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authorMarshall Lochbaum <mwlochbaum@gmail.com>2020-10-26 15:46:38 -0400
committerMarshall Lochbaum <mwlochbaum@gmail.com>2020-10-26 15:46:38 -0400
commit1d6a9cf1441bd6d478977715d82031e77c20ce5c (patch)
tree6fee5b999964c813594e9a5562b9e588d16d8536 /docs/doc/windows.html
parentdd04717b7de252c300d197e5dcfaf9cab33d3ab5 (diff)
Don't include &run in documentation REPL links: it's no longer used
Diffstat (limited to 'docs/doc/windows.html')
-rw-r--r--docs/doc/windows.html22
1 files changed, 11 insertions, 11 deletions
diff --git a/docs/doc/windows.html b/docs/doc/windows.html
index 1e301c9e..dc84bc73 100644
--- a/docs/doc/windows.html
+++ b/docs/doc/windows.html
@@ -9,7 +9,7 @@
<p>The Window function replaces APL's Windowed Reduction, J's more general Infix operator, and Dyalog's Stencil, which is adapted from one case of J's Cut operator.</p>
<h2 id="definition">Definition</h2>
<p>We'll start with the one-axis case. Here Window's left argument is a number between <code><span class='Number'>0</span></code> and <code><span class='Number'>1</span><span class='Function'>+β‰ </span><span class='Value'>𝕩</span></code>. The result is composed of slices of <code><span class='Value'>𝕩</span></code> (contiguous sections of major cells) with length <code><span class='Value'>𝕨</span></code>, starting at each possible index in order.</p>
-<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=NeKGlSJhYmNkZWZnIg==&run">↗️</a><pre> <span class='Number'>5</span><span class='Function'>↕</span><span class='String'>&quot;abcdefg&quot;</span>
+<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=NeKGlSJhYmNkZWZnIg==">↗️</a><pre> <span class='Number'>5</span><span class='Function'>↕</span><span class='String'>&quot;abcdefg&quot;</span>
β”Œβ”€
β•΅"abcde
bcdef
@@ -18,7 +18,7 @@
</pre>
<p>There are <code><span class='Number'>1</span><span class='Function'>+</span><span class='Paren'>(</span><span class='Function'>β‰ </span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Function'>-</span><span class='Value'>𝕨</span></code>, or <code><span class='Paren'>(</span><span class='Function'>β‰ </span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Function'>Β¬</span><span class='Value'>𝕨</span></code>, of these sections, because the starting index must be at least <code><span class='Number'>0</span></code> and at most <code><span class='Paren'>(</span><span class='Function'>β‰ </span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Function'>-</span><span class='Value'>𝕨</span></code>. Another way to find this result is to look at the number of cells in or before a given slice: there are always <code><span class='Value'>𝕨</span></code> in the slice and there are only <code><span class='Function'>β‰ </span><span class='Value'>𝕩</span></code> in total, so the number of slices is the range spanned by these two endpoints.</p>
<p>You can take a slice of an array <code><span class='Value'>𝕩</span></code> that has length <code><span class='Value'>l</span></code> and starts at index <code><span class='Value'>i</span></code> using <code><span class='Value'>l</span><span class='Function'>↑</span><span class='Value'>i</span><span class='Function'>↓</span><span class='Value'>𝕩</span></code> or <code><span class='Value'>l</span><span class='Function'>↑</span><span class='Value'>i</span><span class='Function'>⌽</span><span class='Value'>𝕩</span></code>. The <a href="prefixes.html">Prefixes</a> function returns all the slices that end at the end of the array (<code><span class='Paren'>(</span><span class='Function'>β‰ </span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Function'>=</span><span class='Value'>i</span><span class='Function'>+</span><span class='Value'>l</span></code>), and Suffixes gives the slices that start at the beginning (<code><span class='Value'>i</span><span class='Function'>=</span><span class='Number'>0</span></code>). Windows gives yet another collection of slices: the ones that have a fixed length <code><span class='Value'>l</span><span class='Function'>=</span><span class='Value'>𝕨</span></code>. Selecting one cell from its result gives you the slice starting at that cell's index:</p>
