# Parametric Aggregate Functions

Some aggregate functions can accept not only argument columns (used for compression), but a set of parameters – constants for initialization. The syntax is two pairs of brackets instead of one. The first is for parameters, and the second is for arguments.

## histogram

Calculates an adaptive histogram. It does not guarantee precise results.

histogram(number_of_bins)(values)

The functions uses A Streaming Parallel Decision Tree Algorithm. The borders of histogram bins are adjusted as new data enters a function. In common case, the widths of bins are not equal.

Arguments

valuesExpression resulting in input values.

Parameters

number_of_bins — Upper limit for the number of bins in the histogram. The function automatically calculates the number of bins. It tries to reach the specified number of bins, but if it fails, it uses fewer bins.

Returned values

• Array of Tuples of the following format:
```
[(lower_1, upper_1, height_1), ... (lower_N, upper_N, height_N)]
```

- `lower`  Lower bound of the bin.
- `upper`  Upper bound of the bin.
- `height`  Calculated height of the bin.

Example

SELECT histogram(5)(number + 1)
FROM (
SELECT *
FROM system.numbers
LIMIT 20
)
┌─histogram(5)(plus(number, 1))───────────────────────────────────────────┐
│ [(1,4.5,4),(4.5,8.5,4),(8.5,12.75,4.125),(12.75,17,4.625),(17,20,3.25)] │
└─────────────────────────────────────────────────────────────────────────┘

You can visualize a histogram with the bar function, for example:

WITH histogram(5)(rand() % 100) AS hist
SELECT
arrayJoin(hist).3 AS height,
bar(height, 0, 6, 5) AS bar
FROM
(
SELECT *
FROM system.numbers
LIMIT 20
)
┌─height─┬─bar───┐
│  2.125 │ █▋    │
│   3.25 │ ██▌   │
│  5.625 │ ████▏ │
│  5.625 │ ████▏ │
│  3.375 │ ██▌   │
└────────┴───────┘

In this case, you should remember that you do not know the histogram bin borders.

## sequenceMatch(pattern)(timestamp, cond1, cond2, …)

Checks whether the sequence contains an event chain that matches the pattern.

sequenceMatch(pattern)(timestamp, cond1, cond2, ...)

Arguments

• timestamp — Column considered to contain time data. Typical data types are Date and DateTime. You can also use any of the supported UInt data types.

• cond1, cond2 — Conditions that describe the chain of events. Data type: UInt8. You can pass up to 32 condition arguments. The function takes only the events described in these conditions into account. If the sequence contains data that isn’t described in a condition, the function skips them.

Parameters

Returned values

• 1, if the pattern is matched.
• 0, if the pattern isn’t matched.

Type: UInt8.

Pattern syntax

• (?N) — Matches the condition argument at position N. Conditions are numbered in the [1, 32] range. For example, (?1) matches the argument passed to the cond1 parameter.

• .* — Matches any number of events. You do not need conditional arguments to match this element of the pattern.

• (?t operator value) — Sets the time in seconds that should separate two events. For example, pattern (?1)(?t>1800)(?2) matches events that occur more than 1800 seconds from each other. An arbitrary number of any events can lay between these events. You can use the >=, >, <, <=, == operators.

Examples

Consider data in the t table:

┌─time─┬─number─┐
│    1 │      1 │
│    2 │      3 │
│    3 │      2 │
└──────┴────────┘

Perform the query:

SELECT sequenceMatch('(?1)(?2)')(time, number = 1, number = 2) FROM t
┌─sequenceMatch('(?1)(?2)')(time, equals(number, 1), equals(number, 2))─┐
│                                                                     1 │
└───────────────────────────────────────────────────────────────────────┘

The function found the event chain where number 2 follows number 1. It skipped number 3 between them, because the number is not described as an event. If we want to take this number into account when searching for the event chain given in the example, we should make a condition for it.

