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Window functions

Window functions are expressions with superpowers. They allow you to perform aggregations on groups in the select context. Let's get a feel for what that means. First we create a dataset. The dataset loaded in the snippet below contains information about pokemon:

read_csv

import polars as pl

# then let's load some csv data with information about pokemon
df = pl.read_csv(
    "https://gist.githubusercontent.com/ritchie46/cac6b337ea52281aa23c049250a4ff03/raw/89a957ff3919d90e6ef2d34235e6bf22304f3366/pokemon.csv"
)
print(df.head())

CsvReader · Available on feature csv

use polars::prelude::*;
use reqwest::blocking::Client;

let data: Vec<u8> = Client::new()
    .get("https://gist.githubusercontent.com/ritchie46/cac6b337ea52281aa23c049250a4ff03/raw/89a957ff3919d90e6ef2d34235e6bf22304f3366/pokemon.csv")
    .send()?
    .text()?
    .bytes()
    .collect();

let df = CsvReader::new(std::io::Cursor::new(data))
    .has_header(true)
    .finish()?;

println!("{}", df);

shape: (5, 13)
┌─────┬───────────────────────┬────────┬────────┬───┬─────────┬───────┬────────────┬───────────┐
│ #   ┆ Name                  ┆ Type 1 ┆ Type 2 ┆ … ┆ Sp. Def ┆ Speed ┆ Generation ┆ Legendary │
│ --- ┆ ---                   ┆ ---    ┆ ---    ┆   ┆ ---     ┆ ---   ┆ ---        ┆ ---       │
│ i64 ┆ str                   ┆ str    ┆ str    ┆   ┆ i64     ┆ i64   ┆ i64        ┆ bool      │
╞═════╪═══════════════════════╪════════╪════════╪═══╪═════════╪═══════╪════════════╪═══════════╡
│ 1   ┆ Bulbasaur             ┆ Grass  ┆ Poison ┆ … ┆ 65      ┆ 45    ┆ 1          ┆ false     │
│ 2   ┆ Ivysaur               ┆ Grass  ┆ Poison ┆ … ┆ 80      ┆ 60    ┆ 1          ┆ false     │
│ 3   ┆ Venusaur              ┆ Grass  ┆ Poison ┆ … ┆ 100     ┆ 80    ┆ 1          ┆ false     │
│ 3   ┆ VenusaurMega Venusaur ┆ Grass  ┆ Poison ┆ … ┆ 120     ┆ 80    ┆ 1          ┆ false     │
│ 4   ┆ Charmander            ┆ Fire   ┆ null   ┆ … ┆ 50      ┆ 65    ┆ 1          ┆ false     │
└─────┴───────────────────────┴────────┴────────┴───┴─────────┴───────┴────────────┴───────────┘

Group by aggregations in selection

Below we show how to use window functions to group over different columns and perform an aggregation on them. Doing so allows us to use multiple group by operations in parallel, using a single query. The results of the aggregation are projected back to the original rows. Therefore, a window function will almost always lead to a DataFrame with the same size as the original.

We will discuss later the cases where a window function can change the numbers of rows in a DataFrame.

Note how we call .over("Type 1") and .over(["Type 1", "Type 2"]). Using window functions we can aggregate over different groups in a single select call! Note that, in Rust, the type of the argument to over() must be a collection, so even when you're only using one column, you must provide it in an array.

The best part is, this won't cost you anything. The computed groups are cached and shared between different window expressions.

over

out = df.select(
    "Type 1",
    "Type 2",
    pl.col("Attack").mean().over("Type 1").alias("avg_attack_by_type"),
    pl.col("Defense")
    .mean()
    .over(["Type 1", "Type 2"])
    .alias("avg_defense_by_type_combination"),
    pl.col("Attack").mean().alias("avg_attack"),
)
print(out)

over

let out = df
    .clone()
    .lazy()
    .select([
        col("Type 1"),
        col("Type 2"),
        col("Attack")
            .mean()
            .over(["Type 1"])
            .alias("avg_attack_by_type"),
        col("Defense")
            .mean()
            .over(["Type 1", "Type 2"])
            .alias("avg_defense_by_type_combination"),
        col("Attack").mean().alias("avg_attack"),
    ])
    .collect()?;

println!("{}", out);

