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.

[cvigilv]

Ok, so got it down to:

julia> hvtypes = [BinaryHV, BipolarHV, TernaryHV, RealHV, GradedHV, GradedBipolarHV, FHRR]
7-element Vector{Type}:
 BinaryHV
 BipolarHV
 TernaryHV
 RealHV
 GradedHV
 GradedBipolarHV
 FHRR

julia> map(x -> x(), hvtypes)
7-element Vector{AbstractHV}:
 10000-element BinaryHV with 4994 true and 5006 false
 10000-element BipolarHV with 4979 positives and 5021 negatives
 10000-element TernaryHV with 4997 positives, 0 zeros, and 5003 negatives
 10000-element RealHV{Float64} with μ ± σ = 0.01 ± 0.997
 10000-element GradedHV{Float64} with μ ± σ = 0.5 ± 0.287
 10000-element GradedBipolarHV{Float64} with μ ± σ = 0.014 ± 0.577
 10000-element FHRR{ComplexF64} with μ ± σ = 0.011 - 0.006im ± 1.0

In vectors:

julia> for hv in hvtypes
           display([hv(;D=8) for _ in 1:10])
           println()
       end
10-element Vector{BinaryHV}:
 8-element BinaryHV with 3 true and 5 false
 8-element BinaryHV with 5 true and 3 false
 8-element BinaryHV with 3 true and 5 false
 8-element BinaryHV with 3 true and 5 false
 8-element BinaryHV with 2 true and 6 false
 8-element BinaryHV with 4 true and 4 false
 8-element BinaryHV with 6 true and 2 false
 8-element BinaryHV with 3 true and 5 false
 8-element BinaryHV with 6 true and 2 false
 8-element BinaryHV with 2 true and 6 false

10-element Vector{BipolarHV}:
 8-element BipolarHV with 3 positives and 5 negatives
 8-element BipolarHV with 4 positives and 4 negatives
 8-element BipolarHV with 4 positives and 4 negatives
 8-element BipolarHV with 4 positives and 4 negatives
 8-element BipolarHV with 2 positives and 6 negatives
 8-element BipolarHV with 5 positives and 3 negatives
 8-element BipolarHV with 2 positives and 6 negatives
 8-element BipolarHV with 5 positives and 3 negatives
 8-element BipolarHV with 6 positives and 2 negatives
 8-element BipolarHV with 3 positives and 5 negatives

10-element Vector{TernaryHV}:
 8-element TernaryHV with 4 positives, 0 zeros, and 4 negatives
 8-element TernaryHV with 6 positives, 0 zeros, and 2 negatives
 8-element TernaryHV with 4 positives, 0 zeros, and 4 negatives
 8-element TernaryHV with 3 positives, 0 zeros, and 5 negatives
 8-element TernaryHV with 2 positives, 0 zeros, and 6 negatives
 8-element TernaryHV with 2 positives, 0 zeros, and 6 negatives
 8-element TernaryHV with 3 positives, 0 zeros, and 5 negatives
 8-element TernaryHV with 3 positives, 0 zeros, and 5 negatives
 8-element TernaryHV with 3 positives, 0 zeros, and 5 negatives
 8-element TernaryHV with 4 positives, 0 zeros, and 4 negatives

10-element Vector{RealHV{Float64}}:
 8-element RealHV{Float64} with μ ± σ = -0.495 ± 0.735
 8-element RealHV{Float64} with μ ± σ = 0.125 ± 1.467
 8-element RealHV{Float64} with μ ± σ = 0.109 ± 1.06
 8-element RealHV{Float64} with μ ± σ = 0.283 ± 1.208
 8-element RealHV{Float64} with μ ± σ = -0.802 ± 0.842
 8-element RealHV{Float64} with μ ± σ = -0.153 ± 0.864
 8-element RealHV{Float64} with μ ± σ = -0.088 ± 0.869
 8-element RealHV{Float64} with μ ± σ = -0.289 ± 1.311
 8-element RealHV{Float64} with μ ± σ = -0.507 ± 0.722
 8-element RealHV{Float64} with μ ± σ = -0.227 ± 1.571

