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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 `FiniteDimInnerSpace` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, FiniteDimInnerSpace"><title>alga::linear::FiniteDimInnerSpace - 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 FiniteDimInnerSpace</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.orthonormal_subspace_basis">orthonormal_subspace_basis</a><a href="#tymethod.orthonormalize">orthonormalize</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: 'FiniteDimInnerSpace', 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#113-126' 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=''>FiniteDimInnerSpace</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait FiniteDimInnerSpace: <a class="trait" href="../../alga/linear/trait.InnerSpace.html" title="trait alga::linear::InnerSpace">InnerSpace</a> + <a class="trait" href="../../alga/linear/trait.FiniteDimVectorSpace.html" title="trait alga::linear::FiniteDimVectorSpace">FiniteDimVectorSpace</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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fn <a href='#tymethod.orthonormalize' class='fnname'>orthonormalize</a>(vs: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.slice.html">&mut [Self]</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.usize.html">usize</a>;
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<div class='item-spacer'></div> fn <a href='#tymethod.orthonormal_subspace_basis' class='fnname'>orthonormal_subspace_basis</a><F: <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/function/trait.FnMut.html" title="trait core::ops::function::FnMut">FnMut</a>(<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a>>(vs: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.slice.html">&[Self]</a>, f: F);
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}</pre></div><div class='docblock'><p>A finite-dimensional vector space equipped with an inner product that must coincide
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with the dot product.</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.orthonormalize' class='method'><code id='orthonormalize.v'>fn <a href='#tymethod.orthonormalize' class='fnname'>orthonormalize</a>(vs: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.slice.html">&mut [Self]</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.usize.html">usize</a></code></h3><div class='docblock'><p>Orthonormalizes the given family of vectors. The largest free family of vectors is moved at
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the beginning of the array and its size is returned. Vectors at an indices larger or equal to
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this length can be modified to an arbitrary value.</p>
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</div><h3 id='tymethod.orthonormal_subspace_basis' class='method'><code id='orthonormal_subspace_basis.v'>fn <a href='#tymethod.orthonormal_subspace_basis' class='fnname'>orthonormal_subspace_basis</a><F: <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/function/trait.FnMut.html" title="trait core::ops::function::FnMut">FnMut</a>(<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a>>(vs: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.slice.html">&[Self]</a>, f: F)</code></h3><div class='docblock'><p>Applies the given closure to each element of the orthonormal basis of the subspace
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orthogonal to free family of vectors <code>vs</code>. If <code>vs</code> is not a free family, the result is
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unspecified.</p>
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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'></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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