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 doesn't 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.

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. valuesExpression resulting in input values.

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 don't 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, ...)

!!! warning "Warning" Events that occur at the same second may lay in the sequence in an undefined order affecting the result.

Parameters

• pattern — Pattern string. See Pattern syntax.

• 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.

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 don't 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 don't overlap. It starts to search for the next chain after the current chain is matched.

!!! warning "Warning" Events that occur at the same second may lay in the sequence in an undefined order affecting the result.

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

Parameters

• pattern — Pattern string. See Pattern syntax.

• 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.

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(window, [mode])(timestamp, cond1, cond2, cond3, ...)

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

windowFunnel(window, [mode])(timestamp, cond1, cond2, cond3, ...)

Parameters:

• window — Length of the sliding window in seconds.
• mode - It is an optional argument.
• 'strict' - When the 'strict' is set, the windowFunnel() applies conditions only for the unique values.
• 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).
• cond1, cond2... — Conditions or data describing the chain of events. Data type: UInt8. Values can be 0 or 1.

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.

Returned value

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

Example

Determine if one hour is enough for the user to select a phone and purchase it in the online store.

Set the following chain of events:

1. The user logged in to their account on the store (eventID=1001).
2. The user searches for a phone (eventID = 1003, product = 'phone').
3. The user placed an order (eventID = 1009).

To find out how far the user user_id could get through the chain in an hour in January of 2017, make the query:

SELECT
level,
count() AS c
FROM
(
SELECT
user_id,
windowFunnel(3600)(timestamp, eventID = 1001, eventID = 1003 AND product = 'phone', eventID = 1009) AS level
FROM trend_event
WHERE (event_date >= '2017-01-01') AND (event_date <= '2017-01-31')
GROUP BY user_id
)
GROUP BY level
ORDER BY level

Simply, the level value could only be 0, 1, 2, 3, it means the maxium event action stage that one user could reach.

retention(cond1, cond2, ...)

Retention refers to the ability of a company or product to retain its customers over some specified periods.

cond1, cond2 ... is from one to 32 arguments of type UInt8 that indicate whether a certain condition was met for the event

Example:

Consider you are doing a website analytics, intend to calculate the retention of customers

This could be easily calculate by retention

SELECT
sum(r) AS r1,
sum(r) AS r2,
sum(r) AS r3
FROM
(
SELECT
uid,
retention(date = '2018-08-10', date = '2018-08-11', date = '2018-08-12') AS r
FROM events
WHERE date IN ('2018-08-10', '2018-08-11', '2018-08-12')
GROUP BY uid
)

Simply, r1 means the number of unique visitors who met the cond1 condition, r2 means the number of unique visitors who met cond1 and cond2 conditions, r3 means the number of unique visitors who met 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.