这个函数基于Laurenz Albe在https://www.cybertec-postgresql.com/en/index-your-foreign-key/上的工作，列出所有缺少索引的外键。表的大小如图所示，对于小表，扫描性能可能优于索引表。

--
-- function:    missing_fk_indexes
-- purpose:     List all foreing keys in the database without and index in the referencing table.
-- author:      Based on the work of Laurenz Albe
-- see:         https://www.cybertec-postgresql.com/en/index-your-foreign-key/
--
create or replace function missing_fk_indexes () 
returns table (
  referencing_table regclass,
  fk_columns        varchar,
  table_size        varchar,
  fk_constraint     name,
  referenced_table  regclass
)
language sql as $$
  select
    -- referencing table having ta foreign key declaration
    tc.conrelid::regclass as referencing_table,
    
    -- ordered list of foreign key columns
    string_agg(ta.attname, ', ' order by tx.n) as fk_columns,
    
    -- referencing table size
    pg_catalog.pg_size_pretty (
      pg_catalog.pg_relation_size(tc.conrelid)
    ) as table_size,
    
    -- name of the foreign key constraint
    tc.conname as fk_constraint,
    
    -- name of the target or destination table
    tc.confrelid::regclass as referenced_table
    
  from pg_catalog.pg_constraint tc
  
  -- enumerated key column numbers per foreign key
  cross join lateral unnest(tc.conkey) with ordinality as tx(attnum, n)
  
  -- name for each key column
  join pg_catalog.pg_attribute ta on ta.attnum = tx.attnum and ta.attrelid = tc.conrelid
  
  where not exists (
    -- is there ta matching index for the constraint?
    select 1 from pg_catalog.pg_index i
    where 
      i.indrelid = tc.conrelid and 
      -- the first index columns must be the same as the key columns, but order doesn't matter
      (i.indkey::smallint[])[0:cardinality(tc.conkey)-1] @> tc.conkey) and 
      tc.contype = 'f'
    group by 
      tc.conrelid, 
      tc.conname, 
      tc.confrelid
    order by 
      pg_catalog.pg_relation_size(tc.conrelid) desc
$$;

这样测试，

select * from missing_fk_indexes();

你会看到一个这样的列表。

   referencing_table    |    fk_columns    | table_size |                fk_constraint                 | referenced_table 
------------------------+------------------+------------+----------------------------------------------+------------------
 stk_warehouse          | supplier_id      | 8192 bytes | stk_warehouse_supplier_id_fkey               | stk_supplier
 stk_reference          | supplier_id      | 0 bytes    | stk_reference_supplier_id_fkey               | stk_supplier
 stk_part_reference     | reference_id     | 0 bytes    | stk_part_reference_reference_id_fkey         | stk_reference
 stk_warehouse_part     | part_id          | 0 bytes    | stk_warehouse_part_part_id_fkey              | stk_part
 stk_warehouse_part_log | dst_warehouse_id | 0 bytes    | stk_warehouse_part_log_dst_warehouse_id_fkey | stk_warehouse
 stk_warehouse_part_log | part_id          | 0 bytes    | stk_warehouse_part_log_part_id_fkey          | stk_part
 stk_warehouse_part_log | src_warehouse_id | 0 bytes    | stk_warehouse_part_log_src_warehouse_id_fkey | stk_warehouse
 stk_product_part       | part_id          | 0 bytes    | stk_product_part_part_id_fkey                | stk_part
 stk_purchase           | parent_id        | 0 bytes    | stk_purchase_parent_id_fkey                  | stk_purchase
 stk_purchase           | supplier_id      | 0 bytes    | stk_purchase_supplier_id_fkey                | stk_supplier
 stk_purchase_line      | reference_id     | 0 bytes    | stk_purchase_line_reference_id_fkey          | stk_reference
 stk_order              | freighter_id     | 0 bytes    | stk_order_freighter_id_fkey                  | stk_freighter
 stk_order_line         | product_id       | 0 bytes    | stk_order_line_product_id_fkey               | cnt_product
 stk_order_fulfillment  | freighter_id     | 0 bytes    | stk_order_fulfillment_freighter_id_fkey      | stk_freighter
 stk_part               | sibling_id       | 0 bytes    | stk_part_sibling_id_fkey                     | stk_part
 stk_order_part         | part_id          | 0 bytes    | stk_order_part_part_id_fkey                  | stk_part

对于那些决定在每个引用列上系统地创建和索引的人来说，这个版本可能更有效:

--
-- function:    missing_fk_indexes2
-- purpose:     List all foreing keys in the database without and index in the referencing table.
--              The listing contains create index sentences
-- author:      Based on the work of Laurenz Albe
-- see:         https://www.cybertec-postgresql.com/en/index-your-foreign-key/
--
create or replace function missing_fk_indexes2 () 
returns setof varchar
language sql as $$
  select
    -- create index sentence
    'create index on ' || 
    tc.conrelid::regclass || 
    '(' || 
    string_agg(ta.attname, ', ' order by tx.n) || 
    ')' as create_index
        
  from pg_catalog.pg_constraint tc
  
  -- enumerated key column numbers per foreign key
  cross join lateral unnest(tc.conkey) with ordinality as tx(attnum, n)
  
  -- name for each key column
  join pg_catalog.pg_attribute ta on ta.attnum = tx.attnum and ta.attrelid = tc.conrelid
  
  where not exists (
    -- is there ta matching index for the constraint?
    select 1 from pg_catalog.pg_index i
    where 
      i.indrelid = tc.conrelid and 
      -- the first index columns must be the same as the key columns, but order doesn't matter
      (i.indkey::smallint[])[0:cardinality(tc.conkey)-1] @> tc.conkey) and 
      tc.contype = 'f'
    group by 
      tc.conrelid, 
      tc.conname, 
      tc.confrelid
    order by 
      pg_catalog.pg_relation_size(tc.conrelid) desc
$$;

现在输出的是必须添加到数据库中的创建索引语句。

select * from missing_fk_indexes2();

                   missing_fk_indexes2                    
----------------------------------------------------------
 create index on stk_warehouse(supplier_id)
 create index on stk_reference(supplier_id)
 create index on stk_part_reference(reference_id)
 create index on stk_warehouse_part(part_id)
 create index on stk_warehouse_part_log(dst_warehouse_id)
 create index on stk_warehouse_part_log(part_id)
 create index on stk_warehouse_part_log(src_warehouse_id)
 create index on stk_product_part(part_id)
 create index on stk_purchase(parent_id)
 create index on stk_purchase(supplier_id)
 create index on stk_purchase_line(reference_id)
 create index on stk_order(freighter_id)
 create index on stk_order_line(product_id)
 create index on stk_order_fulfillment(freighter_id)
 create index on stk_part(sibling_id)
 create index on stk_order_part(part_id)

对于PRIMARY KEY，索引将被创建，并带有以下消息:

NOTICE: CREATE TABLE / PRIMARY KEY will create implicit index "index" for table "table" 

对于一个FOREIGN KEY，如果引用的表上没有索引，约束将不会被创建。

引用表上的索引不是必需的(尽管是需要的)，因此不会隐式创建。

我很喜欢EclipseLink 2.5的酷炫性能特性这篇文章中对此的解释

Indexing Foreign Keys The first feature is auto indexing of foreign keys. Most people incorrectly assume that databases index foreign keys by default. Well, they don't. Primary keys are auto indexed, but foreign keys are not. This means any query based on the foreign key will be doing full table scans. This is any OneToMany, ManyToMany or ElementCollection relationship, as well as many OneToOne relationships, and most queries on any relationship involving joins or object comparisons. This can be a major perform issue, and you should always index your foreign keys fields.

下面是一个bash脚本，它使用@sergeyB的SQL生成SQL，为外键上缺失的索引创建索引。

#!/bin/bash

read -r -d '' SQL <<EOM

WITH fk_actions ( code, action ) AS (
    VALUES ( 'a', 'error' ),
        ( 'r', 'restrict' ),
        ( 'c', 'cascade' ),
        ( 'n', 'set null' ),
        ( 'd', 'set default' )
),
fk_list AS (
    SELECT pg_constraint.oid as fkoid, conrelid, confrelid as parentid,
        conname, relname, nspname,
        fk_actions_update.action as update_action,
        fk_actions_delete.action as delete_action,
        conkey as key_cols
    FROM pg_constraint
        JOIN pg_class ON conrelid = pg_class.oid
        JOIN pg_namespace ON pg_class.relnamespace = pg_namespace.oid
        JOIN fk_actions AS fk_actions_update ON confupdtype = fk_actions_update.code
        JOIN fk_actions AS fk_actions_delete ON confdeltype = fk_actions_delete.code
    WHERE contype = 'f'
),
fk_attributes AS (
    SELECT fkoid, conrelid, attname, attnum
    FROM fk_list
        JOIN pg_attribute
            ON conrelid = attrelid
            AND attnum = ANY( key_cols )
    ORDER BY fkoid, attnum
),
fk_cols_list AS (
    SELECT fkoid, array_to_string(array_agg(attname), ':') as cols_list
    FROM fk_attributes
    GROUP BY fkoid
),
index_list AS (
    SELECT indexrelid as indexid,
        pg_class.relname as indexname,
        indrelid,
        indkey,
        indpred is not null as has_predicate,
        pg_get_indexdef(indexrelid) as indexdef
    FROM pg_index
        JOIN pg_class ON indexrelid = pg_class.oid
    WHERE indisvalid
),
fk_index_match AS (
    SELECT fk_list.*,
        indexid,
        indexname,
        indkey::int[] as indexatts,
        has_predicate,
        indexdef,
        array_length(key_cols, 1) as fk_colcount,
        array_length(indkey,1) as index_colcount,
        round(pg_relation_size(conrelid)/(1024^2)::numeric) as table_mb,
        cols_list
    FROM fk_list
        JOIN fk_cols_list USING (fkoid)
        LEFT OUTER JOIN index_list
            ON conrelid = indrelid
            AND (indkey::int2[])[0:(array_length(key_cols,1) -1)] @> key_cols

),
fk_perfect_match AS (
    SELECT fkoid
    FROM fk_index_match
    WHERE (index_colcount - 1) <= fk_colcount
        AND NOT has_predicate
        AND indexdef LIKE '%USING btree%'
),
fk_index_check AS (
    SELECT 'no index' as issue, *, 1 as issue_sort
    FROM fk_index_match
    WHERE indexid IS NULL
    UNION ALL
    SELECT 'questionable index' as issue, *, 2
    FROM fk_index_match
    WHERE indexid IS NOT NULL
        AND fkoid NOT IN (
            SELECT fkoid
            FROM fk_perfect_match)
),
parent_table_stats AS (
    SELECT fkoid, tabstats.relname as parent_name,
        (n_tup_ins + n_tup_upd + n_tup_del + n_tup_hot_upd) as parent_writes,
        round(pg_relation_size(parentid)/(1024^2)::numeric) as parent_mb
    FROM pg_stat_user_tables AS tabstats
        JOIN fk_list
            ON relid = parentid
),
fk_table_stats AS (
    SELECT fkoid,
        (n_tup_ins + n_tup_upd + n_tup_del + n_tup_hot_upd) as writes,
        seq_scan as table_scans
    FROM pg_stat_user_tables AS tabstats
        JOIN fk_list
            ON relid = conrelid
)
SELECT relname as table_name,
    cols_list
FROM fk_index_check
    JOIN parent_table_stats USING (fkoid)
    JOIN fk_table_stats USING (fkoid)
ORDER BY issue_sort, table_mb DESC, table_name;
EOM

DB_NAME="dbname"
DB_USER="dbuser"
DB_PASSWORD="dbpass"
DB_HOSTNAME="hostname"
DB_PORT=5432

export PGPASSWORD="$DB_PASSWORD"
psql -h $DB_HOSTNAME -p $DB_PORT -U $DB_USER -d $DB_NAME -t -A -F"," -c "$SQL" | while read -r line; do
  IFS=','
  parts=($line)
  unset IFS
  tableName=${parts[0]}
  colsList=${parts[1]}

  indexName="${tableName}_${colsList//:/_}_index"
  printf -- "\n--Index: %s\nDROP INDEX IF EXISTS %s;\n
CREATE INDEX %s\n\t\tON %s USING btree\n\t(%s);
  " "$indexName" "$indexName" "$indexName" "$tableName" "$colsList"
done

该查询将列出外键上缺失的索引，原始源。

编辑:注意它不会检查小表(小于9 MB)和其他一些情况。参见最后的WHERE语句。

-- check for FKs where there is no matching index
-- on the referencing side
-- or a bad index

WITH fk_actions ( code, action ) AS (
    VALUES ( 'a', 'error' ),
        ( 'r', 'restrict' ),
        ( 'c', 'cascade' ),
        ( 'n', 'set null' ),
        ( 'd', 'set default' )
),
fk_list AS (
    SELECT pg_constraint.oid as fkoid, conrelid, confrelid as parentid,
        conname, relname, nspname,
        fk_actions_update.action as update_action,
        fk_actions_delete.action as delete_action,
        conkey as key_cols
    FROM pg_constraint
        JOIN pg_class ON conrelid = pg_class.oid
        JOIN pg_namespace ON pg_class.relnamespace = pg_namespace.oid
        JOIN fk_actions AS fk_actions_update ON confupdtype = fk_actions_update.code
        JOIN fk_actions AS fk_actions_delete ON confdeltype = fk_actions_delete.code
    WHERE contype = 'f'
),
fk_attributes AS (
    SELECT fkoid, conrelid, attname, attnum
    FROM fk_list
        JOIN pg_attribute
            ON conrelid = attrelid
            AND attnum = ANY( key_cols )
    ORDER BY fkoid, attnum
),
fk_cols_list AS (
    SELECT fkoid, array_agg(attname) as cols_list
    FROM fk_attributes
    GROUP BY fkoid
),
index_list AS (
    SELECT indexrelid as indexid,
        pg_class.relname as indexname,
        indrelid,
        indkey,
        indpred is not null as has_predicate,
        pg_get_indexdef(indexrelid) as indexdef
    FROM pg_index
        JOIN pg_class ON indexrelid = pg_class.oid
    WHERE indisvalid
),
fk_index_match AS (
    SELECT fk_list.*,
        indexid,
        indexname,
        indkey::int[] as indexatts,
        has_predicate,
        indexdef,
        array_length(key_cols, 1) as fk_colcount,
        array_length(indkey,1) as index_colcount,
        round(pg_relation_size(conrelid)/(1024^2)::numeric) as table_mb,
        cols_list
    FROM fk_list
        JOIN fk_cols_list USING (fkoid)
        LEFT OUTER JOIN index_list
            ON conrelid = indrelid
            AND (indkey::int2[])[0:(array_length(key_cols,1) -1)] @> key_cols

