| Oracle® Database Data Warehousing Guide 11g Release 2 (11.2) Part Number E10810-02 |
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| Oracle® Database Data Warehousing Guide 11g Release 2 (11.2) Part Number E10810-02 |
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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 and partitioned outer join. CASE expressions provide if-then logic useful in many situations. 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: |
|
Reporting |
Calculating shares, for example, market share. Works with these functions: |
|
|
Finding a value in a row a specified number of rows from a current row. |
|
|
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.
This section illustrates the basic analytic functions for ranking, windowing, and reporting.
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$,
RANK() OVER (ORDER BY SUM(amount_sold)) AS default_rank,
RANK() OVER (ORDER BY SUM(amount_sold) DESC NULLS LAST) AS custom_rank
FROM sales, products, customers, times, channels, countries
WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id
AND customers.country_id = countries.country_id AND sales.time_id=times.time_id
AND sales.channel_id=channels.channel_id
AND times.calendar_month_desc IN ('2000-09', '2000-10')
AND country_iso_code='US'
GROUP BY channel_desc;
CHANNEL_DESC SALES$ DEFAULT_RANK CUSTOM_RANK
-------------------- -------------- ------------ -----------
Direct Sales 1,320,497 3 1
Partners 800,871 2 2
Internet 261,278 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 in Example 21-3.
Example 21-3 RANK and DENSE_RANK
SELECT channel_desc, calendar_month_desc,
TO_CHAR(TRUNC(SUM(amount_sold),-5), '9,999,999,999') SALES$,
RANK() OVER (ORDER BY TRUNC(SUM(amount_sold),-5) DESC) AS RANK,
DENSE_RANK() OVER (ORDER BY TRUNC(SUM(amount_sold),-5) DESC) AS DENSE_RANK
FROM sales, products, customers, times, channels
WHERE sales.prod_id=products.prod_id
AND sales.cust_id=customers.cust_id
AND sales.time_id=times.time_id AND sales.channel_id=channels.channel_id
AND times.calendar_month_desc IN ('2000-09', '2000-10')
AND channels.channel_desc<>'Tele Sales'
GROUP BY channel_desc, calendar_month_desc;
CHANNEL_DESC CALENDAR SALES$ 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$, RANK() OVER (PARTITION BY channel_desc
ORDER BY SUM(amount_sold) DESC) AS RANK_BY_CHANNEL
FROM sales, products, customers, times, channels
WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id
AND sales.time_id=times.time_id AND sales.channel_id=channels.channel_id
AND times.calendar_month_desc IN ('2000-08', '2000-09', '2000-10', '2000-11')
AND channels.channel_desc IN ('Direct Sales', 'Internet')
GROUP BY channel_desc, calendar_month_desc;
CHANNEL_DESC CALENDAR SALES$ RANK_BY_CHANNEL
-------------------- -------- -------------- ---------------
Direct Sales 2000-08 1,236,104 1
Direct Sales 2000-10 1,225,584 2
Direct Sales 2000-09 1,217,808 3
Direct Sales 2000-11 1,115,239 4
Internet 2000-11 284,742 1
Internet 2000-10 239,236 2
Internet 2000-09 228,241 3
Internet 2000-08 215,107 4
8 rows selected.
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$, RANK() OVER (PARTITION BY calendar_month_desc
ORDER BY SUM(amount_sold) DESC) AS RANK_WITHIN_MONTH, RANK() OVER (PARTITION
BY channel_desc ORDER BY SUM(amount_sold) DESC) AS RANK_WITHIN_CHANNEL
FROM sales, products, customers, times, channels, countries
WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id
AND customers.country_id = countries.country_id AND sales.time_id=times.time_id
AND sales.channel_id=channels.channel_id
AND times.calendar_month_desc IN ('2000-08', '2000-09', '2000-10', '2000-11')
AND channels.channel_desc IN ('Direct Sales', 'Internet')
GROUP BY channel_desc, calendar_month_desc;
CHANNEL_DESC CALENDAR SALES$ 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 customers.country_id = countries.country_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
--------- ---------- ---------- ----------- ---------- ----------
25-JAN-99 3097.32 1 18 31 14
17-JAN-99 1791.77 2 19 30 13
30-JAN-99 127.69 3 20 29 12
28-JAN-99 120.34 4 21 28 11
23-JAN-99 86.12 5 22 27 10
20-JAN-99 79.07 6 23 26 9
13-JAN-99 56.1 7 24 25 8
07-JAN-99 42.97 8 25 24 7
08-JAN-99 33.81 9 26 23 6
10-JAN-99 22.76 10 27 21 4
02-JAN-99 22.76 10 27 21 4
26-JAN-99 19.84 12 29 20 3
16-JAN-99 11.27 13 30 19 2
14-JAN-99 9.52 14 31 18 1
09-JAN-99 15 1 1 15
12-JAN-99 15 1 1 15
31-JAN-99 15 1 1 15
11-JAN-99 15 1 1 15
19-JAN-99 15 1 1 15
03-JAN-99 15 1 1 15
15-JAN-99 15 1 1 15
21-JAN-99 15 1 1 15
24-JAN-99 15 1 1 15
04-JAN-99 15 1 1 15
06-JAN-99 15 1 1 15
27-JAN-99 15 1 1 15
18-JAN-99 15 1 1 15
01-JAN-99 15 1 1 15
22-JAN-99 15 1 1 15
29-JAN-99 15 1 1 15
05-JAN-99 15 1 1 15
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 four 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 2001-10 1,000,000 1
Direct Sales 2001-09 1,100,000 2
Internet 2001-09 500,000 3
Partners 2001-09 600,000 4
Partners 2001-10 600,000 5
Internet 2001-10 700,000 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. With windowing aggregate functions, you can calculate moving and cumulative versions of SUM, AVERAGE, COUNT, MAX, MIN, and many more functions. They can be used only in the SELECT and ORDER BY clauses of the query. Windowing aggregate functions include the convenient 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:
analytic_function([ arguments ])
OVER (analytic_clause)
where analytic_clause =
[ query_partition_clause ]
[ order_by_clause [ windowing_clause ] ]
and query_partition_clause =
PARTITION BY
{ value_expr[, value_expr ]...
}
and windowing_clause =
{ 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
}
}
Note that the DISTINCT keyword is not supported in windowing functions except for MAX and MIN.
See Also:
Oracle Database SQL Language Reference for further information regarding syntax and restrictionsWindow 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.
An analytic function that uses the RANGE keyword can use multiple sort keys in its ORDER BY clause if it specifies either of these two windows:
RANGE BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW. The short form of this is RANGE UNBOUNDED PRECEDING, which can also be used.
RANGE BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING.
Window boundaries that do not meet these conditions can have only one sort key in the analytic function's ORDER BY clause.
Example 21-7 Cumulative Aggregate Function
The following is an example of cumulative amount_sold by customer ID by quarter in 2000:
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 c.country_id = countries.country_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 7 7 /* 7 */ 10-MAY-00 1 9 /* 7 + (1+1) */ 10-MAY-00 1 9 /* 7 + (1+1) */ 11-MAY-00 2 15 /* 7 + (1+1) + (2+4) */ 11-MAY-00 4 15 /* 7 + (1+1) + (2+4) */ 12-MAY-00 1 16 /* 7 + (1+1) + (2+4) + 1 */ 13-MAY-00 2 23 /* 7 + (1+1) + (2+4) + 1 + (5+2) */ 13-MAY-00 5 23 /* 7 + (1+1) + (2+4) + 1 + (5+2) */
In the output of this example, all dates except May 6 and May 12 return two rows. 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.
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.
The LAG and LEAD functions can be thought of as being related to, and a simplification of, the NTH_VALUE function. With LAG and LEAD, you can only retrieve values from a row at the specified physical offset. If this is insufficient, you can use NTH_VALUE, which enables you to retrieve values from a row based on what is called a logical offset or relative position. You can use the IGNORE NULLS option with the NTH_VALUE function to make it more useful, in the sense that you can specify conditions and filter out rows based on certain conditions. See Example 21-17, "NTH_VALUE", where rows with quantities less than eight are filtered out. This cannot be done with LAG or LEAD, as you would not know the offset to the row.
