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diff --git a/docs/doc/reverse.html b/docs/doc/reverse.html index c90f22f2..cd984689 100644 --- a/docs/doc/reverse.html +++ b/docs/doc/reverse.html @@ -5,10 +5,10 @@ </head> <div class="nav">(<a href="https://github.com/mlochbaum/BQN">github</a>) / <a href="../index.html">BQN</a> / <a href="index.html">doc</a></div> <h1 id="reverse-and-rotate"><a class="header" href="#reverse-and-rotate">Reverse and Rotate</a></h1> -<p>The symbol <code><span class='Function'>β½</span></code> indicates two different array transformations: with no left argument, it reverses the major cells of the array, but with a left argument, it rotates or cycles them around. These two possibilities, first put together in very early versions of APL, can't be considered restrictions or different views of some unifying function, but there are connections between them. Each returns an array with the same <a href="shape.html">shape</a> and all the same elements as <code><span class='Value'>π©</span></code>, possibly in a different arrangement. And elements that start out next to each other in <code><span class='Value'>π©</span></code> generally stay next to each otherβalways, if we consider an element on one edge to be next to the one opposite to it. One might think of them as <a href="https://en.wikipedia.org/wiki/Isometry">isometries</a> preserving a discrete subgroup of the torus, if one were inclined to think such things. On major cells, the two functions decompose the <a href="https://en.wikipedia.org/wiki/Dihedral_group">dihedral group</a> okay I'll stop.</p> -<p>Many uses of Rotate in APL are better handled by <a href="shift.html">shift</a> functions in BQN. If there's no reason to treat the data as cyclic or periodic, it's best to avoid Rotate.</p> +<p>The symbol <code><span class='Function'>β½</span></code> indicates two different array transformations: with no left argument, it reverses the <a href="array.html#cells">major cells</a> of the array, but with a left argument, it rotates or cycles them around. These two possibilities, first put together in very early versions of APL, can't be considered restrictions or different views of some unifying function, but there are connections between them. Each returns an array with the same <a href="shape.html">shape</a> and all the same elements as <code><span class='Value'>π©</span></code>, possibly in a different arrangement. And elements that start out next to each other in <code><span class='Value'>π©</span></code> generally stay next to each otherβalways, if we consider an element on one edge to be next to the one opposite to it. One might think of them as <a href="https://en.wikipedia.org/wiki/Isometry">isometries</a> preserving a discrete subgroup of the torus, if one were inclined to think such things. On major cells, the two functions decompose the <a href="https://en.wikipedia.org/wiki/Dihedral_group">dihedral group</a> okay I'll stop.</p> +<p>If there's no reason the data should be seen as cyclic or periodic, it's best to avoid Rotate: <a href="shift.html">shift</a> functions are probably more appropriate.</p> <h2 id="reverse"><a class="header" href="#reverse">Reverse</a></h2> -<p>There's not too much to say about Reverse. It puts the elements of a list the other way around, or more generally the major cells of an array.</p> +<p>Reverse doesn't make things complicated. It puts the elements of a list the other way around, or more generally the major cells of an array.</p> <a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oy9ICJhYmNkZWZnIgoK4oy9ID4iYWIi4oC/ImNkIuKAvyJlZiIKCuKMvSAnYyc=">βοΈ</a><pre> <span class='Function'>β½</span> <span class='String'>"abcdefg"</span> "gfedcba" @@ -23,7 +23,7 @@ <span class='Error'>Error: β½: Argument cannot be a unit</span> </pre> <p>You can't reverse an atom or rank-0 array because it has no axes to reverse along, or it could be said no ordering to reverse.</p> -<p>To reverse along an axis other than the first, use Cells (<code><span class='Modifier'>Λ</span></code>) or Rank (<code><span class='Modifier2'>β</span></code>).</p> +<p>To reverse along an axis other than the first, use <a href="rank.html#cells">Cells</a> (<code><span class='Modifier'>Λ</span></code>) or <a href="rank.html#rank">Rank</a> (<code><span class='Modifier2'>β</span></code>).</p> <a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oy9y5ggPiJhYiLigL8iY2Qi4oC/ImVmIg==">βοΈ</a><pre> <span class='Function'>β½</span><span class='Modifier'>Λ</span> <span class='Function'>></span><span class='String'>"ab"</span><span class='Ligature'>βΏ</span><span class='String'>"cd"</span><span class='Ligature'>βΏ</span><span class='String'>"ef"</span> ββ β΅"ba @@ -38,7 +38,7 @@ <span class='Function'>β</span><span class='Modifier'>ΛΒ΄</span> <span class='Function'>β½</span> <span class='String'>"abcd"</span> <span class='Comment'># Left to right </span>β¨ β¨ "ab" 'c' β© 'd' β© </pre> -<p>Reverse is its own <a href="undo.html">inverse</a> <code><span class='Function'>β½</span><span class='Modifier'>βΌ</span></code>. As a result, <code><span class='Function'>π½</span><span class='Modifier2'>βΎ</span><span class='Function'>β½</span></code> reverses the argument, applies <code><span class='Function'>π½</span></code>, and reverses again. It's a particularly useful pattern with <a href="scan.html">Scan</a>, as it allows scanning from the end rather than the beginning of the array. For example, <code><span class='Function'>β¨</span><span class='Modifier'>`</span></code> on a list of booleans changes all bits after the first <code><span class='Number'>1</span></code> to <code><span class='Number'>1</span></code>, but <code><span class='Function'>β¨</span><span class='Modifier'>`</span><span class='Modifier2'>βΎ</span><span class='Function'>β½</span></code> does this to all bits before the last <code><span class='Number'>1</span></code>.