polars-pairing

This plugin provides pairing functions to Polars. These functions encode a pair of natural numbers into a single natural number.

Installation

pip install polars-pairing

Functionality and usage

This plugin implements six pairing functions (Hagen¹, Szudzik², Cantor³, Peter⁴, Rosenberg-Strong⁵, and Thotakura⁶), along with their corresponding unpairing functions, as Polars expressions. The pairing functions take two nonnegative integer columns as input and produce a single column containing the encoded pair. Conversely, the unpairing functions accept a single column as input and generate a struct column containing the values of the original pair.

>>> import polars as pl
>>> import polars_pairing as plp

>>> df = pl.DataFrame({
...     "a": [1, 2, 38, 4],
...     "b": [5, 6, 77, 80]
... })
>>> df.select(plp.col("a").pairing.pair(plp.col("b")).alias("pair"))
shape: (4, 1)
┌──────┐
│ pair │
│ ---  │
│ u64  │
╞══════╡
│ 28   │
│ 40   │
│ 6006 │
│ 6408 │
└──────┘

# By default, the Hagen pairing function is used, but you can specify alternative functions:
>>> df.select(
...     plp.col("a").pairing.pair(plp.col("b"), method="hagen").alias("hagen_pair"),
...     plp.col("a").pairing.pair(plp.col("b"), method="szudzik").alias("szudzik_pair"),
...     plp.col("a").pairing.pair(plp.col("b"), method="cantor").alias("cantor_pair"),
...     plp.col("a").pairing.pair(plp.col("b"), method="peter").alias("peter_pair"),
...     plp.col("a").pairing.pair(plp.col("b"), method="rosenberg_strong").alias("rosenberg_strong_pair"),
...     plp.col("a").pairing.pair(plp.col("b"), method="thotakura").alias("thotakura_pair")
... )
shape: (4, 6)
┌────────────┬──────────────┬─────────────┬────────────┬───────────────────────┬────────────────┐
│ hagen_pair ┆ szudzik_pair ┆ cantor_pair ┆ peter_pair ┆ rosenberg_strong_pair ┆ thotakura_pair │
│ ---        ┆ ---          ┆ ---         ┆ ---        ┆ ---                   ┆ ---            │
│ u64        ┆ u64          ┆ u64         ┆ u64        ┆ u64                   ┆ u64            │
╞════════════╪══════════════╪═════════════╪════════════╪═══════════════════════╪════════════════╡
│ 28         ┆ 26           ┆ 26          ┆ 28         ┆ 26                    ┆ 24             │
│ 40         ┆ 38           ┆ 42          ┆ 41         ┆ 38                    ┆ 34             │
│ 6006       ┆ 5967         ┆ 6747        ┆ 6006       ┆ 5967                  ┆ 3194           │
│ 6408       ┆ 6404         ┆ 3650        ┆ 6409       ┆ 6404                  ┆ 3368           │
└────────────┴──────────────┴─────────────┴────────────┴───────────────────────┴────────────────┘

# The corresponding unpairing functions are also available:
>>> df = pl.DataFrame({"p": [28, 40, 6006, 6408]})
>>> df.select(plp.col("p").pairing.unpair().alias("unpair"))
shape: (4, 1)
┌───────────┐
│ unpair    │
│ ---       │
│ struct[2] │
╞═══════════╡
│ {1,5}     │
│ {2,6}     │
│ {38,77}   │
│ {4,80}    │
└───────────┘

>>> df = pl.DataFrame({"p": [26, 38, 5967, 6404]})
>>> df.select(
...     plp.col("p").pairing.unpair(method="szudzik").alias("unpair")
... ).unnest("unpair")
shape: (4, 2)
┌──────┬───────┐
│ Left ┆ Right │
│ ---  ┆ ---   │
│ u64  ┆ u64   │
╞══════╪═══════╡
│ 1    ┆ 5     │
│ 2    ┆ 6     │
│ 38   ┆ 77    │
│ 4    ┆ 80    │
└──────┴───────┘

>>> df = pl.DataFrame({"p": [28, 41, 6006, 6409]})
>>> df.select(
...     plp.col("p").pairing.unpair(method="peter").alias("unpair")
... ).unnest("unpair")
shape: (4, 2)
┌──────┬───────┐
│ Left ┆ Right │
│ ---  ┆ ---   │
│ u64  ┆ u64   │
╞══════╪═══════╡
│ 1    ┆ 5     │
│ 2    ┆ 6     │
│ 38   ┆ 77    │
│ 4    ┆ 80    │
└──────┴───────┘

>>> df = pl.DataFrame({"p": [26, 38, 5967, 6404]})
>>> df.select(
...     plp.col("p").pairing.unpair(method="rosenberg_strong").alias("unpair")
... ).unnest("unpair")
shape: (4, 2)
┌──────┬───────┐
│ Left ┆ Right │
│ ---  ┆ ---   │
│ u64  ┆ u64   │
╞══════╪═══════╡
│ 1    ┆ 5     │
│ 2    ┆ 6     │
│ 38   ┆ 77    │
│ 4    ┆ 80    │
└──────┴───────┘

>>> df = pl.DataFrame({"p": [24, 34, 3194, 3368]})
>>> df.select(
...     plp.col("p").pairing.unpair(method="thotakura").alias("unpair")
... ).unnest("unpair")
shape: (4, 2)
┌──────┬───────┐
│ Left ┆ Right │
│ ---  ┆ ---   │
│ u64  ┆ u64   │
╞══════╪═══════╡
│ 1    ┆ 5     │
│ 2    ┆ 6     │
│ 38   ┆ 77    │
│ 4    ┆ 80    │
└──────┴───────┘