Improve random vector generator
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@ -8,14 +8,29 @@ export rand_on_shell, Q, DescentHistory, realize_gram
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# === guessing ===
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##[TO DO] write a test to confirm that the outputs are on the correct shells
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##[TO DO] this can fail at generating spacelike vectors
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function rand_on_shell(rng::AbstractRNG, shells::Array{T}) where T <: Number
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space_parts = randn(rng, T, 4, size(shells, 1))
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space_self_prods = [dot(x, x) for x in eachcol(space_parts)]
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return [space_parts; sqrt.(space_self_prods .- shells)']
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sconh(t, u) = 0.5*(exp(t) + u*exp(-t))
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function rand_on_sphere(rng::AbstractRNG, ::Type{T}, n) where T
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out = randn(rng, T, n)
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tries_left = 2
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while dot(out, out) < 1e-6 && tries_left > 0
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out = randn(rng, T, n)
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tries_left -= 1
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end
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normalize(out)
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end
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##[TO DO] write a test to confirm that the outputs are on the correct shells
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function rand_on_shell(rng::AbstractRNG, shell::T) where T <: Number
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space_part = rand_on_sphere(rng, T, 4)
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rapidity = randn(rng, T)
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sig = sign(shell)
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[sconh(rapidity, sig)*space_part; sconh(rapidity, -sig)]
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end
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rand_on_shell(rng::AbstractRNG, shells::Array{T}) where T <: Number =
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hcat([rand_on_shell(rng, sh) for sh in shells]...)
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rand_on_shell(shells::Array{<:Number}) = rand_on_shell(Random.default_rng(), shells)
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# === Gram matrix realization ===
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