GNAT notebook

sandbox/GNAT.jl

+### A Pluto.jl notebook ###
+# v0.19.22
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ 510f7d8a-ce11-11ed-2832-cdc20fa6f700
+begin
+	using Pkg; Pkg.activate("..")
+	using Revise
+	using FiniteStateAutomata
+	using Semirings
+	using Random
+	using SparseArrays
+	using LinearAlgebra
+end
+
+# ╔═╡ afc66d19-c7c3-4318-8fa0-f5fc640ca271
+K = LogSemiring{Float32}
+
+# ╔═╡ 2c44097b-35f7-4d50-9e27-a703c653ceb0
+Σ = Set(["a", "b", "c"])
+
+# ╔═╡ fe9d52c8-c152-4961-847a-ac9a1554e07b
+H = K.(randn(length(Σ), 4))
+
+# ╔═╡ cf73fdb5-b276-4f4f-b174-cf4db4f4d216
+N = sparse([], [], K[], length(Σ), length(Σ))
+
+# ╔═╡ ab6a60d4-8c71-4050-9d3d-37e49128da25
+e = ones(K, length(Σ))
+
+# ╔═╡ ba26ff62-d337-418b-8992-8230484b8cab
+Q = size(H, 1) * (size(H, 2) - 1)
+
+# ╔═╡ 313206a0-b8cb-4766-9ac1-fe4ddd29e8d2
+L = FSA(
+	sparsevec(1:length(Σ), H[:, 1], Q),
+	sparse([
+		N sparse(e * H[:, 2]') N;
+		N N sparse(e * H[:, 3]');
+		N N N
+	]),
+	sparsevec(Q - length(Σ) + 1: Q, H[:, end], Q),
+	zero(K),
+	repeat(["a", "b", "c"], 3)
+)
+
+# ╔═╡ d123178c-561d-4780-bde8-6edcc21f9ae9
+N
+
+# ╔═╡ 66659283-01c5-4883-854a-5a03012fb56e
+C = FSA(
+	sparsevec([1], one(K), 4),
+	sparse([1, 1, 1, 2, 3, 4], [1, 2, 3, 4, 4, 4], one(K), 4, 4),
+	sparsevec([4], one(K), 4),
+	zero(K),
+	["a", "b", "a", "c"]
+)
+
+# ╔═╡ 770b840b-c9cd-470b-bb7c-861a33e4fb14
+D = FSA(
+	sparsevec([1], one(K), 3),
+	sparse([1, 1, 2, 3], [1, 2, 3, 1], one(K), 3, 3),
+	sparsevec([3], one(K), 3),
+	zero(K),
+	["a", "b", "c"]
+)
+
+# ╔═╡ 7820e2e6-55df-49ee-8fde-ffb4c69269b5
+C ∩ D
+
+# ╔═╡ b37d3f48-0b23-4700-bb45-050b08209669
+@time L ∩ C
+
+# ╔═╡ 26a8c2c5-27da-4389-bfd8-ca3793dd994e
+I = FSA(
+	kron(L.α, C.α),
+	kron(L.T, C.T),
+	kron(L.ω, C.ω),
+	L.ρ * C.ρ,
+	kron(L.λ, C.λ)
+)
+
+# ╔═╡ 183f8031-b384-408b-8cd6-c84f23693dfc
+M = sparse([1,1,2,3,4,4,5,6,7,7,8,9],[1,3,2,4,1,3,2,4,1,3,2,4], one(K), nstates(L), nstates(C))
+
+# ╔═╡ b605383a-4080-4916-857c-2528f6ad172c
+M' * L.ω
+
+# ╔═╡ e91b7104-7149-4770-8abe-fb0a968bd197
+L
+
+# ╔═╡ 49fb8a23-bae8-4c66-8490-01d7e28f25f9
+begin
+	e3 = ones(K, nstates(C))
+	N3 = spzeros(K, nstates(C), nstates(C))
