Large (almost) triangular spreadsheet?

A spreadsheet model without circular references can be called “triangular”. Excel can form a dependency graph and ordering such that recalculation can be done in one iteration. If there are circular references the spreadsheet needs to perform more iterations before the results converge.

I was given a very large spreadsheet implementing an agricultural country trade model. The question was how near triangular is this? With the Excel tool to find circular references, we only find a single case:

Luckily I have a tool that takes an Excel spreadsheet and parses Excel formulas and produces a GAMS representation of this. Essentially each cell forms an equation:

The whole spreadsheet can be viewed as a fixed point expression:

This is of course just a system of nonlinear equations:

When we solve this spreadsheet model as an NLP with Conopt we get some statistics:

---   67,618 rows  68,707 columns  232,364 non-zeroes ---   776,017 nl-code  103,528 nl-non-zeroes    Iter Phase Ninf   Infeasibility   RGmax    NSB   Step InItr MX OK       0   0        7.3221660778E-07 (Input point)                                 Pre-triangular equations:    22507                                 Post-triangular equations:   13897       1   0        1.2425686171E-07 (After pre-processing)       2   0        3.4325009848E-11 (After scaling)

Graphically, after reordering rows and columns, we have:

This certainly gives an indication we are not close to a triangular model and we need a simultaneous equation solver to handle this type of model.