| <!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="The result of computing a thin (or reduced) QR decomposition."><meta name="keywords" content="rust, rustlang, rust-lang, ThinQR"><title>ThinQR in rulinalg::matrix::decomposition - 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="mobile-topbar"><button class="sidebar-menu-toggle">☰</button><a class="sidebar-logo" href="../../../rulinalg/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="../../../rulinalg/index.html"><div class="logo-container"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></div></a><h2 class="location"><a href="#">ThinQR</a></h2><div class="sidebar-elems"><section><h3><a href="#fields">Fields</a></h3><ul class="block"><li><a href="#structfield.q1">q1</a></li><li><a href="#structfield.r1">r1</a></li></ul><h3><a href="#trait-implementations">Trait Implementations</a></h3><ul class="block"><li><a href="#impl-Clone-for-ThinQR%3CT%3E">Clone</a></li><li><a href="#impl-Debug-for-ThinQR%3CT%3E">Debug</a></li></ul><h3><a href="#synthetic-implementations">Auto Trait Implementations</a></h3><ul class="block"><li><a href="#impl-RefUnwindSafe-for-ThinQR%3CT%3E">RefUnwindSafe</a></li><li><a href="#impl-Send-for-ThinQR%3CT%3E">Send</a></li><li><a href="#impl-Sync-for-ThinQR%3CT%3E">Sync</a></li><li><a href="#impl-Unpin-for-ThinQR%3CT%3E">Unpin</a></li><li><a href="#impl-UnwindSafe-for-ThinQR%3CT%3E">UnwindSafe</a></li></ul><h3><a href="#blanket-implementations">Blanket Implementations</a></h3><ul class="block"><li><a href="#impl-Any-for-ThinQR%3CT%3E">Any</a></li><li><a href="#impl-Borrow%3CT%3E-for-ThinQR%3CT%3E">Borrow<T></a></li><li><a href="#impl-BorrowMut%3CT%3E-for-ThinQR%3CT%3E">BorrowMut<T></a></li><li><a href="#impl-From%3CT%3E-for-ThinQR%3CT%3E">From<T></a></li><li><a href="#impl-Into%3CU%3E-for-ThinQR%3CT%3E">Into<U></a></li><li><a href="#impl-ToOwned-for-ThinQR%3CT%3E">ToOwned</a></li><li><a href="#impl-TryFrom%3CU%3E-for-ThinQR%3CT%3E">TryFrom<U></a></li><li><a href="#impl-TryInto%3CU%3E-for-ThinQR%3CT%3E">TryInto<U></a></li></ul></section><h2><a href="index.html">In rulinalg::matrix::decomposition</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">rulinalg</a>::<wbr><a href="../index.html">matrix</a>::<wbr><a href="index.html">decomposition</a>::<wbr><a class="struct" href="#">ThinQR</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#73-78">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 ThinQR<T> { |
| pub q1: <a class="struct" href="../struct.Matrix.html" title="struct rulinalg::matrix::Matrix">Matrix</a><T>, |
| pub r1: <a class="struct" href="../struct.Matrix.html" title="struct rulinalg::matrix::Matrix">Matrix</a><T>, |
| }</code></pre></div><details class="rustdoc-toggle top-doc" open><summary class="hideme"><span>Expand description</span></summary><div class="docblock"><p>The result of computing a <em>thin</em> (or <em>reduced</em>) QR decomposition.</p> |
| <p>Let <code>A</code> denote the <code>m x n</code> matrix given by <code>A = QR</code>. |
| Then <code>Q</code> is an <code>m x m</code> orthogonal matrix, and <code>R</code> |
| is an <code>m x n</code> upper trapezoidal matrix.</p> |
| <p>If <code>m > n</code>, we may write</p> |
| <div class="example-wrap"><pre class="language-text"><code>A = QR = [ Q1 Q2 ] [ R1 ] = Q1 R1 |
| [ 0 ]</code></pre></div> |
| <p>where <code>Q1</code> is an <code>m x n</code> matrix with orthogonal columns, |
| and <code>R1</code> is an <code>n x n</code> upper triangular matrix. |
| For some applications, the remaining (m - n) columns |
| of the full <code>Q</code> matrix are not needed, in which case |
| the thin QR decomposition is substantially cheaper if |
| <code>m >> n</code>.</p> |
| <p>If <code>m <= n</code>, then the thin QR decomposition coincides with |
| the usual decomposition. See <a href="struct.QR.html">QR</a> for details.</p> |
| <p>To actually compute the QR decomposition, see |
| <a href="struct.HouseholderQr.html">Householder QR</a>.</p> |
| </div></details><h2 id="fields" class="fields small-section-header">Fields<a href="#fields" class="anchor"></a></h2><span id="structfield.q1" class="structfield small-section-header"><a href="#structfield.q1" class="anchor field"></a><code>q1: <a class="struct" href="../struct.Matrix.html" title="struct rulinalg::matrix::Matrix">Matrix</a><T></code></span><div class="docblock"><p>The matrix <code>Q1</code> in the decomposition <code>A = Q1 R1</code>.</p> |
