20 SQL for Analysis and Reporting
The following topics provide information about analytical SQL features and techniques in Oracle. Although these topics are presented in terms of data warehousing, they are applicable to any activity needing analysis and reporting.
20.1 Overview of SQL for Analysis and Reporting
Oracle Database provides a large 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 Ntiles. Moving window calculations allow you to find moving and cumulative aggregations, such as sums and averages. Lag/lead analysis enables direct interrow references so you can calculate periodtoperiod changes. First/last analysis enables you to find the first or last value in an ordered group.
Other SQL elements valuable for analysis and reporting include the CASE
expression and partitioned outer join. CASE
expressions provide ifthen logic useful in many situations. Partitioned outer join is a variant of 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 crosstabular 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 201.
Table 201 Analytic Functions and Their Uses
Type  Used For 

Ranking 
Calculating ranks, percentiles, and ntiles 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 additional elements. The processing flow is represented in Figure 201.
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
andHAVING
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 anORDER
BY
clause at its end, theORDER
BY
is processed to allow for precise output ordering. The processing order is shown in Figure 201. 
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 (n1) 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 202.
20.2 Ranking, Windowing, and Reporting Functions
This section illustrates the basic analytic functions for ranking, windowing, and reporting. It contains the following topics:
20.2.1 Ranking Functions
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:
20.2.1.1 RANK and DENSE_RANK Functions
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 theRANK
function operates. That is,RANK
gets reset whenever the group changes. In effect, the value expressions of thePARTITION
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 ofNULLs
in the ordered sequence, either first or last in the sequence. The order of the sequence would makeNULLs
compare either high or low with respect to nonNULL
values. If the sequence were in ascending order, thenNULLS
FIRST
implies thatNULLs
are smaller than all other nonNULL
values andNULLS
LAST
implies they are larger than nonNULL
values. It is the opposite for descending order. See the example in "Examples: Treatment of NULLs in Ranking Functions". 
If the
NULLS
FIRST
NULLS
LAST
clause is omitted, then the ordering of the null values depends on theASC
orDESC
arguments. Null values are considered larger than any other values. If the ordering sequence isASC
, 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 nondeterministic.
20.2.1.1.1 Ranking Order in RANK and DENSE_RANK Functions
The following example shows how the [ASC  DESC]
option of RANK changes the ranking order.
Example 201 Ranking Order
SELECT channel_desc, TO_CHAR(SUM(amount_sold), '9,999,999,999') SALES$, RANK() OVER (ORDER BY SUM(amount_sold)) AS default_rank, RANK() OVER (ORDER BY SUM(amount_sold) DESC NULLS LAST) AS custom_rank FROM sales, products, customers, times, channels, countries WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id AND customers.country_id = countries.country_id AND sales.time_id=times.time_id AND sales.channel_id=channels.channel_id AND times.calendar_month_desc IN ('200009', '200010') AND country_iso_code='US' GROUP BY channel_desc; CHANNEL_DESC SALES$ 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.
20.2.1.1.2 Ranking on Multiple Expressions
Ranking functions must 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 202 Ranking On Multiple Expressions
SELECT channel_desc, calendar_month_desc, TO_CHAR(TRUNC(SUM(amount_sold),5), '9,999,999,999') SALES$, TO_CHAR(SUM(quantity_sold), '9,999,999,999') SALES_Count, RANK() OVER (ORDER BY TRUNC(SUM(amount_sold), 5) DESC, SUM(quantity_sold) DESC) AS col_rank FROM sales, products, customers, times, channels WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id AND sales.time_id=times.time_id AND sales.channel_id=channels.channel_id AND times.calendar_month_desc IN ('200009', '200010') AND channels.channel_desc<>'Tele Sales' GROUP BY channel_desc, calendar_month_desc; CHANNEL_DESC CALENDAR SALES$ SALES_COUNT COL_RANK      Direct Sales 200010 1,200,000 12,584 1 Direct Sales 200009 1,200,000 11,995 2 Partners 200010 600,000 7,508 3 Partners 200009 600,000 6,165 4 Internet 200009 200,000 1,887 5 Internet 200010 200,000 1,450 6
The sales_count
column breaks the ties for three pairs of values.
If you only want to see the top five results for this query, you can add an ORDER
BY
COL_RANK
FETCH
FIRST
5
ROWS
ONLY
statement. See "Limiting SQL Rows" for further information.
20.2.1.1.3 Example: Difference Between RANK and DENSE_RANK
The difference between RANK
and DENSE_RANK
functions is illustrated in Example 203.
Example 203 RANK and DENSE_RANK
SELECT channel_desc, calendar_month_desc, TO_CHAR(TRUNC(SUM(amount_sold),5), '9,999,999,999') SALES$, RANK() OVER (ORDER BY TRUNC(SUM(amount_sold),5) DESC) AS RANK, DENSE_RANK() OVER (ORDER BY TRUNC(SUM(amount_sold),5) DESC) AS DENSE_RANK FROM sales, products, customers, times, channels WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id AND sales.time_id=times.time_id AND sales.channel_id=channels.channel_id AND times.calendar_month_desc IN ('200009', '200010') AND channels.channel_desc<>'Tele Sales' GROUP BY channel_desc, calendar_month_desc; CHANNEL_DESC CALENDAR SALES$ RANK DENSE_RANK      Direct Sales 200009 1,200,000 1 1 Direct Sales 200010 1,200,000 1 1 Partners 200009 600,000 3 2 Partners 200010 600,000 3 2 Internet 200009 200,000 5 3 Internet 200010 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.
20.2.1.1.4 Ranking Within Groups: Example
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 204 Per Group Ranking Example 1
SELECT channel_desc, calendar_month_desc, TO_CHAR(SUM(amount_sold), '9,999,999,999') SALES$, RANK() OVER (PARTITION BY channel_desc ORDER BY SUM(amount_sold) DESC) AS RANK_BY_CHANNEL FROM sales, products, customers, times, channels WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id AND sales.time_id=times.time_id AND sales.channel_id=channels.channel_id AND times.calendar_month_desc IN ('200008', '200009', '200010', '200011') AND channels.channel_desc IN ('Direct Sales', 'Internet') GROUP BY channel_desc, calendar_month_desc; CHANNEL_DESC CALENDAR SALES$ RANK_BY_CHANNEL     Direct Sales 200008 1,236,104 1 Direct Sales 200010 1,225,584 2 Direct Sales 200009 1,217,808 3 Direct Sales 200011 1,115,239 4 Internet 200011 284,742 1 Internet 200010 239,236 2 Internet 200009 228,241 3 Internet 200008 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 205 Per Group Ranking Example 2
SELECT channel_desc, calendar_month_desc, TO_CHAR(SUM(amount_sold), '9,999,999,999') SALES$, RANK() OVER (PARTITION BY calendar_month_desc ORDER BY SUM(amount_sold) DESC) AS RANK_WITHIN_MONTH, RANK() OVER (PARTITION BY channel_desc ORDER BY SUM(amount_sold) DESC) AS RANK_WITHIN_CHANNEL FROM sales, products, customers, times, channels, countries WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id AND customers.country_id = countries.country_id AND sales.time_id=times.time_id AND sales.channel_id=channels.channel_id AND times.calendar_month_desc IN ('200008', '200009', '200010', '200011') AND channels.channel_desc IN ('Direct Sales', 'Internet') GROUP BY channel_desc, calendar_month_desc; CHANNEL_DESC CALENDAR SALES$ RANK_WITHIN_MONTH RANK_WITHIN_CHANNEL      Direct Sales 200008 1,236,104 1 1 Internet 200008 215,107 2 4 Direct Sales 200009 1,217,808 1 3 Internet 200009 228,241 2 3 Direct Sales 200010 1,225,584 1 2 Internet 200010 239,236 2 2 Direct Sales 200011 1,115,239 1 4 Internet 200011 284,742 2 1
20.2.1.1.5 Example: Per Cube and Rollup Group Ranking
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 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, SUM(amount_sold) SALES$,
RANK() OVER (PARTITION BY GROUPING_ID(channel_desc, country_iso_code)
ORDER BY SUM(amount_sold) DESC) AS RANK_PER_GROUP
FROM sales, customers, times, channels, countries
WHERE sales.time_id=times.time_id AND sales.cust_id=customers.cust_id
AND countries.country_id = customers.country_id AND sales.channel_id = channels.channel_id
AND channels.channel_desc IN ('Direct Sales', 'Internet') AND times.calendar_month_desc='200007'
AND country_iso_code IN ('GB', 'US', 'JP')
GROUP BY cube(channel_desc, country_iso_code);
CHANNEL_DESC CO SALES$ RANK_PER_GROUP
   