10-element Vector{GradedHV{Float64}}:
 8-element GradedHV{Float64} with μ ± σ = 0.46 ± 0.341
 8-element GradedHV{Float64} with μ ± σ = 0.489 ± 0.276
 8-element GradedHV{Float64} with μ ± σ = 0.421 ± 0.325
 8-element GradedHV{Float64} with μ ± σ = 0.516 ± 0.299
 8-element GradedHV{Float64} with μ ± σ = 0.383 ± 0.319
 8-element GradedHV{Float64} with μ ± σ = 0.662 ± 0.256
 8-element GradedHV{Float64} with μ ± σ = 0.504 ± 0.301
 8-element GradedHV{Float64} with μ ± σ = 0.409 ± 0.284
 8-element GradedHV{Float64} with μ ± σ = 0.306 ± 0.295
 8-element GradedHV{Float64} with μ ± σ = 0.525 ± 0.3

10-element Vector{GradedBipolarHV{Float64}}:
 8-element GradedBipolarHV{Float64} with μ ± σ = -0.155 ± 0.674
 8-element GradedBipolarHV{Float64} with μ ± σ = -0.182 ± 0.419
 8-element GradedBipolarHV{Float64} with μ ± σ = 0.188 ± 0.648
 8-element GradedBipolarHV{Float64} with μ ± σ = -0.019 ± 0.535
 8-element GradedBipolarHV{Float64} with μ ± σ = 0.269 ± 0.615
 8-element GradedBipolarHV{Float64} with μ ± σ = 0.322 ± 0.573
 8-element GradedBipolarHV{Float64} with μ ± σ = -0.253 ± 0.439
 8-element GradedBipolarHV{Float64} with μ ± σ = 0.093 ± 0.489
 8-element GradedBipolarHV{Float64} with μ ± σ = 0.137 ± 0.568
 8-element GradedBipolarHV{Float64} with μ ± σ = 0.118 ± 0.633

10-element Vector{FHRR{ComplexF64}}:
 8-element FHRR{ComplexF64} with μ ± σ = 0.081 - 0.195im ± 1.045
 8-element FHRR{ComplexF64} with μ ± σ = -0.106 + 0.097im ± 1.058
 8-element FHRR{ComplexF64} with μ ± σ = 0.103 + 0.067im ± 1.061
 8-element FHRR{ComplexF64} with μ ± σ = 0.063 + 0.177im ± 1.05
 8-element FHRR{ComplexF64} with μ ± σ = 0.065 - 0.477im ± 0.937
 8-element FHRR{ComplexF64} with μ ± σ = -0.058 + 0.124im ± 1.059
 8-element FHRR{ComplexF64} with μ ± σ = -0.243 + 0.507im ± 0.884
 8-element FHRR{ComplexF64} with μ ± σ = -0.199 - 0.001im ± 1.048
 8-element FHRR{ComplexF64} with μ ± σ = 0.081 + 0.105im ± 1.06
 8-element FHRR{ComplexF64} with μ ± σ = -0.044 + 0.022im ± 1.068

In matrices:

julia> for hv in hvtypes
           display(fill(hv(;D=8), 3, 4))
           println()
       end
3×4 Matrix{BinaryHV}:
 [0, 1, 0, 1, 0, 1, 1, 0]  [0, 1, 0, 1, 0, 1, 1, 0]  [0, 1, 0, 1, 0, 1, 1, 0]  [0, 1, 0, 1, 0, 1, 1, 0]
 [0, 1, 0, 1, 0, 1, 1, 0]  [0, 1, 0, 1, 0, 1, 1, 0]  [0, 1, 0, 1, 0, 1, 1, 0]  [0, 1, 0, 1, 0, 1, 1, 0]
 [0, 1, 0, 1, 0, 1, 1, 0]  [0, 1, 0, 1, 0, 1, 1, 0]  [0, 1, 0, 1, 0, 1, 1, 0]  [0, 1, 0, 1, 0, 1, 1, 0]

3×4 Matrix{BipolarHV}:
 [-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]

3×4 Matrix{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]