| </div><span id="structfield.r1" class="structfield small-section-header"><a href="#structfield.r1" class="anchor field"></a><code>r1: <a class="struct" href="../struct.Matrix.html" title="struct rulinalg::matrix::Matrix">Matrix</a><T></code></span><div class="docblock"><p>The upper-triangular matrix <code>R1</code> in the decomposition <code>A = Q1 R1</code>.</p> |
| </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-ThinQR%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="../../../src/rulinalg/matrix/decomposition/qr.rs.html#72">source</a><a href="#impl-Clone-for-ThinQR%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T: Clone> Clone for <a class="struct" href="struct.ThinQR.html" title="struct rulinalg::matrix::decomposition::ThinQR">ThinQR</a><T></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#72">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.ThinQR.html" title="struct rulinalg::matrix::decomposition::ThinQR">ThinQR</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-ThinQR%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="../../../src/rulinalg/matrix/decomposition/qr.rs.html#72">source</a><a href="#impl-Debug-for-ThinQR%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T: Debug> Debug for <a class="struct" href="struct.ThinQR.html" title="struct rulinalg::matrix::decomposition::ThinQR">ThinQR</a><T></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#72">source</a><a href="#method.fmt" class="anchor"></a><h4 class="code-header">fn <a class="fnname">fmt</a>(&self, f: &mut Formatter<'_>) -> Result</h4></section></summary><div class='docblock'>Formats the value using the given formatter. <a>Read more</a></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-ThinQR%3CT%3E" class="impl has-srclink"><a href="#impl-RefUnwindSafe-for-ThinQR%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> RefUnwindSafe for <a class="struct" href="struct.ThinQR.html" title="struct rulinalg::matrix::decomposition::ThinQR">ThinQR</a><T><span class="where fmt-newline">where<br> T: RefUnwindSafe,</span></h3></section><section id="impl-Send-for-ThinQR%3CT%3E" class="impl has-srclink"><a href="#impl-Send-for-ThinQR%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> Send for <a class="struct" href="struct.ThinQR.html" title="struct rulinalg::matrix::decomposition::ThinQR">ThinQR</a><T><span class="where fmt-newline">where<br> T: Send,</span></h3></section><section id="impl-Sync-for-ThinQR%3CT%3E" class="impl has-srclink"><a href="#impl-Sync-for-ThinQR%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> Sync for <a class="struct" href="struct.ThinQR.html" title="struct rulinalg::matrix::decomposition::ThinQR">ThinQR</a><T><span class="where fmt-newline">where<br> T: Sync,</span></h3></section><section id="impl-Unpin-for-ThinQR%3CT%3E" class="impl has-srclink"><a href="#impl-Unpin-for-ThinQR%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> Unpin for <a class="struct" href="struct.ThinQR.html" title="struct rulinalg::matrix::decomposition::ThinQR">ThinQR</a><T><span class="where fmt-newline">where<br> T: Unpin,</span></h3></section><section id="impl-UnwindSafe-for-ThinQR%3CT%3E" class="impl has-srclink"><a href="#impl-UnwindSafe-for-ThinQR%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> UnwindSafe for <a class="struct" href="struct.ThinQR.html" title="struct rulinalg::matrix::decomposition::ThinQR">ThinQR</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-ThinQR%3CT%3E" class="impl has-srclink"><a href="#impl-Any-for-ThinQR%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-ThinQR%3CT%3E" class="impl has-srclink"><a href="#impl-Borrow%3CT%3E-for-ThinQR%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-ThinQR%3CT%3E" class="impl has-srclink"><a href="#impl-BorrowMut%3CT%3E-for-ThinQR%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-ThinQR%3CT%3E" class="impl has-srclink"><a href="#impl-From%3CT%3E-for-ThinQR%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-ThinQR%3CT%3E" class="impl has-srclink"><a href="#impl-Into%3CU%3E-for-ThinQR%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-ThinQR%3CT%3E" class="impl has-srclink"><a href="#impl-ToOwned-for-ThinQR%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-ThinQR%3CT%3E" class="impl has-srclink"><a href="#impl-TryFrom%3CU%3E-for-ThinQR%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-ThinQR%3CT%3E" class="impl has-srclink"><a href="#impl-TryInto%3CU%3E-for-ThinQR%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></div></section></div></main><div id="rustdoc-vars" data-root-path="../../../" data-current-crate="rulinalg" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |
