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 | 2007 | 2008 | 2009 | 2005 | 2006 | 2007 | 2008 | 2009 | |
| VW | 16K | 17K | 18K | 19K | 20K | 8000 | 7000 | 10K | 6000 | 9000 | |
| Honda | 18K | 19K | 20K | 22K | 24K | 10K | 12K | 11K | 14K | 13K | |
| BMW | 25K | 26K | 28K | 30K | 32K | 5000 | 8000 | 8000 | 7000 | 10K | |
See Array Function Example Variables for example array variables used here and below.
ConcatRows(a, rowIndex, colIndex, concatIndex)
Takes an array, a indexed by rowIndex and colIndex, and concatenates each row, flattening the array by eliminating the row dimension. The result is indexed by the concatIndex, which must be an index with size(rowIndex) * size(colIndex) elements. If concatIndex is omitted, a local index named .concatIndex is introduced defined as 1 .. N, where N is size(rowIndex)*size(colIndex).
Library: Array
Example:
ConcatRows(Car_prices, Car_type, Years) →
| .ConcatIndex ▶ | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ... | 13 | 14 | 15 | ||
| 16K | 17K | 18K | 19K | 20K | ... | 28K | 30K | 32K | ||
See Array Function Example Variables for example array variables used here and below.
IndexNames(a)
Returns a list of the identifiers of the indexes of the array a as text values.
Library: Array
Example:
IndexNames(Car_prices) → ['Car_type', 'Years']
IndexesOf(a)
Returns a list of the indexes of the array a as handles (see Handles to objects). It is similar to IndexNames(), except that it returns handles instead of identifiers as text values. It is possible for an array to have more than one local index having identical names. This is not recommended, but where it occurs, the index handles returned by IndexesOf() are unambiguous.
Library: Array
Example:
IndexesOf(Car_prices) → [Car_type, Years]
IndexValue(i)
Some variables have both an index value and a result value. Examples include a self-indexed array; a variable or index defined as a list of identifiers or list of expressions; and a Choice list with a self-domain. IndexValue(i) returns the index value of i, where (i) alone would return its result value.
Library: Array Functions
Example
Variable Cubes := [1, 2, 3, 4]^3 IndexValue(Cubes) → [1, 2, 3, 4] CopyIndex(Cubes) →[1, 4, 9,16]
Variable Colors := Table(Self, Cubes)(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
with Self index ['Red', 'Green', 'Blue']
Colors →
| Colors ▶ | |||
|---|---|---|---|
| Cubes ▼ | Red | Green | Blue |
| 1 | 16K | 18K | 25K |
| 2 | 17K | 19K | 26K |
| 3 | 18K | 20K | 28K |
| 4 | 19K | 22K | 30K |
IndexValue(Colors) → ['Red', 'Green', 'Blue']
Size(u, listLen)
Returns the number of atoms (elementary cells) in array u. The size of an atom (including the
special value null) is 1. The size of an empty list is 0.
Size(I) can be used to find the number of elements in an index I, provided that I is a pure index and not a self-indexed array. When X</code is a self-indexed array, Size(X) returns the number of cells in the array, while Size(IndexValue(X)) returns the number of elements of X’s selfindex.
If an array A contains an implicit dimension, it is not possible to use Size(IndexValue(...)) to obtain the length of the implicit dimension, since the implicit dimension has no name to refer to it by. Setting the optional parameter listLen: true returns the length of the implicit index, or null if there it has no implicit index.
Library: Array Functions
Examples:
Size(Years) → 5
Size(Car_prices) → 15
Size(10) → 1
Size([]) → 0
Size([Years, Car_prices]) → 30
Size([Years, Car_prices], listLen: true) → 2
Subset(d, position, i, resultIndex)
Subset(d) returns the subset of d’s index values that correspond to true values in d. This basic usage, explained in Subset(d), cannot be employed when d has more than one dimension, that is, it does not array abstract. The optional parameters i and resultIndex provide an array-abstractable form that can be applied to multi-dimensional arrays, where the parameter i specifies the index to take the subset over, and resultIndex specifies the index for the final result.
When the number of true elements exceeds N (the number of elements in resultIndex), the index values corresponding to the first N true values are returned. For the cases where there are fewer than N true values, the result is padded with null values. Setting the optional position parameter to true returns the index positions, rather than the index elements, of the true values.
Library: Array
Example:
Index MultiEventCars := 1 .. 4
Subset(Miles > 8000, i: Car_type, resultindex: Car_type) →
Years ▶
Car_type ▼
2005
2006
2007
2008
2009
VW
Honda
Honda
VW
Honda
VW
Honda
«null»
«null»
Honda
«null»
Honda
BMW
«null»
«null»
«null»
«null»
Honda
In the above example, Miles values for Honda exceeded 8,000 in 2008 and 2009.
See Array Function Example Variables for example array variables used here and below.
See Also
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