See "NTH_VALUE Function" and Oracle Database SQL Language Reference for more information.
These functions have the following syntax:
{LAG | LEAD} ( value_expr [, offset] [, default] ) [RESPECT NULLS|IGNORE NULLS]
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. When IGNORE NULLS is specified, the value returned will be from a row at a specified lag or lead offset after ignoring rows with NULLs.
Example 21-14 LAG/LEAD
This example illustrates a typical case of using LAG and 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.
Example 21-15 LAG/LEAD Using IGNORE NULLS
This example illustrates a typical case of using LAG and LEAD with the IGNORE NULLS option:
SELECT prod_id, channel_id, SUM(quantity_sold) quantity,
CASE WHEN SUM(quantity_sold) < 5000 THEN SUM(amount_sold) ELSE NULL END amount,
LAG(CASE WHEN SUM(quantity_sold) < 5000 THEN SUM(amount_sold) ELSE NULL END)
IGNORE NULLS OVER (PARTITION BY prod_id ORDER BY channel_id) lag
FROM sales
WHERE prod_id IN (18,127,138)
GROUP BY prod_id, channel_id;
PROD_ID CHANNEL_ID QUANTITY AMOUNT LAG
-------- ---------- -------- ----------- ----------
18 2 2888 4420923.94
18 3 5615 4420923.94
18 4 1088 1545729.81 4420923.94
127 2 4508 274088.08
127 3 9626 274088.08
127 4 1850 173682.67 274088.08
138 2 1120 127390.3
138 3 3878 393111.15 127390.3
138 4 543 71203.21 393111.15
9 rows selected.
This section illustrates the FIRST_VALUE, LAST_VALUE, and NTH_VALUE functions.
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?"
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.
These functions have syntax as follows:
FIRST_VALUE|LAST_VALUE ( <expr> ) [RESPECT NULLS|IGNORE NULLS] OVER (analytic clause );
Example 21-16 FIRST_VALUE
This example illustrates using the IGNORE NULLS option with FIRST_VALUE:
SELECT prod_id, channel_id, time_id,
CASE WHEN MIN(amount_sold) > 9.5
THEN MIN(amount_sold) ELSE NULL END amount_sold,
FIRST_VALUE(CASE WHEN MIN(amount_sold) > 9.5
THEN min(amount_sold) ELSE NULL END)
IGNORE NULLS OVER (PARTITION BY prod_id
ORDER BY channel_id DESC, time_id
ROWS BETWEEN UNBOUNDED PRECEDING
AND UNBOUNDED FOLLOWING) nv FROM sales
WHERE prod_id = 115 AND time_id BETWEEN '18-DEC-01'
AND '22-DEC-01' GROUP BY prod_id, channel_id, time_id
ORDER BY prod_id;
PROD_ID CHANNEL_ID TIME_ID AMOUNT_SOLD NV
---------- ---------- --------- ----------- ----------
115 4 18-DEC-01 9.66
115 4 19-DEC-01 9.66
115 4 20-DEC-01 9.66
115 4 22-DEC-01 9.66
115 3 18-DEC-01 9.66 9.66
115 3 19-DEC-01 9.66 9.66
115 3 20-DEC-01 9.66 9.66
115 3 21-DEC-01 9.66 9.66
115 3 22-DEC-01 9.66 9.66
115 2 18-DEC-01 9.67 9.66
115 2 19-DEC-01 9.67 9.66
115 2 21-DEC-01 9.67 9.66
115 2 22-DEC-01 9.67 9.66
13 rows selected.
The NTH_VALUE function enables you to find column values from an arbitrary row in the window. This could be used when, for example, you want to retrieve the 5th highest closing price for a company's shares during a year.
The LAG and LEAD functions can be thought of as being related to, and a simplification of, the NTH_VALUE function. With LAG and LEAD, you can only retrieve values from a row at the specified physical offset. If this is insufficient, you can use NTH_VALUE, which enables you to retrieve values from a row based on what is called a logical offset or relative position. You can use the IGNORE NULLS option with the NTH_VALUE, FIRST_VALUE, and LAST_VALUE functions to make it more powerful, in the sense that you can specify conditions and filter out rows based on certain conditions. See Example 21-17, "NTH_VALUE", where rows with quantities less than eight are filtered out. This cannot be done with LAG or LEAD, as you would not know the offset to the row.
See Oracle Database SQL Language Reference for more information.
This function has syntax as follows:
NTH_VALUE (<expr>, <n expr>) [FROM FIRST | FROM LAST] [RESPECT NULLS | IGNORE NULLS] OVER (<window specification>)
expr can be a column, constant, bind variable, or an expression involving them.
n can be a column, constant, bind variable, or an expression involving them.
RESPECT NULLS is the default NULL handling mechanism. It determines whether null values of expr are included in or eliminated from the calculation. The default is RESPECT NULLS.
The FROM FIRST and FROM LAST options determine whether the offset n is from the first or last row. The default is FROM FIRST.
IGNORE NULLS enables you to skip NULLs in measure values.
Example 21-17 NTH_VALUE
The following example returns the amount_sold value of the second channel_id in ascending order for each prod_id in the range between 10 and 20:
SELECT prod_id, channel_id, MIN(amount_sold),
NTH_VALUE(MIN(amount_sold), 2) OVER (PARTITION BY prod_id ORDER BY channel_id
ROWS BETWEEN UNBOUNDED PRECEDING AND UNBOUNDED FOLLOWING) NV
FROM sales
WHERE prod_id BETWEEN 10 AND 20 GROUP BY prod_id, channel_id;
PROD_ID CHANNEL_ID MIN(AMOUNT_SOLD) NV
---------- ---------- ---------------- ----------
13 2 907.34 906.2
13 3 906.2 906.2
13 4 842.21 906.2
14 2 1015.94 1036.72
14 3 1036.72 1036.72
14 4 935.79 1036.72
15 2 871.19 871.19
15 3 871.19 871.19
15 4 871.19 871.19
16 2 266.84 266.84
16 3 266.84 266.84
16 4 266.84 266.84
16 9 11.99 266.84
...
This section illustrates the following advanced analytic aggregate functions:
The LISTAGG function orders data within each group based on the ORDER BY clause and then concatenates the values of the measure column. Its syntax is as follows:
LISTAGG (<expr> [, <delimiter>) WITHIN GROUP (ORDER BY <oby_expression_list>)
expr can be a column, constant, bind variable, or an expression involving them.
delimiter can be a column, constant, bind variable, or an expression involving them.
oby_expression_list can be a list of expressions with optional ordering options to sort in ascending or descending order (ASC or DESC), and to control the sort order of NULLs (NULLS FIRST or NULLS LAST). ASCENDING and NULLS LAST are the defaults.
You can use the LISTAGG function as an aggregate.
Example 21-18 LISTAGG as Aggregate
The following example illustrates using LISTAGG as an aggregate.
SELECT prod_id, LISTAGG(cust_first_name||' '||cust_last_name, '; ')
WITHIN GROUP (ORDER BY amount_sold DESC) cust_list
FROM sales, customers
WHERE sales.cust_id = customers.cust_id AND cust_gender = 'M'
AND cust_credit_limit = 15000 AND prod_id BETWEEN 15 AND 18
AND channel_id = 2 AND time_id > '01-JAN-01'
GROUP BY prod_id;
PROD_ID CUST_LIST
------- -----------------------------------------------
15 Hope Haarper; Roxanne Crocker; ... Mason Murray
16 Manvil Austin; Bud Pinkston; ... Helga Nickols
17 Opal Aaron; Thacher Rudder; ... Roxanne Crocker
18 Boyd Lin; Bud Pinkston; ... Erik Ready
The output has been modified for readability.
You can use the LISTAGG function as a reporting aggregate.
