| <!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="QR decomposition based on Householder reflections."><meta name="keywords" content="rust, rustlang, rust-lang, HouseholderQr"><title>HouseholderQr 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 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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="#">HouseholderQr</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.q">q</a></li><li><a href="#method.unpack_thin">unpack_thin</a></li></ul><h3><a href="#trait-implementations">Trait Implementations</a></h3><ul class="block"><li><a href="#impl-Clone-for-HouseholderQr%3CT%3E">Clone</a></li><li><a href="#impl-Debug-for-HouseholderQr%3CT%3E">Debug</a></li><li><a href="#impl-Decomposition-for-HouseholderQr%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-HouseholderQr%3CT%3E">RefUnwindSafe</a></li><li><a href="#impl-Send-for-HouseholderQr%3CT%3E">Send</a></li><li><a href="#impl-Sync-for-HouseholderQr%3CT%3E">Sync</a></li><li><a href="#impl-Unpin-for-HouseholderQr%3CT%3E">Unpin</a></li><li><a href="#impl-UnwindSafe-for-HouseholderQr%3CT%3E">UnwindSafe</a></li></ul><h3><a href="#blanket-implementations">Blanket Implementations</a></h3><ul class="block"><li><a href="#impl-Any-for-HouseholderQr%3CT%3E">Any</a></li><li><a href="#impl-Borrow%3CT%3E-for-HouseholderQr%3CT%3E">Borrow<T></a></li><li><a href="#impl-BorrowMut%3CT%3E-for-HouseholderQr%3CT%3E">BorrowMut<T></a></li><li><a href="#impl-From%3CT%3E-for-HouseholderQr%3CT%3E">From<T></a></li><li><a href="#impl-Into%3CU%3E-for-HouseholderQr%3CT%3E">Into<U></a></li><li><a href="#impl-ToOwned-for-HouseholderQr%3CT%3E">ToOwned</a></li><li><a href="#impl-TryFrom%3CU%3E-for-HouseholderQr%3CT%3E">TryFrom<U></a></li><li><a href="#impl-TryInto%3CU%3E-for-HouseholderQr%3CT%3E">TryInto<U></a></li><li><a href="#impl-VZip%3CV%3E-for-HouseholderQr%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="#">HouseholderQr</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/qr.rs.html#172">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 HouseholderQr<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>QR decomposition based on Householder reflections.</p> |
| <p>For any <code>m x n</code> matrix <code>A</code>, there exist an <code>m x m</code> |
| orthogonal matrix <code>Q</code> and an <code>m x n</code> upper trapezoidal |
| (triangular) matrix <code>R</code> such that</p> |
| <div class="example-wrap"><pre class="language-text"><code>A = QR.</code></pre></div> |
| <p><code>HouseholderQr</code> holds the result of a QR decomposition |
| procedure based on Householder reflections. The full |
| factors <code>Q</code> and <code>R</code> can be acquired by calling <code>unpack()</code>. |
| However, it turns out that the orthogonal factor <code>Q</code> |
| can be represented much more efficiently than as a |
| full <code>m x m</code> matrix. For this purpose, the <a href="#method.q">q()</a> |
| method provides access to an instance of |
| <a href="struct.HouseholderComposition.html">HouseholderComposition</a> |
| which allows the efficient application of the (implicit) |
| <code>Q</code> matrix.</p> |
| <p>For some applications, it is sufficient to compute a |
| <em>thin</em> (or <em>reduced</em>) QR decomposition. The thin QR decomposition |
| can be obtained by calling <a href="#method.unpack_thin">unpack_thin()</a> |
| on the decomposition object.</p> |
| <h2 id="examples"><a href="#examples">Examples</a></h2> |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>rulinalg::matrix::Matrix; |
| <span class="kw">use </span>rulinalg::matrix::decomposition::{ |
| Decomposition, HouseholderQr, QR |
| }; |
| |
| <span class="kw">let </span>a = <span class="macro">matrix!</span>[ <span class="number">3.0</span>, <span class="number">2.0</span>; |
| -<span class="number">5.0</span>, <span class="number">1.0</span>; |
| <span class="number">4.0</span>, -<span class="number">2.0 </span>]; |
| <span class="kw">let </span>identity = Matrix::identity(<span class="number">3</span>); |
| |
| <span class="kw">let </span>qr = HouseholderQr::decompose(a.clone()); |
| <span class="kw">let </span>QR { q, r } = qr.unpack(); |
| |
| <span class="comment">// Check that `Q` is orthogonal |
| </span><span class="macro">assert_matrix_eq!</span>(<span class="kw-2">&</span>q * q.transpose(), identity, comp = float); |
| <span class="macro">assert_matrix_eq!</span>(q.transpose() * <span class="kw-2">&</span>q, identity, comp = float); |
| |
| <span class="comment">// Check that `A = QR` |
| </span><span class="macro">assert_matrix_eq!</span>(q * r, a, comp = float);</code></pre></div> |
| <h2 id="internal-storage-format"><a href="#internal-storage-format">Internal storage format</a></h2> |
| <p>Upon decomposition, the <code>HouseholderQr</code> struct takes ownership |
