behavior, called "Index Imbedding," allows the structure of the full

incidence matrix to be predicted, and in fact visualized from knowledge

of the Function-Variable Incidence Matrix and the Index Display Matrix.


2.5 Output Set Assignments

 A notion central to iterative solution of a set of equations is

that of the output set assignment. Briefly an output set assignment is

the assignment of one variable to each equation such that no variable

is assigned to more than one equation. Variables which are not assigned

are decision variables and have their values defined prior to the

initiation of a solution procedure. There are, however, many output set

assignments for a set of indexed equations which could be derived by

existing algorithms operating on the full incidence matrix which would

be extremely difficult, if not impossible, to solve using do-loops. As

an example consider Fig. 2-5, where the circled elements are the out-

puts. There is no reasonable or logical way to write a solution pro-

cedure for that output set assignment using do-loops.

 If, however, we assign outputs to the Function-Variable Incidence

Matrix and to the Index Display Matrices, a logical, concise solution

procedure for a set of indexed equations can be implemented using do-

loops. This means that, whenever a function of a given type is being

solved, the output variable will always be of the type assigned to that

function in the FVIM. Similarly, if a function being solved has index

ii with a given value, the variable which is the output will have its

index value corresponding to ii known. The IDM's which need to have

outputs assigned (called "index outputs") are those which occur in

output set assigned incidences of the FVIM. To illustrate the restric-