sparsevector.jl

# This file is a part of Julia. License is MIT: https://julialang.org/license

module SparseVectorTests

using Test
using SparseArrays
using LinearAlgebra
using Random

### Data

spv_x1 = SparseVector(8, [2, 5, 6], [1.25, -0.75, 3.5])

@test isa(spv_x1, SparseVector{Float64,Int})

x1_full = zeros(length(spv_x1))
x1_full[SparseArrays.nonzeroinds(spv_x1)] = nonzeros(spv_x1)

@testset "basic properties" begin
    x = spv_x1
    @test eltype(x) == Float64
    @test ndims(x) == 1
    @test length(x) == 8
    @test size(x) == (8,)
    @test size(x,1) == 8
    @test size(x,2) == 1
    @test !isempty(x)

    @test count(!iszero, x) == 3
    @test nnz(x) == 3
    @test SparseArrays.nonzeroinds(x) == [2, 5, 6]
    @test nonzeros(x) == [1.25, -0.75, 3.5]
    @test count(SparseVector(8, [2, 5, 6], [true,false,true])) == 2
end

@testset "conversion to dense Array" begin
    for (x, xf) in [(spv_x1, x1_full)]
        @test isa(Array(x), Vector{Float64})
        @test Array(x) == xf
        @test Vector(x) == xf
    end
end
@testset "show" begin
    @test occursin("1.25", string(spv_x1))
    @test occursin("-0.75", string(spv_x1))
    @test occursin("3.5", string(spv_x1))
end

### Comparison helper to ensure exact equality with internal structure
function exact_equal(x::AbstractSparseVector, y::AbstractSparseVector)
    eltype(x) == eltype(y) &&
    eltype(SparseArrays.nonzeroinds(x)) == eltype(SparseArrays.nonzeroinds(y)) &&
    length(x) == length(y) &&
    SparseArrays.nonzeroinds(x) == SparseArrays.nonzeroinds(y) &&
    nonzeros(x) == nonzeros(y)
end

@testset "other constructors" begin
    # construct empty sparse vector

    @test exact_equal(spzeros(Float64, 8), SparseVector(8, Int[], Float64[]))

    @testset "from list of indices and values" begin
        @test exact_equal(
            sparsevec(Int[], Float64[], 8),
            SparseVector(8, Int[], Float64[]))

        @test exact_equal(
            sparsevec(Int[], Float64[]),
            SparseVector(0, Int[], Float64[]))

        @test exact_equal(
            sparsevec([3, 3], [5.0, -5.0], 8),
            SparseVector(8, [3], [0.0]))

        @test exact_equal(
            sparsevec([2, 3, 6], [12.0, 18.0, 25.0]),
            SparseVector(6, [2, 3, 6], [12.0, 18.0, 25.0]))

        let x0 = SparseVector(8, [2, 3, 6], [12.0, 18.0, 25.0])
            @test exact_equal(
                sparsevec([2, 3, 6], [12.0, 18.0, 25.0], 8), x0)

            @test exact_equal(
                sparsevec([3, 6, 2], [18.0, 25.0, 12.0], 8), x0)

            @test exact_equal(
                sparsevec([2, 3, 4, 4, 6], [12.0, 18.0, 5.0, -5.0, 25.0], 8),
                SparseVector(8, [2, 3, 4, 6], [12.0, 18.0, 0.0, 25.0]))

            @test exact_equal(
                sparsevec([1, 1, 1, 2, 3, 3, 6], [2.0, 3.0, -5.0, 12.0, 10.0, 8.0, 25.0], 8),
                SparseVector(8, [1, 2, 3, 6], [0.0, 12.0, 18.0, 25.0]))

            @test exact_equal(
                sparsevec([2, 3, 6, 7, 7], [12.0, 18.0, 25.0, 5.0, -5.0], 8),
                SparseVector(8, [2, 3, 6, 7], [12.0, 18.0, 25.0, 0.0]))
        end

        @test exact_equal(
            sparsevec(Any[1, 3], [1, 1]),
            sparsevec([1, 3], [1, 1]))

        @test exact_equal(
            sparsevec(Any[1, 3], [1, 1], 5),
            sparsevec([1, 3], [1, 1], 5))
    end
    @testset "from dictionary" begin
        function my_intmap(x)
            a = Dict{Int,eltype(x)}()
            for i in SparseArrays.nonzeroinds(x)
                a[i] = x[i]
            end
            return a
        end

        let x = spv_x1
            a = my_intmap(x)
            xc = sparsevec(a, 8)
            @test exact_equal(x, xc)

            xc = sparsevec(a)
            @test exact_equal(xc, SparseVector(6, [2, 5, 6], [1.25, -0.75, 3.5]))

            d = Dict{Int, Float64}((1 => 0.0, 2 => 1.0, 3 => 2.0))
            @test exact_equal(sparsevec(d), SparseVector(3, [1, 2, 3], [0.0, 1.0, 2.0]))
        end
    end
    @testset "fillstored!" begin
        x = SparseVector(8, [2, 3, 6], [12.0, 18.0, 25.0])
        y = LinearAlgebra.fillstored!(copy(x), 1)
        @test (x .!= 0) == (y .!= 0)
        @test y == SparseVector(8, [2, 3, 6], [1.0, 1.0, 1.0])
    end

    @testset "sprand & sprandn" begin
        let xr = sprand(1000, 0.9)
            @test isa(xr, SparseVector{Float64,Int})
            @test length(xr) == 1000
            @test all(nonzeros(xr) .>= 0.0)
        end

        let xr = sprand(Float32, 1000, 0.9)
            @test isa(xr, SparseVector{Float32,Int})
            @test length(xr) == 1000
            @test all(nonzeros(xr) .>= 0.0)
        end

        let xr = sprandn(1000, 0.9)
            @test isa(xr, SparseVector{Float64,Int})
            @test length(xr) == 1000
            if !isempty(nonzeros(xr))
                @test any(nonzeros(xr) .> 0.0) && any(nonzeros(xr) .< 0.0)
            end
        end

        let xr = sprandn(ComplexF64, 1000, 0.9)
            @test isa(xr, SparseVector{ComplexF64,Int})
            @test length(xr) == 1000
        end

        let xr = sprand(Bool, 1000, 0.9)
            @test isa(xr, SparseVector{Bool,Int})
            @test length(xr) == 1000
            @test all(nonzeros(xr))
        end

        let r1 = MersenneTwister(0), r2 = MersenneTwister(0)
            @test sprand(r1, 100, .9) == sprand(r2, 100, .9)
            @test sprandn(r1, 100, .9) == sprandn(r2, 100, .9)
            @test sprand(r1, Bool, 100, .9) == sprand(r2,  Bool, 100, .9)
        end
    end
end
### Element access

@testset "getindex" begin
    @testset "single integer index" begin
        for (x, xf) in [(spv_x1, x1_full)]
            for i = 1:length(x)
                @test x[i] == xf[i]
            end
        end
    end
    @testset "generic array index" begin
        let x = sprand(100, 0.5)
            I = rand(1:length(x), 20)
            r = x[I]
            @test isa(r, SparseVector{Float64,Int})
            @test all(!iszero, nonzeros(r))
            @test Array(r) == Array(x)[I]
        end

