| Oracle® Database Data Warehousing Guide 10g Release 1 (10.1) Part Number B10736-01 |
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View PDF |
| Oracle® Database Data Warehousing Guide 10g Release 1 (10.1) Part Number B10736-01 |
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View PDF |
The following topics provide information about how to improve analytical SQL queries in a data warehouse:
Oracle has enhanced SQL's analytical processing capabilities by introducing a new family of analytic SQL functions. These analytic functions enable you to calculate:
Rankings and percentiles
Moving window calculations
Lag/lead analysis
First/last analysis
Linear regression statistics
Ranking functions include cumulative distributions, percent rank, and N-tiles. Moving window calculations allow you to find moving and cumulative aggregations, such as sums and averages. Lag/lead analysis enables direct inter-row references so you can calculate period-to-period changes. First/last analysis enables you to find the first or last value in an ordered group.
Other enhancements to SQL include the CASE expression. CASE expressions provide if-then logic useful in many situations.
In Oracle Database 10g, the SQL reporting capability was further enhanced by the introduction of partitioned outer join. Partitioned outer join is an extension to ANSI outer join syntax that allows users to selectively densify certain dimensions while keeping others sparse. This allows reporting tools to selectively densify dimensions, for example, the ones that appear in their cross-tabular reports while keeping others sparse.
To enhance performance, analytic functions can be parallelized: multiple processes can simultaneously execute all of these statements. These capabilities make calculations easier and more efficient, thereby enhancing database performance, scalability, and simplicity.
Analytic functions are classified as described in Table 21-1.
Table 21-1 Analytic Functions and Their Uses
| Type | Used For |
|---|---|
| Ranking | Calculating ranks, percentiles, and n-tiles of the values in a result set. |
| Windowing | Calculating cumulative and moving aggregates. Works with these functions: SUM, AVG, MIN, MAX, COUNT, VARIANCE, STDDEV, FIRST_VALUE, LAST_VALUE, and new statistical functions |
| Reporting | Calculating shares, for example, market share. Works with these functions: SUM, AVG, MIN, MAX, COUNT (with/without DISTINCT), VARIANCE, STDDEV, RATIO_TO_REPORT, and new statistical functions |
| LAG/LEAD | Finding a value in a row a specified number of rows from a current row. |
| FIRST/LAST | First or last value in an ordered group. |
| Linear Regression | Calculating linear regression and other statistics (slope, intercept, and so on). |
| Inverse Percentile | The value in a data set that corresponds to a specified percentile. |
| Hypothetical Rank and Distribution | The rank or percentile that a row would have if inserted into a specified data set. |
To perform these operations, the analytic functions add several new elements to SQL processing. These elements build on existing SQL to allow flexible and powerful calculation expressions. With just a few exceptions, the analytic functions have these new elements. The processing flow is represented in Figure 21-1.
The essential concepts used in analytic functions are:
Processing order
Query processing using analytic functions takes place in three stages. First, all joins, WHERE, GROUP BY and HAVING clauses are performed. Second, the result set is made available to the analytic functions, and all their calculations take place. Third, if the query has an ORDER BY clause at its end, the ORDER BY is processed to allow for precise output ordering. The processing order is shown in Figure 21-1.
Result set partitions
The analytic functions allow users to divide query result sets into groups of rows called partitions. Note that the term partitions used with analytic functions is unrelated to the table partitions feature. Throughout this chapter, the term partitions refers to only the meaning related to analytic functions. Partitions are created after the groups defined with GROUP BY clauses, so they are available to any aggregate results such as sums and averages. Partition divisions may be based upon any desired columns or expressions. A query result set may be partitioned into just one partition holding all the rows, a few large partitions, or many small partitions holding just a few rows each.
Window
For each row in a partition, you can define a sliding window of data. This window determines the range of rows used to perform the calculations for the current row. Window sizes can be based on either a physical number of rows or a logical interval such as time. The window has a starting row and an ending row. Depending on its definition, the window may move at one or both ends. For instance, a window defined for a cumulative sum function would have its starting row fixed at the first row of its partition, and its ending row would slide from the starting point all the way to the last row of the partition. In contrast, a window defined for a moving average would have both its starting and end points slide so that they maintain a constant physical or logical range.
A window can be set as large as all the rows in a partition or just a sliding window of one row within a partition. When a window is near a border, the function returns results for only the available rows, rather than warning you that the results are not what you want.
When using window functions, the current row is included during calculations, so you should only specify (n-1) when you are dealing with n items.
Current row
Each calculation performed with an analytic function is based on a current row within a partition. The current row serves as the reference point determining the start and end of the window. For instance, a centered moving average calculation could be defined with a window that holds the current row, the six preceding rows, and the following six rows. This would create a sliding window of 13 rows, as shown in Figure 21-2.
A ranking function computes the rank of a record compared to other records in the data set based on the values of a set of measures. The types of ranking function are:
The RANK and DENSE_RANK functions allow you to rank items in a group, for example, finding the top three products sold in California last year. There are two functions that perform ranking, as shown by the following syntax:
RANK ( ) OVER ( [query_partition_clause] order_by_clause ) DENSE_RANK ( ) OVER ( [query_partition_clause] order_by_clause )
The difference between RANK and DENSE_RANK is that DENSE_RANK leaves no gaps in ranking sequence when there are ties. That is, if you were ranking a competition using DENSE_RANK and had three people tie for second place, you would say that all three were in second place and that the next person came in third. The RANK function would also give three people in second place, but the next person would be in fifth place.
The following are some relevant points about RANK:
Ascending is the default sort order, which you may want to change to descending.
The expressions in the optional PARTITION BY clause divide the query result set into groups within which the RANK function operates. That is, RANK gets reset whenever the group changes. In effect, the value expressions of the PARTITION BY clause define the reset boundaries.
If the PARTITION BY clause is missing, then ranks are computed over the entire query result set.
The ORDER BY clause specifies the measures (<value expression>) on which ranking is done and defines the order in which rows are sorted in each group (or partition). Once the data is sorted within each partition, ranks are given to each row starting from 1.
The NULLS FIRST | NULLS LAST clause indicates the position of NULLs in the ordered sequence, either first or last in the sequence. The order of the sequence would make NULLs compare either high or low with respect to non-NULL values. If the sequence were in ascending order, then NULLS FIRST implies that NULLs are smaller than all other non-NULL values and NULLS LAST implies they are larger than non-NULL values. It is the opposite for descending order. See the example in "Treatment of NULLs".
If the NULLS FIRST | NULLS LAST clause is omitted, then the ordering of the null values depends on the ASC or DESC arguments. Null values are considered larger than any other values. If the ordering sequence is ASC, then nulls will appear last; nulls will appear first otherwise. Nulls are considered equal to other nulls and, therefore, the order in which nulls are presented is non-deterministic.
The following example shows how the [ASC | DESC] option changes the ranking order.
Example 21-1 Ranking Order
SELECT channel_desc, TO_CHAR(SUM(amount_sold), '9,999,999,999') SALES$,
RANK() OVER (ORDER BY SUM(amount_sold)) AS default_rank,
RANK() OVER (ORDER BY SUM(amount_sold) DESC NULLS LAST) AS custom_rank
FROM sales, products, customers, times, channels, countries
WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id AND
sales.time_id=times.time_id AND sales.channel_id=channels.channel_id AND
times.calendar_month_desc IN ('2000-09', '2000-10') AND country_iso_code='US'
GROUP BY channel_desc;
CHANNEL_DESC SALES$ DEFAULT_RANK CUSTOM_RANK
-------------------- -------------- ------------ -----------
Direct Sales 2,443,392 3 1
Partners 1,365,963 2 2
Internet 467,478 1 3
While the data in this result is ordered on the measure SALES$, in general, it is not guaranteed by the RANK function that the data will be sorted on the measures. If you want the data to be sorted on SALES$ in your result, you must specify it explicitly with an ORDER BY clause, at the end of the SELECT statement.
Ranking functions need to resolve ties between values in the set. If the first expression cannot resolve ties, the second expression is used to resolve ties and so on. For example, here is a query ranking three of the sales channels over two months based on their dollar sales, breaking ties with the unit sales. (Note that the TRUNC function is used here only to create tie values for this query.)
Example 21-2 Ranking On Multiple Expressions
SELECT channel_desc, calendar_month_desc, TO_CHAR(TRUNC(SUM(amount_sold),-5),
'9,999,999,999') SALES$, TO_CHAR(SUM(quantity_sold), '9,999,999,999')
SALES_Count, RANK() OVER (ORDER BY TRUNC(SUM(amount_sold), -5) DESC, SUM(quantity_sold) DESC) AS col_rank
FROM sales, products, customers, times, channels
WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id AND
sales.time_id=times.time_id AND sales.channel_id=channels.channel_id AND
times.calendar_month_desc IN ('2000-09', '2000-10') AND
channels.channel_desc<>'Tele Sales'
GROUP BY channel_desc, calendar_month_desc;
CHANNEL_DESC CALENDAR SALES$ SALES_COUNT COL_RANK
-------------------- -------- -------------- -------------- ---------
Direct Sales 2000-10 1,200,000 12,584 1
Direct Sales 2000-09 1,200,000 11,995 2
Partners 2000-10 600,000 7,508 3
Partners 2000-09 600,000 6,165 4
Internet 2000-09 200,000 1,887 5
Internet 2000-10 200,000 1,450 6
The sales_count column breaks the ties for three pairs of values.
