Arrays and lists

Arrays are data structures that consist of more than one element. Each element of the array may be:

• a scalar: a single real, integer or Boolean value; or
• an array or list: thus arrays and lists can be nested (to any depth).

Arrays can be created either automatically (when required) or by the user.

Lists are data structures that consist of zero or more elements, and can only be created automatically. Lists are created when values from a population submodel are used outside the submodel itself.

Referring to arrays and lists

An array variable is denoted by enclosing the variable's name in square brackets. Thus, [weight] represents an array of one or more weights. This is a one-dimensional array (a vector), because the variable name is enclosed in a single pair of square brackets. By contrast, [[weight]] is a two-dimensional (rectangular) array of weights. This could be used to represent, for example, the weight of each of 10 varieties of fruit (orange, apple, banana, etc) in each of 20 samples.

Note that the size of the array (also known as its dimensions) is not referred to when the array is used in equations. The dimensions are shown in dimensions field of the equation dialogue box.

An list variable is denoted by enclosing the variable's name in curly brackets. Thus, {weight} represents a list of zero or more weights.

How arrays are made

There are three ways in which an array can appear in a model.

1. An influence arrow might be drawn from a variable inside a fixed-membership, multiple-instance submodel to a variable outside the submodel. As soon as the influence crosses the submodel boundary, what was referred to as a scalar variable inside the submodel becomes an array outside it, since there is now a fixed set of values (one for each submodel instance).

2. The user might build an array inside the equation dialogue for a variable by explicitly listing all the elements of the array. Thus, if you enter [2,4,6,7] in the equation dialogue for a variable, then its value becomes the array consisting of these four values. Note that the square bracket notation has two quite different interpretations. When the square brackets enclose the name of a single variable, then it is understood that this variable is an array. When the square brackets enclose more than one values, then it is understood that the whole structure is an array. This difference is illustrated by the following examples: (a) [weight] and (b) [weight, height]. The first is referring to an array called weight (which could have any number of values). The second is defining an array with two elements, the scalar variable weight and the scalar variable height. The latter has just two elements.

3. The user might use the makearray(…) function.

Processing arrays

Arrays can be processed in a number of ways.

1. You can use a function that is expecting an array as an argument. For example, the function sum(…) will sum the elements of an array.

2. You can use arrays in mathematical expressions. Simile has powerful built-in methods for calculating with array variables which totally avoid the need for looping structures for calculating with arrays. For example, the expression: [k]*[weight] where both arrays have the same number of elements, returns an array with each element equal to the corresponding value of [k] multiplied by the corresponding value of [weight].

3. You can extract particular values from an array. The function element(array,i) returns the i'th element from the array. Thus: element([2,4,6,3],2) returns the value 4 (being the second element of the array).

How lists are made

There is only one way in which a list can appear in a model: by having an influence arrow coming out of a submodel with a variable number of instances. This means:

• a population submodel;
• a relation (association) submodel; or
• a conditional submodel.

Processing lists

Lists must be processed as soon as they appear in the variable outside the submodel which receives an influence arrow from a variable inside it. You cannot pass lists around from one variable to another. Rather, you must perform some legitimate list-processing operation, such as using the function sum(…) to sum the values of the list.

In: Contents >> Working with equations