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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 `NormedSpace` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, NormedSpace"><title>alga::linear::NormedSpace - 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="../../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='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait NormedSpace</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#associated-types">Associated Types</a><div class="sidebar-links"><a href="#associatedtype.RealField">RealField</a><a href="#associatedtype.ComplexField">ComplexField</a></div><a class="sidebar-title" href="#required-methods">Required Methods</a><div class="sidebar-links"><a href="#tymethod.norm">norm</a><a href="#tymethod.norm_squared">norm_squared</a><a href="#tymethod.normalize">normalize</a><a href="#tymethod.normalize_mut">normalize_mut</a><a href="#tymethod.try_normalize">try_normalize</a><a href="#tymethod.try_normalize_mut">try_normalize_mut</a></div><a class="sidebar-title" href="#foreign-impls">Implementations on Foreign Types</a><div class="sidebar-links"><a href="#impl-NormedSpace-for-Complex%3CN%3E">Complex<N></a></div><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>linear</a></p><script>window.sidebarCurrent = {name: 'NormedSpace', 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/alga/linear/vector.rs.html#20-45' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>linear</a>::<wbr><a class="trait" href=''>NormedSpace</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait NormedSpace: <a class="trait" href="../../alga/linear/trait.VectorSpace.html" title="trait alga::linear::VectorSpace">VectorSpace</a><Field = Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.ComplexField" title="type alga::linear::NormedSpace::ComplexField">ComplexField</a>> {
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type <a href='#associatedtype.RealField' class="type">RealField</a>: <a class="trait" href="../../alga/general/trait.RealField.html" title="trait alga::general::RealField">RealField</a>;
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type <a href='#associatedtype.ComplexField' class="type">ComplexField</a>: <a class="trait" href="../../alga/general/trait.ComplexField.html" title="trait alga::general::ComplexField">ComplexField</a><RealField = Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a>>;
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fn <a href='#tymethod.norm_squared' class='fnname'>norm_squared</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a>;
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<div class='item-spacer'></div> fn <a href='#tymethod.norm' class='fnname'>norm</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a>;
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<div class='item-spacer'></div> fn <a href='#tymethod.normalize' class='fnname'>normalize</a>(&self) -> Self;
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<div class='item-spacer'></div> fn <a href='#tymethod.normalize_mut' class='fnname'>normalize_mut</a>(&mut self) -> Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a>;
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<div class='item-spacer'></div> fn <a href='#tymethod.try_normalize' class='fnname'>try_normalize</a>(&self, eps: Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><Self>;
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<div class='item-spacer'></div> fn <a href='#tymethod.try_normalize_mut' class='fnname'>try_normalize_mut</a>(<br> &mut self, <br> eps: Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a><br> ) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a>>;
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}</pre></div><div class='docblock'><p>A normed vector space.</p>
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</div>
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<h2 id='associated-types' class='small-section-header'>Associated Types<a href='#associated-types' class='anchor'></a></h2><div class='methods'><h3 id='associatedtype.RealField' class='method'><code id='RealField.t'>type <a href='#associatedtype.RealField' class="type">RealField</a>: <a class="trait" href="../../alga/general/trait.RealField.html" title="trait alga::general::RealField">RealField</a></code></h3><div class='docblock'><p>The result of the norm (not necessarily the same same as the field used by this vector space).</p>
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</div><h3 id='associatedtype.ComplexField' class='method'><code id='ComplexField.t'>type <a href='#associatedtype.ComplexField' class="type">ComplexField</a>: <a class="trait" href="../../alga/general/trait.ComplexField.html" title="trait alga::general::ComplexField">ComplexField</a><RealField = Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a>></code></h3><div class='docblock'><p>The field of this space must be this complex number.</p>
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</div></div><span class='loading-content'>Loading content...</span>
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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_squared' class='method'><code id='norm_squared.v'>fn <a href='#tymethod.norm_squared' class='fnname'>norm_squared</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a></code></h3><div class='docblock'><p>The squared norm of this vector.</p>