3×4 Matrix{RealHV{Float64}}:
 [-0.171687, -0.315077, 0.471016, 0.343194, 0.232568, 0.148388, 1.54682, -0.202623]  …  [-0.171687, -0.315077, 0.471016, 0.343194, 0.232568, 0.148388, 1.54682, -0.202623]
 [-0.171687, -0.315077, 0.471016, 0.343194, 0.232568, 0.148388, 1.54682, -0.202623]     [-0.171687, -0.315077, 0.471016, 0.343194, 0.232568, 0.148388, 1.54682, -0.202623]
 [-0.171687, -0.315077, 0.471016, 0.343194, 0.232568, 0.148388, 1.54682, -0.202623]     [-0.171687, -0.315077, 0.471016, 0.343194, 0.232568, 0.148388, 1.54682, -0.202623]

3×4 Matrix{GradedHV{Float64}}:
 [0.467411, 0.454642, 0.680632, 0.88582, 0.316106, 0.242007, 0.34407, 0.169342]  …  [0.467411, 0.454642, 0.680632, 0.88582, 0.316106, 0.242007, 0.34407, 0.169342]
 [0.467411, 0.454642, 0.680632, 0.88582, 0.316106, 0.242007, 0.34407, 0.169342]     [0.467411, 0.454642, 0.680632, 0.88582, 0.316106, 0.242007, 0.34407, 0.169342]
 [0.467411, 0.454642, 0.680632, 0.88582, 0.316106, 0.242007, 0.34407, 0.169342]     [0.467411, 0.454642, 0.680632, 0.88582, 0.316106, 0.242007, 0.34407, 0.169342]

3×4 Matrix{GradedBipolarHV{Float64}}:
 [-0.970066, -0.0228868, 0.174237, -0.923973, -0.287612, -0.587565, -0.958541, 0.453084]  …  [-0.970066, -0.0228868, 0.174237, -0.923973, -0.287612, -0.587565, -0.958541, 0.453084]
 [-0.970066, -0.0228868, 0.174237, -0.923973, -0.287612, -0.587565, -0.958541, 0.453084]     [-0.970066, -0.0228868, 0.174237, -0.923973, -0.287612, -0.587565, -0.958541, 0.453084]
 [-0.970066, -0.0228868, 0.174237, -0.923973, -0.287612, -0.587565, -0.958541, 0.453084]     [-0.970066, -0.0228868, 0.174237, -0.923973, -0.287612, -0.587565, -0.958541, 0.453084]

3×4 Matrix{FHRR{ComplexF64}}:
 [-0.997321+0.0731546im, -0.801405+0.598122im, 0.987216+0.159389im, -0.964539+0.263942im, -0.536059+0.84418im, -0.881941+0.47136im, -0.414072+0.910244im, 0.879813-0.47532im]  …  [-0.997321+0.0731546im, -0.801405+0.598122im, 0.987216+0.159389im, -0.964539+0.263942im, -0.536059+0.84418im, -0.881941+0.47136im, -0.414072+0.910244im, 0.879813-0.47532im]
 [-0.997321+0.0731546im, -0.801405+0.598122im, 0.987216+0.159389im, -0.964539+0.263942im, -0.536059+0.84418im, -0.881941+0.47136im, -0.414072+0.910244im, 0.879813-0.47532im]     [-0.997321+0.0731546im, -0.801405+0.598122im, 0.987216+0.159389im, -0.964539+0.263942im, -0.536059+0.84418im, -0.881941+0.47136im, -0.414072+0.910244im, 0.879813-0.47532im]
 [-0.997321+0.0731546im, -0.801405+0.598122im, 0.987216+0.159389im, -0.964539+0.263942im, -0.536059+0.84418im, -0.881941+0.47136im, -0.414072+0.910244im, 0.879813-0.47532im]     [-0.997321+0.0731546im, -0.801405+0.598122im, 0.987216+0.159389im, -0.964539+0.263942im, -0.536059+0.84418im, -0.881941+0.47136im, -0.414072+0.910244im, 0.879813-0.47532im]

And multidimensional arrays (dims > 2):

julia> for hv in hvtypes
           display(fill(hv(;D=8), 3, 4, 2))
           println()
       end
3×4×2 Array{BinaryHV, 3}:
[:, :, 1] =
 [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]
 [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]
 [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]

[:, :, 2] =
 [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]
 [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]
 [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]  [0, 1, 0, 1, 0, 0, 0, 0]