Direct Sales US 616539.04 1
Direct Sales GB 83869.96 2
Internet US 82595.71 3
Direct Sales JP 79047.78 4
Internet JP 7103.39 5
Internet GB 6477.98 6
Direct Sales 779456.78 1
Internet 96177.08 2
US 699134.75 1
GB 90347.94 2
JP 86151.17 3
875633.86 1
20.2.1.1.6 Examples: Treatment of NULLs in Ranking Functions
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       25JAN99 3097.32 1 18 31 14 17JAN99 1791.77 2 19 30 13 30JAN99 127.69 3 20 29 12 28JAN99 120.34 4 21 28 11 23JAN99 86.12 5 22 27 10 20JAN99 79.07 6 23 26 9 13JAN99 56.1 7 24 25 8 07JAN99 42.97 8 25 24 7 08JAN99 33.81 9 26 23 6 10JAN99 22.76 10 27 21 4 02JAN99 22.76 10 27 21 4 26JAN99 19.84 12 29 20 3 16JAN99 11.27 13 30 19 2 14JAN99 9.52 14 31 18 1 09JAN99 15 1 1 15 12JAN99 15 1 1 15 31JAN99 15 1 1 15 11JAN99 15 1 1 15 19JAN99 15 1 1 15 03JAN99 15 1 1 15 15JAN99 15 1 1 15 21JAN99 15 1 1 15 24JAN99 15 1 1 15 04JAN99 15 1 1 15 06JAN99 15 1 1 15 27JAN99 15 1 1 15 18JAN99 15 1 1 15 01JAN99 15 1 1 15 22JAN99 15 1 1 15 29JAN99 15 1 1 15 05JAN99 15 1 1 15
20.2.1.2 APPROX_RANK Function
The APPROX_RANK
function returns the approximate value in a group of values.
This function takes an optional PARTITION BY
clause followed by a mandatory ORDER BY ... DESC
clause. The PARTITION BY
key must be a subset of the GROUP BY
key. The ORDER BY
clause must include either APPROX_COUNT
or APPROX_SUM
.
The APPROX_RANK
function has the following syntax:
SELECT expr_1[, expr_2, … expr_j], APPROX_*(expr_k) agg_1[, APPROX_*(expr_l) agg_2…]
FROM table_name
WHERE …
GROUP BY expr_1[, expr_2, …expr_j]
HAVING APPROX_RANK(PARTITION BY partition_by_clause ORDER BY APPROX_*(expr_k) DESC) <= N1
[AND APPROX_RANK(PARTITION BY partition_by_clause ORDER BY APPROX_*(expr_l) DESC) <= N2…)];
The examples on this page use the hr
(Human Resources) sample
schema provided by Oracle.
In the following example, the query returns the jobs that are among the top 10 total salaries per department. For each job, the total salary and ranking is also given:
SELECT department_id, job_id, APPROX_SUM(salary), APPROX_RANK(PARTITION BY department_id ORDER BY APPROX_SUM(salary) DESC) rk FROM hr.employees GROUP BY department_id, job_id HAVING APPROX_RANK(PARTITION BY department_id ORDER BY APPROX_SUM(salary) DESC) <= 10;
DEPARTMENT_ID JOB_ID APPROX_SUM(SALARY) RK
_____ _________ _________________ ____
10 AD_ASST 4400 1
20 MK_REP 6000 2
20 MK_MAN 13000 1
30 PU_MAN 11000 2
30 PU_CLERK 13900 1
40 HR_REP 6500 1
50 ST_MAN 36400 3
50 ST_CLERK 55700 2
50 SH_CLERK 64300 1
60 IT_PROG 28800 1
70 PR_REP 10000 1
80 SA_MAN 61000 2
80 SA_REP 243500 1
90 AD_PRES 24000 2
90 AD_VP 34000 1
100 FI_MGR 12008 2
100 FI_ACCOUNT 39600 1
110 AC_ACCOUNT 8300 2
110 AC_MGR 12008 1
SA_REP 7000 1
In the following example, the query returns the jobs that are among the top 2 in terms of total salary and among the top 3 in terms of number of employees holding the job titles per department:
SELECT department_id, job_id , APPROX_SUM(salary), APPROX_COUNT(*) FROM employees GROUP BY department_id, job_id HAVING APPROX_RANK(PARTITION BY department_id ORDER BY APPROX_SUM(salary) DESC) <= 2 AND APPROX_RANK(PARTITION BY department_id ORDER BY APPROX_COUNT(*) DESC) <= 3;
DEPTNO JOB APPROX_SUM(SAL) APPROX_COUNT(*)
   
