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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="List of all items in this crate"><title>List of all items in this crate</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/SourceSerif4-Regular-46f98efaafac5295.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" 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href="../static.files/favicon-2c020d218678b618.svg"></head><body class="rustdoc mod sys"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="mobile-topbar"><button class="sidebar-menu-toggle">&#9776;</button></nav><nav class="sidebar"><div class="sidebar-crate"><h2><a href="../argmin_testfunctions/index.html">argmin_testfunctions</a><span class="version">0.1.1</span></h2></div><div class="sidebar-elems"><section><ul class="block"><li><a href="#functions">Functions</a></li></ul></section></div></nav><main><div class="width-limiter"><nav class="sub"><form class="search-form"><span></span><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../help.html">?</a></div><div id="settings-menu" 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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="List of all items in this crate"><title>List of all items in this crate</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/SourceSerif4-Regular-46f98efaafac5295.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" 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3 changes: 3 additions & 0 deletions argmin_testfunctions/fn.matyas_derivative.html
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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Derivative of Matyas test function"><title>matyas_derivative in argmin_testfunctions - Rust</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/SourceSerif4-Regular-46f98efaafac5295.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../static.files/rustdoc-9ee3a5e31a2afa3e.css"><meta name="rustdoc-vars" data-root-path="../" data-static-root-path="../static.files/" data-current-crate="argmin_testfunctions" data-themes="" data-resource-suffix="" data-rustdoc-version="1.75.0 (82e1608df 2023-12-21)" data-channel="1.75.0" data-search-js="search-8fbf244ebcf71464.js" data-settings-js="settings-74424d7eec62a23e.js" ><script src="../static.files/storage-fec3eaa3851e447d.js"></script><script defer src="sidebar-items.js"></script><script defer src="../static.files/main-9dd44ab47b99a0fb.js"></script><noscript><link rel="stylesheet" href="../static.files/noscript-5d8b3c7633ad77ba.css"></noscript><link rel="alternate icon" type="image/png" href="../static.files/favicon-16x16-8b506e7a72182f1c.png"><link rel="alternate icon" type="image/png" href="../static.files/favicon-32x32-422f7d1d52889060.png"><link rel="icon" type="image/svg+xml" href="../static.files/favicon-2c020d218678b618.svg"></head><body class="rustdoc fn"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="mobile-topbar"><button class="sidebar-menu-toggle">&#9776;</button></nav><nav class="sidebar"><div class="sidebar-crate"><h2><a href="../argmin_testfunctions/index.html">argmin_testfunctions</a><span class="version">0.1.1</span></h2></div><div class="sidebar-elems"></div></nav><main><div class="width-limiter"><nav class="sub"><form class="search-form"><span></span><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../static.files/wheel-7b819b6101059cd0.svg"></a></div></form></nav><section id="main-content" class="content"><div class="main-heading"><h1>Function <a href="index.html">argmin_testfunctions</a>::<wbr><a class="fn" href="#">matyas_derivative</a><button id="copy-path" title="Copy item path to clipboard"><img src="../static.files/clipboard-7571035ce49a181d.svg" width="19" height="18" alt="Copy item path"></button></h1><span class="out-of-band"><a class="src" href="../src/argmin_testfunctions/matyas.rs.html#42-52">source</a> · <button id="toggle-all-docs" title="collapse all docs">[<span>&#x2212;</span>]</button></span></div><pre class="rust item-decl"><code>pub fn matyas_derivative&lt;T&gt;(param: &amp;<a class="primitive" href="https://doc.rust-lang.org/1.75.0/std/primitive.array.html">[T; 2]</a>) -&gt; <a class="primitive" href="https://doc.rust-lang.org/1.75.0/std/primitive.array.html">[T; 2]</a><span class="where fmt-newline">where