</p> +<p>Reverse is its own <a href="undo.html">inverse</a> <code><span class='Function'>β½</span><span class='Modifier'>βΌ</span></code>. So with <a href="under.html">Under</a>, <code><span class='Function'>π½</span><span class='Modifier2'>βΎ</span><span class='Function'>β½</span></code> reverses the argument, applies <code><span class='Function'>π½</span></code>, and reverses again. It's a particularly useful pattern with <a href="scan.html">Scan</a>, as it allows scanning from the end rather than the beginning of the array. For example, <code><span class='Function'>β¨</span><span class='Modifier'>`</span></code> on a list of booleans changes all bits after the first <code><span class='Number'>1</span></code> to <code><span class='Number'>1</span></code>, but <code><span class='Function'>β¨</span><span class='Modifier'>`</span><span class='Modifier2'>βΎ</span><span class='Function'>β½</span></code> does this to all bits before the last <code><span class='Number'>1</span></code>.</p> <a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oioYCAgIDDigL8w4oC/MeKAvzDigL8w4oC/MeKAvzAKCuKIqGDijL7ijL0gMOKAvzDigL8x4oC/MOKAvzDigL8x4oC/MA==">βοΈ</a><pre> <span class='Function'>β¨</span><span class='Modifier'>`</span> <span class='Number'>0</span><span class='Ligature'>βΏ</span><span class='Number'>0</span><span class='Ligature'>βΏ</span><span class='Number'>1</span><span class='Ligature'>βΏ</span><span class='Number'>0</span><span class='Ligature'>βΏ</span><span class='Number'>0</span><span class='Ligature'>βΏ</span><span class='Number'>1</span><span class='Ligature'>βΏ</span><span class='Number'>0</span> β¨ 0 0 1 1 1 1 1 β© @@ -74,7 +74,7 @@ "terota" </pre> <h3 id="multiple-axes"><a class="header" href="#multiple-axes">Multiple axes</a></h3> -<p>The easiest way to rotate a later array axis is usually to use the Cells (<code><span class='Modifier'>Λ</span></code>) or Rank (<code><span class='Modifier2'>β</span></code>) modifier.</p> +<p>The easiest way to rotate along a later array axis is usually to use the <a href="rank.html#cells">Cells</a> (<code><span class='Modifier'>Λ</span></code>) or <a href="rank.html#rank">Rank</a> (<code><span class='Modifier2'>β</span></code>) modifier.</p> <a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oqiIHRhYiDihpAgM+KAvzTipYoiYWJjZEFCQ0QwMTIzIgoKMSDijL3LmCB0YWIgICMgUm90YXRlIHRoZSBzZWNvbmQgYXhpcw==">βοΈ</a><pre> <span class='Function'>β’</span> <span class='Value'>tab</span> <span class='Gets'>β</span> <span class='Number'>3</span><span class='Ligature'>βΏ</span><span class='Number'>4</span><span class='Function'>β₯</span><span class='String'>"abcdABCD0123"</span> ββ β΅"abcd @@ -89,7 +89,7 @@ 1230" β </pre> -<p>Rotate also allows <code><span class='Value'>π¨</span></code> to be a list (or unit array) of integers, in which case they're matched with <a href="leading.html">leading axes</a> of <code><span class='Value'>π©</span></code>. This means the length of <code><span class='Value'>π¨</span></code> can't be larger than the rank of <code><span class='Value'>π©</span></code>, or there wouldn't be enough axes to match. This rule also explains why <code><span class='Value'>π©</span></code> has to have rank one or more when <code><span class='Value'>π¨</span></code> is an atom, because <code><span class='Value'>π¨</span></code> is treated as the one-element list <code><span class='Function'>β₯</span><span class='Value'>π¨</span></code> in that case.</p> +<p>Rotate also allows <code><span class='Value'>π¨</span></code> to be a list (or unit array) of integers, in which case they're matched with <a href="leading.html">leading axes</a> of <code><span class='Value'>π©</span></code>. This means the length of <code><span class='Value'>π¨</span></code> can't be larger than the rank of <code><span class='Value'>π©</span></code>, or there wouldn't be enough axes to match. This rule that <code><span class='Value'>π©</span></code> has to have rank one or more when <code><span class='Value'>π¨</span></code> is an atom is a special case, because then <code><span class='Value'>π¨</span></code> is treated as the one-element list <code><span class='Function'>β₯</span><span class='Value'>π¨</span></code>.</p> <a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=M+KAvzTigL8yIOKMvSAianVzdCBhIGxpc3Qi">βοΈ</a><pre> <span class='Number'>3</span><span class='Ligature'>βΏ</span><span class='Number'>4</span><span class='Ligature'>βΏ</span><span class='Number'>2</span> <span class='Function'>β½</span> <span class='String'>"just a list"</span> <span class='Error'>Error: π¨β½π©: Length of compound π¨ must be at most rank of π©</span> </pre> @@ -101,7 +101,7 @@ cdab" β </pre> -<p>The vertical and horizontal rotations are independent, and could also be done with two <code><span class='Function'>β½</span></code>s and a <code><span class='Modifier'>Λ</span></code>. The multi-axis form is more convenient, and can potentially be evaluated faster that multiple separate rotations in the cases where it shows up.</p> +<p>The vertical and horizontal rotations are independent, and could also be done with two <code><span class='Function'>β½</span></code>s and a <code><span class='Modifier'>Λ</span></code>. The multi-axis form is more convenient, and can potentially be evaluated faster than multiple separate rotations in the cases where it shows up.</p> <a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MSDijL0gMiDijL3LmCB0YWI=">βοΈ</a><pre> <span class='Number'>1</span> <span class='Function'>β½</span> <span class='Number'>2</span> <span class='Function'>β½</span><span class='Modifier'>Λ</span> <span class='Value'>tab</span> ββ β΅"CDAB |