The difference between RANK and DENSE_RANK functions is illustrated as follows:
Example 21-3 RANK and DENSE_RANK
SELECT channel_desc, calendar_month_desc,
TO_CHAR(TRUNC(SUM(amount_sold),-4), '9,999,999,999') SALES$,
RANK() OVER (ORDER BY TRUNC(SUM(amount_sold),-4) DESC) AS RANK,
DENSE_RANK() OVER (ORDER BY TRUNC(SUM(amount_sold),-4) DESC) AS DENSE_RANK
FROM sales, products, customers, times, channels
WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id AND
sales.time_id=times.time_id AND sales.channel_id=channels.channel_id AND
times.calendar_month_desc IN ('2000-09', '2000-10') AND
channels.channel_desc<>'Tele Sales'
GROUP BY channel_desc, calendar_month_desc;
CHANNEL_DESC CALENDAR SALES$ RANK DENSE_RANK
-------------------- -------- -------------- --------- ----------
Direct Sales 2000-09 1,200,000 1 1
Direct Sales 2000-10 1,200,000 1 1
Partners 2000-09 600,000 3 2
Partners 2000-10 600,000 3 2
Internet 2000-09 200,000 5 3
Internet 2000-10 200,000 5 3
Note that, in the case of DENSE_RANK, the largest rank value gives the number of distinct values in the data set.
The RANK function can be made to operate within groups, that is, the rank gets reset whenever the group changes. This is accomplished with the PARTITION BY clause. The group expressions in the PARTITION BY subclause divide the data set into groups within which RANK operates. For example, to rank products within each channel by their dollar sales, you could issue the following statement.
Example 21-4 Per Group Ranking Example 1
SELECT channel_desc, calendar_month_desc, TO_CHAR(SUM(amount_sold),
'9,999,999,999') SALES$, RANK() OVER (PARTITION BY channel_desc
ORDER BY SUM(amount_sold) DESC) AS RANK_BY_CHANNEL
FROM sales, products, customers, times, channels
WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id AND
sales.time_id=times.time_id AND sales.channel_id=channels.channel_id AND
times.calendar_month_desc IN ('2000-08', '2000-09', '2000-10', '2000-11')
AND channels.channel_desc IN ('Direct Sales', 'Internet')
GROUP BY channel_desc, calendar_month_desc;
A single query block can contain more than one ranking function, each partitioning the data into different groups (that is, reset on different boundaries). The groups can be mutually exclusive. The following query ranks products based on their dollar sales within each month (rank_of_product_per_region) and within each channel (rank_of_product_total).
Example 21-5 Per Group Ranking Example 2
SELECT channel_desc, calendar_month_desc, TO_CHAR(SUM(amount_sold),
'9,999,999,999') SALES$, RANK() OVER (PARTITION BY calendar_month_desc
ORDER BY SUM(amount_sold) DESC) AS RANK_WITHIN_MONTH, RANK() OVER (PARTITION
BY channel_desc ORDER BY SUM(amount_sold) DESC) AS RANK_WITHIN_CHANNEL
FROM sales, products, customers, times, channels
WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id AND
sales.time_id=times.time_id AND sales.channel_id=channels.channel_id AND
times.calendar_month_desc IN ('2000-08', '2000-09', '2000-10', '2000-11')
AND channels.channel_desc IN ('Direct Sales', 'Internet')
GROUP BY channel_desc, calendar_month_desc;
CHANNEL_DESC CALENDAR SALES$ RANK_WITHIN_MONTH RANK_WITHIN_CHANNEL -------------------- -------- -------------- ----------------- ------------------- Direct Sales 2000-08 1,236,104 1 1 Internet 2000-08 215,107 2 4 Direct Sales 2000-09 1,217,808 1 3 Internet 2000-09 228,241 2 3 Direct Sales 2000-10 1,225,584 1 2 Internet 2000-10 239,236 2 2 Direct Sales 2000-11 1,115,239 1 4 Internet 2000-11 284,742 2 1
Analytic functions, RANK for example, can be reset based on the groupings provided by a CUBE, ROLLUP, or GROUPING SETS operator. It is useful to assign ranks to the groups created by CUBE, ROLLUP, and GROUPING SETS queries. See Chapter 20, " SQL for Aggregation in Data Warehouses" for further information about the GROUPING function.
A sample CUBE and ROLLUP query is the following:
SELECT channel_desc, country_iso_code,
TO_CHAR(SUM(amount_sold), '9,999,999,999')
SALES$, RANK() OVER (PARTITION BY GROUPING_ID(channel_desc, country_iso_code)
ORDER BY SUM(amount_sold) DESC) AS RANK_PER_GROUP
FROM sales, customers, times, channels, countries
WHERE sales.time_id=times.time_id AND sales.cust_id=customers.cust_id AND
sales.channel_id = channels.channel_id AND channels.channel_desc
IN ('Direct Sales', 'Internet') AND times.calendar_month_desc='2000-09'
AND country_iso_code IN ('GB', 'US', 'JP')
GROUP BY CUBE(channel_desc, country_iso_code);
CHANNEL_DESC CO SALES$ RANK_PER_GROUP
-------------------- -- -------------- --------------
Direct Sales GB 1,217,808 1
Direct Sales JP 1,217,808 1
Direct Sales US 1,217,808 1
Internet GB 228,241 4
Internet JP 228,241 4
Internet US 228,241 4
Direct Sales 3,653,423 1
Internet 684,724 2
GB 1,446,049 1
JP 1,446,049 1
US 1,446,049 1
4,338,147 1
NULLs are treated like normal values. Also, for rank computation, a NULL value is assumed to be equal to another NULL value. Depending on the ASC | DESC options provided for measures and the NULLS FIRST | NULLS LAST clause, NULLs will either sort low or high and hence, are given ranks appropriately. The following example shows how NULLs are ranked in different cases:
SELECT times.time_id time, sold,
RANK() OVER (ORDER BY (sold) DESC NULLS LAST) AS NLAST_DESC,
RANK() OVER (ORDER BY (sold) DESC NULLS FIRST) AS NFIRST_DESC,
RANK() OVER (ORDER BY (sold) ASC NULLS FIRST) AS NFIRST,
RANK() OVER (ORDER BY (sold) ASC NULLS LAST) AS NLAST
FROM
(
SELECT time_id , sum(sales.amount_sold) sold
FROM sales, products, customers, countries
WHERE sales.prod_id=products.prod_id AND
sales.cust_id=customers.cust_id AND prod_name IN ('Envoy Ambassador',
'Mouse Pad') AND country_iso_code ='GB'
GROUP BY time_id)
v, times
WHERE v.time_id (+) =times.time_id AND calendar_year=1999
AND calendar_month_number=1
ORDER BY sold DESC NULLS LAST;
TIME SOLD NLAST_DESC NFIRST_DESC NFIRST NLAST
--------- ---------- ---------- ----------- ---------- ----------
14-JAN-99 25241.48 1 13 31 19
21-JAN-99 24365.05 2 14 30 18
10-JAN-99 22901.24 3 15 29 17
20-JAN-99 16578.19 4 16 28 16
16-JAN-99 15881.12 5 17 27 15
30-JAN-99 15637.49 6 18 26 14
17-JAN-99 13262.87 7 19 25 13
25-JAN-99 13227.08 8 20 24 12
03-JAN-99 9885.74 9 21 23 11
28-JAN-99 4471.08 10 22 22 10
27-JAN-99 3453.66 11 23 21 9
23-JAN-99 925.45 12 24 20 8
07-JAN-99 756.87 13 25 19 7
08-JAN-99 571.8 14 26 18 6
13-JAN-99 569.21 15 27 17 5
02-JAN-99 316.87 16 28 16 4
12-JAN-99 195.54 17 29 15 3
26-JAN-99 92.96 18 30 14 2
19-JAN-99 86.04 19 31 13 1
05-JAN-99 20 1 1 20
01-JAN-99 20 1 1 20
31-JAN-99 20 1 1 20
11-JAN-99 20 1 1 20
06-JAN-99 20 1 1 20
18-JAN-99 20 1 1 20
09-JAN-99 20 1 1 20
29-JAN-99 20 1 1 20
22-JAN-99 20 1 1 20
04-JAN-99 20 1 1 20
24-JAN-99 20 1 1 20
15-JAN-99 20 1 1 20
Bottom N is similar to top N except for the ordering sequence within the rank expression. Using the previous example, you can order SUM(s_amount) ascending instead of descending.
The CUME_DIST function (defined as the inverse of percentile in some statistical books) computes the position of a specified value relative to a set of values. The order can be ascending or descending. Ascending is the default. The range of values for CUME_DIST is from greater than 0 to 1. To compute the CUME_DIST of a value x in a set S of size N, you use the formula:
CUME_DIST(x) = number of values in S coming before and including x in the specified order/ N
Its syntax is:
CUME_DIST ( ) OVER ( [query_partition_clause] order_by_clause )
The semantics of various options in the CUME_DIST function are similar to those in the RANK function. The default order is ascending, implying that the lowest value gets the lowest CUME_DIST (as all other values come later than this value in the order). NULLs are treated the same as they are in the RANK function. They are counted toward both the numerator and the denominator as they are treated like non-NULL values. The following example finds cumulative distribution of sales by channel within each month:
SELECT calendar_month_desc AS MONTH, channel_desc,
TO_CHAR(SUM(amount_sold) , '9,999,999,999') SALES$,
CUME_DIST() OVER (PARTITION BY calendar_month_desc ORDER BY
SUM(amount_sold) ) AS CUME_DIST_BY_CHANNEL
FROM sales, products, customers, times, channels
WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id AND
sales.time_id=times.time_id AND sales.channel_id=channels.channel_id AND
times.calendar_month_desc IN ('2000-09', '2000-07','2000-08')
GROUP BY calendar_month_desc, channel_desc;
MONTH CHANNEL_DESC SALES$ CUME_DIST_BY_CHANNEL
-------- -------------------- -------------- --------------------
2000-07 Internet 140,423 .333333333
2000-07 Partners 611,064 .666666667
2000-07 Direct Sales 1,145,275 1
2000-08 Internet 215,107 .333333333
2000-08 Partners 661,045 .666666667
2000-08 Direct Sales 1,236,104 1
2000-09 Internet 228,241 .333333333
2000-09 Partners 666,172 .666666667
2000-09 Direct Sales 1,217,808 1
PERCENT_RANK is similar to CUME_DIST, but it uses rank values rather than row counts in its numerator. Therefore, it returns the percent rank of a value relative to a group of values. The function is available in many popular spreadsheets. PERCENT_RANK of a row is calculated as:
(rank of row in its partition - 1) / (number of rows in the partition - 1)
PERCENT_RANK returns values in the range zero to one. The row(s) with a rank of 1 will have a PERCENT_RANK of zero. Its syntax is:
PERCENT_RANK () OVER ([query_partition_clause] order_by_clause)
NTILE allows easy calculation of tertiles, quartiles, deciles and other common summary statistics. This function divides an ordered partition into a specified number of groups called buckets and assigns a bucket number to each row in the partition. NTILE is a very useful calculation because it lets users divide a data set into fourths, thirds, and other groupings.