SELECT sequenceMatch('(?1)(?2)')(time, number = 1, number = 2, number = 3) FROM t
┌─sequenceMatch('(?1)(?2)')(time, equals(number, 1), equals(number, 2), equals(number, 3))─┐
│                                                                                        0 │
└──────────────────────────────────────────────────────────────────────────────────────────┘

In this case, the function couldn’t find the event chain matching the pattern, because the event for number 3 occured between 1 and 2. If in the same case we checked the condition for number 4, the sequence would match the pattern.

SELECT sequenceMatch('(?1)(?2)')(time, number = 1, number = 2, number = 4) FROM t
┌─sequenceMatch('(?1)(?2)')(time, equals(number, 1), equals(number, 2), equals(number, 4))─┐
│                                                                                        1 │
└──────────────────────────────────────────────────────────────────────────────────────────┘

## sequenceCount(pattern)(time, cond1, cond2, …)

Counts the number of event chains that matched the pattern. The function searches event chains that do not overlap. It starts to search for the next chain after the current chain is matched.

sequenceCount(pattern)(timestamp, cond1, cond2, ...)

Arguments

• timestamp — Column considered to contain time data. Typical data types are Date and DateTime. You can also use any of the supported UInt data types.

• cond1, cond2 — Conditions that describe the chain of events. Data type: UInt8. You can pass up to 32 condition arguments. The function takes only the events described in these conditions into account. If the sequence contains data that isn’t described in a condition, the function skips them.

Parameters

Returned values

• Number of non-overlapping event chains that are matched.

Type: UInt64.

Example

Consider data in the t table:

┌─time─┬─number─┐
│    1 │      1 │
│    2 │      3 │
│    3 │      2 │
│    4 │      1 │
│    5 │      3 │
│    6 │      2 │
└──────┴────────┘

Count how many times the number 2 occurs after the number 1 with any amount of other numbers between them:

SELECT sequenceCount('(?1).*(?2)')(time, number = 1, number = 2) FROM t
┌─sequenceCount('(?1).*(?2)')(time, equals(number, 1), equals(number, 2))─┐
│                                                                       2 │
└─────────────────────────────────────────────────────────────────────────┘

## windowFunnel

Searches for event chains in a sliding time window and calculates the maximum number of events that occurred from the chain.

The function works according to the algorithm:

• The function searches for data that triggers the first condition in the chain and sets the event counter to 1. This is the moment when the sliding window starts.

• If events from the chain occur sequentially within the window, the counter is incremented. If the sequence of events is disrupted, the counter isn’t incremented.

• If the data has multiple event chains at varying points of completion, the function will only output the size of the longest chain.

Syntax

windowFunnel(window, [mode, [mode, ... ]])(timestamp, cond1, cond2, ..., condN)

Arguments

• timestamp — Name of the column containing the timestamp. Data types supported: Date, DateTime and other unsigned integer types (note that even though timestamp supports the UInt64 type, it’s value can’t exceed the Int64 maximum, which is 2^63 - 1).
• cond — Conditions or data describing the chain of events. UInt8.

Parameters

• window — Length of the sliding window, it is the time interval between the first and the last condition. The unit of window depends on the timestamp itself and varies. Determined using the expression timestamp of cond1 <= timestamp of cond2 <= ... <= timestamp of condN <= timestamp of cond1 + window.
• mode — It is an optional argument. One or more modes can be set.
• 'strict' — If same condition holds for sequence of events then such non-unique events would be skipped.
• 'strict_order' — Don't allow interventions of other events. E.g. in the case of A->B->D->C, it stops finding A->B->C at the D and the max event level is 2.
• 'strict_increase' — Apply conditions only to events with strictly increasing timestamps.

Returned value

The maximum number of consecutive triggered conditions from the chain within the sliding time window.
All the chains in the selection are analyzed.

Type: Integer.

Example

Determine if a set period of time is enough for the user to select a phone and purchase it twice in the online store.

