using Test, LinearMaps, LinearAlgebra, SparseArrays
using LinearMaps: LinearMapVector, LinearMapTuple

@testset "composition" begin
    F = @inferred LinearMap(cumsum, reverse ∘ cumsum ∘ reverse, 10; ismutating=false)
    FC = @inferred LinearMap{ComplexF64}(cumsum, reverse ∘ cumsum ∘ reverse, 10; ismutating=false)
    FCM = LinearMaps.CompositeMap{ComplexF64}((FC,))
    L = LowerTriangular(ones(10,10))
    @test_throws DimensionMismatch F * LinearMap(rand(2,2))
    @test_throws ErrorException LinearMaps.CompositeMap{Float64}((FC, LinearMap(rand(10,10))))
    A = 2 * rand(ComplexF64, (10, 10)) .- 1
    B = rand(size(A)...)
    H = LinearMap(Hermitian(A'A))
    S = LinearMap(Symmetric(real(A)'real(A)))
    M = @inferred 1 * LinearMap(A)
    N = @inferred LinearMap(B)
    v = rand(ComplexF64, 10)
    α = rand(ComplexF64)
    @test FCM * v == F * v
    @test @inferred (F * F) * v == @inferred F * (F * v)
    @test @inferred (F * A) * v == @inferred F * (A * v)
    @test @inferred (A * F) * v == @inferred A * (F * v)
    @test @inferred A * (F * F) * v == @inferred A * (F * (F * v))
    F2 = F*F
    FC2 = FC*FC
    F4 = FC2 * F2
    F4v = @inferred LinearMaps.CompositeMap{ComplexF64}([FC2, F2])
    @test occursin("10×10 LinearMaps.CompositeMap{$(eltype(F4))}", sprint((t, s) -> show(t, "text/plain", s), F4))
    @test length(F4.maps) == 4
    @test (@inferred F4 * v) == F4v * v == (@inferred F * (F * (F * (F * v))))
    @test @inferred Matrix(M * transpose(M)) ≈ A * transpose(A)
    @test @inferred !isposdef(M * transpose(M))
    @test @inferred isposdef(LinearMap(M * M', isposdef=true))
    @test @inferred issymmetric(N * N')
    @test @inferred ishermitian(N * N')
    @test @inferred !issymmetric(M' * M)
    @test @inferred ishermitian(M' * M)
    @test @inferred issymmetric(F'F)
    @test @inferred issymmetric(F'*S*F)
    @test @inferred ishermitian(F'F)
    @test @inferred ishermitian(LinearMaps.CompositeMap{ComplexF64}([F, F']))
    @test @inferred ishermitian(F'*H*F)
    @test @inferred ishermitian(LinearMaps.CompositeMap{ComplexF64}([F, H, F']))
    @test @inferred !issymmetric(FC'FC)
    @test @inferred ishermitian(FC'FC)
    @test @inferred ishermitian(FC'*H*FC)
    @test @inferred issymmetric(transpose(F) * F * 3)
    @test @inferred issymmetric(transpose(F) * 3 * F)
    @test @inferred !isposdef(-5*transpose(F) * F)
    @test @inferred ishermitian((M * F)' * M * 4 * F)
    @test @inferred transpose(M * F) == @inferred transpose(F) * transpose(M)
    @test @inferred (4*((-3*M)*2)) == @inferred -12M*2
    @test @inferred (4*((3*(-M))*2)*(-5)) == @inferred -12M*(-10)
    L = @inferred 3 * F + 1im * A + F * M' * F
    LF = 3 * Matrix(F) + 1im * A + Matrix(F) * Matrix(M)' * Matrix(F)
    @test Array(L) ≈ LF
    R1 = rand(ComplexF64, 10, 10); L1 = LinearMap(R1)
    R2 = rand(ComplexF64, 10, 10); L2 = LinearMap(R2)
    R3 = rand(ComplexF64, 10, 10); L3 = LinearMap(R3)
    CompositeR = *(R1, R2, R3)
    CompositeL = prod(LinearMap, [R1, R2, R3])
    @test prod([L1, L2, LinearMap(randn(10, 10))]) isa LinearMaps.CompositeMap{ComplexF64,<:LinearMapVector}
    @test (@inferred prod([L1, L2, L3])) isa LinearMaps.CompositeMap{<:Any,<:LinearMapVector}
    @test prod([L1, L2, L3]) == (@inferred L1 * prod([L2, L3])) == (@inferred prod([L1, L2]) * L3)
    @test (@inferred prod((L1, L2, L3))) isa LinearMaps.CompositeMap{<:Any,<:LinearMapTuple}
    @test (@inferred L1 * L2 * L3) == CompositeL == prod([L1, L2, L3])
    @test Matrix(L1 * L2) ≈ sparse(L1 * L2) ≈ R1 * R2
    @test Matrix(@inferred((α * L1) * (L2 * L3))::LinearMaps.ScaledMap) ≈ α * CompositeR
    @test Matrix(@inferred((L1 * L2) * (L3 * α))::LinearMaps.ScaledMap) ≈ α * CompositeR
    @test @inferred transpose(CompositeL) == transpose(L3) * transpose(L2) * transpose(L1)
    @test @inferred adjoint(CompositeL) == L3' * L2' * L1'
    @test @inferred adjoint(adjoint((CompositeL))) == CompositeL
    @test transpose(transpose((CompositeL))) == CompositeL
    Lt = @inferred transpose(LinearMap(CompositeL))
    @test Lt * v ≈ transpose(CompositeR) * v
    Lc = @inferred adjoint(LinearMap(CompositeL))
    @test Lc * v ≈ adjoint(CompositeR) * v