The buckets are calculated so that each bucket has exactly the same number of rows assigned to it or at most 1 row more than the others. For instance, if you have 100 rows in a partition and ask for an NTILE function with four buckets, 25 rows will be assigned a value of 1, 25 rows will have value 2, and so on. These buckets are referred to as equiheight buckets.
If the number of rows in the partition does not divide evenly (without a remainder) into the number of buckets, then the number of rows assigned for each bucket will differ by one at most. The extra rows will be distributed one for each bucket starting from the lowest bucket number. For instance, if there are 103 rows in a partition which has an NTILE(5) function, the first 21 rows will be in the first bucket, the next 21 in the second bucket, the next 21 in the third bucket, the next 20 in the fourth bucket and the final 20 in the fifth bucket.
The NTILE function has the following syntax:
NTILE (expr) OVER ([query_partition_clause] order_by_clause)
In this, the N in NTILE(N) can be a constant (for example, 5) or an expression.
This function, like RANK and CUME_DIST, has a PARTITION BY clause for per group computation, an ORDER BY clause for specifying the measures and their sort order, and NULLS FIRST | NULLS LAST clause for the specific treatment of NULLs. For example, the following is an example assigning each month's sales total into one of 4 buckets:
SELECT calendar_month_desc AS MONTH , TO_CHAR(SUM(amount_sold),
'9,999,999,999')
SALES$, NTILE(4) OVER (ORDER BY SUM(amount_sold)) AS TILE4
FROM sales, products, customers, times, channels
WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id AND
sales.time_id=times.time_id AND sales.channel_id=channels.channel_id AND
times.calendar_year=2000 AND prod_category= 'Electronics'
GROUP BY calendar_month_desc;
MONTH SALES$ TILE4
-------- -------------- ----------
2000-02 242,416 1
2000-01 257,286 1
2000-03 280,011 1
2000-06 315,951 2
2000-05 316,824 2
2000-04 318,106 2
2000-07 433,824 3
2000-08 477,833 3
2000-12 553,534 3
2000-10 652,225 4
2000-11 661,147 4
2000-09 691,449 4
NTILE ORDER BY statements must be fully specified to yield reproducible results. Equal values can get distributed across adjacent buckets. To ensure deterministic results, you must order on a unique key.
The ROW_NUMBER function assigns a unique number (sequentially, starting from 1, as defined by ORDER BY) to each row within the partition. It has the following syntax:
ROW_NUMBER ( ) OVER ( [query_partition_clause] order_by_clause )
Example 21-6 ROW_NUMBER
SELECT channel_desc, calendar_month_desc,
TO_CHAR(TRUNC(SUM(amount_sold), -5), '9,999,999,999') SALES$,
ROW_NUMBER() OVER (ORDER BY TRUNC(SUM(amount_sold), -6) DESC) AS ROW_NUMBER
FROM sales, products, customers, times, channels
WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id AND
sales.time_id=times.time_id AND sales.channel_id=channels.channel_id AND
times.calendar_month_desc IN ('2001-09', '2001-10')
GROUP BY channel_desc, calendar_month_desc;
CHANNEL_DESC CALENDAR SALES$ ROW_NUMBER
-------------------- -------- -------------- ----------
Direct Sales 2001-09 1,100,000 1
Direct Sales 2001-10 1,000,000 2
Internet 2001-09 500,000 3
Internet 2001-10 700,000 4
Partners 2001-09 600,000 5
Partners 2001-10 600,000 6
Note that there are three pairs of tie values in these results. Like NTILE, ROW_NUMBER is a non-deterministic function, so each tied value could have its row number switched. To ensure deterministic results, you must order on a unique key. Inmost cases, that will require adding a new tie breaker column to the query and using it in the ORDER BY specification.
Windowing functions can be used to compute cumulative, moving, and centered aggregates. They return a value for each row in the table, which depends on other rows in the corresponding window. These functions include moving sum, moving average, moving min/max, cumulative sum, as well as statistical functions. They can be used only in the SELECT and ORDER BY clauses of the query. Two other functions are available: FIRST_VALUE, which returns the first value in the window; and LAST_VALUE, which returns the last value in the window. These functions provide access to more than one row of a table without a self-join. The syntax of the windowing functions is:
{SUM|AVG|MAX|MIN|COUNT|STDDEV|VARIANCE|FIRST_VALUE|LAST_VALUE}
({value expression1 | *}) OVER
([PARTITION BY value expression2[,...])
ORDER BY value expression3 [collate clause>]
[ASC| DESC] [NULLS FIRST | NULLS LAST] [,...]
{ROWS | RANGE} {BETWEEN
{UNBOUNDED PRECEDING | CURRENT ROW | value_expr {PRECEDING | FOLLOWING}} AND
{ UNBOUNDED FOLLOWING | CURRENT ROW | value_expr { PRECEDING | FOLLOWING } }
| { UNBOUNDED PRECEDING | CURRENT ROW | value_expr PRECEDING}}
Window functions' NULL semantics match the NULL semantics for SQL aggregate functions. Other semantics can be obtained by user-defined functions, or by using the DECODE or a CASE expression within the window function.
A logical offset can be specified with constants such as RANGE 10 PRECEDING, or an expression that evaluates to a constant, or by an interval specification like RANGE INTERVAL N DAY/MONTH/YEAR PRECEDING or an expression that evaluates to an interval. With logical offset, there can only be one expression in the ORDER BY expression list in the function, with type compatible to NUMERIC if offset is numeric, or DATE if an interval is specified.
Example 21-7 Cumulative Aggregate Function
The following is an example of cumulative amount_sold by customer ID by quarter in 1999:
SELECT c.cust_id, t.calendar_quarter_desc, TO_CHAR (SUM(amount_sold),
'9,999,999,999.99') AS Q_SALES, TO_CHAR(SUM(SUM(amount_sold))
OVER (PARTITION BY c.cust_id ORDER BY c.cust_id, t.calendar_quarter_desc
ROWS UNBOUNDED
PRECEDING), '9,999,999,999.99') AS CUM_SALES
FROM sales s, times t, customers c
WHERE s.time_id=t.time_id AND s.cust_id=c.cust_id AND t.calendar_year=2000
AND c.cust_id IN (2595, 9646, 11111)
GROUP BY c.cust_id, t.calendar_quarter_desc
ORDER BY c.cust_id, t.calendar_quarter_desc;
CUST_ID CALENDA Q_SALES CUM_SALES
---------- ------- ----------------- -----------------
2595 2000-01 659.92 659.92
2595 2000-02 224.79 884.71
2595 2000-03 313.90 1,198.61
2595 2000-04 6,015.08 7,213.69
9646 2000-01 1,337.09 1,337.09
9646 2000-02 185.67 1,522.76
9646 2000-03 203.86 1,726.62
9646 2000-04 458.29 2,184.91
11111 2000-01 43.18 43.18
11111 2000-02 33.33 76.51
11111 2000-03 579.73 656.24
11111 2000-04 307.58 963.82
In this example, the analytic function SUM defines, for each row, a window that starts at the beginning of the partition (UNBOUNDED PRECEDING) and ends, by default, at the current row.
Nested SUMs are needed in this example since we are performing a SUM over a value that is itself a SUM. Nested aggregations are used very often in analytic aggregate functions.
Example 21-8 Moving Aggregate Function
This example of a time-based window shows, for one customer, the moving average of sales for the current month and preceding two months:
SELECT c.cust_id, t.calendar_month_desc, TO_CHAR (SUM(amount_sold),
'9,999,999,999') AS SALES, TO_CHAR(AVG(SUM(amount_sold))
OVER (ORDER BY c.cust_id, t.calendar_month_desc ROWS 2 PRECEDING), '9,999,999,999')
AS MOVING_3_MONTH_AVG
FROM sales s, times t, customers c
WHERE s.time_id=t.time_id AND s.cust_id=c.cust_id AND
t.calendar_year=1999 AND c.cust_id IN (6510)
GROUP BY c.cust_id, t.calendar_month_desc
ORDER BY c.cust_id, t.calendar_month_desc;
CUST_ID CALENDAR SALES MOVING_3_MONTH
---------- -------- -------------- --------------
6510 1999-04 125 125
6510 1999-05 3,395 1,760
6510 1999-06 4,080 2,533
6510 1999-07 6,435 4,637
6510 1999-08 5,105 5,207
6510 1999-09 4,676 5,405
6510 1999-10 5,109 4,963
6510 1999-11 802 3,529
Note that the first two rows for the three month moving average calculation in the output data are based on a smaller interval size than specified because the window calculation cannot reach past the data retrieved by the query. You need to consider the different window sizes found at the borders of result sets. In other words, you may need to modify the query to include exactly what you want.
Calculating windowing aggregate functions centered around the current row is straightforward. This example computes for all customers a centered moving average of sales for one week in late December 1999. It finds an average of the sales total for the one day preceding the current row and one day following the current row including the current row as well.