shape: (163, 5)
┌─────────┬────────┬────────────────────┬─────────────────────────────────┬────────────┐
│ Type 1  ┆ Type 2 ┆ avg_attack_by_type ┆ avg_defense_by_type_combination ┆ avg_attack │
│ ---     ┆ ---    ┆ ---                ┆ ---                             ┆ ---        │
│ str     ┆ str    ┆ f64                ┆ f64                             ┆ f64        │
╞═════════╪════════╪════════════════════╪═════════════════════════════════╪════════════╡
│ Grass   ┆ Poison ┆ 72.923077          ┆ 67.8                            ┆ 75.349693  │
│ Grass   ┆ Poison ┆ 72.923077          ┆ 67.8                            ┆ 75.349693  │
│ Grass   ┆ Poison ┆ 72.923077          ┆ 67.8                            ┆ 75.349693  │
│ Grass   ┆ Poison ┆ 72.923077          ┆ 67.8                            ┆ 75.349693  │
│ Fire    ┆ null   ┆ 88.642857          ┆ 58.3                            ┆ 75.349693  │
│ …       ┆ …      ┆ …                  ┆ …                               ┆ …          │
│ Fire    ┆ Flying ┆ 88.642857          ┆ 82.0                            ┆ 75.349693  │
│ Dragon  ┆ null   ┆ 94.0               ┆ 55.0                            ┆ 75.349693  │
│ Dragon  ┆ null   ┆ 94.0               ┆ 55.0                            ┆ 75.349693  │
│ Dragon  ┆ Flying ┆ 94.0               ┆ 95.0                            ┆ 75.349693  │
│ Psychic ┆ null   ┆ 53.875             ┆ 51.428571                       ┆ 75.349693  │
└─────────┴────────┴────────────────────┴─────────────────────────────────┴────────────┘

Operations per group

Window functions can do more than aggregation. They can also be viewed as an operation within a group. If, for instance, you want to sort the values within a group, you can write col("value").sort().over("group") and voilà! We sorted by group!

Let's filter out some rows to make this more clear.

filter

filtered = df.filter(pl.col("Type 2") == "Psychic").select(
    "Name",
    "Type 1",
    "Speed",
)
print(filtered)

filter

let filtered = df
    .clone()
    .lazy()
    .filter(col("Type 2").eq(lit("Psychic")))
    .select([col("Name"), col("Type 1"), col("Speed")])
    .collect()?;

println!("{}", filtered);

shape: (7, 3)
┌─────────────────────┬────────┬───────┐
│ Name                ┆ Type 1 ┆ Speed │
│ ---                 ┆ ---    ┆ ---   │
│ str                 ┆ str    ┆ i64   │
╞═════════════════════╪════════╪═══════╡
│ Slowpoke            ┆ Water  ┆ 15    │
│ Slowbro             ┆ Water  ┆ 30    │
│ SlowbroMega Slowbro ┆ Water  ┆ 30    │
│ Exeggcute           ┆ Grass  ┆ 40    │
│ Exeggutor           ┆ Grass  ┆ 55    │
│ Starmie             ┆ Water  ┆ 115   │
│ Jynx                ┆ Ice    ┆ 95    │
└─────────────────────┴────────┴───────┘

Observe that the group Water of column Type 1 is not contiguous. There are two rows of Grass in between. Also note that each pokemon within a group are sorted by Speed in ascending order. Unfortunately, for this example we want them sorted in descending speed order. Luckily with window functions this is easy to accomplish.

over

out = filtered.with_columns(
    pl.col(["Name", "Speed"]).sort_by("Speed", descending=True).over("Type 1"),
)
print(out)

over

let out = filtered
    .lazy()
    .with_columns([cols(["Name", "Speed"])
        .sort_by(["Speed"], [true])
        .over(["Type 1"])])
    .collect()?;
println!("{}", out);

shape: (7, 3)
┌─────────────────────┬────────┬───────┐
│ Name                ┆ Type 1 ┆ Speed │
│ ---                 ┆ ---    ┆ ---   │
│ str                 ┆ str    ┆ i64   │
╞═════════════════════╪════════╪═══════╡
│ Starmie             ┆ Water  ┆ 115   │
│ Slowbro             ┆ Water  ┆ 30    │
│ SlowbroMega Slowbro ┆ Water  ┆ 30    │
│ Exeggutor           ┆ Grass  ┆ 55    │
│ Exeggcute           ┆ Grass  ┆ 40    │
│ Slowpoke            ┆ Water  ┆ 15    │
│ Jynx                ┆ Ice    ┆ 95    │
└─────────────────────┴────────┴───────┘

Polars keeps track of each group's location and maps the expressions to the proper row locations. This will also work over different groups in a single select.

The power of window expressions is that you often don't need a group_by -> explode combination, but you can put the logic in a single expression. It also makes the API cleaner. If properly used a:

  • group_by -> marks that groups are aggregated and we expect a DataFrame of size n_groups
  • over -> marks that we want to compute something within a group, and doesn't modify the original size of the DataFrame except in specific cases

Map the expression result to the DataFrame rows

In cases where the expression results in multiple values per group, the Window function has 3 strategies for linking the values back to the DataFrame rows:

  • mapping_strategy = 'group_to_rows' -> each value is assigned back to one row. The number of values returned should match the number of rows.

  • mapping_strategy = 'join' -> the values are imploded in a list, and the list is repeated on all rows. This can be memory intensive.

  • mapping_strategy = 'explode' -> the values are exploded to new rows. This operation changes the number of rows.