T: <a class="trait" href="https://docs.rs/num-traits/0.2/num_traits/float/trait.Float.html" title="trait num_traits::float::Float">Float</a> + <a class="trait" href="https://docs.rs/num-traits/0.2/num_traits/cast/trait.FromPrimitive.html" title="trait num_traits::cast::FromPrimitive">FromPrimitive</a>,</span></code></pre><details class="toggle top-doc" open><summary class="hideme"><span>Expand description</span></summary><div class="docblock"><p>Derivative of Matyas test function</p>
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4 changes: 4 additions & 0 deletions argmin_testfunctions/fn.matyas_hessian.html
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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Hessian of Matyas test function"><title>matyas_hessian in argmin_testfunctions - Rust</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/SourceSerif4-Regular-46f98efaafac5295.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../static.files/rustdoc-9ee3a5e31a2afa3e.css"><meta name="rustdoc-vars" data-root-path="../" data-static-root-path="../static.files/" data-current-crate="argmin_testfunctions" data-themes="" data-resource-suffix="" data-rustdoc-version="1.75.0 (82e1608df 2023-12-21)" data-channel="1.75.0" data-search-js="search-8fbf244ebcf71464.js" data-settings-js="settings-74424d7eec62a23e.js" ><script src="../static.files/storage-fec3eaa3851e447d.js"></script><script defer src="sidebar-items.js"></script><script defer src="../static.files/main-9dd44ab47b99a0fb.js"></script><noscript><link rel="stylesheet" href="../static.files/noscript-5d8b3c7633ad77ba.css"></noscript><link rel="alternate icon" type="image/png" href="../static.files/favicon-16x16-8b506e7a72182f1c.png"><link rel="alternate icon" type="image/png" href="../static.files/favicon-32x32-422f7d1d52889060.png"><link rel="icon" type="image/svg+xml" href="../static.files/favicon-2c020d218678b618.svg"></head><body class="rustdoc fn"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="mobile-topbar"><button class="sidebar-menu-toggle">&#9776;</button></nav><nav class="sidebar"><div class="sidebar-crate"><h2><a href="../argmin_testfunctions/index.html">argmin_testfunctions</a><span class="version">0.1.1</span></h2></div><div class="sidebar-elems"></div></nav><main><div class="width-limiter"><nav class="sub"><form class="search-form"><span></span><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../static.files/wheel-7b819b6101059cd0.svg"></a></div></form></nav><section id="main-content" class="content"><div class="main-heading"><h1>Function <a href="index.html">argmin_testfunctions</a>::<wbr><a class="fn" href="#">matyas_hessian</a><button id="copy-path" title="Copy item path to clipboard"><img src="../static.files/clipboard-7571035ce49a181d.svg" width="19" height="18" alt="Copy item path"></button></h1><span class="out-of-band"><a class="src" href="../src/argmin_testfunctions/matyas.rs.html#57-65">source</a> · <button id="toggle-all-docs" title="collapse all docs">[<span>&#x2212;</span>]</button></span></div><pre class="rust item-decl"><code>pub fn matyas_hessian&lt;T&gt;(_param: &amp;<a class="primitive" href="https://doc.rust-lang.org/1.75.0/std/primitive.array.html">[T; 2]</a>) -&gt; [<a class="primitive" href="https://doc.rust-lang.org/1.75.0/std/primitive.array.html">[T; 2]</a>; <a class="primitive" href="https://doc.rust-lang.org/1.75.0/std/primitive.array.html">2</a>]<span class="where fmt-newline">where
T: <a class="trait" href="https://docs.rs/num-traits/0.2/num_traits/float/trait.Float.html" title="trait num_traits::float::Float">Float</a> + <a class="trait" href="https://docs.rs/num-traits/0.2/num_traits/cast/trait.FromPrimitive.html" title="trait num_traits::cast::FromPrimitive">FromPrimitive</a>,</span></code></pre><details class="toggle top-doc" open><summary class="hideme"><span>Expand description</span></summary><div class="docblock"><p>Hessian of Matyas test function</p>
<p>Returns [[0.52, -0.48], [-0.48, 0.52]] for any input.</p>
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</pre></div><pre class="rust"><code><span class="comment">// Copyright 2018-2024 argmin developers
//
// Licensed under the Apache License, Version 2.0 &lt;LICENSE-APACHE or
@@ -90,16 +146,72 @@
n026 * (x1.powi(<span class="number">2</span>) + x2.powi(<span class="number">2</span>)) - n048 * x1 * x2
}