Example 21-9 Centered Aggregate
SELECT t.time_id, TO_CHAR (SUM(amount_sold), '9,999,999,999') AS SALES, TO_CHAR(AVG(SUM(amount_sold)) OVER (ORDER BY t.time_id RANGE BETWEEN INTERVAL '1' DAY PRECEDING AND INTERVAL '1' DAY FOLLOWING), '9,999,999,999') AS CENTERED_3_DAY_AVG FROM sales s, times t WHERE s.time_id=t.time_id AND t.calendar_week_number IN (51) AND calendar_year=1999 GROUP BY t.time_id ORDER BY t.time_id; TIME_ID SALES CENTERED_3_DAY --------- -------------- -------------- 20-DEC-99 134,337 106,676 21-DEC-99 79,015 102,539 22-DEC-99 94,264 85,342 23-DEC-99 82,746 93,322 24-DEC-99 102,957 82,937 25-DEC-99 63,107 87,062 26-DEC-99 95,123 79,115
The starting and ending rows for each product's centered moving average calculation in the output data are based on just two days, since the window calculation cannot reach past the data retrieved by the query. Users need to consider the different window sizes found at the borders of result sets: the query may need to be adjusted.
The following example illustrates how window aggregate functions compute values when there are duplicates, that is, when multiple rows are returned for a single ordering value. The query retrieves the quantity sold to several customers during a specified time range. (Although we use an inline view to define our base data set, it has no special significance and can be ignored.) The query defines a moving window that runs from the date of the current row to 10 days earlier.Note that the RANGE keyword is used to define the windowing clause of this example. This means that the window can potentially hold many rows for each value in the range. In this case, there are three pairs of rows with duplicate date values.
Example 21-10 Windowing Aggregate Functions with Logical Offsets
SELECT time_id, daily_sum, SUM(daily_sum) OVER (ORDER BY time_id RANGE BETWEEN INTERVAL '10' DAY PRECEDING AND CURRENT ROW) AS current_group_sum FROM (SELECT time_id, channel_id, SUM(s.quantity_sold) AS daily_sum FROM customers c, sales s, countries WHERE c.cust_id=s.cust_id AND s.cust_id IN (638, 634, 753, 440 ) AND s.time_id BETWEEN '01-MAY-00' AND '13-MAY-00' GROUP BY time_id, channel_id); TIME_ID DAILY_SUM CURRENT_GROUP_SUM --------- ---------- ----------------- 06-MAY-00 161 161 /* 161 */ 10-MAY-00 23 207 /* 161 +(23+23)*/ 10-MAY-00 23 207 /* 161 +(23+23) */ 11-MAY-00 46 345 /* 161 +(23+23)+(46+92) */ 11-MAY-00 92 345 /* 161 +(23+23)+(46+92) */ 12-MAY-00 23 368 /* 161 +(23+23)+(46+92)+23 */ 13-MAY-00 46 529 /* 161 +(23+23)+(46+92)+23+(46+115) */ 13-MAY-00 115 529 /* 161 +(23+23)+(46+92)+23+(46+115) */
In the output of this example, all dates except May 6 and May 12 return two rows with duplicate dates. Examine the commented numbers to the right of the output to see how the values are calculated. Note that each group in parentheses represents the values returned for a single day.
Note that this example applies only when you use the RANGE keyword rather than the ROWS keyword. It is also important to remember that with RANGE, you can only use 1 ORDER BY expression in the analytic function's ORDER BY clause. With the ROWS keyword, you can use multiple order by expressions in the analytic function's ORDER BY clause.
There are situations where it is useful to vary the size of a window for each row, based on a specified condition. For instance, you may want to make the window larger for certain dates and smaller for others. Assume that you want to calculate the moving average of stock price over three working days. If you have an equal number of rows for each day for all working days and no non-working days are stored, then you can use a physical window function. However, if the conditions noted are not met, you can still calculate a moving average by using an expression in the window size parameters.
Expressions in a window size specification can be made in several different sources. the expression could be a reference to a column in a table, such as a time table. It could also be a function that returns the appropriate boundary for the window based on values in the current row. The following statement for a hypothetical stock price database uses a user-defined function in its RANGE clause to set window size:
SELECT t_timekey, AVG(stock_price)
OVER (ORDER BY t_timekey RANGE fn(t_timekey) PRECEDING) av_price
FROM stock, time WHERE st_timekey = t_timekey
ORDER BY t_timekey;
In this statement, t_timekey is a date field. Here, fn could be a PL/SQL function with the following specification:
fn(t_timekey) returns
4 if t_timekey is Monday, Tuesday
2 otherwise
If any of the previous days are holidays, it adjusts the count appropriately.
Note that, when window is specified using a number in a window function with ORDER BY on a date column, then it is converted to mean the number of days. You could have also used the interval literal conversion function, as NUMTODSINTERVAL(fn(t_timekey), 'DAY') instead of just fn(t_timekey) to mean the same thing. You can also write a PL/SQL function that returns an INTERVAL datatype value.
For windows expressed in rows, the ordering expressions should be unique to produce deterministic results. For example, the following query is not deterministic because time_id is not unique in this result set.
Example 21-11 Windowing Aggregate Functions With Physical Offsets
SELECT t.time_id, TO_CHAR(amount_sold, '9,999,999,999') AS INDIV_SALE,
TO_CHAR(SUM(amount_sold) OVER (PARTITION BY t.time_id ORDER BY t.time_id
ROWS UNBOUNDED PRECEDING), '9,999,999,999') AS CUM_SALES
FROM sales s, times t, customers c
WHERE s.time_id=t.time_id AND s.cust_id=c.cust_id AND t.time_id IN
(TO_DATE('11-DEC-1999'), TO_DATE('12-DEC-1999')) AND c.cust_id
BETWEEN 6500 AND 6600
ORDER BY t.time_id;
TIME_ID INDIV_SALE CUM_SALES
--------- ---------- ---------
12-DEC-99 23 23
12-DEC-99 9 32
12-DEC-99 14 46
12-DEC-99 24 70
12-DEC-99 19 89
One way to handle this problem would be to add the prod_id column to the result set and order on both time_id and prod_id.
The FIRST_VALUE and LAST_VALUE functions allow you to select the first and last rows from a window. These rows are especially valuable because they are often used as the baselines in calculations. For instance, with a partition holding sales data ordered by day, you might ask "How much was each day's sales compared to the first sales day (FIRST_VALUE) of the period?" Or you might wish to know, for a set of rows in increasing sales order, "What was the percentage size of each sale in the region compared to the largest sale (LAST_VALUE) in the region?"
If the IGNORE NULLS option is used with FIRST_VALUE, it will return the first non-null value in the set, or NULL if all values are NULL. If IGNORE NULLS is used with LAST_VALUE, it will return the last non-null value in the set, or NULL if all values are NULL. The IGNORE NULLS option is particularly useful in populating an inventory table properly.
After a query has been processed, aggregate values like the number of resulting rows or an average value in a column can be easily computed within a partition and made available to other reporting functions. Reporting aggregate functions return the same aggregate value for every row in a partition. Their behavior with respect to NULLs is the same as the SQL aggregate functions. The syntax is:
{SUM | AVG | MAX | MIN | COUNT | STDDEV | VARIANCE}
([ALL | DISTINCT] {value expression1 | *})
OVER ([PARTITION BY value expression2[,...]])
In addition, the following conditions apply:
An asterisk (*) is only allowed in COUNT(*)
DISTINCT is supported only if corresponding aggregate functions allow it
value expression1 and value expression2 can be any valid expression involving column references or aggregates.
The PARTITION BY clause defines the groups on which the windowing functions would be computed. If the PARTITION BY clause is absent, then the function is computed over the whole query result set.
Reporting functions can appear only in the SELECT clause or the ORDER BY clause. The major benefit of reporting functions is their ability to do multiple passes of data in a single query block and speed up query performance. Queries such as "Count the number of salesmen with sales more than 10% of city sales" do not require joins between separate query blocks.
For example, consider the question "For each product category, find the region in which it had maximum sales". The equivalent SQL query using the MAX reporting aggregate function would be:
SELECT prod_category, country_region, sales
FROM (SELECT SUBSTR(p.prod_category,1,8) AS prod_category, co.country_region, SUM(amount_sold) AS sales,
MAX(SUM(amount_sold)) OVER (PARTITION BY prod_category) AS MAX_REG_SALES
FROM sales s, customers c, countries co, products p
WHERE s.cust_id=c.cust_id AND c.country_id=co.country_id AND
s.prod_id =p.prod_id AND s.time_id = TO_DATE('11-OCT-2001')
GROUP BY prod_category, country_region)
WHERE sales = MAX_REG_SALES;
The inner query with the reporting aggregate function MAX(SUM(amount_sold)) returns:
PROD_CAT COUNTRY_REGION SALES MAX_REG_SALES -------- -------------------- ---------- ------------- Electron Americas 581.92 581.92 Hardware Americas 925.93 925.93 Peripher Americas 3084.48 4290.38 Peripher Asia 2616.51 4290.38 Peripher Europe 4290.38 4290.38 Peripher Oceania 940.43 4290.38 Software Americas 4445.7 4445.7 Software Asia 1408.19 4445.7 Software Europe 3288.83 4445.7 Software Oceania 890.25 4445.7
The full query results are:
PROD_CAT COUNTRY_REGION SALES -------- -------------------- ---------- Electron Americas 581.92 Hardware Americas 925.93 Peripher Europe 4290.38 Software Americas 4445.7
Example 21-12 Reporting Aggregate Example
Reporting aggregates combined with nested queries enable you to answer complex queries efficiently. For example, what if you want to know the best selling products in your most significant product subcategories? The following is a query which finds the 5 top-selling products for each product subcategory that contributes more than 20% of the sales within its product category:
SELECT SUBSTR(prod_category,1,8) AS CATEG, prod_subcategory, prod_id, SALES
FROM (SELECT p.prod_category, p.prod_subcategory, p.prod_id,
SUM(amount_sold) AS SALES,
SUM(SUM(amount_sold)) OVER (PARTITION BY p.prod_category) AS CAT_SALES,
SUM(SUM(amount_sold)) OVER
(PARTITION BY p.prod_subcategory) AS SUBCAT_SALES,
RANK() OVER (PARTITION BY p.prod_subcategory
ORDER BY SUM(amount_sold) ) AS RANK_IN_LINE
FROM sales s, customers c, countries co, products p
WHERE s.cust_id=c.cust_id AND
c.country_id=co.country_id AND s.prod_id=p.prod_id AND
s.time_id=to_DATE('11-OCT-2000')
GROUP BY p.prod_category, p.prod_subcategory, p.prod_id
ORDER BY prod_category, prod_subcategory)
WHERE SUBCAT_SALES>0.2*CAT_SALES AND RANK_IN_LINE<=5;
The RATIO_TO_REPORT function computes the ratio of a value to the sum of a set of values. If the expression value expression evaluates to NULL, RATIO_TO_REPORT also evaluates to NULL, but it is treated as zero for computing the sum of values for the denominator. Its syntax is:
RATIO_TO_REPORT ( expr ) OVER ( [query_partition_clause] )
In this, the following applies:
expr can be any valid expression involving column references or aggregates.
