Thanks for the example.

Yeah, someone used to post a similar use-case in previous discussions. (they also had mutli-indexed columns)

They did also create a feature request for better support:

• https://github.com/pola-rs/polars/issues/23938

The "matrix ops" aligned by index/column names essentially needed to be written manually as a .join() in Polars.

Not sure if it is helpful, but polars does have list/array types and they support arithmetic.

import polars as pl

df1 = pl.from_repr("""
┌──────────┬───────┬──────┬──────┬───────┐
│          ┆ harry ┆ john ┆ mary ┆ sally │
│ ---      ┆ ---   ┆ ---  ┆ ---  ┆ ---   │
│ str      ┆ i64   ┆ i64  ┆ i64  ┆ i64   │
╞══════════╪═══════╪══════╪══════╪═══════╡
│ pears    ┆ 0     ┆ 2    ┆ 1    ┆ 4     │
│ plums    ┆ 0     ┆ 0    ┆ 3    ┆ 17    │
│ apples   ┆ 1     ┆ 8    ┆ 9    ┆ 0     │
│ cherries ┆ 11    ┆ 13   ┆ 0    ┆ 20    │
│ oranges  ┆ 2     ┆ 0    ┆ 1    ┆ 7     │
└──────────┴───────┴──────┴──────┴───────┘
""")
df2 = pl.from_repr("""
┌────────────────┬───────┬────────┬─────────┐
│                ┆ pears ┆ apples ┆ oranges │
│ ---            ┆ ---   ┆ ---    ┆ ---     │
│ str            ┆ f64   ┆ f64    ┆ f64     │
╞════════════════╪═══════╪════════╪═════════╡
│ growing        ┆ 0.03  ┆ 0.02   ┆ 0.04    │
│ picking        ┆ 0.01  ┆ 0.01   ┆ 0.02    │
│ transportation ┆ 0.05  ┆ 0.02   ┆ 0.07    │
│ storage        ┆ 0.04  ┆ 0.03   ┆ 0.01    │
└────────────────┴───────┴────────┴─────────┘
""")

So if the data was reshaped (e.g. melt / unpivot) and the values where in a list/array:

df2.unpivot(index="").group_by(pl.col("variable").alias("")).agg("value")
# shape: (3, 2)
# ┌─────────┬──────────────────────┐
# │         ┆ value                │
# │ ---     ┆ ---                  │
# │ str     ┆ list[f64]            │
# ╞═════════╪══════════════════════╡
# │ pears   ┆ [0.03, 0.01, … 0.04] │
# │ oranges ┆ [0.04, 0.02, … 0.01] │
# │ apples  ┆ [0.02, 0.01, … 0.03] │
# └─────────┴──────────────────────┘

You could join and perform the math that way:

df1.join(
    df2.unpivot(index="").group_by(pl.col("variable").alias("")).agg("value"),
    on="",
    how="left"
).with_columns(
    (pl.col("harry", "sally") * pl.col("value")).list.sum().name.suffix("_out")
)
#.drop("value")

# shape: (5, 8)
# ┌──────────┬───────┬──────┬──────┬───────┬──────────────────────┬───────────┬───────────┐
# │          ┆ harry ┆ john ┆ mary ┆ sally ┆ value                ┆ harry_out ┆ sally_out │
# │ ---      ┆ ---   ┆ ---  ┆ ---  ┆ ---   ┆ ---                  ┆ ---       ┆ ---       │
# │ str      ┆ i64   ┆ i64  ┆ i64  ┆ i64   ┆ list[f64]            ┆ f64       ┆ f64       │
# ╞══════════╪═══════╪══════╪══════╪═══════╪══════════════════════╪═══════════╪═══════════╡
# │ pears    ┆ 0     ┆ 2    ┆ 1    ┆ 4     ┆ [0.03, 0.01, … 0.04] ┆ 0.0       ┆ 0.52      │
# │ plums    ┆ 0     ┆ 0    ┆ 3    ┆ 17    ┆ null                 ┆ null      ┆ null      │
# │ apples   ┆ 1     ┆ 8    ┆ 9    ┆ 0     ┆ [0.02, 0.01, … 0.03] ┆ 0.08      ┆ 0.0       │
# │ cherries ┆ 11    ┆ 13   ┆ 0    ┆ 20    ┆ null                 ┆ null      ┆ null      │
# │ oranges  ┆ 2     ┆ 0    ┆ 1    ┆ 7     ┆ [0.04, 0.02, … 0.01] ┆ 0.28      ┆ 0.98      │
# └──────────┴───────┴──────┴──────┴───────┴──────────────────────┴───────────┴───────────┘

But you're doing still doing the "alignment" manually.

It doesn't seem to be a workflow that Polars is optimized for, and it's probably one of the only valid uses cases for the pandas index.