using LinearMapsAA
using LinearAlgebra: tr, I
using InteractiveUtils: versioninfo

N = 5
forw(X) = [tr(X)] # forward mapping function
𝒜 = LinearMapAA(forw, (1, N*N); idim = (N,N), odim = (1,))

X = ones(5)*(1:5)'
𝒜 * X, tr(X), (N*(N+1))÷2

A = Matrix(𝒜)
A = Int8.(A) # just for nicer display

reshape(A, N, N)

back(y) = y[1] * I(N) # remember `y` is a 1-vector
𝒜 = LinearMapAA(forw, back, (1, N*N); idim = (N,N), odim = (1,))

@assert Matrix(𝒜)' == Matrix(𝒜')
Int8.(Matrix(𝒜'))