From abe8ae4745bb2ebe3b71b047aa92e2ae89a414d5 Mon Sep 17 00:00:00 2001 From: Marshall Lochbaum Date: Wed, 6 Jan 2021 21:55:23 -0500 Subject: Avoid joining units in some documentation --- doc/join.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'doc/join.md') diff --git a/doc/join.md b/doc/join.md index 7a0523dd..50a817e7 100644 --- a/doc/join.md +++ b/doc/join.md @@ -49,7 +49,7 @@ Join requires each element of its argument to be an array, and their ranks to ma However, Join has higher-dimensional uses as well. Given a rank-`m` array of rank-`n` arrays (requiring `m≤n`), it will merge arrays along their first `m` axes. For example, if the argument is a matrix of matrices representing a [block matrix](https://en.wikipedia.org/wiki/Block_matrix), Join will give the corresponding unblocked matrix as its result. - ⊢ m ← (3‿1∾⌜4‿2‿5) ⥊¨ 2‿3⥊↕6 + ⊢ m ← (3‿1≍⌜4‿2‿5) ⥊¨ 2‿3⥊↕6 ∾ m # Join all that together Join has fairly strict requirements on the shapes of its argument elements—although less strict than those of Merge, which requires they all have identical shape. Suppose the argument to Join has rank `m`. Each of its elements must have the same rank, `n`, which is at least `m`. The trailing shapes `m↓⟜≢¨𝕩` must all be identical (the trailing shape `m↓≢∾𝕩` of the result will match these shapes as well). The other entries in the leading shapes need not be the same, but the shape of an element along a particular axis must depend only on the location of the element along that axis in the full array. For a list argument this imposes no restriction, since the one leading shape element is allowed to depend on position along the only axis. But for higher ranks the structure quickly becomes more rigid. -- cgit v1.2.3