Example 21-19 LISTAGG as Reporting Aggregate
This example illustrates using LISTAGG as a reporting aggregate:
connect sh/sh set lines 120 pages 20000 column list format A40 SELECT time_id, prod_id, MIN(amount_sold), LISTAGG(min(amount_sold),';') WITHIN GROUP (ORDER BY prod_id) OVER (PARTITION BY time_id) cust_list FROM sales WHERE time_id > '20-DEC-01' AND prod_id BETWEEN 120 AND 125 GROUP BY prod_id, time_id; TIME_ID PROD_ID MIN(AMOUNT_SOLD) CUST_LIST ------- ------- ---------------- ----------- 21-DEC-01 120 51.36 51.36;10.81 21-DEC-01 121 10.81 51.36;10.81 22-DEC-01 120 51.36 51.36;10.81;20.23;56.12;17.79;15.67 22-DEC-01 121 10.81 51.36;10.81;20.23;56.12;17.79;15.67 22-DEC-01 122 20.23 51.36;10.81;20.23;56.12;17.79;15.67 22-DEC-01 123 56.12 51.36;10.81;20.23;56.12;17.79;15.67 22-DEC-01 124 17.79 51.36;10.81;20.23;56.12;17.79;15.67 22-DEC-01 125 15.67 51.36;10.81;20.23;56.12;17.79;15.67 ...
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 21-20 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 21-20 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 21-21 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 as "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 performs the same computation (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 21-22 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 21-23 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 regression 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 |
|
|
Standard error |
|
|
Total sum of squares |
|
|
Regression sum of squares |
|
|
Residual sum of squares |
|
|
t statistic for slope |
|
|
t statistic for y-intercept |
|
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
Oracle provides 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 Oracle Database PL/SQL Packages and Types Reference for detailed information about the DBMS_STAT_FUNCS package and Oracle Database SQL Language 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 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.
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 Database 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.
The data returned by business intelligence queries is often most usable if presented in a crosstabular format. The pivot_clause of the SELECT statement lets you write crosstabulation queries that rotate rows into columns, aggregating data in the process of the rotation. Pivoting is a key technique in data warehouses. In it, you transform multiple rows of input into fewer and generally wider rows in the data warehouse. When pivoting, an aggregation operator is applied for each item in the pivot column value list. The pivot column cannot contain an arbitrary expression. If you need to pivot on an expression, then you should alias the expression in a view before the PIVOT operation. The basic syntax is as follows:
SELECT ....
FROM <table-expr>
PIVOT
(
aggregate-function(<column>)
FOR <pivot-column> IN (<value1>, <value2>,..., <valuen>)
) AS <alias>
WHERE .....
See Oracle Database SQL Language Reference for pivot_clause syntax.
To illustrate the use of pivoting, create the following view as a basis for later examples:
CREATE VIEW sales_view AS SELECT prod_name product, country_name country, channel_id channel, SUBSTR(calendar_quarter_desc, 6,2) quarter, SUM(amount_sold) amount_sold, SUM(quantity_sold) quantity_sold FROM sales, times, customers, countries, products WHERE sales.time_id = times.time_id AND sales.prod_id = products.prod_id AND sales.cust_id = customers.cust_id AND customers.country_id = countries.country_id GROUP BY prod_name, country_name, channel_id, SUBSTR(calendar_quarter_desc, 6, 2);
The following statement illustrates a typical pivot on the channel column:
SELECT * FROM
(SELECT product, channel, amount_sold
FROM sales_view
) S PIVOT (SUM(amount_sold)
FOR CHANNEL IN (3 AS DIRECT_SALES, 4 AS INTERNET_SALES,
5 AS CATALOG_SALES, 9 AS TELESALES))
ORDER BY product;
PRODUCT DIRECT_SALES INTERNET_SALES CATALOG_SALES TELESALES
---------------------- ------------ -------------- ------------- ---------
...
Internal 6X CD-ROM 229512.97 26249.55
Internal 8X CD-ROM 286291.49 42809.44
Keyboard Wrist Rest 200959.84 38695.36 1522.73
...
Note that the output has created four new aliased columns, DIRECT_SALES, INTERNET_SALES, CATALOG_SALES, and TELESALES, one for each of the pivot values. The output is a sum. If no alias is provided, the column heading will be the values of the IN-list.
You can pivot on more than one column. The following statement illustrates a typical multiple column pivot:
SELECT *
FROM
(SELECT product, channel, quarter, quantity_sold
FROM sales_view
) PIVOT (SUM(quantity_sold)
FOR (channel, quarter) IN
((5, '02') AS CATALOG_Q2,
(4, '01') AS INTERNET_Q1,
(4, '04') AS INTERNET_Q4,
(2, '02') AS PARTNERS_Q2,
(9, '03') AS TELE_Q3
)
);
PRODUCT CATALOG_Q2 INTERNET_Q1 INTERNET_Q4 PARTNERS_Q2 TELE_Q3
------- ---------- ----------- ----------- ----------- -------
...
Bounce 347 632 954
...
Smash Up Boxing 129 280 560
...
Comic Book Heroes 47 155 275
...
Note that this example specifies a multi-column IN-list with column headings designed to match the IN-list members.
You can pivot with multiple aggregates, as shown in the following example:
SELECT *
FROM
(SELECT product, channel, amount_sold, quantity_sold
FROM sales_view
) PIVOT (SUM(amount_sold) AS sums,
SUM(quantity_sold) AS sumq
FOR channel IN (5, 4, 2, 9)
)
ORDER BY product;
PRODUCT 5_SUMS 5_SUMQ 4_SUMS 4_SUMQ 2_SUMS 2_SUMQ 9_SUMS 9_SUMQ ------------- ------ ------ ------ ------ ------ ------ ------ ------ O/S Doc Set English 142780.36 3081 381397.99 8044 6028.66 134 O/S Doc Set French 55503.58 1192 132000.77 2782 ...
Note that the query creates column headings by concatenating the pivot values (or alias) with the alias of the aggregate function, plus an underscore.
You can distinguish between null values that are generated from the use of PIVOT and those that exist in the source data. The following example illustrates nulls that PIVOT generates.
The following query returns rows with 5 columns, column prod_id, and pivot resulting columns Q1, Q1_COUNT_TOTAL, Q2, Q2_COUNT_TOTAL. For each unique value of prod_id, Q1_COUNT_TOTAL returns the total number of rows whose qtr value is Q1, that is, and Q2_COUNT_TOTAL returns the total number of rows whose qtr value is Q2.
Assume we have a table sales2 of the following structure:
PROD_ID QTR AMOUNT_SOLD
------- --- -----------
100 Q1 10
100 Q1 20
100 Q2 NULL
200 Q1 50
SELECT *
FROM sales2
PIVOT
( SUM(amount_sold), COUNT(*) AS count_total
FOR qtr IN ('Q1', 'Q2')
);
PROD_ID "Q1" "Q1_COUNT_TOTAL" "Q2" "Q2_COUNT_TOTAL"
------- ---- ---------------- --------- ----------------
100 20 2 NULL <1> 1
200 50 1 NULL <2> 0
From the result, we know that for prod_id 100, there are 2 sales rows for quarter Q1, and 1 sales row for quarter Q2; for prod_id 200, there is 1 sales row for quarter Q1, and no sales row for quarter Q2.So, in Q2_COUNT_TOTAL, you can identify that NULL<1> comes from a row in the original table whose measure is of null value, while NULL<2> is due to no row being present in the original table for prod_id 200 in quarter Q2.
An unpivot does not reverse a PIVOT operation. Instead, it rotates data from columns into rows. If you are working with pivoted data, an UNPIVOT operation cannot reverse any aggregations that have been made by PIVOT or any other means.
To illustrate unpivoting, first create a pivoted table that includes four columns, for quarters of the year:
CREATE TABLE pivotedTable AS
SELECT *
FROM (SELECT product, quarter, quantity_sold
FROM sales_view
)
PIVOT
(
SUM(quantity_sold)
FOR quarter IN ('01' AS Q1, '02' AS Q2, '03' AS Q3, '04' AS Q4));
The table's contents are the following:
SELECT * FROM pivotedTable ORDER BY product; PRODUCT Q1 Q2 Q3 Q4 ------- ---- ---- ---- ---- Finding Fido 1274 1671 1618 1605 Fly Fishing 716 918 1209 1248 ...