<span class="doccomment">/// Derivative of Matyas test function
</span><span class="kw">pub fn </span>matyas_derivative&lt;T&gt;(param: <span class="kw-2">&amp;</span>[T; <span class="number">2</span>]) -&gt; [T; <span class="number">2</span>]
<span class="kw">where
</span>T: Float + FromPrimitive,
{
<span class="kw">let </span>[x1, x2] = <span class="kw-2">*</span>param;

<span class="kw">let </span>n0_52 = T::from_f64(<span class="number">0.52</span>).unwrap();
<span class="kw">let </span>n0_48 = T::from_f64(<span class="number">0.48</span>).unwrap();

[n0_52 * x1 - n0_48 * x2, n0_52 * x2 - n0_48 * x1]
}

<span class="doccomment">/// Hessian of Matyas test function
///
/// Returns [[0.52, -0.48], [-0.48, 0.52]] for any input.
</span><span class="kw">pub fn </span>matyas_hessian&lt;T&gt;(_param: <span class="kw-2">&amp;</span>[T; <span class="number">2</span>]) -&gt; [[T; <span class="number">2</span>]; <span class="number">2</span>]
<span class="kw">where
</span>T: Float + FromPrimitive,
{
<span class="kw">let </span>n0_52 = T::from_f64(<span class="number">0.52</span>).unwrap();
<span class="kw">let </span>n0_48 = T::from_f64(<span class="number">0.48</span>).unwrap();

[[n0_52, -n0_48], [-n0_48, n0_52]]
}

<span class="attr">#[cfg(test)]
</span><span class="kw">mod </span>tests {
<span class="kw">use super</span>::<span class="kw-2">*</span>;
<span class="kw">use </span>approx::assert_relative_eq;
<span class="kw">use </span>finitediff::FiniteDiff;
<span class="kw">use </span>proptest::prelude::<span class="kw-2">*</span>;
<span class="kw">use </span>std::{f32, f64};

<span class="attr">#[test]
</span><span class="kw">fn </span>test_matyas_optimum() {
<span class="macro">assert_relative_eq!</span>(matyas(<span class="kw-2">&amp;</span>[<span class="number">0_f32</span>, <span class="number">0_f32</span>]), <span class="number">0.0</span>, epsilon = f32::EPSILON);
<span class="macro">assert_relative_eq!</span>(matyas(<span class="kw-2">&amp;</span>[<span class="number">0_f64</span>, <span class="number">0_f64</span>]), <span class="number">0.0</span>, epsilon = f64::EPSILON);
}

<span class="macro">proptest! </span>{
<span class="attr">#[test]
</span><span class="kw">fn </span>test_matyas_derivative(a <span class="kw">in </span>-<span class="number">10.0</span>..<span class="number">10.0</span>, b <span class="kw">in </span>-<span class="number">10.0</span>..<span class="number">10.0</span>) {
<span class="kw">let </span>param = [a, b];
<span class="kw">let </span>derivative = matyas_derivative(<span class="kw-2">&amp;</span>param);
<span class="kw">let </span>derivative_fd = Vec::from(param).central_diff(<span class="kw-2">&amp;</span>|x| matyas(<span class="kw-2">&amp;</span>[x[<span class="number">0</span>], x[<span class="number">1</span>]]));
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..derivative.len() {
<span class="macro">assert_relative_eq!</span>(derivative[i], derivative_fd[i], epsilon = <span class="number">1e-5</span>);
}
}
}

<span class="macro">proptest! </span>{
<span class="attr">#[test]
</span><span class="kw">fn </span>test_matyas_hessian(a <span class="kw">in </span>-<span class="number">10.0</span>..<span class="number">10.0</span>, b <span class="kw">in </span>-<span class="number">10.0</span>..<span class="number">10.0</span>) {
<span class="kw">let </span>param = [a, b];
<span class="kw">let </span>hessian = matyas_hessian(<span class="kw-2">&amp;</span>param);
<span class="kw">let </span>hessian_fd = [[<span class="number">0.52</span>, -<span class="number">0.48</span>], [-<span class="number">0.48</span>, <span class="number">0.52</span>]];
<span class="kw">let </span>n = hessian.len();
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..n {
<span class="macro">assert_eq!</span>(hessian[i].len(), n);
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..n {
<span class="macro">assert_relative_eq!</span>(hessian[i][j], hessian_fd[i][j], epsilon = f64::EPSILON);
}
}
}
}
}
</code></pre></div></section></main></body></html>

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