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Diffstat (limited to 'doc/transpose.md')
| -rw-r--r-- | doc/transpose.md | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/doc/transpose.md b/doc/transpose.md index 64d1cbe2..f1f978ad 100644 --- a/doc/transpose.md +++ b/doc/transpose.md @@ -63,9 +63,9 @@ Axis permutations of the types we've shown generate the complete permutation gro ≢ ⍉⁼⎉¯2 ⍉ a23456 # Restrict Transpose to the first three axes -In a case like this BQN's Dyadic transpose is much easier. +In a case like this the dyadic version of `⍉`, called Reorder Axes, is much easier. -## Dyadic Transpose +## Reorder Axes Transpose also allows a left argument that specifies a permutation of `𝕩`'s axes. For each index `p←i⊑𝕨` in the left argument, axis `i` of `𝕩` is used for axis `p` of the result. Multiple argument axes can be sent to the same result axis, in which case that axis goes along a diagonal of `𝕩`, and the result will have a lower rank than `𝕩`. @@ -85,7 +85,7 @@ In particular, the case with only one axis specified is interesting. Here, the f ≢ 2 ⍉ a23456 # Restrict Transpose to the first three axes -Finally, it's worth noting that, as monadic Transpose moves the first axis to the end, it's equivalent to dyadic Transpose with a "default" left argument: `(=-1˙)⊸⍉`. +Finally, it's worth noting that, as monadic Transpose moves the first axis to the end, it's equivalent to Reorder Axes with a "default" left argument: `(=-1˙)⊸⍉`. ## Definitions @@ -95,4 +95,4 @@ An atom right argument to either valence of Transpose is always enclosed to get Monadic transpose is identical to `(=-1˙)⊸⍉`, except that if `𝕩` is a unit it is returned unchanged (after enclosing, if it's an atom) rather than giving an error. -In dyadic Transpose, `𝕨` is a number or numeric array of rank 1 or less, and `𝕨≤○≠≢𝕩`. Define the result rank `r←(=𝕩)-+´¬∊𝕨` to be the right argument rank minus the number of duplicate entries in the left argument. We require `∧´𝕨<r`. Bring `𝕨` to full length by appending the missing indices: `𝕨∾↩𝕨(¬∘∊˜/⊢)↕r`. Now the result shape is defined to be `⌊´¨𝕨⊔≢𝕩`. Element `i⊑z` of the result `z` is element `(𝕨⊏i)⊑𝕩` of the argument. +In Reorder Axes, `𝕨` is a number or numeric array of rank 1 or less, and `𝕨≤○≠≢𝕩`. Define the result rank `r←(=𝕩)-+´¬∊𝕨` to be the right argument rank minus the number of duplicate entries in the left argument. We require `∧´𝕨<r`. Bring `𝕨` to full length by appending the missing indices: `𝕨∾↩𝕨(¬∘∊˜/⊢)↕r`. Now the result shape is defined to be `⌊´¨𝕨⊔≢𝕩`. Element `i⊑z` of the result `z` is element `(𝕨⊏i)⊑𝕩` of the argument. |