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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `Norm` trait in crate `nalgebra`."><meta name="keywords" content="rust, rustlang, rust-lang, Norm"><title>nalgebra::base::Norm - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="http://nalgebra.org/img/favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">☰</div><a href='../../nalgebra/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait Norm</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#required-methods">Required Methods</a><div class="sidebar-links"><a href="#tymethod.metric_distance">metric_distance</a><a href="#tymethod.norm">norm</a></div><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>nalgebra</a>::<wbr><a href='index.html'>base</a></p><script>window.sidebarCurrent = {name: 'Norm', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>−</span>]</a></span><a class='srclink' href='../../src/nalgebra/base/norm.rs.html#14-23' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>nalgebra</a>::<wbr><a href='index.html'>base</a>::<wbr><a class="trait" href=''>Norm</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait Norm<N: <a class="trait" href="../../nalgebra/trait.ComplexField.html" title="trait nalgebra::ComplexField">ComplexField</a>> {
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fn <a href='#tymethod.norm' class='fnname'>norm</a><R, C, S>(&self, m: &<a class="struct" href="../../nalgebra/base/struct.Matrix.html" title="struct nalgebra::base::Matrix">Matrix</a><N, R, C, S>) -> N::<a class="type" href="../../nalgebra/trait.ComplexField.html#associatedtype.RealField" title="type nalgebra::ComplexField::RealField">RealField</a><br> <span class="where">where<br> R: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> C: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> S: <a class="trait" href="../../nalgebra/base/storage/trait.Storage.html" title="trait nalgebra::base::storage::Storage">Storage</a><N, R, C></span>;
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<div class='item-spacer'></div> fn <a href='#tymethod.metric_distance' class='fnname'>metric_distance</a><R1, C1, S1, R2, C2, S2>(<br> &self, <br> m1: &<a class="struct" href="../../nalgebra/base/struct.Matrix.html" title="struct nalgebra::base::Matrix">Matrix</a><N, R1, C1, S1>, <br> m2: &<a class="struct" href="../../nalgebra/base/struct.Matrix.html" title="struct nalgebra::base::Matrix">Matrix</a><N, R2, C2, S2><br> ) -> N::<a class="type" href="../../nalgebra/trait.ComplexField.html#associatedtype.RealField" title="type nalgebra::ComplexField::RealField">RealField</a><br> <span class="where">where<br> R1: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> C1: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> S1: <a class="trait" href="../../nalgebra/base/storage/trait.Storage.html" title="trait nalgebra::base::storage::Storage">Storage</a><N, R1, C1>,<br> R2: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> C2: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> S2: <a class="trait" href="../../nalgebra/base/storage/trait.Storage.html" title="trait nalgebra::base::storage::Storage">Storage</a><N, R2, C2>,<br> <a class="struct" href="../../nalgebra/base/constraint/struct.ShapeConstraint.html" title="struct nalgebra::base::constraint::ShapeConstraint">ShapeConstraint</a>: <a class="trait" href="../../nalgebra/base/constraint/trait.SameNumberOfRows.html" title="trait nalgebra::base::constraint::SameNumberOfRows">SameNumberOfRows</a><R1, R2> + <a class="trait" href="../../nalgebra/base/constraint/trait.SameNumberOfColumns.html" title="trait nalgebra::base::constraint::SameNumberOfColumns">SameNumberOfColumns</a><C1, C2></span>;
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}</pre></div><div class='docblock'><p>A trait for abstract matrix norms.</p>
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<p>This may be moved to the alga crate in the future.</p>
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</div>