        # issue 24534
        let x = convert(SparseVector{Float64,UInt32},sprandn(100,0.5))
            I = rand(1:length(x), 20)
            r = x[I]
            @test isa(r, SparseVector{Float64,UInt32})
            @test all(!iszero, nonzeros(r))
            @test Array(r) == Array(x)[I]
        end

        # issue 24534
        let x = convert(SparseVector{Float64,UInt32},sprandn(100,0.5))
            I = rand(1:length(x), 20,1)
            r = x[I]
            @test isa(r, SparseMatrixCSC{Float64,UInt32})
            @test all(!iszero, nonzeros(r))
            @test Array(r) == Array(x)[I]
        end
    end
    @testset "boolean array index" begin
        let x = sprand(10, 10, 0.5)
            I = rand(1:size(x, 2), 10)
            bI = falses(size(x, 2))
            bI[I] .= true
            r = x[1,bI]
            @test isa(r, SparseVector{Float64,Int})
            @test all(!iszero, nonzeros(r))
            @test Array(r) == Array(x)[1,bI]
        end

        let x = sprand(10, 0.5)
            I = rand(1:length(x), 5)
            bI = falses(length(x))
            bI[I] .= true
            r = x[bI]
            @test isa(r, SparseVector{Float64,Int})
            @test all(!iszero, nonzeros(r))
            @test Array(r) == Array(x)[bI]
        end
    end
end
@testset "setindex" begin
    let xc = spzeros(Float64, 8)
        xc[3] = 2.0
        @test exact_equal(xc, SparseVector(8, [3], [2.0]))
    end

    let xc = copy(spv_x1)
        xc[5] = 2.0
        @test exact_equal(xc, SparseVector(8, [2, 5, 6], [1.25, 2.0, 3.5]))
    end

    let xc = copy(spv_x1)
        xc[3] = 4.0
        @test exact_equal(xc, SparseVector(8, [2, 3, 5, 6], [1.25, 4.0, -0.75, 3.5]))

        xc[1] = 6.0
        @test exact_equal(xc, SparseVector(8, [1, 2, 3, 5, 6], [6.0, 1.25, 4.0, -0.75, 3.5]))

        xc[8] = -1.5
        @test exact_equal(xc, SparseVector(8, [1, 2, 3, 5, 6, 8], [6.0, 1.25, 4.0, -0.75, 3.5, -1.5]))
    end

    let xc = copy(spv_x1)
        xc[5] = 0.0
        @test exact_equal(xc, SparseVector(8, [2, 5, 6], [1.25, 0.0, 3.5]))

        xc[6] = 0.0
        @test exact_equal(xc, SparseVector(8, [2, 5, 6], [1.25, 0.0, 0.0]))

        xc[2] = 0.0
        @test exact_equal(xc, SparseVector(8, [2, 5, 6], [0.0, 0.0, 0.0]))

        xc[1] = 0.0
        @test exact_equal(xc, SparseVector(8, [2, 5, 6], [0.0, 0.0, 0.0]))
    end
end
@testset "dropstored!" begin
    x = SparseVector(10, [2, 7, 9], [2.0, 7.0, 9.0])
    # Test argument bounds checking for dropstored!(x, i)
    @test_throws BoundsError SparseArrays.dropstored!(x, 0)
    @test_throws BoundsError SparseArrays.dropstored!(x, 11)
    # Test behavior of dropstored!(x, i)
    # --> Test dropping a single stored entry
    @test SparseArrays.dropstored!(x, 2) == SparseVector(10, [7, 9], [7.0, 9.0])
    # --> Test dropping a single nonstored entry
    @test SparseArrays.dropstored!(x, 5) == SparseVector(10, [7, 9], [7.0, 9.0])
end

@testset "findall and findnz" begin
    @test findall(!iszero, spv_x1) == findall(!iszero, x1_full)
    @test findall(spv_x1 .> 1) == findall(x1_full .> 1)
    @test findall(x->x>1, spv_x1) == findall(x->x>1, x1_full)
    @test findnz(spv_x1) == (findall(!iszero, x1_full), filter(x->x!=0, x1_full))
    let xc = SparseVector(8, [2, 3, 5], [1.25, 0, -0.75]), fc = Array(xc)
        @test findall(!iszero, xc) == findall(!iszero, fc)
        @test findnz(xc) == ([2, 3, 5], [1.25, 0, -0.75])
    end
end
### Array manipulation

@testset "copy[!]" begin

    let x = spv_x1
        xc = copy(x)
        @test isa(xc, SparseVector{Float64,Int})
        @test x.nzind !== xc.nzval
        @test x.nzval !== xc.nzval
        @test exact_equal(x, xc)
    end

    let x1 = SparseVector(8, [2, 5, 6], [12.2, 1.4, 5.0])
        x2 = SparseVector(8, [3, 4], [1.2, 3.4])
        copyto!(x2, x1)
        @test x2 == x1
        x2 = SparseVector(8, [2, 4, 8], [10.3, 7.4, 3.1])
        copyto!(x2, x1)
        @test x2 == x1
        x2 = SparseVector(8, [1, 3, 4, 7], [0.3, 1.2, 3.4, 0.1])
        copyto!(x2, x1)
        @test x2 == x1
        x2 = SparseVector(10, [3, 4], [1.2, 3.4])
        copyto!(x2, x1)
        @test x2[1:8] == x1
        @test x2[9:10] == spzeros(2)
        x2 = SparseVector(10, [3, 4, 9], [1.2, 3.4, 17.8])
        copyto!(x2, x1)
        @test x2[1:8] == x1
        @test x2[9] == 17.8
        @test x2[10] == 0
        x2 = SparseVector(10, [3, 4, 5, 6, 9], [8.3, 7.2, 1.2, 3.4, 17.8])
        copyto!(x2, x1)
        @test x2[1:8] == x1
        @test x2[9] == 17.8
        @test x2[10] == 0
        x2 = SparseVector(6, [3, 4], [1.2, 3.4])
        @test_throws BoundsError copyto!(x2, x1)
    end

    let x1 = sparse([2, 1, 2], [1, 3, 3], [12.2, 1.4, 5.0], 2, 4)
        x2 = SparseVector(8, [3, 4], [1.2, 3.4])
        copyto!(x2, x1)
        @test x2[:] == x1[:]
        x2 = SparseVector(8, [2, 4, 8], [10.3, 7.4, 3.1])
        copyto!(x2, x1)
        @test x2[:] == x1[:]
        x2 = SparseVector(8, [1, 3, 4, 7], [0.3, 1.2, 3.4, 0.1])
        copyto!(x2, x1)
        @test x2[:] == x1[:]
        x2 = SparseVector(10, [3, 4], [1.2, 3.4])
        copyto!(x2, x1)
        @test x2[1:8] == x1[:]
        @test x2[9:10] == spzeros(2)
        x2 = SparseVector(10, [3, 4, 9], [1.2, 3.4, 17.8])
        copyto!(x2, x1)
        @test x2[1:8] == x1[:]
        @test x2[9] == 17.8
        @test x2[10] == 0
        x2 = SparseVector(10, [3, 4, 5, 6, 9], [8.3, 7.2, 1.2, 3.4, 17.8])
        copyto!(x2, x1)
        @test x2[1:8] == x1[:]
        @test x2[9] == 17.8
        @test x2[10] == 0
        x2 = SparseVector(6, [3, 4], [1.2, 3.4])
        @test_throws BoundsError copyto!(x2, x1)
    end

    let x1 = SparseVector(8, [2, 5, 6], [12.2, 1.4, 5.0])
        x2 = sparse([1, 2], [2, 2], [1.2, 3.4], 2, 4)
        copyto!(x2, x1)
        @test x2[:] == x1[:]
        x2 = sparse([2, 2, 2], [1, 3, 4], [10.3, 7.4, 3.1], 2, 4)
        copyto!(x2, x1)
        @test x2[:] == x1[:]
        x2 = sparse([1, 1, 2, 1], [1, 2, 2, 4], [0.3, 1.2, 3.4, 0.1], 2, 4)
        copyto!(x2, x1)
        @test x2[:] == x1[:]
        x2 = sparse([1, 2], [2, 2], [1.2, 3.4], 2, 5)
        copyto!(x2, x1)
        @test x2[1:8] == x1
        @test x2[9:10] == spzeros(2)
        x2 = sparse([1, 2, 1], [2, 2, 5], [1.2, 3.4, 17.8], 2, 5)
        copyto!(x2, x1)
        @test x2[1:8] == x1
        @test x2[9] == 17.8
        @test x2[10] == 0
        x2 = sparse([1, 2, 1, 2, 1], [2, 2, 3, 3, 5], [8.3, 7.2, 1.2, 3.4, 17.8], 2, 5)
        copyto!(x2, x1)
        @test x2[1:8] == x1
        @test x2[9] == 17.8
        @test x2[10] == 0
        x2 = sparse([1, 2], [2, 2], [1.2, 3.4], 2, 3)
        @test_throws BoundsError copyto!(x2, x1)
    end
end
@testset "vec/reinterpret/float/complex" begin
    a = SparseVector(8, [2, 5, 6], Int32[12, 35, 72])
    # vec
    @test vec(a) == a

    # float
    af = float(a)
    @test float(af) == af
    @test isa(af, SparseVector{Float64,Int})
    @test exact_equal(af, SparseVector(8, [2, 5, 6], [12., 35., 72.]))
    @test sparsevec(transpose(transpose(af))) == af

    # complex
    acp = complex(af)
    @test complex(acp) == acp
    @test isa(acp, SparseVector{ComplexF64,Int})
    @test exact_equal(acp, SparseVector(8, [2, 5, 6], complex([12., 35., 72.])))
    @test sparsevec((acp')') == acp
end

@testset "Type conversion" begin
    let x = convert(SparseVector, sparse([2, 5, 6], [1, 1, 1], [1.25, -0.75, 3.5], 8, 1))
        @test isa(x, SparseVector{Float64,Int})
        @test exact_equal(x, spv_x1)
    end

    let x = spv_x1, xf = x1_full
        xc = convert(SparseVector, xf)
        @test isa(xc, SparseVector{Float64,Int})
        @test exact_equal(xc, x)

        xc = convert(SparseVector{Float32,Int}, x)
        xf32 = SparseVector(8, [2, 5, 6], [1.25f0, -0.75f0, 3.5f0])
        @test isa(xc, SparseVector{Float32,Int})
        @test exact_equal(xc, xf32)

        xc = convert(SparseVector{Float32}, x)
        @test isa(xc, SparseVector{Float32,Int})
        @test exact_equal(xc, xf32)

        xm = convert(SparseMatrixCSC, x)
        @test isa(xm, SparseMatrixCSC{Float64,Int})
        @test Array(xm) == reshape(xf, 8, 1)

        xm = convert(SparseMatrixCSC{Float32}, x)
        @test isa(xm, SparseMatrixCSC{Float32,Int})
        @test Array(xm) == reshape(convert(Vector{Float32}, xf), 8, 1)
    end
end

@testset "Concatenation" begin
    let m = 80, n = 100
        A = Vector{SparseVector{Float64,Int}}(undef, n)
        tnnz = 0
        for i = 1:length(A)
            A[i] = sprand(m, 0.3)
            tnnz += nnz(A[i])
        end

        H = hcat(A...)
        @test isa(H, SparseMatrixCSC{Float64,Int})
        @test size(H) == (m, n)
        @test nnz(H) == tnnz
        Hr = zeros(m, n)
        for j = 1:n
            Hr[:,j] = Array(A[j])
        end
        @test Array(H) == Hr

        V = vcat(A...)
        @test isa(V, SparseVector{Float64,Int})
        @test length(V) == m * n
        Vr = vec(Hr)
        @test Array(V) == Vr
    end

    @testset "concatenation of sparse vectors with other types" begin
        # Test that concatenations of combinations of sparse vectors with various other
        # matrix/vector types yield sparse arrays
        let N = 4
            spvec = spzeros(N)
            spmat = spzeros(N, 1)
            densevec = fill(1., N)
            densemat = fill(1., N, 1)
            diagmat = Diagonal(densevec)
            # Test that concatenations of pairwise combinations of sparse vectors with dense
            # vectors/matrices, sparse matrices, or special matrices yield sparse arrays
            for othervecormat in (densevec, densemat, spmat)
                @test issparse(vcat(spvec, othervecormat))
                @test issparse(vcat(othervecormat, spvec))
            end
            for othervecormat in (densevec, densemat, spmat, diagmat)
                @test issparse(hcat(spvec, othervecormat))
                @test issparse(hcat(othervecormat, spvec))
                @test issparse(hvcat((2,), spvec, othervecormat))
                @test issparse(hvcat((2,), othervecormat, spvec))
                @test issparse(cat(spvec, othervecormat; dims=(1,2)))
                @test issparse(cat(othervecormat, spvec; dims=(1,2)))
            end
            # The preceding tests should cover multi-way combinations of those types, but for good
            # measure test a few multi-way combinations involving those types
            @test issparse(vcat(spvec, densevec, spmat, densemat))
            @test issparse(vcat(densevec, spvec, densemat, spmat))
            @test issparse(hcat(spvec, densemat, spmat, densevec, diagmat))
            @test issparse(hcat(densemat, spmat, spvec, densevec, diagmat))
            @test issparse(hvcat((5,), diagmat, densevec, spvec, densemat, spmat))
            @test issparse(hvcat((5,), spvec, densemat, diagmat, densevec, spmat))
            @test issparse(cat(densemat, diagmat, spmat, densevec, spvec; dims=(1,2)))
            @test issparse(cat(spvec, diagmat, densevec, spmat, densemat; dims=(1,2)))
        end
        @testset "vertical concatenation of SparseVectors with different el- and ind-type (#22225)" begin
            spv6464 = SparseVector(0, Int64[], Int64[])
            @test isa(vcat(spv6464, SparseVector(0, Int64[], Int32[])), SparseVector{Int64,Int64})
            @test isa(vcat(spv6464, SparseVector(0, Int32[], Int64[])), SparseVector{Int64,Int64})
            @test isa(vcat(spv6464, SparseVector(0, Int32[], Int32[])), SparseVector{Int64,Int64})
        end
    end
end
@testset "sparsemat: combinations with sparse matrix" begin
    let S = sprand(4, 8, 0.5)
        Sf = Array(S)
        @assert isa(Sf, Matrix{Float64})

        # get a single column
        for j = 1:size(S,2)
            col = S[:, j]
            @test isa(col, SparseVector{Float64,Int})
            @test length(col) == size(S,1)
            @test Array(col) == Sf[:,j]
        end

        # Get a reshaped vector
        v = S[:]
        @test isa(v, SparseVector{Float64,Int})
        @test length(v) == length(S)
        @test Array(v) == Sf[:]

        # Get a linear subset
        for i=0:length(S)
            v = S[1:i]
            @test isa(v, SparseVector{Float64,Int})
            @test length(v) == i
            @test Array(v) == Sf[1:i]
        end
        for i=1:length(S)+1
            v = S[i:end]
            @test isa(v, SparseVector{Float64,Int})
            @test length(v) == length(S) - i + 1
            @test Array(v) == Sf[i:end]
        end
        for i=0:div(length(S),2)
            v = S[1+i:end-i]
            @test isa(v, SparseVector{Float64,Int})
            @test length(v) == length(S) - 2i
            @test Array(v) == Sf[1+i:end-i]
        end
    end

    let r = [1,10], S = sparse(r, r, r)
        Sf = Array(S)
        @assert isa(Sf, Matrix{Int})

        inds = [1,1,1,1,1,1]
        v = S[inds]
        @test isa(v, SparseVector{Int,Int})
        @test length(v) == length(inds)
        @test Array(v) == Sf[inds]

        inds = [2,2,2,2,2,2]
        v = S[inds]
        @test isa(v, SparseVector{Int,Int})
        @test length(v) == length(inds)
        @test Array(v) == Sf[inds]

        # get a single column
        for j = 1:size(S,2)
            col = S[:, j]
            @test isa(col, SparseVector{Int,Int})
            @test length(col) == size(S,1)
            @test Array(col) == Sf[:,j]
        end

        # Get a reshaped vector
        v = S[:]
        @test isa(v, SparseVector{Int,Int})
        @test length(v) == length(S)
        @test Array(v) == Sf[:]

        # Get a linear subset
        for i=0:length(S)
            v = S[1:i]
            @test isa(v, SparseVector{Int,Int})
            @test length(v) == i
            @test Array(v) == Sf[1:i]
        end
        for i=1:length(S)+1
            v = S[i:end]
            @test isa(v, SparseVector{Int,Int})
            @test length(v) == length(S) - i + 1
            @test Array(v) == Sf[i:end]
        end
        for i=0:div(length(S),2)
            v = S[1+i:end-i]
            @test isa(v, SparseVector{Int,Int})
            @test length(v) == length(S) - 2i
            @test Array(v) == Sf[1+i:end-i]
        end
    end
end
## math

### Data

rnd_x0 = sprand(50, 0.6)
rnd_x0f = Array(rnd_x0)

rnd_x1 = sprand(50, 0.7) * 4.0
rnd_x1f = Array(rnd_x1)

spv_x1 = SparseVector(8, [2, 5, 6], [1.25, -0.75, 3.5])
spv_x2 = SparseVector(8, [1, 2, 6, 7], [3.25, 4.0, -5.5, -6.0])

@testset "Arithmetic operations" begin

    let x = spv_x1, x2 = spv_x2
        # negate
        @test exact_equal(-x, SparseVector(8, [2, 5, 6], [-1.25, 0.75, -3.5]))

        # abs and abs2
        @test exact_equal(abs.(x), SparseVector(8, [2, 5, 6], abs.([1.25, -0.75, 3.5])))
        @test exact_equal(abs2.(x), SparseVector(8, [2, 5, 6], abs2.([1.25, -0.75, 3.5])))

        # plus and minus
        xa = SparseVector(8, [1,2,5,6,7], [3.25,5.25,-0.75,-2.0,-6.0])

        @test exact_equal(x + x, x * 2)
        @test exact_equal(x + x2, xa)
        @test exact_equal(x2 + x, xa)

        xb = SparseVector(8, [1,2,5,6,7], [-3.25,-2.75,-0.75,9.0,6.0])
        @test exact_equal(x - x, SparseVector(8, Int[], Float64[]))
        @test exact_equal(x - x2, xb)
        @test exact_equal(x2 - x, -xb)

        @test Array(x) + x2 == Array(xa)
        @test Array(x) - x2 == Array(xb)
        @test x + Array(x2) == Array(xa)
        @test x - Array(x2) == Array(xb)

        # multiplies
        xm = SparseVector(8, [2, 6], [5.0, -19.25])
        @test exact_equal(x .* x, abs2.(x))
        @test exact_equal(x .* x2, xm)
        @test exact_equal(x2 .* x, xm)

        @test Array(x) .* x2 == Array(xm)
        @test x .* Array(x2) == Array(xm)

        # max & min
        @test exact_equal(max.(x, x), x)
        @test exact_equal(min.(x, x), x)
        @test exact_equal(max.(x, x2),
            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

    ### Complex

    let x = spv_x1, x2 = spv_x2
        # complex
        @test exact_equal(complex.(x, x),
            SparseVector(8, [2,5,6], [1.25+1.25im, -0.75-0.75im, 3.5+3.5im]))
        @test exact_equal(complex.(x, x2),
            SparseVector(8, [1,2,5,6,7], [3.25im, 1.25+4.0im, -0.75+0.0im, 3.5-5.5im, -6.0im]))
        @test exact_equal(complex.(x2, x),
            SparseVector(8, [1,2,5,6,7], [3.25+0.0im, 4.0+1.25im, -0.75im, -5.5+3.5im, -6.0+0.0im]))

