Writing Array-Abstractable Definitions

This article was written April 2003 by Lonnie Chrisman, Ph.D., of Lumina Decision Systems, updated Nov 2005, and originally in a PDF format. It was transferred to the Analytica Wiki Feb 2010.

The Benefits of Array Abstraction

One of the most powerful and useful features of Analytica is Intelligent Array Abstraction™. When we give the variable Profit the definition Revenue-Expenses, Analytica automatically carries through any dimensions of Revenue and Expenses, seamlessly making the correspondence if the same dimension occurs in each. If the Revenue and Expenses variables are broken down by (i.e., indexed by) department and project, the resulting Profit will also be broken down across these two dimensions. A conventional programming language would force the modeler to explicitly loop over these dimensions when computing Profit, and a spreadsheet would require the modeler to explicitly copy the same formula to every cell in the two-dimensional grid. This manual overhead imposed on the modeler in those environments is distracting, and fundamentally unnecessary, since the relationship between Profit, Revenue and Expenses is entirely separate from whatever the dimensions happen to be in a particular model. This principle of separating the fundamental relationships between quantities (variables) and their dimensionality is what we call (Intelligent) Array Abstraction.

Once one has mastered the basics of array abstraction, it is hard to imagine going back to a more primitive modeling environment (such as a spreadsheet or standard programming language) without such a capability for any non-trivial modeling application. Array abstraction provides a flexibility that goes hand-in-hand with the modeling process. When we begin prototyping a model, the optimum dimensions to include are seldom clear. The modeling process usually involves the elucidation of relevant variables, specification of fundamental relationships, and experimentation with tradeoffs between richness of knowledge to build off of, computational complexity, and levels of detail. The determination of the appropriate dimensionality for key variables is a task that usually falls most naturally after elucidation of relationships between variables. Array abstraction allows the modeler to do just this – once an abstractable model is in place, dimensions can be added and removed with little effort. This can be contrasted with spreadsheets and conventional programming languages where one must commit to the dimensionality of variables early in the modeling process, and because every computational step involves explicit defined iteration over the specified dimensions, altering the dimensionality of variables tends to be extremely tedious.

Array abstraction also promotes correctness. Opportunities to make errors when copying cell references in a spreadsheet abound, are quite common in practice and are hard to verify; likewise, it is quite easy to make mistakes when writing explicit looping constructs in conventional programming languages, such as accidentally confusing the correspondence between dimensions. Separated from the clutter of all these looping constructs, the clarity of variable definitions in Analytica is far more apparent. Furthermore, array abstraction leaves one with a sense of confidence that solid portions of the model are and will remain correct, regardless of other modifications or dimensional adjustments that may be made outside of that sub-model. In Analytica, array abstraction enables a number of other important capabilities. A major one of those is the uncertainty analysis that is built into Analytica. Uncertainty analysis in Analytica operates by adding a dimension to the uncertain variables in your model, named the Run dimension. Since your (presumably abstractable) model describes the relationships between variables, what is true without that dimension should also be true with that dimension, and thus Analytica can seamlessly propagate that dimension through the computations, even though as a modeler, you might not have conceptualized your variables up front as being dimensioned by Run.

Another important capability arising from array abstraction is What If analysis. Adding new dimensions to key input variables enables one to simultaneously explore and compare multiple scenarios, without having the logic of your model. “What-if” analyses are also often the bases decision making by exploring spaces of possible decisions.