-<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MuKKjzXihpUiYWJjZGVmZyIKNeKGkTLihpMiYWJjZGVmZyI=&run">↗️</a><pre> <span class='Number'>2</span><span class='Function'>⊏</span><span class='Number'>5</span><span class='Function'>↕</span><span class='String'>&quot;abcdefg&quot;</span>
+<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MuKKjzXihpUiYWJjZGVmZyIKNeKGkTLihpMiYWJjZGVmZyI=">↗️</a><pre> <span class='Number'>2</span><span class='Function'>⊏</span><span class='Number'>5</span><span class='Function'>↕</span><span class='String'>&quot;abcdefg&quot;</span>
"cdefg"
<span class='Number'>5</span><span class='Function'>↑</span><span class='Number'>2</span><span class='Function'>↓</span><span class='String'>&quot;abcdefg&quot;</span>
"cdefg"
@@ -26,7 +26,7 @@
<p>Windows differs from Prefixes and Suffixes in that it doesn't add a layer of nesting (it doesn't enclose each slice). This is possible because the slices have a fixed size.</p>
<h3 id="multiple-dimensions">Multiple dimensions</h3>
<p>The above description applies to a higher-rank right argument. As an example, we'll look at two-row slices of a shape <code><span class='Number'>3</span><span class='Ligature'>β€Ώ</span><span class='Number'>4</span></code> array. For convenience, we will enclose each slice. Note that slices always have the same rank as the argument array.</p>
-<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=POKOiTIgMuKGlSIwMTIzIuKIviJhYmNkIuKJjSJBQkNEIg==&run">↗️</a><pre> <span class='Function'>&lt;</span><span class='Modifier2'>βŽ‰</span><span class='Number'>2</span> <span class='Number'>2</span><span class='Function'>↕</span><span class='String'>&quot;0123&quot;</span><span class='Function'>∾</span><span class='String'>&quot;abcd&quot;</span><span class='Function'>≍</span><span class='String'>&quot;ABCD&quot;</span>
+<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=POKOiTIgMuKGlSIwMTIzIuKIviJhYmNkIuKJjSJBQkNEIg==">↗️</a><pre> <span class='Function'>&lt;</span><span class='Modifier2'>βŽ‰</span><span class='Number'>2</span> <span class='Number'>2</span><span class='Function'>↕</span><span class='String'>&quot;0123&quot;</span><span class='Function'>∾</span><span class='String'>&quot;abcd&quot;</span><span class='Function'>≍</span><span class='String'>&quot;ABCD&quot;</span>
β”Œβ”€
Β· β”Œβ”€ β”Œβ”€
β•΅"0123 β•΅"abcd
@@ -35,7 +35,7 @@
β”˜
</pre>
<p>Passing a list as the left argument to Windows takes slices along any number of leading axes. Here are all the shape <code><span class='Number'>2</span><span class='Ligature'>β€Ώ</span><span class='Number'>2</span></code> slices:</p>
-<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=POKOiTIgMuKAvzLihpUiMDEyMyLiiL4iYWJjZCLiiY0iQUJDRCI=&run">↗️</a><pre> <span class='Function'>&lt;</span><span class='Modifier2'>βŽ‰</span><span class='Number'>2</span> <span class='Number'>2</span><span class='Ligature'>β€Ώ</span><span class='Number'>2</span><span class='Function'>↕</span><span class='String'>&quot;0123&quot;</span><span class='Function'>∾</span><span class='String'>&quot;abcd&quot;</span><span class='Function'>≍</span><span class='String'>&quot;ABCD&quot;</span>
+<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=POKOiTIgMuKAvzLihpUiMDEyMyLiiL4iYWJjZCLiiY0iQUJDRCI=">↗️</a><pre> <span class='Function'>&lt;</span><span class='Modifier2'>βŽ‰</span><span class='Number'>2</span> <span class='Number'>2</span><span class='Ligature'>β€Ώ</span><span class='Number'>2</span><span class='Function'>↕</span><span class='String'>&quot;0123&quot;</span><span class='Function'>∾</span><span class='String'>&quot;abcd&quot;</span><span class='Function'>≍</span><span class='String'>&quot;ABCD&quot;</span>
β”Œβ”€
β•΅ β”Œβ”€ β”Œβ”€ β”Œβ”€
β•΅"01 β•΅"12 β•΅"23
@@ -54,7 +54,7 @@