),
fk_perfect_match AS (
    SELECT fkoid
    FROM fk_index_match
    WHERE (index_colcount - 1) <= fk_colcount
        AND NOT has_predicate
        AND indexdef LIKE '%USING btree%'
),
fk_index_check AS (
    SELECT 'no index' as issue, *, 1 as issue_sort
    FROM fk_index_match
    WHERE indexid IS NULL
    UNION ALL
    SELECT 'questionable index' as issue, *, 2
    FROM fk_index_match
    WHERE indexid IS NOT NULL
        AND fkoid NOT IN (
            SELECT fkoid
            FROM fk_perfect_match)
),
parent_table_stats AS (
    SELECT fkoid, tabstats.relname as parent_name,
        (n_tup_ins + n_tup_upd + n_tup_del + n_tup_hot_upd) as parent_writes,
        round(pg_relation_size(parentid)/(1024^2)::numeric) as parent_mb
    FROM pg_stat_user_tables AS tabstats
        JOIN fk_list
            ON relid = parentid
),
fk_table_stats AS (
    SELECT fkoid,
        (n_tup_ins + n_tup_upd + n_tup_del + n_tup_hot_upd) as writes,
        seq_scan as table_scans
    FROM pg_stat_user_tables AS tabstats
        JOIN fk_list
            ON relid = conrelid
)
SELECT nspname as schema_name,
    relname as table_name,
    conname as fk_name,
    issue,
    table_mb,
    writes,
    table_scans,
    parent_name,
    parent_mb,
    parent_writes,
    cols_list,
    indexdef
FROM fk_index_check
    JOIN parent_table_stats USING (fkoid)
    JOIN fk_table_stats USING (fkoid)
WHERE table_mb > 9
    AND ( writes > 1000
        OR parent_writes > 1000
        OR parent_mb > 10 )
ORDER BY issue_sort, table_mb DESC, table_name, fk_name;

这个函数基于Laurenz Albe在https://www.cybertec-postgresql.com/en/index-your-foreign-key/上的工作，列出所有缺少索引的外键。表的大小如图所示，对于小表，扫描性能可能优于索引表。

--
-- function:    missing_fk_indexes
-- purpose:     List all foreing keys in the database without and index in the referencing table.
-- author:      Based on the work of Laurenz Albe
-- see:         https://www.cybertec-postgresql.com/en/index-your-foreign-key/
--
create or replace function missing_fk_indexes () 
returns table (
  referencing_table regclass,
  fk_columns        varchar,
  table_size        varchar,
  fk_constraint     name,
  referenced_table  regclass
)
language sql as $$
  select
    -- referencing table having ta foreign key declaration
    tc.conrelid::regclass as referencing_table,
    
    -- ordered list of foreign key columns
    string_agg(ta.attname, ', ' order by tx.n) as fk_columns,
    
    -- referencing table size
    pg_catalog.pg_size_pretty (
      pg_catalog.pg_relation_size(tc.conrelid)
    ) as table_size,
    
    -- name of the foreign key constraint
    tc.conname as fk_constraint,
    
    -- name of the target or destination table
    tc.confrelid::regclass as referenced_table
    
  from pg_catalog.pg_constraint tc
  
  -- enumerated key column numbers per foreign key
  cross join lateral unnest(tc.conkey) with ordinality as tx(attnum, n)
  
  -- name for each key column
  join pg_catalog.pg_attribute ta on ta.attnum = tx.attnum and ta.attrelid = tc.conrelid
  
  where not exists (
    -- is there ta matching index for the constraint?
    select 1 from pg_catalog.pg_index i
    where 
      i.indrelid = tc.conrelid and 
      -- the first index columns must be the same as the key columns, but order doesn't matter
      (i.indkey::smallint[])[0:cardinality(tc.conkey)-1] @> tc.conkey) and 
      tc.contype = 'f'
    group by 
      tc.conrelid, 
      tc.conname, 
      tc.confrelid
    order by 
      pg_catalog.pg_relation_size(tc.conrelid) desc
$$;

这样测试，

select * from missing_fk_indexes();

