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| -rw-r--r-- | docs/doc/pick.html | 129 | ||||
| -rw-r--r-- | docs/doc/primitive.html | 4 |
3 files changed, 132 insertions, 2 deletions
diff --git a/docs/doc/index.html b/docs/doc/index.html index 16511895..e32dd8f8 100644 --- a/docs/doc/index.html +++ b/docs/doc/index.html @@ -49,6 +49,7 @@ <li><a href="match.html">Match</a> (<code><span class='Function'>≡≢</span></code>)</li> <li><a href="map.html">Mapping</a> (<code><span class='Modifier'>¨⌜</span></code>)</li> <li><a href="order.html">Ordering functions</a> (<code><span class='Function'>∧∨⍋⍒</span></code>)</li> +<li><a href="pick.html">Pick</a> (<code><span class='Function'>⊑</span></code>)</li> <li><a href="prefixes.html">Prefixes and Suffixes</a> (<code><span class='Function'>↑↓</span></code>)</li> <li><a href="range.html">Range</a> (<code><span class='Function'>↕</span></code>)</li> <li><a href="repeat.html">Repeat</a> (<code><span class='Modifier2'>⍟</span></code>)</li> diff --git a/docs/doc/pick.html b/docs/doc/pick.html new file mode 100644 index 00000000..3f5495aa --- /dev/null +++ b/docs/doc/pick.html @@ -0,0 +1,129 @@ +<head> + <link href="../favicon.ico" rel="shortcut icon" type="image/x-icon"/> + <link href="../style.css" rel="stylesheet"/> + <title>BQN: Pick</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="pick">Pick</h1> +<p>Pick (<code><span class='Function'>⊑</span></code>) chooses elements from <code><span class='Value'>𝕩</span></code> based on <a href="indices.html">index</a> lists from <code><span class='Value'>𝕨</span></code>. <code><span class='Value'>𝕨</span></code> can be a plain list, or even one number if <code><span class='Value'>𝕩</span></code> is a list, in order to get one element from <code><span class='Value'>𝕩</span></code>. It can also be an array of index lists, or have deeper array structure: each index list will be replaced with the element of <code><span class='Value'>𝕩</span></code> at that index, effectively applying to <code><span class='Value'>𝕨</span></code> at <a href="depth.html#the-depth-modifier">depth</a> 1.</p> +<p>With no <code><span class='Value'>𝕨</span></code>, monadic <code><span class='Function'>⊑</span><span class='Value'>𝕩</span></code> takes the first element of <code><span class='Value'>𝕩</span></code> in index order, or its fill element if <code><span class='Value'>𝕩</span></code> is empty (causing an error if no fill is known).</p> +<p>While sometimes "scatter-point" indexing is necessary, using Pick to select multiple elements from <code><span class='Value'>𝕩</span></code> is less array-oriented than <a href="select.html">Select</a> (<code><span class='Function'>⊏</span></code>), and probably slower. Consider rearranging your data so that you can select along axes instead of picking out elements.</p> +<h2 id="one-element">One element</h2> +<p>When the left argument is a number, Pick gets an element from a list:</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MiDiipEgMOKAvzHigL8y4oC/M+KAvzQKMiDiipEgImFiYyIKMiDiipEg4p+oQCwgMOKAvzHigL8y4oC/MywgImFiYyLin6k=">↗️</a><pre> <span class='Number'>2</span> <span class='Function'>⊑</span> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>4</span> +2 + <span class='Number'>2</span> <span class='Function'>⊑</span> <span class='String'>"abc"</span> +'c' + <span class='Number'>2</span> <span class='Function'>⊑</span> <span class='Bracket'>⟨</span><span class='String'>@</span><span class='Separator'>,</span> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Separator'>,</span> <span class='String'>"abc"</span><span class='Bracket'>⟩</span> +"abc" +</pre> +<p>A negative number <code><span class='Value'>𝕨</span></code> behaves like <code><span class='Value'>𝕨</span><span class='Function'>+≠</span><span class='Value'>𝕩</span></code>, so that <code><span class='Number'>¯1</span></code> will select the last element, and <code><span class='Function'>-≠</span><span class='Value'>𝕩</span></code> the first. A number in <code><span class='Value'>𝕨</span></code> must be an integer less than <code><span class='Function'>≠</span><span class='Value'>𝕩</span></code> but not less than <code><span