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Matrix Storage Conventions for Band and Tridiagonal Matrices

A general  tridiagonal matrix of order n is stored globally in three one-dimensional arrays dl, d, du of length n containing the subdiagonal, diagonal, and superdiagonal elements, respectively. Note the mild change from LAPACK in which dl and du were actually of global length n-1. To make the distribution of the vectors consistent, we have chosen to make them all of length n. Note that dl(1)=du(n)=0.

Similarly, a symmetric  tridiagonal matrix is stored globally in two one-dimensional arrays d, e of length n containing the diagonal and off-diagonal elements, respectively. Again, there is a slight departure from LAPACK in which e was of global length n-1. Here, e(n)=0.

The vectors (DL, D, DU) or (D, E) representing these matrices must be block distributed to a one-dimensional process grid. These vectors can be equivalently distributed block-row or block-column since vectors are one-dimensional data structures. Note that when inputting vectors to these special-purpose low-diagonal routines, LLD_ can be ignored, since it is assumed that the local portions of the vectors are of unit stride.

Susan Blackford
Tue May 13 09:21:01 EDT 1997