| <!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 Lp norm"><meta name="keywords" content="rust, rustlang, rust-lang, Lp"><title>Lp in rusty_machine::linalg::norm - 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" 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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="#">Lp</a></h2><div class="sidebar-elems"><section><h3><a href="#variants">Variants</a></h3><ul class="block"><li><a href="#variant.Float">Float</a></li><li><a href="#variant.Infinity">Infinity</a></li><li><a href="#variant.Integer">Integer</a></li></ul><h3><a href="#trait-implementations">Trait Implementations</a></h3><ul class="block"><li><a href="#impl-Debug-for-Lp%3CT%3E">Debug</a></li><li><a href="#impl-MatrixNorm%3CT%2C%20M%3E-for-Lp%3CT%3E">MatrixNorm<T, M></a></li><li><a href="#impl-VectorNorm%3CT%3E-for-Lp%3CT%3E">VectorNorm<T></a></li></ul><h3><a href="#synthetic-implementations">Auto Trait Implementations</a></h3><ul class="block"><li><a href="#impl-RefUnwindSafe-for-Lp%3CT%3E">RefUnwindSafe</a></li><li><a href="#impl-Send-for-Lp%3CT%3E">Send</a></li><li><a href="#impl-Sync-for-Lp%3CT%3E">Sync</a></li><li><a href="#impl-Unpin-for-Lp%3CT%3E">Unpin</a></li><li><a href="#impl-UnwindSafe-for-Lp%3CT%3E">UnwindSafe</a></li></ul><h3><a href="#blanket-implementations">Blanket Implementations</a></h3><ul class="block"><li><a href="#impl-Any-for-Lp%3CT%3E">Any</a></li><li><a href="#impl-Borrow%3CT%3E-for-Lp%3CT%3E">Borrow<T></a></li><li><a href="#impl-BorrowMut%3CT%3E-for-Lp%3CT%3E">BorrowMut<T></a></li><li><a href="#impl-From%3CT%3E-for-Lp%3CT%3E">From<T></a></li><li><a href="#impl-Into%3CU%3E-for-Lp%3CT%3E">Into<U></a></li><li><a href="#impl-TryFrom%3CU%3E-for-Lp%3CT%3E">TryFrom<U></a></li><li><a href="#impl-TryInto%3CU%3E-for-Lp%3CT%3E">TryInto<U></a></li><li><a href="#impl-VZip%3CV%3E-for-Lp%3CT%3E">VZip<V></a></li><li><a href="#impl-VectorMetric%3CT%3E-for-Lp%3CT%3E">VectorMetric<T></a></li></ul></section><h2><a href="index.html">In rusty_machine::linalg::norm</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">Enum <a href="../../index.html">rusty_machine</a>::<wbr><a href="../index.html">linalg</a>::<wbr><a href="index.html">norm</a>::<wbr><a class="enum" href="#">Lp</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/norm/mod.rs.html#139">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 enum"><code>pub enum Lp<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>{ |
| Infinity, |
| Integer(i32), |
| Float(T), |
| }</code></pre></div><details class="rustdoc-toggle top-doc" open><summary class="hideme"><span>Expand description</span></summary><div class="docblock"><p>The Lp norm</p> |
| <p>The |
| <a href="https://en.wikipedia.org/wiki/Norm_(mathematics)#p-norm">Lp norm</a> |
| computes the <code>p</code>th root of the sum of elements |
| to the <code>p</code>th power.</p> |
| <p>The Lp norm requires <code>p</code> to be greater than |
| or equal <code>1</code>.</p> |
| <p>We use an enum for this norm to allow us to explicitly handle |
| special cases at compile time. For example, we have an <code>Infinity</code> |
| variant which handles the special case when the <code>Lp</code> norm is a |
| supremum over absolute values. The <code>Integer</code> variant gives us a |
| performance boost when <code>p</code> is an integer.</p> |
| <p>You should avoid matching directly against this enum as it is likely |
| to grow.</p> |
| </div></details><h2 id="variants" class="variants small-section-header">Variants<a href="#variants" class="anchor"></a></h2><h3 id="variant.Infinity" class="variant small-section-header"><a href="#variant.Infinity" class="anchor field"></a><code>Infinity</code></h3><div class="docblock"><p>The L-infinity norm (supremum)</p> |
