Xpress-SLP Statistics

When a matrix is read in using XSLPreadprob, statistics on the model are produced. They should be interpreted as described in the numbered footnotes:

Reading Problem xxx                                               (1)
Problem Statistics
        1920 (      0 spare) rows                                 (2)
         899 (      0 spare) structural columns                   (3)
        6683 (   3000 spare) non-zero elements                    (4)
Global Statistics
      0 entities   0 sets    0 set members                        (5)
Xpress-SLP Statistics:
        3632 coefficients                                         (6)
          14 extended variable arrays                             (7)
           1 user functions                                       (8)
        1011 SLP variables                                        (9)

Notes:

1. Standard output from XPRSreadprob reading the linear part of the problem
2. Number of rows declared in the ROWS section
3. Number of columns with at least one constant coefficient
4. Number of constant elements
5. Integer and SOS statistics if appropriate
6. Number of non-constant coefficients
7. Number of XVs defined
8. Number of user functions defined
9. Number of variables identified as SLP variables (interacting with a non-linear coefficient)

When the original problem is SLP-presolved prior to augmentation, the following statistics are produced:

Xpress-SLP Presolve:	
    3 presolve passes                                            (10)
  247 SLP variables newly identified as fixed                    (11)
  425 determining rows fixed                                     (12)
   32 coefficients identified as fixed                           (13)
   58 columns fixed to zero (56 SLP variables)                   (14)
  367 columns fixed to nonzero (360 SLP variables)               (15)
  139 column deltas deleted                                      (16)
   34 column bounds tightened (6 SLP variables)                  (17)

Notes:

10. Presolve is an iterative process. Each iteration refines the problem until no further progress is made. The number of iterations (presolve passes) can be limited by using XSLP_PRESOLVEPASSES
11. SLP variables which are deduced to be fixed by virtue of constraints in the model (over and above any which are fixed by bounds in the original problem)
12. Number of determining rows which have fixed variables and constant coefficients
13. Number of coefficients which are fixed because they are functions of constants and fixed variables
14. Total number of columns fixed to zero (number of fixed SLP variables shown in brackets)
15. Total number of columns fixed to nonzero values (number of fixed SLP variables shown in brackets)
16. Total number of deltas deleted because the SLP variable is fixed
17. Total number of bounds tightened by virtue of constraints in the model.

If any of these items is zero, it will be omitted. Unless specifically requested by setting additional bits of control XSLP_PRESOLVE, newly fixed variables and tightened bounds are not actually applied to the model. However, they are used in the initial augmentation and during cascading to ensure that the starting points for each iteration are within the tighter bounds.

When the original problem is augmented prior to optimization, the following statistics are produced:

Xpress-SLP Augmentation Statistics:	
  Columns:	
         754 implicit SLP variables                              (18)
        1010 delta vectors                                       (19)
        2138 penalty error vectors (1177 positive, 961 negative) (20)
  Rows:	
        1370 nonlinear constraints                               (21)
        1010 update rows                                         (22)
           1 penalty error rows                                  (23)
  Coefficients:	
       11862 non-constant coefficients                           (24)

Notes:

18. SLP variables appearing only in coefficients and having no constant elements
19. Number of delta vectors created
20. Numbers of penalty error vectors
21. Number of constraints containing nonlinear terms
22. Number of update rows (equals number of delta vectors)
23. Number of rows totaling penalty vectors (error or delta)
24. Number of non-constant coefficients in the linear augmented matrix

• The total number of rows in the augmented matrix is (2) + (22) + (23)
• The total number of columns in the augmented matrix is (3) + (18) + (19) + (20) + (23)
• The total number of elements in the original matrix is (4) + (6)
• The total number of elements in the augmented matrix is (4) + (24) + (19) + 2*(20) + 2*(23)

If the matrix is read in using the XPRSloadxxx and XSLPloadxxx functions then these statistics may not be produced. However, most of the values are accessible through Xpress NonLinear integer attributes using the XSLPgetintattrib function.