list_sem

Applies to VAST Cluster 5.5.

Functions › List, struct and map functions › Aggregate a list. Returns the standard error of the mean of the elements of a numeric list: the population standard deviation divided by the square root of the number of elements. NULL elements are skipped.

Syntax

list_sem(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_sem. 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_sem"'

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_sem(l) computes the population standard deviation of the n non-NULL elements of l, as list_stddev_pop does, and divides it by the square root of n:

• [1.0, 2.0, 3.0, 10.0] has a population standard deviation of 3.5355339059327378; divided by 2 (the square root of 4), that's 1.7677669529663689.
• [1.0, 2.0] gives 0.35355339059327373 (0.5 divided by the square root of 2).
• A single element, or elements that are all the same, give 0.0.

It uses the population standard deviation, not the sample one (list_stddev_samp). For the sample-based standard error, divide list_stddev_samp(l) by the square root of the number of elements yourself.

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

[(None, None, None, None)]
[(0.0, 0.0, 0.47140452079103173, 'DOUBLE')]
OSError: SEM is out of range!
OSError: SEM is out of range!
OSError: SEM 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 standard error of the mean of each row's numbers. Row 2's NULL is skipped, so [3, NULL, 3] gives 0.0; the empty list and the NULL list give NULL:

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

[(1, [1, 2, 3], 0.47140452079103173), (2, [3, None, 3], 0.0), (3, [], None), (4, None, None), (5, [-5, 0, -5, 10], 3.0618621784789726)]

The rows whose mean is uncertain by more than 1:

run(f"SELECT id, nums FROM {TABLE} WHERE list_sem(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_sem() always runs in the Query Engine:

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

┌───────────────────────────┐
│         PROJECTION        │
│    ────────────────────   │
│             #1            │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│           FILTER          │
│    ────────────────────   │
│  (list_aggr(CAST(nums AS  │
│  DOUBLE[]), 'sem') > 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_sem() 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 standard error if you filter on it often. Compute it when you write the rows and keep it in its own column: sem > 1 is pushed down, list_sem(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 that their squares overflow a DOUBLE, the query fails with SEM 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_sem:

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

OSError: SEM is out of range!

• 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_sem 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_sem(l), list_stddev_pop(l), list_stddev_samp(l), list_var_pop(l) "
    "FROM (SELECT [1.0, 2.0, 3.0, 10.0]::DOUBLE[] AS l)")

[(1.7677669529663689, 3.5355339059327378, 4.08248290463863, 12.5)]

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_avg: the mean of a list.
• Where filters run and pushdowns.
• EXPLAIN: how to read a plan.