diff options
| author | Marshall Lochbaum <mwlochbaum@gmail.com> | 2021-06-30 22:44:44 -0400 |
|---|---|---|
| committer | Marshall Lochbaum <mwlochbaum@gmail.com> | 2021-06-30 22:45:15 -0400 |
| commit | 15281037815c136b70d1410e4000e570d6ec019a (patch) | |
| tree | 33efa06bd41f63f7843050353e0ce6626112c822 /docs/doc | |
| parent | 775ac2d9832065f15f3d4d953a8ab6c99b222558 (diff) | |
Select documentation, single-axis case only
Diffstat (limited to 'docs/doc')
| -rw-r--r-- | docs/doc/index.html | 1 | ||||
| -rw-r--r-- | docs/doc/primitive.html | 4 | ||||
| -rw-r--r-- | docs/doc/select.html | 163 |
3 files changed, 166 insertions, 2 deletions
diff --git a/docs/doc/index.html b/docs/doc/index.html index 484a7227..16511895 100644 --- a/docs/doc/index.html +++ b/docs/doc/index.html @@ -54,6 +54,7 @@ <li><a href="repeat.html">Repeat</a> (<code><span class='Modifier2'>⍟</span></code>)</li> <li><a href="reverse.html">Reverse and Rotate</a> (<code><span class='Function'>⌽</span></code>)</li> <li><a href="scan.html">Scan</a> (<code><span class='Modifier'>`</span></code>)</li> +<li><a href="select.html">Select</a> (<code><span class='Function'>⊏</span></code>)</li> <li><a href="selfcmp.html">Self-comparison functions</a> (<code><span class='Function'>⊐⊒∊⍷</span></code>)</li> <li><a href="shift.html">Shift functions</a> (<code><span class='Function'>»«</span></code>)</li> <li><a href="couple.html">Solo, Couple, and Merge</a> (<code><span class='Function'>≍></span></code>)</li> diff --git a/docs/doc/primitive.html b/docs/doc/primitive.html index 9eddb08d..638595d9 100644 --- a/docs/doc/primitive.html +++ b/docs/doc/primitive.html @@ -196,8 +196,8 @@ </tr> <tr> <td><code><span class='Function'>⊏</span></code></td> -<td>First Cell*</td> -<td>Select*</td> +<td><a href="select.html">First Cell</a>*</td> +<td><a href="select.html">Select</a>*</td> </tr> <tr> <td><code><span class='Function'>⊑</span></code></td> diff --git a/docs/doc/select.html b/docs/doc/select.html new file mode 100644 index 00000000..13589621 --- /dev/null +++ b/docs/doc/select.html @@ -0,0 +1,163 @@ +<head> + <link href="../favicon.ico" rel="shortcut icon" type="image/x-icon"/> + <link href="../style.css" rel="stylesheet"/> + <title>BQN: Select</title> +</head> +<div class="nav"><a href="https://github.com/mlochbaum/BQN">BQN</a> / <a href="../index.html">main</a> / <a href="index.html">doc</a></div> +<h1 id="select">Select</h1> +<svg viewBox='-148.8 -17.4 480 208.8'> + <g font-family='BQN,monospace' font-size='22px' text-anchor='middle'> + <rect class='code' stroke-width='1.5' rx='12' x='-96' y='0' width='374.4' height='174'/> + <g class='lilac' stroke-width='2' stroke-linecap='round'> + <line x1='88.32' x2='7.68' y1='46.4' y2='81.2'/> + <line x1='48' x2='48' y1='46.4' y2='81.2'/> + <line x1='51.84' x2='92.16' y1='46.4' y2='81.2'/> + <line x1='232.32' x2='151.68' y1='46.4' y2='81.2'/> + <line x1='0' x2='0' y1='104.4' y2='139.2'/> + <line x1='48' x2='48' y1='104.4' y2='139.2'/> + <line x1='96' x2='96' y1='104.4' y2='139.2'/> + <line x1='144' x2='144' y1='104.4' y2='139.2'/> + </g> + <text dy='0.32em' x='0' y='34.8'><tspan class='String'>'s'</tspan></text> + <text dy='0.32em' x='48' y='34.8'><tspan class='String'>'e'</tspan></text> + <text dy='0.32em' x='96' y='34.8'><tspan class='String'>'l'</tspan></text> + <text dy='0.32em' x='144' y='34.8'><tspan class='String'>'e'</tspan></text> + <text dy='0.32em' x='192' y='34.8'><tspan class='String'>'c'</tspan></text> + <text dy='0.32em' x='240' y='34.8'><tspan class='String'>'t'</tspan></text> + <text dy='0.32em' x='0' y='92.8'><tspan class='Number'>2</tspan></text> + <text dy='0.32em' x='48' y='92.8'><tspan class='Number'>1</tspan></text> + <text