refactor: improve string representations

[cvigilv]

I was playing around with doing some changes to the string representations as during my time using this I found them difficult to parse for some problems. For example, the old version was:

julia> TernaryHV()
10000-element TernaryHV
mean ± std : 0.002 ± 1.0

julia> [TernaryHV() for _ in 1:100]
100-element Vector{TernaryHV}:
 10000-element TernaryHV - m ± sd: 0.0 ± 1.0
 10000-element TernaryHV - m ± sd: -0.0 ± 1.0
 10000-element TernaryHV - m ± sd: -0.0 ± 1.0
 10000-element TernaryHV - m ± sd: 0.0 ± 1.0
 10000-element TernaryHV - m ± sd: 0.0 ± 1.0
 ⋮
 10000-element TernaryHV - m ± sd: -0.0 ± 1.0
 10000-element TernaryHV - m ± sd: 0.0 ± 1.0
 10000-element TernaryHV - m ± sd: 0.0 ± 1.0
 10000-element TernaryHV - m ± sd: 0.0 ± 1.0
 10000-element TernaryHV - m ± sd: 0.0 ± 1.0

and the new is:

julia> TernaryHV()
10000-element TernaryHV with μ ± σ = -0.004 ± 1.0:
 -1
  1
 -1
 -1
 -1
  ⋮
  1
 -1
  1
 -1
  1

julia> [TernaryHV() for _ in 1:100]
100-element Vector{TernaryHV}:
 [-1, -1, 1, 1, 1, 1, -1, -1, 1, 1  …  1, 1, -1, -1, 1, 1, -1, 1, -1, 1]
 [-1, 1, -1, -1, 1, 1, 1, 1, -1, 1  …  1, 1, 1, -1, 1, 1, -1, -1, -1, 1]
 [-1, -1, -1, -1, -1, -1, 1, -1, 1, -1  …  -1, -1, -1, -1, 1, 1, 1, -1, -1, 1]
 [-1, -1, -1, 1, -1, -1, 1, -1, 1, -1  …  1, 1, -1, 1, -1, -1, 1, 1, -1, 1]
 [-1, 1, -1, 1, -1, 1, 1, -1, 1, 1  …  -1, 1, 1, 1, 1, 1, 1, -1, 1, 1]
 ⋮
 [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1  …  1, -1, -1, 1, 1, -1, -1, -1, -1, -1]
 [-1, -1, -1, -1, 1, -1, 1, 1, 1, -1  …  1, -1, -1, -1, -1, -1, -1, -1, -1, 1]
 [-1, -1, 1, 1, 1, 1, -1, 1, 1, 1  …  -1, -1, -1, 1, -1, -1, -1, 1, -1, 1]
 [-1, 1, 1, 1, -1, 1, -1, 1, 1, -1  …  1, -1, 1, 1, 1, -1, -1, 1, 1, -1]
 [-1, -1, -1, 1, -1, -1, -1, -1, -1, 1  …  1, -1, 1, 1, -1, -1, -1, 1, 1, 1]

This version is closer to how vectors are represented in Julia. I think something in between would be better, but I would like to know your opinion before investing more time into this as this takes some tinkering since it's more about UX than anything.

I would combine the built-in vector print for long-style and the type one-liner for the short form:

10000-element TernaryHV with μ ± σ = -0.004 ± 1.0:
-1
1
...
1
1



10000-element TernaryHV (μ ± σ = -0.004 ± 1.0)

[cvigilv]

Other types:

julia> BipolarHV()
10000-element BipolarHV with 5056 positives and 4944 negatives:
 -1
  1
  1
  1
  1
  ⋮
 -1
 -1
 -1
 -1
 -1

julia> BinaryHV()
10000-element BinaryHV with 5036 true and 4964 false:
 0
 1
 0
 0
 0
 ⋮
 1
 0
 1
 0
 1

julia> RealHV()
10000-element RealHV{Float64} with μ ± σ = -0.006 ± 1.006:
  2.6116202595969775
 -1.892508377213708
  0.9741403645815744
  0.1405009525163469
  0.07264655332880232
  ⋮
 -1.4794770328987807
  1.034756806145206
  1.0380093547827494
 -0.45964829544811403
 -0.09244997040145336

julia> GradedBipolarHV()
10000-element GradedBipolarHV{Float64} with μ ± σ = 0.005 ± 0.582:
  0.6717833224869785
  0.5510791674269708
  0.49664159888119963
 -0.9390257335078157
  0.49205261393994837
  ⋮
 -0.7215113112299928
 -0.4892236308339185
  0.7215516291881439
 -0.2712029753388182
 -0.6529738849222699

julia> GradedHV()
10000-element GradedHV{Float64} with μ ± σ = 0.501 ± 0.288:
 0.7441905938351135
 0.10305724672731151
 0.7835908217384924
 0.08008971804310389
 0.9566298321570428
 ⋮
 0.2922459670460071
 0.032410308351557705
 0.5892633828477645
 0.04585572654633515
 0.5148917368076651

Thinking on adding the distribution function for the relevant hypervectors, LMKWYT

[cvigilv]

I was thinking on this styles:

D-element BinaryHV with X trues & Y falses
D-element BipolarHV with X positives & Y negatives
D-element TernaryHV with X positives, Y zeros & Z negatives
D-element RealHV{T} with μ ± σ = X ± Y (distr = Distributions.Normal{Float64}(μ=0.0, σ=1.0) )
D-element GradedHV{T} with μ ± σ = X ± Y (distr = Distributions.Beta{Float64}(α=1.0, β=1.0) )
D-element GradedBipolarHV{T} with μ ± σ = X ± Y (distr = ...)

Alternatively, I was thinking on something along the line of:

BinaryHV(D=D, true=X, false=Y)
BipolarHV(D=D, positive=X, negative=Y)
TernaryHV(D=D, positives=X, zero=Y, negative=Z)
RealHV{T}(D=D, μ = X, σ = Y, distr=Distributions.Normal{Float64}(μ=0.0, σ=1.0))
...

[MichielStock]

Good for me. The representations can still be improved.