# Functions that create arrays

Usually, the most convenient way to create an array of numbers or text values is as an edit table. When viewing the definition of the variable, choose Table from the expr menu to create an edit table (see Defining a variable as an edit table). If you want to define a table by explicitly listing its indexes and providing expressions to generate its values or sub-arrays, you might find Array more convenient.

If you select expr from the expr menu, it displays it as a table expression in the Definition field (rather than a separate edit table), listing the indexes and values.

## Array(i1, i2, … in, a)

Assigns a set of indexes, «i1», «i2», … «in», as the indexes of the array «a», with «i1» as the index of the outermost dimension (changing least rapidly), «i2» as the second outermost, and so on. «a» is an expression returning an array which typically has at least «n» dimensions, each dimension with the number of elements matching the corresponding index. You can use array to change the index variable(s) from one to another with the same number(s) of elements. Array is one of the few places where you actually need to worry about the order of the indexes in the array representation.

Use Array to specify an array directly as an expression. Array is similar to Table; in addition, it lets you define an array with repeated values (see Example 3 below), and change indexes of a previously defined array (see Example 4).

Library: Array

Example 1

Definition viewed as an expression:

Index Car_type := ['VW', 'Honda', 'BMW']
Array(Car_type, [32, 34, 18])

Definition viewed as a table:

VW Honda BMW
32 34 18

Example 2

If an array has multiple dimensions, then the elements are listed in nested brackets, following the structure of the array as an array of arrays (of arrays..., and so on, according to the number of dimensions).

Definition viewed as an expression:

Array(Car_type, Years, [[8K, 7K, 10K, 6K, 9K], [10K, 12K, 11K, 14K, 13k], [5K, 8K, 8K, 7K, 10k]])

Definition viewed as a table:

Years ▶
Car_type ▼ 2005 2006 2007 2008 2009
VW 8000 7000 10K 6000 9000
Honda 10K 12K 11K 14K 13K
BMW 5000 8000 8000 7000 10K

The size of each array in square brackets must match the size of the corresponding index. In this case, there is an array of three elements (for the three car types), and each element is an array of four elements (for the four years). An error message displays if these sizes don’t match. See also Size(u, listLen).

Example 3

If an element is a scalar where an array is expected, Array() expands it to create an array with the scalar value repeated across a dimension.

Definition viewed as an expression:

Array(Car_type, Years, [[8K, 7K, 10K, 6K, 9K], 13K, [5K, 8K, 8K, 7K, 10k]])

Definition viewed as a table:

Years ▶
Car_type ▼ 2005 2006 2007 2008 2009
VW 8000 7000 10K 6000 9000
Honda 13K 13K 13K 13K 13K
BMW 5000 8000 8000 7000 10K

Example 4

Use Array() to change an index of a previously defined array.

Index Car_model := ['Jetta', 'Accord', '320']
Variable Table_a:= Table(Car_type) (32, 34, 18)
Variable Table_b:= Array(Car_model, Table_a) →
Jetta Accord 320
32 34 18
Tip
There are some significant disadvantages to using the Array function to change the index of an array in the fashion demonstrated in Example 4. Specifically, if a second dimension were later added to Table_a, the index that the Array() function changes might not be the one you intended. The preferred method for changing the index, which does fully generalize when Table_a has many dimensions, is to use the slice operator (see Tip on re-indexing) as follows:
Table_a [@Car_type = @car_model]

## Table(i1, i2, … in) (u, u2, u3, … um)

This function is automatically created when you select Table from the expr menu to create an edit table. You can view it as an expression in this form in the definition of the variable by selecting expression from the expr menu. It. creates an n-dimensional array of m elements, indexed by the indexes «i1», «i2», … «in». In the set of indexes, «i1» is the index of the outermost dimension, varying the least rapidly.

The second set of parameters, «u1», «u2» … «um», specifies the values in the array. The number of values, m, must equal the product of the sizes of all of the dimensions.

Each «u» is an expression that evaluates to a number, text value or probability distribution. It can also evaluate to an array, causing the dimensions of the entire table to increase. «u» cannot be a literal list.

Both sets of parameters are enclosed in parentheses; the separating commas are optional except if the table values are negative.

Use Table() to specify an array directly as an expression. Table() is similar to Array(); Table() requires m numeric or text values.

A definition created as a table from the expr menu uses Table() in expression view.

Library: Array

Example 1: Definition viewed as an expression:

Table(Car_type) (32, 34, 18)

Definition viewed as a table:

VW Honda BMW
32 34 18

Example 2

Definition viewed as an expression:

Table(Car_type, Years) (8K, 7K, 10K, 6K, 9K, 10K, 12K, 11K, 14K, 13K, 5K, 8K, 8K, 7K, 10K)

Definition viewed as a table:

Years ▶
Car_type ▼ 2005 2006 2007 2008 2009
VW 8000 7000 10K 6000 9000
Honda 10K 12K 11K 14K 13K
BMW 5000 8000 8000 7000 10K

It looks like this when viewed as an edit table:

Years ▶
Car_type ▼ 2005 2006 2007 2008 2009
VW 0 0 0 0 0
Honda 0 0 0 0 0
BMW 0 0 0 0 0

## IntraTable(i1, i2, … in) (u1, u2, u3, … um)

IntraTable() generalizes the Table function to permit functional dependencies between cells. These dependencies can be denoted as intra-cell dependencies, and hence, the table as a whole as an IntraTable. An IntraTable behaves identically to an edit table in all other respects.

The presence of intra-cell dependencies produces a table that is reminiscent of a spreadsheet, with dependencies between individual cells. As such, it is advisable to avoid IntraTable if you don’t need to, since it can easily be abused and lead to inflexible and hard-to-maintain models.

To create an IntraTable, while editing a definition select Other... on the expr menu and select IntraTable in the Array Functions library.

Within cells, you can apply slice and subscript notation to the Self keyword to reference other cells within the table. The intra-cell dependencies must not form a directed loop, which would imply that a cell is defined indirectly in terms of itself, otherwise an error will result when the table is evaluated.

The following example contains two cells that illustrate intra-cell references, with examples of both subscript and slice notation.

Years ▶
Car_type ▼ 2005 2006 2007 2008 2009
VW 8000 7000 10K 6000 9000
Honda 10K Self[Years = Years - 1]*1.05 11K 14K 13K
BMW 5000 (Self[Car_type = ’VW’] + 

Self[Years = 2005, @Car_type = @Car_Type - 2])/2

8000 7000 10K

When evaluated, the following array results:

Years ▶
Car_type ▼ 2005 2006 2007 2008 2009
VW 8000 7000 10K 6000 9000
Honda 10K 10.5K 11K 14K 13K
BMW 5000 7500 8000 7000 10K