sparse vector views remain sparse

src/sparsevector.jl

@@ -95,6 +95,9 @@ const SparseVectorView{Tv,Ti}  = SubArray{Tv,1,<:AbstractSparseVector{Tv,Ti},Tup
 const SparseVectorUnion{Tv,Ti} = Union{AbstractCompressedVector{Tv,Ti}, SparseColumnView{Tv,Ti}, SparseVectorView{Tv,Ti}}
 const AdjOrTransSparseVectorUnion{Tv,Ti} = LinearAlgebra.AdjOrTrans{Tv, <:SparseVectorUnion{Tv,Ti}}
 
+# allows for views of a subset of the sparse vector indices
+const SparseVectorPartialView{Tv,Ti} = SubArray{Tv,1,<:AbstractSparseVector{Tv,Ti},<:Tuple{AbstractUnitRange},false}
+
 ### Basic properties
 
 length(x::SparseVector) = getfield(x, :n)
@@ -114,6 +117,7 @@ function nnz(x::SparseColumnView)
     return length(nzrange(parent(x), colidx))
 end
 nnz(x::SparseVectorView) = nnz(x.parent)
+nnz(x::SparseVectorPartialView) = length(nonzeroinds(x))
 
 """
     nzrange(x::SparseVectorUnion, col)
@@ -135,6 +139,12 @@ function nonzeros(x::SparseColumnView)
 end
 nonzeros(x::SparseVectorView) = nonzeros(parent(x))
 
+function nonzeros(x::SparseVectorPartialView)
+    (first_idx, last_idx) = _partialview_end_indices(x)
+    nzvals = nonzeros(parent(x))
+    return view(nzvals, first_idx:last_idx)
+end
+
 nonzeroinds(x::SparseVector) = getfield(x, :nzind)
 nonzeroinds(x::FixedSparseVector) = getfield(x, :nzind)
 function nonzeroinds(x::SparseColumnView)
@@ -145,10 +155,37 @@ function nonzeroinds(x::SparseColumnView)
 end
 nonzeroinds(x::SparseVectorView) = nonzeroinds(parent(x))
 
+# return the first and last nonzero indices of the parent that belong to the view
+# return end+1:end if no nonzero in the parent
+function _partialview_end_indices(x::SparseVectorPartialView)
+    p = parent(x)
+    nzinds = nonzeroinds(p)
+    if isempty(nzinds)
+        last_idx = length(nzinds)
+        first_idx = last_idx + 1
+    else
+        first_idx = findfirst(>=(x.indices[1][begin]), nzinds)
+        last_idx = findlast(<=(x.indices[1][end]), nzinds)
+        # empty view
+        if first_idx === nothing || last_idx === nothing
+            last_idx = length(nzinds)
+            first_idx = last_idx+1
+        end
+    end
+    return (first_idx, last_idx)
+end
+
+function nonzeroinds(x::SparseVectorPartialView)
+    isempty(x.indices[1]) && return indtype(parent(x))[]
+    (first_idx, last_idx) = _partialview_end_indices(x)
+    nzinds = nonzeroinds(parent(x))
+    return @view(nzinds[first_idx:last_idx]) .- (x.indices[1][begin] - 1)
+end
+
 rowvals(x::SparseVectorUnion) = nonzeroinds(x)
 
 indtype(x::SparseColumnView) = indtype(parent(x))
-indtype(x::SparseVectorView) = indtype(parent(x))
+indtype(x::Union{SparseVectorView, SparseVectorPartialView}) = indtype(parent(x))
 
 
 function Base.sizehint!(v::SparseVector, newlen::Integer)
@@ -1573,6 +1610,22 @@ for (fun, mode) in [(:+, 1), (:-, 1), (:*, 0), (:min, 2), (:max, 2)]
     end
 end
 