dy='0.32em' x='96' y='92.8'><tspan class='Number'>1</tspan></text> + <text dy='0.32em' x='144' y='92.8'><tspan class='Number'>5</tspan></text> + <text dy='0.32em' x='0' y='150.8'><tspan class='String'>'l'</tspan></text> + <text dy='0.32em' x='48' y='150.8'><tspan class='String'>'e'</tspan></text> + <text dy='0.32em' x='96' y='150.8'><tspan class='String'>'e'</tspan></text> + <text dy='0.32em' x='144' y='150.8'><tspan class='String'>'t'</tspan></text> + <g fill='currentColor' font-size='12' opacity='0.75'> + <text dy='0.32em' x='0' y='15.66'>0</text> + <text dy='0.32em' x='48' y='15.66'>1</text> + <text dy='0.32em' x='96' y='15.66'>2</text> + <text dy='0.32em' x='144' y='15.66'>3</text> + <text dy='0.32em' x='192' y='15.66'>4</text> + <text dy='0.32em' x='240' y='15.66'>5</text> + </g> + <g font-size='18px' text-anchor='end'> + <text dy='0.32em' x='-38.4' y='34.8'><tspan class='Value'>𝕩</tspan></text> + <text dy='0.32em' x='-38.4' y='92.8'><tspan class='Value'>𝕨</tspan> </text> + <text dy='0.32em' x='-38.4' y='150.8'><tspan class='Value'>𝕨</tspan><tspan class='Function'>⊏</tspan><tspan class='Value'>𝕩</tspan></text> + </g> + </g> +</svg> + +<p>The function Select (<code><span class='Function'>⊏</span></code>) reorganizes the array <code><span class='Value'>𝕩</span></code> along one or more axes based on <a href="indices.html">indices</a> given by <code><span class='Value'>𝕨</span></code>. The result has the same <a href="depth.html">depth</a> as <code><span class='Value'>𝕩</span></code>, since its elements are always elements of <code><span class='Value'>𝕩</span></code>. This means it differs from Pick (<code><span class='Function'>⊑</span></code>), which takes elements from <code><span class='Value'>𝕩</span></code> but can arrange them in any nested structure, including returning an element directly.</p> +<p>The monadic form First Cell (<code><span class='Function'>⊏</span></code>) gets the major cell with index 0, so that <code><span class='Function'>⊏</span><span class='Value'>𝕩</span></code> is identical to <code><span class='Number'>0</span><span class='Function'>⊏</span><span class='Value'>𝕩</span></code>.</p> +<h2 id="single-selection">Single selection</h2> +<p>Each axis of a BQN array is numbered starting at zero. Major cells are arranged along the first axis; in accordance with the <a href="leading.html">leading axis</a> principle, Select returns a major cell of <code><span class='Value'>𝕩</span></code> when <code><span class='Value'>𝕨</span></code> is an atom.</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MiDiio8gImFiY2RlZiIgICMgQW4gZW5jbG9zZWQgZWxlbWVudAoKMiDiipEgImFiY2RlZiIgICMgUGljayBnZXRzIGEgbm9uLWVuY2xvc2VkIGVsZW1lbnQKCjIg4oqPID4ibnVsIuKAvyJvbmUi4oC/InR3byLigL8idHJlIuKAvyJmb3IiCgowIOKKjyA8NSAgIyBObyBmaXJzdCBheGlzIHRvIHNlbGVjdCBmcm9t">↗️</a><pre> <span class='Number'>2</span> <span class='Function'>⊏</span> <span class='String'>"abcdef"</span> <span class='Comment'># An enclosed element +</span>┌· +·'c' + ┘ + + <span class='Number'>2</span> <span class='Function'>⊑</span> <span class='String'>"abcdef"</span> <span class='Comment'># Pick gets a non-enclosed element +</span>'c' + + <span class='Number'>2</span> <span class='Function'>⊏</span> <span class='Function'>></span><span class='String'>"nul"</span><span class='Ligature'>‿</span><span class='String'>"one"</span><span class='Ligature'>‿</span><span class='String'>"two"</span><span class='Ligature'>‿</span><span class='String'>"tre"</span><span class='Ligature'>‿</span><span class='String'>"for"</span> +"two" + + <span class='Number'>0</span> <span class='Function'>⊏</span> <span class='Function'><</span><span class='Number'>5</span> <span class='Comment'># No first axis to select from +</span>ERROR +</pre> +<p>As a major cell of <code><span class='Value'>𝕩</span></code>, the result has rank one less than it and its shape is <code><span class='Number'>1</span><span class='Function'>↓≢</span><span class='Value'>𝕩</span></code>. <code><span class='Value'>𝕩</span></code> must have rank one or more.