Add realdot

Project.toml

@@ -3,6 +3,9 @@ uuid = "c1ae055f-0cd5-4b69-90a6-9a35b1a98df9"
 authors = ["David Widmann"]
 version = "0.1.0"
 
+[deps]
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+
 [compat]
 julia = "1"
 

README.md

@@ -4,3 +4,10 @@
 [![Coverage](https://codecov.io/gh/devmotion/RealDot.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/devmotion/RealDot.jl)
 [![Coverage](https://coveralls.io/repos/github/devmotion/RealDot.jl/badge.svg?branch=main)](https://coveralls.io/github/devmotion/RealDot.jl?branch=main)
 [![Code Style: Blue](https://img.shields.io/badge/code%20style-blue-4495d1.svg)](https://github.com/invenia/BlueStyle)
+
+This package only contains and exports a single function `realdot(x, y)`. It computes
+`real(LinearAlgebra.dot(x, y))` while avoiding computing the imaginary part of
+`LinearAlgebra.dot((x, y)` if possible.
+
+This function can be useful e.g. if you define pullbacks for non-holomorphic functions
+(see e.g. [this discussion in the ChainRulesCore.jl repo](https://github.com/JuliaDiff/ChainRulesCore.jl/pull/474)). It was implemented initially in [ChainRules.jl](https://github.com/JuliaDiff/ChainRules.jl) in [this PR](https://github.com/JuliaDiff/ChainRules.jl/pull/216) as `_realconjtimes`.

src/RealDot.jl

@@ -1,5 +1,22 @@
 module RealDot
 
-# Write your package code here.
+using LinearAlgebra: LinearAlgebra
+
+export realdot
+
+"""
+    realdot(x, y)
+
+Compute `real(dot(x, y))` while avoiding computing the imaginary part if possible.
+
+This function can be useful if you work with derivatives of functions on complex
+numbers. In particular, this computation shows up in pullbacks for non-holomorphic
+functions.
+"""
+@inline realdot(x, y) = real(LinearAlgebra.dot(x, y))
+@inline realdot(x::Number, y::Number) = muladd(real(x), real(y), imag(x) * imag(y))
+@inline realdot(x::Real, y::Number) = x * real(y)
+@inline realdot(x::Number, y::Real) = real(x) * y
+@inline realdot(x::Real, y::Real) = x * y
 
 end

test/runtests.jl

@@ -1,6 +1,34 @@
 using RealDot
+using LinearAlgebra
 using Test
 
+# struct need to be defined outside of tests for julia 1.0 compat
+# custom complex number to test fallback definition
+struct CustomComplex{T}
+    re::T
+    im::T
+end
+
+Base.real(x::CustomComplex) = x.re
+Base.imag(x::CustomComplex) = x.im
+
+function LinearAlgebra.dot(a::CustomComplex, b::Number)
+    return CustomComplex(reim((a.re - a.im * im) * b)...)
+end
+function LinearAlgebra.dot(a::Number, b::CustomComplex)
+    return CustomComplex(reim(conj(a) * (b.re + b.im * im))...)
+end
+function LinearAlgebra.dot(a::CustomComplex, b::CustomComplex)
+    return CustomComplex(reim((a.re - a.im * im) * (b.re + b.im * im))...)
+end
+
 @testset "RealDot.jl" begin
-    # Write your tests here.
+    scalars = (randn(), randn(ComplexF64), CustomComplex(reim(randn(ComplexF64))...))
+    arrays = (randn(10), randn(ComplexF64, 10))
+
+    for inputs in (scalars, arrays)
+        for x in inputs, y in inputs
+            @test realdot(x, y) == real(dot(x, y))
+        end
+    end
 end