The PARTITION BY clause defines the groups on which the RATIO_TO_REPORT function is to be computed. If the PARTITION BY clause is absent, then the function is computed over the whole query result set.
Example 21-13 RATIO_TO_REPORT
To calculate RATIO_TO_REPORT of sales for each channel, you might use the following syntax:
SELECT ch.channel_desc, TO_CHAR(SUM(amount_sold),'9,999,999') AS SALES,
TO_CHAR(SUM(SUM(amount_sold)) OVER (), '9,999,999') AS TOTAL_SALES,
TO_CHAR(RATIO_TO_REPORT(SUM(amount_sold)) OVER (), '9.999')
AS RATIO_TO_REPORT
FROM sales s, channels ch
WHERE s.channel_id=ch.channel_id AND s.time_id=to_DATE('11-OCT-2000')
GROUP BY ch.channel_desc;
CHANNEL_DESC SALES TOTAL_SALE RATIO_
-------------------- ---------- ---------- ------
Direct Sales 14,447 23,183 .623
Internet 345 23,183 .015
Partners 8,391 23,183 .362
The LAG and LEAD functions are useful for comparing values when the relative positions of rows can be known reliably. They work by specifying the count of rows which separate the target row from the current row. Because the functions provide access to more than one row of a table at the same time without a self-join, they can enhance processing speed. The LAG function provides access to a row at a given offset prior to the current position, and the LEAD function provides access to a row at a given offset after the current position.
These functions have the following syntax:
{LAG | LEAD} ( value_expr [, offset] [, default] )
OVER ( [query_partition_clause] order_by_clause )
offset is an optional parameter and defaults to 1. default is an optional parameter and is the value returned if offset falls outside the bounds of the table or partition.
Example 21-14 LAG/LEAD
SELECT time_id, TO_CHAR(SUM(amount_sold),'9,999,999') AS SALES,
TO_CHAR(LAG(SUM(amount_sold),1) OVER (ORDER BY time_id),'9,999,999') AS LAG1,
TO_CHAR(LEAD(SUM(amount_sold),1) OVER (ORDER BY time_id),'9,999,999') AS LEAD1
FROM sales
WHERE time_id>=TO_DATE('10-OCT-2000') AND time_id<=TO_DATE('14-OCT-2000')
GROUP BY time_id;
TIME_ID SALES LAG1 LEAD1
--------- ---------- ---------- ----------
10-OCT-00 238,479 23,183
11-OCT-00 23,183 238,479 24,616
12-OCT-00 24,616 23,183 76,516
13-OCT-00 76,516 24,616 29,795
14-OCT-00 29,795 76,516
See "Data Densification for Reporting" for information showing how to use the LAG/LEAD functions for doing period-to-period comparison queries on sparse data.
The FIRST/LAST aggregate functions allow you to rank a data set and work with its top-ranked or bottom-ranked rows. After finding the top or bottom ranked rows, an aggregate function is applied to any desired column. That is, FIRST/LAST lets you rank on column A but return the result of an aggregate applied on the first-ranked or last-ranked rows of column B. This is valuable because it avoids the need for a self-join or subquery, thus improving performance. These functions' syntax begins with a regular aggregate function (MIN, MAX, SUM, AVG, COUNT, VARIANCE, STDDEV) that produces a single return value per group. To specify the ranking used, the FIRST/LAST functions add a new clause starting with the word KEEP.
These functions have the following syntax:
aggregate_function KEEP ( DENSE_RANK LAST ORDER BY
expr [ DESC | ASC ] [NULLS { FIRST | LAST }]
[, expr [ DESC | ASC ] [NULLS { FIRST | LAST }]]...)
[OVER query_partitioning_clause]
Note that the ORDER BY clause can take multiple expressions.
You can use the FIRST/LAST family of aggregates as regular aggregate functions.
Example 21-15 FIRST/LAST Example 1
The following query lets us compare minimum price and list price of our products. For each product subcategory within the Men's clothing category, it returns the following:
List price of the product with the lowest minimum price
Lowest minimum price
List price of the product with the highest minimum price
Highest minimum price
SELECT prod_subcategory, MIN(prod_list_price) KEEP (DENSE_RANK FIRST ORDER BY (prod_min_price)) AS LP_OF_LO_MINP, MIN(prod_min_price) AS LO_MINP, MAX(prod_list_price) KEEP (DENSE_RANK LAST ORDER BY (prod_min_price)) AS LP_OF_HI_MINP, MAX(prod_min_price) AS HI_MINP FROM products WHERE prod_category='Electronics' GROUP BY prod_subcategory; PROD_SUBCATEGORY LP_OF_LO_MINP LO_MINP LP_OF_HI_MINP HI_MINP ---------------- ------------- ------- ------------- ---------- Game Consoles 299.99 299.99 299.99 299.99 Home Audio 499.99 499.99 599.99 599.99 Y Box Accessories 7.99 7.99 20.99 20.99 Y Box Games 7.99 7.99 29.99 29.99
You can also use the FIRST/LAST family of aggregates as reporting aggregate functions. An example is calculating which months had the greatest and least increase in head count throughout the year. The syntax for these functions is similar to the syntax for any other reporting aggregate.
Consider the example in Example 21-15 for FIRST/LAST. What if we wanted to find the list prices of individual products and compare them to the list prices of the products in their subcategory that had the highest and lowest minimum prices?
The following query lets us find that information for the Documentation subcategory by using FIRST/LAST as reporting aggregates.
Example 21-16 FIRST/LAST Example 2
SELECT prod_id, prod_list_price,
MIN(prod_list_price) KEEP (DENSE_RANK FIRST ORDER BY (prod_min_price))
OVER(PARTITION BY (prod_subcategory)) AS LP_OF_LO_MINP,
MAX(prod_list_price) KEEP (DENSE_RANK LAST ORDER BY (prod_min_price))
OVER(PARTITION BY (prod_subcategory)) AS LP_OF_HI_MINP
FROM products WHERE prod_subcategory = 'Documentation';
PROD_ID PROD_LIST_PRICE LP_OF_LO_MINP LP_OF_HI_MINP
---------- --------------- ------------- -------------
40 44.99 44.99 44.99
41 44.99 44.99 44.99
42 44.99 44.99 44.99
43 44.99 44.99 44.99
44 44.99 44.99 44.99
45 44.99 44.99 44.99
Using the FIRST and LAST functions as reporting aggregates makes it easy to include the results in calculations such "Salary as a percent of the highest salary."
Using the CUME_DIST function, you can find the cumulative distribution (percentile) of a set of values. However, the inverse operation (finding what value computes to a certain percentile) is neither easy to do nor efficiently computed. To overcome this difficulty, the PERCENTILE_CONT and PERCENTILE_DISC functions were introduced. These can be used both as window reporting functions as well as normal aggregate functions.
These functions need a sort specification and a parameter that takes a percentile value between 0 and 1. The sort specification is handled by using an ORDER BY clause with one expression. When used as a normal aggregate function, it returns a single value for each ordered set.
PERCENTILE_CONT, which is a continuous function computed by interpolation, and PERCENTILE_DISC, which is a step function that assumes discrete values. Like other aggregates, PERCENTILE_CONT and PERCENTILE_DISC operate on a group of rows in a grouped query, but with the following differences:
They require a parameter between 0 and 1 (inclusive). A parameter specified out of this range will result in error. This parameter should be specified as an expression that evaluates to a constant.
They require a sort specification. This sort specification is an ORDER BY clause with a single expression. Multiple expressions are not allowed.
[PERCENTILE_CONT | PERCENTILE_DISC]( constant expression )
WITHIN GROUP ( ORDER BY single order by expression
[ASC|DESC] [NULLS FIRST| NULLS LAST])
We use the following query to return the 17 rows of data used in the examples of this section:
SELECT cust_id, cust_credit_limit, CUME_DIST()
OVER (ORDER BY cust_credit_limit) AS CUME_DIST
FROM customers WHERE cust_city='Marshal';
CUST_ID CUST_CREDIT_LIMIT CUME_DIST
---------- ----------------- ----------
28344 1500 .173913043
8962 1500 .173913043
36651 1500 .173913043
32497 1500 .173913043
15192 3000 .347826087
102077 3000 .347826087
102343 3000 .347826087
8270 3000 .347826087
21380 5000 .52173913
13808 5000 .52173913
101784 5000 .52173913
30420 5000 .52173913
10346 7000 .652173913
31112 7000 .652173913
35266 7000 .652173913
3424 9000 .739130435
100977 9000 .739130435
103066 10000 .782608696
35225 11000 .956521739
14459 11000 .956521739
17268 11000 .956521739
100421 11000 .956521739
41496 15000 1
PERCENTILE_DISC(x) is computed by scanning up the CUME_DIST values in each group till you find the first one greater than or equal to x, where x is the specified percentile value. For the example query where PERCENTILE_DISC(0.5), the result is 5,000, as the following illustrates:
SELECT PERCENTILE_DISC(0.5) WITHIN GROUP
(ORDER BY cust_credit_limit) AS perc_disc, PERCENTILE_CONT(0.5) WITHIN GROUP
(ORDER BY cust_credit_limit) AS perc_cont
FROM customers WHERE cust_city='Marshal';
PERC_DISC PERC_CONT
--------- ---------
5000 5000
The result of PERCENTILE_CONT is computed by linear interpolation between rows after ordering them. To compute PERCENTILE_CONT(x), we first compute the row number = RN= (1+x*(n-1)), where n is the number of rows in the group and x is the specified percentile value. The final result of the aggregate function is computed by linear interpolation between the values from rows at row numbers CRN = CEIL(RN) and FRN = FLOOR(RN).
