3.2.9 The GROUPS, ROWS or CONSTRAINTS Data Cards
(Group/Row-Wise)

The GROUPS, ROWS and CONSTRAINTS indicator cards are used interchangeably to announce the names of the groups which make up the objective function and, for constrained problems, the names of the constraints (or rows, as they are often known in linear programming applications). In addition, the entries for the linear elements are input here. The user may give a scaling factor for the groups or constraints. Furthermore, groups which are linear combinations of previous groups may be specified. The syntax for the data cards which follow these indicator cards is given in Figure 3.10.

Figure 3.10: Possible data cards for GROUPS, ROWS, or CONSTRAINTS
(row-wise)

The one- or two-character string in data field 1 specifies the type of group, row or constraint to be input. Possible values for the first character and their interpretations are exactly as in Section 3.2.6.

The string group-name in data field 2 gives the name of the group (or row or constraint) under consideration. This name may be up to ten characters long excepting that the name `SCALE' is not allowed. For X and Z data cards, the expanded array name must be valid and the integer indices must have been defined in a parameter assignment (see Section 3.2.3). The kind of group (N, L, G or E) will be taken to be that which is defined on the first occurrence of a data card for that group. Subsequent contradictory information will be ignored.

The string $$$$$$$$$$ in data field 3 is used for three purposes.

• It may be used to specify that the group mentioned in field 2 has a linear element involving the variable given in field 3. In this case, the string in field 3 must have been defined in the VARIABLES section. If an array definition is being made, the string in field 3 must be an array name. The numerical value of the coefficient of the linear term corresponding to the variable must now be specified. On Z cards, the value is that previously associated with the real parameter r-p-a-name given in field 5. On other cards, the actual numerical value numerical-vl may occupy up to 12 characters in data field 4.

• It may be used to announce that the group function under consideration is to be scaled; in this case field 3 will contain the string `SCALE'. The numerical value of the scale factor, that is the factor by which the group is to be divided, is now specified exactly as above.

  In these first two cases, fields 5 and 6 may be used to define further coefficients or a scale factor for non Z cards.

• If the first character in field 1 is a D, the current group is to be formed as a linear combination of the groups mentioned in fields 3 and 5; the multiplication factors are then recorded in fields 4 and 6 respectively. Thus we will have
  
  $$\mbox{group in field~2} = \mbox{group in field~3} * \mbox{field~4} + \mbox{group in field~5} * \mbox{field~6}.$$
  
  
  In this case, the names of the groups in fields 3 and 5 must have already been defined. The multiplication factors may occupy up to 12 locations in fields 4 and 6.