  Many matrices associated with fast transforms posess a certain low-rank
property characterized by the existence of several block partitionings of the
matrix, where each block is of low rank. Provided that these partitionings are
known, there exist algorithms, called butterfly factorization algorithms, that
approximate the matrix into a product of sparse factors, thus enabling a rapid
evaluation of the associated linear operator. This paper proposes a new method
to identify algebraically these block partitionings for a matrix admitting a
butterfly factorization, without any analytical assumption on its entries.