你会看到一个这样的列表。

   referencing_table    |    fk_columns    | table_size |                fk_constraint                 | referenced_table 
------------------------+------------------+------------+----------------------------------------------+------------------
 stk_warehouse          | supplier_id      | 8192 bytes | stk_warehouse_supplier_id_fkey               | stk_supplier
 stk_reference          | supplier_id      | 0 bytes    | stk_reference_supplier_id_fkey               | stk_supplier
 stk_part_reference     | reference_id     | 0 bytes    | stk_part_reference_reference_id_fkey         | stk_reference
 stk_warehouse_part     | part_id          | 0 bytes    | stk_warehouse_part_part_id_fkey              | stk_part
 stk_warehouse_part_log | dst_warehouse_id | 0 bytes    | stk_warehouse_part_log_dst_warehouse_id_fkey | stk_warehouse
 stk_warehouse_part_log | part_id          | 0 bytes    | stk_warehouse_part_log_part_id_fkey          | stk_part
 stk_warehouse_part_log | src_warehouse_id | 0 bytes    | stk_warehouse_part_log_src_warehouse_id_fkey | stk_warehouse
 stk_product_part       | part_id          | 0 bytes    | stk_product_part_part_id_fkey                | stk_part
 stk_purchase           | parent_id        | 0 bytes    | stk_purchase_parent_id_fkey                  | stk_purchase
 stk_purchase           | supplier_id      | 0 bytes    | stk_purchase_supplier_id_fkey                | stk_supplier
 stk_purchase_line      | reference_id     | 0 bytes    | stk_purchase_line_reference_id_fkey          | stk_reference
 stk_order              | freighter_id     | 0 bytes    | stk_order_freighter_id_fkey                  | stk_freighter
 stk_order_line         | product_id       | 0 bytes    | stk_order_line_product_id_fkey               | cnt_product
 stk_order_fulfillment  | freighter_id     | 0 bytes    | stk_order_fulfillment_freighter_id_fkey      | stk_freighter
 stk_part               | sibling_id       | 0 bytes    | stk_part_sibling_id_fkey                     | stk_part
 stk_order_part         | part_id          | 0 bytes    | stk_order_part_part_id_fkey                  | stk_part

对于那些决定在每个引用列上系统地创建和索引的人来说，这个版本可能更有效:

--
-- function:    missing_fk_indexes2
-- purpose:     List all foreing keys in the database without and index in the referencing table.
--              The listing contains create index sentences
-- author:      Based on the work of Laurenz Albe
-- see:         https://www.cybertec-postgresql.com/en/index-your-foreign-key/
--
create or replace function missing_fk_indexes2 () 
returns setof varchar
language sql as $$
  select
    -- create index sentence
    'create index on ' || 
    tc.conrelid::regclass || 
    '(' || 
    string_agg(ta.attname, ', ' order by tx.n) || 
    ')' as create_index
        
  from pg_catalog.pg_constraint tc
  
  -- enumerated key column numbers per foreign key
  cross join lateral unnest(tc.conkey) with ordinality as tx(attnum, n)
  
  -- name for each key column
  join pg_catalog.pg_attribute ta on ta.attnum = tx.attnum and ta.attrelid = tc.conrelid
  
  where not exists (
    -- is there ta matching index for the constraint?
    select 1 from pg_catalog.pg_index i
    where 
      i.indrelid = tc.conrelid and 
      -- the first index columns must be the same as the key columns, but order doesn't matter
      (i.indkey::smallint[])[0:cardinality(tc.conkey)-1] @> tc.conkey) and 
      tc.contype = 'f'
    group by 
      tc.conrelid, 
      tc.conname, 
      tc.confrelid
    order by 
      pg_catalog.pg_relation_size(tc.conrelid) desc
$$;

现在输出的是必须添加到数据库中的创建索引语句。

select * from missing_fk_indexes2();

                   missing_fk_indexes2                    
----------------------------------------------------------
 create index on stk_warehouse(supplier_id)
 create index on stk_reference(supplier_id)
 create index on stk_part_reference(reference_id)
 create index on stk_warehouse_part(part_id)
 create index on stk_warehouse_part_log(dst_warehouse_id)
 create index on stk_warehouse_part_log(part_id)
 create index on stk_warehouse_part_log(src_warehouse_id)
 create index on stk_product_part(part_id)
 create index on stk_purchase(parent_id)
 create index on stk_purchase(supplier_id)
 create index on stk_purchase_line(reference_id)
 create index on stk_order(freighter_id)
 create index on stk_order_line(product_id)
 create index on stk_order_fulfillment(freighter_id)
 create index on stk_part(sibling_id)
 create index on stk_order_part(part_id)