A self-defined AbstractMatrix's subtype does not respect a self-defined Base.zero for its elements, which is a subtype of Number, when performing matrix multiplication #1334
Description
Consider the Viterbi semiring (max-times semiring), in which the binary operations are defined as:
– addition: max
– multiplication: *
with -Inf as the additive identity and 1 as the multiplicative identity.
A minimal working example is given below:
struct ViterbiSymbol{T<:Number} <: Number
v::T
end
Base.zero(::Type{ViterbiSymbol}) = ViterbiSymbol{Float64}(-Inf)
Base.one(::Type{ViterbiSymbol{T}}) where {T} = ViterbiSymbol{T}(1)
Base.:+(a::ViterbiSymbol{T}, b::ViterbiSymbol{T}) where {T} = ViterbiSymbol{T}(max(a.v, b.v))
Base.:*(a::ViterbiSymbol{T}, b::ViterbiSymbol{T}) where {T} = ViterbiSymbol{T}(a.v * b.v)
Base.promote_rule(::Type{ViterbiSymbol{Int}}, ::Type{ViterbiSymbol{Float64}}) = ViterbiSymbol{Float64}
Base.convert(::Type{ViterbiSymbol{Float64}}, v::ViterbiSymbol{Int}) = ViterbiSymbol{Float64}(float(v.v))
struct ViterbiMatrix{T<:Number} <: AbstractMatrix{ViterbiSymbol{T}}
m::Matrix{ViterbiSymbol{T}}
end
function ViterbiMatrix(e::Union{typeof(zero),typeof(one)}, size::Tuple{Int,Int})
if e === zero
m::Matrix{ViterbiSymbol{Float64}} = fill(e(ViterbiSymbol), size) # all "0"
else # e is one, all "0" except diagonal being "1"
m = fill(zero(ViterbiSymbol), size[2], size[2])
foreach(i -> m[i, i] = e(ViterbiSymbol), 1:size[2])
end
return ViterbiMatrix{Float64}(m)
end
Base.size(a::ViterbiMatrix) = Base.size(a.m)
Base.getindex(a::ViterbiMatrix, i::Vararg{Int,2}) = Base.getindex(a.m, i[1], i[2])
Base.:+(a::ViterbiMatrix, b::ViterbiMatrix) = ViterbiMatrix(a.m + b.m)
Base.:*(a::ViterbiMatrix, b::ViterbiMatrix) = ViterbiMatrix(a.m * b.m)
Base.typed_hvcat(
::Type{ViterbiSymbol}, rows::Tuple{Vararg{Int}}, xs::Number...
) = ViterbiMatrix(Matrix{ViterbiSymbol{eltype(rows)}}(reshape(collect(xs), rows)'))
A = ViterbiSymbol[1 2; 3 4];
O = ViterbiMatrix(zero, size(A))
display(A)
display(O)
display(A * O) # expected: all -Inf, got all 0.0
display(A * O == O) # expected: true, got falseIf my understanding is correct, the function _rmul_or_fill! is called to create an all-zero matrix to fill in during multiplication. This function calls zero(eltype(C)), but it seems to use the method zero(::Type{Number}) -> 0 instead of the custom zero method defined above, which returns ViterbiSymbol(-Inf).