Description

S3L_gen_band_factor performs the LU factorization of an n x n general banded array with lower bandwidth bl and upper bandwidth bl. The non-zero diagonals of the array should be stored in an S3L array a of size [2*bl+2*bu+1,n].

In the more general case, a can be a multidimensional array, where axis_r and axis_d denote the array axes whose extents are 2*bl+2*bu+1 and n respectively. The format of the array a is described in the following example:

Example:

Consider a 7 x 7 (n=7) banded array with bl = 1, bu = 2. c is the main diagonal, b is the first superdiagonal and a the second. d is the first subdiagonal. The contents of the composite array a used as input to S3L_gen_band_factor should have the following organization:

Example 8-52

 *   *   *   *   *   *   *
 *   *   *   *   *   *   *
 *   *   *   *   *   *   *
 *   *  a0  a1  a2  a3  a4
 *  b0  b1  b2  b3  b4  b5
c0  c1  c2  c3  c4  c5  c6
d0  d1  d2  d3  d4  d5   *

Note that, items denoted by '*' are not referenced.

If a is two-dimensional, S3L_gen_band_factor is more efficient when axis_r is the first axis, axis_d is the second axis, and array a is block-distributed along the second axis. For C programs, the indices of the first and second axes are 0 and 1, respectively. For Fortran programs, the corresponding indices are 1 and 2.

If a has more than two dimensions, S3L_gen_band_factor is most efficient when axes axis_r and axis_d of a are local (that is, are not distributed).