The following UNPIVOT operation will rotate the quarter columns into rows. For each product, there will be four rows, one for each quarter.
SELECT *
FROM pivotedTable
UNPIVOT INCLUDE NULLS
(
quantity_sold
FOR quarter IN (Q1, Q2, Q3, Q4))
ORDER BY product, quarter;
PRODUCT QU QUANTITY_SOLD
------- -- -------------
256MB Memory Card Q1 1179
256MB Memory Card Q2 1533
256MB Memory Card Q3 1455
256MB Memory Card Q4 1374
...
64MB Memory Card Q1 414
64MB Memory Card Q2 215
64MB Memory Card Q3
64MB Memory Card Q4 81
...
Note the use of INCLUDE NULLS in this example. You can also use EXCLUDE NULLS, which is the default setting.
If you want to use a wildcard argument or subquery in your pivoting columns, you can do so with PIVOT XML syntax. With PIVOT XML, the output of the operation is properly formatted XML.
The following example illustrates using the wildcard keyword, ANY. It will output XML that includes all channel values in sales_view:
SELECT *
FROM
(SELECT product, channel, quantity_sold
FROM sales_view
) PIVOT XML(SUM(quantity_sold)
FOR channel IN (ANY)
);
Note that the keyword ANY is available in PIVOT operations only as part of an XML operation. This output includes data for cases where the channel exists in the data set. Also note that aggregation functions must specify a GROUP BY clause to return multiple values, yet the pivot_clause does not contain an explicit GROUP BY clause. Instead, the pivot_clause performs an implicit GROUP BY.
The following example illustrates using a subquery. It will output XML that includes all channel values and the sales data corresponding to each channel:
SELECT *
FROM
(SELECT product, channel, quantity_sold
FROM sales_view
) PIVOT XML(SUM(quantity_sold)
FOR channel IN (SELECT DISTINCT channel_id FROM CHANNELS)
);
The output densifies the data to include all possible channels for each product.
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 sparse 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 2043.16 Bounce 2000 23 2731.14 Bounce 2000 24 4419.36 Bounce 2000 25 0 Bounce 2000 26 0 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 26 0 Bounce 2001 27 2125.12 Bounce 2001 28 0 Bounce 2001 29 2467.92 Bounce 2001 30 2620.17
Note that in this query, a WHERE condition was placed for weeks between 20 and 30 in the inline view for the time dimension. This was introduced to keep the result set small.
N-dimensional data is typically displayed as a dense 2-dimensional cross tab of (n - 2) page dimensions. This requires that all dimension values for the two dimensions appearing in the cross tab be filled in. The following is another example where the partitioned outer join capability can be used for filling the gaps on two dimensions:
WITH v1 AS
(SELECT p.prod_id, country_id, calendar_year,
SUM(quantity_sold) units, SUM(amount_sold) sales
FROM sales s, products p, customers c, times t
WHERE s.prod_id in (147, 148) AND t.time_id = s.time_id AND
c.cust_id = s.cust_id AND p.prod_id = s.prod_id
GROUP BY p.prod_id, country_id, calendar_year),
v2 AS --countries to use for densifications
(SELECT DISTINCT country_id
FROM customers
WHERE country_id IN (52782, 52785, 52786, 52787, 52788)),
v3 AS --years to use for densifications
(SELECT DISTINCT calendar_year FROM times)
SELECT v4.prod_id, v4.country_id, v3.calendar_year, units, sales
FROM
(SELECT prod_id, v2.country_id, calendar_year, units, sales
FROM v1 PARTITION BY (prod_id)
RIGHT OUTER JOIN v2 --densifies on country
ON (v1.country_id = v2.country_id)) v4
PARTITION BY (prod_id,country_id)
RIGHT OUTER JOIN v3 --densifies on year
ON (v4.calendar_year = v3.calendar_year)
ORDER BY 1, 2, 3;
In this query, the WITH subquery factoring clause v1 summarizes sales data at the product, country, and year level. This result is sparse but users may want to see all the country, year combinations for each product. To achieve this, we take each partition of v1 based on product values and outer join it on the country dimension first. This will give us all values of country for each product. We then take that result and partition it on product and country values and then outer join it on time dimension. This will give us all time values for each product and country combination.
PROD_ID COUNTRY_ID CALENDAR_YEAR UNITS SALES
---------- ---------- ------------- ---------- ----------
147 52782 1998
147 52782 1999 29 209.82
147 52782 2000 71 594.36
147 52782 2001 345 2754.42
147 52782 2002
147 52785 1998 1 7.99
147 52785 1999
147 52785 2000
147 52785 2001
147 52785 2002
147 52786 1998 1 7.99
147 52786 1999
147 52786 2000 2 15.98
147 52786 2001
147 52786 2002
147 52787 1998
147 52787 1999
147 52787 2000
147 52787 2001
147 52787 2002
147 52788 1998
147 52788 1999
147 52788 2000 1 7.99
147 52788 2001
147 52788 2002
148 52782 1998 139 4046.67
148 52782 1999 228 5362.57
148 52782 2000 251 5629.47
148 52782 2001 308 7138.98
148 52782 2002
148 52785 1998
148 52785 1999
148 52785 2000
148 52785 2001
148 52785 2002
148 52786 1998
148 52786 1999
148 52786 2000
148 52786 2001
148 52786 2002
148 52787 1998
148 52787 1999
148 52787 2000
148 52787 2001
148 52787 2002
148 52788 1998 4 117.23
148 52788 1999
148 52788 2000
148 52788 2001
148 52788 2002
An inventory table typically tracks quantity of units available for various products. This table is sparse: it only stores a row for a product when there is an event. For a sales table, the event is a sale, and for the inventory table, the event is a change in quantity available for a product. For example, consider the following inventory table:
CREATE TABLE invent_table (
product VARCHAR2(10),
time_id DATE,
quant NUMBER);
INSERT INTO invent_table VALUES
('bottle', TO_DATE('01/04/01', 'DD/MM/YY'), 10);
INSERT INTO invent_table VALUES
('bottle', TO_DATE('06/04/01', 'DD/MM/YY'), 8);
INSERT INTO invent_table VALUES
('can', TO_DATE('01/04/01', 'DD/MM/YY'), 15);
INSERT INTO invent_table VALUES
('can', TO_DATE('04/04/01', 'DD/MM/YY'), 11);
The inventory table now has the following rows:
PRODUCT TIME_ID QUANT ---------- --------- ----- bottle 01-APR-01 10 bottle 06-APR-01 8 can 01-APR-01 15 can 04-APR-01 11
For reporting purposes, users may want to see this inventory data differently. For example, they may want to see all values of time for each product. This can be accomplished using partitioned outer join. In addition, for the newly inserted rows of missing time periods, users may want to see the values for quantity of units column to be carried over from the most recent existing time period. The latter can be accomplished using analytic window function LAST_VALUE value. Here is the query and the desired output:
WITH v1 AS
(SELECT time_id
FROM times
WHERE times.time_id BETWEEN
TO_DATE('01/04/01', 'DD/MM/YY')
AND TO_DATE('07/04/01', 'DD/MM/YY'))
SELECT product, time_id, quant quantity,
LAST_VALUE(quant IGNORE NULLS)
OVER (PARTITION BY product ORDER BY time_id)
repeated_quantity
FROM
(SELECT product, v1.time_id, quant
FROM invent_table PARTITION BY (product)
RIGHT OUTER JOIN v1
ON (v1.time_id = invent_table.time_id))
ORDER BY 1, 2;
The inner query computes a partitioned outer join on time within each product. The inner query densifies the data on the time dimension (meaning the time dimension will now have a row for each day of the week). However, the measure column quantity will have nulls for the newly added rows (see the output in the column quantity in the following results.