</p> +<p>The index <code><span class='Value'>𝕨</span></code> has to be an integer less than <code><span class='Function'>≠</span><span class='Value'>𝕩</span></code>. It can be negative, in which case it must be greater than or equal to <code><span class='Function'>-≠</span><span class='Value'>𝕩</span></code>. Negative indices select from the end of <code><span class='Value'>𝕩</span></code>, in that <code><span class='Number'>¯1</span></code> indicates the last major cell and <code><span class='Function'>-≠</span><span class='Value'>𝕩</span></code> indicates the first. If <code><span class='Function'>≠</span><span class='Value'>𝕩</span></code> is 0, then no index is valid.</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=wq8yIOKKjyAiYWJjZGVmIgoKMCDiio8gIiI=">↗️</a><pre> <span class='Number'>¯2</span> <span class='Function'>⊏</span> <span class='String'>"abcdef"</span> +┌· +·'e' + ┘ + + <span class='Number'>0</span> <span class='Function'>⊏</span> <span class='String'>""</span> +ERROR +</pre> +<p>The monadic case First Cell (<code><span class='Function'>⊏</span><span class='Value'>𝕩</span></code>) is identical to <code><span class='Number'>0</span><span class='Function'>⊏</span><span class='Value'>𝕩</span></code>. It has the same restrictions: <code><span class='Value'>𝕩</span></code> must have rank 1 or more, and length 1 or more (this differs from First (<code><span class='Function'>⊑</span></code>), which removes the length requirement to return a fill element).</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oqPICJhYmMiCgriio8gImFiYyLiiY0iZGVmIgoK4oqPIOKJjSAiYWJjIgoK4oqPICdhJw==">↗️</a><pre> <span class='Function'>⊏</span> <span class='String'>"abc"</span> +┌· +·'a' + ┘ + + <span class='Function'>⊏</span> <span class='String'>"abc"</span><span class='Function'>≍</span><span class='String'>"def"</span> +"abc" + + <span class='Function'>⊏</span> <span class='Function'>≍</span> <span class='String'>"abc"</span> +"abc" + + <span class='Function'>⊏</span> <span class='String'>'a'</span> +ERROR +</pre> +<h2 id="first-axis-selection">First-axis selection</h2> +<p>If <code><span class='Value'>𝕨</span></code> is an array of numbers (including any empty array), then each number indicates a major cell of <code><span class='Value'>𝕩</span></code>. In the simplest case, a list of numbers gives a result with the same rank as <code><span class='Value'>𝕩</span></code> but maybe not the same length.</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MuKAvzPigL8z4oC/MOKAvzTigL8xIOKKjyAiT2xaRXQiCgrin6jin6kg4oqPICJPbFpFdCI=">↗️</a><pre> <span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>1</span> <span class='Function'>⊏</span> <span class='String'>"OlZEt"</span> +"ZEEOtl" + + <span class='Bracket'>⟨⟩</span> <span class='Function'>⊏</span> <span class='String'>"OlZEt"</span> +⟨⟩ +</pre> +<p>To find the first and last cells of <code><span class='Value'>𝕩</span></code>, use <code><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>¯1</span></code> for the left argument.</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oqiIG0g4oaQIDPigL814oC/N+KAvzExIHzijJwgw5fLnOKGlTcKCjDigL/CrzEg4oqPIG0=">↗️</a><pre> <span class='Function'>⊢</span> <span class='Value'>m</span> <span class='Gets'>←</span> <span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>5</span><span class='Ligature'>‿</span><span class='Number'>7</span><span class='Ligature'>‿</span><span class='Number'>11</span> <span class='Function'>|</span><span class='Modifier'>⌜</span> <span class='Function'>×</span><span class='Modifier'>˜</span><span class='Function'>↕</span><span class='Number'>7</span> +┌─ +╵ 0 1 1 0 1 1 0 + 0 1 4 4 1 0 1 + 0 1 4 2 2 4 1 + 0 1 4 9 5 3 3 + ┘ + + <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>¯1</span> <span class='Function'>⊏</span> <span class='Value'>m</span> +┌─ +╵ 0 1 1 0 1 1 0 + 0 1 4 9 5 3 3 + ┘ +</pre> +<p>More generally, <code><span class='Value'>𝕨</span></code> can be an array of any rank. Each of its 0-cells—containing a single number—is replaced with a cell of <code><span class='Value'>𝕩</span></code> in the result. The result's shape is then made up of the shape of <code><span class='Value'>𝕨</span></code> and the major cell shape of <code><span class='Value'>𝕩</span></code>: it's <code><span class='Paren'>(</span><span class='Function'>≢</span><span class='Value'>𝕨</span><span class='Paren'>)</span><span class='Function'>∾</span><span class='Number'>1</span><span class='Function'>↓≢</span><span class='Value'>𝕩</span></code>. When <code><span class='Value'>𝕩</span></code> is a list, the result has the same shape as <code><span class='Value'>𝕨</span></code>. Elements of <code><span class='Value'>𝕨</span></code> are replaced one-for-one with elements of <code><span class='Value'>𝕩</span></code>.</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MnxtCgooMnxtKSDiio8gIiAqIg==">↗️</a><pre> <span class='Number'>2</span><span class='Function'>|</span><span class='Value'>m</span> +┌─ +╵ 0 1 1 0 1 1 0 + 0 1 0 0 1 0 1 + 0 1 0 0 0 0 1 + 0 1 0 1 1 1 1 + ┘ + + <span class='Paren'>(</span><span class='Number'>2</span><span class='Function'>|</span><span class='Value'>m</span><span class='Paren'>)</span> <span class='Function'>⊏</span> <span class='String'>" *"</span> +┌─ +╵" ** ** + * * * + * * + * ****" + ┘ +</pre> +<p>Another special case is when <code><span class='Value'>𝕨</span></code> is a unit. Now the result shape will be the major cell shape of <code><span class='Value'>𝕩</span></code>. In fact it's the same as the atom case above, that is, for a number <code><span class='Value'>n</span></code>, <code><span class='Paren'>(</span><span class='Function'><</span><span class='Value'>n</span><span class='Paren'>)</span><span class='Function'>⊏</span><span class='Value'>𝕩</span></code> is the same as <code><span class='Value'>n</span><span class='Function'>⊏</span><span class='Value'>𝕩</span></code>.</p> +<p>The general case can result in a complicated array. Remember that the initial axes come from <code><span class='Value'>𝕨</span></code> while later ones come from <code><span class='Value'>𝕩</span></code>.</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=ImF3QTAiICvijJwg4oaVNAoKMiDihpUg4oaVNAoKKDIg4oaVIOKGlTQpIOKKjyAiYXdBMCIgK+KMnCDihpU0">↗️</a><pre> <span class='String'>"awA0"</span> <span class='Function'>+</span><span class='Modifier'>⌜</span> <span class='Function'>↕</span><span class='Number'>4</span> +┌─ +╵"abcd + wxyz + ABCD + 0123" + ┘ + + <span class='Number'>2</span> <span class='Function'>↕</span> <span class='Function'>↕</span><span class='Number'>4</span> +┌─ +╵ 0 1 + 1 2 + 2 3 + ┘ + + <span class='Paren'>(</span><span class='Number'>2</span> <span class='Function'>↕</span> <span class='Function'>↕</span><span class='Number'>4</span><span class='Paren'>)</span> <span class='Function'>⊏</span> <span class='String'>"awA0"</span> <span class='Function'>+</span><span class='Modifier'>⌜</span> <span class='Function'>↕</span><span class='Number'>4</span> +┌─ +╎"abcd + wxyz + + ·wxyz + ABCD + + ·ABCD + 0123" + ┘ +</pre> +<h2 id="multi-axis-selection">Multi-axis selection</h2> |