Rank Polymorphism Configuration for Multi-Dimensional Array Processing

Answer

The standard way to specify the axis of operation in APL rank polymorphism is to use the axis operator [n] (or equivalently the rank operator ⍤k) where n (or k) indicates the axis or sub‑array rank on which the function should act.

Confirmed facts

• The axis operator f[axis] array applies f to each sub‑vector along the chosen axis while leaving all other dimensions unchanged.
• The rank operator f⍤k array treats the array as a collection of k-rank cells; the result retains the outer dimensions and only the selected rank is reduced by f.
• Both operators avoid creating a full copy of the array; they work on views of the selected cells, so intermediate memory usage is proportional to the size of the processed cells.

Likely explanation / steps for this case

1. Identify the axis you want to preserve (e.g., axis 2 of a 3‑D array).
2. Choose the appropriate operator:
   • If you want to apply a function along that axis and drop it, use f[axis] array.
   • If you want to keep the axis but control the rank of the sub‑arrays processed, use f⍤k array where k equals the rank of the sub‑arrays you wish to feed to f.
3. Apply the function, e.g., result ← +[2] A to sum along axis 2, or result ← +⍤2 A to sum each matrix (rank‑2) cell.
4. Verify the output shape with ⍴result; it should match the expected dimensionality (all original axes except the one reduced by f).
5. If memory is a concern, reuse a temporary variable or enable in‑place variants offered by your APL interpreter.

Missing diagnostic detail

To determine the exact numeric value for axis or k, you need to know whether your APL dialect uses 0‑based or 1‑based axis numbering for the axis operator. Please confirm the indexing origin of your APL implementation so the correct axis can be specified.