| <!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="Cholesky decomposition."><meta name="keywords" content="rust, rustlang, rust-lang, Cholesky"><title>Cholesky in rusty_machine::linalg - Rust</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../normalize.css"><link rel="stylesheet" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../ayu.css" disabled><link rel="stylesheet" href="../../dark.css" disabled><link rel="stylesheet" href="../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../storage.js"></script><script defer src="sidebar-items.js"></script><script defer src="../../main.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../favicon.svg"></head><body class="rustdoc struct"><!--[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">☰</button><a class="sidebar-logo" href="../../rusty_machine/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a><h2></h2></nav><nav class="sidebar"><a class="sidebar-logo" href="../../rusty_machine/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a><h2 class="location"><a href="#">Cholesky</a></h2><div class="sidebar-elems"><section><h3><a href="#implementations">Methods</a></h3><ul class="block"><li><a href="#method.decompose">decompose</a></li><li><a href="#method.det">det</a></li><li><a href="#method.inverse">inverse</a></li><li><a href="#method.solve">solve</a></li></ul><h3><a href="#trait-implementations">Trait Implementations</a></h3><ul class="block"><li><a href="#impl-Clone-for-Cholesky%3CT%3E">Clone</a></li><li><a href="#impl-Debug-for-Cholesky%3CT%3E">Debug</a></li><li><a href="#impl-Decomposition-for-Cholesky%3CT%3E">Decomposition</a></li></ul><h3><a href="#synthetic-implementations">Auto Trait Implementations</a></h3><ul class="block"><li><a href="#impl-RefUnwindSafe-for-Cholesky%3CT%3E">RefUnwindSafe</a></li><li><a href="#impl-Send-for-Cholesky%3CT%3E">Send</a></li><li><a href="#impl-Sync-for-Cholesky%3CT%3E">Sync</a></li><li><a href="#impl-Unpin-for-Cholesky%3CT%3E">Unpin</a></li><li><a href="#impl-UnwindSafe-for-Cholesky%3CT%3E">UnwindSafe</a></li></ul><h3><a href="#blanket-implementations">Blanket Implementations</a></h3><ul class="block"><li><a href="#impl-Any-for-Cholesky%3CT%3E">Any</a></li><li><a href="#impl-Borrow%3CT%3E-for-Cholesky%3CT%3E">Borrow<T></a></li><li><a href="#impl-BorrowMut%3CT%3E-for-Cholesky%3CT%3E">BorrowMut<T></a></li><li><a href="#impl-From%3CT%3E-for-Cholesky%3CT%3E">From<T></a></li><li><a href="#impl-Into%3CU%3E-for-Cholesky%3CT%3E">Into<U></a></li><li><a href="#impl-ToOwned-for-Cholesky%3CT%3E">ToOwned</a></li><li><a href="#impl-TryFrom%3CU%3E-for-Cholesky%3CT%3E">TryFrom<U></a></li><li><a href="#impl-TryInto%3CU%3E-for-Cholesky%3CT%3E">TryInto<U></a></li><li><a href="#impl-VZip%3CV%3E-for-Cholesky%3CT%3E">VZip<V></a></li></ul></section><h2><a href="index.html">In rusty_machine::linalg</a></h2></div></nav><main><div class="width-limiter"><nav class="sub"><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" 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="../../wheel.svg"></a></div></div></form></nav><section id="main-content" class="content"><div class="main-heading"><h1 class="fqn">Struct <a href="../index.html">rusty_machine</a>::<wbr><a href="index.html">linalg</a>::<wbr><a class="struct" href="#">Cholesky</a><button id="copy-path" onclick="copy_path(this)" title="Copy item path to clipboard"><img src="../../clipboard.svg" width="19" height="18" alt="Copy item path"></button></h1><span class="out-of-band"><a class="srclink" href="../../src/rulinalg/matrix/decomposition/cholesky.rs.html#94">source</a> · <a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class="inner">−</span>]</a></span></div><div class="item-decl"><pre class="rust struct"><code>pub struct Cholesky<T> { /* private fields */ }</code></pre></div><details class="rustdoc-toggle top-doc" open><summary class="hideme"><span>Expand description</span></summary><div class="docblock"><p>Cholesky decomposition.</p> |
| <p>Given a square, symmetric positive definite matrix A, |
| there exists an invertible lower triangular matrix L |
| such that</p> |
| <p>A = L L<sup>T</sup>.</p> |
| <p>This is called the Cholesky decomposition of A. |