Window expression rules

The evaluations of window expressions are as follows (assuming we apply it to a pl.Int32 column):

over

# aggregate and broadcast within a group
# output type: -> Int32
pl.sum("foo").over("groups")

# sum within a group and multiply with group elements
# output type: -> Int32
(pl.col("x").sum() * pl.col("y")).over("groups")

# sum within a group and multiply with group elements
# and aggregate the group to a list
# output type: -> List(Int32)
(pl.col("x").sum() * pl.col("y")).over("groups", mapping_strategy="join")

# sum within a group and multiply with group elements
# and aggregate the group to a list
# then explode the list to multiple rows

# This is the fastest method to do things over groups when the groups are sorted
(pl.col("x").sum() * pl.col("y")).over("groups", mapping_strategy="explode")

over

// aggregate and broadcast within a group
// output type: -> i32
let _ = sum("foo").over([col("groups")]);
// sum within a group and multiply with group elements
// output type: -> i32
let _ = (col("x").sum() * col("y"))
    .over([col("groups")])
    .alias("x1");
// sum within a group and multiply with group elements
// and aggregate the group to a list
// output type: -> ChunkedArray<i32>
let _ = (col("x").sum() * col("y"))
    .over([col("groups")])
    .alias("x2");
// note that it will require an explicit `list()` call
// sum within a group and multiply with group elements
// and aggregate the group to a list
// the flatten call explodes that list

// This is the fastest method to do things over groups when the groups are sorted
let _ = (col("x").sum() * col("y"))
    .over([col("groups")])
    .flatten()
    .alias("x3");

More examples

For more exercise, below are some window functions for us to compute:

  • sort all pokemon by type
  • select the first 3 pokemon per type as "Type 1"
  • sort the pokemon within a type by speed in descending order and select the first 3 as "fastest/group"
  • sort the pokemon within a type by attack in descending order and select the first 3 as "strongest/group"
  • sort the pokemon within a type by name and select the first 3 as "sorted_by_alphabet"

over · implode

out = df.sort("Type 1").select(
    pl.col("Type 1").head(3).over("Type 1", mapping_strategy="explode"),
    pl.col("Name")
    .sort_by(pl.col("Speed"), descending=True)
    .head(3)
    .over("Type 1", mapping_strategy="explode")
    .alias("fastest/group"),
    pl.col("Name")
    .sort_by(pl.col("Attack"), descending=True)
    .head(3)
    .over("Type 1", mapping_strategy="explode")
    .alias("strongest/group"),
    pl.col("Name")
    .sort()
    .head(3)
    .over("Type 1", mapping_strategy="explode")
    .alias("sorted_by_alphabet"),
)
print(out)

over · implode

let out = df
    .clone()
    .lazy()
    .select([
        col("Type 1").head(Some(3)).over(["Type 1"]).flatten(),
        col("Name")
            .sort_by(["Speed"], [true])
            .head(Some(3))
            .over(["Type 1"])
            .flatten()
            .alias("fastest/group"),
        col("Name")
            .sort_by(["Attack"], [true])
            .head(Some(3))
            .over(["Type 1"])
            .flatten()
            .alias("strongest/group"),
        col("Name")
            .sort(false)
            .head(Some(3))
            .over(["Type 1"])
            .flatten()
            .alias("sorted_by_alphabet"),
    ])
    .collect()?;
println!("{:?}", out);

shape: (43, 4)
┌────────┬───────────────────────┬───────────────────────┬───────────────────────────┐
│ Type 1 ┆ fastest/group         ┆ strongest/group       ┆ sorted_by_alphabet        │
│ ---    ┆ ---                   ┆ ---                   ┆ ---                       │
│ str    ┆ str                   ┆ str                   ┆ str                       │
╞════════╪═══════════════════════╪═══════════════════════╪═══════════════════════════╡
│ Bug    ┆ BeedrillMega Beedrill ┆ PinsirMega Pinsir     ┆ Beedrill                  │
│ Bug    ┆ Scyther               ┆ BeedrillMega Beedrill ┆ BeedrillMega Beedrill     │
│ Bug    ┆ PinsirMega Pinsir     ┆ Pinsir                ┆ Butterfree                │
│ Dragon ┆ Dragonite             ┆ Dragonite             ┆ Dragonair                 │
│ Dragon ┆ Dragonair             ┆ Dragonair             ┆ Dragonite                 │
│ …      ┆ …                     ┆ …                     ┆ …                         │
│ Rock   ┆ Aerodactyl            ┆ Golem                 ┆ AerodactylMega Aerodactyl │
│ Rock   ┆ Kabutops              ┆ Kabutops              ┆ Geodude                   │
│ Water  ┆ Starmie               ┆ GyaradosMega Gyarados ┆ Blastoise                 │
│ Water  ┆ Tentacruel            ┆ Kingler               ┆ BlastoiseMega Blastoise   │
│ Water  ┆ Poliwag               ┆ Gyarados              ┆ Cloyster                  │
└────────┴───────────────────────┴───────────────────────┴───────────────────────────┘