diff --git a/sandbox/example.jl b/sandbox/example.jl
index 4618a0c0f78fb6d4e76734f37e97e9116acb1eac..1a6c9bb32a3b6ae8ca0ff08501a160778d75c3ef 100644
--- a/sandbox/example.jl
+++ b/sandbox/example.jl
@@ -13,6 +13,7 @@ begin
using FSALinalg
using LinearAlgebra
using SparseArrays
+ using Semirings
end
# â•”â•â•¡ 33a02e4e-44a6-4d66-9a1a-0372b96695d6
@@ -38,7 +39,7 @@ where:
"""
# â•”â•â•¡ 87e1cf8e-da52-4c85-ab6a-bb352a84d779
-K = Float32
+K = LogSemiring{Float32}
# â•”â•â•¡ 8602a2b5-16ca-4cec-8041-c6362aa66a48
M1 = FSA(
@@ -46,7 +47,7 @@ M1 = FSA(
sparse([3, 2, 2], [1, 1, 3], K[2.5, 2.5, 1.5], 3, 3),
sparsevec([1], K[3.5], 3),
K(0.5),
- ["1", "2", "3"]
+ ["a", "b", "c"]
)
# â•”â•â•¡ 9400b791-605f-4cb5-a3d7-71af5a034504
@@ -61,6 +62,97 @@ M2 = FSA(
# â•”â•â•¡ 78aa5aa2-87a7-4bf6-80a2-71fd79bf03d1
parent(M1)
+# â•”â•â•¡ 45d44224-9e88-482c-95d8-d1a793b3fd79
+renorm(M1)
+
+# â•”â•â•¡ 6d6c0896-dbd3-41d1-8f90-04120bd26087
+cumsum(M1 |> renorm)
+
+# â•”â•â•¡ 1bfd0d49-8833-4b05-978c-9830d5c6bc33
+M1
+
+# â•”â•â•¡ e7a6ab1c-262e-4a3b-a34b-e2485dfbeedf
+R = ProductSemiring{Tuple{ProbSemiring{Float64}, UnionConcatSemiring{StringMonoid}}}
+
+# â•”â•â•¡ 992b92d0-e402-4cec-a232-0a2c6e71d9c7
+one(zero(R))
+
+# â•”â•â•¡ 57c74af2-73fe-4c57-af46-7eedff77e119
+T1 = UnionConcatSemiring{StringMonoid}
+
+# â•”â•â•¡ edf219c8-9663-4af9-8ace-3ace909fad07
+T1(Set(StringMonoid["b"])) * T1(Set(StringMonoid["a"]))
+
+# â•”â•â•¡ ff37939d-195b-4a80-863d-89baf53c2341
+convert(M1) do v, l
+ if isnothing(l) && iszero(v)
+ return ProductSemiring(
+ (
+ v,
+ zero(UnionConcatSemiring{StringMonoid})
+ )
+ )
+ elseif isnothing(l)
+ return ProductSemiring(
+ (
+ v,
+ one(UnionConcatSemiring{StringMonoid})
+ )
+ )
+ else
+ return ProductSemiring((v, UnionConcatSemiring{StringMonoid}(Set(StringMonoid[l]))))
+ end
+end
+
+# â•”â•â•¡ 08ad3fe4-5be2-4512-b11e-07c6c0a9b786
+function Base.isequal(A1::AbstractFSA{K}, A2::AbstractFSA{K}) where K
+ L = UnionConcatSemiring{StringMonoid}
+ R = ProductSemiring{Tuple{K, L}}
+
+
+ Dâ‚— = spdiagm(
+ [R((one(K), Set(StringMonoid[l]))) for l in A1.λ]
+ )
+ [ProductSemiring((v, L(Set(StringMonoid[λ(A1)[i]])))) for (i, v) in zip(initstates(A1)...)]
+ [ProductSemiring((v, L(Set(StringMonoid[λ(A1)[i]])))) for (i, v) in zip(finalstates(A1)...)]
+ # FSA(
+ # Dâ‚— * sparsevec(initstates(A1)[1], one())
+ # )
+end
+
+# â•”â•â•¡ 6b4504c0-6775-49bf-91fb-759c8d528395
+isequal(M1, M2)
+
+# â•”â•â•¡ 7a4e1c92-e01a-4b08-9b98-416a502aef17
+L = [R((one(ProbSemiring{Float64}), Set(StringMonoid[l]))) for l in M1.λ]
+
+# â•”â•â•¡ b34b0f0c-1bfc-4e4b-a388-8550fd62d628
+SM1 = FSA(
+ spdiagm(L) * sparsevec(findnz(α(M1))[1], one(R), nstates(M1)),
+ sparse(findnz(T(M1))[1:2]..., one(R), nstates(M1), nstates(M1)) * spdiagm(L),
+ sparsevec(findnz(ω(M1))[1], one(R), nstates(M1)),
+ ! iszero(Ï(M1)) ? one(R) : zero(R),
+ M1.λ
+)
+
+# â•”â•â•¡ a7b8be4a-a77c-4b26-85d8-f38b2d91965d
+cumsum(SM1) == cumsum(SM1)
+
+# â•”â•â•¡ 780eb548-9bb3-40a4-8c95-f5dbb371f070
+sum(T(SM1)' * spdiagm(α(SM1)), dims = 2)
+
+# â•”â•â•¡ 6413cd1f-22d1-4cc0-bd03-39d3df88c823
+sum(spdiagm(α(SM1)) * T(SM1), dims=2)
+
+# â•”â•â•¡ 0fae1d09-a501-43d3-89f7-2245f6f6d1fd
+T(SM1)' * α(SM1)
+
+# â•”â•â•¡ a7e8863d-73cb-4921-8c1a-cd68ba3c5e5b
+v₀ = α(SM1) .* λ(SM1)
+
+# â•”â•â•¡ ce204f13-d907-47df-84bc-7a6aca678583
+SM1.T' * SM1.T' * vâ‚€
+
# â•”â•â•¡ 50a6809e-c10d-41be-9217-00512fd387e2
md"""
## FSA Operations
@@ -98,7 +190,7 @@ where:
"""
# â•”â•â•¡ 590ea7ba-eeae-4f03-8189-a199714001fe
-M1 ∪ M2
+M1 ∪ M2 |> renorm
# â•”â•â•¡ 5a2320c0-69c9-4ab2-b350-767b9db2d228
md"""
@@ -270,6 +362,15 @@ M1.T' * spdiagm(M1.α)
# â•”â•â•¡ e7dd85e6-e03e-48ad-96fd-6b9e7c4cb968
M2
+# â•”â•â•¡ 6d64bbd1-dbe5-463d-9fd5-bf72fb92ad45
+Tuple{LogSemiring{Float64}, BoolSemiring}.parameters
+
+# â•”â•â•¡ 235dfa07-9c56-47a2-a4a8-0b540625bc26
+
+
+# â•”â•â•¡ 941c7e7a-6b6d-48a8-8426-426b9ddcb9e1
+isbitstype(Core.SimpleVector)
+
# â•”â•â•¡ 7ad2f7f3-e6b6-4707-ac81-22c51d4a8316
function DFS(M, v, visited, order)
ws = v == 0 ? M.α : M.T[v,:]
@@ -418,6 +519,16 @@ end
# â•”â•â•¡ 5433be8c-61fa-4262-839a-d9a137c05377
edges, states = determinize(M3)
+# â•”â•â•¡ 03289f26-13cf-418f-853a-228b6427cf33
+function conv(f::Function, A::AbstractFSA{K}) where K
+
+ sparsevec(initstates(A)[1], [f(i, v) for (i, v) in zip(initstates(A)...)], nstates(A))
+ sparse(edges(A)[1], edges(A)[2], [f(j, v) for (i, j, v) in zip(edges(A)...)], nstates(A), nstates(A))
+end
+
+# â•”â•â•¡ aea78dcc-02a2-44d4-a24e-acb088d61bc3
+edges
+
# â•”â•â•¡ 143d6069-6978-43ed-815f-5cf19de83fbf
function fsadet(M, edges, states)
state2idx = Dict(q => i for (i, q) in enumerate(sort(collect(states))))
@@ -493,6 +604,26 @@ C .* Z3
# â• â•8602a2b5-16ca-4cec-8041-c6362aa66a48
# â• â•9400b791-605f-4cb5-a3d7-71af5a034504
# â• â•78aa5aa2-87a7-4bf6-80a2-71fd79bf03d1
+# â• â•45d44224-9e88-482c-95d8-d1a793b3fd79
+# â• â•6d6c0896-dbd3-41d1-8f90-04120bd26087
+# â• â•1bfd0d49-8833-4b05-978c-9830d5c6bc33
+# â• â•e7a6ab1c-262e-4a3b-a34b-e2485dfbeedf
+# â• â•992b92d0-e402-4cec-a232-0a2c6e71d9c7
+# â• â•57c74af2-73fe-4c57-af46-7eedff77e119
+# â• â•edf219c8-9663-4af9-8ace-3ace909fad07