| For not too ill-conditioned A, the computation |
| of the decomposition is very robust, and it takes about |
| half the effort of an LU decomposition with partial pivoting.</p> |
| <h2 id="applications"><a href="#applications">Applications</a></h2> |
| <p>The Cholesky decomposition can be thought of as a specialized |
| LU decomposition for symmetric positive definite matrices, |
| and so its applications are similar to that of LU.</p> |
| <p>The following example shows how to compute the Cholesky |
| decomposition of a given matrix. In this example, we also |
| unpack the decomposition to retrieve the L matrix, |
| but in many practical applications we are not so concerned |
| with the factor itself. Instead, we may wish to |
| solve linear systems or compute the determinant or the |
| inverse of a symmetric positive definite matrix. |
| In this case, see the next subsections.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>rulinalg::matrix::decomposition::Cholesky; |
| |
| <span class="comment">// Need to import Decomposition if we want to unpack |
| </span><span class="kw">use </span>rulinalg::matrix::decomposition::Decomposition; |
| |
| <span class="kw">let </span>x = <span class="macro">matrix!</span>[ <span class="number">1.0</span>, <span class="number">3.0</span>, <span class="number">1.0</span>; |
| <span class="number">3.0</span>, <span class="number">13.0</span>, <span class="number">11.0</span>; |
| <span class="number">1.0</span>, <span class="number">11.0</span>, <span class="number">21.0 </span>]; |
| <span class="kw">let </span>cholesky = Cholesky::decompose(x) |
| .expect(<span class="string">"Matrix is SPD."</span>); |
| |
| <span class="comment">// Obtain the matrix factor L |
| </span><span class="kw">let </span>l = cholesky.unpack(); |
| |
| <span class="macro">assert_matrix_eq!</span>(l, <span class="macro">matrix!</span>[<span class="number">1.0</span>, <span class="number">0.0</span>, <span class="number">0.0</span>; |
| <span class="number">3.0</span>, <span class="number">2.0</span>, <span class="number">0.0</span>; |
| <span class="number">1.0</span>, <span class="number">4.0</span>, <span class="number">2.0</span>], comp = float);</code></pre></div> |
| <h3 id="solving-linear-systems"><a href="#solving-linear-systems">Solving linear systems</a></h3> |
| <p>After having decomposed the matrix, one may efficiently |
| solve linear systems for different right-hand sides.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">let </span>b1 = <span class="macro">vector!</span>[ <span class="number">3.0</span>, <span class="number">2.0</span>, <span class="number">1.0</span>]; |
| <span class="kw">let </span>b2 = <span class="macro">vector!</span>[-<span class="number">2.0</span>, <span class="number">1.0</span>, <span class="number">0.0</span>]; |
| <span class="kw">let </span>y1 = cholesky.solve(b1).expect(<span class="string">"Matrix is invertible."</span>); |
| <span class="kw">let </span>y2 = cholesky.solve(b2).expect(<span class="string">"Matrix is invertible."</span>); |
| <span class="macro">assert_vector_eq!</span>(y1, <span class="macro">vector!</span>[ <span class="number">23.25</span>, -<span class="number">7.75</span>, <span class="number">3.0 </span>]); |
| <span class="macro">assert_vector_eq!</span>(y2, <span class="macro">vector!</span>[-<span class="number">22.25</span>, <span class="number">7.75</span>, -<span class="number">3.00 </span>]);</code></pre></div> |
| <h3 id="computing-the-inverse-of-a-matrix"><a href="#computing-the-inverse-of-a-matrix">Computing the inverse of a matrix</a></h3> |
| <p>While computing the inverse explicitly is rarely |
| the best solution to any given problem, it is sometimes |
| necessary. In this case, it is easily accessible |
| through the <code>inverse()</code> method on <code>Cholesky</code>.</p> |
| <h2 id="computing-the-determinant-of-a-matrix"><a href="#computing-the-determinant-of-a-matrix">Computing the determinant of a matrix</a></h2> |
| <p>As with LU decomposition, the <code>Cholesky</code> decomposition |
| exposes a method <code>det</code> for computing the determinant |