<p>Using <a href="group.html">Group</a> we could also write <code><span class='Value'>i</span><span class='Function'>βŠ‘</span><span class='Value'>z</span></code> ←→ <code><span class='Value'>𝕩</span><span class='Function'>βŠ‘</span><span class='Modifier'>˜</span><span class='Paren'>(</span><span class='Value'>𝕨</span><span class='Function'>∾</span><span class='Modifier2'>β—‹</span><span class='Paren'>(</span><span class='Function'>↕</span><span class='Modifier2'>∘</span><span class='Function'>β‰ </span><span class='Paren'>)</span><span class='Function'>β‰’</span><span class='Value'>𝕩</span><span class='Paren'>)</span> <span class='Function'>+</span><span class='Modifier'>´¨</span><span class='Modifier2'>∘</span><span class='Function'>βŠ”</span> <span class='Value'>i</span></code>.</p>
<h2 id="symmetry">Symmetry</h2>
<p>Let's look at an earlier example, along with its transpose.</p>
-<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=e+KfqPCdlaks4o2J8J2VqeKfqX014oaVImFiY2RlZmci&run">↗️</a><pre> <span class='Brace'>{</span><span class='Bracket'>⟨</span><span class='Value'>𝕩</span><span class='Separator'>,</span><span class='Function'>⍉</span><span class='Value'>𝕩</span><span class='Bracket'>⟩</span><span class='Brace'>}</span><span class='Number'>5</span><span class='Function'>↕</span><span class='String'>&quot;abcdefg&quot;</span>
+<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=e+KfqPCdlaks4o2J8J2VqeKfqX014oaVImFiY2RlZmci">↗️</a><pre> <span class='Brace'>{</span><span class='Bracket'>⟨</span><span class='Value'>𝕩</span><span class='Separator'>,</span><span class='Function'>⍉</span><span class='Value'>𝕩</span><span class='Bracket'>⟩</span><span class='Brace'>}</span><span class='Number'>5</span><span class='Function'>↕</span><span class='String'>&quot;abcdefg&quot;</span>
β”Œβ”€
Β· β”Œβ”€ β”Œβ”€
β•΅"abcde β•΅"abc
@@ -66,29 +66,29 @@
β”˜
</pre>
<p>Although the two arrays have different shapes, they are identical where they overlap.</p>
-<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4omh4peLKDPigL8z4oq44oaRKeKfnOKNiTXihpUiYWJjZGVmZyI=&run">↗️</a><pre> <span class='Function'>≑</span><span class='Modifier2'>β—‹</span><span class='Paren'>(</span><span class='Number'>3</span><span class='Ligature'>β€Ώ</span><span class='Number'>3</span><span class='Modifier2'>⊸</span><span class='Function'>↑</span><span class='Paren'>)</span><span class='Modifier2'>⟜</span><span class='Function'>⍉</span><span class='Number'>5</span><span class='Function'>↕</span><span class='String'>&quot;abcdefg&quot;</span>
+<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4omh4peLKDPigL8z4oq44oaRKeKfnOKNiTXihpUiYWJjZGVmZyI=">↗️</a><pre> <span class='Function'>≑</span><span class='Modifier2'>β—‹</span><span class='Paren'>(</span><span class='Number'>3</span><span class='Ligature'>β€Ώ</span><span class='Number'>3</span><span class='Modifier2'>⊸</span><span class='Function'>↑</span><span class='Paren'>)</span><span class='Modifier2'>⟜</span><span class='Function'>⍉</span><span class='Number'>5</span><span class='Function'>↕</span><span class='String'>&quot;abcdefg&quot;</span>
1
</pre>
<p>In other words, the i'th element of slice j is the same as the j'th element of slice i: it is the <code><span class='Value'>i</span><span class='Function'>+</span><span class='Value'>j</span></code>'th element of the argument. So transposing still gives a possible result of Windows, but with a different slice length.</p>
-<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=eyg14oaV8J2VqSniiaHijYkoM+KGlfCdlakpfSJhYmNkZWZnIg==&run">↗️</a><pre> <span class='Brace'>{</span><span class='Paren'>(</span><span class='Number'>5</span><span class='Function'>↕</span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Function'>≑⍉</span><span class='Paren'>(</span><span class='Number'>3</span><span class='Function'>↕</span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Brace'>}</span><span class='String'>&quot;abcdefg&quot;</span>
+<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=eyg14oaV8J2VqSniiaHijYkoM+KGlfCdlakpfSJhYmNkZWZnIg==">↗️</a><pre> <span class='Brace'>{</span><span class='Paren'>(</span><span class='Number'>5</span><span class='Function'>↕</span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Function'>≑⍉</span><span class='Paren'>(</span><span class='Number'>3</span><span class='Function'>↕</span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Brace'>}</span><span class='String'>&quot;abcdefg&quot;</span>