    # convert to AbstractMatrix
    for A in (LinearMap(sprandn(10, 10, 0.3)), LinearMap(rand()*I, 10))
        for B in (LinearMap(sprandn(10, 10, 0.3)), LinearMap(rand()*I, 10))
            AA = convert(AbstractMatrix, A*B)
            if A isa LinearMaps.UniformScalingMap && B isa LinearMaps.UniformScalingMap
                @test isdiag(AA)
            else
                @test issparse(AA)
            end
        end
    end

    # test inplace operations
    w = similar(v)
    mul!(w, L, v)
    @test w ≈ LF * v

    # test composition of several maps with shared data #31
    global sizes = ( (5, 2), (3, 3), (3, 2), (2, 2), (9, 2), (7, 1) )
    N = length(sizes) - 1
    global Lf = []
    global Lt = []
    global Lc = []

    # build list of operators [LN, ..., L2, L1] for each mode
    for (fi, i) in [ (Symbol("f$i"), i) for i in 1:N]
        @eval begin
            function ($fi)(source)
                dest = ones(prod(sizes[$i + 1]))
                tmp = reshape(source, sizes[$i])
                return conj.($i * dest)
            end
            insert!(Lf, 1, LinearMap($fi, prod(sizes[$i + 1]), prod(sizes[$i])))
            insert!(Lt, 1, LinearMap(x -> x, $fi, prod(sizes[$i]), prod(sizes[$i + 1])))
            insert!(Lc, 1, LinearMap{ComplexF64}(x -> x, $fi, prod(sizes[$i]), prod(sizes[$i + 1])))
        end
    end
    @test size(prod(Lf[1:N])) == (prod(sizes[end]), prod(sizes[1]))
    @test isreal(prod(Lf[1:N]))
    # multiply as composition and as recursion
    v1 = ones(prod(sizes[1]))
    u1 = ones(prod(sizes[1]))
    w1 = im.*ones(ComplexF64, prod(sizes[1]))
    for i = N:-1:1
        v2 = prod(Lf[i:N]) * ones(prod(sizes[1]))
        u2 = transpose(LinearMap(prod(Lt[N:-1:i]))) * ones(prod(sizes[1]))
        w2 = adjoint(LinearMap(prod(Lc[N:-1:i]))) * ones(prod(sizes[1]))

        v1 = Lf[i] * v1
        u1 = transpose(Lt[i]) * u1
        w1 = adjoint(Lc[i]) * w1

        @test v1 == v2
        @test u1 == u2
        @test w1 == w2
    end
    L1 = LinearMap(rand(2,3))
    L2 = LinearMap(rand(4,2))
    L3 = LinearMap(rand(3, 4))
    L4 = LinearMap(rand(5, 3))
    Ls = L4*L3*L2*L1
    X = rand(size(Ls, 2), 10)
    Y = similar(X, (size(Ls, 1), size(X, 2)))
    @test mul!(Y, Ls, X) ≈ L4.lmap * L3.lmap * L2.lmap * L1.lmap * X

    # test isposdef on a case where sufficient conditions work
    B = LinearMap([1 0; 0 1], isposdef=true) # isposdef!
    C = B' * B * B * B * B # no B' at end on purpose
    @test @inferred isposdef(C)
    @test @inferred isposdef(LinearMaps.CompositeMap{Float64}([B, B, B, B, B']))
    @test @inferred isposdef(B * B) # even case for empty tuple test
    @test @inferred isposdef(LinearMaps.CompositeMap{Float64}([B, B]))

    M = LinearMap(cumsum, 3)
    for i in 1:4
        P = prod(fill(M, i))
        @test P isa LinearMaps.CompositeMap{<:Any,<:LinearMapVector}
        @test P * ones(3) == (LowerTriangular(ones(3,3))^i) * ones(3)
    end
end