| of the decomposed matrix. This is a very cheap operation.</p> |
| </div></details><h2 id="implementations" class="small-section-header">Implementations<a href="#implementations" class="anchor"></a></h2><div id="implementations-list"><details class="rustdoc-toggle implementors-toggle" open><summary><section id="impl-Cholesky%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="../../src/rulinalg/matrix/decomposition/cholesky.rs.html#98">source</a><a href="#impl-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> <a class="struct" href="struct.Cholesky.html" title="struct rusty_machine::linalg::Cholesky">Cholesky</a><T><span class="where fmt-newline">where<br> T: 'static + <a class="trait" href="../../num_traits/float/trait.Float.html" title="trait num_traits::float::Float">Float</a>,</span></h3></section></summary><div class="impl-items"><details class="rustdoc-toggle method-toggle" open><summary><section id="method.decompose" class="method has-srclink"><a class="srclink rightside" href="../../src/rulinalg/matrix/decomposition/cholesky.rs.html#116">source</a><h4 class="code-header">pub fn <a href="#method.decompose" class="fnname">decompose</a>(matrix: <a class="struct" href="struct.Matrix.html" title="struct rusty_machine::linalg::Matrix">Matrix</a><T>) -> Result<<a class="struct" href="struct.Cholesky.html" title="struct rusty_machine::linalg::Cholesky">Cholesky</a><T>, <a class="struct" href="../../rulinalg/error/struct.Error.html" title="struct rulinalg::error::Error">Error</a>></h4></section></summary><div class="docblock"><p>Computes the Cholesky decomposition A = L L<sup>T</sup> |
| for the given square, symmetric positive definite matrix.</p> |
| <p>Note that the implementation cannot reliably and efficiently |
| verify that the matrix truly is symmetric positive definite matrix, |
| so it is the responsibility of the user to make sure that this is |
| the case. In particular, if the input matrix is not SPD, |
| the returned decomposition may not be a valid decomposition |
| for the input matrix.</p> |
| <h5 id="errors"><a href="#errors">Errors</a></h5> |
| <ul> |
| <li>A diagonal entry is effectively zero to working precision.</li> |
| <li>A diagonal entry is negative.</li> |
| </ul> |
| <h5 id="panics"><a href="#panics">Panics</a></h5> |
| <ul> |
| <li>The matrix must be square.</li> |
| </ul> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="method.det" class="method has-srclink"><a class="srclink rightside" href="../../src/rulinalg/matrix/decomposition/cholesky.rs.html#175">source</a><h4 class="code-header">pub fn <a href="#method.det" class="fnname">det</a>(&self) -> T</h4></section></summary><div class="docblock"><p>Computes the determinant of the decomposed matrix.</p> |
| <p>Note that the determinant of an empty matrix is considered |
| to be equal to 1.</p> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="method.solve" class="method has-srclink"><a class="srclink rightside" href="../../src/rulinalg/matrix/decomposition/cholesky.rs.html#194">source</a><h4 class="code-header">pub fn <a href="#method.solve" class="fnname">solve</a>(&self, b: <a class="struct" href="struct.Vector.html" title="struct rusty_machine::linalg::Vector">Vector</a><T>) -> Result<<a class="struct" href="struct.Vector.html" title="struct rusty_machine::linalg::Vector">Vector</a><T>, <a class="struct" href="../../rulinalg/error/struct.Error.html" title="struct rulinalg::error::Error">Error</a>></h4></section></summary><div class="docblock"><p>Solves the linear system Ax = b.</p> |
| <p>Here A is the decomposed matrix and b is the |
| supplied vector.</p> |
| <h5 id="errors-1"><a href="#errors-1">Errors</a></h5> |
| <p>If the matrix is sufficiently ill-conditioned, |
| it is possible that the solution cannot be obtained.</p> |
| <h5 id="panics-1"><a href="#panics-1">Panics</a></h5> |
| <ul> |
| <li>The supplied right-hand side vector must be |
| dimensionally compatible with the supplied matrix.</li> |
