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authorMarshall Lochbaum <mwlochbaum@gmail.com>2020-10-03 16:38:35 -0400
committerMarshall Lochbaum <mwlochbaum@gmail.com>2020-10-03 16:38:35 -0400
commit673de1c627a2046123e1693e9e6508399a028508 (patch)
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<p>Monadic transpose is identical to <code><span class='Paren'>(</span><span class='Function'>=-</span><span class='Number'>1</span><span class='Modifier'>ห™</span><span class='Paren'>)</span><span class='Modifier2'>โŠธ</span><span class='Function'>โ‰</span></code>, except that if the argument is a unit it is returned unchanged rather than giving an error.</p>
<p>An atom right argument to dyadic Transpose is always enclosed to get an 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'>๐•จ</span><span class='Function'>โ‰ค</span><span class='Modifier2'>โ—‹</span><span class='Function'>โ‰ โ‰ข</span><span class='Value'>๐•ฉ</span></code>. Define the result rank <code><span class='Value'>r</span><span class='Gets'>โ†</span><span class='Paren'>(</span><span class='Function'>=</span><span class='Value'>๐•ฉ</span><span class='Paren'>)</span><span class='Function'>-+</span><span class='Modifier'>ยด</span><span class='Function'>ยฌโˆŠ</span><span class='Value'>๐•จ</span></code> to be the argument rank minus the number of duplicate entries in the left argument. We require <code><span class='Function'>โˆง</span><span class='Modifier'>ยด</span><span class='Value'>๐•จ</span><span class='Function'>&lt;</span><span class='Value'>r</span></code>. Bring <code><span class='Value'>๐•จ</span></code> to full length by appending the missing indices: <code><span class='Value'>๐•จ</span><span class='Function'>โˆพ</span><span class='Gets'>โ†ฉ</span><span class='Value'>๐•จ</span><span class='Paren'>(</span><span class='Function'>ยฌ</span><span class='Modifier2'>โˆ˜</span><span class='Function'>โˆŠ</span><span class='Modifier'>หœ</span><span class='Function'>/โŠข</span><span class='Paren'>)</span><span class='Function'>โ†•</span><span class='Value'>r</span></code>. Now the result shape is defined to be <code><span class='Function'>โŒŠ</span><span class='Modifier'>ยดยจ</span><span class='Value'>๐•จ</span><span class='Function'>โŠ”โ‰ข</span><span class='Value'>๐•ฉ</span></code>. Element <code><span class='Value'>i</span><span class='Function'>โŠ‘</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'>๐•จ</span><span class='Function'>โŠ</span><span class='Value'>i</span><span class='Paren'>)</span><span class='Function'>โŠ‘</span><span class='Value'>๐•ฉ</span></code> of the argument.</p>
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