| of the matrix and repurposes its storage to compactly |
| store the factors <code>Q</code> and <code>R</code>. |
| In addition, a vector <code>tau</code> of size <code>min(m, n)</code> |
| holds auxiliary information about the Householder reflectors |
| which together constitute the <code>Q</code> matrix.</p> |
| <p>Specifically, given an input matrix <code>A</code>, |
| the upper triangular factor <code>R</code> is stored in <code>A_ij</code> for |
| <code>j >= i</code>. The orthogonal factor <code>Q</code> is implicitly stored |
| as the composition of <code>p := min(m, n)</code> Householder reflectors |
| <code>Q_i</code>, such that</p> |
| <div class="example-wrap"><pre class="language-text"><code>Q = Q_1 * Q_2 * ... * Q_p.</code></pre></div> |
| <p>Each such Householder reflection <code>Q_i</code> corresponds to a |
| transformation of the form (using MATLAB-like colon notation)</p> |
| <div class="example-wrap"><pre class="language-text"><code>Q_i [1:(i-1), 1:(i-1)] = I |
| Q_i [i:m, i:m] = I - τ_i * v_i * transpose(v_i)</code></pre></div> |
| <p>where <code>I</code> denotes the identity matrix of appropriate size, |
| <code>v_i</code> is the <em>Householder vector</em> normalized in such a way that |
| its first element is implicitly <code>1</code> (and thus does not need to |
| be stored) and <code>τ_i</code> is an appropriate scale factor. Each vector |
| <code>v_i</code> has length <code>m - i + 1</code>, and since the first element does not |
| need to be stored, each <code>v_i</code> can be stored in column <code>i</code> of |
| the matrix <code>A</code>.</p> |
| <p>The scale factors <code>τ_i</code> are stored in a separate vector.</p> |
| <p>This storage scheme should be compatible with LAPACK, although |
| this has yet to be put to the test. For the same reason, |
| the internal storage is not exposed in the public API at this point.</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-HouseholderQr%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="../../src/rulinalg/matrix/decomposition/qr.rs.html#177">source</a><a href="#impl-HouseholderQr%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> <a class="struct" href="struct.HouseholderQr.html" title="struct rusty_machine::linalg::HouseholderQr">HouseholderQr</a><T><span class="where fmt-newline">where<br> T: <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/qr.rs.html#180">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>) -> <a class="struct" href="struct.HouseholderQr.html" title="struct rusty_machine::linalg::HouseholderQr">HouseholderQr</a><T></h4></section></summary><div class="docblock"><p>Decomposes the given matrix into implicitly stored factors |
| <code>Q</code> and <code>R</code> as described in the struct documentation.</p> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="method.q" class="method has-srclink"><a class="srclink rightside" href="../../src/rulinalg/matrix/decomposition/qr.rs.html#228">source</a><h4 class="code-header">pub fn <a href="#method.q" class="fnname">q</a>(&self) -> <a class="struct" href="struct.HouseholderComposition.html" title="struct rusty_machine::linalg::HouseholderComposition">HouseholderComposition</a><'_, T></h4></section></summary><div class="docblock"><p>Returns the orthogonal factor <code>Q</code> as an instance of a |
| <a href="struct.HouseholderComposition.html">HouseholderComposition</a> |
| operator.</p> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="method.unpack_thin" class="method has-srclink"><a class="srclink rightside" href="../../src/rulinalg/matrix/decomposition/qr.rs.html#250">source</a><h4 class="code-header">pub fn <a href="#method.unpack_thin" class="fnname">unpack_thin</a>(self) -> <a class="struct" href="struct.ThinQR.html" title="struct rusty_machine::linalg::ThinQR">ThinQR</a><T></h4></section></summary><div class="docblock"><p>Computes the <em>thin</em> (or reduced) QR decomposition.</p> |
| <p>If <code>m <= n</code>, the thin QR decomposition coincides with the |
| usual QR decomposition. See <a href="struct.ThinQR.html">ThinQR</a> |
| for details.</p> |
| <h5 id="examples-1"><a href="#examples-1">Examples</a></h5> |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>rulinalg::matrix::decomposition::{HouseholderQr, ThinQR}; |
| <span class="kw">let </span>x = <span class="macro">matrix!</span>[<span class="number">3.0</span>, <span class="number">2.0</span>; |
| <span class="number">1.0</span>, <span class="number">2.0</span>; |
| <span class="number">4.0</span>, <span class="number">5.0</span>]; |
| <span class="kw">let </span>ThinQR { q1, r1 } = HouseholderQr::decompose(x).unpack_thin();</code></pre></div> |
