The material in these lectures is taken from the following research paper:
U. Banerjee, ``Unimodular transformations of double loops'' [].Banerjee's paper gives a simplified account of the theory in the context only of perfect doubly-nested loops with well-known dependences.
Monica Lam's group at Stanford have used these ideas to build a public-domain prototype compiler system ``SUIF''. The following paper describes how SUIF uses unimodular transformations to optimise locality:
M.E. Wolf and M.S. Lam, ``A data locality optimizing algorithm'' [1].The Stanford work overcomes many of the restrictions of Banerjee's paper, but lies beyond the scope of this course.