3×4×2 Array{BipolarHV, 3}:
[:, :, 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]

[:, :, 2] =
 [-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]

3×4×2 Array{TernaryHV, 3}:
[:, :, 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]

[:, :, 2] =
 [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]

3×4×2 Array{RealHV{Float64}, 3}:
[:, :, 1] =
 [1.04051, 0.461499, -0.263889, -0.517142, 0.738812, -0.0204501, -0.966136, -0.381489]  …  [1.04051, 0.461499, -0.263889, -0.517142, 0.738812, -0.0204501, -0.966136, -0.381489]
 [1.04051, 0.461499, -0.263889, -0.517142, 0.738812, -0.0204501, -0.966136, -0.381489]     [1.04051, 0.461499, -0.263889, -0.517142, 0.738812, -0.0204501, -0.966136, -0.381489]
 [1.04051, 0.461499, -0.263889, -0.517142, 0.738812, -0.0204501, -0.966136, -0.381489]     [1.04051, 0.461499, -0.263889, -0.517142, 0.738812, -0.0204501, -0.966136, -0.381489]

[:, :, 2] =
 [1.04051, 0.461499, -0.263889, -0.517142, 0.738812, -0.0204501, -0.966136, -0.381489]  …  [1.04051, 0.461499, -0.263889, -0.517142, 0.738812, -0.0204501, -0.966136, -0.381489]
 [1.04051, 0.461499, -0.263889, -0.517142, 0.738812, -0.0204501, -0.966136, -0.381489]     [1.04051, 0.461499, -0.263889, -0.517142, 0.738812, -0.0204501, -0.966136, -0.381489]
 [1.04051, 0.461499, -0.263889, -0.517142, 0.738812, -0.0204501, -0.966136, -0.381489]     [1.04051, 0.461499, -0.263889, -0.517142, 0.738812, -0.0204501, -0.966136, -0.381489]

3×4×2 Array{GradedHV{Float64}, 3}:
[:, :, 1] =
 [0.666839, 0.733592, 0.284642, 0.254711, 0.777862, 0.657296, 0.403583, 0.317517]  …  [0.666839, 0.733592, 0.284642, 0.254711, 0.777862, 0.657296, 0.403583, 0.317517]
 [0.666839, 0.733592, 0.284642, 0.254711, 0.777862, 0.657296, 0.403583, 0.317517]     [0.666839, 0.733592, 0.284642, 0.254711, 0.777862, 0.657296, 0.403583, 0.317517]
 [0.666839, 0.733592, 0.284642, 0.254711, 0.777862, 0.657296, 0.403583, 0.317517]     [0.666839, 0.733592, 0.284642, 0.254711, 0.777862, 0.657296, 0.403583, 0.317517]

[:, :, 2] =
 [0.666839, 0.733592, 0.284642, 0.254711, 0.777862, 0.657296, 0.403583, 0.317517]  …  [0.666839, 0.733592, 0.284642, 0.254711, 0.777862, 0.657296, 0.403583, 0.317517]
 [0.666839, 0.733592, 0.284642, 0.254711, 0.777862, 0.657296, 0.403583, 0.317517]     [0.666839, 0.733592, 0.284642, 0.254711, 0.777862, 0.657296, 0.403583, 0.317517]
 [0.666839, 0.733592, 0.284642, 0.254711, 0.777862, 0.657296, 0.403583, 0.317517]     [0.666839, 0.733592, 0.284642, 0.254711, 0.777862, 0.657296, 0.403583, 0.317517]

3×4×2 Array{GradedBipolarHV{Float64}, 3}:
[:, :, 1] =
 [0.205278, 0.97772, 0.220871, 0.754317, -0.495529, 0.673231, -0.634751, -0.615472]  …  [0.205278, 0.97772, 0.220871, 0.754317, -0.495529, 0.673231, -0.634751, -0.615472]
 [0.205278, 0.97772, 0.220871, 0.754317, -0.495529, 0.673231, -0.634751, -0.615472]     [0.205278, 0.97772, 0.220871, 0.754317, -0.495529, 0.673231, -0.634751, -0.615472]
 [0.205278, 0.97772, 0.220871, 0.754317, -0.495529, 0.673231, -0.634751, -0.615472]     [0.205278, 0.97772, 0.220871, 0.754317, -0.495529, 0.673231, -0.634751, -0.615472]