| </ul> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="method.inverse" class="method has-srclink"><a class="srclink rightside" href="../../src/rulinalg/matrix/decomposition/cholesky.rs.html#209">source</a><h4 class="code-header">pub fn <a href="#method.inverse" class="fnname">inverse</a>(&self) -> Result<<a class="struct" href="struct.Matrix.html" title="struct rusty_machine::linalg::Matrix">Matrix</a><T>, <a class="struct" href="../../rulinalg/error/struct.Error.html" title="struct rulinalg::error::Error">Error</a>></h4></section></summary><div class="docblock"><p>Computes the inverse of the decomposed matrix.</p> |
| <h5 id="errors-2"><a href="#errors-2">Errors</a></h5> |
| <p>If the matrix is sufficiently ill-conditioned, |
| it is possible that the inverse cannot be obtained.</p> |
| </div></details></div></details></div><h2 id="trait-implementations" class="small-section-header">Trait Implementations<a href="#trait-implementations" class="anchor"></a></h2><div id="trait-implementations-list"><details class="rustdoc-toggle implementors-toggle" open><summary><section id="impl-Clone-for-Cholesky%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="../../src/rulinalg/matrix/decomposition/cholesky.rs.html#93">source</a><a href="#impl-Clone-for-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> Clone for <a class="struct" href="struct.Cholesky.html" title="struct rusty_machine::linalg::Cholesky">Cholesky</a><T><span class="where fmt-newline">where<br> T: Clone,</span></h3></section></summary><div class="impl-items"><details class="rustdoc-toggle method-toggle" open><summary><section id="method.clone" class="method trait-impl has-srclink"><a class="srclink rightside" href="../../src/rulinalg/matrix/decomposition/cholesky.rs.html#93">source</a><a href="#method.clone" class="anchor"></a><h4 class="code-header">fn <a class="fnname">clone</a>(&self) -> <a class="struct" href="struct.Cholesky.html" title="struct rusty_machine::linalg::Cholesky">Cholesky</a><T></h4></section></summary><div class='docblock'>Returns a copy of the value. <a>Read more</a></div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="method.clone_from" class="method trait-impl has-srclink"><span class="since rightside" title="Stable since Rust version 1.0.0">1.0.0</span><a href="#method.clone_from" class="anchor"></a><h4 class="code-header">const fn <a class="fnname">clone_from</a>(&mut self, source: &Self)</h4></section></summary><div class='docblock'>Performs copy-assignment from <code>source</code>. <a>Read more</a></div></details></div></details><details class="rustdoc-toggle implementors-toggle" open><summary><section id="impl-Debug-for-Cholesky%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="../../src/rulinalg/matrix/decomposition/cholesky.rs.html#93">source</a><a href="#impl-Debug-for-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> Debug for <a class="struct" href="struct.Cholesky.html" title="struct rusty_machine::linalg::Cholesky">Cholesky</a><T><span class="where fmt-newline">where<br> T: Debug,</span></h3></section></summary><div class="impl-items"><details class="rustdoc-toggle method-toggle" open><summary><section id="method.fmt" class="method trait-impl has-srclink"><a class="srclink rightside" href="../../src/rulinalg/matrix/decomposition/cholesky.rs.html#93">source</a><a href="#method.fmt" class="anchor"></a><h4 class="code-header">fn <a class="fnname">fmt</a>(&self, f: &mut Formatter<'_>) -> Result<(), Error></h4></section></summary><div class='docblock'>Formats the value using the given formatter. <a>Read more</a></div></details></div></details><details class="rustdoc-toggle implementors-toggle" open><summary><section id="impl-Decomposition-for-Cholesky%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="../../src/rulinalg/matrix/decomposition/cholesky.rs.html#237">source</a><a href="#impl-Decomposition-for-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> <a class="trait" href="trait.Decomposition.html" title="trait rusty_machine::linalg::Decomposition">Decomposition</a> for <a class="struct" href="struct.Cholesky.html" title="struct rusty_machine::linalg::Cholesky">Cholesky</a><T><span class="where fmt-newline">where<br> T: <a class="trait" href="../../num_traits/identities/trait.Zero.html" title="trait num_traits::identities::Zero">Zero</a>,</span></h3></section></summary><div class="impl-items"><details class="rustdoc-toggle" open><summary><section id="associatedtype.Factors" class="associatedtype trait-impl has-srclink"><a href="#associatedtype.Factors" class="anchor"></a><h4 class="code-header">type <a href="trait.Decomposition.html#associatedtype.Factors" class="associatedtype">Factors</a> = <a class="struct" href="struct.Matrix.html" title="struct rusty_machine::linalg::Matrix">Matrix</a><T></h4></section></summary><div class='docblock'>The type representing the ordered set of factors |
