list_skewness

Applies to VAST Cluster 5.5.

Functions › List, struct and map functions › Aggregate a list. Returns the sample skewness of the elements of a numeric list: how lopsided the values are around their mean. It needs at least three non-NULL elements.

Syntax

list_skewness(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_skewness. 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) and measurements (vals). Row 2 has a NULL element, row 3 has empty lists, row 4 has no values, and row 5's measurements are close to the largest DOUBLE:

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_skewness"'

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[])")
run(f"INSERT INTO {TABLE} VALUES "
    "(1, [1, 2, 3], [0.5, 2.5, -1.0]), "
    "(2, [3, NULL, 3], [2.0, NULL]), "
    "(3, [], []), "
    "(4, NULL, NULL), "
    "(5, [-5, 0, -5, 10], [1e308, 1e308, -1e-308])")

[]
[]
[(5,)]

What it does

list_skewness(l) measures the asymmetry of the n non-NULL elements of l. It's the sample skewness: the third central moment divided by the second raised to the power 1.5, multiplied by sqrt(n(n-1)) / (n-2) to correct for the sample size.

• A symmetric list gives 0.0: [1.0, 2.0, 3.0].
• A long tail of high values gives a positive result: [1.0, 2.0, 10.0] gives 1.6523167403329886 and [1.0, 2.0, 3.0, 10.0] gives 1.763632614803888.
• Fewer than three non-NULL elements give NULL.
• Elements that are all the same give NaN, not NULL: there's no spread to divide by.

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_skewness(NULL), list_skewness(NULL::BIGINT[]), list_skewness([]::DOUBLE[]), "
    "list_skewness([NULL, NULL]::DOUBLE[])")
run("SELECT list_skewness([1.0]), list_skewness([1.0, 2.0]), list_skewness([1.0, 2.0, 3.0]), list_skewness([5, 5, 5, 5]), "
    "typeof(list_skewness([1, 2]))")
run("SELECT list_skewness(['NaN'::DOUBLE, 1.0, 2.0])")
run("SELECT list_skewness(['inf'::DOUBLE, 1.0, 2.0])")
run("SELECT list_skewness([1e308, -1e308, 1e308])")
run(f"SELECT list_skewness(123) FROM {TABLE} LIMIT 1")

[(None, None, None, None)]
[(None, None, 0.0, nan, 'DOUBLE')]
OSError: SKEW is out of range!
OSError: SKEW is out of range!
OSError: SKEW is out of range!
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 skewness of each row's numbers. Row 1 is symmetric (0.0), and row 5's 10 gives it a positive skew. Row 2 has only two non-NULL elements, so its result is NULL:

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

[(1, [1, 2, 3], 0.0), (2, [3, None, 3], None), (3, [], None), (4, None, None), (5, [-5, 0, -5, 10], 1.4142135623730951)]

The rows whose numbers lean towards high values:

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

[(5, [-5, 0, -5, 10])]

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_skewness() always runs in the Query Engine:

• In the SELECT list, a projection step computes list_skewness() for each row the scan returns.
• In WHERE, the scan sends the list for every row, and a FILTER step computes list_skewness() 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_skewness(nums) > 1")

┌───────────────────────────┐
│         PROJECTION        │
│    ────────────────────   │
│             #1            │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│           FILTER          │
│    ────────────────────   │
│  (list_aggr(CAST(nums AS  │
│  DOUBLE[]), 'skewness') > │
│            1.0)           │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│         VAST_SCAN         │
│    ────────────────────   │
│    Function: VAST_SCAN    │
│                           │
│        Projections:       │
│            nums           │
│             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_skewness() 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 skewness if you filter on it often. Compute it when you write the rows and keep it in its own column: skew > 1 is pushed down, list_skewness(nums) > 1 isn't.

Limitations and errors

• NaN, infinity and overflow fail the whole query. If any row's list holds NaN or an infinite value, or values large enough to overflow a DOUBLE in the calculation, the query fails with SKEW is out of range! and returns no rows. Row 5's measurements (1e308 twice) are enough. Keep such values out of the lists you pass to list_skewness:

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

OSError: SKEW is out of range!

• A list of equal values gives NaN, not NULL. See NULLs and edge cases.
• 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_skewness 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_skewness(l), list_kurtosis(l), list_kurtosis_pop(l) FROM (SELECT [1.0, 2.0, 3.0, 10.0]::DOUBLE[] AS l)")

[(1.763632614803888, 3.227999999999999, -0.7696000000000001)]

Clean up:

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

[]
[]

See also

• List, struct and map functions: all the list functions.
• list_kurtosis: how heavy a list's tails are.
• Where filters run and pushdowns.
• EXPLAIN: how to read a plan.