1
</pre>
<p>In general, we need a more complicated transposeβ€”swapping the first set of <code><span class='Function'>β‰ </span><span class='Value'>𝕨</span></code> axes with the second set. Note again the use of Span, our slice-length to slice-number converter.</p>
-<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=eygoNeKAvzbCrDLigL8yKeKGlfCdlakpIOKJoSAy4oC/M+KNiSgy4oC/MuKGlfCdlakpfSDihpU14oC/NuKAvzc=&run">↗️</a><pre> <span class='Brace'>{</span><span class='Paren'>((</span><span class='Number'>5</span><span class='Ligature'>β€Ώ</span><span class='Number'>6</span><span class='Function'>Β¬</span><span class='Number'>2</span><span class='Ligature'>β€Ώ</span><span class='Number'>2</span><span class='Paren'>)</span><span class='Function'>↕</span><span class='Value'>𝕩</span><span class='Paren'>)</span> <span class='Function'>≑</span> <span class='Number'>2</span><span class='Ligature'>β€Ώ</span><span class='Number'>3</span><span class='Function'>⍉</span><span class='Paren'>(</span><span class='Number'>2</span><span class='Ligature'>β€Ώ</span><span class='Number'>2</span><span class='Function'>↕</span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Brace'>}</span> <span class='Function'>↕</span><span class='Number'>5</span><span class='Ligature'>β€Ώ</span><span class='Number'>6</span><span class='Ligature'>β€Ώ</span><span class='Number'>7</span>
+<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=eygoNeKAvzbCrDLigL8yKeKGlfCdlakpIOKJoSAy4oC/M+KNiSgy4oC/MuKGlfCdlakpfSDihpU14oC/NuKAvzc=">↗️</a><pre> <span class='Brace'>{</span><span class='Paren'>((</span><span class='Number'>5</span><span class='Ligature'>β€Ώ</span><span class='Number'>6</span><span class='Function'>Β¬</span><span class='Number'>2</span><span class='Ligature'>β€Ώ</span><span class='Number'>2</span><span class='Paren'>)</span><span class='Function'>↕</span><span class='Value'>𝕩</span><span class='Paren'>)</span> <span class='Function'>≑</span> <span class='Number'>2</span><span class='Ligature'>β€Ώ</span><span class='Number'>3</span><span class='Function'>⍉</span><span class='Paren'>(</span><span class='Number'>2</span><span class='Ligature'>β€Ώ</span><span class='Number'>2</span><span class='Function'>↕</span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Brace'>}</span> <span class='Function'>↕</span><span class='Number'>5</span><span class='Ligature'>β€Ώ</span><span class='Number'>6</span><span class='Ligature'>β€Ώ</span><span class='Number'>7</span>
1
</pre>
<h2 id="applications">Applications</h2>
<p>Windows can be followed up with a reduction on each slice to give a windowed reduction. Here we take running sums of 3 values.</p>
-<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=K8K0y5gz4oaVIOKfqDIsNiwwLDEsNCwz4p+p&run">↗️</a><pre> <span class='Function'>+</span><span class='Modifier'>´˘</span><span class='Number'>3</span><span class='Function'>↕</span> <span class='Bracket'>⟨</span><span class='Number'>2</span><span class='Separator'>,</span><span class='Number'>6</span><span class='Separator'>,</span><span class='Number'>0</span><span class='Separator'>,</span><span class='Number'>1</span><span class='Separator'>,</span><span class='Number'>4</span><span class='Separator'>,</span><span class='Number'>3</span><span class='Bracket'>⟩</span>
+<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=K8K0y5gz4oaVIOKfqDIsNiwwLDEsNCwz4p+p">↗️</a><pre> <span class='Function'>+</span><span class='Modifier'>´˘</span><span class='Number'>3</span><span class='Function'>↕</span> <span class='Bracket'>⟨</span><span class='Number'>2</span><span class='Separator'>,</span><span class='Number'>6</span><span class='Separator'>,</span><span class='Number'>0</span><span class='Separator'>,</span><span class='Number'>1</span><span class='Separator'>,</span><span class='Number'>4</span><span class='Separator'>,</span><span class='Number'>3</span><span class='Bracket'>⟩</span>
⟨ 8 7 5 8 ⟩
</pre>