        # real, imag and conj

        @test real(x) === x
        @test exact_equal(imag(x), spzeros(Float64, length(x)))
        @test conj(x) === x

        xcp = complex.(x, x2)
        @test exact_equal(real(xcp), x)
        @test exact_equal(imag(xcp), x2)
        @test exact_equal(conj(xcp), complex.(x, -x2))
    end
end
@testset "Zero-preserving math functions: sparse -> sparse" begin
    x1operations = (floor, ceil, trunc, round)
    x0operations = (log1p,  expm1,  sinpi,
                    sin,    tan,    sind,   tand,
                    asin,   atan,   asind,  atand,
                    sinh,   tanh,   asinh,  atanh)

    for (spvec, densevec, operations) in (
            (rnd_x0, rnd_x0f, x0operations),
            (rnd_x1, rnd_x1f, x1operations) )
        for op in operations
            spresvec = op.(spvec)
            @test spresvec == op.(densevec)
            @test all(!iszero, spresvec.nzval)
            resvaltype = typeof(op(zero(eltype(spvec))))
            resindtype = SparseArrays.indtype(spvec)
            @test isa(spresvec, SparseVector{resvaltype,resindtype})
        end
    end
end
@testset "Non-zero-preserving math functions: sparse -> dense" begin
    for op in (exp, exp2, exp10, log, log2, log10,
            cos, cosd, acos, cosh, cospi,
            csc, cscd, acot, csch, acsch,
            cot, cotd, acosd, coth,
            sec, secd, acotd, sech, asech)
        spvec = rnd_x0
        densevec = rnd_x0f
        spresvec = op.(spvec)
        @test spresvec == op.(densevec)
        resvaltype = typeof(op(zero(eltype(spvec))))
        resindtype = SparseArrays.indtype(spvec)
        @test isa(spresvec, SparseVector{resvaltype,resindtype})
    end
end

### Reduction

@testset "sum, norm" begin
    x = spv_x1
    @test sum(x) == 4.0
    @test sum(abs, x) == 5.5
    @test sum(abs2, x) == 14.375

    @test norm(x) == sqrt(14.375)
    @test norm(x, 1) == 5.5
    @test norm(x, 2) == sqrt(14.375)
    @test norm(x, Inf) == 3.5
end

@testset "maximum, minimum" begin
    let x = spv_x1
        @test maximum(x) == 3.5
        @test minimum(x) == -0.75
        @test maximum(abs, x) == 3.5
        @test minimum(abs, x) == 0.0
    end

    let x = abs.(spv_x1)
        @test maximum(x) == 3.5
        @test minimum(x) == 0.0
    end

    let x = -abs.(spv_x1)
        @test maximum(x) == 0.0
        @test minimum(x) == -3.5
    end

    let x = SparseVector(3, [1, 2, 3], [-4.5, 2.5, 3.5])
        @test maximum(x) == 3.5
        @test minimum(x) == -4.5
        @test maximum(abs, x) == 4.5
        @test minimum(abs, x) == 2.5
    end

    let x = spzeros(Float64, 8)
        @test maximum(x) == 0.0
        @test minimum(x) == 0.0
        @test maximum(abs, x) == 0.0
        @test minimum(abs, x) == 0.0
    end
end

### linalg

@testset "BLAS Level-1" begin

    let x = sprand(16, 0.5), x2 = sprand(16, 0.4)
        xf = Array(x)
        xf2 = Array(x2)

        @testset "axpy!" begin
            for c in [1.0, -1.0, 2.0, -2.0]
                y = Array(x)
                @test LinearAlgebra.axpy!(c, x2, y) === y
                @test y == Array(x2 * c + x)
            end
        end
        @testset "scale" begin
            α = 2.5
            sx = SparseVector(x.n, x.nzind, x.nzval * α)
            @test exact_equal(x * α, sx)
            @test exact_equal(x * (α + 0.0*im), complex(sx))
            @test exact_equal(α * x, sx)
            @test exact_equal((α + 0.0*im) * x, complex(sx))
            @test exact_equal(x * α, sx)
            @test exact_equal(α * x, sx)
            @test exact_equal(x .* α, sx)
            @test exact_equal(α .* x, sx)
            @test exact_equal(x / α, SparseVector(x.n, x.nzind, x.nzval / α))

            xc = copy(x)
            @test rmul!(xc, α) === xc
            @test exact_equal(xc, sx)
            xc = copy(x)
            @test lmul!(α, xc) === xc
            @test exact_equal(xc, sx)
            xc = copy(x)
            @test rmul!(xc, complex(α, 0.0)) === xc
            @test exact_equal(xc, sx)
            xc = copy(x)
            @test lmul!(complex(α, 0.0), xc) === xc
            @test exact_equal(xc, sx)
        end

        @testset "dot" begin
            dv = dot(xf, xf2)
            @test dot(x, x) == sum(abs2, x)
            @test dot(x2, x2) == sum(abs2, x2)
            @test dot(x, x2) ≈ dv
            @test dot(x2, x) ≈ dv
            @test dot(Array(x), x2) ≈ dv
            @test dot(x, Array(x2)) ≈ dv
        end
    end

    let x = complex.(sprand(32, 0.6), sprand(32, 0.6)),
        y = complex.(sprand(32, 0.6), sprand(32, 0.6))
        xf = Array(x)::Vector{ComplexF64}
        yf = Array(y)::Vector{ComplexF64}
        @test dot(x, x) ≈ dot(xf, xf)
        @test dot(x, y) ≈ dot(xf, yf)
    end
end

@testset "BLAS Level-2" begin
    @testset "dense A * sparse x -> dense y" begin
        let A = randn(9, 16), x = sprand(16, 0.7)
            xf = Array(x)
            for α in [0.0, 1.0, 2.0], β in [0.0, 0.5, 1.0]
                y = rand(9)
                rr = α*A*xf + β*y
                @test mul!(y, A, x, α, β) === y
                @test y ≈ rr
            end
            y = A*x
            @test isa(y, Vector{Float64})
            @test A*x ≈ A*xf
        end

        let A = randn(16, 9), x = sprand(16, 0.7)
            xf = Array(x)
            for α in [0.0, 1.0, 2.0], β in [0.0, 0.5, 1.0]
                y = rand(9)
                rr = α*A'xf + β*y
                @test mul!(y, transpose(A), x, α, β) === y
                @test y ≈ rr
            end
            y = *(transpose(A), x)
            @test isa(y, Vector{Float64})
            @test y ≈ *(transpose(A), xf)
        end
    end
    @testset "sparse A * sparse x -> dense y" begin
        let A = sprandn(9, 16, 0.5), x = sprand(16, 0.7)
            Af = Array(A)
            xf = Array(x)
            for α in [0.0, 1.0, 2.0], β in [0.0, 0.5, 1.0]
                y = rand(9)
                rr = α*Af*xf + β*y
                @test mul!(y, A, x, α, β) === y
                @test y ≈ rr
            end
            y = SparseArrays.densemv(A, x)
            @test isa(y, Vector{Float64})
            @test y ≈ Af*xf
        end

        let A = sprandn(16, 9, 0.5), x = sprand(16, 0.7)
            Af = Array(A)
            xf = Array(x)
            for α in [0.0, 1.0, 2.0], β in [0.0, 0.5, 1.0]
                y = rand(9)
                rr = α*Af'xf + β*y
                @test mul!(y, transpose(A), x, α, β) === y
                @test y ≈ rr
            end
            y = SparseArrays.densemv(A, x; trans='T')
            @test isa(y, Vector{Float64})
            @test y ≈ *(transpose(Af), xf)
        end