| </div><h3 id="variant.Integer" class="variant small-section-header"><a href="#variant.Integer" class="anchor field"></a><code>Integer(i32)</code></h3><div class="docblock"><p>The Lp norm where p is an integer</p> |
| </div><h3 id="variant.Float" class="variant small-section-header"><a href="#variant.Float" class="anchor field"></a><code>Float(T)</code></h3><div class="docblock"><p>The Lp norm where p is a float</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-Debug-for-Lp%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="../../../src/rulinalg/norm/mod.rs.html#138">source</a><a href="#impl-Debug-for-Lp%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> Debug for <a class="enum" href="enum.Lp.html" title="enum rusty_machine::linalg::norm::Lp">Lp</a><T><span class="where fmt-newline">where<br> T: Debug + <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.fmt" class="method trait-impl has-srclink"><a class="srclink rightside" href="../../../src/rulinalg/norm/mod.rs.html#138">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-MatrixNorm%3CT%2C%20M%3E-for-Lp%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="../../../src/rulinalg/norm/mod.rs.html#183">source</a><a href="#impl-MatrixNorm%3CT%2C%20M%3E-for-Lp%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T, M> <a class="trait" href="trait.MatrixNorm.html" title="trait rusty_machine::linalg::norm::MatrixNorm">MatrixNorm</a><T, M> for <a class="enum" href="enum.Lp.html" title="enum rusty_machine::linalg::norm::Lp">Lp</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>,<br> M: <a class="trait" href="../trait.BaseMatrix.html" title="trait rusty_machine::linalg::BaseMatrix">BaseMatrix</a><T>,</span></h3></section></summary><div class="impl-items"><details class="rustdoc-toggle method-toggle" open><summary><section id="method.norm" class="method trait-impl has-srclink"><a class="srclink rightside" href="../../../src/rulinalg/norm/mod.rs.html#184">source</a><a href="#method.norm" class="anchor"></a><h4 class="code-header">fn <a href="trait.MatrixNorm.html#tymethod.norm" class="fnname">norm</a>(&self, m: &M) -> T</h4></section></summary><div class='docblock'>Computes the matrix norm.</div></details></div></details><details class="rustdoc-toggle implementors-toggle" open><summary><section id="impl-VectorNorm%3CT%3E-for-Lp%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="../../../src/rulinalg/norm/mod.rs.html#148">source</a><a href="#impl-VectorNorm%3CT%3E-for-Lp%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> <a class="trait" href="trait.VectorNorm.html" title="trait rusty_machine::linalg::norm::VectorNorm">VectorNorm</a><T> for <a class="enum" href="enum.Lp.html" title="enum rusty_machine::linalg::norm::Lp">Lp</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.norm-1" class="method trait-impl has-srclink"><a class="srclink rightside" href="../../../src/rulinalg/norm/mod.rs.html#149">source</a><a href="#method.norm-1" class="anchor"></a><h4 class="code-header">fn <a href="trait.VectorNorm.html#tymethod.norm" class="fnname">norm</a>(&self, v: &<a class="struct" href="../struct.Vector.html" title="struct rusty_machine::linalg::Vector">Vector</a><T>) -> T</h4></section></summary><div class='docblock'>Computes the vector norm.