| </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-HouseholderQr%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="../../src/rulinalg/matrix/decomposition/qr.rs.html#171">source</a><a href="#impl-Clone-for-HouseholderQr%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html" title="trait core::clone::Clone">Clone</a> for <a class="struct" href="struct.HouseholderQr.html" title="struct rusty_machine::linalg::HouseholderQr">HouseholderQr</a><T><span class="where fmt-newline">where<br> T: <a class="trait" href="https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html" title="trait core::clone::Clone">Clone</a>,</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/qr.rs.html#171">source</a><a href="#method.clone" class="anchor"></a><h4 class="code-header">fn <a href="https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html#tymethod.clone" class="fnname">clone</a>(&self) -> <a class="struct" href="struct.HouseholderQr.html" title="struct rusty_machine::linalg::HouseholderQr">HouseholderQr</a><T></h4></section></summary><div class='docblock'>Returns a copy of the value. <a href="https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html#tymethod.clone">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="rightside"><span class="since" title="Stable since Rust version 1.0.0">1.0.0</span> · <a class="srclink" href="https://doc.rust-lang.org/nightly/src/core/clone.rs.html#132-134">source</a></span><a href="#method.clone_from" class="anchor"></a><h4 class="code-header">const fn <a href="https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html#method.clone_from" class="fnname">clone_from</a>(&mut self, source: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Self)</h4></section></summary><div class='docblock'>Performs copy-assignment from <code>source</code>. <a href="https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html#method.clone_from">Read more</a></div></details></div></details><details class="rustdoc-toggle implementors-toggle" open><summary><section id="impl-Debug-for-HouseholderQr%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="../../src/rulinalg/matrix/decomposition/qr.rs.html#171">source</a><a href="#impl-Debug-for-HouseholderQr%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/core/fmt/trait.Debug.html" title="trait core::fmt::Debug">Debug</a> for <a class="struct" href="struct.HouseholderQr.html" title="struct rusty_machine::linalg::HouseholderQr">HouseholderQr</a><T><span class="where fmt-newline">where<br> T: <a class="trait" href="https://doc.rust-lang.org/nightly/core/fmt/trait.Debug.html" title="trait core::fmt::Debug">Debug</a>,</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/qr.rs.html#171">source</a><a href="#method.fmt" class="anchor"></a><h4 class="code-header">fn <a href="https://doc.rust-lang.org/nightly/core/fmt/trait.Debug.html#tymethod.fmt" class="fnname">fmt</a>(&self, f: &mut <a class="struct" href="https://doc.rust-lang.org/nightly/core/fmt/struct.Formatter.html" title="struct core::fmt::Formatter">Formatter</a><'_>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/result/enum.Result.html" title="enum core::result::Result">Result</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.unit.html">()</a>, <a class="struct" href="https://doc.rust-lang.org/nightly/core/fmt/struct.Error.html" title="struct core::fmt::Error">Error</a>></h4></section></summary><div class='docblock'>Formats the value using the given formatter. <a href="https://doc.rust-lang.org/nightly/core/fmt/trait.Debug.html#tymethod.fmt">Read more</a></div></details></div></details><details class="rustdoc-toggle implementors-toggle" open><summary><section id="impl-Decomposition-for-HouseholderQr%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="../../src/rulinalg/matrix/decomposition/qr.rs.html#278">source</a><a href="#impl-Decomposition-for-HouseholderQr%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.HouseholderQr.html" title="struct rusty_machine::linalg::HouseholderQr">HouseholderQr</a><T><span class="where fmt-newline">where<br> T: <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" 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.QR.html" title="struct rusty_machine::linalg::QR">QR</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/qr.rs.html#280">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.QR.html" title="struct rusty_machine::linalg::QR">QR</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-HouseholderQr%3CT%3E" class="impl has-srclink"><a href="#impl-RefUnwindSafe-for-HouseholderQr%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/core/panic/unwind_safe/trait.RefUnwindSafe.html" title="trait core::panic::unwind_safe::RefUnwindSafe">RefUnwindSafe</a> for <a class="struct" href="struct.HouseholderQr.html" title="struct rusty_machine::linalg::HouseholderQr">HouseholderQr</a><T><span class="where fmt-newline">where<br> T: <a