Other array functions
AddIndex(a, i)
Adds one or more indexes to an array. The result is constant (does not vary) along any of the indexes that are added.
A basic philosophy in Analytica is that a value only needs to contain an index if its data varies along that index; hence, this function is an unnecessary function in almost all “normal” cases. When arrays with different dimensionalities get combined, array abstraction treats the values as if they are constant across the missing dimensions, so there is no need for you to add the dimensions explicitly, and is generally undesirable to do so.
Library: Array
Example: A vector on index ones, indexed by Period:
AddIndex(1, Period) :=
| Period ▶ | ||
|---|---|---|
| Early | Middle | Late |
| 1 | 1 | 1 |
AddIndex(Rate_of_inflation, Period) :=
| Years ▶ | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Period ▼ | 2005 | 2006 | 2007 | 2008 | 2009 | ||||||
| Early | 1 | 1.01 | 1.02 | 1.03 | 1.04 | ||||||
| Middle | 1 | 1.01 | 1.02 | 1.03 | 1.04 | Late | 1 | 1.01 | 1.02 | 1.03 | 1.04 |
AddIndex(Miles, Period, MaintType)
A 4-D array indexed by Car_type, Years, Period and MaintType. Each slice along a given Period and MaintType contains the data from Miles.
AddIndex(Miles, ... IndexesOf(Cost_of_ownership))
Contains the data from Miles, with all the dimensions of Cost_of_ownership.
Aggregate(x, map, i, targetIndex)
Converts from an array x indexed by fine-grain index i, to an array indexed by the coarser-grained index targetIndex. Map is an array indexed by i, specifying for each element if i the value of targetIndex that the i-value maps to. An optional parameter, positional:true, can be specified if map contains the target index position rather than the target index value.
Aggregate is used when many index elements in i correspond to the same targetIndex element. By default, the values mapping to the same target position are aggregated by summing them. An optional parameter, type, can be used to specify alternative aggregation methods. Common aggregation methods include: “Sum”, “Max”, “Min”, “Average”, “Last”, “First”, and “Median”, but in general any built-in or user-defined function able to accept two parameters, an array and index, such as with a declaration: (A : Array[I] ; I : Index), can be named.
An optional parameter, defaultValue, specifies the value to use when no value maps to a given target position.
Library: Array
Example: To use Aggregate, you need to define the many-to-one map, here from Time to Period:
Index Period := ['Early', 'Middle', 'Late']
Variable Time2Period :=
\[Index_a]Array_s →
| Time ▶ | |||||
|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | |
| 'Early' | 'Middle' | 'Middle' | 'Late' | 'Late' | |
Aggregate(Cost_of_ownership, Time2Period, Time, Period) →
| Period ▶ | |||
|---|---|---|---|
| CarType ▼ | Early | Middle | Late |
| VW | 2810 | 6049 | 6669 |
| Honda | 3535 | 7744 | 8531 |
| BMW | 3185 | 6703 | 7185 |
Aggregate(Cost_of_ownership, Time2Period, Time, Period, type: 'Average')
→
| Period ▶ | |||
|---|---|---|---|
| CarType ▼ | Early | Middle | Late |
| VW | 2810 | 3025 | 3335 |
| Honda | 3535 | 3872 | 4266 |
| BMW | 3185 | 3352 | 3593 |
Concat(a1, a2, i, j, k)
Appends array a2 to array a1. i and j are indexes of a1 and a2, respectively. k is the index of the resulting dimension, and usually consists of the list created by concatenating i and j. When k is omitted and the result has two or more dimensions, a local index named .k will automatically be created by concatenating the elements of i and j, and the result will be indexed by this .k.
The parameter i (or j) can be omitted when a1 (or a2) is one-dimensional, if a1 (or a2) is indexed by a local index .k created by a previous call to Concat, when a1 (or a2) contains an implicit dimension, or when a1 (or a2) is atomic. The default to a local index .k makes it easy to nest calls to Concat when concatenating three or more arrays (or indexes) together. When a1 (or a2) is not array valued an i (or j) is omitted, a single element is concatenated to the front of a2 (or to the end of a1).
Library: Array
Examples: These examples use these variables:
Index Years :=
| 2005 | 2006 | 2007 | 2008 | 2009 |
Index More_years :=
| 2010 | 2011 | 2012 |
Index All_years := Concat(Years, More_years) →
| 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 |
Variable More_prices :=
| More_years ▶ | |||
|---|---|---|---|
| CarType ▼ | 2010 | 2011 | 2012 |
| VW | 21K | 22K | 24K |
| Honda | 25K | 28K | 29K |
| BMW | 32K | 33K | 35K |
Concat(Car_prices, More_prices, Years, More_years, All_years) →
| Car_type ▶ | |||||||
|---|---|---|---|---|---|---|---|
| All_years ▼ | VW | Honda | BMW | ||||
| 2005 | 16K | 18K | 25K | ||||
| 2006 | 17K | 19K | 26K | ||||
| 2007 | 18K | 20K | 28K | 2008 | 19K | 22K | 30K |
| 2009 | 20K | 24K | 32K | ||||
| 2010 | 21K | 25K | 32K | 2011 | 22K | 28K | 33K |
| 2012 | 24K | 29K | 35K | ||||
Example of nested usage and local .k index:
Concat(Car_prices, Concat(' ', Miles, , Years), Years) →
| .K ▶ | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Car_type ▼ | 2005 | 2006 | ||||||||||||
| VW | 17K | 19K | 26K | |||||||||||
| Honda | 18K | 20K | 28K | BMW | 19K | 22K | 30K | |||||||
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