10 MANAGER 2450 1
10 PRESIDENT 5000 1
20 MANAGER 2975 1
20 ANALYST 6000 2
30 MANAGER 2850 1
30 SALESPERSON 5600 4
The following example reports the accuracy of the approximate aggregate using the MAX_ERROR
attribute:
SELECT department_id, job_id , APPROX_SUM(salary) sum_salary, APPROX_SUM(salary,'MAX_ERROR') sum_salary_err
FROM employees
GROUP BY department_id, job_id
HAVING APPROX_RANK(PARTITION BY department_id ORDER BY APPROX_SUM(salary) DESC) <= 2;
DEPARTMENT_ID JOB_ID SUM_SALARY SUM_SALARY_ERR
________________ _____________ _____________ _________________
10 AD_ASST 4400 0
20 MK_REP 6000 0
20 MK_MAN 13000 0
30 PU_MAN 11000 0
30 PU_CLERK 13900 0
40 HR_REP 6500 0
50 ST_CLERK 55700 0
50 SH_CLERK 64300 0
60 IT_PROG 28800 0
70 PR_REP 10000 0
80 SA_MAN 61000 0
80 SA_REP 243500 0
90 AD_PRES 24000 0
90 AD_VP 34000 0
100 FI_MGR 12008 0
100 FI_ACCOUNT 39600 0
110 AC_ACCOUNT 8300 0
110 AC_MGR 12008 0
SA_REP 7000 0
See Also:
20.2.1.3 Bottom N Ranking Functions
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.
20.2.1.4 CUME_DIST Function
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 nonNULL
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$, CUME_DIST() OVER (PARTITION BY calendar_month_desc ORDER BY SUM(amount_sold) ) AS CUME_DIST_BY_CHANNEL FROM sales, products, customers, times, channels WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id AND sales.time_id=times.time_id AND sales.channel_id=channels.channel_id AND times.calendar_month_desc IN ('200009', '200007','200008') GROUP BY calendar_month_desc, channel_desc; MONTH CHANNEL_DESC SALES$ CUME_DIST_BY_CHANNEL     200007 Internet 140,423 .333333333 200007 Partners 611,064 .666666667 200007 Direct Sales 1,145,275 1 200008 Internet 215,107 .333333333 200008 Partners 661,045 .666666667 200008 Direct Sales 1,236,104 1 200009 Internet 228,241 .333333333 200009 Partners 666,172 .666666667 200009 Direct Sales 1,217,808 1
20.2.1.5 PERCENT_RANK Function
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)
20.2.1.6 NTILE Function
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    200002 242,416 1 200001 257,286 1 200003 280,011 1 200006 315,951 2 200005 316,824 2 200004 318,106 2 200007 433,824 3 200008 477,833 3 200012 553,534 3 200010 652,225 4 200011 661,147 4 200009 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.
20.2.1.7 ROW_NUMBER Function
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 206 ROW_NUMBER
SELECT channel_desc, calendar_month_desc, TO_CHAR(TRUNC(SUM(amount_sold), 5), '9,999,999,999') SALES$, ROW_NUMBER() OVER (ORDER BY TRUNC(SUM(amount_sold), 6) DESC) AS ROW_NUMBER FROM sales, products, customers, times, channels WHERE sales.prod_id=products.prod_id AND sales.cust_id=customers.cust_id AND sales.time_id=times.time_id AND sales.channel_id=channels.channel_id AND times.calendar_month_desc IN ('202109', '202110') GROUP BY channel_desc, calendar_month_desc; CHANNEL_DESC CALENDAR SALES$ ROW_NUMBER     Direct Sales 202109 1,200,000 1 Direct Sales 202110 1,200,000 2 Internet 202110 200,000 3 Partners 202110 600,000 4 Partners 202109 600,000 5 Internet 202109 200,000 6
Note that there are three pairs of tie values in these results. Like NTILE
, ROW_NUMBER
is a nondeterministic function, so each tied value could have its row number switched. To ensure deterministic results, you must order on a unique key. In most cases, that will require adding a new tie breaker column to the query and using it in the ORDER
BY
specification.
20.2.2 Windowing Functions
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 selfjoin.
The syntax of the windowing function is:
analytic_function([ arguments ]) OVER {window_name  (analytic_clause)} where analytic_clause = [ window_name  query_partition_clause ] [ order_by_clause [ windowing_clause ] ] and query_partition_clause = PARTITION BY { value_expr[, value_expr ]... } and windowing_clause = { ROWS  RANGE  GROUPS } { 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 } } [ EXCLUDE CURRENT ROW  EXCLUDE GROUP  EXCLUDE TIES  EXCLUDE NO OTHERS ]
Note the following:
 The
DISTINCT
keyword is not supported in windowing functions except forMAX
andMIN
.  If
GROUPS
is specified, then as is similar toROWS
,value_expr
must be either a constant or an expression and must evaluate to a positive numeric value.
See Also:
Oracle Database SQL Language Reference for further information regarding syntax and restrictions
This section contains the following topics:
20.2.2.1 Examples of Window Clauses
A window clause can be implemented within a windowing function as shown in these examples.
In these examples note that instead of repeating the same analytic clause multiple times, we can define a window name for it and refer to the name in multiple windowing functions. The second example also shows how one window name can be built on top of another window name.
select ename, deptno, sal,
sum(sal) over (w1) sum_sal,
min(sal) over (w1) min_sal,
avg(sal) over (w1) avg_sal,
sum(sal) over (w2) cum_sal
from emp
window w1 as (partition by deptno),
w2 as (partition by deptno order by sal);
select ename, deptno, sal,
sum(sal) over (w1 order by sal) cum_sal1,
sum(sal) over (w2) cum_sal2
from emp
window w1 as (partition by deptno),
w2 as (w1 order by sal);
select ename, deptno, sal,
min(sal) over w1 min_sal_3,
max(sal) over w1 max_sal_3
from emp
window w1 as (partition by deptno order by sal
rows between 1 preceding and 1 following);
Note:
When the window name is specified with a windowing clause, it can only be referenced directly (without parentheses). The example below demonstrates this restriction. Notice that the window name w1
is in parentheses in several places.
select ename, deptno, sal,
min(sal) over (w1) min_sal_3,
max(sal) over w1 max_sal_3
from emp
window w1 as (partition by deptno order by sal
rows between 1 preceding and 1 following);
This query results in the following error.
ERROR at line 2:
ORA32785: cannot reference a window name defined with WINDOWING clause
20.2.2.2 Examples of Windowing Clause Extensions
A windowing clause extension can be implemented within a windowing function as shown in these examples.
The following example shows windowing clauses using the ROWS and EXCLUDE clause with various options.
select sal,
sum(sal) over (w rows between 1 preceding and 1 following
exclude current row) as exclude_current_row,
sum(sal) over (w rows between 1 preceding and 1 following
exclude group) as exclude_group,
sum(sal) over (w rows between 1 preceding and 1 following
exclude ties) as exclude_ties,
sum(sal) over (w rows between 1 preceding and 1 following
exclude no others) as exclude_no_others
from emp
window w as (order by sal);
The following example shows windowing clauses using the RANGE and EXCLUDE clause with various options.
select sal,
sum(sal) over (w range between 100 preceding and 100 following
exclude current row) as exclude_current_row,
sum(sal) over (w range between 100 preceding and 100 following
exclude group) as exclude_group,
sum(sal) over (w range between 100 preceding and 100 following
exclude ties) as exclude_ties,
sum(sal) over (w range between 100 preceding and 100 following
exclude no others) as exclude_no_others
from emp
window w as (order by sal);
The following example shows windowing clauses using the GROUPS and EXCLUDE clause with various options.
select sal,
sum(sal) over (w groups between 1 preceding and 1 following
exclude current row) as exclude_current_row,
sum(sal) over (w groups between 1 preceding and 1 following
exclude group) as exclude_group,
sum(sal) over (w groups between 1 preceding and 1 following
exclude ties) as exclude_ties,
sum(sal) over (w groups between 1 preceding and 1 following
exclude no others) as exclude_no_others
from emp
window w as (order by sal);
20.2.2.3 About Treatment of NULLs as Input to Window Functions
Window functions' NULL
semantics match the NULL
semantics for SQL aggregate functions. Other semantics can be obtained by userdefined functions, or by using the DECODE
or a CASE
expression within the window function.
20.2.2.4 Windowing Functions with Logical Offset
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 isRANGE
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 207 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=2022 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 CALENDAR_QUARTER_DESC Q_SALES CUM_SALES __________ _______________________ __________ _____________ 2595 202201 98.16 98.16 2595 202202 95.11 193.27 2595 202204 10,902.18 11,095.45 9646 202201 422.64 422.64 9646 202202 1,220.11 1,642.75 9646 202203 1,121.65 2,764.40 9646 202204 1,381.58 4,145.98 11111 202201 6,080.14 6,080.14 11111 202202 3,322.30 9,402.44 11111 202203 1,073.12 10,475.56 11111 202204 1,420.24 11,895.80
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 SUM
s are needed in this example because you are performing a SUM
over a value that is itself a SUM
. Nested aggregations are used very often in analytic aggregate functions.
Example 208 Moving Aggregate Function
This example of a timebased 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 199904 125 125 6510 199905 3,395 1,760 6510 199906 4,080 2,533 6510 199907 6,435 4,637 6510 199908 5,105 5,207 6510 199909 4,676 5,405 6510 199910 5,109 4,963 6510 199911 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 must 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.
20.2.2.5 Centered Aggregate Function
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.
The example below uses thesh
sample
schema.
Example 209 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 sh.sales s, sh.times t WHERE s.time_id=t.time_id AND t.calendar_week_number IN (51) AND calendar_year=2022 GROUP BY t.time_id ORDER BY t.time_id; TIME_ID SALES CENTERED_3_DAY_AVG ____________ ______________ __________________ 17DEC22 281,264 197,907 18DEC22 114,550 161,631 19DEC22 89,080 103,482 20DEC22 106,816 109,094 21DEC22 131,385 87,102 22DEC22 23,104 85,469 23DEC22 101,917 62,511
The starting and ending rows for each product's centered moving average calculation in the output data are based on just two days, because the window calculation cannot reach past the data retrieved by the query. As in the prior example, you must consider the different window sizes found at the borders of result sets: the query may need to be adjusted.
20.2.2.6 Windowing Aggregate Functions in the Presence of Duplicates