| that when multiplied yields the decomposed matrix. <a href="trait.Decomposition.html#associatedtype.Factors">Read more</a></div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="method.unpack" class="method trait-impl has-srclink"><a class="srclink rightside" href="../../src/rulinalg/matrix/decomposition/cholesky.rs.html#240">source</a><a href="#method.unpack" class="anchor"></a><h4 class="code-header">fn <a href="trait.Decomposition.html#tymethod.unpack" class="fnname">unpack</a>(self) -> <a class="struct" href="struct.Matrix.html" title="struct rusty_machine::linalg::Matrix">Matrix</a><T></h4></section></summary><div class='docblock'>Extract the individual factors from this decomposition.</div></details></div></details></div><h2 id="synthetic-implementations" class="small-section-header">Auto Trait Implementations<a href="#synthetic-implementations" class="anchor"></a></h2><div id="synthetic-implementations-list"><section id="impl-RefUnwindSafe-for-Cholesky%3CT%3E" class="impl has-srclink"><a href="#impl-RefUnwindSafe-for-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> RefUnwindSafe for <a class="struct" href="struct.Cholesky.html" title="struct rusty_machine::linalg::Cholesky">Cholesky</a><T><span class="where fmt-newline">where<br> T: RefUnwindSafe,</span></h3></section><section id="impl-Send-for-Cholesky%3CT%3E" class="impl has-srclink"><a href="#impl-Send-for-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> Send for <a class="struct" href="struct.Cholesky.html" title="struct rusty_machine::linalg::Cholesky">Cholesky</a><T><span class="where fmt-newline">where<br> T: Send,</span></h3></section><section id="impl-Sync-for-Cholesky%3CT%3E" class="impl has-srclink"><a href="#impl-Sync-for-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> Sync for <a class="struct" href="struct.Cholesky.html" title="struct rusty_machine::linalg::Cholesky">Cholesky</a><T><span class="where fmt-newline">where<br> T: Sync,</span></h3></section><section id="impl-Unpin-for-Cholesky%3CT%3E" class="impl has-srclink"><a href="#impl-Unpin-for-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> Unpin for <a class="struct" href="struct.Cholesky.html" title="struct rusty_machine::linalg::Cholesky">Cholesky</a><T><span class="where fmt-newline">where<br> T: Unpin,</span></h3></section><section id="impl-UnwindSafe-for-Cholesky%3CT%3E" class="impl has-srclink"><a href="#impl-UnwindSafe-for-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> UnwindSafe for <a class="struct" href="struct.Cholesky.html" title="struct rusty_machine::linalg::Cholesky">Cholesky</a><T><span class="where fmt-newline">where<br> T: UnwindSafe,</span></h3></section></div><h2 id="blanket-implementations" class="small-section-header">Blanket Implementations<a href="#blanket-implementations" class="anchor"></a></h2><div id="blanket-implementations-list"><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-Any-for-Cholesky%3CT%3E" class="impl has-srclink"><a href="#impl-Any-for-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> Any for T<span class="where fmt-newline">where<br> T: 'static + ?Sized,</span></h3></section></summary><div class="impl-items"><details class="rustdoc-toggle method-toggle" open><summary><section id="method.type_id" class="method trait-impl has-srclink"><a href="#method.type_id" class="anchor"></a><h4 class="code-header">fn <a class="fnname">type_id</a>(&self) -> TypeId</h4></section></summary><div class='docblock'>Gets the <code>TypeId</code> of <code>self</code>. <a>Read more</a></div></details></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-Borrow%3CT%3E-for-Cholesky%3CT%3E" class="impl has-srclink"><a