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| author | Marshall Lochbaum <mwlochbaum@gmail.com> | 2020-09-04 21:33:13 -0400 |
|---|---|---|
| committer | Marshall Lochbaum <mwlochbaum@gmail.com> | 2020-09-04 21:33:13 -0400 |
| commit | 015d9cd399100427b3e82fb183c81d034f00cd8c (patch) | |
| tree | 64470d2b546b3691483e35dcadaf925988ffcd37 /docs/doc/transpose.html | |
| parent | cf072f50d2e1c600c788d37645721a94c55377c8 (diff) | |
Use atom for non-array throughout docs
Diffstat (limited to 'docs/doc/transpose.html')
| -rw-r--r-- | docs/doc/transpose.html | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/docs/doc/transpose.html b/docs/doc/transpose.html index 5f0900b8..c8b54b42 100644 --- a/docs/doc/transpose.html +++ b/docs/doc/transpose.html @@ -87,7 +87,7 @@ <p>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: <code><span class='Paren'>(</span><span class='Function'>=-</span><span class='Number'>1</span><span class='Modifier'>˜</span><span class='Paren'>)</span><span class='Modifier2'>⊸</span><span class='Function'>⍉</span></code>.</p> <h2 id="definitions">Definitions</h2> <p>Here we define the two valences of Transpose more precisely.</p> -<p>A non-array right argument to Transpose is always enclosed to get a scalar array before doing anything else.</p> -<p>Monadic transpose is identical to <code><span class='Paren'>(</span><span class='Function'>=-</span><span class='Number'>1</span><span class='Modifier'>˜</span><span class='Paren'>)</span><span class='Modifier2'>⊸</span><span class='Function'>⍉</span></code>, except that for scalar arguments it returns the array unchanged rather than giving an error.</p> -<p>In Dyadic transpose, the left argument is a number or numeric array of rank 1 or less, and <code><span class='Value'>𝕨</span><span class='Function'>≤</span><span class='Modifier2'>○</span><span class='Function'>≠≢</span><span class='Value'>𝕩</span></code>. Define the result rank <code><span class='Value'>r</span><span class='Gets'>←</span><span class='Paren'>(</span><span class='Function'>=</span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Function'>-+</span><span class='Modifier'>´</span><span class='Function'>¬∊</span><span class='Value'>𝕨</span></code> to be the argument rank minus the number of duplicate entries in the left argument. We require <code><span class='Function'>∧</span><span class='Modifier'>´</span><span class='Value'>𝕨</span><span class='Function'><</span><span class='Value'>r</span></code>. Bring <code><span class='Value'>𝕨</span></code> to full length by appending the missing indices: <code><span class='Value'>𝕨</span><span class='Function'>∾</span><span class='Gets'>↩</span><span class='Value'>𝕨</span><span class='Paren'>(</span><span class='Function'>¬</span><span class='Modifier2'>∘</span><span class='Function'>∊</span><span class='Modifier'>˜</span><span class='Function'>/⊢</span><span class='Paren'>)</span><span class='Function'>↕</span><span class='Value'>r</span></code>. Now the result shape is defined to be <code><span class='Function'>⌊</span><span class='Modifier'>´¨</span><span class='Value'>𝕨</span><span class='Function'>⊔≢</span><span class='Value'>𝕩</span></code>. Element <code><span class='Value'>i</span><span class='Function'>⊑</span><span class='Value'>z</span></code> of the result <code><span class='Value'>z</span></code> is element <code><span class='Paren'>(</span><span class='Value'>𝕨</span><span class='Function'>⊏</span><span class='Value'>i</span><span class='Paren'>)</span><span class='Function'>⊑</span><span class='Value'>𝕩</span></code> of the argument.</p> +<p>Monadic transpose is identical to <code><span class='Paren'>(</span><span class='Function'>=-</span><span class='Number'>1</span><span class='Modifier'>˜</span><span class='Paren'>)</span><span class='Modifier2'>⊸</span><span class='Function'>⍉</span></code>, except that for scalar arguments (including atoms) it returns the array unchanged rather than giving an error.</p> +<p>An atom right argument to dyadic Transpose is always enclosed to get a scalar array before doing anything else.</p> +<p>In dyadic Transpose, the left argument is a number or numeric array of rank 1 or less, and <code><span class='Value'>𝕨</span><span class='Function'>≤</span><span class='Modifier2'>○</span><span class='Function'>≠≢</span><span class='Value'>𝕩</span></code>. Define the result rank <code><span class='Value'>r</span><span class='Gets'>←</span><span class='Paren'>(</span><span class='Function'>=</span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Function'>-+</span><span class='Modifier'>´</span><span class='Function'>¬∊</span><span class='Value'>𝕨</span></code> to be the argument rank minus the number of duplicate entries in the left argument. We require <code><span class='Function'>∧</span><span class='Modifier'>´</span><span class='Value'>𝕨</span><span class='Function'><</span><span class='Value'>r</span></code>. Bring <code><span class='Value'>𝕨</span></code> to full length by appending the missing indices: <code><span class='Value'>𝕨</span><span class='Function'>∾</span><span class='Gets'>↩</span><span class='Value'>𝕨</span><span class='Paren'>(</span><span class='Function'>¬</span><span class='Modifier2'>∘</span><span class='Function'>∊</span><span class='Modifier'>˜</span><span class='Function'>/⊢</span><span class='Paren'>)</span><span class='Function'>↕</span><span class='Value'>r</span></code>. Now the result shape is defined to be <code><span class='Function'>⌊</span><span class='Modifier'>´¨</span><span class='Value'>𝕨</span><span class='Function'>⊔≢</span><span class='Value'>𝕩</span></code>. Element <code><span class='Value'>i</span><span class='Function'>⊑</span><span class='Value'>z</span></code> of the result <code><span class='Value'>z</span></code> is element <code><span class='Paren'>(</span><span class='Value'>𝕨</span><span class='Function'>⊏</span><span class='Value'>i</span><span class='Paren'>)</span><span class='Function'>⊑</span><span class='Value'>𝕩</span></code> of the argument.</p> |
