types must then be decision variables. The variable types which are

decisions are called the "FVIM decisions."

3.1.3 Index Outputs

 The concept of index outputs was also introduced in Chapter 2.

When the IDM is treated as an incidence matrix and output set assigned,

the assignments made are called the "index outputs."

3.1.4 Index Decisions

 Just as the FVIM may have both outputs and decisions, so may the

IDM. If any columns in an IDM remain unassigned after the index outputs

are chosen those columns are the "index decisions."

3.1.5 Imbedded Loops

 The concept of index imbedding was introduced in the last chapter.

The natural way to achieve index imbedding in a FORTRAN program is to

define each index in a "do-loop" and nest the do-loops. Figure 3-1

illustrates a typical nesting of do-loops. The innermost loop, loop 3,

is executed seven times for each pass through the next innermost loop,

loop 2. Similarly, loop 2 is executed five times for each pass through

loop 1. The index imbedding represented by this nesting of do-loops

would be 13 imbedded in 12 which is in turn imbedded in Il. In terms of

incidence matrices, each 12 incidence would actually represent an 13

IDM. The nested do-loops are termed "imbedded loops." The indices are

said to be "nested inside" or "nested outside" the other indices.

3.1.6 Decomposed Problem and Expanded Problem

 As was seen in the last chapter, the FVIM and IDM's contain all of

 the structural information necessary to describe a set of indexed

 equations. The problem representation in terms of the FVIM and IDM's

 is called the "decomposed problem." When represented in terms of the


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