Although full decoupling may not be possible for a set of indexed

 equations, a partial decoupling may be. A partial decoupling results

 when some function types are decoupled from the set of equations, but

 not enough to render the FVIM acyclic. As a result a subset of the

 original function and variable types must be solved simultaneously. If

 full decoupling is not possible, there will, in general, be a partial

 decoupling for each set of index incrementing directions. Since a

 partial decoupling results in a smaller set of equations which must be

 solved simultaneously than does no decoupling, it would be desirable to

 choose one of the partial decoupling schemes for the solution procedure.

 It is possible to characterize the "degree of decoupling" by the

 expected number of functions decoupled (where the expected number for a

 function is calculated from its expected index ranges, not the blocking

 factor). The different partial decoupling schemes could then be

 compared quantitatively and the one exhibiting the greatest degree of

 decoupling chosen for the solution procedure. This is the strategy

 adopted by GENIE.


 4.2 Index Output Set Assignments

 Index outputs are assigned by treating the IDM's for each variable

index as an incidence matrix. The IDM's are output set assigned by

conventional output set assignment methods. The resulting output set

assignment is then available for defining the index outputs, should that

be necessary.

 As indicated in Chapter 3, it is sometimes desirable to assign

index outputs to the IDM resulting from a logical "OR" or a logical

"AND" being performed over all IDM's for a function index. Both of