<p>A common task is to act on windows with an initial or final element so the total length stays the same. When using windows of length 2, the best way to accomplish this is with <a href="shift.html">shift functions</a> like <code><span class='Function'>Β«</span></code> or <code><span class='Function'>Β»</span></code>. If the window length is longer or variable, then a trick with Windows works better: add the elements, and then use windows matching the original length. Here we invert <code><span class='Function'>+</span><span class='Modifier'>`</span></code>, which requires we take pairwise differences starting at initial value 0.</p>
-<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=LeKfnCgwwrviiqIpICtgIDPigL8y4oC/MeKAvzEKKC3LnMud4omg4oaVMOKIvuKKoikgK2AgM+KAvzLigL8x4oC/MQ==&run">↗️</a><pre> <span class='Function'>-</span><span class='Modifier2'>⟜</span><span class='Paren'>(</span><span class='Number'>0</span><span class='Function'>»⊒</span><span class='Paren'>)</span> <span class='Function'>+</span><span class='Modifier'>`</span> <span class='Number'>3</span><span class='Ligature'>β€Ώ</span><span class='Number'>2</span><span class='Ligature'>β€Ώ</span><span class='Number'>1</span><span class='Ligature'>β€Ώ</span><span class='Number'>1</span>
+<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=LeKfnCgwwrviiqIpICtgIDPigL8y4oC/MeKAvzEKKC3LnMud4omg4oaVMOKIvuKKoikgK2AgM+KAvzLigL8x4oC/MQ==">↗️</a><pre> <span class='Function'>-</span><span class='Modifier2'>⟜</span><span class='Paren'>(</span><span class='Number'>0</span><span class='Function'>»⊒</span><span class='Paren'>)</span> <span class='Function'>+</span><span class='Modifier'>`</span> <span class='Number'>3</span><span class='Ligature'>β€Ώ</span><span class='Number'>2</span><span class='Ligature'>β€Ώ</span><span class='Number'>1</span><span class='Ligature'>β€Ώ</span><span class='Number'>1</span>
⟨ 3 2 1 1 ⟩
<span class='Paren'>(</span><span class='Function'>-</span><span class='Modifier'>˜˝</span><span class='Function'>≠↕</span><span class='Number'>0</span><span class='Function'>∾⊒</span><span class='Paren'>)</span> <span class='Function'>+</span><span class='Modifier'>`</span> <span class='Number'>3</span><span class='Ligature'>β€Ώ</span><span class='Number'>2</span><span class='Ligature'>β€Ώ</span><span class='Number'>1</span><span class='Ligature'>β€Ώ</span><span class='Number'>1</span>
⟨ 3 2 1 1 ⟩
</pre>
<p>With Windows, we can modify the 3-element running sum above to keep the length constant by starting with two zeros.</p>
-<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=KCvLneKJoOKGlSgy4qWKMCniirjiiL4pIOKfqDIsNiwwLDEsNCwz4p+p&run">↗️</a><pre> <span class='Paren'>(</span><span class='Function'>+</span><span class='Modifier'>˝</span><span class='Function'>≠↕</span><span class='Paren'>(</span><span class='Number'>2</span><span class='Function'>β₯Š</span><span class='Number'>0</span><span class='Paren'>)</span><span class='Modifier2'>⊸</span><span class='Function'>∾</span><span class='Paren'>)</span> <span class='Bracket'>⟨</span><span class='Number'>2</span><span class='Separator'>,</span><span class='Number'>6</span><span class='Separator'>,</span><span class='Number'>0</span><span class='Separator'>,</span><span class='Number'>1</span><span class='Separator'>,</span><span class='Number'>4</span><span class='Separator'>,</span><span class='Number'>3</span><span class='Bracket'>⟩</span>
+<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=KCvLneKJoOKGlSgy4qWKMCniirjiiL4pIOKfqDIsNiwwLDEsNCwz4p+p">↗️</a><pre> <span class='Paren'>(</span><span class='Function'>+</span><span class='Modifier'>˝</span><span class='Function'>≠↕</span><span class='Paren'>(</span><span class='Number'>2</span><span class='Function'>β₯Š</span><span class='Number'>0</span><span class='Paren'>)</span><span class='Modifier2'>⊸</span><span class='Function'>∾</span><span class='Paren'>)</span> <span class='Bracket'>⟨</span><span class='Number'>2</span><span class='Separator'>,</span><span class='Number'>6</span><span class='Separator'>,</span><span class='Number'>0</span><span class='Separator'>,</span><span class='Number'>1</span><span class='Separator'>,</span><span class='Number'>4</span><span class='Separator'>,</span><span class='Number'>3</span><span class='Bracket'>⟩</span>
⟨ 2 8 8 7 5 8 ⟩
</pre>