 0.907753 0.453501 0.307607 0.440711 0.896696
0.96409 0.556647 0.784155 0.699887 0.47419 0.35258 0.788991 0.481014
julia> mat = InfRandMatrix(Xoshiro(), ∞, 7; dist = Exponential()) # tall random matrix
ℵ₀×7 InfRandMatrix{Float64, InfRandVector{Float64, Exponential{Float64}, Xoshiro}, Infinities.Infinity, Int64} with indices OneToInf()×Base.OneTo(7):
2.3061 0.381158 0.405392 0.0152963 0.424681 0.880358 1.3035
0.988759 0.238397 1.32133 2.33813 0.626563 1.06349 1.19391
2.00946 2.7429 0.97791 1.68287 0.712554 1.26766 0.0432282
0.260173 0.947835 0.668184 0.405158 1.81257 0.195216 3.52343
1.0597 0.680587 0.616505 0.100519 0.387551 2.80689 0.63101
⋮
julia> mat = InfRandMatrix(; dist = InfiniteRandomArrays.Normal{Float32}()) # if you don't want to depend on Distributions.jl for normal sampling
ℵ₀×ℵ₀ InfRandMatrix{Float32, InfRandVector{Float32, InfiniteRandomArrays.Normal{Float32}, Xoshiro}, Infinities.Infinity, Infinities.Infinity} with indices OneToInf()×OneToInf():
0.306927 -0.15094 1.04316 -1.13007 -1.14508 -0.0463847 0.744666 …
-1.34004 -0.314993 1.01494 -1.91199 -1.52208 -0.552572 -0.760699
0.194879 0.0223698 0.196902 0.675849 1.60287 -0.233533 -1.4827
0.717089 1.12661 0.749318 0.0874666 1.06572 -1.05195 1.64873
-2.94036 -2.05101 -0.384845 0.905886 0.912348 -0.845594 -0.737711
⋮ ⋮ ⋱
⋮You can also generate random infinite random banded matrices.
julia> using InfiniteRandomArrays, BandedMatrices
julia> brand(∞, 2)
ℵ₀×ℵ₀ BandedMatrix{Float64} with bandwidths (-2, 2) with data 1×ℵ₀ InfRandMatrix{Float64, InfRandVector{Float64, Type{Float64}, Random.Xoshiro}, Int64, Infinities.Infinity} with indices Base.OneTo(1)×OneToInf() with indices 1:∞×OneToInf():
⋅ ⋅ 0.723141 ⋅ ⋅ ⋅ ⋅ …
⋅ ⋅ ⋅ 0.186655 ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ 0.676184 ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ 0.0671784 ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 0.360374
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ …
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋮ ⋮ ⋱
julia> brandn(∞, ∞, 0, 1)
ℵ₀×ℵ₀ BandedMatrix{Float64} with bandwidths (0, 1) with data 2×ℵ₀ InfRandMatrix{Float64, InfRandVector{Float64, InfiniteRandomArrays.Normal{Float64}, Random.Xoshiro}, Int64, Infinities.Infinity} with indices Base.OneTo(2)×OneToInf() with indices 1:∞×OneToInf():
-0.194233 1.40483 ⋅ ⋅ ⋅ ⋅ …
⋅ 1.31805 -0.773853 ⋅ ⋅ ⋅
⋅ ⋅ 0.396964 0.813132 ⋅ ⋅
⋅ ⋅ ⋅ -0.938625 -0.449394 ⋅
⋅ ⋅ ⋅ ⋅ 0.962001 -0.355942
⋅ ⋅ ⋅ ⋅ ⋅ -0.155913 …
⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋮ ⋮ ⋱
julia> brandn(2, ∞, -1, 3)
2×ℵ₀ BandedMatrix{Float64} with bandwidths (-1, 3) with data 3×ℵ₀ InfRandMatrix{Float64, InfRandVector{Float64, InfiniteRandomArrays.Normal{Float64}, Random.Xoshiro}, Int64, Infinities.Infinity} with indices Base.OneTo(3)×OneToInf() with indices 1:2×OneToInf():
⋅ -0.452139 0.695347 0.0522877 ⋅ ⋅ ⋅ ⋅ ⋅ …
⋅ ⋅ 0.386502 -1.22294 -0.211329 ⋅ ⋅ ⋅ ⋅
julia> brandn(∞, (-2, 1))
ℵ₀×ℵ₀ BandedMatrix{Float64} with bandwidths (2, 1) with data 4×ℵ₀ InfRandMatrix{Float64, InfRandVector{Float64, InfiniteRandomArrays.Normal{Float64}, Random.Xoshiro}, Int64, Infinities.Infinity} with indices Base.OneTo(4)×OneToInf() with indices 1:∞×OneToInf():
0.112621 0.228737 ⋅ ⋅ ⋅ ⋅ …
0.256487 -0.420693 -0.957109 ⋅ ⋅ ⋅
-0.348874 -0.979824 0.852881 -1.166 ⋅ ⋅
⋅ 0.487066 0.961304 -0.197319 0.892409 ⋅
⋅ ⋅ 0.5048 0.012266 0.150144 1.0133
⋅ ⋅ ⋅ 0.171971 0.380894 -0.566895 …
⋅ ⋅ ⋅ ⋅ 0.675937 0.698617
⋮ ⋮ ⋱