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 NULL s | first_value(column IGNORE NULLS) |
last_value(expr any) | Skips trailing NULL s | 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 INTERVAL
s).
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:
![Figure 2: A moving SUM of three values Moving SUM of three values](/images/blog/windowing/moving-sum.jpg)
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