Alignment

An array, a is aligned with an array b if they are distributed over the equivalent process groups and their ranges are all equivalent:

$$\begin{array}{lll} \mbox{\tt a.grp()} & \approx & \mbox{\t... ...tt a.rng(R-1)} & \approx & \mbox{\tt b.rng(R-1)} \end{array}$$

Informally, two groups or two ranges are equivalent if they are structurally equivalent. The informal meaning of array alignment is that corresponding elements of the two arrays are stored on the same process, or replicated over the same group of processes. The array, a is aligned with b with replicated-alignment in some dimensions if the groups are equivalent, and the ranges of a can be paired with equivalent ranges of b by omitting the ranges of b associated with the specified dimensions.