Difference between revisions of "Associative vs. Positional Indexing"

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[[Category:Doc Status C]] <!-- For Lumina use, do not change -->
 
[[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:
+
__TOC__
  
Year&rarr;
+
When accessing array elements from Analytica 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'''''.
{| class="wikitable"
+
 
 +
Suppose Index <code>Year</code> has the following elements:
 +
 
 +
:<code>Index Year :=</code>
 +
:{| class="wikitable"
 
| 2007 || 2008 || 2009 || 2010 || 2011 || 2012  
 
| 2007 || 2008 || 2009 || 2010 || 2011 || 2012  
 
|}
 
|}
  
And variable Earnings evaluates to an array indexed by Year,
+
And variable <code>Earnings</code> evaluates to an array indexed by <code>Year</code>,
  
{| class="wikitable"
+
:<code>Variable Earnings :=</code>
! Year &rarr; !! 2007 !! 2008 !! 2009 !! 2010 !! 2011 !! 2012  
+
:{| class="wikitable"
 +
! colspan="6" | Year &#9654;
 +
|-
 +
! 2007 !! 2008 !! 2009 !! 2010 !! 2011 !! 2012  
 
|-
 
|-
!Earnings&rarr; || 4.5M || 5.6M || 6.6M || 7.9M || 9.0M || 10.1M
+
| 4.5M || 5.6M || 6.6M || 7.9M || 9.0M || 10.1M
 
|}
 
|}
  
 
Then we can access particular elements of Earnings either associatively:
 
Then we can access particular elements of Earnings either associatively:
:[[Subscript/Slice Operator|Earnings[Year=2009] ]] &rarr; 6.6M
+
:<code>Earnings[Year = 2009] &rarr; 6.6M</code>
 
or by position:
 
or by position:
:[[Subscript/Slice Operator|Earnings[@Year=3] ]] &rarr; 6.6M
+
:<code>Earnings[@Year = 3] &rarr; 6.6M</code>
  
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.:
+
Referring to an index element '''''associatively''''' is generally referred to as [[Subscript/Slice Operator|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
+
:<code>Subscript(Earnings, Year, 2009) &rarr; 6.6M</code>
Referring to an index element by position is called ''slicing'', and can equivalently be accomplished using the [[Slice]] function, e.g.:
+
Referring to an index element by '''''position''''' is called [[Subscript/Slice Operator|slicing]], and can equivalently be accomplished using the [[Slice]] function, e.g.:
:[[Slice]](Earnings,Year,3) &rarr; 6.6M
+
:<code>Slice(Earnings, Year, 3) &rarr; 6.6M</code>
  
 
Positions in Analytica are always 1-based, and range from 1 to [[Size]](I).
 
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'].
+
For text elements, associational lookup is case-sensitive, i.e., <code>A[L = 'low']</code> is not the same as <code>A[L = 'Low']</code>.
  
= Associative / Positional Duals =
+
== 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.
 
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.
  
{| class="wikitable"
+
:{| class="wikitable"
|+ Associational / Positional Duals
+
! Associational !! Positional || Notes
! Associational !! By Position || Notes
 
 
|-
 
|-
| [[Subscript/Slice Operator|A[I=x] ]] || [[Subscript/Slice Operator|A[@I=n] ]] || &nbsp;
+
| [[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/Slice Operator|A[I = J] ]] || [[Subscript/Slice Operator|A[@I = @J] ]] || Variation referred to as ''re-indexing''
 
|-
 
|-
| [[Subscript]](A,I,x) || [[Slice]](A,I,n) || &nbsp;
+
| [[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.
+
| [[Slice]](I, n) || [[Index Position Operator::@|@[I = x] ]] || [[Slice]](I, n) : returns the «n»th element of an index.
[[Index Position Operator::@|@[I=x] ]] : returns the position of element x in 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;
+
| [[ArgMax]](A, I) || [[ArgMax]](A, I, position: true) || &nbsp;
 
|-
 
|-
| [[ArgMin]](A,I) || [[ArgMin]](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.   
+
| [[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.
+
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;
+
| [[For..Do|For]] x:=I Do... || [[For..Do|For]] n := [[Position operator|@I]] Do... || &nbsp;
 
|-
 
|-
 
| [[IndexValue]](I) || [[Position operator|@I]]
 
| [[IndexValue]](I) || [[Position operator|@I]]
 
| The elements of an index or the position along an index.
 
