Define new dot method for abstract vectors (JuliaLang#22392)

* Define dot product between Number and AbstractArray

* Define dot between abstract arrays

* Added docs for dot between arrays

* Revert "Define dot product between Number and AbstractArray"

This reverts commit d46cdc7.

* Define new dot method between AbstractVectors

base/linalg/generic.jl

@@ -678,7 +678,8 @@ dot(x::Number, y::Number) = vecdot(x, y)
     dot(x, y)
     ⋅(x,y)
 
-Compute the dot product. For complex vectors, the first vector is conjugated.
+Compute the dot product between two vectors. For complex vectors, the first vector is conjugated.
+When the vectors have equal lengths, calling `dot` is semantically equivalent to `sum(vx'vy for (vx,vy) in zip(x, y))`.
 
 # Example
 
@@ -690,7 +691,29 @@ julia> dot([im; im], [1; 1])
 0 - 2im
 ```
 """
-dot(x::AbstractVector, y::AbstractVector) = vecdot(x, y)
+function dot(x::AbstractVector, y::AbstractVector)
+    if length(x) != length(y)
+        throw(DimensionMismatch("dot product arguments have lengths $(length(x)) and $(length(y))"))
+    end
+    ix = start(x)
+    if done(x, ix)
+        # we only need to check the first vector, since equal lengths have been asserted
+        return zero(eltype(x))'zero(eltype(y))
+    end
+    @inbounds (vx, ix) = next(x, ix)
+    @inbounds (vy, iy) = next(y, start(y))
+    s = vx'vy
+    while !done(x, ix)
+        @inbounds (vx, ix) = next(x, ix)
+        @inbounds (vy, iy) = next(y, iy)
+        s += vx'vy
+    end
+    return s
+end
+
+# Call optimized BLAS methods for vectors of numbers
+dot(x::AbstractVector{<:Number}, y::AbstractVector{<:Number}) = vecdot(x, y)
+
 
 ###########################################################################################
 

test/linalg/matmul.jl

@@ -258,6 +258,9 @@ end
     @test dot(x, 1:2,y, 1:2) == convert(elty, 12.5)
     @test x.'*y == convert(elty, 29.0)
     @test_throws MethodError dot(rand(elty, 2, 2), randn(elty, 2, 2))
+    X = convert(Vector{Matrix{elty}},[reshape(1:4, 2, 2), ones(2, 2)])
+    res = convert(Matrix{elty}, [7.0 13.0; 13.0 27.0])
+    @test dot(X, X) == res
 end
 
 vecdot_(x,y) = invoke(vecdot, Tuple{Any,Any}, x,y) # generic vecdot