class='Function'>-≠</span><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=wq8yIOKKkSAw4oC/MeKAvzLigL8z4oC/NArCrzIg4oqRICJhYmMi">↗️</a><pre> <span class='Number'>¯2</span> <span class='Function'>⊑</span> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>4</span> +3 + <span class='Number'>¯2</span> <span class='Function'>⊑</span> <span class='String'>"abc"</span> +'b' +</pre> +<p>Making <code><span class='Value'>𝕩</span></code> a list is only a special case. In general <code><span class='Value'>𝕨</span></code> can be a list of numbers whose length is <code><span class='Value'>𝕩</span></code>'s rank. So when <code><span class='Function'>=</span><span class='Value'>𝕩</span></code> is 1, <code><span class='Value'>𝕨</span></code> can be length-1 list. For convenience, a number is also allowed, but not an enclosed number (which could be confused with the nested case).</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4p+oMiww4p+pIOKKkSDihpU04oC/NQ==">↗️</a><pre> <span class='Bracket'>⟨</span><span class='Number'>2</span><span class='Separator'>,</span><span class='Number'>0</span><span class='Bracket'>⟩</span> <span class='Function'>⊑</span> <span class='Function'>↕</span><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>5</span> +⟨ 2 0 ⟩ +</pre> +<p>Above we see that picking from the result of <a href="range.html">Range</a> gives the index. For something slightly more interesting, here's a character array:</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oqiIGEg4oaQICdhJyArIOKliuKfnCjihpXDl8K0KSA04oC/NQoy4oC/MCDiipEgYQox4oC/wq8xIOKKkSBh">↗️</a><pre> <span class='Function'>⊢</span> <span class='Value'>a</span> <span class='Gets'>←</span> <span class='String'>'a'</span> <span class='Function'>+</span> <span class='Function'>⥊</span><span class='Modifier2'>⟜</span><span class='Paren'>(</span><span class='Function'>↕×</span><span class='Modifier'>´</span><span class='Paren'>)</span> <span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>5</span> +┌─ +╵"abcde + fghij + klmno + pqrst" + ┘ + <span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>0</span> <span class='Function'>⊑</span> <span class='Value'>a</span> +'k' + <span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>¯1</span> <span class='Function'>⊑</span> <span class='Value'>a</span> +'j' +</pre> +<p>This applies even if <code><span class='Value'>𝕩</span></code> is a unit. By definition it has rank 0, so the only possible value for <code><span class='Value'>𝕨</span></code> is the empty list. This extracts an <a href="enclose.html">enclosed</a> element, and returns an atom unchanged—the atom is promoted to an array by enclosing it, then the action of Pick undoes this. But there's rarely a reason to use this case, because the monadic form First accomplishes the same thing.</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4p+o4p+pIOKKkSA8J2EnCuKfqOKfqSDiipEgJ2En">↗️</a><pre> <span class='Bracket'>⟨⟩</span> <span class='Function'>⊑</span> <span class='Function'><</span><span class='String'>'a'</span> +'a' + <span class='Bracket'>⟨⟩</span> <span class='Function'>⊑</span> <span class='String'>'a'</span> +'a' +</pre> +<h3 id="first">First</h3> +<p>With no left argument, <code><span class='Function'>⊑</span></code> is called First, and performs a slight generalization of Pick with a default left argument <code><span class='Number'>0</span><span class='Modifier'>¨</span><span class='Function'>≢</span><span class='Value'>𝕩</span></code>. For a non-empty array it returns the first element in index order.</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oqRIDwnYScK4oqRICJGaXJzdCIK4oqRIOKGlTTigL8y4oC/NeKAvzE=">↗️</a><pre> <span class='Function'>⊑</span> <span class='Function'><</span><span class='String'>'a'</span> +'a' + <span class='Function'>⊑</span> <span class='String'>"First"</span> +'F' + <span class='Function'>⊑</span> <span class='Function'>↕</span><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>5</span><span class='Ligature'>‿</span><span class='Number'>1</span> +⟨ 0 0 0 0 ⟩ +</pre> +<p>If <code><span class='Value'>𝕩</span></code> is empty then Pick always results in an error. First never gives an error: instead it returns the fill