Window Functions

Examples

-- generate a "row_number" column containing incremental identifiers for each row
SELECT row_number() OVER () FROM sales;
-- generate a "row_number" column, by order of time
SELECT row_number() OVER (ORDER BY time) FROM sales;
-- generate a "row_number" column, by order of time partitioned by region
SELECT row_number() OVER (PARTITION BY region ORDER BY time) FROM sales;
-- compute the difference between the current amount, and the previous amount, by order of time
SELECT amount - lag(amount) OVER (ORDER BY time) FROM sales;
-- compute the percentage of the total amount of sales per region for each row
SELECT amount / SUM(amount) OVER (PARTITION BY region) FROM sales;

Syntax

Window functions can only be used in the SELECT clause. To share OVER specifications between functions, use the statement's WINDOW clause and use the OVER window-name syntax.

General-Purpose Window Functions

The table below shows the available general window functions.

Function	Return Type	Description	Example
row_number()	bigint	The number of the current row within the partition, counting from 1.	row_number()
rank()	bigint	The rank of the current row with gaps; same as row_number of its first peer.	rank()
dense_rank()	bigint	The rank of the current row without gaps; this function counts peer groups.	dense_rank()
rank_dense()	bigint	Alias for dense_rank.	rank_dense()
percent_rank()	double	The relative rank of the current row: (rank() - 1) / (total partition rows - 1).	percent_rank()
cume_dist()	double	The cumulative distribution: (number of partition rows preceding or peer with current row) / total partition rows.	cume_dist()
ntile(num_buckets integer)	bigint	An integer ranging from 1 to the argument value, dividing the partition as equally as possible.	ntile(4)
lag(expr any [, offset integer [, default any ]])	same type as expr	Returns expr evaluated at the row that is offset rows before the current row within the partition; if there is no such row, instead return default (which must be of the same type as expr). Both offset and default are evaluated with respect to the current row. If omitted, offset defaults to 1 and default to null.	lag(column, 3, 0)
lead(expr any [, offset integer [, default any ]])	same type as expr	Returns expr evaluated at the row that is offset rows after the current row within the partition; if there is no such row, instead return default (which must be of the same type as expr). Both offset and default are evaluated with respect to the current row. If omitted, offset defaults to 1 and default to null.	lead(column, 3, 0)
first_value(expr any)	same type as expr	Returns expr evaluated at the row that is the first row of the window frame.	first_value(column)
last_value(expr any)	same type as expr	Returns expr evaluated at the row that is the last row of the window frame.	last_value(column)
nth_value(expr any, nth integer)	same type as expr	Returns expr evaluated at the nth row of the window frame (counting from 1); null if no such row.	nth_value(column, 2)
first(expr any)	same type as expr	Alias for first_value.	first(column)
last(expr any)	same type as expr	Alias for last_value.	last(column)

Aggregate Window Functions

All aggregate functions can be used in a windowing context.

Ignoring NULLs

The following functions support the IGNORE NULLS specification:

Function	Description	Example
lag(expr any [, offset integer [, default any ]])	Skips NULL values when counting.	lag(column, 3 IGNORE NULLS)
lead(expr any [, offset integer [, default any ]])	Skips NULL values when counting.	lead(column, 3 IGNORE NULLS)
first_value(expr any)	Skips leading NULLs	first_value(column IGNORE NULLS)
last_value(expr any)	Skips trailing NULLs	last_value(column IGNORE NULLS)
nth_value(expr any, nth integer)	Skips NULL values when counting.	nth_value(column, 2 IGNORE NULLS)

Note that there is no comma separating the arguments from the IGNORE NULLS specification.

The inverse of IGNORE NULLS is RESPECT NULLS, which is the default for all functions.

Evaluation

Windowing works by breaking a relation up into independent partitions, ordering those partitions, and then computing a new column for each row as a function of the nearby values. Some window functions depend only on the partition boundary and the ordering, but a few (including all the aggregates) also use a frame. Frames are specified as a number of rows on either side (preceding or following) of the current row. The distance can either be specified as a number of rows or a range of values using the partition's ordering value and a distance.

The full syntax is shown in the diagram at the top of the page, and this diagram visually illustrates computation environment:

Partition and Ordering

Partitioning breaks the relation up into independent, unrelated pieces. Partitioning is optional, and if none is specified then the entire relation is treated as a single partition. Window functions cannot access values outside of the partition containing the row they are being evaluated at.

Ordering is also optional, but without it the results are not well-defined. Each partition is ordered using the same ordering clause.

Here is a table of power generation data. After partitioning by plant and ordering by date, it will have this layout:

Plant	Date	MWh
Boston	2019-01-02	564337
Boston	2019-01-03	507405
Boston	2019-01-04	528523
Boston	2019-01-05	469538
Boston	2019-01-06	474163
Boston	2019-01-07	507213
Boston	2019-01-08	613040
Boston	2019-01-09	582588
Boston	2019-01-10	499506
Boston	2019-01-11	482014
Boston	2019-01-12	486134
Boston	2019-01-13	531518
Worcester	2019-01-02	118860
Worcester	2019-01-03	101977
Worcester	2019-01-04	106054
Worcester	2019-01-05	92182
Worcester	2019-01-06	94492
Worcester	2019-01-07	99932
Worcester	2019-01-08	118854
Worcester	2019-01-09	113506
Worcester	2019-01-10	96644
Worcester	2019-01-11	93806
Worcester	2019-01-12	98963
Worcester	2019-01-13	107170

In what follows, we shall use this table (or small sections of it) to illustrate various pieces of window function evaluation.

The simplest window function is ROW_NUMBER(). This function just computes the 1-based row number within the partition using the query:

SELECT "Plant", "Date", row_number() over (partition by "Plant" order by "Date") AS "Row"
FROM "History"
ORDER BY 1, 2

The result will be

Plant	Date	Row
Boston	2019-01-02	1
Boston	2019-01-03	2
Boston	2019-01-04	3
...	...	...
Worcester	2019-01-02	1
Worcester	2019-01-03	2
Worcester	2019-01-04	3
...	...	...

Note that even though the function is computed with an ORDER BY clause, the result does not have to be sorted, so the SELECT also needs to be explicitly sorted if that is desired.

Framing

Framing specifies a set of rows relative to each row where the function is evaluated. The distance from the current row is given as an expression either PRECEDING or FOLLOWING the current row. This distance can either be specified as an integral number of ROWS or as a RANGE delta expression from the value of the ordering expression. For a RANGE specification, there must be only one ordering expression, and it has to support addition and subtraction (i.e., numbers or INTERVALs). The default values for frames are from UNBOUNDED PRECEDING to CURRENT ROW. It is invalid for a frame to start after it ends.

ROW Framing

Here is a simple ROW frame query, using an aggregate function:

SELECT points,
    SUM(points) OVER (
        ROWS BETWEEN 1 PRECEDING
                 AND 1 FOLLOWING) we
FROM results

This query computes the SUM of each point and the points on either side of it:

Notice that at the edge of the partition, there are only two values added together. This is because frames are cropped to the edge of the partition.

RANGE Framing

Returning to the power data, suppose the data is noisy. We might want to compute a 7 day moving average for each plant to smooth out the noise. To do this, we can use this window query:

SELECT "Plant", "Date",
    AVG("MWh") OVER (
        PARTITION BY "Plant"
        ORDER BY "Date" ASC
        RANGE BETWEEN INTERVAL 3 DAYS PRECEDING
                  AND INTERVAL 3 DAYS FOLLOWING)
        AS "MWh 7-day Moving Average"
FROM "Generation History"
ORDER BY 1, 2

This query partitions the data by Plant (to keep the different power plants' data separate), orders each plant's partition by Date (to put the energy measurements next to each other), and uses a RANGE frame of three days on either side of each day for the AVG (to handle any missing days). This is the result:

Plant	Date	MWh 7-day Moving Average
Boston	2019-01-02	517450.75
Boston	2019-01-03	508793.20
Boston	2019-01-04	508529.83
...	...	...
Boston	2019-01-13	499793.00
Worcester	2019-01-02	104768.25
Worcester	2019-01-03	102713.00
Worcester	2019-01-04	102249.50
...	...	...

WINDOW Clauses

Multiple different OVER clauses can be specified in the same SELECT, and each will be computed separately. Often, however, we want to use the same layout for multiple window functions. The WINDOW clause can be used to define a named window that can be shared between multiple window functions:

SELECT "Plant", "Date",
    MIN("MWh") OVER seven AS "MWh 7-day Moving Minimum",
    AVG("MWh") OVER seven AS "MWh 7-day Moving Average",
    MAX("MWh") OVER seven AS "MWh 7-day Moving Maximum"
FROM "Generation History"
WINDOW seven AS (
    PARTITION BY "Plant"
    ORDER BY "Date" ASC
    RANGE BETWEEN INTERVAL 3 DAYS PRECEDING
              AND INTERVAL 3 DAYS FOLLOWING)
ORDER BY 1, 2

The three window functions will also share the data layout, which will improve performance.

Multiple windows can be defined in the same WINDOW clause by comma-separating them:

SELECT "Plant", "Date",
    MIN("MWh") OVER seven AS "MWh 7-day Moving Minimum",
    AVG("MWh") OVER seven AS "MWh 7-day Moving Average",
    MAX("MWh") OVER seven AS "MWh 7-day Moving Maximum",
    MIN("MWh") OVER three AS "MWh 3-day Moving Minimum",
    AVG("MWh") OVER three AS "MWh 3-day Moving Average",
    MAX("MWh") OVER three AS "MWh 3-day Moving Maximum"
FROM "Generation History"
WINDOW
    seven AS (
        PARTITION BY "Plant"
        ORDER BY "Date" ASC
        RANGE BETWEEN INTERVAL 3 DAYS PRECEDING
                  AND INTERVAL 3 DAYS FOLLOWING),
    three AS (
        PARTITION BY "Plant"
        ORDER BY "Date" ASC
        RANGE BETWEEN INTERVAL 1 DAYS PRECEDING
        AND INTERVAL 1 DAYS FOLLOWING)
ORDER BY 1, 2

The queries above do not use a number of clauses commonly found in select statements, like WHERE, GROUP BY, etc. For more complex queries you can find where WINDOW clauses fall in the canonical order of a select statement here.

Box and Whisker Queries

All aggregates can be used as windowing functions, including the complex statistical functions. These function implementations have been optimised for windowing, and we can use the window syntax to write queries that generate the data for moving box-and-whisker plots:

SELECT "Plant", "Date",
    MIN("MWh") OVER seven AS "MWh 7-day Moving Minimum",
    QUANTILE_CONT("MWh", [0.25, 0.5, 0.75]) OVER seven
        AS "MWh 7-day Moving IQR",
    MAX("MWh") OVER seven AS "MWh 7-day Moving Maximum",
FROM "Generation History"
WINDOW seven AS (
    PARTITION BY "Plant"
    ORDER BY "Date" ASC
    RANGE BETWEEN INTERVAL 3 DAYS PRECEDING
              AND INTERVAL 3 DAYS FOLLOWING)
ORDER BY 1, 2