Centering a Polars column and retrieving the scalar mean in one expressions-only pipeline

Learn how to center a column and get its scalar mean in Polars using expressions. See ScalarColumn, broadcasting, and implode to keep memory efficient.

Centering a column in Polars while also retrieving the scalar mean looks innocent, but it raises a practical question: how do you stick to expressions, avoid eager detours, and keep the memory layout efficient when one result is a scalar and the other is a column?

Repro case: scalar + column from the same expression graph

The setup is minimal. We compute the mean of a single column and build a centered version of that column using only expressions.

import polars as pl
import numpy as np
frame = pl.DataFrame({"probe": np.array([0., 1, 2, 3, 4])})
avg_expr = pl.col("probe").mean().alias("avg")
res_avg = frame.select(avg_expr)
shifted_expr = pl.col("probe") - avg_expr
res_shifted = frame.select(shifted_expr)

It’s natural to try selecting both at once. The display will show the scalar mean as if it was expanded across all rows, which looks like broadcasting and can be confusing in terms of perceived storage behavior.

What’s actually happening

Polars has a concept called a ScalarColumn that can hold scalars. The fact that you see a broadcast in the output doesn’t automatically mean a copy is performed for every row. However, it’s not a hard guarantee, so there are cases where a copy will occur.

If you want the visual representation to reflect the underlying memory layout—one scalar and one non-scalar without row-wise repetition—you can change how you present the non-scalar result.

Solution: make the non-scalar explicit with implode

To keep both results together while preserving the idea of a single scalar next to a single collection, implode the non-scalar expression. This yields a one-row DataFrame with a scalar and a list, aligning the display with the intended layout.

out = frame.select(
    pl.col("probe").mean().alias("avg"),
    (pl.col("probe") - pl.col("probe").mean()).implode().alias("centered")
)

The resulting schema shows a single f64 scalar and a list[f64] for the centered values, both computed through expressions without an eager step.

Why this matters

When working with expressions in Polars, it’s common to mix scalar aggregations and column-wise transformations in the same select. Understanding how scalars are represented and how the display relates to memory layout helps avoid wrong assumptions about storage overhead. Using implode aligns the output with what you intend: a single scalar value alongside a compact vector-like field, produced in one pass.

Takeaways

If you need both a scalar and a derived column from the same expression plan, remember that a scalar may appear broadcasted in the display even when it isn’t always copied internally. If you want the output to reflect a single scalar next to a single collection, implode the non-scalar expression and keep everything in the expression pipeline. In cases where this pattern doesn’t fit your workflow, calculating the scalar eagerly and proceeding afterward is a viable alternative, though it may not generalize as well.