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 an inline view was used to define the 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 2010 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 sh.customers c, sh.sales s, sh.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 '01MAY22' AND '13MAY23' GROUP BY time_id, channel_id); TIME_ID DAILY_SUM CURRENT_GROUP_SUM ____________ ____________ ____________________ 06MAY22 4 12 06MAY22 8 12 10MAY22 5 24 10MAY22 4 24 10MAY22 3 24 12MAY22 3 33 12MAY22 6 33 16MAY22 2 45 16MAY22 6 45 16MAY22 4 45 05JUN22 4 16 05JUN22 12 16 . . .
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.
20.2.2.7 Varying Window Size for Each Row
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 nonworking 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 userdefined 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
data type value.
20.2.2.8 Windowing Aggregate Functions with Physical Offsets
For windows expressed in rows, the ordering expressions should be unique to produce
deterministic results. For this example, which uses the Oracleprovided sh
sample schema, the following query is not deterministic because time_id
is
not unique in this result set.
Example 2011 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 sh.sales s, sh.times t, sh.customers c WHERE s.time_id=t.time_id AND s.cust_id=c.cust_id AND t.time_id IN (TO_DATE('11DEC2022'), TO_DATE('12DEC2022')) AND c.cust_id BETWEEN 6500 AND 6600 ORDER BY t.time_id; TIME_ID INDIV_SALE CUM_SALES ____________ ___________ ___________ 11DEC22 61 61 11DEC22 152 214 11DEC22 209 423 11DEC22 21 444 11DEC22 62 506 11DEC22 208 714 11DEC22 22 736 11DEC22 25 761 11DEC22 22 783 11DEC22 115 899 11DEC22 115 1,014 11DEC22 112 1,126 11DEC22 204 1,330
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
.
20.2.2.9 Parallel PartitionWise Operations with Windowing Functions
SQL windowing functions can have a query partitioning clause that can partition a query result into groups based on expressions used in the clause. For parallel queries on partitioned tables, the partitioning defined by the clause can be used to perform a partitionwise operation if the requirements for such operations are satisfied. This achieves faster SQL windowing queries on partitioned tables.
20.2.3 Reporting Functions
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
andvalue 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 thePARTITION
BY
clause is absent, then the function is computed over the whole query result set.
See Also:
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 against the sh
sample
schema 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 sh.sales s, sh.customers c, sh.countries co, sh.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('11OCT2021') 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_CATEGORY COUNTRY_REGION SALES MAX_REG_SALES ________________ _________________ __________ ________________ Baseball Americas 10208.6 10208.6 Baseball Asia 1592.8 10208.6 Baseball Europe 4174.76 10208.6 Cricket Americas 4577.73 4577.73 Cricket Asia 731.14 4577.73 Cricket Europe 1898.42 4577.73
The full query results are:
PROD_CATEGORY COUNTRY_REGION SALES ________________ _________________ __________ Baseball Americas 10208.6 Cricket Americas 4577.73
Example 2012 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
topselling products for each product subcategory that contributes more than 20% of the
sales within its product category. You can run this against the sh
sample
schema.
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 sh.sales s, sh.customers c, sh.countries co, sh.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('11OCT2022') 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;
20.2.3.1 RATIO_TO_REPORT Function
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 theRATIO_TO_REPORT
function is to be computed. If thePARTITION
BY
clause is absent, then the function is computed over the whole query result set.
Example 2013 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 sh.sales s, sh.channels ch WHERE s.channel_id=ch.channel_id AND s.time_id=to_DATE('11OCT2019') GROUP BY ch.channel_desc; CHANNEL_DESC SALES TOTAL_SALES RATIO_TO_REPORT _______________ _____________ ______________ __________________ Partners 7,764 28,158 .276 Direct Sales 14,798 28,158 .526 Internet 5,596 28,158 .199
20.2.4 LAG/LEAD Functions
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 selfjoin, 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. "LAG/LEAD Syntax" describes the syntax of these functions.
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 2017, 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.
20.2.4.1 LAG/LEAD Syntax
These functions have the following syntax:
{LAG  LEAD} ( value_expr [, offset] [, default] ) [RESPECT NULLSIGNORE 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 2014 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('10OCT2019') AND time_id<=TO_DATE('22OCT2019') GROUP BY time_id; TIME_ID SALES LAG1 LEAD1 ____________ _____________ _____________ _____________ 10OCT19 179,364 28,158 11OCT19 28,158 179,364 22,243 12OCT19 22,243 28,158 57,482 13OCT19 57,482 22,243 110,980 14OCT19 110,980 57,482 30,011 15OCT19 30,011 110,980 81,224 16OCT19 81,224 30,011 158,634 17OCT19 158,634 81,224 77,557 18OCT19 77,557 158,634 84,686 19OCT19 84,686 77,557 190,446 20OCT19 190,446 84,686 227,484 21OCT19 227,484 190,446 20,439 22OCT19 20,439 227,484
See "Data Densification for Reporting" for information showing how to use the LAG
/LEAD
functions for doing periodtoperiod comparison queries on sparse data.
Example 2015 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.
20.2.5 FIRST_VALUE, LAST_VALUE, and NTH_VALUE Functions
This section illustrates the FIRST_VALUE
, LAST_VALUE
, and NTH_VALUE
functions that are described in the following topics:
20.2.5.1 FIRST_VALUE and LAST_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 returns the first nonnull value in the set, or NULL
if all values are NULL
. If IGNORE
NULLS
is used with LAST_VALUE
, it returns the last nonnull 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_VALUELAST_VALUE ( <expr> ) [RESPECT NULLSIGNORE NULLS] OVER (analytic clause );
Example 2016 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 '18DEC20' AND '22DEC20' GROUP BY prod_id, channel_id, time_id ORDER BY prod_id; PROD_ID CHANNEL_ID TIME_ID AMOUNT_SOLD NV      115 2 18DEC20 10.91 115 2 20DEC20 10.91 115 2 21DEC20 10.91 115 2 22DEC20 10.91 115 3 18DEC20 0.91 10.91 115 3 20DEC20 0.91 10.91 115 3 21DEC20 10.91 10.91 115 3 22DEC20 10.8 10.91 115 4 18DEC20 10.91 115 4 21DEC20 10.91 13 rows selected.
20.2.5.2 NTH_VALUE Function
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 2017, 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 ofexpr
are included in or eliminated from the calculation. The default isRESPECT
NULLS
. 
The
FROM
FIRST
andFROM
LAST
options determine whether the offsetn
is from the first or last row. The default isFROM
FIRST
. 
IGNORE
NULLS
enables you to skip NULLs in measure values.
Example 2017 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 sh.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 ...
20.3 Advanced Aggregates for Analysis
Oracle Database provides multiple SQL functions to perform advanced aggregations. Additionally, for certain exact functions, corresponding functions that return approximate results are provided.
This section illustrates the following advanced analytic aggregate functions:
20.3.1 About Approximate Aggregates
Approximate aggregates are computed using SQL functions that return approximate results. They are used primarily in data exploration queries where exact values are not required and approximations are acceptable.
The APPROX_COUNT_DISTINCT
function returns the approximate number of rows containing a distinct value for a specified expression. The APPROX_COUNT_DISTINCT_DETAIL
and APPROX_COUNT_DISTINCT_AGG
functions enable you to compute varying aggregated levels of approximate distinct value counts within specified groupings. The result of these aggregations can be stored in tables or materialized views for further analysis or answering user queries.
The APPROX_COUNT_DISTINCT_DETAIL
function creates a baselevel summary, in binary format, containing tuples for all the dimensions listed in the WHERE
clause. The APPROX_COUNT_DISTINCT_AGG
function uses the data generated by the APPROX_COUNT_DISTINCT_DETAIL
function to extract the higher level tuples in binary format. This avoids having to rerun the original calculation (in this case, the calculation with APPROX_COUNT_DISTINCT
). The aggregate data that uses a binary format is converted into a humanreadable format using TO_APPROX_COUNT_DISTINCT
.
Figure 203 describes an example of using APPROX_COUNT_DISTINCT_DETAIL
to obtain the approximate number of distinct products sold each month. The sales data selected from the my_sales
table is aggregated by year and month and stored in the SALES_APPROX_MONTH
table using a query such as the following:
INSERT INTO sales_approx_month
(SELECT year, month, APPROX_COUNT_DISTINCT_DETAIL(prod_id) approx_month
FROM my_sales
GROUP BY year, month);
Notice that the values stored in approx_month
are binary values. Use the TO_APPROX_COUNT_DISTINCT
function to display these binary values in human readable format. To display the distinct number of products sold, aggregated by year and month, use the TO_APPROX_COUNT_DISTINCT
function on the approx_month
column. To display data aggregated by year, use the TO_APPROX_COUNT_DISTINCT
function along with the APPROX_COUNT_DISTINCT_AGG
function on the data stored in the approx_month
column.
Figure 203 Displaying Approximate Aggregates Using SQL Functions
Description of "Figure 203 Displaying Approximate Aggregates Using SQL Functions"
Another approach to computing the approximate number of distinct products sold each year could be to use the APPROX_COUNT_DISTINCT_AGG
to aggregate the monthly detail stored in the SALES_APPROX_MONTH
table and store the results in a table or materialized view.
Properties of SQL Functions that Return Approximate Percentile Results
SQL functions that provide approximate percentile results include APPROX_PERCENTILE
, APPROX_PERCENTILE_DETAIL
, and APPROX_PERCENTILE_AGG
. These functions have the following additional properties:

ERROR_RATE
Indicates the accuracy of the interpolated percentile values by computing the error rate of the approximate calculation

CONFIDENCE
Indicates the confidence in the accuracy of the error rate (when error rate is specified)

DETERMINISTIC
Controls the algorithm used to calculate approximations
If you need consistent and repeatable results, then use
DETERMINISTIC
. This would typically be the case where results need to be shared with other users
See Also:

APPROX_COUNT_DISTINCT
in Oracle Database SQL Language Reference 
APPROX_COUNT_DISTINCT_DETAIL
in Oracle Database SQL Language Reference for information about the function and theERROR_RATE
,CONFIDENCE
, andDETERMINISTIC
properties 
APPROX_COUNT_DISTINCT_AGG
in Oracle Database SQL Language Reference 
TO_APPROX_COUNT_DISTINCT
in Oracle Database SQL Language Reference
20.3.2 LISTAGG Function
The LISTAGG
function orders data within each group based on the ORDER
BY
clause and then concatenates the values of the measure column.
In releases prior to Oracle Database 12c Release 2 (12.2), if the concatenated value returned by the LISTAGG
function exceeds the maximum length supported for the return data type, then the following error is returned:
ORA01489: result of string concatenation is too long
Starting with Oracle Database 12c Release 2 (12.2), you can truncate the return string to fit within the maximum length supported for the return data type and display a truncation literal to indicate that the return value was truncated. The truncation is performed after the last complete data value thereby ensuring that no incomplete data value is displayed.
The syntax of the LISTAGG
function is as follows:
LISTAGG ( [ALL] [DISTINCT] <measure_column> [,<delimiter>] [ON OVERFLOW TRUNCATE [truncate_literal]  ON OVERFLOW ERROR [WITH  WITHOUT COUNT]]) WITHIN GROUP (ORDER BY <oby_expression_list>)
DISTINCT
removes duplicate values from the list.
measure_column
can be a column, constant, bind variable, or an expression involving them.
When the return string does not fit within the maximum length supported for the data type, you can either display an error or truncate the return string and display a truncation literal. The default is ON OVERFLOW ERROR
, which displays an error when truncation occurs.
truncate_literal
can be NULL
, a string literal, or constant expression. It is appended to the end of the list of values, after the last delimiter, when LISTAGG
returns a value that is larger than the maximum length supported for the return data type. The default value is an ellipsis (...).
WITH COUNT
displays the number of data values that were truncated from the LISTAGG
output because the maximum length supported for the return data type was exceeded. This is the default option. Use WITHOUT COUNT
to omit displaying a count at the end of the LISTAGG
function when the string is truncated.
delimiter
can be NULL
(default value), a string literal, bind variable, or constant expression. This is a mandatory parameter. If no delimiter is specified, then NULL
is used as the delimiter.
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.
See Also:
Oracle Database SQL
Language Reference for information about the maximum length supported for the VARCHAR2
data type
20.3.2.1 LISTAGG as Aggregate
You can use the LISTAGG
function as an aggregate.
Example 2018 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 > '01JAN01' 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. In this case, the ellipsis indicate that some values before the last customer name have been omitted from the output.
Example 2019 LISTAGG with Return String Exceeding the Maximum Permissible Length
This example orders data within each group specified by the GROUP BY
clause and concatenates the values in the cust_first_name
and cust_last_name
columns. If the list of concatenated names exceeds the maximum length supported for the VARCHAR2
data type, then the list is truncated to the last complete name. At the end of the list, the overflow literal of ’...’ is appended followed by the number of values that were truncated.
SELECT country_region,
LISTAGG(s.CUST_FIRST_NAME' ' s.CUST_LAST_NAME, ';' ON OVERFLOW TRUNCATE WITH COUNT) WITHIN GROUP (ORDER BY s.cust_id) AS customer_names
FROM countries c, customers s
WHERE c.country_id = s.country_id
GROUP BY c.country_region
ORDER BY c.country_region;
COUNTRY_REGION

CUSTOMER_NAMES

Africa
Laurice Lincoln;Kirsten Newkirk;Verna Yarborough;Chloe Dwyer;Betty Sampler;Terry
Hole;Waren Parkburg;Uwe Feldman;Douglas Hanson;Woodrow Lazar;Alfred Doctor;Stac
.
.
Zwolinsky;Buzz Milenova;Abbie Venkayala
COUNTRY_REGION

CUSTOMER_NAMES

Americas
Linette Ingram;Vida Puleo;Gertrude Atkins;Sibil Haul;Raina Cassidy;Kaula Daley;G
abriela Sean;Dolores Moore;Erica Vandermark;Madallyn Ladd;Carolyn Hinkle;Leonora
.
.
emphill;Urban Smyth;Murry Ivy;Steven Lauers;...(21482)
COUNTRY_REGION

CUSTOMER_NAMES

Asia
Harriett Charles;Willa Fitz;Faith Fischer;Gay Nance;Maggie Cain;Neda Clatterbuck
;Justa Killman;Penelope Oliver;Mandisa Grandy;Marette Overton;Astrid Rice;Poppy
.
.
ob Gentile;Lynn Hardesty;Mabel Barajas;...(1648)
COUNTRY_REGION

CUSTOMER_NAMES

Europe
Abigail Kessel;Anne Koch;Buick Emmerson;Frank Hardy;Macklin Gowen;Rosamond Kride
r;Raina Silverberg;Gloria Saintclair;Macy Littlefield;Yuri Finch;Bertilde Sexton
.
.
el Floyd;Lincoln Sean;Morel Gregory;Kane Speer;...(30284)
COUNTRY_REGION

CUSTOMER_NAMES

Middle East
Dalila Rockwell;Alma Elliott;Cara Jeffreys;Joy Sandstrum;Elizabeth Barone;Whitby
Burnns;Geoffrey Door;Austin Dutton;Tobin Newcomer;Blake Overton;Lona Kimball;Lo
.
.
edy;Brandon Moy;Sydney Fenton
COUNTRY_REGION

CUSTOMER_NAMES

Oceania
Fredericka Umstatt;Viola Nettles;Alyce Reagan;Catherine Odenwalld;Mauritia Linde
green;Heidi Schmidt;Ray Wade;Cicily Graham;Myrtle Joseph;Joan Morales;Brenda Obr
.
.
;Fredie Elgin;Gilchrist Lease;Guthrey Cain;...(793)
6 rows selected.
Example 2020 LISTAGG with Repeating Values Removed Using DISTINCT
This example orders data within each group specified by the GROUP BY
clause and concatenates the values in the prod_cateogry
and prod_desc
columns. If the list of concatenated names exceeds the maximum length supported for the VARCHAR2
data type, then the list is truncated to the last complete string. The DISTINCT
keyword specifies that duplicate values in the specified measure column must be removed.
SELECT cust_id, LISTAGG( DISTINCT prod_category':'prod_desc,' ; ' ON OVERFLOW TRUNCATE WITH COUNT)
WITHIN GROUP (ORDER BY amount_sold)
FROM sh.sales, sh.products
WHERE sales.prod_id=products.prod_id
AND amount_sold > 200 AND products.prod_id BETWEEN 10 and 15
AND time_id > '01JAN01'
GROUP BY cust_id;
20.3.2.2 LISTAGG as Reporting Aggregate
You can use the LISTAGG
function as a reporting aggregate.
Example 2021 LISTAGG as Reporting Aggregate
This example illustrates using LISTAGG
as a reporting aggregate. It
extracts the lowest unit cost for each product within each time period.
SELECT time_id, prod_id, LISTAGG(MIN(unit_cost),';') WITHIN GROUP (ORDER BY prod_id) OVER (PARTITION BY time_id) lowest_unit_cost FROM sh.sales_transactions_ext WHERE time_id BETWEEN '20DEC01' AND '22DEC01' AND prod_id BETWEEN 120 AND 125 GROUP BY time_id, prod_id; TIME_ID PROD_ID LOWEST_UNIT_COST    20DEC01 121 9.11;9.27;15.84;43.95 20DEC01 122 9.11;9.27;15.84;43.95 20DEC01 123 9.11;9.27;15.84;43.95 21DEC01 120 9.11;9.27 21DEC01 121 9.11;9.27 22DEC01 120 9.11;9.27;15.84;43.95;16.06;12.66 22DEC01 121 9.11;9.27;15.84;43.95;16.06;12.66 22DEC01 122 9.11;9.27;15.84;43.95;16.06;12.66 22DEC01 123 9.11;9.27;15.84;43.95;16.06;12.66 22DEC01 124 9.11;9.27;15.84;43.95;16.06;12.66 22DEC01 125 9.11;9.27;15.84;43.95;16.06;12.66
20.3.3 FIRST/LAST Functions
The FIRST/LAST
aggregate functions allow you to rank a data set and work with its topranked or bottomranked 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 firstranked or lastranked rows of column B. This is valuable because it avoids the need for a selfjoin or subquery, thus improving performance. These functions' syntax begins with a regular aggregate function (AVG
, BIT_AND_AGG
, BIT_OR_AGG
, BIT_XOR_AGG
, CHECKSUM
, COUNT
, KURTOSIS_POP
, KURTOSIS_SAMP
, MAX
, MIN
, SKEWNESS_POP
, SKEWNESS_SAMP
, STDDEV
, SUM
, and VARIANCE
) 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 FIRST  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.
This section contains the following topics:
20.3.3.1 FIRST/LAST As Regular Aggregates
You can use the FIRST
/LAST
family of aggregates as regular aggregate functions.
Example 2022 FIRST/LAST Example 1
The following query lets us compare minimum price and list price of our products. For each product subcategory within the Tennis 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 sh.products WHERE prod_category='Tennis' GROUP BY prod_subcategory; PROD_SUBCATEGORY LP_OF_LO_MINP LO_MINP LP_OF_HI_MINP HI_MINP      Tennis Balls 11.99 11.99 20.99 20.99 Tennis Racquet 299.99 299.99 599.99 599.99 Tennis Racquet Grip 7.99 7.99 7.99 7.99 Tennis Strings 19.99 19.99 29.99 29.99
20.3.3.2 FIRST/LAST As Reporting Aggregates
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 2022 for FIRST/LAST
. What if you 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 Cricket subcategory by
using FIRST/LAST
as reporting aggregates.
Example 2023 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 sh.products WHERE prod_subcategory = 'Cricket'; PROD_ID PROD_LIST_PRICE LP_OF_LO_MINP LP_OF_HI_MINP     48 11.99 6.99 22.99 113 22.99 6.99 22.99 114 18.99 6.99 22.99 115 8.99 6.99 22.99 116 11.99 6.99 22.99 117 8.99 6.99 22.99 118 7.99 6.99 22.99 119 6.99 6.99 22.99
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."
20.3.4 Inverse Percentile Functions
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
is a continuous function computed by interpolation and PERCENTILE_DISC
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 results 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.
Starting with Oracle Database 12c Release 2 (12.2), the approximate inverse distribution function APPROX_PERCENTILE
returns an approximate interpolated value that would fall into that percentile value with respect to the sort specification.
20.3.4.1 Normal Aggregate Syntax
[PERCENTILE_CONT  PERCENTILE_DISC]( constant expression ) WITHIN GROUP ( ORDER BY single order by expression [ASCDESC] [NULLS FIRST NULLS LAST])
20.3.4.2 Inverse Percentile Example Basis
Use the following queries to return customer data from the sh
sample schema.
SELECT cust_id, cust_credit_limit, CUME_DIST() OVER (ORDER BY cust_credit_limit) AS CUME_DIST FROM sh.customers WHERE cust_city='Marshal'; CUST_ID CUST_CREDIT_LIMIT CUME_DIST    32497 1500 0.173913043478260869565217391304347826087 28344 1500 0.173913043478260869565217391304347826087 36651 1500 0.173913043478260869565217391304347826087 8962 1500 0.173913043478260869565217391304347826087 102343 3000 0.3478260869565217391304347826086956521739 102077 3000 0.3478260869565217391304347826086956521739 8270 3000 0.3478260869565217391304347826086956521739 15192 3000 0.3478260869565217391304347826086956521739 101784 5000 0.5217391304347826086956521739130434782609 13808 5000 0.5217391304347826086956521739130434782609 30420 5000 0.5217391304347826086956521739130434782609 21380 5000 0.5217391304347826086956521739130434782609 35266 7000 0.6521739130434782608695652173913043478261 10346 7000 0.6521739130434782608695652173913043478261 31112 7000 0.6521739130434782608695652173913043478261 100977 9000 0.7391304347826086956521739130434782608696 3424 9000 0.7391304347826086956521739130434782608696 103066 10000 0.7826086956521739130434782608695652173913 100421 11000 0.9565217391304347826086956521739130434783 14459 11000 0.9565217391304347826086956521739130434783 17268 11000 0.9565217391304347826086956521739130434783 35225 11000 0.9565217391304347826086956521739130434783 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 sh.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)
, you first compute the row number = RN
= (1+x*(n1)), 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 is: 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 you compute PERCENTILE_CONT(0.5)
. Here n is 17. The row number RN
= (1 + 0.5*(n1))= 9 for both groups. Putting this into the formula, (FRN=CRN=9
), you 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) = (1211.67)*(value of row 11)+(11.6711)*(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 sh.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.
20.3.4.3 As Reporting Aggregates
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 [ASCDESC] [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 sh.customers WHERE cust_city='Marshal'; CUST_ID CUST_CREDIT_LIMIT PERC_DISC PERC_CONT     32497 1500 5000 5000 28344 1500 5000 5000 36651 1500 5000 5000 8962 1500 5000 5000 102343 3000 5000 5000 102077 3000 5000 5000 8270 3000 5000 5000 15192 3000 5000 5000 101784 5000 5000 5000 13808 5000 5000 5000 30420 5000 5000 5000 21380 5000 5000 5000 35266 7000 5000 5000 10346 7000 5000 5000 31112 7000 5000 5000 100977 9000 5000 5000 3424 9000 5000 5000 103066 10000 5000 5000 100421 11000 5000 5000 14459 11000 5000 5000 17268 11000 5000 5000 35225 11000 5000 5000 41496 15000 5000 5000
20.3.4.4 Restrictions on Inverse Percentile Functions
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 is 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 nonnull values. You can use the NULLS
FIRST
/NULLS
LAST
option in the ORDER
BY
clause, but they will be ignored as NULLs
are ignored.
20.3.4.5 Using Percentile Functions that Return Approximate Results
Oracle Database provides a set of SQL functions that return approximate percentile results. These functions can be used to monitor quality, track social media activity, monitor performance, and search for outliers within a data set.
The following SQL functions compute and display approximate percentile results:

APPROX_PERCENTILE
Returns an approximate interpolated value that falls into the percentile value with respect to a sort specification. It can process large amounts of data significantly faster than the
PERCENTILE_CONT
with negligible deviation from the exact result. 
APPROX_PERCENTILE_DETAIL
Calculates approximate percentile information, called a detail, within a set of data that is specified using a
GROUP BY
clause. Detail information created with this function is stored in binary format and is meant to be consumed by both theTO_APPROX_PERCENTILE
andAPPROX_PERCENT_DETAIL_AGG
functions. 
APPROX_PERCENTILE_AGG
Performs aggregations on the details created using the
APPROX_PERCENTILE_DETAIL
function. 
TO_APPROX_PECENTILE
Displays the results of detail or aggregation, which are stored as BLOB values, in human readable format.
The detail and the higher level aggregated data can be stored in tables or materialized views for further analysis.
Example: Displaying Approximate Percentile Sales Data Within a Country or State
This example from the sh
sample schema uses
APPROX_PERCENTILE_DETAIL
to perform percentile calculations once,
store the results in table, and then perform approximate aggregations based on the
stored data. The TO_APPROX_PERCENTILE
function is used to display the
results of the percentile calculations in humanreadable format.
20.3.5 Hypothetical Rank Functions
These functions provide functionality useful for whatif 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 [ASCDESC] [NULLS FIRSTNULLS 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 2024 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 sh.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 2025 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 sh.products WHERE prod_subcategory LIKE 'Baseball%' GROUP BY prod_subcategory; PROD_SUBCATEGORY HRANK HPERC_ HCUME_     Baseball Clothing 3 .000 .333 Baseballs 6 .000 .167
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.
20.3.6 Linear Regression Functions
The regression functions support the fitting of an ordinaryleastsquares 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.
20.3.6.1 REGR_COUNT Function
REGR_COUNT
returns the number of nonnull 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.
20.3.6.2 REGR_AVGY and REGR_AVGX Functions
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.
20.3.6.4 REGR_R2 Function
The REGR_R2
function computes the coefficient of determination (usually called "Rsquared" 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.
20.3.6.5 REGR_SXX, REGR_SYY, and REGR_SXY Functions
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)
20.3.6.6 Linear Regression Statistics Examples
Some common diagnostic statistics that accompany linear regression analysis are given in Table 202. Note that Oracle enables you to calculate all of these.
Table 202 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 yintercept 

20.3.6.7 Sample Linear Regression Calculation
In this example from the sh
sample schema, you compute an
ordinaryleastsquares 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 sh.sales s, sh.products p WHERE s.prod_id=p.prod_id AND p.prod_category LIKE 'Baseball%' AND s.time_id=to_DATE('10OCT2020') GROUP BY s.channel_id; CHANNEL_ID SLOPE INTCPT RSQR COUNT AVGLISTP AVGQSOLD _____________ ________ _________ _______ ________ ____________________________________________ ___________ 2 0 1 1 238 103.103445378151260504201680672268907563 1 3 0 1 1 169 152.179349112426035502958579881656804734 1 4 0 1 1 75 46.41666666666666666666666666666666666667 1
20.3.7 About Statistical Aggregates
Oracle Database 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 Also:

Oracle Database PL/SQL Packages and Types Reference for detailed information about the
DBMS_STAT_FUNCS
package 
Oracle Database SQL Language Reference for detailed information about syntax and semantics
This section contains the following topics:
20.3.7.1 Descriptive Statistics
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)
Starting with Oracle Database 12c Release 2 (12.2), the approximate inverse distribution function APPROX_MEDIAN
provides an approximate median value of the specified expression.
See Also:
20.3.7.2 Hypothesis Testing  Parametric Tests
You can calculate the following descriptive statistics:

OneSample TTest
STATS_T_TEST_ONE (expr1, expr2 (a constant) [, return_value])

PairedSamples TTest
STATS_T_TEST_PAIRED (expr1, expr2 [, return_value])

IndependentSamples TTest. Pooled Variances
STATS_T_TEST_INDEP (expr1, expr2 [, return_value])

IndependentSamples TTest, Unpooled Variances
STATS_T_TEST_INDEPU (expr1, expr2 [, return_value])

The FTest
STATS_F_TEST (expr1, expr2 [, return_value])

OneWay ANOVA
STATS_ONE_WAY_ANOVA (expr1, expr2 [, return_value])
20.3.7.3 Crosstab Statistics
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 chisquared

Significance of observed chisquared

Degree of freedom for chisquared

Phi coefficient, Cramer's V statistic

Contingency coefficient

Cohen's Kappa
20.3.7.4 Hypothesis Testing  NonParametric Tests
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])

MannWhitney Test
STATS_MW_TEST (expr1, expr2 [, return_value])

KolmogorovSmirnov Test
STATS_KS_TEST (expr1, expr2 [, return_value])
20.3.7.5 NonParametric Correlation
You can calculate the following parametric statistics:

Spearman's rho Coefficient
CORR_S (expr1, expr2 [, return_value])

Kendall's taub 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.
20.3.8 About UserDefined Aggregates
Oracle offers a facility for creating your own functions, called userdefined 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 userdefined functions are programmed for parallel processing.

Object data types can be processed.
As a simple example of a userdefined 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 userdefined 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 userdefined 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 wellparallelized in SQL. Even the earlier example, the skew statistic, can be created using standard, albeit lengthy, SQL.
20.4 Pivoting Operations
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 <tableexpr> PIVOT ( aggregatefunction(<column>) AS <alias> FOR <pivotcolumn> IN (<value1>, <value2>,..., <valuen>) ) AS <alias> WHERE .....
See Oracle Database SQL Language Reference for pivot_clause
syntax.
This section contains the following topics:
20.4.1 Creating the View Used for Pivoting Examples
The pivoting and unpivoting examples in this section are based on the
sales_view
view created here.
Example 2026 Creating the SALES_VIEW View for Pivoting Examples
The following example creates the sales_view
view that is used as the basis to illustrate the use of pivoting.
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 sh.sales, sh.times, sh.customers, sh.countries, sh.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);
20.4.2 Pivoting Example
The following statement illustrates a typical pivot on the channel
column of view sales_view
created as described in Example 2026:
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 _____________________________________________ _______________ _________________ ________________ ____________ 11" Youth Field Master Glove 229512.97 26249.55 11.5" Youth Triple Stripe Series Glove 391230.15 53767.53 12" Premium Series Glove 495494.7 49750.07 12.75" Premium Series Glove 577851.94 152500.6 13" Field Master Series Glove 286291.49 42809.44 2 Competition Grade NFHS Baseballs 153199.63 28768.04 5172.75 5 Point Batting Tee 1546466.39 196999.42 6 Gallon Empty Ball Bucket 158223.55 102388.63 ... ...
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.
20.4.3 Pivoting on Multiple Columns
You can pivot on more than one column. The following statement illustrates a typical multiple column pivot on the view sales_view
created as described in Example 2026:
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 _________________________________ _____________ ______________ ______________ ______________ _______ 12" Premium Series Glove 197 401 494 12.75" Premium Series Glove 635 898 930 Soccer Ball  Size 5 279 484 872 Pro Style Batting Tee 217 400 865 Match Used Autograph Racquet 195 335 641 Cricket Ball  Training Ball 355 423 774 ...
Note that this example specifies a multicolumn IN
list with column headings designed to match the IN
list members.
20.4.4 Pivoting: Multiple Aggregates
You can pivot with multiple aggregates, as shown in the following example that pivots on multiple aggregates from the sales_view
created in Example 2026:
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 _____________________________________________ _________ _________ _____________ _________ _____________ _________ ___________ _________ 11" Youth Field Master Glove 26249.55 861 60554.68 1886 11.5" Youth Triple Stripe Series Glove 53767.53 1370 132582.67 3103 12" Premium Series Glove 49750.07 1170 100341.35 2094 12.75" Premium Series Glove 152500.6 2770 316811.53 5361 13" Field Master Series Glove 42809.44 1223 183990.15 4881 2 Competition Grade NFHS Baseballs 28768.04 1195 62693.53 2596 5172.75 225 ...
Note that the query creates column headings by concatenating the pivot values, the underscore character (_), and the alias of the aggregate column. If the length of the generated column heading exceeds the maximum length of a column name, then an ORA00918
error is returned. To avoid this error, use AS
alias
to specify a shorter column alias for the pivot column heading, the aggregate value column name, or both. "Pivoting on Multiple Columns" demonstrates using an alias for the pivot values.
See Also:
Oracle Database SQL Language Reference for information about the maximum length of column names
20.4.5 Distinguishing PIVOTGenerated Nulls from Nulls in Source Data
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 you 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, you 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
.
20.4.6 Wildcard and Subquery Pivoting with XML Operations
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 outputs 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) );
See **INTERNAL XREF ERROR** for the syntax that creates the view sales_view
.
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 outputs 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.
20.5 Unpivoting Operations
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. The following command creates a table based on the view sales_view
created as described in Example 2026:
CREATE TABLE pivotedTable AS SELECT * FROM (SELECT product, quarter, quantity_sold, amount_sold FROM sales_view) PIVOT ( SUM(quantity_sold) AS sumq, SUM(amount_sold) AS suma FOR quarter IN ('01' AS Q1, '02' AS Q2, '03' AS Q3, '04' AS Q4));
The table's contents resemble the following:
SELECT * FROM pivotedTable ORDER BY product; PRODUCT Q1_SUMQ Q1_SUMA Q2_SUMQ Q2_SUMA Q3_SUMQ Q3_SUMA Q4_SUMQ Q4_SUMA _____________________________________________ __________ _____________ __________ _____________ __________ _____________ __________ _____________ 11" Youth Field Master Glove 2750 91653.75 2069 69199.25 2487 82265.49 2217 73198.71 11.5" Youth Triple Stripe Series Glove 3524 157638.52 2898 128662.03 3351 147640.32 3270 143639.48 12" Premium Series Glove 3196 161666.11 3074 153903.54 3504 172981.83 3234 157034.64 12.75" Premium Series Glove 4338 261078.2 2992 178748.85 5392 323570.59 4708 283766.43 13" Field Master Series Glove 2983 114058.14 2074 80042.09 4183 161536.24 4079 157454.61 2 Competition Grade NFHS Baseballs 3376 83585.33 1699 41743.94 2654 65205.61 2427 59299.07 ...
The following UNPIVOT
operation rotates the quarter columns into rows. For each product, there will be four rows, one for each quarter.
SELECT product, DECODE(quarter, 'Q1_SUMQ', 'Q1', 'Q2_SUMQ', 'Q2', 'Q3_SUMQ', 'Q3', 'Q4_SUMQ', 'Q4') AS quarter, quantity_sold FROM pivotedTable UNPIVOT INCLUDE NULLS (quantity_sold FOR quarter IN (Q1_SUMQ, Q2_SUMQ, Q3_SUMQ, Q4_SUMQ)) ORDER BY product, quarter; PRODUCT QU QUANTITY_SOLD    1.44MB External 3.5" Diskette Q1 6098 1.44MB External 3.5" Diskette Q2 5112 1.44MB External 3.5" Diskette Q3 6050 1.44MB External 3.5" Diskette Q4 5848 128MB Memory Card Q1 1963 128MB Memory Card Q2 2361 128MB Memory Card Q3 3069 128MB Memory Card Q4 2832 ...
Note the use of INCLUDE
NULLS
in this example. You can also use EXCLUDE
NULLS
, which is the default setting.
In addition, you can also unpivot using two columns, as in the following:
SELECT product, quarter, quantity_sold, amount_sold FROM pivotedTable UNPIVOT INCLUDE NULLS ( (quantity_sold, amount_sold) FOR quarter IN ((Q1_SUMQ, Q1_SUMA) AS 'Q1', (Q2_SUMQ, Q2_SUMA) AS 'Q2', (Q3_SUMQ, Q3_SUMA) AS 'Q3', (Q4_SUMQ, Q4_SUMA) AS 'Q4')) ORDER BY product, quarter; PRODUCT QU QUANTITY_SOLD AMOUNT_SOLD     1.44MB External 3.5" Diskette Q1 6098 58301.33 1.44MB External 3.5" Diskette Q2 5112 49001.56 1.44MB External 3.5" Diskette Q3 6050 56974.3 1.44MB External 3.5" Diskette Q4 5848 55341.28 128MB Memory Card Q1 1963 110763.63 128MB Memory Card Q2 2361 132123.12 128MB Memory Card Q3 3069 170710.4 128MB Memory Card Q4 2832 157736.6
20.6 Data Densification for Reporting
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.
This section contains the following topics:
20.6.1 About Partition Join Syntax
The syntax for partitioned outer join extends the 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.
20.6.2 Sample of Sparse Data
A typical situation with a sparse dimension is shown in the following example, which computes the weekly sales and yeartodate sales for the product Bounce for weeks 2030 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 sh.Sales s, sh.Times t, sh.Products p WHERE s.Time_id = t.Time_id AND s.Prod_id = p.Prod_id AND p.Prod_name LIKE ('Tennis%') AND t.Calendar_Year IN (2020,2021) 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 __________________ _______ _______ __________ Tennis Balls He 2020 29 2072.4 Tennis Balls He 2020 30 2730.46 Tennis Balls He 2021 30 3854.76 Tennis Strings 2020 25 3051.6 Tennis Strings 2020 23 2555.41 Tennis Strings 2021 21 3776.64 Tennis Strings 2021 24 2875.29 Tennis Strings 2020 26 949.72 Tennis Strings 2020 20 849.84 Tennis Strings 2020 21 379.96 Tennis Strings 2020 22 335.62 Tennis Grip Ove 2020 29 293.64 Tennis Grip Ove 2021 27 265.08 Tennis Racquet 2021 26 63.92 ...
In this example, you would expect 22 rows of data (11 weeks each from 2 years) if the data were dense. However, you get only 18 rows because weeks 25 and 26 are missing in 2000, and weeks 26 and 28 in 2001.
20.6.3 Filling Gaps in Data
You can take the sparse data of the query shown in Sample of Sparse Data and do a partitioned outer join with a dense set of time data. In the following query, you alias the original query as v
and you select data from the times
table, which you alias as t
. Here you 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 sh.Sales s, sh.Times t, sh.Products p WHERE s.Time_id = t.Time_id AND s.Prod_id = p.Prod_id AND p.Prod_name LIKE ('Baseball%') AND t.Calendar_Year IN (2019,2021) 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 (2019, 2021) 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 __________________ _______ _______ ______________ Baseball Is Lif 2019 20 0 Baseball Is Lif 2019 21 0 Baseball Is Lif 2019 22 0 Baseball Is Lif 2019 23 0 Baseball Is Lif 2019 24 0 Baseball Is Lif 2019 25 0 Baseball Is Lif 2019 26 0 Baseball Is Lif 2019 27 5088.35 Baseball Is Lif 2019 28 2890.79 Baseball Is Lif 2019 29 4993.36 Baseball Is Lif 2019 30 5340.06 Baseball Is Lif 2021 20 8686.19 Baseball Is Lif 2021 21 6725.1 Baseball Is Lif 2021 22 7494.93 Baseball Is Lif 2021 23 1010.34 Baseball Is Lif 2021 24 6656.23 Baseball Is Lif 2021 25 0 Baseball Is Lif 2021 26 7925.89 Baseball Is Lif 2021 27 4145.25 Baseball Is Lif 2021 28 3520.6 Baseball Is Lif 2021 29 9874.68 Baseball Is Lif 2021 30 6380.98
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.
20.6.4 Filling Gaps in Two Dimensions
Ndimensional data is typically displayed as a dense 2dimensional 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 sh.sales s, sh.products p, sh.customers c, sh.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, you 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. You 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 2019 147 52782 2020 29 209.82 147 52782 2021 71 594.36 147 52782 2022 345 2754.42 147 52782 2023 147 52785 2019 1 7.99 147 52785 2020 147 52785 2021 147 52785 2022 147 52785 2023 147 52786 2019 1 7.99 147 52786 2020 147 52786 2021 2 15.98 147 52786 2022
20.6.5 Filling Gaps in an Inventory Table
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('01/04/21', 'DD/MM/YY'), 10); 1 row inserted. SQL> INSERT INTO invent_table VALUES ('bottle', TO_DATE('06/04/21', 'DD/MM/YY'), 8); 1 row inserted. SQL> INSERT INTO invent_table VALUES ('can', TO_DATE('01/04/21', 'DD/MM/YY'), 15); 1 row inserted. SQL> INSERT INTO invent_table VALUES ('can', TO_DATE('04/04/21', 'DD/MM/YY'), 11); 1 row inserted.
The inventory table now has the following rows:
PRODUCT TIME_ID QUANT __________ ____________ ________ bottle 01APR21 10 bottle 06APR21 8 can 01APR21 15 can 04APR21 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 sh.times WHERE times.time_id BETWEEN TO_DATE('01/04/21', 'DD/MM/YY') AND TO_DATE('07/04/21', '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 nonnull value in the window due to the option IGNORE
NULLS
, which you can use with both LAST_VALUE
and FIRST_VALUE
. You see the desired output in the column repeated_quantity
in the following output:
PRODUCT TIME_ID QUANTITY REPEATED_QUANTITY __________ ____________ ___________ ____________________ bottle 01APR21 10 10 bottle 02APR21 10 bottle 03APR21 10 bottle 04APR21 10 bottle 05APR21 10 bottle 06APR21 8 8 bottle 07APR21 8 can 01APR21 15 15 can 02APR21 15 can 03APR21 15 can 04APR21 11 11 can 05APR21 11 can 06APR21 11 can 07APR21 11
20.6.6 Computing Data Values to Fill Gaps
Examples in sections Filling Gaps in Data, Filling Gaps in Two Dimensions, and Filling Gaps in an Inventory Table 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 nonnull value.
For example, the following query computes monthly totals for products 64MB Memory card and DVDR 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 wraps 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 sh.sales s, sh.products p, sh.times t WHERE s.prod_id IN (122,136) AND calendar_year = 2020 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 = 2020) t LEFT OUTER JOIN V PARTITION BY (prod_name) USING (calendar_month_desc); PROD_NAME CALENDAR_MONTH_DESC UNITS SALES COMPUTED_UNITS COMPUTED_SALES _______________ ____________________ _____ __________ ________________ _______________ Soccer Jerse 202001 27 940.92 Soccer Jerse 202002 27 940.92 Soccer Jerse 202003 27 940.92 Soccer Jerse 202004 27 940.92 Soccer Jerse 202005 27 940.92 Soccer Jerse 202006 27 940.92 Soccer Jerse 202007 27 940.92 Soccer Jerse 202008 27 940.92 Soccer Jerse 202009 27 940.92 Soccer Jerse 202010 34 1206.75 34 1206.75 Soccer Jerse 202011 41 1425.49 41 1425.49 Soccer Jerse 202012 6 190.52 6 190.52 Wide Brim Ha 202001 30 631.17 30 631.17 Wide Brim Ha 202002 25 484.22 25 484.22 ...
20.7 Time Series Calculations on Densified Data
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, you calculate weekly yeartodate 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 sh.Sales s, sh.Times t, sh.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 (2020,2021) 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 (2020, 2021) 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 __________________ _______ _______ ________________ ___________________ Tennis Balls 12 2020 20 2222.52 2222.52 Tennis Balls He 2020 20 0 Tennis Grip Ove 2020 20 0 Tennis Racquet 2020 20 0 Tennis Strings 2020 20 1775.4 6623.44 Tennis Strings 2020 20 985.45 6623.44 Tennis Strings 2020 20 3012.75 6623.44 Tennis Strings 2020 20 849.84 6623.44 Tennis Balls 12 2020 21 1468.75 3691.27 Tennis Balls He 2020 21 248.78 248.78 Tennis Grip Ove 2020 21 20.7 20.7 Tennis Racquet 2020 21 113.76 113.76 Tennis Strings 2020 21 1043.74 10609.1 Tennis Strings 2020 21 2057.76 10609.1 Tennis Strings 2020 21 504.2 10609.1 Tennis Strings 2020 21 379.96 10609.1 Tennis Balls 12 2020 22 1270 4961.27 Tennis Balls He 2020 22 0 248.78 Tennis Grip Ove 2020 22 0 20.7
This section contains the following topics:
20.7.1 PeriodtoPeriod Comparison for One Time Level: Example
How do you use this feature to compare values across time periods? Specifically, how do you calculate a yearoveryear sales comparison at the week level? The following query returns on the same row, for each product, the yeartodate sales for each week of 2021 with that of 2020.
Note that in this example you 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 wraps 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 sh.Sales s, sh.Times t, sh.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 (2020,2021) 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 (2020, 2021)) t ON (v.week = t.week AND v.Year = t.Year) ) dense_sales ) year_over_year_sales WHERE Year = 2021 AND Week BETWEEN 30 AND 40 ORDER BY 1, 2, 3;
In the FROM
clause of the inline view dense_sales
, you 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 yeartodate sales (the weekly_ytd_sales
column). Thus, the view dense_sales
computes the yeartodate 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 yeartodate 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. You 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 yeartodate sales in the specified weeks of years 2001 and 2000.
20.7.2 PeriodtoPeriod Comparison for Multiple Time Levels: Example
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, you could compare sales versus the prior period at the year, quarter, month and day levels. How can you create a query which performs a yearoveryear comparison of yeartodate sales for all levels of our time hierarchy?
You 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:

Create a view called
cube_prod_time
, which holds a hierarchical cube of sales aggregated acrosstimes
andproducts
. 
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
.See "Create the View edge_time, which is a Complete Set of Date Values".

Finally, for maximum performance, create a materialized view,
mv_prod_time
, built using the same definition ascube_prod_time
.See "Create the Materialized View mv_prod_time to Support Faster Performance".

Create the comparison query.
See "Create the Comparison Query".
For more information regarding hierarchical cubes, see SQL for Aggregation in Data Warehouses. The materialized view is defined in the following section.
Create the Hierarchical Cube View
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 you 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.
Create the View edge_time, which is a Complete Set of Date Values
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);
Create the Materialized View mv_prod_time to Support Faster Performance
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 you 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);
Create the Comparison Query
You have now set the stage for our comparison query. You can obtain periodtoperiod 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 you 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 singlelevel 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 ('200108' ) AND gid_t IN (0, 1)) OR day and month data (qtr IN ('200103' ) 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 01AUG01_3 0 0 0 0 0 139 02AUG01_3 1347.53 0 1347.53 0 1347.53 139 03AUG01_3 0 1347.53 1347.53 42.36 42.36 139 04AUG01_3 57.83 0 57.83 995.75 937.92 139 05AUG01_3 0 57.83 57.83 0 0 139 06AUG01_3 0 0 0 0 0 139 07AUG01_3 134.81 0 134.81 880.27 745.46 139 08AUG01_3 1289.89 134.81 1155.08 0 1289.89 139 09AUG01_3 0 1289.89 1289.89 0 0 139 10AUG01_3 0 0 0 0 0 139 11AUG01_3 0 0 0 0 0 139 12AUG01_3 0 0 0 0 0 139 13AUG01_3 0 0 0 0 0 139 14AUG01_3 0 0 0 0 0 139 15AUG01_3 38.49 0 38.49 1104.55 1066.06 139 16AUG01_3 0 38.49 38.49 0 0 139 17AUG01_3 77.17 0 77.17 1052.03 974.86 139 18AUG01_3 2467.54 77.17 2390.37 0 2467.54 139 19AUG01_3 0 2467.54 2467.54 127.08 127.08 139 20AUG01_3 0 0 0 0 0 139 21AUG01_3 0 0 0 0 0 139 22AUG01_3 0 0 0 0 0 139 23AUG01_3 1371.43 0 1371.43 0 1371.43 139 24AUG01_3 153.96 1371.43 1217.47 2091.3 1937.34 139 25AUG01_3 0 153.96 153.96 0 0 139 26AUG01_3 0 0 0 0 0 139 27AUG01_3 1235.48 0 1235.48 0 1235.48 139 28AUG01_3 173.3 1235.48 1062.18 2075.64 1902.34 139 29AUG01_3 0 173.3 173.3 0 0 139 30AUG01_3 0 0 0 0 0 139 31AUG01_3 0 0 0 0 0 139 200108_2 8347.43 7213.21 1134.22 8368.98 21.55 139 200103_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.
20.7.3 Creating a Custom Member in a Dimension: Example
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 SQL for Modeling for more information on this topic.
As an example of a task, what if you want to define a new member for the
time
dimension? You want to create a 13th member of the Month level in
the 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 2021.
The solution has two steps. Note that you 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 '202113_2', 2021, 5, '202105', 13, '202113', null, null, 8  <gid_of_mon>;
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 userdefined 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;
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 two products,
the rollup values of the results are necessarily repetitions of lower level aggregations.
20.8 Miscellaneous Analysis and Reporting Capabilities
This section illustrates the following additional analytic capabilities:
20.8.1 WIDTH_BUCKET Function
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. "WIDTH_BUCKET Syntax" describes the WIDTH_BUCKET
syntax.
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.
20.8.1.1 WIDTH_BUCKET Syntax
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 2027.
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 you 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 closedopen 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 204 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 openclosed 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 2027 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. You 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
20.8.2 Linear Algebra
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.
See Also:
Oracle Database PL/SQL Packages and Types Reference for further information regarding the use of the UTL_NLA
package and linear algebra
Example 2028 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, /*discount coupons*/ dmail NUMBER, /*direct mailers*/
Then you can build the following salesmarketing 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 salesmarketing model reasonable for year 2020 data? That is, is the multiplecorrelation 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 = 2020;
You could also solve questions such as "What is the expected baseline sales revenue of a store without any marketing programs in 2020?" or "Which component of the marketing program was the most effective in 2021? That is, a dollar increase in which program produced the greatest expected increase in sales?"
20.8.3 CASE Expressions
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, 2029, 3039, 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.
See Also:
"Creating Histograms Using CASE Statement" for information about using CASE
to create histograms
Example 2029 CASE
This statements in this example uses the hr
(Human Resources) sample
schema.
Suppose you wanted to find the average salary of all employees in the company. If an
employee's salary is less than $50000, you want the query to use $50000 instead. Without a
CASE
statement, you might choose to write this query as
follows:
SELECT AVG(foo(e.salary)) FROM hr.employees e;
In the above example, foo
is a function that returns its input if
the input is greater than 14000, and returns 14000 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 follows.
SELECT AVG(CASE when e.salary > 14000 THEN e.salary ELSE 14000 end) AS avg_sal_14k_floor FROM hr.employees e;
Using a CASE
expression lets you avoid developing custom functions and can also perform faster.
Example 2030 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. You might have had a query find the average
salary for all employees in the salary ranges 014000 and 1400124000. It would look
like:
SELECT AVG(CASE WHEN e.salary BETWEEN 0 AND 1400 THEN e.salary ELSE null END) avg14000, AVG(CASE WHEN e.salary BETWEEN 14001 AND 24000 THEN e.salary ELSE null END) avg24000 FROM employees e;
Although this query places the aggregates of independent subsets data into separate columns, by adding a CASE
expression to the GROUP
BY
clause you 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
.
20.8.3.1 Creating Histograms Using CASE Statement
You can use the CASE
statement when you want to obtain histograms with userdefined 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 2031 Histogram Example 1
SELECT SUM(CASE WHEN cust_credit_limit BETWEEN 0 AND 3999 THEN 1 ELSE 0 END) AS "03999", SUM(CASE WHEN cust_credit_limit BETWEEN 4000 AND 7999 THEN 1 ELSE 0 END) AS "40007999", SUM(CASE WHEN cust_credit_limit BETWEEN 8000 AND 11999 THEN 1 ELSE 0 END) AS "800011999", SUM(CASE WHEN cust_credit_limit BETWEEN 12000 AND 16000 THEN 1 ELSE 0 END) AS "1200016000" FROM customers WHERE cust_city = 'Marshal'; 03999 40007999 800011999 1200016000     8 7 7 1
Example 2032 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
20.8.4 Frequent Itemsets in SQL Analytics
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 pointofsale 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.

SQLbased 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 "Business Intelligence Query Example 4: Frequent Itemsets".
20.9 Limiting SQL Rows
You can limit the rows returned from SQL queries by either a specific number of rows or a percentage of rows. In some cases, you may need the query results to be ordered before the number of rows returned is limited. A query which first sorts its rows and then limits the number of rows returned is often called a TopN query, and it offers a straightforward way of creating reports or just a simple view of basic questions, such as "Who are the ten highestpaid employees?" It is also useful for user interfaces that provide the first few rows of a data set for browsing. When you issue a TopN query, you may also want to specify an offset: the offset excludes the leading rows of the query result set. The query then returns the specified number or percent of rows starting with the first row after the offset. An offset enables you to modify typical questions, so that the question about highestpaid employees might skip the top ten employees and return only those from eleventh to twentieth place in the salary rankings. In a similar manner, you could query the employees by salary, skip the top ten employees and then return the top 10% of the remaining employees.
Queries that limit the rows returned have been possible using the ROW_NUMBER
window function, the ROWNUM
pseudocolumn, and other techniques for some time, but can now be written more simply with the ANSI SQL standard syntax of row_limiting_clause. When using this clause, you can ensure a deterministic sort order, as needed for TopN queries, by including an ORDER
BY
clause in the query. The row_limiting_clause
clause appears as the last part of a SELECT
, after the ORDER
BY
clause, and it starts with either the keyword FETCH
or OFFSET
. Its basic syntax is as follows:
[ OFFSET offset { ROW  ROWS } ] [ FETCH { FIRST  NEXT } [ { rowcount  percent PERCENT } ] { ROW  ROWS } { ONLY  WITH TIES } ]
This syntax is illustrated in the following sections.
OFFSET
This specifies the number of rows to skip before row limiting begins. offset
must be a number. If you specify a negative number, then offset is treated as 0. If you specify NULL
, or a number greater than or equal to the number of rows returned by the query, then 0 rows are returned. If offset
includes a fraction, then the fractional portion is truncated. If you do not specify this clause, then offset
is 0 and row limiting begins with the first row. To improve readability, Oracle offers the option of using either ROW
or ROWS
 both are equivalent.
FETCH
This specifies the number of rows or percentage of rows to return. If you do not specify this clause, then all rows are returned, beginning at the offset
+ 1 row. If you use the WITH
TIES
keywords, your query will also include all rows that match the sort key of the last qualified row.
To illustrate how you can limit the number of rows returned in a query, consider the
following statements. These statements are run against the
hr
(Human Resources) schema provided by
Oracle.
SELECT employee_id, last_name FROM hr.employees ORDER BY employee_id FETCH FIRST 5 ROWS ONLY; EMPLOYEE_ID LAST_NAME   100 King 101 Yang 102 Garcia 103 James 104 Miller
In this statement, the first 5 employees with the lowest employee_id
values are returned.
To return the next set of 5 employees, add an OFFSET
to the statement:
SELECT employee_id, last_name FROM hr.employees ORDER BY employee_id OFFSET 5 ROWS FETCH NEXT 5 ROWS ONLY; EMPLOYEE_ID LAST_NAME   105 Austin 106 Pataballa 107 Lorentz 108 Greenberg 109 Faviet
In this statement, FETCH
FIRST
and FETCH
NEXT
are equivalent, but FETCH
NEXT
is clearer when OFFSET
is used.
The offset can be a larger value, such as 10, as in the following statement:
SELECT employee_id, last_name FROM hr.employees ORDER BY employee_id OFFSET 10 ROWS FETCH NEXT 5 ROWS ONLY; EMPLOYEE_ID LAST_NAME   105 Williams 106 Jackson 107 Nguyen 108 Gruenberg 109 Faviet
You can choose to return values by percentage instead of a fixed number. To illustrate this, the following statement returns the 5 percent of employees with the lowest salaries:
SELECT employee_id, last_name, salary FROM hr.employees ORDER BY salary FETCH FIRST 5 PERCENT ROWS ONLY; EMPLOYEE_ID LAST_NAME SALARY    132 Olson 2100 128 Markle 2200 136 Philtanker 2200 127 Landry 2400 135 Gee 2400
In the following result set, 5% is six rows. This is important if you use
OFFSET
, because the percentage calculation
is based on the entire result set before the offset is applied. An
example of using OFFSET
is the following
statement:
SELECT employee_id, last_name, salary FROM hr.employees ORDER BY salary, employee_id OFFSET 6 ROWS FETCH FIRST 5 PERCENT ROWS ONLY; EMPLOYEE_ID LAST_NAME SALARY    132 Olson 2100 128 Markle 2200 136 Philtanker 2200 127 Landry 2400 135 Gee 2400 119 Colmenares 2500
This statement still returns six rows, but starts with the seventh row of the result set. The additional employee_id
added to the ORDER
BY
clause was to guarantee a deterministic sort.
You have the option of returning tie values by using WITH
TIES
. This would return the 5 percent with the lowest salaries, plus all additional employees with the same salary as the last row fetched:
SELECT employee_id, last_name, salary FROM hr.employees ORDER BY salary FETCH FIRST 5 PERCENT ROWS WITH TIES; EMPLOYEE_ID LAST_NAME SALARY ______________ _____________ _________ 132 Olson 2100 128 Markle 2200 136 Philtanker 2200 127 Landry 2400 135 Gee 2400 119 Colmenares 2500 131 Marlow 2500 140 Patel 2500 144 Vargas 2500 182 Sullivan 2500 191 Perkins 2500
You could issue the same query, but skip the first 5 values with the following statement:
SELECT employee_id, last_name, salary FROM hr.employees ORDER BY salary OFFSET 5 ROWS FETCH FIRST 5 PERCENT ROWS WITH TIES; EMPLOYEE_ID LAST_NAME SALARY    119 Colmenares 2500 131 Marlow 2500 140 Patel 2500 144 Vargas 2500 182 Sullivan 2500 191 Perkins 2500
20.9.1 SQL Row Limiting Restrictions and Considerations
The row_limiting_clause
clause is subject to the following restrictions:

You cannot specify this clause with the
for_update_clause
. 
If you specify this clause, then the select list cannot contain the sequence pseudocolumns
CURRVAL
orNEXTVAL
. 
Materialized views are not eligible for an incremental refresh if the defining query contains this clause.
See Also:
Oracle Database SQL Language Reference for further information regarding syntax and restrictions