Fix 3-arg dot for empty arrays (#1485)

Author: dkarrasch

src/bidiag.jl

@@ -1209,7 +1209,7 @@ function dot(x::AbstractVector, B::Bidiagonal, y::AbstractVector)
     nx, ny = length(x), length(y)
     (nx == size(B, 1) == ny) || throw(DimensionMismatch())
     if nx ≤ 1
-        nx == 0 && return dot(zero(eltype(x)), zero(eltype(B)), zero(eltype(y)))
+        nx == 0 && return zero(dot(zero(eltype(x)), zero(eltype(B)), zero(eltype(y))))
         return dot(x[1], B.dv[1], y[1])
     end
     ev, dv = B.ev, B.dv

src/generic.jl

@@ -1027,6 +1027,8 @@ dot(x, A, y) = dot(x, A*y) # generic fallback for cases that are not covered by
 
 function dot(x::AbstractVector, A::AbstractMatrix, y::AbstractVector)
     (axes(x)..., axes(y)...) == axes(A) || throw(DimensionMismatch())
+    # outermost zero call to avoid spurious sign ambiguity (like 0.0 - 0.0im)
+    any(isempty, (x, y)) && return zero(dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y))))
     T = typeof(dot(first(x), first(A), first(y)))
     s = zero(T)
     i₁ = first(eachindex(x))

src/hessenberg.jl

@@ -360,7 +360,7 @@ function dot(x::AbstractVector, H::UpperHessenberg, y::AbstractVector)
     m = size(H, 1)
     (length(x) == m == length(y)) || throw(DimensionMismatch())
     if iszero(m)
-        return dot(zero(eltype(x)), zero(eltype(H)), zero(eltype(y)))
+        return zero(dot(zero(eltype(x)), zero(eltype(H)), zero(eltype(y))))
     end
     x₁ = x[1]
     r = dot(x₁, H[1,1], y[1])

src/symmetric.jl

@@ -719,6 +719,7 @@ function dot(x::AbstractVector, A::RealHermSymComplexHerm, y::AbstractVector)
     require_one_based_indexing(x, y)
     n = length(x)
     (n == length(y) == size(A, 1)) || throw(DimensionMismatch())
+    iszero(n) && return zero(dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y))))
     data = A.data
     r = dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y)))
     iszero(n) && return r

src/triangular.jl

@@ -849,7 +849,7 @@ function dot(x::AbstractVector, A::UpperTriangular, y::AbstractVector)
     m = size(A, 1)
     (length(x) == m == length(y)) || throw(DimensionMismatch())
     if iszero(m)
-        return dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y)))
+        return zero(dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y))))
     end
     x₁ = x[1]
     r = dot(x₁, A[1,1], y[1])
@@ -870,7 +870,7 @@ function dot(x::AbstractVector, A::UnitUpperTriangular, y::AbstractVector)
     m = size(A, 1)
     (length(x) == m == length(y)) || throw(DimensionMismatch())
     if iszero(m)
-        return dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y)))
+        return zero(dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y))))
     end
     x₁ = first(x)
     r = dot(x₁, y[1])
@@ -892,7 +892,7 @@ function dot(x::AbstractVector, A::LowerTriangular, y::AbstractVector)
     m = size(A, 1)
     (length(x) == m == length(y)) || throw(DimensionMismatch())
     if iszero(m)
-        return dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y)))
+        return zero(dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y))))
     end
     r = zero(typeof(dot(first(x), first(A), first(y))))
     @inbounds for j in axes(A, 2)
@@ -912,7 +912,7 @@ function dot(x::AbstractVector, A::UnitLowerTriangular, y::AbstractVector)
     m = size(A, 1)
     (length(x) == m == length(y)) || throw(DimensionMismatch())
     if iszero(m)
-        return dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y)))
+        return zero(dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y))))
     end
     r = zero(typeof(dot(first(x), first(y))))
     @inbounds for j in axes(A, 2)

src/tridiag.jl

@@ -246,7 +246,7 @@ function dot(x::AbstractVector, S::SymTridiagonal, y::AbstractVector)
     nx, ny = length(x), length(y)
     (nx == size(S, 1) == ny) || throw(DimensionMismatch("dot"))
     if nx ≤ 1
-        nx == 0 && return dot(zero(eltype(x)), zero(eltype(S)), zero(eltype(y)))
+        nx == 0 && return zero(dot(zero(eltype(x)), zero(eltype(S)), zero(eltype(y))))
         return dot(x[1], S.dv[1], y[1])
     end
     dv, ev = S.dv, S.ev
@@ -965,7 +965,7 @@ function dot(x::AbstractVector, A::Tridiagonal, y::AbstractVector)
     nx, ny = length(x), length(y)
     (nx == size(A, 1) == ny) || throw(DimensionMismatch())
     if nx ≤ 1
-        nx == 0 && return dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y)))
+        nx == 0 && return zero(dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y))))
         return dot(x[1], A.d[1], y[1])
     end
     @inbounds begin

test/generic.jl

@@ -733,6 +733,10 @@ end
         @test dot(x, B', y) ≈ dot(B*x, y)
         elty <: Real && @test dot(x, transpose(B), y) ≈ dot(x, transpose(B)*y)
     end
+    for (m, n) in ((0, 0), (1, 0), (0, 1))
+        v = zeros(ComplexF64, m); a = zeros(ComplexF64, m, n); w = zeros(Float64, n)
+        @test dot(v, a, w) === zero(ComplexF64)
+    end
 end
 
 @testset "condskeel #34512" begin