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Working with equations : Enumerated types

Enumerated types

Enumerated types allow you to refer to a each object in a collection by name, where the alternative is to use an arbitrary index number. To understand what is meant by an arbitrary index number, consider the following contrasting situations.

Let's say, for example, that you want to model soil water dynamics, with the soil divided into (say) four layers. You would create a submodel with four instances, numbered 1 to 4. You can then find the value for water content in the third layer using an expression such as element([water],3). In this case, the index number refers meaningfully to the layer number.

Now, suppose you wanted to model the growth and yield of four fruit trees: say apples, oranges, lemons and pears. You could use the above approach, creating a submodel with four instances, but in this case you would have to remember that instance 1 is "apples", 2 is "oranges", and so on. The index number is now arbitrary, since any order would be as good as any other.

The enumerated type mechanism enables you to associate the name of each fruit with each instance of the submodel, and to use this name (rather than a number) when referring to a particular instance. This considerably increases the clarity of your model, since someone trying to follow the logic of the model does not need to keep on checking up on the correspondence between an integer number and some more meaningful label.

Defining an enumerated type

Before you can use an enumerated type, you must define it. Enumerated types are defined at the level of the submodel. All submodels contained within the submodel in which the type is defined also have access to the definition. It is therefore most simple to define it for the whole model (so that any submodel in the model can then use it). To do this:

  1. Go into the submodel properties dialogue for the Desktop, either by doubleclicking on the background or by selecting "Properties..." from the edit or context menus
  2. Click on the "Advanced" tab in the Properties dialogue window to view the advanced options.
  3. Click in the edit field above the "Add type" button, type in the name for the enumerated type, e.g. "fruit", and click the "Add type" button.
  4. Click on the word "fruit" now entered into the Enumerated types list, to highlight it.
  5. Type "apples" into the same edit field, and click on "Add member".
  6. Repeat for "oranges", "lemons" and "pears". If at any stage the word "fruit" becomes un-selected, select it again to enable you to add new members.
  7. To see what the list of values is for "fruit", hover over the name and observe the pop-up reminder.
  8. You can now (or at some later stage) define additional enumerated types in the same way.

Alternatively, once you have supplied the name of the type, you can read the members from a file. To do this, click on the "Get from file" button. This displays the table entry dialogue, and you can use this as if you were specifying a data table to load. However, the data is not actually loaded; instead, all the different values are listed, removing duplicates, and these are made into the members of your enumerated type. The values must be textual, not numbers, so only data entry from columns or grids is allowed.

Using an enumerated type

The following model diagram will serve to illustrate how an enumerated type can be used. It shows a variable size inside a multiple-instance submodel (one instance for each fruit). This variable is exported as an array outside the submodel, then one value is picked up from this array.

If this model were set up without using an enumerated type, then the following would be used:

Submodel fruit: Number of instances (using specified dimensions): 4

Variable size: if index(1)==1 then 4.2 else 3.7

Variable sizes: [size] (Dimensions are automatically set to 4)

Variable size_apples: element([sizes],1)

If this model (with the same model diagram) were set up using an enumerated type (e.g. fruit, as defined above), then the following would be used:

Submodel fruit: Number of instances (using specified dimensions): fruit (i.e. the name of the enumerated type is entered into the dimensions edit field, and automatically sets the number of instances for the submodel to the number of values in the enumerated type - in this case, four.)

Variable size: if index(1)=="apples" then 4.2 else 3.7

Variable sizes: [size] (dimensions are automatically set to fruit)

Variable size_apples: element([sizes],"apples")

Things to note:

The same enumerated type can be used in several places. For example, you could have another submodel that also has dimensions of fruit.

A component's value can be a member of an enumerated type, either specified as a constant or the result of a function such as posgreatest() that returns an array index. Such a value can be used to index an array, or tested for equality with another member of the same type.

Note that the only test we can do with an enumerated type value is a test of equality with the index of a submodel (if index(1)=="apples"...). We can't use the greater-than or less-than operators, since the list is unordered (what a statistician would call nominal rather than ordinal).

Additional considerations

You can use the member names as indices when reading parameter values from a file. This is particularly convenient when the file was used to create the list of member names.

For example, the following file could be used

fruit, price

apples, 7.0

oranges, 7.4

lemons, 7.2

pears, 8.1

Using array functions

You can use the makearray function to create an array. For example, the equation


will create an array with dimensions (size) equal to the number of members in the enumerated type "fruit". It will be populated with values of 1. You can use the test place_in(n)==member to set each value separately. For example, the equation

makearray(if place_in(1)=="apples" then 7.0 elseif place_in(1)=="oranges" then 7.4 elseif place_in(1)=="lemons" then 7.2 else 8.1, "fruit")

will result in the same array as the above table.

Why is it called an enumerated type?

In programming, a type is a set of values from which a variable may take its value. Thus if a variable is of type "integer", then this set of values is all the whole numbers. If it is of type "real", then it is the set of all decimal values that can be represented on the computer. If it is an enumerated type, then the set of values is defined by an explicit list of all the values that the variable is allowed to take. The standard example is the enumerated type "days of the week", in which the set of allowed values is given by the list [Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday]. A particular variable (e.g. "washing day") can be defined to be of this type: we then know that its value must be one of these seven possible values.

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