Which axis should a 1‑D array align to when broadcasting against a 2‑D array in APL?

Answer

The APL language standard does not prescribe a single axis for broadcasting a 1‑D operand with a 2‑D operand; the choice is left to each implementation.

Confirmed facts

• In Dyalog APL the vector is aligned to the last axis of the matrix, i.e. it is treated as a row and added to each row.
• In GNU APL the vector is aligned to the first axis, i.e. it is treated as a column and added to each column.
• The ISO/IEC 13751:2001 APL standard leaves this case unspecified, allowing dialects to differ.

How to verify in your dialect

1. Create a 2‑D array, e.g. M ← 3 3⍴⍳9.
2. Create a 1‑D vector, e.g. V ← ⍳3.
3. Apply a dyadic function, e.g. R ← M + V.
4. Inspect the shape with ⍴R. If the shape remains 3 3 and the vector was added to each row, the alignment is the last axis (Dyalog style). If the shape is still 3 3 but the vector was added to each column, the alignment is the first axis (GNU APL style).

Missing diagnostic detail

To give a definitive recommendation for your code, please specify which APL dialect (or implementation) you are targeting, as the default axis differs between Dyalog and GNU APL.