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Aggregate Product function extends SQL

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19 Feb 2015CPOL2 min read
Technique to extend capability of standard SQL by adding the Aggregate Product Function

Preamble

The suggested solution extends the capability of Structured Query Language (SQL) by adding the Aggregate Product function. Entire 'pure SQL' solution is encapsulated into a single query, portable to any SQL backed databases, for example, Microsoft Access or SQL Server.
 

1. Underlying Math Transforms

SQL Aggregate Product function based on this Math transfom

Fig.1. SQL Aggregate Product function based on this underlying Math transfom

Standard SQL contains several aggregate functions (Sum, Count, Min, Max, etc.) with noticeable absence of aggregate Product. As a reminder, Product function P of multiple arguments (X1, X2,...XN) is defined as:
 

N
P(Xi)=X1*X2*...XN .................................................(1)
i=1

 
Database engine cannot perform the aggregate product calculation directly, but it can calculate sums. Simple mathematical transforms provide a workaround enabling to compute the product P by using the standard built-in mathematical Log(), Exp() and SQL aggregated Sum() functions; the core technique is illustrated by mathematical formulas (2) and (3):
 

Log(X1*X2*... XN)= Log(X1)+Log(X2)+...Log(XN) ......................(2),

 

N           N
P(Xi)= Exp(SUM(Log(Xi))) ............................................(3)
i=1         i=1

 
The last formula (3) could be translated into SQL statement in a rather straightforward manner, enabling the calculation of aggregate Product by means of standard built-in SQL functions.
 

2. Programming Technique: Math-to-SQL Translation

 
This simple yet practical example will demonstrate the SQL programming technique enabling to calculate the Product of all positive numbers {2, 4, 5, 7, 8} stored in a Microsoft Access Table1. Based on the precondition that there are no any negative values, a simple SQL query can do the job of calculating Product (SQL 1):
 

SQL
SELECT Exp(Sum(Log([Num]))) AS P FROM Table1

 
The statement could be modified with IIf() conditional operator added in order to handle zeros(SQL 2):
 

SQL
SELECT Exp(Sum(IIf([Num]=0,0,Log([Num]))))*IIf(Min([Num])=0,0,1) AS P
FROM Table1

 
The solution has been implemented/tested in Microsoft Access 2003/2007; it is also portable to any other SQL-backed Database. For detailed discussion of this SQL technique, please refer to the online article [1], published by the author and included in the reference section.
 

References

1. Aggregate Product function extends SQL

License

This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

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About the Author

DrABELL
Software Developer (Senior)
United States United States
Dr. Alexander Bell is a seasoned full-stack Software Engineer (Win/Web/Mobile). He holds PhD in Electrical and Computer Engineering, authored 37 inventions and published 300+ technical articles. Currently focused on multiple Android/Mobile development projects and Big Data' Machine Learning, AI, IoT. Alex participated in App Innovation Contests (AIC 2102/2013) with multiple winning submissions. Sample portfolio apps and publications:

  1. Aggregate Product function extends SQL
  2. Use SQL to generate large data sequence
  3. HTML5/CSS3 graphic enhancement: buttons, inputs
  4. Advanced CSS3 Styling of HTML5 SELECT Element
  5. YouTube™ API for ASP.NET
  6. HTML5 Tables Formatting: Alternate Rows, Color Gradients, Shadows

Comments and Discussions

 
Questiongeneralization to the level of a semigroup? Pin
Vadim Stadnik20-Feb-15 0:08
MemberVadim Stadnik20-Feb-15 0:08 
AnswerRe: generalization to the level of a semigroup? Pin
DrABELL21-Feb-15 10:36
MemberDrABELL21-Feb-15 10:36 
GeneralMy vote of 5 Pin
Scott Burkow20-Feb-13 7:31
MemberScott Burkow20-Feb-13 7:31 
GeneralRe: My vote of 5 Pin
DrABELL20-Feb-13 18:46
MemberDrABELL20-Feb-13 18:46 
GeneralRe: My vote of 5 Pin
Scott Burkow21-Feb-13 8:21
MemberScott Burkow21-Feb-13 8:21 
GeneralRe: My vote of 5 Pin
DrABELL21-Feb-13 11:39
MemberDrABELL21-Feb-13 11:39 
GeneralRe: My vote of 5 Pin
Scott Burkow22-Feb-13 5:56
MemberScott Burkow22-Feb-13 5:56 
GeneralRe: My vote of 5 Pin
DrABELL22-Feb-13 7:44
MemberDrABELL22-Feb-13 7:44 
GeneralRe: My vote of 5 Pin
Scott Burkow22-Feb-13 8:40
MemberScott Burkow22-Feb-13 8:40 
GeneralReason for my vote of 5 Excellent example of using a little ... Pin
MacMaverick23-Mar-11 1:51
MemberMacMaverick23-Mar-11 1:51 
GeneralRe: Many thanks! Kind regards/wishes, Alex Pin
DrABELL23-Mar-11 3:57
MemberDrABELL23-Mar-11 3:57 
GeneralReason for my vote of 5 Simple & unusual Pin
A.J.Wegierski14-Mar-11 19:52
MemberA.J.Wegierski14-Mar-11 19:52 
GeneralRe: Many thanks! Pin
DrABELL15-Mar-11 3:33
MemberDrABELL15-Mar-11 3:33 
GeneralShort URL to the article: http://exm.nr/PrdSQL Pin
DrABELL4-Jan-11 9:37
MemberDrABELL4-Jan-11 9:37 

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