Fix converting empty tensors to array (#180)

* Fix conversion of empty tensor

* Add tests for empty tensor conversion

* Add `zero(::ElementarySpace)`

* Fix failing tests

* Add explicit test for issue #178

* Fix wrong type

* `eltype` should determine precision

* Add entry to docs

* small fix

* small fix attempt II

Fixes #178

Author: lkdvos

docs/src/lib/spaces.md

@@ -90,6 +90,7 @@ dual
 conj
 flip
 ⊕
+zero(::ElementarySpace)
 oneunit
 supremum
 infimum

src/spaces/cartesianspace.jl

@@ -48,6 +48,7 @@ sectors(V::CartesianSpace) = OneOrNoneIterator(dim(V) != 0, Trivial())
 sectortype(::Type{CartesianSpace}) = Trivial
 
 Base.oneunit(::Type{CartesianSpace}) = CartesianSpace(1)
+Base.zero(::Type{CartesianSpace}) = CartesianSpace(0)
 ⊕(V₁::CartesianSpace, V₂::CartesianSpace) = CartesianSpace(V₁.d + V₂.d)
 fuse(V₁::CartesianSpace, V₂::CartesianSpace) = CartesianSpace(V₁.d * V₂.d)
 flip(V::CartesianSpace) = V

src/spaces/complexspace.jl

@@ -49,6 +49,7 @@ sectortype(::Type{ComplexSpace}) = Trivial
 Base.conj(V::ComplexSpace) = ComplexSpace(dim(V), !isdual(V))
 
 Base.oneunit(::Type{ComplexSpace}) = ComplexSpace(1)
+Base.zero(::Type{ComplexSpace}) = ComplexSpace(0)
 function ⊕(V₁::ComplexSpace, V₂::ComplexSpace)
     return isdual(V₁) == isdual(V₂) ?
            ComplexSpace(dim(V₁) + dim(V₂), isdual(V₁)) :

src/spaces/generalspace.jl

@@ -35,6 +35,9 @@ sectortype(::Type{<:GeneralSpace}) = Trivial
 field(::Type{GeneralSpace{𝔽}}) where {𝔽} = 𝔽
 InnerProductStyle(::Type{<:GeneralSpace}) = NoInnerProduct()
 
+Base.oneunit(::Type{GeneralSpace{𝔽}}) where {𝔽} = GeneralSpace{𝔽}(1, false, false)
+Base.zero(::Type{GeneralSpace{𝔽}}) where {𝔽} = GeneralSpace{𝔽}(0, false, false)
+
 dual(V::GeneralSpace{𝔽}) where {𝔽} = GeneralSpace{𝔽}(dim(V), !isdual(V), isconj(V))
 Base.conj(V::GeneralSpace{𝔽}) where {𝔽} = GeneralSpace{𝔽}(dim(V), isdual(V), !isconj(V))
 

src/spaces/gradedspace.jl

@@ -132,6 +132,7 @@ function Base.axes(V::GradedSpace{I}, c::I) where {I<:Sector}
 end
 
 Base.oneunit(S::Type{<:GradedSpace{I}}) where {I<:Sector} = S(one(I) => 1)
+Base.zero(S::Type{<:GradedSpace{I}}) where {I<:Sector} = S(one(I) => 0)
 
 # TODO: the following methods can probably be implemented more efficiently for
 # `FiniteGradedSpace`, but we don't expect them to be used often in hot loops, so

src/spaces/vectorspaces.jl

@@ -128,6 +128,14 @@ that this is different from `one(V::S)`, which returns the empty product space
 """
 Base.oneunit(V::ElementarySpace) = oneunit(typeof(V))
 
+"""
+    zero(V::S) where {S<:ElementarySpace} -> S
+
+Return the corresponding vector space of type `S` that represents the zero-dimensional or empty space.
+This is, with a slight abuse of notation, the zero element of the direct sum of vector spaces. 
+"""
+Base.zero(V::ElementarySpace) = zero(typeof(V))
+
 """
     ⊕(V₁::S, V₂::S, V₃::S...) where {S<:ElementarySpace} -> S
     oplus(V₁::S, V₂::S, V₃::S...) where {S<:ElementarySpace} -> S

src/tensors/abstracttensor.jl

@@ -497,21 +497,13 @@ function Base.convert(::Type{Array}, t::AbstractTensorMap)
     else
         cod = codomain(t)
         dom = domain(t)
-        local A
+        T = sectorscalartype(I) <: Complex ? complex(scalartype(t)) :
+            sectorscalartype(I) <: Integer ? scalartype(t) : float(scalartype(t))
+        A = zeros(T, dims(cod)..., dims(dom)...)
         for (f₁, f₂) in fusiontrees(t)
             F = convert(Array, (f₁, f₂))
-            if !(@isdefined A)
-                if eltype(F) <: Complex
-                    T = complex(float(scalartype(t)))
-                elseif eltype(F) <: Integer
-                    T = scalartype(t)
-                else
-                    T = float(scalartype(t))
-                end
-                A = fill(zero(T), (dims(cod)..., dims(dom)...))
-            end
             Aslice = StridedView(A)[axes(cod, f₁.uncoupled)..., axes(dom, f₂.uncoupled)...]
-            axpy!(1, StridedView(_kron(convert(Array, t[f₁, f₂]), F)), Aslice)
+            add!(Aslice, StridedView(_kron(convert(Array, t[f₁, f₂]), F)))
         end
         return A
     end

