Index Position Operator::@
The position of value «x» in an index «i» is the integer «n» where «x» is the «n»'th element of «i». «n» is a number between 1 and Size(i). The first element of «i» is at position 1; the last element of «i» is at position Size(i). The position operator @ offers three ways to work with positions:
- @i → an array of integers from 1 to Size(«i») indexed by «i».
- @[i = x] → the position of value «x» in index «i» -- or 0 if «x» is not an element of «i»
- e[@i = n] → the «n»'th Slice of the value of expression «e» over index «i».
These turn out to make many array operations much simpler than prior to release 4.0.
== Examples ==Click here to download example model
We'll use the following indexes for illustration:
Index Car_type := ['VW', 'Honda', 'BMW']Index Time := [0, 1, 2, 3, 4]Index Years := Time + 2007@CarType →
Car_Type ▶ 'VW' 'Honda' 'BMW' 1 2 3
@[Car_type = 'Honda'] → 2Car_type[@Car_type = 2] → 'Honda'@Time →
Time ▶ 0 1 2 3 4 1 2 3 4 5
@[Time = 2] → 3Time[@Time = 3] → 2(Time + 2007)[@Time = 3] → 2009
You can use the slice variation to re-index an array by another array having the same length but different elements. Suppose Revenue is indexed by Time, then this returns the same array indexed by Years:
Revenue[Time = @Years]
Notes
@I is equivalent to Cumulate(1, I).
If an index has duplicate elements, then subscripting (associative indexing) is ambiguous. For example,
Index In1 := ['a', 'b', 'a', 'c']Index In2 := ['a', 'b', 'a', 'c']Variable A := Array(In1, [7, 4, 5, 9])
If you were to re-index using A[In1 = In2], you would obtain:
A[In1 = In2] →
In2 ▶ 'a' 'b' 'a' 'c' 7 4 7 9
Since A[In1 = 'a'] returns 7. Because of the duplicate in the index values, an array value was lost. When duplicates are possible, accessing elements by position removes the ambiguity:
A[@In1 = @In2] →
In2 ▶ 'a' 'b' 'a' 'c' 7 4 5 9
In variable definitions, it is more often the case that associative access (subscripting, non-positional) is preferred. Associative access is more robust when elements are added to indexes. For example, Revenue[Region='Europe'] doesn't break when a new region is inserted, while Revenue[@Region = 5] would change. However, in User-Defined Functions, positional indexing (i.e., is of the @ operator) is often more robust than associative indexing. For example, when a function uses two equal-length indexes (e.g., for a square matrix), with positional indexing the expression does not have to assume the indexes have identical elements or no duplicate elements.