The final result will be: PERCENTILE_CONT(X) = if (CRN = FRN = RN), then (value of expression from row at RN) else (CRN - RN) * (value of expression for row at FRN) + (RN -FRN) * (value of expression for row at CRN).
Consider the previous example query, where we compute PERCENTILE_CONT(0.5). Here n is 17. The row number RN = (1 + 0.5*(n-1))= 9 for both groups. Putting this into the formula, (FRN=CRN=9), we return the value from row 9 as the result.
Another example is, if you want to compute PERCENTILE_CONT(0.66). The computed row number RN=(1 + 0.66*(n-1))= (1 + 0.66*16)= 11.67. PERCENTILE_CONT(0.66) = (12-11.67)*(value of row 11)+(11.67-11)*(value of row 12). These results are:
SELECT PERCENTILE_DISC(0.66) WITHIN GROUP
(ORDER BY cust_credit_limit) AS perc_disc, PERCENTILE_CONT(0.66) WITHIN GROUP
(ORDER BY cust_credit_limit) AS perc_cont
FROM customers WHERE cust_city='Marshal';
PERC_DISC PERC_CONT
---------- ----------
9000 8040
Inverse percentile aggregate functions can appear in the HAVING clause of a query like other existing aggregate functions.
You can also use the aggregate functions PERCENTILE_CONT, PERCENTILE_DISC as reporting aggregate functions. When used as reporting aggregate functions, the syntax is similar to those of other reporting aggregates.
[PERCENTILE_CONT | PERCENTILE_DISC](constant expression) WITHIN GROUP ( ORDER BY single order by expression [ASC|DESC] [NULLS FIRST| NULLS LAST]) OVER ( [PARTITION BY value expression [,...]] )
This query computes the same thing (median credit limit for customers in this result set, but reports the result for every row in the result set, as shown in the following output:
SELECT cust_id, cust_credit_limit, PERCENTILE_DISC(0.5) WITHIN GROUP
(ORDER BY cust_credit_limit) OVER () AS perc_disc,
PERCENTILE_CONT(0.5) WITHIN GROUP (ORDER BY cust_credit_limit)
OVER () AS perc_cont
FROM customers WHERE cust_city='Marshal';
CUST_ID CUST_CREDIT_LIMIT PERC_DISC PERC_CONT
---------- ----------------- ---------- ----------
28344 1500 5000 5000
8962 1500 5000 5000
36651 1500 5000 5000
32497 1500 5000 5000
15192 3000 5000 5000
102077 3000 5000 5000
102343 3000 5000 5000
8270 3000 5000 5000
21380 5000 5000 5000
13808 5000 5000 5000
101784 5000 5000 5000
30420 5000 5000 5000
10346 7000 5000 5000
31112 7000 5000 5000
35266 7000 5000 5000
3424 9000 5000 5000
100977 9000 5000 5000
103066 10000 5000 5000
35225 11000 5000 5000
14459 11000 5000 5000
17268 11000 5000 5000
100421 11000 5000 5000
41496 15000 5000 5000
For PERCENTILE_DISC, the expression in the ORDER BY clause can be of any data type that you can sort (numeric, string, date, and so on). However, the expression in the ORDER BY clause must be a numeric or datetime type (including intervals) because linear interpolation is used to evaluate PERCENTILE_CONT. If the expression is of type DATE, the interpolated result is rounded to the smallest unit for the type. For a DATE type, the interpolated value will be rounded to the nearest second, for interval types to the nearest second (INTERVAL DAY TO SECOND) or to the month(INTERVAL YEAR TO MONTH).
Like other aggregates, the inverse percentile functions ignore NULLs in evaluating the result. For example, when you want to find the median value in a set, Oracle Database ignores the NULLs and finds the median among the non-null values. You can use the NULLS FIRST/NULLS LAST option in the ORDER BY clause, but they will be ignored as NULLs are ignored.
These functions provide functionality useful for what-if analysis. As an example, what would be the rank of a row, if the row was hypothetically inserted into a set of other rows?
This family of aggregates takes one or more arguments of a hypothetical row and an ordered group of rows, returning the RANK, DENSE_RANK, PERCENT_RANK or CUME_DIST of the row as if it was hypothetically inserted into the group.
[RANK | DENSE_RANK | PERCENT_RANK | CUME_DIST]( constant expression [, ...] ) WITHIN GROUP ( ORDER BY order by expression [ASC|DESC] [NULLS FIRST|NULLS LAST][, ...] )
Here, constant expression refers to an expression that evaluates to a constant, and there may be more than one such expressions that are passed as arguments to the function. The ORDER BY clause can contain one or more expressions that define the sorting order on which the ranking will be based. ASC, DESC, NULLS FIRST, NULLS LAST options will be available for each expression in the ORDER BY.
Example 21-17 Hypothetical Rank and Distribution Example 1
Using the list price data from the products table used throughout this section, you can calculate the RANK, PERCENT_RANK and CUME_DIST for a hypothetical sweater with a price of $50 for how it fits within each of the sweater subcategories. The query and results are:
SELECT cust_city, RANK(6000) WITHIN GROUP (ORDER BY CUST_CREDIT_LIMIT DESC) AS HRANK, TO_CHAR(PERCENT_RANK(6000) WITHIN GROUP (ORDER BY cust_credit_limit),'9.999') AS HPERC_RANK, TO_CHAR(CUME_DIST (6000) WITHIN GROUP (ORDER BY cust_credit_limit),'9.999') AS HCUME_DIST FROM customers WHERE cust_city LIKE 'Fo%' GROUP BY cust_city; CUST_CITY HRANK HPERC_ HCUME_ ------------------------------ ---------- ------ ------ Fondettes 13 .455 .478 Fords Prairie 18 .320 .346 Forest City 47 .370 .378 Forest Heights 38 .456 .464 Forestville 58 .412 .418 Forrestcity 51 .438 .444 Fort Klamath 59 .356 .363 Fort William 30 .500 .508 Foxborough 52 .414 .420
Unlike the inverse percentile aggregates, the ORDER BY clause in the sort specification for hypothetical rank and distribution functions may take multiple expressions. The number of arguments and the expressions in the ORDER BY clause should be the same and the arguments must be constant expressions of the same or compatible type to the corresponding ORDER BY expression. The following is an example using two arguments in several hypothetical ranking functions.
Example 21-18 Hypothetical Rank and Distribution Example 2
SELECT prod_subcategory, RANK(10,8) WITHIN GROUP (ORDER BY prod_list_price DESC,prod_min_price) AS HRANK, TO_CHAR(PERCENT_RANK(10,8) WITHIN GROUP (ORDER BY prod_list_price, prod_min_price),'9.999') AS HPERC_RANK, TO_CHAR(CUME_DIST (10,8) WITHIN GROUP (ORDER BY prod_list_price, prod_min_price),'9.999') AS HCUME_DIST FROM products WHERE prod_subcategory LIKE 'Recordable%' GROUP BY prod_subcategory; PROD_SUBCATEGORY HRANK HPERC_ HCUME_ -------------------- ----- ------ ------ Recordable CDs 4 .571 .625 Recordable DVD Discs 5 .200 .333
These functions can appear in the HAVING clause of a query just like other aggregate functions. They cannot be used as either reporting aggregate functions or windowing aggregate functions.
The regression functions support the fitting of an ordinary-least-squares regression line to a set of number pairs. You can use them as both aggregate functions or windowing or reporting functions.
The functions are as follows:
Oracle applies the function to the set of (e1, e2) pairs after eliminating all pairs for which either of e1 or e2 is null. e1 is interpreted as a value of the dependent variable (a "y value"), and e2 is interpreted as a value of the independent variable (an "x value"). Both expressions must be numbers.
The regression functions are all computed simultaneously during a single pass through the data. They are frequently combined with the COVAR_POP, COVAR_SAMP, and CORR functions.
REGR_COUNT returns the number of non-null number pairs used to fit the regression line. If applied to an empty set (or if there are no (e1, e2) pairs where neither of e1 or e2 is null), the function returns 0.
REGR_AVGY and REGR_AVGX compute the averages of the dependent variable and the independent variable of the regression line, respectively. REGR_AVGY computes the average of its first argument (e1) after eliminating (e1, e2) pairs where either of e1 or e2 is null. Similarly, REGR_AVGX computes the average of its second argument (e2) after null elimination. Both functions return NULL if applied to an empty set.
The REGR_SLOPE function computes the slope of the regression line fitted to non-null (e1, e2) pairs.
The REGR_INTERCEPT function computes the y-intercept of the regression line. REGR_INTERCEPT returns NULL whenever slope or the regression averages are NULL.
The REGR_R2 function computes the coefficient of determination (usually called "R-squared" or "goodness of fit") for the regression line.
REGR_R2 returns values between 0 and 1 when the regression line is defined (slope of the line is not null), and it returns NULL otherwise. The closer the value is to 1, the better the regression line fits the data.
REGR_SXX, REGR_SYY and REGR_SXY functions are used in computing various diagnostic statistics for regression analysis. After eliminating (e1, e2) pairs where either of e1 or e2 is null, these functions make the following computations:
REGR_SXX: REGR_COUNT(e1,e2) * VAR_POP(e2) REGR_SYY: REGR_COUNT(e1,e2) * VAR_POP(e1) REGR_SXY: REGR_COUNT(e1,e2) * COVAR_POP(e1, e2)
Some common diagnostic statistics that accompany linear regression analysis are given in Table 21-2, "Common Diagnostic Statistics and Their Expressions ". Note that this release's new functions allow you to calculate all of these.