+for fun in (:+, :-)
+    @eval @propagate_inbounds function $(fun)(x::Union{SparseVectorUnion{Tx},SparseVectorPartialView{Tx}}, y::Union{SparseVectorUnion{Ty},SparseVectorPartialView{Ty}}) where {Tx, Ty}
+        @boundscheck axes(x) == axes(y) || throw(DimensionMismatch("$(axes(x)), $(axes(y))"))
+        T = promote_type(Tx, Ty)
+        res = spzeros(T, length(x))
+        copyto!(res, x)
+        nzinds = nonzeroinds(y)
+        nzvals = nonzeros(y)
+        @inbounds for nzidx in eachindex(nzinds)
+            res[nzinds[nzidx]] = $fun(res[nzinds[nzidx]], nzvals[nzidx])
+        end
+        dropzeros!(res)
+        return res
+    end
+end
+
 ### Reduction
 Base.reducedim_initarray(A::SparseVectorUnion, region, v0, ::Type{R}) where {R} =
     fill!(Array{R}(undef, Base.to_shape(Base.reduced_indices(A, region))), v0)

test/linalg.jl

@@ -708,6 +708,19 @@ end
     end
 end
 
+@testset "Adding sparse-backed SymTridiagonal (#46355)" begin
+    a = SymTridiagonal(sparsevec(Int[1]), sparsevec(Int[]))
+    @test a + a == Matrix(a) + Matrix(a)
+
+    # symtridiagonal with non-empty off-diagonal
+    b = SymTridiagonal(sparsevec(Int[1, 2, 3]), sparsevec(Int[1, 2]))
+    @test b + b == Matrix(b) + Matrix(b)
+
+    # a symtridiagonal with an additional off-diagonal element
+    c = SymTridiagonal(sparsevec(Int[1, 2, 3]), sparsevec(Int[1, 2, 3]))
+    @test c + c == Matrix(c) + Matrix(c)
+end
+
 @testset "kronecker product" begin
     for (m,n) in ((5,10), (13,8))
         a = sprand(m, 5, 0.4); a_d = Matrix(a)

test/sparsevector.jl

@@ -778,6 +778,35 @@ spv_x2 = SparseVector(8, [1, 2, 6, 7], [3.25, 4.0, -5.5, -6.0])
             SparseVector(8, Int[1, 2, 6], Float64[3.25, 4.0, 3.5]))
         @test exact_equal(min.(x, x2),
             SparseVector(8, Int[2, 5, 6, 7], Float64[1.25, -0.75, -5.5, -6.0]))
+
+    end
+
+    test_vectors = [
+        (spv_x1, spv_x2),
+        (SparseVector(5, [1], [1.0]), SparseVector(5, [1], [3.0])),
+        (SparseVector(5, [2], [1.0]), SparseVector(5, [1], [3.0])),
+        (SparseVector(5, [1], [1.0]), SparseVector(5, [2], [3.0])),
+        (SparseVector(5, [3], [2.0]), SparseVector(5, [4], [3.0])),
+        (SparseVector(5, Int[], Float64[]), SparseVector(5, [4], [3.0])),
+    ]
+    @testset "View operations $((collect(xa), collect(xb))), op $op" for (xa, xb) in test_vectors, op in (-, +)
+        r1 = op(@view(xa[1:end]), @view(xb[1:end]))
+        @test r1 == op(xa, xb)
+        @test r1 isa SparseVector
+        r2 = op(@view(xa[2:end-1]), @view(xb[2:end-1]))
+        @test r2 == op(xa, xb)[2:end-1]
+        @test r2 isa SparseVector
+        r3 = op(@view(xb[1:end]), big.(xa))
+        @test r3 == big.(op(xb, xa))
+        @test r3 isa SparseVector
+        # empty views
+        r4 = op(@view(xa[1:2]), @view(xb[1:2]))
+        @test r4 == op(xa, xb)[1:2]
+        @test r4 == @view(op(xa, xb)[1:2])
+        @test r4 isa SparseVector
+        r5 = op(@view(xa[end-1:end]), @view(xb[end-1:end]))
+        @test r5 == op(xa, xb)[end-1:end]
+        @test r5 isa SparseVector
     end
 
     ### Complex