Analytica - Intelligent Multidimensional Arrays

Intelligent Multidimensional Arrays

Analytica uses index objects to track the dimensions of multidimensional arrays. An index object has a name and a list of elements. When two multidimensional values are combined, for example in an expression such as

Profit = Revenue − Expenses

where Revenue and Expenses are each multidimensional, Analytica repeats the profit calculation over each dimension, but recognizes when same dimension occurs in both values and treats it as the same dimension during the calculation, in a process called intelligent array abstraction™. Unlike in many programming languages, there is no inherent ordering to the dimensions in a multidimensional array. This avoids duplicated formulas and explicit FOR loops, both common sources of modeling errors. The simplified expressions made possible by intelligent array abstraction allow the model to be more accessible, interpretable, and transparent.

Another consequence of intelligent array abstraction is that new dimensions can be introduced or removed from an existing model, without requiring changes to the model structure or changes to variable definitions. For example, while creating a model, the model builder might assume a particular variable, for example discount_rate, contains a single number. Later, after constructing a model, a user might replace the single number with a table of numbers, perhaps discount_rate broken down by Country and by Economic_scenario. These new divisions may reflect the fact that the effective discount rate is not the same for international divisions of a company, and that different rates are applicable to different hypothetical scenarios. Analytica automatically propagates these new dimensions to any results that depend upon discount_rate, so for example, the result for Net_present_value will become multidimensional and contain these new dimensions. In essence, Analytica repeats the same calculation using the discount rate for each possible combination of Country and Economic_scenario.

This flexibility is important when exploring computation tradeoffs between the level of detail, computation time, available data, and overall size or dimensionality of parametric spaces. Such adjustments are common after models have been fully constructed as a way of exploring what-if scenarios and overall relationships between variables.