+	M3 = sparse([1,1,2,3],[1,3,2,4], one(K), size(H,1), nstates(C))
+	T3 = [
+		N3 sparse(e3 * (M3'*H[:, 2])') .* C.T N3;
+		N3 N3 sparse(e3 * (M3'*H[:, 2])') .* C.T;
+		N3 N3 N3;
+	]
+	T3
+end
+
+# ╔═╡ 29a16022-6ebc-4e74-8245-e7293fcb160a
+A3=FSA(
+	sparsevec(1:nstates(C), C.α .* (M3' * H[:, 1]), nstates(C) * (size(H, 2)- 1)),
+	T3,
+	sparsevec( (size(H, 2) - 2) * nstates(C) + 1 : (size(H, 2) - 1) * nstates(C), C.ω .* (M3' * H[:,end]), nstates(C) * (size(H, 2)- 1)),
+	C.ρ * L.ρ,
+	repeat(C.λ, size(H, 2) -1)
+)
+
+# ╔═╡ ada373ae-0e4e-42ca-80a5-98be29aca610
+G = DenseFSA(H, sort(collect(Σ)), zero(K))
+
+# ╔═╡ 049d12b4-0107-4ecc-89e4-45d3955bdd0b
+@time G ∩ C
+
+# ╔═╡ 54888ef8-6ee9-446d-9b78-364fe35e52b6
+G, L
+
+# ╔═╡ b2290feb-24a1-4f7d-8216-7c69ea363a67
+L
+
+# ╔═╡ 5c3893f7-b64f-410f-9be2-5c2023fd9093
+# C = A ∩ B
+
+# ╔═╡ 5ecadd35-feea-459f-9776-3a2762b0de9f
+# FSA(C)
+
+# ╔═╡ 2ea1644a-8836-443b-a1ee-8d13dbd4a534
+H[:, 2]
+
+# ╔═╡ 68d8f4b3-48e1-49ca-b910-c65c2ec19768
+ones(K, 3) * H[:,2]'
+
+# ╔═╡ Cell order:
+# ╠═510f7d8a-ce11-11ed-2832-cdc20fa6f700
+# ╠═afc66d19-c7c3-4318-8fa0-f5fc640ca271
+# ╠═2c44097b-35f7-4d50-9e27-a703c653ceb0
+# ╠═fe9d52c8-c152-4961-847a-ac9a1554e07b
+# ╠═cf73fdb5-b276-4f4f-b174-cf4db4f4d216
+# ╠═ab6a60d4-8c71-4050-9d3d-37e49128da25
+# ╠═ba26ff62-d337-418b-8992-8230484b8cab
+# ╠═313206a0-b8cb-4766-9ac1-fe4ddd29e8d2
+# ╠═d123178c-561d-4780-bde8-6edcc21f9ae9
+# ╠═66659283-01c5-4883-854a-5a03012fb56e
+# ╠═770b840b-c9cd-470b-bb7c-861a33e4fb14
+# ╠═7820e2e6-55df-49ee-8fde-ffb4c69269b5
+# ╠═b37d3f48-0b23-4700-bb45-050b08209669
+# ╠═049d12b4-0107-4ecc-89e4-45d3955bdd0b
+# ╠═54888ef8-6ee9-446d-9b78-364fe35e52b6
+# ╠═26a8c2c5-27da-4389-bfd8-ca3793dd994e
+# ╠═183f8031-b384-408b-8cd6-c84f23693dfc
+# ╠═b605383a-4080-4916-857c-2528f6ad172c
+# ╠═e91b7104-7149-4770-8abe-fb0a968bd197
+# ╠═49fb8a23-bae8-4c66-8490-01d7e28f25f9
+# ╠═29a16022-6ebc-4e74-8245-e7293fcb160a
+# ╠═ada373ae-0e4e-42ca-80a5-98be29aca610
+# ╠═b2290feb-24a1-4f7d-8216-7c69ea363a67
+# ╠═5c3893f7-b64f-410f-9be2-5c2023fd9093
+# ╠═5ecadd35-feea-459f-9776-3a2762b0de9f
+# ╠═2ea1644a-8836-443b-a1ee-8d13dbd4a534
+# ╠═68d8f4b3-48e1-49ca-b910-c65c2ec19768