list_entropy

Applies to VAST Cluster 5.5.

Functions › List, struct and map functions › Aggregate a list. Returns the Shannon entropy of the values in a list, in bits: how unpredictable an element picked from the list is. It works on lists of any type, and NULL elements are skipped.

Syntax

list_entropy(l)

Returns: DOUBLE.

Set up the examples

The examples connect with the ADBC driver, as in VAST Query Engine (ADBC), and work in a schema called docs_sql_fn_lists_list_entropy. Set QE_ENDPOINT, AWS_ACCESS_KEY_ID, AWS_SECRET_ACCESS_KEY and VASTDB_BUCKET (SQL reference), and run the blocks in order in one Python session. Below each block is the output you should see.

This block connects, defines the run() and plan() helpers, and creates a table of five rows of lists: whole numbers (nums), measurements (vals) and words (words). Row 2 has NULL elements, row 3 has empty lists, row 4 has no values, and row 5 has non-ASCII words and an empty string:

import os
import re

import adbc_driver_manager
import adbc_driver_manager.dbapi as dbapi
import adbc_driver_vastdb

BUCKET = os.environ["VASTDB_BUCKET"]
SCHEMA = f'"{BUCKET}/docs_sql_fn_lists_list_entropy"'

conn = dbapi.connect(
    driver=adbc_driver_vastdb.get_driver_path(),
    db_kwargs={
        "vast.db.endpoint": os.environ["QE_ENDPOINT"],
        "vast.db.access_key": os.environ["AWS_ACCESS_KEY_ID"],
        "vast.db.secret_key": os.environ["AWS_SECRET_ACCESS_KEY"],
    },
    autocommit=True,
)

def server_message(e):
    """The server's message in a driver error, without the request ID or the echoed statement."""
    text = re.sub(r"\[req=0x[0-9a-f]+\]: ", "", str(e))
    found = (re.search(r'message: "(.*?)", request_id', text, re.S)
             or re.search(r"description: (.*)\)", text, re.S))
    message = found.group(1) if found else text.strip().splitlines()[-1]
    message = re.sub(r"^Plan query: '.*?' failed with: ", "", message, flags=re.S)
    message = re.split(r"\\n|\n", message)[0].replace('\\"', '"')
    return message.replace(BUCKET, "<bucket>")

def run(sql):
    """Run one statement. Print the rows it returns, or the error."""
    try:
        with conn.cursor() as cur:
            cur.execute(sql)
            rows = cur.fetchall() if cur.description else []
    except (adbc_driver_manager.Error, OSError) as e:
        print(f"{type(e).__name__}: {server_message(e)}")
    else:
        print(rows)

def plan(sql):
    """Print the plan without its ~N Rows lines: the table's row count, which can still be 0 just after an insert."""
    with conn.cursor() as cur:
        cur.execute("EXPLAIN " + sql)
        steps = cur.fetchall()[0][1]
    print("\n".join(line for line in steps.splitlines() if "Rows" not in line))

TABLE = f"{SCHEMA}.samples"
run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}")
run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, nums BIGINT[], vals DOUBLE[], words VARCHAR[])")
run(f"INSERT INTO {TABLE} VALUES "
    "(1, [1, 2, 3], [0.5, 2.5, -1.0], ['a', 'b', 'c']), "
    "(2, [3, NULL, 3], [2.0, NULL], ['b', NULL, 'B']), "
    "(3, [], [], []), "
    "(4, NULL, NULL, NULL), "
    "(5, [-5, 0, -5, 10], [1e308, 1e308, -1e-308], ['\u00e9', 'Zo\u00eb', '\U0001F1EB\U0001F1F7', ''])")

[]
[]
[(5,)]

What it does

list_entropy(l) counts how often each distinct non-NULL value occurs in l, turns the counts into proportions p, and returns the sum of -p × log2(p):

• One value repeated gives 0.0: [1, 1, 1].
• Two values, equally often, give 1.0 (one bit): [1, 1, 2, 2]. Four values, equally often, give 2.0: [1, 2, 3, 4].
• Uneven counts give less than equal ones: ['a', 'a', 'b'] gives 0.9182958340544893.
• Only how often values occur matters, not their size or order, so it works on text and other types as well as numbers. Text is compared exactly: 'b' and 'B' are different values.

The counts are those of list_histogram.