Set the following chain of events:

1. The user logged in to their account on the store (eventID = 1003).
2. The user searches for a phone (eventID = 1007, product = 'phone').
3. The user placed an order (eventID = 1009).
4. The user made the order again (eventID = 1010).

Input table:

┌─event_date─┬─user_id─┬───────────timestamp─┬─eventID─┬─product─┐
│ 2019-01-28 │       1 │ 2019-01-29 10:00:00 │    1003 │ phone   │
└────────────┴─────────┴─────────────────────┴─────────┴─────────┘
┌─event_date─┬─user_id─┬───────────timestamp─┬─eventID─┬─product─┐
│ 2019-01-31 │       1 │ 2019-01-31 09:00:00 │    1007 │ phone   │
└────────────┴─────────┴─────────────────────┴─────────┴─────────┘
┌─event_date─┬─user_id─┬───────────timestamp─┬─eventID─┬─product─┐
│ 2019-01-30 │       1 │ 2019-01-30 08:00:00 │    1009 │ phone   │
└────────────┴─────────┴─────────────────────┴─────────┴─────────┘
┌─event_date─┬─user_id─┬───────────timestamp─┬─eventID─┬─product─┐
│ 2019-02-01 │       1 │ 2019-02-01 08:00:00 │    1010 │ phone   │
└────────────┴─────────┴─────────────────────┴─────────┴─────────┘

Find out how far the user user_id could get through the chain in a period in January-February of 2019.

Query:

SELECT
level,
count() AS c
FROM
(
SELECT
user_id,
windowFunnel(6048000000000000)(timestamp, eventID = 1003, eventID = 1009, eventID = 1007, eventID = 1010) AS level
FROM trend
WHERE (event_date >= '2019-01-01') AND (event_date <= '2019-02-02')
GROUP BY user_id
)
GROUP BY level
ORDER BY level ASC;

Result:

┌─level─┬─c─┐
│     4 │ 1 │
└───────┴───┘

## retention

The function takes as arguments a set of conditions from 1 to 32 arguments of type UInt8 that indicate whether a certain condition was met for the event.
Any condition can be specified as an argument (as in WHERE).

The conditions, except the first, apply in pairs: the result of the second will be true if the first and second are true, of the third if the first and third are true, etc.

Syntax

retention(cond1, cond2, ..., cond32);

Arguments

• cond — An expression that returns a UInt8 result (1 or 0).

Returned value

The array of 1 or 0.

• 1 — Condition was met for the event.
• 0 — Condition wasn’t met for the event.

Type: UInt8.

Example

Let’s consider an example of calculating the retention function to determine site traffic.

1. Сreate a table to illustrate an example.

CREATE TABLE retention_test(date Date, uid Int32) ENGINE = Memory;

INSERT INTO retention_test SELECT '2020-01-01', number FROM numbers(5);
INSERT INTO retention_test SELECT '2020-01-02', number FROM numbers(10);
INSERT INTO retention_test SELECT '2020-01-03', number FROM numbers(15);

Input table:

Query:

SELECT * FROM retention_test

Result:

┌───────date─┬─uid─┐
│ 2020-01-01 │   0 │
│ 2020-01-01 │   1 │
│ 2020-01-01 │   2 │
│ 2020-01-01 │   3 │
│ 2020-01-01 │   4 │
└────────────┴─────┘
┌───────date─┬─uid─┐
│ 2020-01-02 │   0 │
│ 2020-01-02 │   1 │
│ 2020-01-02 │   2 │
│ 2020-01-02 │   3 │
│ 2020-01-02 │   4 │
│ 2020-01-02 │   5 │
│ 2020-01-02 │   6 │
│ 2020-01-02 │   7 │
│ 2020-01-02 │   8 │
│ 2020-01-02 │   9 │
└────────────┴─────┘
┌───────date─┬─uid─┐
│ 2020-01-03 │   0 │
│ 2020-01-03 │   1 │
│ 2020-01-03 │   2 │
│ 2020-01-03 │   3 │
│ 2020-01-03 │   4 │
│ 2020-01-03 │   5 │
│ 2020-01-03 │   6 │
│ 2020-01-03 │   7 │
│ 2020-01-03 │   8 │
│ 2020-01-03 │   9 │
│ 2020-01-03 │  10 │
│ 2020-01-03 │  11 │
│ 2020-01-03 │  12 │
│ 2020-01-03 │  13 │
│ 2020-01-03 │  14 │
└────────────┴─────┘

