build based on e94bc15

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-10-05T18:36:55","documenter_version":"1.1.0"}}
+{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-10-05T19:33:37","documenter_version":"1.1.0"}}

dev/convergence/index.html

@@ -15,4 +15,4 @@
 convergenceplot(r)</code></pre><img src="aa70c007.png" alt="Example block output"/><p>In the extreme case of a function with a singularity on the domain, the convergence can be substantially affected:</p><pre><code class="language-julia hljs">f = x -&gt; abs(x - 1/8)
 r = approximate(f, unit_interval, stats=true)
 convergenceplot(r)</code></pre><img src="f036fc9f.png" alt="Example block output"/><p>In such a case, we might get improvement by increasing the number of allowed consecutive failures via the <code>lookahead</code> keyword argument:</p><pre><code class="language-julia hljs">r = approximate(f, unit_interval, stats=true, lookahead=20)
-convergenceplot(r)</code></pre><img src="10298161.png" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Walkthrough</a><a class="docs-footer-nextpage" href="../minimax/">Minimax »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Thursday 5 October 2023 18:36">Thursday 5 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+convergenceplot(r)</code></pre><img src="10298161.png" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Walkthrough</a><a class="docs-footer-nextpage" href="../minimax/">Minimax »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Thursday 5 October 2023 19:33">Thursday 5 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/index.html

@@ -3,7 +3,7 @@
 const shg = current_figure
 f = x -> exp(cos(4x) - sin(3x))
 lines(-1..1, f)</code></pre><img src="index-8263853f.png" alt="Example block output"/><p>To create a rational function that approximates <span>$f$</span> well on this domain, we use the continuous form of the AAA algorithm:</p><pre><code class="language-julia hljs">r = aaa(f)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Barycentric function with 20 nodes and values:
-    -1.0=&gt;0.598982,  -0.986111=&gt;0.599042,  -0.944444=&gt;0.605944,  …  1.0=&gt;0.451688</code></pre><p>The result is a type (19,19) rational approximant that can be evaluated like a function:</p><pre><code class="language-julia hljs">f(0.5) - r(0.5)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">3.236300116782331e-14</code></pre><p>We see that this approximation has more than 13 accurate over most of the interval:</p><pre><code class="language-julia hljs">lines(-1..1, x -&gt; f(x)-r(x))</code></pre><img src="index-9630b374.png" alt="Example block output"/><p>The rational approximant interpolates <span>$f$</span> at greedily selected nodes:</p><pre><code class="language-julia hljs">x = nodes(r)
+    -1.0=&gt;0.598982,  -0.986111=&gt;0.599042,  -0.944444=&gt;0.605944,  …  1.0=&gt;0.451688</code></pre><p>The result is a type (19,19) rational approximant that can be evaluated like a function:</p><pre><code class="language-julia hljs">f(0.5) - r(0.5)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">3.236300116782331e-14</code></pre><p>We see that this approximation has more than 13 accurate digits over most of the interval:</p><pre><code class="language-julia hljs">lines(-1..1, x -&gt; f(x)-r(x))</code></pre><img src="index-9630b374.png" alt="Example block output"/><p>The rational approximant interpolates <span>$f$</span> at greedily selected nodes:</p><pre><code class="language-julia hljs">x = nodes(r)
 scatter!(x, 0*x, markersize = 12, color=:black)
 shg()</code></pre><img src="index-95d1c23d.png" alt="Example block output"/><p>Here&#39;s another smooth example, the hyperbolic secant function:</p><pre><code class="language-julia hljs">f = sech
 r = aaa(f)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Barycentric function with 7 nodes and values:
@@ -54,4 +54,4 @@
 lines!([(0, 8), (0, -8)], color=:white, linewidth=5)
 scatter!(φ.(nodes(r.fun)), color=:black, markersize=10)
 limits!(-8, 8, -8, 8)
-shg()</code></pre><img src="index-1bb9e9e9.png" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="convergence/">Convergence »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Thursday 5 October 2023 18:36">Thursday 5 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+shg()</code></pre><img src="index-1bb9e9e9.png" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="convergence/">Convergence »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Thursday 5 October 2023 19:33">Thursday 5 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/minimax/index.html

@@ -7,4 +7,4 @@
 errorplot(r)</code></pre><img src="c04b70be.png" alt="Example block output"/><p>As you can see above, the error is now nearly equioscillatory over the interval. Moreover, the interpolation nodes appear to have shifted to resemble Chebyshev points of the first kind. If we try minimax approximation on the unit circle, however, equioscillation tends to lead to equally spaced nodes:</p><pre><code class="language-julia hljs">f = z -&gt; cos(4z) - sin(3z)
 r = approximate(f, unit_circle, max_degree=10)
 r = minimax(r, 20)
-errorplot(r, use_abs=false)</code></pre><img src="406a744d.png" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../convergence/">« Convergence</a><a class="docs-footer-nextpage" href="../mode/">Discrete vs. continuous »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Thursday 5 October 2023 18:36">Thursday 5 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+errorplot(r, use_abs=false)</code></pre><img src="406a744d.png" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../convergence/">« Convergence</a><a class="docs-footer-nextpage" href="../mode/">Discrete vs. continuous »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Thursday 5 October 2023 19:33">Thursday 5 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/mode/index.html

@@ -12,4 +12,4 @@
 println("nearest pole is $(minimum(dist(z, I) for z in poles(r))) away")
 println(&quot;error = $(maximum(abs, @. f(xx) - r(xx) ))&quot;)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">nearest pole is 0.004428389360923072 away
 error = 0.14091753428877052</code></pre><p>In the continuous mode (<a href="https://arxiv.org/abs/2305.03677">Driscoll, Nakatsukasa, Trefethen</a>) used by the <code>approximate</code> method, the samples are refined adaptively to try to ensure that the approximation is accurate everywhere:</p><pre><code class="language-julia hljs">r = approximate(f, I)
-println(&quot;error = $(maximum(abs, @. f(xx) - r(xx) ))&quot;)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">error = 7.616129948928574e-13</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../minimax/">« Minimax</a><a class="docs-footer-nextpage" href="../functions/">Functions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Thursday 5 October 2023 18:36">Thursday 5 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+println(&quot;error = $(maximum(abs, @. f(xx) - r(xx) ))&quot;)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">error = 7.616129948928574e-13</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../minimax/">« Minimax</a><a class="docs-footer-nextpage" href="../functions/">Functions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Thursday 5 October 2023 19:33">Thursday 5 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>