Added ConjArray wrapper type for conjugate views

By default, this is used only in conjugation with `RowVector`, so that
both `transpose(vec)` and `ctranspose(vec)` both return views.

NEWS.md

@@ -208,6 +208,10 @@ Library improvements
 
   * `notify` now returns a count of tasks woken up ([#19841]).
 
+  * Introduced a wrapper type for lazy complex conjugation of arrays, `ConjArray`.
+    Currently, it is used by default for the new `RowVector` type only, and
+    enforces that both `transpose(vec)` and `ctranspose(vec)` are views not copies.
+
 Compiler/Runtime improvements
 -----------------------------
 

base/exports.jl

@@ -49,6 +49,7 @@ export
     Complex128,
     Complex64,
     Complex32,
+    ConjArray,
     DenseMatrix,
     DenseVecOrMat,
     DenseVector,

base/linalg/conjarray.jl

@@ -0,0 +1,45 @@
+# This file is a part of Julia. License is MIT: http://julialang.org/license
+
+"""
+    ConjArray(array)
+
+A lazy-view wrapper of an `AbstractArray`, taking the elementwise complex
+conjugate. This type is usually constructed (and unwrapped) via the `conj()`
+function (or related `ctranspose()`), but currently this is the default behavior
+for `RowVector` only.
+"""
+immutable ConjArray{T, N, A <: AbstractArray} <: AbstractArray{T, N}
+    parent::A
+end
+
+@inline ConjArray{T,N}(a::AbstractArray{T,N}) = ConjArray{conj_type(T), N, typeof(a)}(a)
+
+# This type can cause the element type to change under conjugation - e.g. an array of complex arrays.
+@inline conj_type(x) = conj_type(typeof(x))
+@inline conj_type{T}(::Type{T}) = promote_op(conj, T)
+
+@inline parent(c::ConjArray) = c.parent
+@inline parent_type(c::ConjArray) = parent_type(typeof(c))
+@inline parent_type{T,N,A}(::Type{ConjArray{T,N,A}}) = A
+
+@inline size(a::ConjArray) = size(a.parent)
+linearindexing{CA <: ConjArray}(::Union{CA,Type{CA}}) = linearindexing(parent_type(CA))
+
+@propagate_inbounds getindex{T,N}(a::ConjArray{T,N}, i::Int) = conj(getindex(a.parent, i))
+@propagate_inbounds getindex{T,N}(a::ConjArray{T,N}, i::Vararg{Int,N}) = conj(getindex(a.parent, i...))
+@propagate_inbounds setindex!{T,N}(a::ConjArray{T,N}, v, i::Int) = setindex!(a.parent, conj(v), i)
+@propagate_inbounds setindex!{T,N}(a::ConjArray{T,N}, v, i::Vararg{Int,N}) = setindex!(a.parent, conj(v), i...)
+
+# Currently, this is default behavior for RowVector only
+"""
+    conj(rowvector)
+
+Returns a `ConjArray` lazy view of the input, where each element is conjugated.
+"""
+@inline conj(rv::RowVector) = RowVector(_conj(parent(rv)))
+@inline conj(a::ConjArray) = parent(a)
+
+@inline _conj(a::AbstractArray) = ConjArray(a)
+@inline _conj{T<:Real}(a::AbstractArray{T}) = a
+@inline _conj(a::ConjArray) = parent(a)
+@inline _conj{T<:Real}(a::ConjArray{T}) = parent(a)

base/linalg/linalg.jl

@@ -22,6 +22,7 @@ export
 
 # Types
     RowVector,
+    ConjArray,
     SymTridiagonal,
     Tridiagonal,
     Bidiagonal,
@@ -239,6 +240,7 @@ copy_oftype{T,N,S}(A::AbstractArray{T,N}, ::Type{S}) = convert(AbstractArray{S,N
 
 include("transpose.jl")
 include("rowvector.jl")
+include("conjarray.jl")
 
 include("exceptions.jl")
 include("generic.jl")

base/linalg/rowvector.jl

@@ -67,18 +67,18 @@ julia> transpose(v)
 ```
 """
 @inline transpose(vec::AbstractVector) = RowVector(vec)
-@inline ctranspose{T}(vec::AbstractVector{T}) = RowVector(conj(vec))
+@inline ctranspose{T}(vec::AbstractVector{T}) = RowVector(_conj(vec))
 @inline ctranspose{T<:Real}(vec::AbstractVector{T}) = RowVector(vec)
 
 @inline transpose(rowvec::RowVector) = rowvec.vec
-@inline ctranspose{T}(rowvec::RowVector{T}) = conj(rowvec.vec)
+@inline ctranspose{T}(rowvec::RowVector{T}) = _conj(rowvec.vec)
 @inline ctranspose{T<:Real}(rowvec::RowVector{T}) = rowvec.vec
 
 parent(rowvec::RowVector) = rowvec.vec
 
 # Strictly, these are unnecessary but will make things stabler if we introduce
 # a "view" for conj(::AbstractArray)
-@inline conj(rowvec::RowVector) = RowVector(conj(rowvec.vec))
+@inline conj(rowvec::RowVector) = RowVector(_conj(rowvec.vec))
 @inline conj{T<:Real}(rowvec::RowVector{T}) = rowvec
 
 # AbstractArray interface

doc/src/stdlib/linalg.md

@@ -100,6 +100,7 @@ Base.LinAlg.istriu
 Base.LinAlg.isdiag
 Base.LinAlg.ishermitian
 Base.LinAlg.RowVector
+Base.LinAlg.ConjArray
 Base.transpose
 Base.transpose!
 Base.ctranspose

test/choosetests.jl

@@ -130,7 +130,7 @@ function choosetests(choices = [])
                    "linalg/diagonal", "linalg/pinv", "linalg/givens",
                    "linalg/cholesky", "linalg/lu", "linalg/symmetric",
                    "linalg/generic", "linalg/uniformscaling", "linalg/lq",
-                   "linalg/hessenberg", "linalg/rowvector"]
+                   "linalg/hessenberg", "linalg/rowvector", "linalg/conjarray"]
     if Base.USE_GPL_LIBS
         push!(linalgtests, "linalg/arnoldi")
     end

test/linalg/conjarray.jl

@@ -0,0 +1,23 @@
+# This file is a part of Julia. License is MIT: http://julialang.org/license
+
+@testset "RowVector" begin
+
+@testset "Core" begin
+    m = [1+im 2; 2 4-im]
+    cm = ConjArray(m)
+    @test cm[1,1] == 1-im
+    @test trace(cm*m) == 27
+
+    v = [[1+im], [1-im]]
+    cv = ConjArray(v)
+    @test cv[1] == [1-im]
+end
+
+@testset "RowVector conjugates" begin
+   v = [1+im, 1-im]
+   rv = v'
+   @test (parent(rv) isa ConjArray)
+   @test rv' === v
+end
+
+end