[:, :, 2] =
 [0.205278, 0.97772, 0.220871, 0.754317, -0.495529, 0.673231, -0.634751, -0.615472]  …  [0.205278, 0.97772, 0.220871, 0.754317, -0.495529, 0.673231, -0.634751, -0.615472]
 [0.205278, 0.97772, 0.220871, 0.754317, -0.495529, 0.673231, -0.634751, -0.615472]     [0.205278, 0.97772, 0.220871, 0.754317, -0.495529, 0.673231, -0.634751, -0.615472]
 [0.205278, 0.97772, 0.220871, 0.754317, -0.495529, 0.673231, -0.634751, -0.615472]     [0.205278, 0.97772, 0.220871, 0.754317, -0.495529, 0.673231, -0.634751, -0.615472]

3×4×2 Array{FHRR{ComplexF64}, 3}:
[:, :, 1] =
 [0.934752-0.3553im, -0.529971-0.848016im, 0.258655+0.96597im, 0.283604-0.958942im, 0.824143-0.566381im, 0.831777+0.55511im, 0.826788-0.562514im, -0.230161-0.973153im]  …  [0.934752-0.3553im, -0.529971-0.848016im, 0.258655+0.96597im, 0.283604-0.958942im, 0.824143-0.566381im, 0.831777+0.55511im, 0.826788-0.562514im, -0.230161-0.973153im]
 [0.934752-0.3553im, -0.529971-0.848016im, 0.258655+0.96597im, 0.283604-0.958942im, 0.824143-0.566381im, 0.831777+0.55511im, 0.826788-0.562514im, -0.230161-0.973153im]     [0.934752-0.3553im, -0.529971-0.848016im, 0.258655+0.96597im, 0.283604-0.958942im, 0.824143-0.566381im, 0.831777+0.55511im, 0.826788-0.562514im, -0.230161-0.973153im]
 [0.934752-0.3553im, -0.529971-0.848016im, 0.258655+0.96597im, 0.283604-0.958942im, 0.824143-0.566381im, 0.831777+0.55511im, 0.826788-0.562514im, -0.230161-0.973153im]     [0.934752-0.3553im, -0.529971-0.848016im, 0.258655+0.96597im, 0.283604-0.958942im, 0.824143-0.566381im, 0.831777+0.55511im, 0.826788-0.562514im, -0.230161-0.973153im]

[:, :, 2] =
 [0.934752-0.3553im, -0.529971-0.848016im, 0.258655+0.96597im, 0.283604-0.958942im, 0.824143-0.566381im, 0.831777+0.55511im, 0.826788-0.562514im, -0.230161-0.973153im]  …  [0.934752-0.3553im, -0.529971-0.848016im, 0.258655+0.96597im, 0.283604-0.958942im, 0.824143-0.566381im, 0.831777+0.55511im, 0.826788-0.562514im, -0.230161-0.973153im]
 [0.934752-0.3553im, -0.529971-0.848016im, 0.258655+0.96597im, 0.283604-0.958942im, 0.824143-0.566381im, 0.831777+0.55511im, 0.826788-0.562514im, -0.230161-0.973153im]     [0.934752-0.3553im, -0.529971-0.848016im, 0.258655+0.96597im, 0.283604-0.958942im, 0.824143-0.566381im, 0.831777+0.55511im, 0.826788-0.562514im, -0.230161-0.973153im]
 [0.934752-0.3553im, -0.529971-0.848016im, 0.258655+0.96597im, 0.283604-0.958942im, 0.824143-0.566381im, 0.831777+0.55511im, 0.826788-0.562514im, -0.230161-0.973153im]     [0.934752-0.3553im, -0.529971-0.848016im, 0.258655+0.96597im, 0.283604-0.958942im, 0.824143-0.566381im, 0.831777+0.55511im, 0.826788-0.562514im, -0.230161-0.973153im]

[cvigilv]

Adding the distribution function was too much information, making it difficult to follow. I think that argument is unlikely to be changed by the users; therefore, I left it out for now.

LMKWYT to merge.