Variable group algorithm

It is not easy to identify the sequence of variable groupings that minimizes the number of calls to the nonlinear system. Ciutk, Powell, and Reid (1974) proposed a heuristic algorithm that is often optimal. It is easy to describe We start with the first variable and identify the functions that depend on it Next we check if the second variable does not interfere with the functions with which the first variable interacts. If so, we go on with the third variable. Any new variable introduced into the sequence ako increments the number of functions involved. When no additional variables can be added to the list, thk means that the first group has been identified and we can go on with the next group until all the N variables of the system have been collected. Clearly, the matrix structure of the Jacobian must be known for this procedure to be applied. Thk means that the user must identify the Boolean of the Jacobian, that k, the matrix that contains the dependencies of each function from the system variables (see Figure 2.11). 

The following module is based on the algorithm in (ref. 2). Its concise structure is due to cyclic renumbering of both groups of variables, so that always x is expressed and always from the first equation. 

The match-search algorithm described above works well for similar Feature Trees of equal sizes or if one tree is fully contained in the other tree. However, as the algorithm cannot generate inner-NIL matches, variable linker regions between pharmacophoric groups cannot be modeled (see Fig. 4.5). 

---