element for <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=4oqRICIiCuKKkSDiiaLPgAriipEgMOKGkTzin6giICAiLOKGlTTin6k=">↗️</a><pre> <span class='Function'>⊑</span> <span class='String'>""</span> +' ' + <span class='Function'>⊑</span> <span class='Function'>≢</span><span class='Number'>π</span> +0 + <span class='Function'>⊑</span> <span class='Number'>0</span><span class='Function'>↑<</span><span class='Bracket'>⟨</span><span class='String'>" "</span><span class='Separator'>,</span><span class='Function'>↕</span><span class='Number'>4</span><span class='Bracket'>⟩</span> +⟨ " " ⟨ 0 0 0 0 ⟩ ⟩ +</pre> +<p>So one way to find the fill element for an array <code><span class='Value'>𝕩</span></code> of any shape is <code><span class='Function'>⊑</span><span class='Number'>0</span><span class='Function'>⥊</span><span class='Value'>𝕩</span></code>.</p> +<p>In APL it's common to get the last element of a list with an idiom that translates to <code><span class='Function'>⊑⌽</span></code>, or First-<a href="reverse.html">Reverse</a>. I prefer to use <a href="fold.html">Fold</a> with the Right <a href="identity.html">identity function</a>.</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oqR4oy9ICJsYXN0IgriiqLCtCAibGFzdCI=">↗️</a><pre> <span class='Function'>⊑⌽</span> <span class='String'>"last"</span> +'t' + <span class='Function'>⊢</span><span class='Modifier'>´</span> <span class='String'>"last"</span> +'t' +</pre> +<h2 id="many-elements">Many elements</h2> +<p>Pick also accepts a list of indices:</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=YSAgIyBEZWZpbmVkIGFib3ZlCgrin6gy4oC/MCwgMeKAv8KvMSwgM+KAvzEsIMKvMeKAv8KvMeKfqSDiipEgYQ==">↗️</a><pre> <span class='Value'>a</span> <span class='Comment'># Defined above +</span>┌─ +╵"abcde + fghij + klmno + pqrst" + ┘ + + <span class='Bracket'>⟨</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Separator'>,</span> <span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>¯1</span><span class='Separator'>,</span> <span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Separator'>,</span> <span class='Number'>¯1</span><span class='Ligature'>‿</span><span class='Number'>¯1</span><span class='Bracket'>⟩</span> <span class='Function'>⊑</span> <span class='Value'>a</span> +"kjqt" +</pre> +<p>These indices have to be lists, since if they're numbers it just looks like <code><span class='Value'>𝕨</span></code> is one list index.</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4p+oMiwxLDAswq8x4p+pIOKKkSAiYWJjIiAgIyDwnZWpIGRvZXNuJ3QgaGF2ZSByYW5rIDQhCgrin6gyLDEsMCzCrzHin6kg4qWKwqjiirjiipEgImFiYyIKCuKfqDIsMSwwLMKvMeKfqSDiio8gImFiYyIgICMgQmV0dGVyIHdheQ==">↗️</a><pre> <span class='Bracket'>⟨</span><span class='Number'>2</span><span class='Separator'>,</span><span class='Number'>1</span><span class='Separator'>,</span><span class='Number'>0</span><span class='Separator'>,</span><span class='Number'>¯1</span><span class='Bracket'>⟩</span> <span class='Function'>⊑</span> <span class='String'>"abc"</span> <span class='Comment'># 𝕩 doesn't have rank 4! +</span>ERROR + + <span class='Bracket'>⟨</span><span class='Number'>2</span><span class='Separator'>,</span><span class='Number'>1</span><span class='Separator'>,</span><span class='Number'>0</span><span class='Separator'>,</span><span class='Number'>¯1</span><span class='Bracket'>⟩</span> <span class='Function'>⥊</span><span class='Modifier'>¨</span><span class='Modifier2'>⊸</span><span class='Function'>⊑</span> <span class='String'>"abc"</span> +"cbac" + + <span class='Bracket'>⟨</span><span class='Number'>2</span><span class='Separator'>,</span><span class='Number'>1</span><span class='Separator'>,</span><span class='Number'>0</span><span class='Separator'>,</span><span class='Number'>¯1</span><span class='Bracket'>⟩</span> <span class='Function'>⊏</span> <span class='String'>"abc"</span> <span class='Comment'># Better way +</span>"cbac" +</pre> +<p>It's much more general than just a list of indices though. As long as your indices are lists, you can arrange them in any array structure with arbitrary nesting.