| The elements of an index or the position along an index.
 
|-
 
|-
| [[SubIndex]](A,U,I) || [[PositionInIndex]](A,U,I) || &nbsp;
+
| [[SubIndex]](A, U, I) || [[PositionInIndex]](A, U, I) || &nbsp;
 
|-
 
|-
| (no equiv) || [[Rank]](A,I) || [[Rank]] is related to [[SortIndex]], which returns positions.
+
| (no equiv) || [[Rank]](A, I) || [[Rank]] is related to [[SortIndex]], which returns positions.
 
There is no logical associational dual.
 
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  
+
| [[SortIndex]](A, I) ||  [[Index..Do|Index]] J := @I Do [[SortIndex]](A[@I = @J], J) || No built-in positional dual  
 
|-
 
|-
 
| [[Subset]](D)  
 
| [[Subset]](D)  
 
| In Analytica 4.2 or better:
 
| In Analytica 4.2 or better:
:[[Subset]](D,position:true)
+
:[[Subset]](D, position: true)
 
In Analytica 4.1 or earlier:
 
In Analytica 4.1 or earlier:
:[[Index..Do|Index]] I:=1..[[Size]](D) Do [[Subset]]([[Array]](I,D))  
+
:[[Index..Do|Index]] I := 1..[[Size]](D) Do [[Subset]]([[Array]](I, D))  
 
| D must be 1-D.  
 
| D must be 1-D.  
 
No built-in positional dual prior to release 4.2.
 
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.
+
| [[Unique]](A, I) || [[Unique]](A, I, position: true) || Only works in Analytica 4.0 and above.
 
|}
 
|}
  
= When to Use Assocational vs. Positional =
+
== 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.
 
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  
+
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 <code>Division</code>, expressions such as  
Expenses[Division='Marketing']
+
:<code>Expenses[Division = 'Marketing']</code>
continue to refer to the correct data, while the positional dual, Expenses[@Division=6], would break in such a case.
+
continue to refer to the correct data, while the positional dual, <code>Expenses[@Division = 6]</code>, 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.
+
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 ambiguity.  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 occasionally 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.
 
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.
+
Finally, some operations are inherently positional or associational by the nature of what is being done.  For example, referring the the previous element of an array, <code>A[@I = @I-1]</code>, is inherently positional.  An "outer join" of two arrays, such as <code>Salary_by_paygrade[Person = Paygrade_by_person]</code>, is naturally associational.
  
= [[Table Splicing]] =
+
== 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]].   
 
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.
 
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.
 +
 +
==See Also==
 +
* [[Table Splicing]]

Revision as of 20:58, 11 January 2016


When accessing array elements from Analytica 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:

Index Year :=
2007 2008 2009 2010 2011 2012

And variable Earnings evaluates to an array indexed by Year,

Variable Earnings :=
Year ▶
2007 2008 2009 2010 2011 2012
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 referred 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).

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.

Associational Positional Notes
A[I = x] A[@I = n]  
A[I = J] A[@I = @J] Variation referred to as re-indexing
Subscript(A, I, x) Slice(A, I, n)  
Slice(I, n) @[I = x] Slice(I, n) : returns the «n»th 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 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, which returns positions.

There is no logical associational dual.

SortIndex(A, I) 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 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 ambiguity. 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 occasionally 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, referring 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, 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 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.

See Also

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