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</div><h3 id='tymethod.norm' class='method'><code id='norm.v'>fn <a href='#tymethod.norm' class='fnname'>norm</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a></code></h3><div class='docblock'><p>The norm of this vector.</p>
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</div><h3 id='tymethod.normalize' class='method'><code id='normalize.v'>fn <a href='#tymethod.normalize' class='fnname'>normalize</a>(&self) -> Self</code></h3><div class='docblock'><p>Returns a normalized version of this vector.</p>
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</div><h3 id='tymethod.normalize_mut' class='method'><code id='normalize_mut.v'>fn <a href='#tymethod.normalize_mut' class='fnname'>normalize_mut</a>(&mut self) -> Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a></code></h3><div class='docblock'><p>Normalizes this vector in-place and returns its norm.</p>
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</div><h3 id='tymethod.try_normalize' class='method'><code id='try_normalize.v'>fn <a href='#tymethod.try_normalize' class='fnname'>try_normalize</a>(&self, eps: Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><Self></code></h3><div class='docblock'><p>Returns a normalized version of this vector unless its norm as smaller or equal to <code>eps</code>.</p>
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</div><h3 id='tymethod.try_normalize_mut' class='method'><code id='try_normalize_mut.v'>fn <a href='#tymethod.try_normalize_mut' class='fnname'>try_normalize_mut</a>(&mut self, eps: Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a>></code></h3><div class='docblock'><p>Normalizes this vector in-place or does nothing if its norm is smaller or equal to <code>eps</code>.</p>
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<p>If the normalization succeeded, returns the old normal of this vector.</p>
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</div></div><span class='loading-content'>Loading content...</span>
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<h2 id='foreign-impls' class='small-section-header'>Implementations on Foreign Types<a href='#foreign-impls' class='anchor'></a></h2><h3 id='impl-NormedSpace-for-Complex%3CN%3E' class='impl'><code class='in-band'>impl<N: <a class="trait" href="../../alga/general/trait.RealField.html" title="trait alga::general::RealField">RealField</a>> <a class="trait" href="../../alga/linear/trait.NormedSpace.html" title="trait alga::linear::NormedSpace">NormedSpace</a> for <a class="struct" href="../../num_complex/struct.Complex.html" title="struct num_complex::Complex">Complex</a><N></code><a href='#impl-NormedSpace-for-Complex%3CN%3E' class='anchor'></a><a class='srclink' href='../../src/alga/linear/vector.rs.html#230-277' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.RealField-1' class="type"><code id='RealField.t-1'>type <a href='#associatedtype.RealField' class="type">RealField</a> = N</code></h4><h4 id='associatedtype.ComplexField-1' class="type"><code id='ComplexField.t-1'>type <a href='#associatedtype.ComplexField' class="type">ComplexField</a> = N</code></h4><h4 id='method.norm_squared' class="method hidden"><code id='norm_squared.v-1'>fn <a href='#method.norm_squared' class='fnname'>norm_squared</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a></code><a class='srclink' href='../../src/alga/linear/vector.rs.html#235-237' title='goto source code'>[src]</a></h4><h4 id='method.norm' class="method hidden"><code id='norm.v-1'>fn <a href='#method.norm' class='fnname'>norm</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a></code><a class='srclink' href='../../src/alga/linear/vector.rs.html#240-242' title='goto source code'>[src]</a></h4><h4 id='method.normalize' class="method hidden"><code id='normalize.v-1'>fn <a href='#method.normalize' class='fnname'>normalize</a>(&self) -> Self</code><a class='srclink' href='../../src/alga/linear/vector.rs.html#245-247' title='goto source code'>[src]</a></h4><h4 id='method.normalize_mut' class="method hidden"><code id='normalize_mut.v-1'>fn <a href='#method.normalize_mut' class='fnname'>normalize_mut</a>(&mut self) -> Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a></code><a class='srclink' href='../../src/alga/linear/vector.rs.html#250-254' title='goto source code'>[src]</a></h4><h4 id='method.try_normalize' class="method hidden"><code id='try_normalize.v-1'>fn <a href='#method.try_normalize' class='fnname'>try_normalize</a>(&self, eps: Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><Self></code><a class='srclink' href='../../src/alga/linear/vector.rs.html#257-264' title='goto source code'>[src]</a></h4><h4 id='method.try_normalize_mut' class="method hidden"><code id='try_normalize_mut.v-1'>fn <a href='#method.try_normalize_mut' class='fnname'>try_normalize_mut</a>(&mut self, eps: Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><Self::<a class="type" href="../../alga/linear/trait.NormedSpace.html#associatedtype.RealField" title="type alga::linear::NormedSpace::RealField">RealField</a>></code><a class='srclink' href='../../src/alga/linear/vector.rs.html#267-276' title='goto source code'>[src]</a></h4></div><span class='loading-content'>Loading
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