The outer query uses the analytic function LAST_VALUE. Applying this function partitions the data by product and orders the data on the time dimension column (time_id). For each row, the function finds the last non-null value in the window due to the option IGNORE NULLS, which you can use with both LAST_VALUE and FIRST_VALUE. We see the desired output in the column repeated_quantity in the following output:
PRODUCT TIME_ID QUANTITY REPEATED_QUANTITY ---------- --------- -------- ----------------- bottle 01-APR-01 10 10 bottle 02-APR-01 10 bottle 03-APR-01 10 bottle 04-APR-01 10 bottle 05-APR-01 10 bottle 06-APR-01 8 8 bottle 07-APR-01 8 can 01-APR-01 15 15 can 02-APR-01 15 can 03-APR-01 15 can 04-APR-01 11 11 can 05-APR-01 11 can 06-APR-01 11 can 07-APR-01 11
Examples in previous section illustrate how to use partitioned outer join to fill gaps in one or more dimensions. However, the result sets produced by partitioned outer join have null values for columns that are not included in the PARTITION BY list. Typically, these are measure columns. Users can make use of analytic SQL functions to replace those null values with a non-null value.
For example, the following query computes monthly totals for products 64MB Memory card and DVD-R Discs (product IDs 122 and 136) for the year 2000. It uses partitioned outer join to densify data for all months. For the missing months, it then uses the analytic SQL function AVG to compute the sales and units to be the average of the months when the product was sold.
If working in SQL*Plus, the following two commands will wrap the column headings for greater readability of results:
col computed_units heading 'Computed|_units'
col computed_sales heading 'Computed|_sales'
WITH V AS
(SELECT substr(p.prod_name,1,12) prod_name, calendar_month_desc,
SUM(quantity_sold) units, SUM(amount_sold) sales
FROM sales s, products p, times t
WHERE s.prod_id IN (122,136) AND calendar_year = 2000
AND t.time_id = s.time_id
AND p.prod_id = s.prod_id
GROUP BY p.prod_name, calendar_month_desc)
SELECT v.prod_name, calendar_month_desc, units, sales,
NVL(units, AVG(units) OVER (partition by v.prod_name)) computed_units,
NVL(sales, AVG(sales) OVER (partition by v.prod_name)) computed_sales
FROM
(SELECT DISTINCT calendar_month_desc
FROM times
WHERE calendar_year = 2000) t
LEFT OUTER JOIN V
PARTITION BY (prod_name)
USING (calendar_month_desc);
computed computed
PROD_NAME CALENDAR UNITS SALES _units _sales
------------ -------- ---------- ---------- ---------- ----------
64MB Memory 2000-01 112 4129.72 112 4129.72
64MB Memory 2000-02 190 7049 190 7049
64MB Memory 2000-03 47 1724.98 47 1724.98
64MB Memory 2000-04 20 739.4 20 739.4
64MB Memory 2000-05 47 1738.24 47 1738.24
64MB Memory 2000-06 20 739.4 20 739.4
64MB Memory 2000-07 72.6666667 2686.79
64MB Memory 2000-08 72.6666667 2686.79
64MB Memory 2000-09 72.6666667 2686.79
64MB Memory 2000-10 72.6666667 2686.79
64MB Memory 2000-11 72.6666667 2686.79
64MB Memory 2000-12 72.6666667 2686.79
DVD-R Discs, 2000-01 167 3683.5 167 3683.5
DVD-R Discs, 2000-02 152 3362.24 152 3362.24
DVD-R Discs, 2000-03 188 4148.02 188 4148.02
DVD-R Discs, 2000-04 144 3170.09 144 3170.09
DVD-R Discs, 2000-05 189 4164.87 189 4164.87
DVD-R Discs, 2000-06 145 3192.21 145 3192.21
DVD-R Discs, 2000-07 124.25 2737.71
DVD-R Discs, 2000-08 124.25 2737.71
DVD-R Discs, 2000-09 1 18.91 1 18.91
DVD-R Discs, 2000-10 124.25 2737.71
DVD-R Discs, 2000-11 124.25 2737.71
DVD-R Discs, 2000-12 8 161.84 8 161.84
Densification is not just for reporting purpose. It also enables certain types of calculations, especially, time series calculations. Time series calculations are easier when data is dense along the time dimension. Dense data has a consistent number of rows for each time periods which in turn make it simple to use analytic window functions with physical offsets.
To illustrate, let us first take the example on "Filling Gaps in Data", and let's add an analytic function to that query. In the following enhanced version, we calculate weekly year-to-date sales alongside the weekly sales. The NULL values that the partitioned outer join inserts in making the time series dense are handled in the usual way: the SUM function treats them as 0's.
SELECT Product_Name, t.Year, t.Week, NVL(Sales,0) Current_sales,
SUM(Sales)
OVER (PARTITION BY Product_Name, t.year ORDER BY t.week) Cumulative_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 CURRENT_SALES CUMULATIVE_SALES
--------------- ---------- ---------- ------------- ----------------
Bounce 2000 20 801 801
Bounce 2000 21 4062.24 4863.24
Bounce 2000 22 2043.16 6906.4
Bounce 2000 23 2731.14 9637.54
Bounce 2000 24 4419.36 14056.9
Bounce 2000 25 0 14056.9
Bounce 2000 26 0 14056.9
Bounce 2000 27 2297.29 16354.19
Bounce 2000 28 1443.13 17797.32
Bounce 2000 29 1927.38 19724.7
Bounce 2000 30 1927.38 21652.08
Bounce 2001 20 1483.3 1483.3
Bounce 2001 21 4184.49 5667.79
Bounce 2001 22 2609.19 8276.98
Bounce 2001 23 1416.95 9693.93
Bounce 2001 24 3149.62 12843.55
Bounce 2001 25 2645.98 15489.53
Bounce 2001 26 0 15489.53
Bounce 2001 27 2125.12 17614.65
Bounce 2001 28 0 17614.65
Bounce 2001 29 2467.92 20082.57
Bounce 2001 30 2620.17 22702.74
How do we use this feature to compare values across time periods? Specifically, how do we calculate a year-over-year sales comparison at the week level? The following query returns on the same row, for each product, the year-to-date sales for each week of 2001 with that of 2000.
Note that in this example we start with a WITH clause. This improves readability of the query and lets us focus on the partitioned outer join. If working in SQL*Plus, the following command will wrap the column headings for greater readability of results:
col Weekly_ytd_sales_prior_year heading 'Weekly_ytd|_sales_|prior_year'
WITH v AS
(SELECT SUBSTR(p.Prod_Name,1,6) Prod, 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 ('Y Box') AND
t.Calendar_Year in (2000,2001) AND
t.Calendar_Week_Number BETWEEN 30 AND 40
GROUP BY p.Prod_Name, t.Calendar_Year, t.Calendar_Week_Number)
SELECT Prod , Year, Week, Sales,
Weekly_ytd_sales, Weekly_ytd_sales_prior_year
FROM
(SELECT Prod, Year, Week, Sales, Weekly_ytd_sales,
LAG(Weekly_ytd_sales, 1) OVER
(PARTITION BY Prod , Week ORDER BY Year) Weekly_ytd_sales_prior_year
FROM
(SELECT v.Prod Prod , t.Year Year, t.Week Week,
NVL(v.Sales,0) Sales, SUM(NVL(v.Sales,0)) OVER
(PARTITION BY v.Prod , t.Year ORDER BY t.week) weekly_ytd_sales
FROM v
PARTITION BY (v.Prod )
RIGHT OUTER JOIN
(SELECT DISTINCT Calendar_Week_Number Week, Calendar_Year Year
FROM Times
WHERE Calendar_Year IN (2000, 2001)) t
ON (v.week = t.week AND v.Year = t.Year)
) dense_sales
) year_over_year_sales
WHERE Year = 2001 AND Week BETWEEN 30 AND 40
ORDER BY 1, 2, 3;
Weekly_ytd
_sales_
PROD YEAR WEEK SALES WEEKLY_YTD_SALES prior_year
------ ---------- ---------- ---------- ---------------- ----------
Y Box 2001 30 7877.45 7877.45 0
Y Box 2001 31 13082.46 20959.91 1537.35
Y Box 2001 32 11569.02 32528.93 9531.57
Y Box 2001 33 38081.97 70610.9 39048.69
Y Box 2001 34 33109.65 103720.55 69100.79
Y Box 2001 35 0 103720.55 71265.35
Y Box 2001 36 4169.3 107889.85 81156.29
Y Box 2001 37 24616.85 132506.7 95433.09
Y Box 2001 38 37739.65 170246.35 107726.96
Y Box 2001 39 284.95 170531.3 118817.4
Y Box 2001 40 10868.44 181399.74 120969.69
In the FROM clause of the inline view dense_sales, we use a partitioned outer join of aggregate view v and time view t to fill gaps in the sales data along the time dimension. The output of the partitioned outer join is then processed by the analytic function SUM ... OVER to compute the weekly year-to-date sales (the weekly_ytd_sales column). Thus, the view dense_sales computes the year-to-date sales data for each week, including those missing in the aggregate view s. The inline view year_over_year_sales then computes the year ago weekly year-to-date sales using the LAG function. The LAG function labeled weekly_ytd_sales_prior_year specifies a PARTITION BY clause that pairs rows for the same week of years 2000 and 2001 into a single partition. We then pass an offset of 1 to the LAG function to get the weekly year to date sales for the prior year.The outermost query block selects data from year_over_year_sales with the condition yr = 2001, and thus the query returns, for each product, its weekly year-to-date sales in the specified weeks of years 2001 and 2000.