+# â• â•b34b0f0c-1bfc-4e4b-a388-8550fd62d628
+# â• â•03289f26-13cf-418f-853a-228b6427cf33
+# â• â•aea78dcc-02a2-44d4-a24e-acb088d61bc3
+# â• â•ff37939d-195b-4a80-863d-89baf53c2341
+# â• â•08ad3fe4-5be2-4512-b11e-07c6c0a9b786
+# â• â•6b4504c0-6775-49bf-91fb-759c8d528395
+# â• â•7a4e1c92-e01a-4b08-9b98-416a502aef17
+# â• â•a7b8be4a-a77c-4b26-85d8-f38b2d91965d
+# â• â•780eb548-9bb3-40a4-8c95-f5dbb371f070
+# â• â•6413cd1f-22d1-4cc0-bd03-39d3df88c823
+# â• â•0fae1d09-a501-43d3-89f7-2245f6f6d1fd
+# â• â•a7e8863d-73cb-4921-8c1a-cd68ba3c5e5b
+# â• â•ce204f13-d907-47df-84bc-7a6aca678583
# ╟─50a6809e-c10d-41be-9217-00512fd387e2
# ╟─e252d8ea-9763-4030-9440-59e3a63ec4c2
# â• â•590ea7ba-eeae-4f03-8189-a199714001fe
@@ -519,6 +650,9 @@ C .* Z3
# â• â•d3256762-6488-4b11-8490-261a98fad0b2
# â• â•747e8dbb-d41a-442d-a483-bef308ef7f40
# â• â•e7dd85e6-e03e-48ad-96fd-6b9e7c4cb968
+# â• â•6d64bbd1-dbe5-463d-9fd5-bf72fb92ad45
+# â• â•235dfa07-9c56-47a2-a4a8-0b540625bc26
+# â• â•941c7e7a-6b6d-48a8-8426-426b9ddcb9e1
# â• â•7ad2f7f3-e6b6-4707-ac81-22c51d4a8316
# â• â•6b705783-890d-49f2-b3a2-6228897e2fb4
# â• â•2a1daba5-9035-4a5c-b32d-c73c022135c6
diff --git a/src/ops.jl b/src/ops.jl
index 4132979eabdfc30c724c68e636fc41ca955a1ed6..e8ebcbac27f10d258d79bc02a894f0fc70e40c22 100644
--- a/src/ops.jl
+++ b/src/ops.jl
@@ -9,7 +9,7 @@ Accumulate the weight of all the paths of length less or equal to
function Base.cumsum(A::AbstractFSA; v₀ = α(A), n = nstates(A))
v = vâ‚€
σ = dot(v, ω(A)) + Ï(A)
- for i in 2:n
+ for i in 1:n
v = T(A)' * v
σ += dot(v, ω(A))
end
@@ -43,12 +43,12 @@ Return the concatenation of the given FSA.
function Base.cat(A1::AbstractFSA{K,L}, A2::AbstractFSA{K,L}) where {K,L}
D1, D2 = size(T(A1), 1), size(T(A2), 1)
FSA(
- vcat(α(A1), zero(K) * α(A2)),
+ vcat(α(A1), iszero(Ï(A1)) ? spzeros(K, D2) : Ï(A1) * α(A2)),
[T(A1) (ω(A1) * α(A2)');
spzeros(K, D2, D1) T(A2)],
- vcat(zero(K) * ω(A1), ω(A2)),
+ vcat(iszero(Ï(A2)) ? spzeros(K, D1) : ω(A1) * Ï(A2), ω(A2)),
Ï(A1) * Ï(A2),
- vcat(λ(A2), λ(A2))
+ vcat(λ(A1), λ(A2))
)
end
Base.cat(A1::AbstractFSA{K,L}, AN::AbstractFSA{K,L}...) where {K,L} =
diff --git a/test/runtests.jl b/test/runtests.jl
index ddba6db43cf9fde432342dce4630141f523b2bc1..b2cdb22ba623ed18afeba6306fdc3147e2a3b133 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -51,11 +51,20 @@ end
@test all(Ï(A2) ≈ Ï2)
@test all(λ(A2) .== λ2)
+ # union
B12 = convert((w, l) -> f(L, w, l), union(A1, A2))
cs_B12 = cumsum(B12)
cs_B1_B2 = cumsum(B1) + cumsum(B2)
@test cs_B12.tval[1] ≈ cs_B1_B2.tval[1]
@test cs_B12.tval[2] == cs_B1_B2.tval[2]
+
+ # concatenation
+ B12 = convert((w, l) -> f(L, w, l), cat(A1, A2))
+ cs_B12 = cumsum(B12)
+ cs_B1_B2 = cumsum(B2) * cumsum(B1)
+ @test cs_B12.tval[1] ≈ cs_B1_B2.tval[1]
+ @test cs_B12.tval[2] == cs_B1_B2.tval[2]
+
end
end