At the moment factorize plays the role of both a transform (a Plan) and a coordinate transformation. But sometimes its convenient to work directly with transforms. For example, at the moment I'm trying to do the analogue of fft(randn(3,3,3), 1) for a Chebyshev() basis but factorizations are inherently matrix/vec.
My plan is to add an extra function plan_transform(basis, array, dim) to support this functionality.