View source for Associative vs. Positional Indexing

[[Category:Concepts]]
[[Category:Doc Status C]] <!-- For Lumina use, do not change -->

When accessing array elements from Analyica expressions, we must identify which position along an index that we wish to access.  In Analytica, this can usually be done either associatively or positionally.

Suppose Index Year has the following elements:

Year&rarr;
{| border="1" 
| 2007 || 2008 || 2009 || 2010 || 2011 || 2012 
|}

And variable Earnings evaluates to an array indexed by Year,

{|border="1"
! Year &rarr; !! 2007 !! 2008 !! 2009 !! 2010 !! 2011 !! 2012 
|-
!Earnings&rarr; || 4.5M || 5.6M || 6.6M || 7.9M || 9.0M || 10.1M
|}

Then we can access particular elements of Earnings either associatively:
:[[Subscript/Slice Operator|Earnings[Year=2009] ]] &rarr; 6.6M
or by position:
:[[Subscript/Slice Operator|Earnings[@Year=3] ]] &rarr; 6.6M

Referring to an index element associatively is generally refered to as ''subscripting'', and can also be accomplished using the [[Subscript]] function, which is equivalent to the above, e.g.:
:[[Subscript]](Earnings,Year,2009) &rarr; 6.6M
Referring to an index element by position is called ''slicing'', and can equivalently be accomplished using the [[Slice]] function, e.g.:
:[[Slice]](Earnings,Year,3) &rarr; 6.6M

Positions in Analytica are always 1-based, and range from 1 to [[Size]](I).

For text elements, associational lookup is case-sensitive, i.e., A[L='low'] is not the same as A[L='Low'].

= Associative / Positional Duals =

Tare many functions that either require an index element be specified, or return an index position or element.  Most built-in functions that identify to an index element associationally have a positional dual, and vise versa.  The following table indicates associational / positional duals.

{| border="1"
|+ Associational / Positional Duals
! Associational !! By Position || Notes
|-
| [[Subscript/Slice Operator|A[I=x] ]] || [[Subscript/Slice Operator|A[@I=n] ]] || &nbsp;
|-
| [[Subscript/Slice Operator|A[I=J] ]] || [[Subscript/Slice Operator|A[@I=@J] ]] || variation refered to as re-indexing
|-
| [[Subscript]](A,I,x) || [[Slice]](A,I,n) || &nbsp;
|-
| [[Slice]](I,n) || [[Index Position Operator::@|@[I=x] ]] || [[Slice]](I,n) : returns the nth element of an index.
[[Index Position Operator::@|@[I=x] ]] : returns the position of element x in an index.
|-
| [[ArgMax]](A,I) || [[ArgMax]](A,I,position:true) || &nbsp;
|-
| [[ArgMin]](A,I) || [[ArgMin]](A,I,position:true) || &nbsp;
|-
| [[Choice]](I,n) || [[Choice]](I,n,result:I) || The second parameter is always positional.  
The return value here is the element of I or the position along I.
|-
| [[For..Do|For]] x:=I Do... || [[For..Do|For]] n:=[[Position operator|@I]] Do... || &nbsp;
|-
| [[IndexValue]](I) || [[Position operator|@I]]
| The elements of an index or the position along an index.
|-
| [[SubIndex]](A,U,I) || [[PositionInIndex]](A,U,I) || &nbsp;
|-
| (no equiv) || [[Rank]](A,I) || [[Rank]] is related to [[SortIndex]], which returns positions.
There is no logical associational dual.
|-
| [[SortIndex]](A,I) ||  [[Index..Do|Index]] J:=@I Do [[SortIndex]](A[@I=@J],J) || no built-in positional dual 
|-
| [[Subset]](D) 
| In Analytica 4.2 or better:
:[[Subset]](D,position:true)
In Analytica 4.1 or earlier:
:[[Index..Do|Index]] I:=1..[[Size]](D) Do [[Subset]]([[Array]](I,D)) 
| D must be 1-D. 
No built-in positional dual prior to release 4.2.
|-
| [[Unique]](A,I) || [[Unique]](A,I,position:true) || Only works in Analytica 4.0 and above.
|}

= When to Use Assocational vs. Positional =

Here we consider when it is preferable to use associational (subscript) indexing, when is it better to use positional (slice) indexing, and when ''must'' you use one or the other.

Associational (subscript) indexing is the more commonly used in variable definitions because it tends to result in more flexible models.  If a new element it inserted into an index, say Division, expressions such as 
 Expenses[Division='Marketing']
continue to refer to the correct data, while the positional dual, Expenses[@Division=6], would break in such a case.

On the other hand, if an index has, or potentially may have, duplicate elements, then associational indexing is ambiguous.  In this case, positional indexing is required to avoid the abiguity.  For this reason, positional indexing is often preferred in the definitions of [[User-Defined Functions]], where you may not want to assume uniqueness of elements in an index.   It is usually a poor practice to create indexes with duplicate elements, but there are occassionally legitimate cases for having non-unique elements.

A second case where positional indexing is appropriate is when dealing with square matricies.  Square matricies have two indexes of the same length.  If you can be certain that the two indexes have exactly the same elements, then associational indexes works fine, but in the more general case where only the length can be assumed, then positional indexing must be used.

Finally, some operations are inherently positional or associational by the nature of what is being done.  For example, refering the the previous element of an array, A[@I=@I-1], is inherently positional.  An "outer join" of two arrays, such as Salary_by_paygrade[Person=Paygrade_by_person], is naturally associational.

= [[Table Splicing]] =

When an index changes, perhaps because a user inserted or deleted elements, or because something impacting the computation of its [[IndexValue]] changed, [[Table|edit tables]] based on that index must be spliced.  This means that rows may need to be moved around, deleted, or added (with empty or default values).  This modification of existing edit tables is referred to as [[Table Splicing|splicing]].  

For a given index, you can specify whether tables that depend on it should splice associationally or positionally when the index value changes.  See [[Table Splicing]] for more information.