View source for What's new in 4.0/Operator::@

[[category:Operators]]

(new to 4.0) 

The ''''position'''' of value x in an index i is the number between 1 and n (=Size(i)) for which Slice(i, n) = x.  The position operator "@" returns the numeric position of elements in an index.  The first element of an index is at position 1, the last element of an index is at position [[size]](i), etc.

You can use "@" in three ways:

:'''@i''' --> an array of integers from 1 to Size('''i''') indexed by '''i'''.
:'''@[i=x]'''   --> the position of value '''x''' in index '''i''' -- or NULL if '''x''' is not an element of '''i'''
:'''e[@i=n]'''  --> the '''n'''th [[Slice]] of expression '''e''' over index '''i'''.

= Examples =

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

{| border="0"
| @CarType -->
|
{| border="1"
! colspan="3" text-align="left" | Car_Type >>
|-
! 'VW' !! 'Honda' !! 'BMW'
|-
| 1 || 2 || 3
|}
|}

 @[Car_type='Honda'] --> 2

 Car_type[@Car_type=2] --> 'Honda'

{| border="0"
| @Time -->
|
{| border="1"
! colspan="5" text-align="left" | Time >>
|-
! 0 !! 1 !! 2 !! 3 !! 4 
|-
| 1 || 2 || 3 || 4 || 5
|}
|}

 @[Time=2] --> 3

 Time[@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[@Year=@Time]

= 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,[7,3,5,9])
If you were to re-index using A[In1=In2], you would obtain:
{| border="0"
| A[In1=In2] --> 
|
{| border="1"
! colspan="4" | 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:
{| border="0"
| A[@In1=@In2] --> 
|
{| border="1"
! colspan="4" | 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.

= See Also =

* [[Slice]]
* [[Subscript]]
* [[PositionInIndex]]
* [[Subscript/Slice Operator]]