        let A = complex.(sprandn(7, 8, 0.5), sprandn(7, 8, 0.5)),
            x = complex.(sprandn(8, 0.6), sprandn(8, 0.6)),
            x2 = complex.(sprandn(7, 0.75), sprandn(7, 0.75))
            Af = Array(A)
            xf = Array(x)
            x2f = Array(x2)
            @test SparseArrays.densemv(A, x; trans='N') ≈ Af * xf
            @test SparseArrays.densemv(A, x2; trans='T') ≈ transpose(Af) * x2f
            @test SparseArrays.densemv(A, x2; trans='C') ≈ Af'x2f
            @test_throws ArgumentError SparseArrays.densemv(A, x; trans='D')
        end
    end
    @testset "sparse A * sparse x -> sparse y" begin
        let A = sprandn(9, 16, 0.5), x = sprand(16, 0.7), x2 = sprand(9, 0.7)
            Af = Array(A)
            xf = Array(x)
            x2f = Array(x2)

            y = A*x
            @test isa(y, SparseVector{Float64,Int})
            @test all(nonzeros(y) .!= 0.0)
            @test Array(y) ≈ Af * xf

            y = *(transpose(A), x2)
            @test isa(y, SparseVector{Float64,Int})
            @test all(nonzeros(y) .!= 0.0)
            @test Array(y) ≈ Af'x2f
        end

        let A = complex.(sprandn(7, 8, 0.5), sprandn(7, 8, 0.5)),
            x = complex.(sprandn(8, 0.6), sprandn(8, 0.6)),
            x2 = complex.(sprandn(7, 0.75), sprandn(7, 0.75))
            Af = Array(A)
            xf = Array(x)
            x2f = Array(x2)

            y = A*x
            @test isa(y, SparseVector{ComplexF64,Int})
            @test Array(y) ≈ Af * xf

            y = *(transpose(A), x2)
            @test isa(y, SparseVector{ComplexF64,Int})
            @test Array(y) ≈ transpose(Af) * x2f

            y = *(adjoint(A), x2)
            @test isa(y, SparseVector{ComplexF64,Int})
            @test Array(y) ≈ Af'x2f
        end
    end
    @testset "ldiv ops with triangular matrices and sparse vecs (#14005)" begin
        m = 10
        sparsefloatvecs = SparseVector[sprand(m, 0.4) for k in 1:3]
        sparseintvecs = SparseVector[SparseVector(m, sprvec.nzind, round.(Int, sprvec.nzval*10)) for sprvec in sparsefloatvecs]
        sparsecomplexvecs = SparseVector[SparseVector(m, sprvec.nzind, complex.(sprvec.nzval, sprvec.nzval)) for sprvec in sparsefloatvecs]

        sprmat = sprand(m, m, 0.2)
        sparsefloatmat = I + sprmat/(2m)
        sparsecomplexmat = I + SparseMatrixCSC(m, m, sprmat.colptr, sprmat.rowval, complex.(sprmat.nzval, sprmat.nzval)/(4m))
        sparseintmat = 10m*I + SparseMatrixCSC(m, m, sprmat.colptr, sprmat.rowval, round.(Int, sprmat.nzval*10))

        denseintmat = I*10m + rand(1:m, m, m)
        densefloatmat = I + randn(m, m)/(2m)
        densecomplexmat = I + randn(Complex{Float64}, m, m)/(4m)

        inttypes = (Int32, Int64, BigInt)
        floattypes = (Float32, Float64, BigFloat)
        complextypes = (Complex{Float32}, Complex{Float64})
        eltypes = (inttypes..., floattypes..., complextypes...)

        for eltypemat in eltypes
            (densemat, sparsemat) = eltypemat in inttypes ? (denseintmat, sparseintmat) :
                                    eltypemat in floattypes ? (densefloatmat, sparsefloatmat) :
                                    eltypemat in complextypes && (densecomplexmat, sparsecomplexmat)
            densemat = convert(Matrix{eltypemat}, densemat)
            sparsemat = convert(SparseMatrixCSC{eltypemat}, sparsemat)
            trimats = (LowerTriangular(densemat), UpperTriangular(densemat),
                       LowerTriangular(sparsemat), UpperTriangular(sparsemat) )
            unittrimats = (LinearAlgebra.UnitLowerTriangular(densemat), LinearAlgebra.UnitUpperTriangular(densemat),
                           LinearAlgebra.UnitLowerTriangular(sparsemat), LinearAlgebra.UnitUpperTriangular(sparsemat) )

            for eltypevec in eltypes
                spvecs = eltypevec in inttypes ? sparseintvecs :
                         eltypevec in floattypes ? sparsefloatvecs :
                         eltypevec in complextypes && sparsecomplexvecs
                spvecs = SparseVector[SparseVector(m, spvec.nzind, convert(Vector{eltypevec}, spvec.nzval)) for spvec in spvecs]

                for spvec in spvecs
                    fspvec = convert(Array, spvec)
                    # test out-of-place left-division methods
                    for mat in (trimats..., unittrimats...)
                        @test \(mat, spvec)            ≈ \(mat, fspvec)
                        @test \(adjoint(mat), spvec)   ≈ \(adjoint(mat), fspvec)
                        @test \(transpose(mat), spvec) ≈ \(transpose(mat), fspvec)
                    end
                    # test in-place left-division methods not involving quotients
                    if eltypevec == typeof(zero(eltypemat)*zero(eltypevec) + zero(eltypemat)*zero(eltypevec))
                        for mat in unittrimats
                            @test ldiv!(mat, copy(spvec)) ≈ ldiv!(mat, copy(fspvec))
                            @test ldiv!(adjoint(mat), copy(spvec)) ≈ ldiv!(adjoint(mat), copy(fspvec))
                            @test ldiv!(transpose(mat), copy(spvec)) ≈ ldiv!(transpose(mat), copy(fspvec))
                        end
                    end
                    # test in-place left-division methods involving quotients
                    if eltypevec == typeof((zero(eltypemat)*zero(eltypevec) + zero(eltypemat)*zero(eltypevec))/one(eltypemat))
                        for mat in trimats
                            @test ldiv!(mat, copy(spvec)) ≈ ldiv!(mat, copy(fspvec))
                            @test ldiv!(adjoint(mat), copy(spvec)) ≈ ldiv!(adjoint(mat), copy(fspvec))
                            @test ldiv!(transpose(mat), copy(spvec)) ≈ ldiv!(transpose(mat), copy(fspvec))
                        end
                    end
                end
            end
        end
    end
    @testset "#16716" begin
        # The preceding tests miss the edge case where the sparse vector is empty
        origmat = [-1.5 -0.7; 0.0 1.0]
        transmat = copy(origmat')
        utmat = UpperTriangular(origmat)
        ltmat = LowerTriangular(transmat)
        uutmat = LinearAlgebra.UnitUpperTriangular(origmat)
        ultmat = LinearAlgebra.UnitLowerTriangular(transmat)

        zerospvec = spzeros(Float64, 2)
        zerodvec = zeros(Float64, 2)

        for mat in (utmat, ltmat, uutmat, ultmat)
            @test isequal(\(mat, zerospvec), zerodvec)
            @test isequal(\(adjoint(mat), zerospvec), zerodvec)
            @test isequal(\(transpose(mat), zerospvec), zerodvec)
            @test isequal(ldiv!(mat, copy(zerospvec)), zerospvec)
            @test isequal(ldiv!(adjoint(mat), copy(zerospvec)), zerospvec)
            @test isequal(ldiv!(transpose(mat), copy(zerospvec)), zerospvec)
        end
    end
end