2. Group users by unique ID uid using the retention function.

Query:

SELECT
uid,
retention(date = '2020-01-01', date = '2020-01-02', date = '2020-01-03') AS r
FROM retention_test
WHERE date IN ('2020-01-01', '2020-01-02', '2020-01-03')
GROUP BY uid
ORDER BY uid ASC

Result:

┌─uid─┬─r───────┐
│   0 │ [1,1,1] │
│   1 │ [1,1,1] │
│   2 │ [1,1,1] │
│   3 │ [1,1,1] │
│   4 │ [1,1,1] │
│   5 │ [0,0,0] │
│   6 │ [0,0,0] │
│   7 │ [0,0,0] │
│   8 │ [0,0,0] │
│   9 │ [0,0,0] │
│  10 │ [0,0,0] │
│  11 │ [0,0,0] │
│  12 │ [0,0,0] │
│  13 │ [0,0,0] │
│  14 │ [0,0,0] │
└─────┴─────────┘

3. Calculate the total number of site visits per day.

Query:

SELECT
sum(r[1]) AS r1,
sum(r[2]) AS r2,
sum(r[3]) AS r3
FROM
(
SELECT
uid,
retention(date = '2020-01-01', date = '2020-01-02', date = '2020-01-03') AS r
FROM retention_test
WHERE date IN ('2020-01-01', '2020-01-02', '2020-01-03')
GROUP BY uid
)

Result:

┌─r1─┬─r2─┬─r3─┐
│  5 │  5 │  5 │
└────┴────┴────┘

Where:

• r1- the number of unique visitors who visited the site during 2020-01-01 (the cond1 condition).
• r2- the number of unique visitors who visited the site during a specific time period between 2020-01-01 and 2020-01-02 (cond1 and cond2 conditions).
• r3- the number of unique visitors who visited the site during a specific time period between 2020-01-01 and 2020-01-03 (cond1 and cond3 conditions).

## uniqUpTo(N)(x)

Calculates the number of different argument values ​​if it is less than or equal to N. If the number of different argument values is greater than N, it returns N + 1.

Recommended for use with small Ns, up to 10. The maximum value of N is 100.

For the state of an aggregate function, it uses the amount of memory equal to 1 + N * the size of one value of bytes.
For strings, it stores a non-cryptographic hash of 8 bytes. That is, the calculation is approximated for strings.

The function also works for several arguments.

It works as fast as possible, except for cases when a large N value is used and the number of unique values is slightly less than N.

Usage example:

Problem: Generate a report that shows only keywords that produced at least 5 unique users.
Solution: Write in the GROUP BY query SearchPhrase HAVING uniqUpTo(4)(UserID) >= 5

## sumMapFiltered(keys_to_keep)(keys, values)

Same behavior as sumMap except that an array of keys is passed as a parameter. This can be especially useful when working with a high cardinality of keys.

## sequenceNextNode

Returns a value of the next event that matched an event chain.

Experimental function, SET allow_experimental_funnel_functions = 1 to enable it.

Syntax

sequenceNextNode(direction, base)(timestamp, event_column, base_condition, event1, event2, event3, ...)

Parameters

• direction — Used to navigate to directions.

• forward — Moving forward.
• backward — Moving backward.
• base — Used to set the base point.

• head — Set the base point to the first event.
• tail — Set the base point to the last event.
• first_match — Set the base point to the first matched event1.
• last_match — Set the base point to the last matched event1.

Arguments

• timestamp — Name of the column containing the timestamp. Data types supported: Date, DateTime and other unsigned integer types.
• event_column — Name of the column containing the value of the next event to be returned. Data types supported: String and Nullable(String).
• base_condition — Condition that the base point must fulfill.
• event1, event2, ... — Conditions describing the chain of events. UInt8.

Returned values

• event_column[next_index] — If the pattern is matched and next value exists.
• NULL - If the pattern isn’t matched or next value doesn't exist.

Type: Nullable(String).

Example

It can be used when events are A->B->C->D->E and you want to know the event following B->C, which is D.

The query statement searching the event following A->B:

CREATE TABLE test_flow (
dt DateTime,
id int,
page String)
ENGINE = MergeTree()
PARTITION BY toYYYYMMDD(dt)
ORDER BY id;

INSERT INTO test_flow VALUES (1, 1, 'A') (2, 1, 'B') (3, 1, 'C') (4, 1, 'D') (5, 1, 'E');

SELECT id, sequenceNextNode('forward', 'head')(dt, page, page = 'A', page = 'A', page = 'B') as next_flow FROM test_flow GROUP BY id;

Result:

┌─id─┬─next_flow─┐
│  1 │ C         │
└────┴───────────┘

ALTER TABLE test_flow DELETE WHERE 1 = 1 settings mutations_sync = 1;

INSERT INTO test_flow VALUES (1, 1, 'Home') (2, 1, 'Gift') (3, 1, 'Exit');
INSERT INTO test_flow VALUES (1, 2, 'Home') (2, 2, 'Home') (3, 2, 'Gift') (4, 2, 'Basket');
SELECT id, sequenceNextNode('forward', 'head')(dt, page, page = 'Home', page = 'Home', page = 'Gift') FROM test_flow GROUP BY id;

dt   id   page
1970-01-01 09:00:01    1   Home // Base point, Matched with Home
1970-01-01 09:00:03    1   Exit // The result

1970-01-01 09:00:01    2   Home // Base point, Matched with Home
1970-01-01 09:00:02    2   Home // Unmatched with Gift

1970-01-01 09:00:01    3   Gift // Base point, Unmatched with Home
1970-01-01 09:00:02    3   Home

Behavior for backward and tail

SELECT id, sequenceNextNode('backward', 'tail')(dt, page, page = 'Basket', page = 'Basket', page = 'Gift') FROM test_flow GROUP BY id;

dt   id   page
1970-01-01 09:00:01    1   Home
1970-01-01 09:00:03    1   Exit // Base point, Unmatched with Basket

1970-01-01 09:00:01    2   Home
1970-01-01 09:00:02    2   Home // The result

1970-01-01 09:00:02    3   Home // The result

Behavior for forward and first_match

SELECT id, sequenceNextNode('forward', 'first_match')(dt, page, page = 'Gift', page = 'Gift') FROM test_flow GROUP BY id;

dt   id   page
1970-01-01 09:00:01    1   Home
1970-01-01 09:00:02    1   Gift // Base point
1970-01-01 09:00:03    1   Exit // The result

1970-01-01 09:00:01    2   Home
1970-01-01 09:00:02    2   Home
1970-01-01 09:00:03    2   Gift // Base point
1970-01-01 09:00:04    2   Basket  The result

1970-01-01 09:00:01    3   Gift // Base point
1970-01-01 09:00:02    3   Home // The result
SELECT id, sequenceNextNode('forward', 'first_match')(dt, page, page = 'Gift', page = 'Gift', page = 'Home') FROM test_flow GROUP BY id;

dt   id   page
1970-01-01 09:00:01    1   Home
1970-01-01 09:00:02    1   Gift // Base point
1970-01-01 09:00:03    1   Exit // Unmatched with Home

1970-01-01 09:00:01    2   Home
1970-01-01 09:00:02    2   Home
1970-01-01 09:00:03    2   Gift // Base point
1970-01-01 09:00:04    2   Basket // Unmatched with Home