</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-Lp%3CT%3E" class="impl has-srclink"><a href="#impl-RefUnwindSafe-for-Lp%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> RefUnwindSafe for <a class="enum" href="enum.Lp.html" title="enum rusty_machine::linalg::norm::Lp">Lp</a><T><span class="where fmt-newline">where<br> T: RefUnwindSafe,</span></h3></section><section id="impl-Send-for-Lp%3CT%3E" class="impl has-srclink"><a href="#impl-Send-for-Lp%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> Send for <a class="enum" href="enum.Lp.html" title="enum rusty_machine::linalg::norm::Lp">Lp</a><T><span class="where fmt-newline">where<br> T: Send,</span></h3></section><section id="impl-Sync-for-Lp%3CT%3E" class="impl has-srclink"><a href="#impl-Sync-for-Lp%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> Sync for <a class="enum" href="enum.Lp.html" title="enum rusty_machine::linalg::norm::Lp">Lp</a><T><span class="where fmt-newline">where<br> T: Sync,</span></h3></section><section id="impl-Unpin-for-Lp%3CT%3E" class="impl has-srclink"><a href="#impl-Unpin-for-Lp%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> Unpin for <a class="enum" href="enum.Lp.html" title="enum rusty_machine::linalg::norm::Lp">Lp</a><T><span class="where fmt-newline">where<br> T: Unpin,</span></h3></section><section id="impl-UnwindSafe-for-Lp%3CT%3E" class="impl has-srclink"><a href="#impl-UnwindSafe-for-Lp%3CT%3E" class="anchor"></a><h3 class="code-header">impl<T> UnwindSafe for <a class="enum" href="enum.Lp.html" title="enum rusty_machine::linalg::norm::Lp">Lp</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-Lp%3CT%3E" class="impl has-srclink"><a href="#impl-Any-for-Lp%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-Lp%3CT%3E" class="impl has-srclink"><a href="#impl-Borrow%3CT%3E-for-Lp%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-Lp%3CT%3E" class="impl has-srclink"><a href="#impl-BorrowMut%3CT%3E-for-Lp%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-Lp%3CT%3E" class="impl has-srclink"><a href="#impl-From%3CT%3E-for-Lp%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-Lp%3CT%3E" class="impl has-srclink"><a href="#impl-Into%3CU%3E-for-Lp%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-TryFrom%3CU%3E-for-Lp%3CT%3E" class="impl has-srclink"><a href="#impl-TryFrom%3CU%3E-for-Lp%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-Lp%3CT%3E" class="impl has-srclink"><a href="#impl-TryInto%3CU%3E-for-Lp%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-Lp%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-Lp%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><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-VectorMetric%3CT%3E-for-Lp%3CT%3E" class="impl has-srclink"><a class="srclink rightside" href="../../../src/rulinalg/norm/mod.rs.html#68">source</a><a href="#impl-VectorMetric%3CT%3E-for-Lp%3CT%3E" class="anchor"></a><h3 class="code-header">impl<U, T> <a class="trait" href="trait.VectorMetric.html" title="trait rusty_machine::linalg::norm::VectorMetric">VectorMetric</a><T> for U<span class="where fmt-newline">where<br> U: <a class="trait" href="trait.VectorNorm.html" title="trait rusty_machine::linalg::norm::VectorNorm">VectorNorm</a><T>,<br> T: Copy + Sub<T, Output = T>,</span></h3></section></summary><div class="impl-items"><details class="rustdoc-toggle method-toggle" open><summary><section id="method.metric" class="method trait-impl has-srclink"><a class="srclink rightside" href="../../../src/rulinalg/norm/mod.rs.html#70">source</a><a href="#method.metric" class="anchor"></a><h4 class="code-header">fn <a href="trait.VectorMetric.html#tymethod.metric" class="fnname">metric</a>(&self, v1: &<a class="struct" href="../struct.Vector.html" title="struct rusty_machine::linalg::Vector">Vector</a><T>, v2: &<a class="struct" href="../struct.Vector.html" title="struct rusty_machine::linalg::Vector">Vector</a><T>) -> T</h4></section></summary><div class='docblock'>Computes the metric distance between two vectors.</div></details></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> |