test/bugfixes.jl

@@ -22,4 +22,11 @@
         @test w == v
         @test scalartype(w) == Float64
     end
+
+    # https://github.com/Jutho/TensorKit.jl/issues/178
+    @testset "Issue #178" begin
+        t = rand(U1Space(1 => 1) ← U1Space(1 => 1)')
+        a = convert(Array, t)
+        @test a == zeros(size(a))
+    end
 end

test/spaces.jl

@@ -66,12 +66,14 @@ println("------------------------------------")
         @test length(sectors(V)) == 1
         @test @constinferred(TensorKit.hassector(V, Trivial()))
         @test @constinferred(dim(V)) == d == @constinferred(dim(V, Trivial()))
-        @test dim(@constinferred(typeof(V)())) == 0
-        @test (sectors(typeof(V)())...,) == ()
+        @test dim(@constinferred(zero(V))) == 0
+        @test (sectors(zero(V))...,) == ()
         @test @constinferred(TensorKit.axes(V)) == Base.OneTo(d)
         @test ℝ^d == ℝ[](d) == CartesianSpace(d) == typeof(V)(d)
         W = @constinferred ℝ^1
         @test @constinferred(oneunit(V)) == W == oneunit(typeof(V))
+        @test @constinferred(zero(V)) == ℝ^0 == zero(typeof(V))
+        @test @constinferred(⊕(V, zero(V))) == V
         @test @constinferred(⊕(V, V)) == ℝ^(2d)
         @test @constinferred(⊕(V, oneunit(V))) == ℝ^(d + 1)
         @test @constinferred(⊕(V, V, V, V)) == ℝ^(4d)
@@ -111,12 +113,14 @@ println("------------------------------------")
         @test length(sectors(V)) == 1
         @test @constinferred(TensorKit.hassector(V, Trivial()))
         @test @constinferred(dim(V)) == d == @constinferred(dim(V, Trivial()))
-        @test dim(@constinferred(typeof(V)())) == 0
-        @test (sectors(typeof(V)())...,) == ()
+        @test dim(@constinferred(zero(V))) == 0
+        @test (sectors(zero(V))...,) == ()
         @test @constinferred(TensorKit.axes(V)) == Base.OneTo(d)
         @test ℂ^d == Vect[Trivial](d) == Vect[](Trivial() => d) == ℂ[](d) == typeof(V)(d)
         W = @constinferred ℂ^1
         @test @constinferred(oneunit(V)) == W == oneunit(typeof(V))
+        @test @constinferred(zero(V)) == ℂ^0 == zero(typeof(V))
+        @test @constinferred(⊕(V, zero(V))) == V
         @test @constinferred(⊕(V, V)) == ℂ^(2d)
         @test_throws SpaceMismatch (⊕(V, V'))
         # promote_except = ErrorException("promotion of types $(typeof(ℝ^d)) and " *
@@ -200,11 +204,12 @@ println("------------------------------------")
         @test eval(Meta.parse(sprint(show, V))) == V
         @test eval(Meta.parse(sprint(show, typeof(V)))) == typeof(V)
         # space with no sectors
-        @test dim(@constinferred(typeof(V)())) == 0
+        @test dim(@constinferred(zero(V))) == 0
         # space with a single sector
         W = @constinferred GradedSpace(one(I) => 1)
         @test W == GradedSpace(one(I) => 1, randsector(I) => 0)
         @test @constinferred(oneunit(V)) == W == oneunit(typeof(V))
+        @test @constinferred(zero(V)) == GradedSpace(one(I) => 0)
         # randsector never returns trivial sector, so this cannot error
         @test_throws ArgumentError GradedSpace(one(I) => 1, randsector(I) => 0, one(I) => 3)
         @test eval(Meta.parse(sprint(show, W))) == W
@@ -226,6 +231,7 @@ println("------------------------------------")
         if hasfusiontensor(I)
             @test @constinferred(TensorKit.axes(V)) == Base.OneTo(dim(V))
         end
+        @test @constinferred(⊕(V, zero(V))) == V
         @test @constinferred(⊕(V, V)) == Vect[I](c => 2dim(V, c) for c in sectors(V))
         @test @constinferred(⊕(V, V, V, V)) == Vect[I](c => 4dim(V, c) for c in sectors(V))
         @test @constinferred(⊕(V, oneunit(V))) ==

test/tensors.jl

@@ -126,6 +126,11 @@ for V in spacelist
                         @test t === @constinferred TensorMap(t.data, W)
                     end
                 end
+                for T in (Int, Float32, ComplexF64)
+                    t = randn(T, V1 ⊗ V2 ← zero(V1))
+                    a = convert(Array, t)
+                    @test norm(a) == 0
+                end
             end
         end
         @timedtestset "Basic linear algebra" begin
@@ -466,7 +471,7 @@ for V in spacelist
                     end
                 end
                 @testset "empty tensor" begin
-                    t = randn(T, V1 ⊗ V2, typeof(V1)())
+                    t = randn(T, V1 ⊗ V2, zero(V1))
                     @testset "leftorth with $alg" for alg in
                                                       (TensorKit.QR(), TensorKit.QRpos(),
                                                        TensorKit.QL(), TensorKit.QLpos(),