While the prior example shows us a way to create comparisons for a single time level, it would be even more useful to handle multiple time levels in a single query. For example, we could compare sales versus the prior period at the year, quarter, month and day levels. How can we create a query which performs a year-over-year comparison of year-to-date sales for all levels of our time hierarchy?
We will take several steps to perform this task. The goal is a single query with comparisons at the day, week, month, quarter, and year level. The steps are as follows:
We will create a view called cube_prod_time, which holds a hierarchical cube of sales aggregated across times and products.
Then we will create a view of the time dimension to use as an edge of the cube. The time edge, which holds a complete set of dates, will be partitioned outer joined to the sparse data in the view cube_prod_time.
Finally, for maximum performance, we will create a materialized view, mv_prod_time, built using the same definition as cube_prod_time.
For more information regarding hierarchical cubes, see Chapter 20, "SQL for Aggregation in Data Warehouses". The materialized view is defined in Step 1 in the following section.
The materialized view shown in the following may already exist in your system; if not, create it now. If you must generate it, note that we limit the query to just two products to keep processing time short:
CREATE OR REPLACE VIEW cube_prod_time AS
SELECT
(CASE
WHEN ((GROUPING(calendar_year)=0 )
AND (GROUPING(calendar_quarter_desc)=1 ))
THEN (TO_CHAR(calendar_year) || '_0')
WHEN ((GROUPING(calendar_quarter_desc)=0 )
AND (GROUPING(calendar_month_desc)=1 ))
THEN (TO_CHAR(calendar_quarter_desc) || '_1')
WHEN ((GROUPING(calendar_month_desc)=0 )
AND (GROUPING(t.time_id)=1 ))
THEN (TO_CHAR(calendar_month_desc) || '_2')
ELSE (TO_CHAR(t.time_id) || '_3')
END) Hierarchical_Time,
calendar_year year, calendar_quarter_desc quarter,
calendar_month_desc month, t.time_id day,
prod_category cat, prod_subcategory subcat, p.prod_id prod,
GROUPING_ID(prod_category, prod_subcategory, p.prod_id,
calendar_year, calendar_quarter_desc, calendar_month_desc,t.time_id) gid,
GROUPING_ID(prod_category, prod_subcategory, p.prod_id) gid_p,
GROUPING_ID(calendar_year, calendar_quarter_desc,
calendar_month_desc, t.time_id) gid_t,
SUM(amount_sold) s_sold, COUNT(amount_sold) c_sold, COUNT(*) cnt
FROM SALES s, TIMES t, PRODUCTS p
WHERE s.time_id = t.time_id AND
p.prod_name IN ('Bounce', 'Y Box') AND s.prod_id = p.prod_id
GROUP BY
ROLLUP(calendar_year, calendar_quarter_desc, calendar_month_desc, t.time_id),
ROLLUP(prod_category, prod_subcategory, p.prod_id);
Because this view is limited to two products, it returns just over 2200 rows. Note that the column Hierarchical_Time contains string representations of time from all levels of the time hierarchy. The CASE expression used for the Hierarchical_Time column appends a marker (_0, _1, ...) to each date string to denote the time level of the value. A _0 represents the year level, _1 is quarters, _2 is months, and _3 is day. Note that the GROUP BY clause is a concatenated ROLLUP which specifies the rollup hierarchy for the time and product dimensions. The GROUP BY clause is what determines the hierarchical cube contents.
edge_time is the source for filling time gaps in the hierarchical cube using a partitioned outer join. The column Hierarchical_Time in edge_time will be used in a partitioned join with the Hierarchical_Time column in the view cube_prod_time. The following statement defines edge_time:
CREATE OR REPLACE VIEW edge_time AS
SELECT
(CASE
WHEN ((GROUPING(calendar_year)=0 )
AND (GROUPING(calendar_quarter_desc)=1 ))
THEN (TO_CHAR(calendar_year) || '_0')
WHEN ((GROUPING(calendar_quarter_desc)=0 )
AND (GROUPING(calendar_month_desc)=1 ))
THEN (TO_CHAR(calendar_quarter_desc) || '_1')
WHEN ((GROUPING(calendar_month_desc)=0 )
AND (GROUPING(time_id)=1 ))
THEN (TO_CHAR(calendar_month_desc) || '_2')
ELSE (TO_CHAR(time_id) || '_3')
END) Hierarchical_Time,
calendar_year yr, calendar_quarter_number qtr_num,
calendar_quarter_desc qtr, calendar_month_number mon_num,
calendar_month_desc mon, time_id - TRUNC(time_id, 'YEAR') + 1 day_num,
time_id day,
GROUPING_ID(calendar_year, calendar_quarter_desc,
calendar_month_desc, time_id) gid_t
FROM TIMES
GROUP BY ROLLUP
(calendar_year, (calendar_quarter_desc, calendar_quarter_number),
(calendar_month_desc, calendar_month_number), time_id);
The materialized view definition is a duplicate of the view cube_prod_time defined earlier. Because it is a duplicate query, references to cube_prod_time will be rewritten to use the mv_prod_time materialized view. The following materialized may already exist in your system; if not, create it now. If you must generate it, note that we limit the query to just two products to keep processing time short.
CREATE MATERIALIZED VIEW mv_prod_time
REFRESH COMPLETE ON DEMAND AS
SELECT
(CASE
WHEN ((GROUPING(calendar_year)=0 )
AND (GROUPING(calendar_quarter_desc)=1 ))
THEN (TO_CHAR(calendar_year) || '_0')
WHEN ((GROUPING(calendar_quarter_desc)=0 )
AND (GROUPING(calendar_month_desc)=1 ))
THEN (TO_CHAR(calendar_quarter_desc) || '_1')
WHEN ((GROUPING(calendar_month_desc)=0 )
AND (GROUPING(t.time_id)=1 ))
THEN (TO_CHAR(calendar_month_desc) || '_2')
ELSE (TO_CHAR(t.time_id) || '_3')
END) Hierarchical_Time,
calendar_year year, calendar_quarter_desc quarter,
calendar_month_desc month, t.time_id day,
prod_category cat, prod_subcategory subcat, p.prod_id prod,
GROUPING_ID(prod_category, prod_subcategory, p.prod_id,
calendar_year, calendar_quarter_desc, calendar_month_desc,t.time_id) gid,
GROUPING_ID(prod_category, prod_subcategory, p.prod_id) gid_p,
GROUPING_ID(calendar_year, calendar_quarter_desc,
calendar_month_desc, t.time_id) gid_t,
SUM(amount_sold) s_sold, COUNT(amount_sold) c_sold, COUNT(*) cnt
FROM SALES s, TIMES t, PRODUCTS p
WHERE s.time_id = t.time_id AND
p.prod_name IN ('Bounce', 'Y Box') AND s.prod_id = p.prod_id
GROUP BY
ROLLUP(calendar_year, calendar_quarter_desc, calendar_month_desc, t.time_id),
ROLLUP(prod_category, prod_subcategory, p.prod_id);
We have now set the stage for our comparison query. We can obtain period-to-period comparison calculations at all time levels. It requires applying analytic functions to a hierarchical cube with dense data along the time dimension.