href="#impl-Borrow%3CT%3E-for-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> Borrow<T> for T<span class="where fmt-newline">where<br> T: ?Sized,</span></h3></section></summary><div class="impl-items"><details class="rustdoc-toggle method-toggle" open><summary><section id="method.borrow" class="method trait-impl has-srclink"><span class="since rightside" title="const unstable">const: <a href="https://github.com/rust-lang/rust/issues/91522" title="Tracking issue for const_borrow">unstable</a></span><a href="#method.borrow" class="anchor"></a><h4 class="code-header">fn <a class="fnname">borrow</a>(&self) -> &T</h4></section></summary><div class='docblock'>Immutably borrows from an owned value. <a>Read more</a></div></details></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-BorrowMut%3CT%3E-for-Cholesky%3CT%3E" class="impl has-srclink"><a href="#impl-BorrowMut%3CT%3E-for-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> BorrowMut<T> for T<span class="where fmt-newline">where<br> T: ?Sized,</span></h3></section></summary><div class="impl-items"><details class="rustdoc-toggle method-toggle" open><summary><section id="method.borrow_mut" class="method trait-impl has-srclink"><span class="since rightside" title="const unstable">const: <a href="https://github.com/rust-lang/rust/issues/91522" title="Tracking issue for const_borrow">unstable</a></span><a href="#method.borrow_mut" class="anchor"></a><h4 class="code-header">fn <a class="fnname">borrow_mut</a>(&mut self) -> &mut T</h4></section></summary><div class='docblock'>Mutably borrows from an owned value. <a>Read more</a></div></details></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-From%3CT%3E-for-Cholesky%3CT%3E" class="impl has-srclink"><a href="#impl-From%3CT%3E-for-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> From<T> for T</h3></section></summary><div class="impl-items"><details class="rustdoc-toggle method-toggle" open><summary><section id="method.from" class="method trait-impl has-srclink"><span class="since rightside" title="const unstable">const: <a href="https://github.com/rust-lang/rust/issues/88674" title="Tracking issue for const_convert">unstable</a></span><a href="#method.from" class="anchor"></a><h4 class="code-header">fn <a class="fnname">from</a>(t: T) -> T</h4></section></summary><div class="docblock"><p>Returns the argument unchanged.</p> |
| </div></details></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-Into%3CU%3E-for-Cholesky%3CT%3E" class="impl has-srclink"><a href="#impl-Into%3CU%3E-for-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T, U> Into<U> for T<span class="where fmt-newline">where<br> U: From<T>,</span></h3></section></summary><div class="impl-items"><details class="rustdoc-toggle method-toggle" open><summary><section id="method.into" class="method trait-impl has-srclink"><span class="since rightside" title="const unstable">const: <a href="https://github.com/rust-lang/rust/issues/88674" title="Tracking issue for const_convert">unstable</a></span><a href="#method.into" class="anchor"></a><h4 class="code-header">fn <a class="fnname">into</a>(self) -> U</h4></section></summary><div class="docblock"><p>Calls <code>U::from(self)</code>.</p> |
| <p>That is, this conversion is whatever the implementation of |
| <code>[From]<T> for U</code> chooses to do.</p> |
| </div></details></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-ToOwned-for-Cholesky%3CT%3E" class="impl has-srclink"><a href="#impl-ToOwned-for-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> ToOwned for T<span class="where fmt-newline">where<br> T: Clone,</span></h3></section></summary><div class="impl-items"><details class="rustdoc-toggle" open><summary><section id="associatedtype.Owned" class="associatedtype trait-impl has-srclink"><a href="#associatedtype.Owned" class="anchor"></a><h4 class="code-header">type <a class="associatedtype">Owned</a> = T</h4></section></summary><div class='docblock'>The resulting type after obtaining ownership.