Add documentation about the user directory search algorithm (#16320)

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Improve documentation of the user directory search algorithm.

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User Directory API Implementation
=================================
# User Directory API Implementation
The user directory is currently maintained based on the 'visible' users
on this particular server - i.e. ones which your account shares a room with, or
who are present in a publicly viewable room present on the server.
The user directory is maintained based on users that are 'visible' to the homeserver -
i.e. ones which are local to the server and ones which any local user shares a
room with.
The directory info is stored in various tables, which can (typically after
DB corruption) get stale or out of sync. If this happens, for now the
The directory info is stored in various tables, which can sometimes get out of
sync (although this is considered a bug). If this happens, for now the
solution to fix it is to use the [admin API](usage/administration/admin_api/background_updates.md#run)
and execute the job `regenerate_directory`. This should then start a background task to
flush the current tables and regenerate the directory.
flush the current tables and regenerate the directory. Depending on the size
of your homeserver (number of users and rooms) this can take a while.
Data model
----------
## Data model
There are five relevant tables that collectively form the "user directory".
Three of them track a master list of all the users we could search for.
The last two (collectively called the "search tables") track who can
see who.
Three of them track a list of all known users. The last two (collectively called
the "search tables") track which users are visible to each other.
From all of these tables we exclude three types of local user:
- support users
- appservice users
- deactivated users
* `user_directory`. This contains the user_id, display name and avatar we'll
return when you search the directory.
- Because there's only one directory entry per user, it's important that we only
ever put publicly visible names here. Otherwise we might leak a private
A description of each table follows:
* `user_directory`. This contains the user ID, display name and avatar of each user.
- Because there is only one directory entry per user, it is important that it
only contain publicly visible information. Otherwise, this will leak the
nickname or avatar used in a private room.
- Indexed on rooms. Indexed on users.
* `user_directory_search`. To be joined to `user_directory`. It contains an extra
column that enables full text search based on user ids and display names.
Different schemas for SQLite and Postgres with different code paths to match.
column that enables full text search based on user IDs and display names.
Different schemas for SQLite and Postgres are used.
- Indexed on the full text search data. Indexed on users.
* `user_directory_stream_pos`. When the initial background update to populate
the directory is complete, we record a stream position here. This indicates
that synapse should now listen for room changes and incrementally update
the directory where necessary.
the directory where necessary. (See [stream positions](development/synapse_architecture/streams.html).)
* `users_in_public_rooms`. Contains associations between users and the public rooms they're in.
Used to determine which users are in public rooms and should be publicly visible in the directory.
* `users_in_public_rooms`. Contains associations between users and the public
rooms they're in. Used to determine which users are in public rooms and should
be publicly visible in the directory. Both local and remote users are tracked.
* `users_who_share_private_rooms`. Rows are triples `(L, M, room id)` where `L`
is a local user and `M` is a local or remote user. `L` and `M` should be
different, but this isn't enforced by a constraint.
Note that if two local users share a room then there will be two entries:
`(user1, user2, !room_id)` and `(user2, user1, !room_id)`.
## Configuration options
The exact way user search works can be tweaked via some server-level
[configuration options](usage/configuration/config_documentation.md#user_directory).
The information is not repeated here, but the options are mentioned below.
## Search algorithm
If `search_all_users` is `false`, then results are limited to users who:
1. Are found in the `users_in_public_rooms` table, or
2. Are found in the `users_who_share_private_rooms` where `L` is the requesting
user and `M` is the search result.
Otherwise, if `search_all_users` is `true`, no such limits are placed and all
users known to the server (matching the search query) will be returned.
By default, locked users are not returned. If `show_locked_users` is `true` then
no filtering on the locked status of a user is done.
The user provided search term is lowercased and normalized using [NFKC](https://en.wikipedia.org/wiki/Unicode_equivalence#Normalization),
this treats the string as case-insensitive, canonicalizes different forms of the
same text, and maps some "roughly equivalent" characters together.
The search term is then split into words:
* If [ICU](https://en.wikipedia.org/wiki/International_Components_for_Unicode) is
available, then the system's [default locale](https://unicode-org.github.io/icu/userguide/locale/#default-locales)
will be used to break the search term into words. (See the
[installation instructions](setup/installation.md) for how to install ICU.)
* If unavailable, then runs of ASCII characters, numbers, underscores, and hypens
are considered words.
The queries for PostgreSQL and SQLite are detailed below, by their overall goal
is to find matching users, preferring users who are "real" (e.g. not bots,
not deactivated). It is assumed that real users will have an display name and
avatar set.
### PostgreSQL
The above words are then transformed into two queries:
1. "exact" which matches the parsed words exactly (using [`to_tsquery`](https://www.postgresql.org/docs/current/textsearch-controls.html#TEXTSEARCH-PARSING-QUERIES));
2. "prefix" which matches the parsed words as prefixes (using `to_tsquery`).
Results are composed of all rows in the `user_directory_search` table whose information
matches one (or both) of these queries. Results are ordered by calculating a weighted
score for each result, higher scores are returned first:
* 4x if a user ID exists.
* 1.2x if the user has a display name set.
* 1.2x if the user has an avatar set.
* 0x-3x by the full text search results using the [`ts_rank_cd` function](https://www.postgresql.org/docs/current/textsearch-controls.html#TEXTSEARCH-RANKING)
against the "exact" search query; this has four variables with the following weightings:
* `D`: 0.1 for the user ID's domain
* `C`: 0.1 for unused
* `B`: 0.9 for the user's display name (or an empty string if it is not set)
* `A`: 0.1 for the user ID's localpart
* 0x-1x by the full text search results using the `ts_rank_cd` function against the
"prefix" search query. (Using the same weightings as above.)
* If `prefer_local_users` is `true`, then 2x if the user is local to the homeserver.
Note that `ts_rank_cd` returns a weight between 0 and 1. The initial weighting of
all results is 1.
### SQLite
Results are composed of all rows in the `user_directory_search` whose information
matches the query. Results are ordered by the following information, with each
subsequent column used as a tiebreaker, for each result:
1. By the [`rank`](https://www.sqlite.org/windowfunctions.html#built_in_window_functions)
of the full text search results using the [`matchinfo` function](https://www.sqlite.org/fts3.html#matchinfo). Higher
ranks are returned first.
2. If `prefer_local_users` is `true`, then users local to the homeserver are
returned first.
3. Users with a display name set are returned first.
4. Users with an avatar set are returned first.