@testset "fkeep!" begin
    x = sparsevec(1:7, [3., 2., -1., 1., -2., -3., 3.], 7)
    # droptol
    xdrop = SparseArrays.droptol!(copy(x), 1.5)
    @test exact_equal(xdrop, SparseVector(7, [1, 2, 5, 6, 7], [3., 2., -2., -3., 3.]))
    SparseArrays.droptol!(xdrop, 2.5)
    @test exact_equal(xdrop, SparseVector(7, [1, 6, 7], [3., -3., 3.]))
    SparseArrays.droptol!(xdrop, 3.)
    @test exact_equal(xdrop, SparseVector(7, Int[], Float64[]))

    xdrop = copy(x)
    # This will keep index 1, 3, 4, 7 in xdrop
    f_drop(i, x) = (abs(x) == 1.) || (i in [1, 7])
    SparseArrays.fkeep!(xdrop, f_drop)
    @test exact_equal(xdrop, SparseVector(7, [1, 3, 4, 7], [3., -1., 1., 3.]))
end

@testset "dropzeros[!] with length=$m" for m in (10, 20, 30)
    Random.seed!(123)
    nzprob, targetnumposzeros, targetnumnegzeros = 0.4, 5, 5
    v = sprand(m, nzprob)
    struczerosv = findall(x -> x == 0, v)
    poszerosinds = unique(rand(struczerosv, targetnumposzeros))
    negzerosinds = unique(rand(struczerosv, targetnumnegzeros))
    vposzeros = copy(v)
    vposzeros[poszerosinds] .= 2
    vnegzeros = copy(v)
    vnegzeros[negzerosinds] .= -2
    vbothsigns = copy(vposzeros)
    vbothsigns[negzerosinds] .= -2
    map!(x -> x == 2 ? 0.0 : x, vposzeros.nzval, vposzeros.nzval)
    map!(x -> x == -2 ? -0.0 : x, vnegzeros.nzval, vnegzeros.nzval)
    map!(x -> x == 2 ? 0.0 : x == -2 ? -0.0 : x, vbothsigns.nzval, vbothsigns.nzval)
    for vwithzeros in (vposzeros, vnegzeros, vbothsigns)
        # Basic functionality / dropzeros!
        @test dropzeros!(copy(vwithzeros)) == v
        @test dropzeros!(copy(vwithzeros), trim = false) == v
        # Basic functionality / dropzeros
        @test dropzeros(vwithzeros) == v
        @test dropzeros(vwithzeros, trim = false) == v
        # Check trimming works as expected
        @test length(dropzeros!(copy(vwithzeros)).nzval) == length(v.nzval)
        @test length(dropzeros!(copy(vwithzeros)).nzind) == length(v.nzind)
        @test length(dropzeros!(copy(vwithzeros), trim = false).nzval) == length(vwithzeros.nzval)
        @test length(dropzeros!(copy(vwithzeros), trim = false).nzind) == length(vwithzeros.nzind)
    end
end

@testset "original dropzeros! test" begin
    xdrop = sparsevec(1:7, [3., 2., -1., 1., -2., -3., 3.], 7)
    xdrop.nzval[[2, 4, 6]] .= 0.0
    SparseArrays.dropzeros!(xdrop)
    @test exact_equal(xdrop, SparseVector(7, [1, 3, 5, 7], [3, -1., -2., 3.]))
end

# It's tempting to share data between a SparseVector and a SparseMatrix,
# but if that's done, then modifications to one or the other will cause
# an inconsistent state:
sv = sparse(1:10)
sm = convert(SparseMatrixCSC, sv)
sv[1] = 0
@test Array(sm)[2:end] == 2:10

# Ensure that sparsevec with all-zero values returns an array of zeros
@test sparsevec([1,2,3],[0,0,0]) == [0,0,0]

@testset "stored zero semantics" begin
    # Compare stored zero semantics between SparseVector and SparseMatrixCSC
    let S = SparseMatrixCSC(10,1,[1,6],[1,3,5,6,7],[0,1,2,0,3]), x = SparseVector(10,[1,3,5,6,7],[0,1,2,0,3])
        @test nnz(S) == nnz(x) == 5
        for I = (:, 1:10, Vector(1:10))
            @test S[I,1] == S[I] == x[I] == x
            @test nnz(S[I,1]) == nnz(S[I]) == nnz(x[I]) == nnz(x)
        end
        for I = (2:9, 1:2, 9:10, [3,6,1], [10,9,8], [])
            @test S[I,1] == S[I] == x[I]
            @test nnz(S[I,1]) == nnz(S[I]) == nnz(x[I])
        end
        @test S[[1 3 5; 2 4 6]] == x[[1 3 5; 2 4 6]]
        @test nnz(S[[1 3 5; 2 4 6]]) == nnz(x[[1 3 5; 2 4 6]])
    end
end

@testset "Issue 14013" begin
    s14013 = sparse([10.0 0.0 30.0; 0.0 1.0 0.0])
    a14013 = [10.0 0.0 30.0; 0.0 1.0 0.0]
    @test s14013 == a14013
    @test vec(s14013) == s14013[:] == a14013[:]
    @test Array(s14013)[1,:] == s14013[1,:] == a14013[1,:] == [10.0, 0.0, 30.0]
    @test Array(s14013)[2,:] == s14013[2,:] == a14013[2,:] == [0.0, 1.0, 0.0]
end
@testset "Issue 14046" begin
    s14046 = sprand(5, 1.0)
    @test spzeros(5) + s14046 == s14046
    @test 2*s14046 == s14046 + s14046
end
@testset "Issue 14589" begin
    # test vectors with no zero elements
    let x = sparsevec(1:7, [3., 2., -1., 1., -2., -3., 3.], 7)
        @test Vector(sort(x)) == sort(Vector(x))
    end
    # test vectors with all zero elements
    let x = sparsevec(Int64[], Float64[], 7)
        @test Vector(sort(x)) == sort(Vector(x))
    end
    # test vector with sparsity approx 1/2
    let x = sparsevec(1:7, [3., 2., -1., 1., -2., -3., 3.], 15)
        @test Vector(sort(x)) == sort(Vector(x))
        # apply three distinct transformations where zeros sort into start/middle/end
        @test Vector(sort(x, by=abs)) == sort(Vector(x), by=abs)
        @test Vector(sort(x, by=sign)) == sort(Vector(x), by=sign)
        @test Vector(sort(x, by=inv)) == sort(Vector(x), by=inv)
    end
end
@testset "fill!" begin
    for Tv in [Float32, Float64, Int64, Int32, ComplexF64]
        for Ti in [Int16, Int32, Int64, BigInt]
            sptypes = (SparseMatrixCSC{Tv, Ti}, SparseVector{Tv, Ti})
            sizes = [(3, 4), (3,)]
            for (siz, Sp) in zip(sizes, sptypes)
                arr = rand(Tv, siz...)
                sparr = Sp(arr)
                x = rand(Tv)
                @test fill!(sparr, x) == fill(x, siz)
                @test fill!(sparr, 0) == fill(0, siz)
            end
        end
    end
end