</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4p+oMuKAvzAsIOKfqOKfqDHigL/CrzEsIDPigL8x4p+pLCDCrzHigL/CrzHin6nin6kg4oqRIGEKCijin6gy4oC/MCwgMeKAv8KvMeKfqeKJjeKfqDPigL8xLCDCrzHigL/CrzHin6kpIOKKkSBhCgoo4p+oMuKAvzAsIDwx4oC/wq8x4p+p4omN4p+oPDPigL8xLCDCrzHigL/CrzHin6kpIOKKkSBh">↗️</a><pre> <span class='Bracket'>⟨</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Separator'>,</span> <span class='Bracket'>⟨⟨</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>¯1</span><span class='Separator'>,</span> <span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Bracket'>⟩</span><span class='Separator'>,</span> <span class='Number'>¯1</span><span class='Ligature'>‿</span><span class='Number'>¯1</span><span class='Bracket'>⟩⟩</span> <span class='Function'>⊑</span> <span class='Value'>a</span> +⟨ 'k' ⟨ "jq" 't' ⟩ ⟩ + + <span class='Paren'>(</span><span class='Bracket'>⟨</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Separator'>,</span> <span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>¯1</span><span class='Bracket'>⟩</span><span class='Function'>≍</span><span class='Bracket'>⟨</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Separator'>,</span> <span class='Number'>¯1</span><span class='Ligature'>‿</span><span class='Number'>¯1</span><span class='Bracket'>⟩</span><span class='Paren'>)</span> <span class='Function'>⊑</span> <span class='Value'>a</span> +┌─ +╵"kj + qt" + ┘ + + <span class='Paren'>(</span><span class='Bracket'>⟨</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Separator'>,</span> <span class='Function'><</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>¯1</span><span class='Bracket'>⟩</span><span class='Function'>≍</span><span class='Bracket'>⟨</span><span class='Function'><</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Separator'>,</span> <span class='Number'>¯1</span><span class='Ligature'>‿</span><span class='Number'>¯1</span><span class='Bracket'>⟩</span><span class='Paren'>)</span> <span class='Function'>⊑</span> <span class='Value'>a</span> +┌─ +╵ 'k' ┌· + ·'j' + ┘ + ┌· 't' + ·'q' + ┘ + ┘ +</pre> +<p>This option is easily described using the <a href="depth.html#the-depth-modifier">Depth modifier</a>. Pick applies to depth-1 components of the left argument and the entire right argument, which corresponds to a depth operand of <code><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>∞</span></code>. The left argument components have to be lists of numbers, or Pick gives an error.</p> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=KOKfqDLigL8wLCA8MeKAv8KvMeKfqeKJjeKfqDwz4oC/MSwgwq8x4oC/wq8x4p+pKSDiipHimocx4oC/4oieIGEKCuKfqOKfqDIsM+KfqSwx4p+pIOKKkSBhICAjIDEgaXNuJ3QgYSB2YWxpZCBpbmRleA==">↗️</a><pre> <span class='Paren'>(</span><span class='Bracket'>⟨</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Separator'>,</span> <span class='Function'><</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>¯1</span><span class='Bracket'>⟩</span><span class='Function'>≍</span><span class='Bracket'>⟨</span><span class='Function'><</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Separator'>,</span> <span class='Number'>¯1</span><span class='Ligature'>‿</span><span class='Number'>¯1</span><span class='Bracket'>⟩</span><span class='Paren'>)</span> <span class='Function'>⊑</span><span class='Modifier2'>⚇</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>∞</span> <span class='Value'>a</span> +┌─ +╵ 'k' ┌· + ·'j' + ┘ + ┌· 't' + ·'q' + ┘ + ┘ + + <span class='Bracket'>⟨⟨</span><span class='Number'>2</span><span class='Separator'>,</span><span class='Number'>3</span><span class='Bracket'>⟩</span><span class='Separator'>,</span><span class='Number'>1</span><span class='Bracket'>⟩</span> <span class='Function'>⊑</span> <span class='Value'>a</span> <span class='Comment'># 1 isn't a valid index +</span>ERROR +</pre> diff --git a/docs/doc/primitive.html b/docs/doc/primitive.html index 638595d9..46f8d444 100644 --- a/docs/doc/primitive.html +++ b/docs/doc/primitive.html @@ -201,8 +201,8 @@ </tr> <tr> <td><code><span class='Function'>⊑</span></code></td> -<td><a href="https://aplwiki.com/wiki/First">First</a></td> -<td>Pick*</td> +<td><a href="pick.html#first">First</a></td> +<td><a href="pick.html">Pick</a>*</td> </tr> <tr> <td><code><span class='Function'>⊐</span></code></td> |