Some of the calculations we can achieve for each time level are:
Sum of sales for prior period at all levels of time.
Variance in sales over prior period.
Sum of sales in the same period a year ago at all levels of time.
Variance in sales over the same period last year.
The following example performs all four of these calculations. It uses a partitioned outer join of the views cube_prod_time and edge_time to create an inline view of dense data called dense_cube_prod_time. The query then uses the LAG function in the same way as the prior single-level example. The outer WHERE clause specifies time at three levels: the days of August 2001, the entire month, and the entire third quarter of 2001. Note that the last two rows of the results contain the month level and quarter level aggregations.Note that to make the results easier to read if you are using SQL*Plus, the column headings should be adjusted with the following commands. The commands will fold the column headings to reduce line length:
col sales_prior_period heading 'sales_prior|_period' col variance_prior_period heading 'variance|_prior|_period' col sales_same_period_prior_year heading 'sales_same|_period_prior|_year' col variance_same_period_p_year heading 'variance|_same_period|_prior_year'
Here is the query comparing current sales to prior and year ago sales:
SELECT SUBSTR(prod,1,4) prod, SUBSTR(Hierarchical_Time,1,12) ht,
sales, sales_prior_period,
sales - sales_prior_period variance_prior_period,
sales_same_period_prior_year,
sales - sales_same_period_prior_year variance_same_period_p_year
FROM
(SELECT cat, subcat, prod, gid_p, gid_t,
Hierarchical_Time, yr, qtr, mon, day, sales,
LAG(sales, 1) OVER (PARTITION BY gid_p, cat, subcat, prod,
gid_t ORDER BY yr, qtr, mon, day)
sales_prior_period,
LAG(sales, 1) OVER (PARTITION BY gid_p, cat, subcat, prod,
gid_t, qtr_num, mon_num, day_num ORDER BY yr)
sales_same_period_prior_year
FROM
(SELECT c.gid, c.cat, c.subcat, c.prod, c.gid_p,
t.gid_t, t.yr, t.qtr, t.qtr_num, t.mon, t.mon_num,
t.day, t.day_num, t.Hierarchical_Time, NVL(s_sold,0) sales
FROM cube_prod_time c
PARTITION BY (gid_p, cat, subcat, prod)
RIGHT OUTER JOIN edge_time t
ON ( c.gid_t = t.gid_t AND
c.Hierarchical_Time = t.Hierarchical_Time)
) dense_cube_prod_time
) --side by side current and prior year sales
WHERE prod IN (139) AND gid_p=0 AND --1 product and product level data
( (mon IN ('2001-08' ) AND gid_t IN (0, 1)) OR --day and month data
(qtr IN ('2001-03' ) AND gid_t IN (3))) --quarter level data
ORDER BY day;
variance sales_same variance
sales_prior _prior _period_prior _same_period
PROD HT SALES _period _period _year _prior_year
---- ------------ ---------- ----------- ---------- ------------- ------------
139 01-AUG-01_3 0 0 0 0 0
139 02-AUG-01_3 1347.53 0 1347.53 0 1347.53
139 03-AUG-01_3 0 1347.53 -1347.53 42.36 -42.36
139 04-AUG-01_3 57.83 0 57.83 995.75 -937.92
139 05-AUG-01_3 0 57.83 -57.83 0 0
139 06-AUG-01_3 0 0 0 0 0
139 07-AUG-01_3 134.81 0 134.81 880.27 -745.46
139 08-AUG-01_3 1289.89 134.81 1155.08 0 1289.89
139 09-AUG-01_3 0 1289.89 -1289.89 0 0
139 10-AUG-01_3 0 0 0 0 0
139 11-AUG-01_3 0 0 0 0 0
139 12-AUG-01_3 0 0 0 0 0
139 13-AUG-01_3 0 0 0 0 0
139 14-AUG-01_3 0 0 0 0 0
139 15-AUG-01_3 38.49 0 38.49 1104.55 -1066.06
139 16-AUG-01_3 0 38.49 -38.49 0 0
139 17-AUG-01_3 77.17 0 77.17 1052.03 -974.86
139 18-AUG-01_3 2467.54 77.17 2390.37 0 2467.54
139 19-AUG-01_3 0 2467.54 -2467.54 127.08 -127.08
139 20-AUG-01_3 0 0 0 0 0
139 21-AUG-01_3 0 0 0 0 0
139 22-AUG-01_3 0 0 0 0 0
139 23-AUG-01_3 1371.43 0 1371.43 0 1371.43
139 24-AUG-01_3 153.96 1371.43 -1217.47 2091.3 -1937.34
139 25-AUG-01_3 0 153.96 -153.96 0 0
139 26-AUG-01_3 0 0 0 0 0
139 27-AUG-01_3 1235.48 0 1235.48 0 1235.48
139 28-AUG-01_3 173.3 1235.48 -1062.18 2075.64 -1902.34
139 29-AUG-01_3 0 173.3 -173.3 0 0
139 30-AUG-01_3 0 0 0 0 0
139 31-AUG-01_3 0 0 0 0 0
139 2001-08_2 8347.43 7213.21 1134.22 8368.98 -21.55
139 2001-03_1 24356.8 28862.14 -4505.34 24168.99 187.81
The first LAG function (sales_prior_period) partitions the data on gid_p, cat, subcat, prod, gid_t and orders the rows on all the time dimension columns. It gets the sales value of the prior period by passing an offset of 1. The second LAG function (sales_same_period_prior_year) partitions the data on additional columns qtr_num, mon_num, and day_num and orders it on yr so that, with an offset of 1, it can compute the year ago sales for the same period. The outermost SELECT clause computes the variances.
In many analytical SQL tasks, it is helpful to define custom members in a dimension. For instance, you might define a specialized time period for analyses. You can use a partitioned outer join to temporarily add a member to a dimension. Note that the new SQL MODEL clause is suitable for creating more complex scenarios involving new members in dimensions. See Chapter 22, "SQL for Modeling" for more information on this topic.
As an example of a task, what if we want to define a new member for our time dimension? We want to create a 13th member of the Month level in our time dimension. This 13th month is defined as the summation of the sales for each product in the first month of each quarter of year 2001.
The solution has two steps. Note that we will build this solution using the views and tables created in the prior example. Two steps are required. First, create a view with the new member added to the appropriate dimension. The view uses a UNION ALL operation to add the new member. To query using the custom member, use a CASE expression and a partitioned outer join.
Our new member for the time dimension is created with the following view:
CREATE OR REPLACE VIEW time_c AS (SELECT * FROM edge_time UNION ALL SELECT '2001-13_2', 2001, 5, '2001-05', 13, '2001-13', null, null, 8 -- <gid_of_mon> FROM DUAL);
In this statement, the view time_c is defined by performing a UNION ALL of the edge_time view (defined in the prior example) and the user-defined 13th month. The gid_t value of 8 was chosen to differentiate the custom member from the standard members. The UNION ALL specifies the attributes for a 13th month member by doing a SELECT from the DUAL table. Note that the grouping id, column gid_t, is set to 8, and the quarter number is set to 5.
Then, the second step is to use an inline view of the query to perform a partitioned outer join of cube_prod_time with time_c. This step creates sales data for the 13th month at each level of product aggregation. In the main query, the analytic function SUM is used with a CASE expression to compute the 13th month, which is defined as the summation of the first month's sales of each quarter.
