Sketch random vector generator

This needs to be rewritten: it can fail at generating spacelike vectors.

engine-proto/gram-test/Engine.jl

@@ -2,8 +2,23 @@ module Engine
 
 using LinearAlgebra
 using SparseArrays
+using Random
 
-export Q, DescentHistory, realize_gram
+export rand_on_shell, Q, DescentHistory, realize_gram
+
+# === guessing ===
+
+##[TO DO] write a test to confirm that the outputs are on the correct shells
+##[TO DO] this can fail at generating spacelike vectors
+function rand_on_shell(rng::AbstractRNG, shells::Array{T}) where T <: Number
+  space_parts = randn(rng, T, 4, size(shells, 1))
+  space_self_prods = [dot(x, x) for x in eachcol(space_parts)]
+  return [space_parts; sqrt.(space_self_prods .- shells)']
+end
+
+rand_on_shell(shells::Array{<:Number}) = rand_on_shell(Random.default_rng(), shells)
+
+# === Gram matrix realization ===
 
 # the Lorentz form
 Q = diagm([1, 1, 1, 1, -1])