class="trait" href="https://doc.rust-lang.org/nightly/core/panic/unwind_safe/trait.RefUnwindSafe.html" title="trait core::panic::unwind_safe::RefUnwindSafe">RefUnwindSafe</a>,</span></h3></section><section id="impl-Send-for-HouseholderQr%3CT%3E" class="impl has-srclink"><a href="#impl-Send-for-HouseholderQr%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Send.html" title="trait core::marker::Send">Send</a> for <a class="struct" href="struct.HouseholderQr.html" title="struct rusty_machine::linalg::HouseholderQr">HouseholderQr</a><T><span class="where fmt-newline">where<br> T: <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Send.html" title="trait core::marker::Send">Send</a>,</span></h3></section><section id="impl-Sync-for-HouseholderQr%3CT%3E" class="impl has-srclink"><a href="#impl-Sync-for-HouseholderQr%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sync.html" title="trait core::marker::Sync">Sync</a> for <a class="struct" href="struct.HouseholderQr.html" title="struct rusty_machine::linalg::HouseholderQr">HouseholderQr</a><T><span class="where fmt-newline">where<br> T: <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sync.html" title="trait core::marker::Sync">Sync</a>,</span></h3></section><section id="impl-Unpin-for-HouseholderQr%3CT%3E" class="impl has-srclink"><a href="#impl-Unpin-for-HouseholderQr%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Unpin.html" title="trait core::marker::Unpin">Unpin</a> for <a class="struct" href="struct.HouseholderQr.html" title="struct rusty_machine::linalg::HouseholderQr">HouseholderQr</a><T><span class="where fmt-newline">where<br> T: <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Unpin.html" title="trait core::marker::Unpin">Unpin</a>,</span></h3></section><section id="impl-UnwindSafe-for-HouseholderQr%3CT%3E" class="impl has-srclink"><a href="#impl-UnwindSafe-for-HouseholderQr%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/core/panic/unwind_safe/trait.UnwindSafe.html" title="trait core::panic::unwind_safe::UnwindSafe">UnwindSafe</a> for <a class="struct" href="struct.HouseholderQr.html" title="struct rusty_machine::linalg::HouseholderQr">HouseholderQr</a><T><span class="where fmt-newline">where<br> T: <a class="trait" href="https://doc.rust-lang.org/nightly/core/panic/unwind_safe/trait.UnwindSafe.html" title="trait core::panic::unwind_safe::UnwindSafe">UnwindSafe</a>,</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-HouseholderQr%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="https://doc.rust-lang.org/nightly/src/core/any.rs.html#200">source</a><a href="#impl-Any-for-HouseholderQr%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/core/any/trait.Any.html" title="trait core::any::Any">Any</a> for T<span class="where fmt-newline">where<br> T: 'static + ?<a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sized.html" title="trait core::marker::Sized">Sized</a>,</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 class="srclink rightside" href="https://doc.rust-lang.org/nightly/src/core/any.rs.html#201">source</a><a href="#method.type_id" class="anchor"></a><h4 class="code-header">fn <a href="https://doc.rust-lang.org/nightly/core/any/trait.Any.html#tymethod.type_id" class="fnname">type_id</a>(&self) -> <a class="struct" href="https://doc.rust-lang.org/nightly/core/any/struct.TypeId.html" title="struct core::any::TypeId">TypeId</a></h4></section></summary><div class='docblock'>Gets the <code>TypeId</code> of <code>self</code>. <a href="https://doc.rust-lang.org/nightly/core/any/trait.Any.html#tymethod.type_id">Read more</a></div></details></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-Borrow%3CT%3E-for-HouseholderQr%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="https://doc.rust-lang.org/nightly/src/core/borrow.rs.html#211">source</a><a href="#impl-Borrow%3CT%3E-for-HouseholderQr%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/core/borrow/trait.Borrow.html" title="trait core::borrow::Borrow">Borrow</a><T> for T<span class="where fmt-newline">where<br> T: ?<a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sized.html" title="trait core::marker::Sized">Sized</a>,</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="rightside"><span class="since" title="const unstable">const: <a href="https://github.com/rust-lang/rust/issues/91522" title="Tracking issue for const_borrow">unstable</a></span> · <a class="srclink" href="https://doc.rust-lang.org/nightly/src/core/borrow.rs.html#213">source</a></span><a href="#method.borrow" class="anchor"></a><h4 class="code-header">fn <a href="https://doc.rust-lang.org/nightly/core/borrow/trait.Borrow.html#tymethod.borrow" class="fnname">borrow</a>(&self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>T</h4></section></summary><div class='docblock'>Immutably borrows from an owned value. <a href="https://doc.rust-lang.org/nightly/core/borrow/trait.Borrow.html#tymethod.borrow">Read more</a></div></details></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-BorrowMut%3CT%3E-for-HouseholderQr%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="https://doc.rust-lang.org/nightly/src/core/borrow.rs.html#220">source</a><a href="#impl-BorrowMut%3CT%3E-for-HouseholderQr%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/core/borrow/trait.BorrowMut.html" title="trait core::borrow::BorrowMut">BorrowMut</a><T> for T<span class="where fmt-newline">where<br> T: ?