SELECT * FROM (SELECT SUBSTR(cat,1,12) cat, SUBSTR(subcat,1,12) subcat,
prod, mon, mon_num,
SUM(CASE WHEN mon_num IN (1, 4, 7, 10)
THEN s_sold
ELSE NULL
END)
OVER (PARTITION BY gid_p, prod, subcat, cat, yr) sales_month_13
FROM
(SELECT c.gid, c.prod, c.subcat, c.cat, gid_p,
t.gid_t, t.day, t.mon, t.mon_num,
t.qtr, t.yr, NVL(s_sold,0) s_sold
FROM cube_prod_time c
PARTITION BY (gid_p, prod, subcat, cat)
RIGHT OUTER JOIN time_c t
ON (c.gid_t = t.gid_t AND
c.Hierarchical_Time = t.Hierarchical_Time)
)
)
WHERE mon_num=13;
CAT SUBCAT PROD MON MON_NUM SALES_MONTH_13
------------ ------------ ---------- -------- ---------- --------------
Electronics Game Console 16 2001-13 13 762334.34
Electronics Y Box Games 139 2001-13 13 75650.22
Electronics Game Console 2001-13 13 762334.34
Electronics Y Box Games 2001-13 13 75650.22
Electronics 2001-13 13 837984.56
2001-13 13 837984.56
The SUM function uses a CASE to limit the data to months 1, 4, 7, and 10 within each year. Due to the tiny data set, with just 2 products, the rollup values of the results are necessarily repetitions of lower level aggregations. For more realistic set of rollup values, you can include more products from the Game Console and Y Box Games subcategories in the underlying materialized view.
This section illustrates the following additional analytic capabilities:
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 21-24.
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 21-24 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
Linear algebra is a branch of mathematics with a wide range of practical applications. Many areas have tasks that can be expressed using linear algebra, and here are some examples from several fields: statistics (multiple linear regression and principle components analysis), data mining (clustering and classification), bioinformatics (analysis of microarray data), operations research (supply chain and other optimization problems), econometrics (analysis of consumer demand data), and finance (asset allocation problems). Various libraries for linear algebra are freely available for anyone to use. Oracle's UTL_NLA package exposes matrix PL/SQL data types and wrapper PL/SQL subprograms for two of the most popular and robust of these libraries, BLAS and LAPACK.
Linear algebra depends on matrix manipulation. Performing matrix manipulation in PL/SQL in the past required inventing a matrix representation based on PL/SQL's native data types and then writing matrix manipulation routines from scratch. This required substantial programming effort and the performance of the resulting implementation was limited. If developers chose to send data to external packages for processing rather than create their own routines, data transfer back and forth could be time consuming. Using the UTL_NLA package lets data stay within Oracle, removes the programming effort, and delivers a fast implementation.
Example 21-25 Linear Algebra
Here is an example of how Oracle's linear algebra support could be used for business analysis. It invokes a multiple linear regression application built using the UTL_NLA package. The multiple regression application is implemented in an object called OLS_Regression. Note that sample files for the OLS Regression object can be found in $ORACLE_HOME/plsql/demo.
Consider the scenario of a retailer analyzing the effectiveness of its marketing program. Each of its stores allocates its marketing budget over the following possible programs: media advertisements (media), promotions (promo), discount coupons (disct), and direct mailers (dmail). The regression analysis builds a linear relationship between the amount of sales that an average store has in a given year (sales) and the spending on the four components of the marketing program. Suppose that the marketing data is stored in the following table:
sales_marketing_data ( /* Store information*/ store_no NUMBER, year NUMBER, /* Sales revenue (in dollars)*/ sales NUMBER, /* sales amount*/ /* Marketing expenses (in dollars)*/ media NUMBER, /*media advertisements*/ promo NUMBER, /*promotions*/ disct NUMBER, /*dicount coupons*/ dmail NUMBER, /*direct mailers*/
Then you can build the following sales-marketing linear model using coefficients:
Sales Revenue = a + b Media Advisements
+ c Promotions
+ d Discount Coupons
+ e Direct Mailer
This model can be implemented as the following view, which refers to the OLS regression object:
CREATE OR REPLACE VIEW sales_marketing_model (year, ols)
AS SELECT year,
OLS_Regression(
/* mean_y => */
AVG(sales),
/* variance_y => */
var_pop(sales),
/* MV mean vector => */
UTL_NLA_ARRAY_DBL (AVG(media),AVG(promo),
AVG(disct),AVG(dmail)),
/* VCM variance covariance matrix => */
UTL_NLA_ARRAY_DBL (var_pop(media),covar_pop(media,promo),
covar_pop(media,disct),covar_pop(media,dmail),
var_pop(promo),covar_pop(promo,disct),
covar_pop(promo,dmail),var_pop(disct),
covar_pop(disct,dmail),var_pop(dmail)),
/* CV covariance vector => */
UTL_NLA_ARRAY_DBL (covar_pop(sales,media),covar_pop(sales,promo),
covar_pop(sales,disct),covar_pop(sales,dmail)))
FROM sales_marketing_data
GROUP BY year;
Using this view, a marketing program manager can perform an analysis such as "Is this sales-marketing model reasonable for year 2004 data? That is, is the multiple-correlation greater than some acceptable value, say, 0.9?" The SQL for such a query might be as follows:
SELECT model.ols.getCorrelation(1)
AS "Applicability of Linear Model"
FROM sales_marketing_model model
WHERE year = 2004;
You could also solve questions such as "What is the expected base-line sales revenue of a store without any marketing programs in 2003?" or "Which component of the marketing program was the most effective in 2004? That is, a dollar increase in which program produced the greatest expected increase in sales?"
See Oracle Database PL/SQL Packages and Types Reference for further information regarding the use of the UTL_NLA package and linear algebra.
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 CASE statements is:
CASE expr WHEN comparison_expr THEN return_expr [, WHEN comparison_expr THEN return_expr]... [ELSE else_expr] END
Simple CASE expressions test if the expr value equals the comparison_expr.
The syntax for searched CASE statements is:
CASE WHEN condition THEN return_expr [, WHEN condition THEN return_expr] ... ELSE else_expr] END
You can use any kind of condition in a searched CASE expression, not just an equality test.
You can specify only 65,535 arguments and each WHEN ... THEN pair counts as two arguments. To avoid exceeding this limit, you can nest CASE expressions so that the return_expr itself is a CASE expression.
Example 21-26 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 might choose to write this query as follows:
SELECT AVG(foo(e.salary)) FROM employees e;
Note that this runs against the hr sample schema. 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.salary > 2000 THEN e.salary ELSE 2000 end) AS avg_sal_2k_floor FROM employees e;
Using a CASE expression lets you avoid developing custom functions and can also perform faster.
Example 21-27 CASE for Aggregating Independent Subsets
Using CASE inside aggregate functions is a convenient way to perform aggregates on multiple subsets of data when a plain GROUP BY will not suffice. For instance, the preceding example could have included multiple AVG columns in its SELECT list, each with its own CASE expression. We might have had a query find the average salary for all employees in the salary ranges 0-2000 and 2000-5000. It would look like:
SELECT AVG(CASE WHEN e.sal BETWEEN 0 AND 2000 THEN e.sal ELSE null END) avg2000,
AVG(CASE WHEN e.sal BETWEEN 2001 AND 5000 THEN e.sal ELSE null END) avg5000
FROM emps e;
Although this query places the aggregates of independent subsets data into separate columns, by adding a CASE expression to the GROUP BY clause we can display the aggregates as the rows of a single column. The next section shows the flexibility of this approach with two approaches to creating histograms with CASE.
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 21-28 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 21-29 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
Instead of counting how often a given event occurs (for example, how often someone has purchased milk at the grocery), you may find it useful to count how often multiple events occur together (for example, how often someone has purchased both milk and cereal together at the grocery store). You can count these multiple events using what is called a frequent itemset, which is, as the name implies, a set of items. 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 practical motivation for using a frequent itemset is to find those itemsets that occur most often. If you analyze 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 itemset calculations are integrated with the database, operating on top of relational tables and accessed through SQL. This integration provides the following 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 Oracle Database PL/SQL Packages and Types Reference for more information. In addition, there is an example of frequent itemset usage in "Frequent itemsets".
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