Summary

maps each statement instance to its new position in the transformed loop's exec sequence

gives new dependence distance vector, giving test for validity

Captures skewing, interchange and reversal

Compose transformations by matrix multiplication

Resulting loop's bounds may be a little tricky

Efficient algorithms exist [] to maximise parallelism by skewing and loop interchanging

Efficient algorithms exist to optimise cache performance by finding the combination of blocking, block size, interchange and skewing which leads to the best reuse []