list_var_pop

Applies to VAST Cluster 5.5.

Functions › List, struct and map functions › Aggregate a list. Returns the population variance of the elements of a numeric list: the mean of the squared differences from the mean. NULL elements are skipped.

Syntax

list_var_pop(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_var_pop. 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_var_pop"'

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_var_pop(l) treats the non-NULL elements of l as a whole population of n values. It computes their mean, then the mean of the squared differences from it: the sum of (x - mean)² divided by n.

• [1.0, 2.0, 3.0, 10.0] has a mean of 4 and a variance of 12.5.
• A single element, or elements that are all the same, give 0.0.
• NULL elements are skipped: [3, NULL, 3] is treated as [3, 3].

For a sample, which divides by n - 1, use list_var_samp.

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

[(None, None, None, None)]
[(0.0, 0.0, 0.6666666666666666, 'DOUBLE')]
OSError: VARPOP is out of range!
OSError: VARPOP is out of range!
OSError: VARPOP 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 variance of each row's numbers. Row 2's NULL is skipped, so [3, NULL, 3] has a variance of 0.0; the empty list and the NULL list give NULL:

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

[(1, [1, 2, 3], 0.6666666666666666), (2, [3, None, 3], 0.0), (3, [], None), (4, None, None), (5, [-5, 0, -5, 10], 37.5)]

The rows whose numbers vary by more than 1:

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

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

┌───────────────────────────┐
│         PROJECTION        │
│    ────────────────────   │
│             #1            │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│           FILTER          │
│    ────────────────────   │
│  (list_aggr(CAST(nums AS  │
│  DOUBLE[]), 'var_pop') > 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_var_pop() 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 variance if you filter on it often. Compute it when you write the rows and keep it in its own column: variance > 1 is pushed down, list_var_pop(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 VARPOP 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_var_pop:

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

OSError: VARPOP 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_var_pop 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_var_pop(l), list_var_samp(l), list_stddev_pop(l), list_stddev_samp(l) "
    "FROM (SELECT [1.0, 2.0, 3.0, 10.0]::DOUBLE[] AS l)")

[(12.5, 16.666666666666668, 3.5355339059327378, 4.08248290463863)]

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.
• var_pop: the population variance of a column, across rows.
• Where filters run and pushdowns.
• EXPLAIN: how to read a plan.