Table 21-2 Common Diagnostic Statistics and Their Expressions
| Type of Statistic | Expression |
|---|---|
| Adjusted R2 | 1-((1 - REGR_R2)*((REGR_COUNT-1)/(REGR_COUNT-2))) |
| Standard error | SQRT((REGR_SYY-(POWER(REGR_SXY,2)/REGR_SXX))/(REGR_COUNT-2)) |
| Total sum of squares | REGR_SYY |
| Regression sum of squares | POWER(REGR_SXY,2) / REGR_SXX |
| Residual sum of squares | REGR_SYY - (POWER(REGR_SXY,2)/REGR_SXX) |
| t statistic for slope | REGR_SLOPE * SQRT(REGR_SXX) / (Standard error) |
| t statistic for y-intercept | REGR_INTERCEPT / ((Standard error) * SQRT((1/REGR_COUNT)+(POWER(REGR_AVGX,2)/REGR_SXX)) |
In this example, we compute an ordinary-least-squares regression line that expresses the quantity sold of a product as a linear function of the product's list price. The calculations are grouped by sales channel. The values SLOPE, INTCPT, RSQR are slope, intercept, and coefficient of determination of the regression line, respectively. The (integer) value COUNT is the number of products in each channel for whom both quantity sold and list price data are available.
SELECT s.channel_id, REGR_SLOPE(s.quantity_sold, p.prod_list_price) SLOPE,
REGR_INTERCEPT(s.quantity_sold, p.prod_list_price) INTCPT,
REGR_R2(s.quantity_sold, p.prod_list_price) RSQR,
REGR_COUNT(s.quantity_sold, p.prod_list_price) COUNT,
REGR_AVGX(s.quantity_sold, p.prod_list_price) AVGLISTP,
REGR_AVGY(s.quantity_sold, p.prod_list_price) AVGQSOLD
FROM sales s, products p WHERE s.prod_id=p.prod_id
AND p.prod_category='Electronics' AND s.time_id=to_DATE('10-OCT-2000')
GROUP BY s.channel_id;
CHANNEL_ID SLOPE INTCPT RSQR COUNT AVGLISTP AVGQSOLD
---------- ---------- ---------- ---------- ---------- ---------- ----------
2 0 1 1 39 466.656667 1
3 0 1 1 60 459.99 1
4 0 1 1 19 526.305789 1
Instead of counting how often a given event occurs (for example, how often someone has purchased milk at the grocery), frequent itemsets provides a mechanism for counting how often multiple events occur together (for example, how often someone has purchased both milk and cereal together at the grocery store).
The input to the frequent-itemsets operation is a set of data that represents collections of items (itemsets). Some examples of itemsets could be all of the products that a given customer purchased in a single trip to the grocery store (commonly called a market basket), the web-pages that a user accessed in a single session, or the financial services that a given customer utilizes. The notion of a frequent itemset is to find those itemsets that occur most often. If you apply the frequent-itemset operator to a grocery store's point-of-sale data, you might, for example, discover that milk and bananas are the most commonly bought pair of items.
Frequent itemsets have thus been used in business intelligence environments for many years, with the most common one being for market basket analysis in the retail industry. Frequent itemsets are integrated with the database, operating on top of relational tables and accessed through SQL. This integration provides a couple of key benefits:
Applications that previously relied on frequent itemset operations now benefit from significantly improved performance as well as simpler implementation.
SQL-based applications that did not previously use frequent itemsets can now be easily extended to take advantage of this functionality.
Frequent itemsets analysis is performed with the PL/SQL package DBMS_FREQUENT_ITEMSETS. See PL/SQL Packages and Types Reference for more information.
Oracle introduces a set of SQL statistical functions and a statistics package, DBMS_STAT_FUNCS. This section lists some of the new functions along with basic syntax.
See PL/SQL Packages and Types Reference for detailed information about the DBMS_STAT_FUNCS package and Oracle Database SQL Reference for syntax and semantics.
You can calculate the following descriptive statistics:
Median of a Data Set
Median (expr) [OVER (query_partition_clause)]
Mode of a Data Set
STATS_MODE (expr)
You can calculate the following descriptive statistics:
One-Sample T-Test
STATS_T_TEST_ONE (expr1, expr2 (a constant) [, return_value])
Paired-Samples T-Test
STATS_T_TEST_PAIRED (expr1, expr2 [, return_value])
Independent-Samples T-Test. Pooled Variances
STATS_T_TEST_INDEP (expr1, expr2 [, return_value])
Independent-Samples T-Test, Unpooled Variances
STATS_T_TEST_INDEPU (expr1, expr2 [, return_value])
The F-Test
STATS_F_TEST (expr1, expr2 [, return_value])
One-Way ANOVA
STATS_ONE_WAY_ANOVA (expr1, expr2 [, return_value])
You can calculate crosstab statistics using the following syntax:
STATS_CROSSTAB (expr1, expr2 [, return_value])
Can return any one of the following:
Observed value of chi-squared
Significance of observed chi-squared
Degree of freedom for chi-squared
Phi coefficient, Cramer's V statistic
Contingency coefficient
Cohen's Kappa
You can calculate hypothesis statistics using the following syntax:
STATS_BINOMIAL_TEST (expr1, expr2, p [, return_value])
Binomial Test/Wilcoxon Signed Ranks Test
STATS_WSR_TEST (expr1, expr2 [, return_value])
Mann-Whitney Test
STATS_MW_TEST (expr1, expr2 [, return_value])
Kolmogorov-Smirnov Test
STATS_KS_TEST (expr1, expr2 [, return_value])
You can calculate the following parametric statistics:
Spearman's rho Coefficient
CORR_S (expr1, expr2 [, return_value])
Kendall's tau-b Coefficient
CORR_K (expr1, expr2 [, return_value])
In addition to the functions, this release has a new PL/SQL package, DBMS_STAT_FUNCS. It contains the descriptive statistical function SUMMARY along with functions to support distribution fitting. The SUMMARY function summarizes a numerical column of a table with a variety of descriptive statistics. The five distribution fitting functions support normal, uniform, Weibull, Poisson, and exponential distributions.
For a given expression, the WIDTH_BUCKET function returns the bucket number that the result of this expression will be assigned after it is evaluated. You can generate equiwidth histograms with this function. Equiwidth histograms divide data sets into buckets whose interval size (highest value to lowest value) is equal. The number of rows held by each bucket will vary. A related function, NTILE, creates equiheight buckets.
Equiwidth histograms can be generated only for numeric, date or datetime types. So the first three parameters should be all numeric expressions or all date expressions. Other types of expressions are not allowed. If the first parameter is NULL, the result is NULL. If the second or the third parameter is NULL, an error message is returned, as a NULL value cannot denote any end point (or any point) for a range in a date or numeric value dimension. The last parameter (number of buckets) should be a numeric expression that evaluates to a positive integer value; 0, NULL, or a negative value will result in an error.
Buckets are numbered from 0 to (n+1). Bucket 0 holds the count of values less than the minimum. Bucket(n+1) holds the count of values greater than or equal to the maximum specified value.
The WIDTH_BUCKET takes four expressions as parameters. The first parameter is the expression that the equiwidth histogram is for. The second and third parameters are expressions that denote the end points of the acceptable range for the first parameter. The fourth parameter denotes the number of buckets.
WIDTH_BUCKET(expression, minval expression, maxval expression, num buckets)
Consider the following data from table customers, that shows the credit limits of 17 customers. This data is gathered in the query shown in Example 21-19.
CUST_ID CUST_CREDIT_LIMIT
--------- -----------------
10346 7000
35266 7000
41496 15000
35225 11000
3424 9000
28344 1500
31112 7000
8962 1500
15192 3000
21380 5000
36651 1500
30420 5000
8270 3000
17268 11000
14459 11000
13808 5000
32497 1500
100977 9000
102077 3000
103066 10000
101784 5000
100421 11000
102343 3000
In the table customers, the column cust_credit_limit contains values between 1500 and 15000, and we can assign the values to four equiwidth buckets, numbered from 1 to 4, by using WIDTH_BUCKET (cust_credit_limit, 0, 20000, 4). Ideally each bucket is a closed-open interval of the real number line, for example, bucket number 2 is assigned to scores between 5000.0000 and 9999.9999..., sometimes denoted [5000, 10000) to indicate that 5,000 is included in the interval and 10,000 is excluded. To accommodate values outside the range [0, 20,000), values less than 0 are assigned to a designated underflow bucket which is numbered 0, and values greater than or equal to 20,000 are assigned to a designated overflow bucket which is numbered 5 (num buckets + 1 in general). See Figure 21-3 for a graphical illustration of how the buckets are assigned.
You can specify the bounds in the reverse order, for example, WIDTH_BUCKET (cust_credit_limit, 20000, 0, 4). When the bounds are reversed, the buckets will be open-closed intervals. In this example, bucket number 1 is (15000,20000], bucket number 2 is (10000,15000], and bucket number 4, is (0,5000]. The overflow bucket will be numbered 0 (20000, +infinity), and the underflow bucket will be numbered 5 (-infinity, 0].
It is an error if the bucket count parameter is 0 or negative.
Example 21-19 WIDTH_BUCKET
The following query shows the bucket numbers for the credit limits in the customers table for both cases where the boundaries are specified in regular or reverse order. We use a range of 0 to 20,000.
SELECT cust_id, cust_credit_limit,
WIDTH_BUCKET(cust_credit_limit,0,20000,4) AS WIDTH_BUCKET_UP,
WIDTH_BUCKET(cust_credit_limit,20000, 0, 4) AS WIDTH_BUCKET_DOWN
FROM customers WHERE cust_city = 'Marshal';
CUST_ID CUST_CREDIT_LIMIT WIDTH_BUCKET_UP WIDTH_BUCKET_DOWN
---------- ----------------- --------------- -----------------
10346 7000 2 3
35266 7000 2 3
41496 15000 4 2
35225 11000 3 2
3424 9000 2 3
28344 1500 1 4
31112 7000 2 3
8962 1500 1 4
15192 3000 1 4
21380 5000 2 4
36651 1500 1 4
30420 5000 2 4
8270 3000 1 4
17268 11000 3 2
14459 11000 3 2
13808 5000 2 4
32497 1500 1 4
100977 9000 2 3
102077 3000 1 4
103066 10000 3 3
101784 5000 2 4
100421 11000 3 2
102343 3000 1 4
Oracle offers a facility for creating your own functions, called user-defined aggregate functions. These functions are written in programming languages such as PL/SQL, Java, and C, and can be used as analytic functions or aggregates in materialized views. See Oracle Data Cartridge Developer's Guide for further information regarding syntax and restrictions.
The advantages of these functions are:
Highly complex functions can be programmed using a fully procedural language.
Higher scalability than other techniques when user-defined functions are programmed for parallel processing.
Object datatypes can be processed.
As a simple example of a user-defined aggregate function, consider the skew statistic. This calculation measures if a data set has a lopsided distribution about its mean. It will tell you if one tail of the distribution is significantly larger than the other. If you created a user-defined aggregate called udskew and applied it to the credit limit data in the prior example, the SQL statement and results might look like this:
SELECT USERDEF_SKEW(cust_credit_limit) FROM customers WHERE cust_city='Marshal'; USERDEF_SKEW ============ 0.583891
Before building user-defined aggregate functions, you should consider if your needs can be met in regular SQL. Many complex calculations are possible directly in SQL, particularly by using the CASE expression.
Staying with regular SQL will enable simpler development, and many query operations are already well-parallelized in SQL. Even the earlier example, the skew statistic, can be created using standard, albeit lengthy, SQL.
Oracle now supports simple and searched CASE statements. CASE statements are similar in purpose to the DECODE statement, but they offer more flexibility and logical power. They are also easier to read than traditional DECODE statements, and offer better performance as well. They are commonly used when breaking categories into buckets like age (for example, 20-29, 30-39, and so on). The syntax for simple statements is:
expr WHEN comparison_expr THEN return_expr [, WHEN comparison_expr THEN return_expr]...
The syntax for searched statements is:
WHEN condition THEN return_expr [, WHEN condition THEN return_expr]...
You can specify only 255 arguments and each WHEN ... THEN pair counts as two arguments. For a workaround to this limit, see Oracle Database SQL Reference.
Example 21-20 CASE
Suppose you wanted to find the average salary of all employees in the company. If an employee's salary is less than $2000, you want the query to use $2000 instead. Without a CASE statement, you would have to write this query as follows,
SELECT AVG(foo(e.sal)) FROM emps e;
In this, foo is a function that returns its input if the input is greater than 2000, and returns 2000 otherwise. The query has performance implications because it needs to invoke a function for each row. Writing custom functions can also add to the development load.
Using CASE expressions in the database without PL/SQL, this query can be rewritten as:
SELECT AVG(CASE when e.sal > 2000 THEN e.sal ELSE 2000 end) FROM emps e;
Using a CASE expression lets you avoid developing custom functions and can also perform faster.
You can use the CASE statement when you want to obtain histograms with user-defined buckets (both in number of buckets and width of each bucket). The following are two examples of histograms created with CASE statements. In the first example, the histogram totals are shown in multiple columns and a single row is returned. In the second example, the histogram is shown with a label column and a single column for totals, and multiple rows are returned.
Example 21-21 Histogram Example 1
SELECT SUM(CASE WHEN cust_credit_limit BETWEEN 0 AND 3999 THEN 1 ELSE 0 END)
AS "0-3999",
SUM(CASE WHEN cust_credit_limit BETWEEN 4000 AND 7999 THEN 1 ELSE 0 END)
AS "4000-7999",
SUM(CASE WHEN cust_credit_limit BETWEEN 8000 AND 11999 THEN 1 ELSE 0 END)
AS "8000-11999",
SUM(CASE WHEN cust_credit_limit BETWEEN 12000 AND 16000 THEN 1 ELSE 0 END)
AS "12000-16000"
FROM customers WHERE cust_city = 'Marshal';
0-3999 4000-7999 8000-11999 12000-16000
---------- ---------- ---------- -----------
8 7 7 1
Example 21-22 Histogram Example 2
SELECT (CASE WHEN cust_credit_limit BETWEEN 0 AND 3999 THEN ' 0 - 3999' WHEN cust_credit_limit BETWEEN 4000 AND 7999 THEN ' 4000 - 7999' WHEN cust_credit_limit BETWEEN 8000 AND 11999 THEN ' 8000 - 11999' WHEN cust_credit_limit BETWEEN 12000 AND 16000 THEN '12000 - 16000' END) AS BUCKET, COUNT(*) AS Count_in_Group FROM customers WHERE cust_city = 'Marshal' GROUP BY (CASE WHEN cust_credit_limit BETWEEN 0 AND 3999 THEN ' 0 - 3999' WHEN cust_credit_limit BETWEEN 4000 AND 7999 THEN ' 4000 - 7999' WHEN cust_credit_limit BETWEEN 8000 AND 11999 THEN ' 8000 - 11999' WHEN cust_credit_limit BETWEEN 12000 AND 16000 THEN '12000 - 16000' END); BUCKET COUNT_IN_GROUP ------------- -------------- 0 - 3999 8 4000 - 7999 7 8000 - 11999 7 12000 - 16000 1
Data is normally stored in sparse form. That is, if no value exists for a given combination of dimension values, no row exists in the fact table. However, you may want to view the data in dense form, with rows for all combination of dimension values displayed even when no fact data exist for them. For example, if a product did not sell during a particular time period, you may still want to see the product for that time period with zero sales value next to it. Moreover, time series calculations can be performed most easily when data is dense along the time dimension. This is because dense data will fill a consistent number of rows for each period, which in turn makes it simple to use the analytic windowing functions with physical offsets. Data densification is the process of converting spare data into dense form. To overcome the problem of sparsity, you can use a partitioned outer join to fill the gaps in a time series or any other dimension. Such a join extends the conventional outer join syntax by applying the outer join to each logical partition defined in a query. Oracle logically partitions the rows in your query based on the expression you specify in the PARTITION BY clause. The result of a partitioned outer join is a UNION of the outer joins of each of the partitions in the logically partitioned table with the table on the other side of the join. Note that you can use this type of join to fill the gaps in any dimension, not just the time dimension. Most of the examples here focus on the time dimension because it is the dimension most frequently used as a basis for comparisons.
The syntax for partitioned outer join extends the ANSI SQL JOIN clause with the phrase PARTITION BY followed by an expression list. The expressions in the list specify the group to which the outer join is applied. The following are the two forms of syntax normally used for partitioned outer join:
SELECT .....
FROM table_reference
PARTITION BY (expr [, expr ]... )
RIGHT OUTER JOIN table_reference
SELECT .....
FROM table_reference
LEFT OUTER JOIN table_reference
PARTITION BY {expr [,expr ]...)
Note that FULL OUTER JOIN is not supported with a partitioned outer join.
A typical situation with a sparse dimension is shown in the following example, which computes the weekly sales and year-to-date sales for the product Bounce for weeks 20-30 in 2000 and 2001:
SELECT SUBSTR(p.Prod_Name,1,15) Product_Name, t.Calendar_Year Year,
t.Calendar_Week_Number Week, SUM(Amount_Sold) Sales
FROM Sales s, Times t, Products p
WHERE s.Time_id = t.Time_id AND s.Prod_id = p.Prod_id AND
p.Prod_name IN ('Bounce') AND t.Calendar_Year IN (2000,2001) AND
t.Calendar_Week_Number BETWEEN 20 AND 30
GROUP BY p.Prod_Name, t.Calendar_Year, t.Calendar_Week_Number;
PRODUCT_NAME YEAR WEEK SALES
--------------- ---------- ---------- ----------
Bounce 2000 20 801
Bounce 2000 21 4062.24
Bounce 2000 22 2043.16
Bounce 2000 23 2731.14
Bounce 2000 24 4419.36
Bounce 2000 27 2297.29
Bounce 2000 28 1443.13
Bounce 2000 29 1927.38
Bounce 2000 30 1927.38
Bounce 2001 20 1483.3
Bounce 2001 21 4184.49
Bounce 2001 22 2609.19
Bounce 2001 23 1416.95
Bounce 2001 24 3149.62
Bounce 2001 25 2645.98
Bounce 2001 27 2125.12
Bounce 2001 29 2467.92
Bounce 2001 30 2620.17
In this example, we would expect 22 rows of data (11 weeks each from 2 years) if the data were dense. However we get only 18 rows because weeks 25 and 26 are missing in 2000, and weeks 26 and 28 in 2001.
We can take the sparse data of the preceding query and do a partitioned outer join with a dense set of time data. In the following query, we alias our original query as v and we select data from the times table, which we alias as t. Here we retrieve 22 rows because there are no gaps in the series. The four added rows each have 0 as their Sales value set to 0 by using the NVL function.
SELECT Product_Name, t.Year, t.Week, NVL(Sales,0) dense_sales
FROM
(SELECT SUBSTR(p.Prod_Name,1,15) Product_Name,
t.Calendar_Year Year, t.Calendar_Week_Number Week, SUM(Amount_Sold) Sales
FROM Sales s, Times t, Products p
WHERE s.Time_id = t.Time_id AND s.Prod_id = p.Prod_id AND
p.Prod_name IN ('Bounce') AND t.Calendar_Year IN (2000,2001) AND
t.Calendar_Week_Number BETWEEN 20 AND 30
GROUP BY p.Prod_Name, t.Calendar_Year, t.Calendar_Week_Number) v
PARTITION BY (v.Product_Name)
RIGHT OUTER JOIN
(SELECT DISTINCT Calendar_Week_Number Week, Calendar_Year Year
FROM Times
WHERE Calendar_Year IN (2000, 2001)
AND Calendar_Week_Number BETWEEN 20 AND 30) t
ON (v.week = t.week AND v.Year = t.Year)
ORDER BY t.year, t.week;
PRODUCT_NAME YEAR WEEK DENSE_SALES --------------- ---------- ---------- ----------- Bounce 2000 20 801 Bounce 2000 21 4062.24 Bounce 2000 22