1970-01-01 09:00:01    3   Gift // Base point
1970-01-01 09:00:02    3   Home // Matched with Home
1970-01-01 09:00:03    3   Gift // The result

Behavior for backward and last_match

SELECT id, sequenceNextNode('backward', 'last_match')(dt, page, page = 'Gift', page = 'Gift') FROM test_flow GROUP BY id;

dt   id   page
1970-01-01 09:00:01    1   Home // The result
1970-01-01 09:00:02    1   Gift // Base point
1970-01-01 09:00:03    1   Exit

1970-01-01 09:00:01    2   Home
1970-01-01 09:00:02    2   Home // The result
1970-01-01 09:00:03    2   Gift // Base point

1970-01-01 09:00:02    3   Home // The result
1970-01-01 09:00:03    3   Gift // Base point
SELECT id, sequenceNextNode('backward', 'last_match')(dt, page, page = 'Gift', page = 'Gift', page = 'Home') FROM test_flow GROUP BY id;

dt   id   page
1970-01-01 09:00:01    1   Home // Matched with Home, the result is null
1970-01-01 09:00:02    1   Gift // Base point
1970-01-01 09:00:03    1   Exit

1970-01-01 09:00:01    2   Home // The result
1970-01-01 09:00:02    2   Home // Matched with Home
1970-01-01 09:00:03    2   Gift // Base point

1970-01-01 09:00:01    3   Gift // The result
1970-01-01 09:00:02    3   Home // Matched with Home
1970-01-01 09:00:03    3   Gift // Base point

Behavior for base_condition

CREATE TABLE test_flow_basecond
(
`dt` DateTime,
`id` int,
`page` String,
`ref` String
)
ENGINE = MergeTree
PARTITION BY toYYYYMMDD(dt)
ORDER BY id;

INSERT INTO test_flow_basecond VALUES (1, 1, 'A', 'ref4') (2, 1, 'A', 'ref3') (3, 1, 'B', 'ref2') (4, 1, 'B', 'ref1');
SELECT id, sequenceNextNode('forward', 'head')(dt, page, ref = 'ref1', page = 'A') FROM test_flow_basecond GROUP BY id;

dt   id   page   ref
1970-01-01 09:00:01    1   A      ref4 // The head can not be base point because the ref column of the head unmatched with 'ref1'.
1970-01-01 09:00:02    1   A      ref3
1970-01-01 09:00:03    1   B      ref2
1970-01-01 09:00:04    1   B      ref1
```

``` sql
SELECT id, sequenceNextNode('backward', 'tail')(dt, page, ref = 'ref4', page = 'B') FROM test_flow_basecond GROUP BY id;

dt   id   page   ref
1970-01-01 09:00:01    1   A      ref4
1970-01-01 09:00:02    1   A      ref3
1970-01-01 09:00:03    1   B      ref2
1970-01-01 09:00:04    1   B      ref1 // The tail can not be base point because the ref column of the tail unmatched with 'ref4'.
SELECT id, sequenceNextNode('forward', 'first_match')(dt, page, ref = 'ref3', page = 'A') FROM test_flow_basecond GROUP BY id;

dt   id   page   ref
1970-01-01 09:00:01    1   A      ref4 // This row can not be base point because the ref column unmatched with 'ref3'.
1970-01-01 09:00:02    1   A      ref3 // Base point
1970-01-01 09:00:03    1   B      ref2 // The result
1970-01-01 09:00:04    1   B      ref1
SELECT id, sequenceNextNode('backward', 'last_match')(dt, page, ref = 'ref2', page = 'B') FROM test_flow_basecond GROUP BY id;

dt   id   page   ref
1970-01-01 09:00:01    1   A      ref4
1970-01-01 09:00:02    1   A      ref3 // The result
1970-01-01 09:00:03    1   B      ref2 // Base point
1970-01-01 09:00:04    1   B      ref1 // This row can not be base point because the ref column unmatched with 'ref2'.