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<h2 id='required-methods' class='small-section-header'>Required methods<a href='#required-methods' class='anchor'></a></h2><div class='methods'><h3 id='tymethod.norm' class='method'><code id='norm.v'>fn <a href='#tymethod.norm' class='fnname'>norm</a><R, C, S>(&self, m: &<a class="struct" href="../../nalgebra/base/struct.Matrix.html" title="struct nalgebra::base::Matrix">Matrix</a><N, R, C, S>) -> N::<a class="type" href="../../nalgebra/trait.ComplexField.html#associatedtype.RealField" title="type nalgebra::ComplexField::RealField">RealField</a> <span class="where fmt-newline">where<br> R: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> C: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> S: <a class="trait" href="../../nalgebra/base/storage/trait.Storage.html" title="trait nalgebra::base::storage::Storage">Storage</a><N, R, C>, </span></code></h3><div class='docblock'><p>Apply this norm to the given matrix.</p>
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</div><h3 id='tymethod.metric_distance' class='method'><code id='metric_distance.v'>fn <a href='#tymethod.metric_distance' class='fnname'>metric_distance</a><R1, C1, S1, R2, C2, S2>(<br> &self, <br> m1: &<a class="struct" href="../../nalgebra/base/struct.Matrix.html" title="struct nalgebra::base::Matrix">Matrix</a><N, R1, C1, S1>, <br> m2: &<a class="struct" href="../../nalgebra/base/struct.Matrix.html" title="struct nalgebra::base::Matrix">Matrix</a><N, R2, C2, S2><br>) -> N::<a class="type" href="../../nalgebra/trait.ComplexField.html#associatedtype.RealField" title="type nalgebra::ComplexField::RealField">RealField</a> <span class="where fmt-newline">where<br> R1: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> C1: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> S1: <a class="trait" href="../../nalgebra/base/storage/trait.Storage.html" title="trait nalgebra::base::storage::Storage">Storage</a><N, R1, C1>,<br> R2: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> C2: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> S2: <a class="trait" href="../../nalgebra/base/storage/trait.Storage.html" title="trait nalgebra::base::storage::Storage">Storage</a><N, R2, C2>,<br> <a class="struct" href="../../nalgebra/base/constraint/struct.ShapeConstraint.html" title="struct nalgebra::base::constraint::ShapeConstraint">ShapeConstraint</a>: <a class="trait" href="../../nalgebra/base/constraint/trait.SameNumberOfRows.html" title="trait nalgebra::base::constraint::SameNumberOfRows">SameNumberOfRows</a><R1, R2> + <a class="trait" href="../../nalgebra/base/constraint/trait.SameNumberOfColumns.html" title="trait nalgebra::base::constraint::SameNumberOfColumns">SameNumberOfColumns</a><C1, C2>, </span></code></h3><div class='docblock'><p>Use the metric induced by this norm to compute the metric distance between the two given matrices.</p>
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</div></div><span class='loading-content'>Loading content...</span>
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<h2 id='implementors' class='small-section-header'>Implementors<a href='#implementors' class='anchor'></a></h2><div class='item-list' id='implementors-list'><h3 id='impl-Norm%3CN%3E' class='impl'><code class='in-band'>impl<N: <a class="trait" href="../../nalgebra/trait.ComplexField.html" title="trait nalgebra::ComplexField">ComplexField</a>> Norm<N> for <a class="struct" href="../../nalgebra/base/struct.EuclideanNorm.html" title="struct nalgebra::base::EuclideanNorm">EuclideanNorm</a></code><a href='#impl-Norm%3CN%3E' class='anchor'></a><a class='srclink' href='../../src/nalgebra/base/norm.rs.html#32-49' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.norm' class="method hidden"><code id='norm.v-1'>fn <a href='#method.norm' class='fnname'>norm</a><R, C, S>(&self, m: &<a class="struct" href="../../nalgebra/base/struct.Matrix.html" title="struct nalgebra::base::Matrix">Matrix</a><N, R, C, S>) -> N::<a class="type" href="../../nalgebra/trait.ComplexField.html#associatedtype.RealField" title="type nalgebra::ComplexField::RealField">RealField</a> <span class="where fmt-newline">where<br> R: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> C: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> S: <a class="trait" href="../../nalgebra/base/storage/trait.Storage.html" title="trait nalgebra::base::storage::Storage">Storage</a><N, R, C>, </span></code><a class='srclink' href='../../src/nalgebra/base/norm.rs.html#34-37' title='goto source code'>[src]</a></h4><h4 id='method.metric_distance' class="method hidden"><code id='metric_distance.v-1'>fn <a href='#method.metric_distance' class='fnname'>metric_distance</a><R1, C1, S1, R2, C2, S2>(<br> &self, <br> m1: &<a class="struct" href="../../nalgebra/base/struct.Matrix.html" title="struct nalgebra::base::Matrix">Matrix</a><N, R1, C1, S1>, <br> m2: &<a class="struct" href="../../nalgebra/base/struct.Matrix.html" title="struct nalgebra::base::Matrix">Matrix</a><N, R2, C2, S2><br>) -> N::<a class="type" href="../../nalgebra/trait.ComplexField.html#associatedtype.RealField" title="type nalgebra::ComplexField::RealField">RealField</a> <span class="where fmt-newline">where<br> R1: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> C1: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> S1: <a class="trait" href="../../nalgebra/base/storage/trait.Storage.html" title="trait nalgebra::base::storage::Storage">Storage</a><N, R1, C1>,<br> R2: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> C2: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> S2: <a class="trait" href="../../nalgebra/base/storage/trait.Storage.html" title="trait nalgebra::base::storage::Storage">Storage</a><N, R2, C2>,<br> <a class="struct" href="../../nalgebra/base/constraint/struct.ShapeConstraint.html" title="struct nalgebra::base::constraint::ShapeConstraint">ShapeConstraint</a>: <a class="trait" href="../../nalgebra/base/constraint/trait.SameNumberOfRows.html" title="trait nalgebra::base::constraint::SameNumberOfRows">SameNumberOfRows</a><R1, R2> + <a class="trait" href="../../nalgebra/base/constraint/trait.SameNumberOfColumns.html" title="trait nalgebra::base::constraint::SameNumberOfColumns">SameNumberOfColumns</a><C1, C2>, </span></code><a class='srclink' href='../../src/nalgebra/base/norm.rs.html#40-48' title='goto source code'>[src]</a></h4></div><h3 id='impl-Norm%3CN%3E-1' class='impl'><code class='in-band'>impl<N: <a class="trait" href="../../nalgebra/trait.ComplexField.html" title="trait nalgebra::ComplexField">ComplexField</a>> Norm<N> for <a class="struct" href="../../nalgebra/base/struct.LpNorm.html" title="struct nalgebra::base::LpNorm">LpNorm</a></code><a href='#impl-Norm%3CN%3E-1' class='anchor'></a><a class='srclink' href='../../src/nalgebra/base/norm.rs.html#51-70' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.norm-1' class="method hidden"><code id='norm.v-2'>fn <a href='#method.norm-1' class='fnname'>norm</a><R, C, S>(&self, m: &<a class="struct" href="../../nalgebra/base/struct.Matrix.html" title="struct nalgebra::base::Matrix">Matrix</a><N, R, C, S>) -> N::<a class="type" href="../../nalgebra/trait.ComplexField.html#associatedtype.RealField" title="type nalgebra::ComplexField::RealField">RealField</a> <span class="where fmt-newline">where<br> R: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> C: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> S: <a class="trait" href="../../nalgebra/base/storage/trait.Storage.html" title="trait nalgebra::base::storage::Storage">Storage</a><N, R, C>, </span></code><a class='srclink' href='../../src/nalgebra/base/norm.rs.html#53-58' title='goto source code'>[src]</a></h4><h4 id='method.metric_distance-1' class="method hidden"><code id='metric_distance.v-2'>fn <a href='#method.metric_distance-1' class='fnname'>metric_distance</a><R1, C1, S1, R2, C2, S2>(<br> &self, <br> m1: &<a class="struct" href="../../nalgebra/base/struct.Matrix.html" title="struct nalgebra::base::Matrix">Matrix</a><N, R1, C1, S1>, <br> m2: &<a class="struct" href="../../nalgebra/base/struct.Matrix.html" title="struct nalgebra::base::Matrix">Matrix</a><N, R2, C2, S2><br>) -> N::<a class="type" href="../../nalgebra/trait.ComplexField.html#associatedtype.RealField" title="type nalgebra::ComplexField::RealField">RealField</a> <span class="where fmt-newline">where<br> R1: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> C1: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> S1: <a class="trait" href="../../nalgebra/base/storage/trait.Storage.html" title="trait nalgebra::base::storage::Storage">Storage</a><N, R1, C1>,<br> R2: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> C2: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> S2: <a class="trait" href="../../nalgebra/base/storage/trait.Storage.html" title="trait nalgebra::base::storage::Storage">Storage</a><N, R2, C2>,<br> <a class="struct" href="../../nalgebra/base/constraint/struct.ShapeConstraint.html" title="struct nalgebra::base::constraint::ShapeConstraint">ShapeConstraint</a>: <a class="trait" href="../../nalgebra/base/constraint/trait.SameNumberOfRows.html" title="trait nalgebra::base::constraint::SameNumberOfRows">SameNumberOfRows</a><R1, R2> + <a class="trait" href="../../nalgebra/base/constraint/trait.SameNumberOfColumns.html" title="trait nalgebra::base::constraint::SameNumberOfColumns">SameNumberOfColumns</a><C1, C2>, </span></code><a class='srclink' href='../../src/nalgebra/base/norm.rs.html#61-69' title='goto source code'>[src]</a></h4></div><h3 id='impl-Norm%3CN%3E-2' class='impl'><code class='in-band'>impl<N: <a class="trait" href="../../nalgebra/trait.ComplexField.html" title="trait nalgebra::ComplexField">ComplexField</a>> Norm<N> for <a class="struct" href="../../nalgebra/base/struct.UniformNorm.html" title="struct nalgebra::base::UniformNorm">UniformNorm</a></code><a href='#impl-Norm%3CN%3E-2' class='anchor'></a><a class='srclink' href='../../src/nalgebra/base/norm.rs.html#72-95' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.norm-2' class="method hidden"><code id='norm.v-3'>fn <a href='#method.norm-2' class='fnname'>norm</a><R, C, S>(&self, m: &<a class="struct" href="../../nalgebra/base/struct.Matrix.html" title="struct nalgebra::base::Matrix">Matrix</a><N, R, C, S>) -> N::<a class="type" href="../../nalgebra/trait.ComplexField.html#associatedtype.RealField" title="type nalgebra::ComplexField::RealField">RealField</a> <span class="where fmt-newline">where<br> R: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> C: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> S: <a class="trait" href="../../nalgebra/base/storage/trait.Storage.html" title="trait nalgebra::base::storage::Storage">Storage</a><N, R, C>, </span></code><a class='srclink' href='../../src/nalgebra/base/norm.rs.html#74-79' title='goto source code'>[src]</a></h4><h4 id='method.metric_distance-2' class="method hidden"><code id='metric_distance.v-3'>fn <a href='#method.metric_distance-2' class='fnname'>metric_distance</a><R1, C1, S1, R2, C2, S2>(<br> &self, <br> m1: &<a class="struct" href="../../nalgebra/base/struct.Matrix.html" title="struct nalgebra::base::Matrix">Matrix</a><N, R1, C1, S1>, <br> m2: &<a class="struct" href="../../nalgebra/base/struct.Matrix.html" title="struct nalgebra::base::Matrix">Matrix</a><N, R2, C2, S2><br>) -> N::<a class="type" href="../../nalgebra/trait.ComplexField.html#associatedtype.RealField" title="type nalgebra::ComplexField::RealField">RealField</a> <span class="where fmt-newline">where<br> R1: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> C1: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> S1: <a class="trait" href="../../nalgebra/base/storage/trait.Storage.html" title="trait nalgebra::base::storage::Storage">Storage</a><N, R1, C1>,<br> R2: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> C2: <a class="trait" href="../../nalgebra/base/dimension/trait.Dim.html" title="trait nalgebra::base::dimension::Dim">Dim</a>,<br> S2: <a class="trait" href="../../nalgebra/base/storage/trait.Storage.html" title="trait nalgebra::base::storage::Storage">Storage</a><N, R2, C2>,<br> <a class="struct" href="../../nalgebra/base/constraint/struct.ShapeConstraint.html" title="struct nalgebra::base::constraint::ShapeConstraint">ShapeConstraint</a>: <a class="trait" href="../../nalgebra/base/constraint/trait.SameNumberOfRows.html" title="trait nalgebra::base::constraint::SameNumberOfRows">SameNumberOfRows</a><R1, R2> + <a class="trait" href="../../nalgebra/base/constraint/trait.SameNumberOfColumns.html" title="trait nalgebra::base::constraint::SameNumberOfColumns">SameNumberOfColumns</a><C1, C2>, </span></code><a class='srclink' href='../../src/nalgebra/base/norm.rs.html#82-94' title='goto source code'>[src]</a></h4></div></div><span class='loading-content'>Loading content...</span><script type="text/javascript">window.inlined_types=new Set([]);</script><script type="text/javascript" async
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