<a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sized.html" title="trait core::marker::Sized">Sized</a>,</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="rightside"><span class="since" title="const unstable">const: <a href="https://github.com/rust-lang/rust/issues/91522" title="Tracking issue for const_borrow">unstable</a></span> · <a class="srclink" href="https://doc.rust-lang.org/nightly/src/core/borrow.rs.html#221">source</a></span><a href="#method.borrow_mut" class="anchor"></a><h4 class="code-header">fn <a href="https://doc.rust-lang.org/nightly/core/borrow/trait.BorrowMut.html#tymethod.borrow_mut" class="fnname">borrow_mut</a>(&mut self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&mut </a>T</h4></section></summary><div class='docblock'>Mutably borrows from an owned value. <a href="https://doc.rust-lang.org/nightly/core/borrow/trait.BorrowMut.html#tymethod.borrow_mut">Read more</a></div></details></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-From%3CT%3E-for-HouseholderQr%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="https://doc.rust-lang.org/nightly/src/core/convert/mod.rs.html#733">source</a><a href="#impl-From%3CT%3E-for-HouseholderQr%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.From.html" title="trait core::convert::From">From</a><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="rightside"><span class="since" title="const unstable">const: <a href="https://github.com/rust-lang/rust/issues/88674" title="Tracking issue for const_convert">unstable</a></span> · <a class="srclink" href="https://doc.rust-lang.org/nightly/src/core/convert/mod.rs.html#736">source</a></span><a href="#method.from" class="anchor"></a><h4 class="code-header">fn <a href="https://doc.rust-lang.org/nightly/core/convert/trait.From.html#tymethod.from" 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-HouseholderQr%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="https://doc.rust-lang.org/nightly/src/core/convert/mod.rs.html#717">source</a><a href="#impl-Into%3CU%3E-for-HouseholderQr%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T, U> <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.Into.html" title="trait core::convert::Into">Into</a><U> for T<span class="where fmt-newline">where<br> U: <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.From.html" title="trait core::convert::From">From</a><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="rightside"><span class="since" title="const unstable">const: <a href="https://github.com/rust-lang/rust/issues/88674" title="Tracking issue for const_convert">unstable</a></span> · <a class="srclink" href="https://doc.rust-lang.org/nightly/src/core/convert/mod.rs.html#725">source</a></span><a href="#method.into" class="anchor"></a><h4 class="code-header">fn <a href="https://doc.rust-lang.org/nightly/core/convert/trait.Into.html#tymethod.into" 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><a href="https://doc.rust-lang.org/nightly/core/convert/trait.From.html" title="From">From</a><T> for U</code> chooses to do.</p> |
| </div></details></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-ToOwned-for-HouseholderQr%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="https://doc.rust-lang.org/nightly/src/alloc/borrow.rs.html#83">source</a><a href="#impl-ToOwned-for-HouseholderQr%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/alloc/borrow/trait.ToOwned.html" title="trait alloc::borrow::ToOwned">ToOwned</a> for T<span class="where fmt-newline">where<br> T: <a class="trait" href="https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html" title="trait core::clone::Clone">Clone</a>,</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 href="https://doc.rust-lang.org/nightly/alloc/borrow/trait.ToOwned.html#associatedtype.Owned" 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 class="srclink rightside" href="https://doc.rust-lang.org/nightly/src/alloc/borrow.rs.html#88">source</a><a href="#method.to_owned" class="anchor"></a><h4 class="code-header">fn <a href="https://doc.rust-lang.org/nightly/alloc/borrow/trait.ToOwned.html#tymethod.to_owned" class="fnname">to_owned</a>(&self) -> T</h4></section></summary><div class='docblock'>Creates owned data from borrowed data, usually by cloning. <a