</div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="method.to_owned" class="method trait-impl has-srclink"><a href="#method.to_owned" class="anchor"></a><h4 class="code-header">fn <a class="fnname">to_owned</a>(&self) -> T</h4></section></summary><div class='docblock'>Creates owned data from borrowed data, usually by cloning. <a>Read more</a></div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="method.clone_into" class="method trait-impl has-srclink"><a href="#method.clone_into" class="anchor"></a><h4 class="code-header">fn <a class="fnname">clone_into</a>(&self, target: &mut T)</h4></section></summary><div class='docblock'>Uses borrowed data to replace owned data, usually by cloning. <a>Read more</a></div></details></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-TryFrom%3CU%3E-for-Cholesky%3CT%3E" class="impl has-srclink"><a href="#impl-TryFrom%3CU%3E-for-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T, U> TryFrom<U> for T<span class="where fmt-newline">where<br> U: Into<T>,</span></h3></section></summary><div class="impl-items"><details class="rustdoc-toggle" open><summary><section id="associatedtype.Error-1" class="associatedtype trait-impl has-srclink"><a href="#associatedtype.Error-1" class="anchor"></a><h4 class="code-header">type <a class="associatedtype">Error</a> = Infallible</h4></section></summary><div class='docblock'>The type returned in the event of a conversion error.</div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="method.try_from" class="method trait-impl has-srclink"><span class="since rightside" title="const unstable">const: <a href="https://github.com/rust-lang/rust/issues/88674" title="Tracking issue for const_convert">unstable</a></span><a href="#method.try_from" class="anchor"></a><h4 class="code-header">fn <a class="fnname">try_from</a>(value: U) -> Result<T, <T as TryFrom<U>>::Error></h4></section></summary><div class='docblock'>Performs the conversion.</div></details></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-TryInto%3CU%3E-for-Cholesky%3CT%3E" class="impl has-srclink"><a href="#impl-TryInto%3CU%3E-for-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T, U> TryInto<U> for T<span class="where fmt-newline">where<br> U: TryFrom<T>,</span></h3></section></summary><div class="impl-items"><details class="rustdoc-toggle" open><summary><section id="associatedtype.Error" class="associatedtype trait-impl has-srclink"><a href="#associatedtype.Error" class="anchor"></a><h4 class="code-header">type <a class="associatedtype">Error</a> = <U as TryFrom<T>>::Error</h4></section></summary><div class='docblock'>The type returned in the event of a conversion error.</div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="method.try_into" class="method trait-impl has-srclink"><span class="since rightside" title="const unstable">const: <a href="https://github.com/rust-lang/rust/issues/88674" title="Tracking issue for const_convert">unstable</a></span><a href="#method.try_into" class="anchor"></a><h4 class="code-header">fn <a class="fnname">try_into</a>(self) -> Result<U, <U as TryFrom<T>>::Error></h4></section></summary><div class='docblock'>Performs the conversion.</div></details></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-VZip%3CV%3E-for-Cholesky%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="../../src/ppv_lite86/types.rs.html#221">source</a><a href="#impl-VZip%3CV%3E-for-Cholesky%3CT%3E" class="anchor"></a><h3 class="code-header">impl<V, T> <a class="trait" href="../../ppv_lite86/types/trait.VZip.html" title="trait ppv_lite86::types::VZip">VZip</a><V> for T<span class="where fmt-newline">where<br> V: <a class="trait" href="../../ppv_lite86/types/trait.MultiLane.html" title="trait ppv_lite86::types::MultiLane">MultiLane</a><T>,</span></h3></section></summary><div class="impl-items"><section id="method.vzip" class="method trait-impl has-srclink"><a class="srclink rightside" href="../../src/ppv_lite86/types.rs.html#226">source</a><a href="#method.vzip" class="anchor"></a><h4 class="code-header">fn <a href="../../ppv_lite86/types/trait.VZip.html#tymethod.vzip" class="fnname">vzip</a>(self) -> V</h4></section></div></details></div></section></div></main><div id="rustdoc-vars" data-root-path="../../" data-current-crate="rusty_machine" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |
