5. OUTPUT


 5.1 Program Iessages--Output for the first sample problem is shown in
 Figure 3. The output begins with a set of program messages. These
 messages are produced automatically at various points in the execution
 of the program without any direct instruction by the user. First, there
 is a listing of the control cards as they are executed. Note that after
 the matrix is read in, there is a statement of the dimensions of the prob-
 lem and the number of entries specified. The row dimension is the actual
 size of the square LCP matrix plus 3 extra rows used for computational
 purposes. The column dimenison is the number of columns in the A matrix,
 i.e. the quantity variables in our sample problem.
 After the SOLVE statement, a two line message is printed for each
inversion. This indicates the iteration number, the number of trans-
formations and the number of entries in the transformation matrix and the
inversion type prior to performing the inversion. The inversion type is
an indication of the reason for re-inverting at that particular moment.
A type "0" inversion, which is the case in the sample problem, is the
usual type of inversion, and is caused by a request from the algorithm
for a new inverse. The two inversions that occur in this program are
generated when: a) work is initiated to find a feasible solution for
the primal subproblem Ax = b; and b) when upon reaching a feasible
solution, the basis is extended to include dual variables (See Appendix
D for further explanation). The algorithm may also call for an invert
if it has difficulty in identifying a proper pivot element. There are
two other types of inversions: a) type "1" which is caused by reaching
a multiple of the inversion frequency set by the user or the program
(default is every 10000 iterations). For a large problem requiring
considerable time, it is advisable to invert routinely in the interest of
maintaining computational accuracy; b) type "2" inversion is the result
of running out of available storage for the transformation matrix. A new
inverse will generally be more compact, and thus the program can be
allowed to proceed.
 After the inversion is carried out, a message is printed to that
effect, the number of slack variables in the current basis is indicated,
followed by a "poor column" count and an update of the transformations