Given a list of column names in the variable column_names(more than 20, but in this example reduced to 3) and the dataframe below:

df = pl.DataFrame({
    "column1": [2, 1, 3],
    "column2": [0, 2, 0],
    "column3": [0, 0, 4]
})

Output:
┌─────────┬─────────┬─────────┐
│ column1 ┆ column2 ┆ column3 │
│ ---     ┆ ---     ┆ ---     │
│ i64     ┆ i64     ┆ i64     │
╞═════════╪═════════╪═════════╡
│ 2       ┆ 0       ┆ 0       │
│ 1       ┆ 2       ┆ 0       │
│ 3       ┆ 0       ┆ 4       │
└─────────┴─────────┴─────────┘

The original dataframe is sparse and I would like to condense it into the following format with the following tranformations:

1. Condense the values into a column of lists named column_values. The corresponding column name will appear in another column named column_names
2. All values below a certain threshold will not appear in column values. In the below example, only values more than 1 are included (the second row is missing the intended 1)
3. Column values should be arranged in descending order, with the corresponding column name also arranged in the same order
4. Please try to minimize memory usage!

The output should look like this:

┌────────────────────────┬───────────────┐
│ column_names           ┆ column_values │
│ ---                    ┆ ---           │
│ list[str]              ┆ list[i64]     │
╞════════════════════════╪═══════════════╡
│ ["column1"]            ┆ [2]           │
│ ["column2"]            ┆ [2]           │
│ ["column3", "column1"] ┆ [4, 3]        │
└────────────────────────┴───────────────┘