href="https://doc.rust-lang.org/nightly/alloc/borrow/trait.ToOwned.html#tymethod.to_owned">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 class="srclink rightside" href="https://doc.rust-lang.org/nightly/src/alloc/borrow.rs.html#92">source</a><a href="#method.clone_into" class="anchor"></a><h4 class="code-header">fn <a href="https://doc.rust-lang.org/nightly/alloc/borrow/trait.ToOwned.html#method.clone_into" class="fnname">clone_into</a>(&self, target: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&mut </a>T)</h4></section></summary><div class='docblock'>Uses borrowed data to replace owned data, usually by cloning. <a href="https://doc.rust-lang.org/nightly/alloc/borrow/trait.ToOwned.html#method.clone_into">Read more</a></div></details></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-TryFrom%3CU%3E-for-HouseholderQr%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="https://doc.rust-lang.org/nightly/src/core/convert/mod.rs.html#775">source</a><a href="#impl-TryFrom%3CU%3E-for-HouseholderQr%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T, U> <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html" title="trait core::convert::TryFrom">TryFrom</a><U> for T<span class="where fmt-newline">where<br> U: <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.Into.html" title="trait core::convert::Into">Into</a><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 href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html#associatedtype.Error" class="associatedtype">Error</a> = <a class="enum" href="https://doc.rust-lang.org/nightly/core/convert/enum.Infallible.html" title="enum core::convert::Infallible">Infallible</a></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="rightside"><span class="since" title="const unstable">const: <a href="https://github.com/rust-lang/rust/issues/88674" title="Tracking issue for const_convert">unstable</a></span> · <a class="srclink" href="https://doc.rust-lang.org/nightly/src/core/convert/mod.rs.html#781">source</a></span><a href="#method.try_from" class="anchor"></a><h4 class="code-header">fn <a href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html#tymethod.try_from" class="fnname">try_from</a>(value: U) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/result/enum.Result.html" title="enum core::result::Result">Result</a><T, <T as <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html" title="trait core::convert::TryFrom">TryFrom</a><U>>::<a class="associatedtype" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html#associatedtype.Error" title="type core::convert::TryFrom::Error">Error</a>></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-HouseholderQr%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="https://doc.rust-lang.org/nightly/src/core/convert/mod.rs.html#760">source</a><a href="#impl-TryInto%3CU%3E-for-HouseholderQr%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T, U> <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryInto.html" title="trait core::convert::TryInto">TryInto</a><U> for T<span class="where fmt-newline">where<br> U: <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html" title="trait core::convert::TryFrom">TryFrom</a><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 href="https://doc.rust-lang.org/nightly/core/convert/trait.TryInto.html#associatedtype.Error" class="associatedtype">Error</a> = <U as <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html" title="trait core::convert::TryFrom">TryFrom</a><T>>::<a class="associatedtype" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html#associatedtype.Error" title="type core::convert::TryFrom::Error">Error</a></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="rightside"><span class="since" title="const unstable">const: <a href="https://github.com/rust-lang/rust/issues/88674" title="Tracking issue for const_convert">unstable</a></span> · <a class="srclink" href="https://doc.rust-lang.org/nightly/src/core/convert/mod.rs.html#766">source</a></span><a href="#method.try_into" class="anchor"></a><h4 class="code-header">fn <a href="https://doc.rust-lang.org/nightly/core/convert/trait.TryInto.html#tymethod.try_into" class="fnname">try_into</a>(self) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/result/enum.Result.html" title="enum core::result::Result">Result</a><U, <U as <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html" title="trait core::convert::TryFrom">TryFrom</a><T>>::<a class="associatedtype" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html#associatedtype.Error" title="type core::convert::TryFrom::Error">Error</a>></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-HouseholderQr%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-HouseholderQr%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> |
