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1.0 (stable)
Window Functions

DuckDB supports window functions, which can use multiple rows to calculate a value for each row. Window functions are blocking operators, i.e., they require their entire input to be buffered, making them one of the most memory-intensive operators in SQL.

Examples

Generate a row_number column with 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.

Name Description
cume_dist() The cumulative distribution: (number of partition rows preceding or peer with current row) / total partition rows.
dense_rank() The rank of the current row without gaps; this function counts peer groups.
first(expr[ IGNORE NULLS]) Returns expr evaluated at the row that is the first row (with a non-null value of expr if IGNORE NULLS is set) of the window frame.
first_value(expr[ IGNORE NULLS]) Returns expr evaluated at the row that is the first row (with a non-null value of expr if IGNORE NULLS is set) of the window frame.
lag(expr[, offset[, default]][ IGNORE NULLS]) Returns expr evaluated at the row that is offset rows (among rows with a non-null value of expr if IGNORE NULLS is set) before the current row within the window frame; 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.
last(expr[ IGNORE NULLS]) Returns expr evaluated at the row that is the last row (among rows with a non-null value of expr if IGNORE NULLS is set) of the window frame.
last_value(expr[ IGNORE NULLS]) Returns expr evaluated at the row that is the last row (among rows with a non-null value of expr if IGNORE NULLS is set) of the window frame.
lead(expr[, offset[, default]][ IGNORE NULLS]) Returns expr evaluated at the row that is offset rows after the current row (among rows with a non-null value of expr if IGNORE NULLS is set) within the window frame; 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.
nth_value(expr, nth[ IGNORE NULLS]) Returns expr evaluated at the nth row (among rows with a non-null value of expr if IGNORE NULLS is set) of the window frame (counting from 1); NULL if no such row.
ntile(num_buckets) An integer ranging from 1 to num_buckets, dividing the partition as equally as possible.
percent_rank() The relative rank of the current row: (rank() - 1) / (total partition rows - 1).
rank_dense() The rank of the current row with gaps; same as row_number of its first peer.
rank() The rank of the current row with gaps; same as row_number of its first peer.
row_number() The number of the current row within the partition, counting from 1.

cume_dist()

Description The cumulative distribution: (number of partition rows preceding or peer with current row) / total partition rows.
Return Type DOUBLE
Example cume_dist()

dense_rank()

Description The rank of the current row without gaps; this function counts peer groups.
Return Type BIGINT
Example dense_rank()

first(expr[ IGNORE NULLS])

Description Returns expr evaluated at the row that is the first row (with a non-null value of expr if IGNORE NULLS is set) of the window frame.
Return Type Same type as expr
Example first(column)
Alias first_value(column)

first_value(expr[ IGNORE NULLS])

Description Returns expr evaluated at the row that is the first row (with a non-null value of expr if IGNORE NULLS is set) of the window frame.
Return Type Same type as expr
Example first_value(column)
Alias first(column)

lag(expr[, offset[, default]][ IGNORE NULLS])

Description Returns expr evaluated at the row that is offset rows (among rows with a non-null value of expr if IGNORE NULLS is set) before the current row within the window frame; 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.
Return Type Same type as expr
Aliases lag(column, 3, 0)

last(expr[ IGNORE NULLS])

Description Returns expr evaluated at the row that is the last row (among rows with a non-null value of expr if IGNORE NULLS is set) of the window frame.
Return Type Same type as expr
Example last(column)
Alias last_value(column)

last_value(expr[ IGNORE NULLS])

Description Returns expr evaluated at the row that is the last row (among rows with a non-null value of expr if IGNORE NULLS is set) of the window frame.
Return Type Same type as expr
Example last_value(column)
Alias last(column)

lead(expr[, offset[, default]][ IGNORE NULLS])

Description Returns expr evaluated at the row that is offset rows after the current row (among rows with a non-null value of expr if IGNORE NULLS is set) within the window frame; 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.
Return Type Same type as expr
Aliases lead(column, 3, 0)

nth_value(expr, nth[ IGNORE NULLS])

Description Returns expr evaluated at the nth row (among rows with a non-null value of expr if IGNORE NULLS is set) of the window frame (counting from 1); NULL if no such row.
Return Type Same type as expr
Aliases nth_value(column, 2)

ntile(num_buckets)

Description An integer ranging from 1 to num_buckets, dividing the partition as equally as possible.
Return Type BIGINT
Example ntile(4)

percent_rank()

Description The relative rank of the current row: (rank() - 1) / (total partition rows - 1).
Return Type DOUBLE
Example percent_rank()

rank_dense()

Description The rank of the current row with gaps; same as row_number of its first peer.
Return Type BIGINT
Example rank_dense()
Alias rank()

rank()

Description The rank of the current row with gaps; same as row_number of its first peer.
Return Type BIGINT
Example rank()
Alias rank_dense()

row_number()

Description The number of the current row within the partition, counting from 1.
Return Type BIGINT
Example row_number()

Aggregate Window Functions

All aggregate functions can be used in a windowing context, including the optional FILTER clause. The first and last aggregate functions are shadowed by the respective general-purpose window functions, with the minor consequence that the FILTER clause is not available for these but IGNORE NULLS is.

Nulls

All general-purpose window functions that accept IGNORE NULLS respect nulls by default. This default behavior can optionally be made explicit via RESPECT NULLS.

In contrast, all aggregate window functions (except for list and its aliases, which can be made to ignore nulls via a FILTER) ignore nulls and do not accept RESPECT NULLS. For example, sum(column) OVER (ORDER BY time) AS cumulativeColumn computes a cumulative sum where rows with a NULL value of column have the same value of cumulativeColumn as the row that preceeds them.

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:

The Window 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, available as a CSV file (power-plant-generation-history.csv). To load the data, run:

CREATE TABLE "Generation History" AS
    FROM 'power-plant-generation-history.csv';

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 "Generation History"
ORDER BY 1, 2;

The result will be the following:

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. Using the EXCLUDE clause, rows around the current row can be excluded from the frame.

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:

Moving SUM of three values

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

EXCLUDE Clause

The EXCLUDE clause allows rows around the current row to be excluded from the frame. It has the following options:

  • EXCLUDE NO OTHERS: exclude nothing (default)
  • EXCLUDE CURRENT ROW: exclude the current row from the window frame
  • EXCLUDE GROUP: exclude the current row and all its peers (according to the columns specified by ORDER BY) from the window frame
  • EXCLUDE TIES: exclude only the current row’s peers from the window frame

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 the SELECT statement.

Filtering the Results of Window Functions Using QUALIFY

Window functions are executed after the WHERE and HAVING clauses have been already evaluated, so it’s not possible to use these clauses to filter the results of window functions The QUALIFY clause avoids the need for a subquery or WITH clause to perform this filtering.

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;
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Last modified: 2024-06-12