Associative vs. Positional Indexing

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→

2007

2008

2009

2010

2011

2012

And variable Earnings evaluates to an array indexed by Year,

Year →	2007	2008	2009	2010	2011	2012
Earnings→	4.5M	5.6M	6.6M	7.9M	9.0M	10.1M

Then we can access particular elements of Earnings either associatively:

Earnings[Year=2009] → 6.6M

or by position:

Earnings[@Year=3] → 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) → 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) → 6.6M

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

Associative / Positional Duals

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

Associational / Positional Duals

Associational	By Position	Notes
A[I=x]	A[@I=n]
Subscript(A,I,x)	Slice(A,I,n)
Slice(I,n)	@[I=x]	Slice(I,n) : returns the nth element of an index. @[I=x]  : returns the position of element x in an index.
ArgMax(A,I)	ArgMax(A,I,position:true)
ArgMin(A,I)	ArgMin(A,I,position:true)
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 x:=I Do...	For n:=@I Do...
IndexValue(I)	@I or 1..Size(I) || The elements of an index or the position along an index.
SubIndex(A,U,I)	PositionInIndex(A,U,I)
(no equiv)	Rank(A,I)	Rank is related to SortIndex, returns positions. There is no logical associational dual.
SortIndex(A,I)	?	See below
Subset(D)	?	see below
Unique(A,I)	?	see below

Functions without Duals

Three built-in Analytica functions, SortIndex, Subset and Unique, are missing a built-in dual function. All three are associational, and in these three cases positional equivalents do make sense and are needed on occassion. Until such duals are added to the set of built-in Analytica functions, the following discussions how to express the positional equivalents.

SortIndex(A,I) returns a permutation of I such that A[I=SortIndex(A,I)] are in ascending sorted order. However, if I might contains duplicates, the result of SortIndex does not unique identify the corresponding element, in which case a positional dual of SortIndex must be used. This is accomplished as follows:

Index J:=@I Do SortIndex(A[@I=J],J)