NULLs and edge cases

The same cases, as the cluster returns them. They use the table and helpers from Set up the examples:

run("SELECT list_entropy(NULL), list_entropy(NULL::BIGINT[]), list_entropy([]::BIGINT[]), list_entropy([NULL, 1])")
run("SELECT list_entropy([1, 1, 1]), list_entropy(['a', 'a', 'b']), list_entropy(['NaN'::DOUBLE, 'NaN'::DOUBLE]), "
    "typeof(list_entropy([1, 2]))")
run(f"SELECT list_entropy(123) FROM {TABLE} LIMIT 1")

[(None, None, 0.0, 0.0)]
[(0.0, 0.9182958340544893, 1.0, 'DOUBLE')]
InternalError: Binder Error: No function matches the given name and argument types 'list_aggr(INTEGER_LITERAL, STRING_LITERAL)'. You might need to add explicit type casts.

Examples

The entropy of each row's lists. Row 1's three different values give 1.5849625007211559 (log2 of 3) in every column. Row 2's words ['b', NULL, 'B'] give 1.0: the NULL is skipped and 'b' and 'B' differ. Row 3's empty lists give 0.0, and row 4's NULL lists give NULL:

run(f"SELECT id, list_entropy(nums), list_entropy(vals), list_entropy(words) FROM {TABLE} ORDER BY id LIMIT 10")

[(1, 1.5849625007211559, 1.5849625007211559, 1.5849625007211559), (2, 0.0, 0.0, 1.0), (3, 0.0, 0.0, 0.0), (4, None, None, None), (5, 1.5, 0.9182958340544893, 2.0)]

The rows whose words are more varied than one bit:

run(f"SELECT id, words FROM {TABLE} WHERE list_entropy(words) > 1 ORDER BY id LIMIT 10")

[(1, ['a', 'b', 'c']), (5, ['é', 'Zoë', '🇫🇷', ''])]

How it runs in VAST

The Query Engine runs on the cluster's CNodes, and a query on a table starts with a scan in VAST DataBase (VAST_SCAN). The scan reads a list column whole, and list_entropy() always runs in the Query Engine:

• In the SELECT list, a projection step computes list_entropy() for each row the scan returns.
• In WHERE, the scan sends the list for every row, and a FILTER step computes list_entropy() and keeps the rows that match. No rows are skipped in storage.

The plan of the WHERE example shows the FILTER step above the scan:

plan(f"SELECT id FROM {TABLE} WHERE list_entropy(words) > 1")

┌───────────────────────────┐
│         PROJECTION        │
│    ────────────────────   │
│             #1            │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│           FILTER          │
│    ────────────────────   │
│ (list_aggr(words, 'entropy│
│         ') > 1.0)         │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│         VAST_SCAN         │
│    ────────────────────   │
│    Function: VAST_SCAN    │
│                           │
│        Projections:       │
│           words           │
│             id            │
│                           │
└───────────────────────────┘

Make it faster

• Add a condition on a plain column. A comparison of a column with a constant, such as id > 1, is evaluated in VAST DataBase, so list_entropy() runs only on the rows that pass it. The plan for id > 1 alone has no FILTER step:

plan(f"SELECT id FROM {TABLE} WHERE id > 1")

┌───────────────────────────┐
│         VAST_SCAN         │
│    ────────────────────   │
│    Function: VAST_SCAN    │
│      Projections: id      │
│                           │
└───────────────────────────┘

• Store the entropy if you filter on it often. Compute it when you write the rows and keep it in its own column: entropy > 1 is pushed down, list_entropy(words) > 1 isn't.

Limitations and errors

• An empty list gives 0.0, not NULL. Test for empty lists separately if you need to tell them apart from lists of one repeated value, for example with len(l) = 0.
• NaN values aren't grouped. Each NaN counts as a value of its own.
• Lists only. Any other type fails with No function matches the given name and argument types. The error names list_aggr, the list aggregate that list_entropy runs on, and its accepted form list_aggr(ANY[], VARCHAR, [ANY...]) -> ANY.
• ORDER BY needs a LIMIT. Without one, the query fails with The operator 'ORDER_BY' type=1 is currently not supported for this usage.

Similar functions

run("SELECT list_entropy(l), list_histogram(l), list_unique(l), list_approx_count_distinct(l) "
    "FROM (SELECT [3, 1, NULL, 3, 10] AS l)")

[(1.5, [(1, 1), (3, 2), (10, 1)], 3, 3)]

Clean up:

run(f"DROP TABLE IF EXISTS {TABLE}")
run(f"DROP SCHEMA IF EXISTS {SCHEMA}")
conn.close()

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See also

• List, struct and map functions: all the list functions.
• list_histogram: how often each value occurs.
• Where filters run and pushdowns.
• EXPLAIN: how to read a plan.