@testset "13130 and 16661" begin
    @test issparse([sprand(10,10,.1) sprand(10,.1)])
    @test issparse([sprand(10,1,.1); sprand(10,.1)])

    @test issparse([sprand(10,10,.1) rand(10)])
    @test issparse([sprand(10,1,.1)  rand(10)])
    @test issparse([sprand(10,2,.1) sprand(10,1,.1) rand(10)])
    @test issparse([sprand(10,1,.1); rand(10)])

    @test issparse([sprand(10,.1)  rand(10)])
    @test issparse([sprand(10,.1); rand(10)])
end

mutable struct t20488 end

@testset "show" begin
    io = IOBuffer()
    show(io, MIME"text/plain"(), sparsevec(Int64[1], [1.0]))
    @test String(take!(io)) == "1-element SparseArrays.SparseVector{Float64,Int64} with 1 stored entry:\n  [1]  =  1.0"
    show(io, MIME"text/plain"(),  spzeros(Float64, Int64, 2))
    @test String(take!(io)) == "2-element SparseArrays.SparseVector{Float64,Int64} with 0 stored entries"
    show(io, similar(sparsevec(rand(3) .+ 0.1), t20488))
    @test String(take!(io)) == "  [1]  =  #undef\n  [2]  =  #undef\n  [3]  =  #undef"
end

@testset "spzeros with index type" begin
    @test typeof(spzeros(Float32, Int16, 3)) == SparseVector{Float32,Int16}
end

@testset "corner cases of broadcast arithmetic operations with scalars (#21515)" begin
    # test both scalar literals and variables
    areequal(a, b, c) = isequal(a, b) && isequal(b, c)
    inf, zeroh, zv, spzv = Inf, 0.0, zeros(1), spzeros(1)
    @test areequal(spzv .* Inf,  spzv .* inf,    sparsevec(zv .* Inf))
    @test areequal(Inf .* spzv,  inf .* spzv,    sparsevec(Inf .* zv))
    @test areequal(spzv ./ 0.0,  spzv ./ zeroh,  sparsevec(zv ./ 0.0))
    @test areequal(0.0 .\ spzv,  zeroh .\ spzv,  sparsevec(0.0 .\ zv))
end

@testset "similar for SparseVector" begin
    A = SparseVector(10, Int[1, 3, 5, 7], Float64[1.0, 3.0, 5.0, 7.0])
    # test similar without specifications (preserves stored-entry structure)
    simA = similar(A)
    @test typeof(simA) == typeof(A)
    @test size(simA) == size(A)
    @test simA.nzind == A.nzind
    @test length(simA.nzval) == length(A.nzval)
    # test similar with entry type specification (preserves stored-entry structure)
    simA = similar(A, Float32)
    @test typeof(simA) == SparseVector{Float32,eltype(A.nzind)}
    @test size(simA) == size(A)
    @test simA.nzind == A.nzind
    @test length(simA.nzval) == length(A.nzval)
    # test similar with entry and index type specification (preserves stored-entry structure)
    simA = similar(A, Float32, Int8)
    @test typeof(simA) == SparseVector{Float32,Int8}
    @test size(simA) == size(A)
    @test simA.nzind == A.nzind
    @test length(simA.nzval) == length(A.nzval)
    # test similar with Dims{1} specification (preserves nothing)
    simA = similar(A, (6,))
    @test typeof(simA) == typeof(A)
    @test size(simA) == (6,)
    @test length(simA.nzind) == 0
    @test length(simA.nzval) == 0
    # test similar with entry type and Dims{1} specification (preserves nothing)
    simA = similar(A, Float32, (6,))
    @test typeof(simA) == SparseVector{Float32,eltype(A.nzind)}
    @test size(simA) == (6,)
    @test length(simA.nzind) == 0
    @test length(simA.nzval) == 0
    # test similar with entry type, index type, and Dims{1} specification (preserves nothing)
    simA = similar(A, Float32, Int8, (6,))
    @test typeof(simA) == SparseVector{Float32,Int8}
    @test size(simA) == (6,)
    @test length(simA.nzind) == 0
    @test length(simA.nzval) == 0
    # test entry points to similar with entry type, index type, and non-Dims shape specification
    @test similar(A, Float32, Int8, 6, 6) == similar(A, Float32, Int8, (6, 6))
    @test similar(A, Float32, Int8, 6) == similar(A, Float32, Int8, (6,))
    # test similar with Dims{2} specification (preserves storage space only, not stored-entry structure)
    simA = similar(A, (6,6))
    @test typeof(simA) == SparseMatrixCSC{eltype(A.nzval),eltype(A.nzind)}
    @test size(simA) == (6,6)
    @test simA.colptr == fill(1, 6+1)
    @test length(simA.rowval) == length(A.nzind)
    @test length(simA.nzval) == length(A.nzval)
    # test similar with entry type and Dims{2} specification (preserves storage space only)
    simA = similar(A, Float32, (6,6))
    @test typeof(simA) == SparseMatrixCSC{Float32,eltype(A.nzind)}
    @test size(simA) == (6,6)
    @test simA.colptr == fill(1, 6+1)
    @test length(simA.rowval) == length(A.nzind)
    @test length(simA.nzval) == length(A.nzval)
    # test similar with entry type, index type, and Dims{2} specification (preserves storage space only)
    simA = similar(A, Float32, Int8, (6,6))
    @test typeof(simA) == SparseMatrixCSC{Float32, Int8}
    @test size(simA) == (6,6)
    @test simA.colptr == fill(1, 6+1)
    @test length(simA.rowval) == length(A.nzind)
    @test length(simA.nzval) == length(A.nzval)
end

@testset "Fast operations on full column views" begin
    n = 1000
    A = sprandn(n, n, 0.01)
    for j in 1:5:n
        Aj, Ajview = A[:, j], view(A, :, j)
        @test norm(Aj)          == norm(Ajview)
        @test dot(Aj, copy(Aj)) == dot(Ajview, Aj) # don't alias since it takes a different code path
        @test rmul!(Aj, 0.1)    == rmul!(Ajview, 0.1)
        @test Aj*0.1            == Ajview*0.1
        @test 0.1*Aj            == 0.1*Ajview
        @test Aj/0.1            == Ajview/0.1
        @test LinearAlgebra.axpy!(1.0, Aj,     sparse(fill(1., n))) ==
              LinearAlgebra.axpy!(1.0, Ajview, sparse(fill(1., n)))
        @test LinearAlgebra.lowrankupdate!(Matrix(1.0*I, n, n), fill(1.0, n), Aj) ==
              LinearAlgebra.lowrankupdate!(Matrix(1.0*I, n, n), fill(1.0, n), Ajview)
    end
end

end # module