<!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="Source to the Rust file `/home/mrh/.cargo/registry/src/github.com-1ecc6299db9ec823/alga-0.9.1/src/linear/vector.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>vector.rs.html -- source</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 source"><!--[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></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"><pre class="line-numbers"><span id="1"> 1</span>
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</pre><div class="example-wrap"><pre class="rust ">
<span class="kw">use</span> <span class="ident">num</span>;
<span class="kw">use</span> <span class="ident">num_complex</span>::<span class="ident">Complex</span>;
<span class="kw">use</span> <span class="ident">std</span>::<span class="ident">ops</span>::{
<span class="ident">Add</span>, <span class="ident">AddAssign</span>, <span class="ident">Div</span>, <span class="ident">DivAssign</span>, <span class="ident">Index</span>, <span class="ident">IndexMut</span>, <span class="ident">Mul</span>, <span class="ident">MulAssign</span>, <span class="ident">Neg</span>, <span class="ident">Sub</span>, <span class="ident">SubAssign</span>,
};
<span class="kw">use</span> <span class="kw">crate</span>::<span class="ident">general</span>::{<span class="ident">ClosedAdd</span>, <span class="ident">ClosedDiv</span>, <span class="ident">ClosedMul</span>, <span class="ident">ComplexField</span>, <span class="ident">Field</span>, <span class="ident">Module</span>, <span class="ident">RealField</span>};
<span class="doccomment">/// A vector space has a module structure over a field instead of a ring.</span>
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">VectorSpace</span>: <span class="ident">Module</span><span class="op"><</span><span class="ident">Ring</span> <span class="op">=</span> <span class="op"><</span><span class="self">Self</span> <span class="kw">as</span> <span class="ident">VectorSpace</span><span class="op">></span>::<span class="ident">Field</span><span class="op">></span>
<span class="comment">/* +
ClosedDiv<<Self as VectorSpace>::Field> */</span>
{
<span class="doccomment">/// The underlying scalar field.</span>
<span class="kw">type</span> <span class="ident">Field</span>: <span class="ident">Field</span>;
}
<span class="doccomment">/// A normed vector space.</span>
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">NormedSpace</span>: <span class="ident">VectorSpace</span><span class="op"><</span><span class="ident">Field</span> <span class="op">=</span> <span class="op"><</span><span class="self">Self</span> <span class="kw">as</span> <span class="ident">NormedSpace</span><span class="op">></span>::<span class="ident">ComplexField</span><span class="op">></span> {
<span class="doccomment">/// The result of the norm (not necessarily the same same as the field used by this vector space).</span>
<span class="kw">type</span> <span class="ident">RealField</span>: <span class="ident">RealField</span>;
<span class="doccomment">/// The field of this space must be this complex number.</span>
<span class="kw">type</span> <span class="ident">ComplexField</span>: <span class="ident">ComplexField</span><span class="op"><</span><span class="ident">RealField</span> <span class="op">=</span> <span class="self">Self</span>::<span class="ident">RealField</span><span class="op">></span>;
<span class="doccomment">/// The squared norm of this vector.</span>
<span class="kw">fn</span> <span class="ident">norm_squared</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>::<span class="ident">RealField</span>;
<span class="doccomment">/// The norm of this vector.</span>
<span class="kw">fn</span> <span class="ident">norm</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>::<span class="ident">RealField</span>;
<span class="doccomment">/// Returns a normalized version of this vector.</span>
<span class="kw">fn</span> <span class="ident">normalize</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>;
<span class="doccomment">/// Normalizes this vector in-place and returns its norm.</span>
<span class="kw">fn</span> <span class="ident">normalize_mut</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>::<span class="ident">RealField</span>;
<span class="doccomment">/// Returns a normalized version of this vector unless its norm as smaller or equal to `eps`.</span>
<span class="kw">fn</span> <span class="ident">try_normalize</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">eps</span>: <span class="self">Self</span>::<span class="ident">RealField</span>) <span class="op">-</span><span class="op">></span> <span class="prelude-ty">Option</span><span class="op"><</span><span class="self">Self</span><span class="op">></span>;
<span class="doccomment">/// Normalizes this vector in-place or does nothing if its norm is smaller or equal to `eps`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// If the normalization succeeded, returns the old normal of this vector.</span>
<span class="kw">fn</span> <span class="ident">try_normalize_mut</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">eps</span>: <span class="self">Self</span>::<span class="ident">RealField</span>) <span class="op">-</span><span class="op">></span> <span class="prelude-ty">Option</span><span class="op"><</span><span class="self">Self</span>::<span class="ident">RealField</span><span class="op">></span>;
}
<span class="doccomment">/// A vector space equipped with an inner product.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// It must be a normed space as well and the norm must agree with the inner product.</span>
<span class="doccomment">/// The inner product must be symmetric, linear in its first argument, and positive definite.</span>
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">InnerSpace</span>: <span class="ident">NormedSpace</span> {
<span class="doccomment">/// Computes the inner product of `self` with `other`.</span>
<span class="kw">fn</span> <span class="ident">inner_product</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>::<span class="ident">ComplexField</span>;
<span class="doccomment">/// Measures the angle between two vectors.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">angle</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>::<span class="ident">RealField</span> {
<span class="kw">let</span> <span class="ident">prod</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">inner_product</span>(<span class="ident">other</span>);
<span class="kw">let</span> <span class="ident">n1</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">norm</span>();
<span class="kw">let</span> <span class="ident">n2</span> <span class="op">=</span> <span class="ident">other</span>.<span class="ident">norm</span>();
<span class="kw">if</span> <span class="ident">n1</span> <span class="op">=</span><span class="op">=</span> <span class="ident">num</span>::<span class="ident">zero</span>() <span class="op">|</span><span class="op">|</span> <span class="ident">n2</span> <span class="op">=</span><span class="op">=</span> <span class="ident">num</span>::<span class="ident">zero</span>() {
<span class="ident">num</span>::<span class="ident">zero</span>()
} <span class="kw">else</span> {
<span class="kw">let</span> <span class="ident">cang</span> <span class="op">=</span> <span class="ident">prod</span>.<span class="ident">real</span>() <span class="op">*</span> <span class="ident">n1</span> <span class="op">*</span> <span class="ident">n2</span>;
<span class="kw">if</span> <span class="ident">cang</span> <span class="op">></span> <span class="ident">num</span>::<span class="ident">one</span>() {
<span class="ident">num</span>::<span class="ident">zero</span>()
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">cang</span> <span class="op"><</span> <span class="op">-</span><span class="ident">num</span>::<span class="ident">one</span>::<span class="op"><</span><span class="self">Self</span>::<span class="ident">RealField</span><span class="op">></span>() {
<span class="self">Self</span>::<span class="ident">RealField</span>::<span class="ident">pi</span>()
} <span class="kw">else</span> {
<span class="ident">cang</span>.<span class="ident">acos</span>()
}
}
}
}
<span class="doccomment">/// A finite-dimensional vector space.</span>
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">FiniteDimVectorSpace</span>:
<span class="ident">VectorSpace</span>
<span class="op">+</span> <span class="ident">Index</span><span class="op"><</span><span class="ident">usize</span>, <span class="ident">Output</span> <span class="op">=</span> <span class="op"><</span><span class="self">Self</span> <span class="kw">as</span> <span class="ident">VectorSpace</span><span class="op">></span>::<span class="ident">Field</span><span class="op">></span>
<span class="op">+</span> <span class="ident">IndexMut</span><span class="op"><</span><span class="ident">usize</span>, <span class="ident">Output</span> <span class="op">=</span> <span class="op"><</span><span class="self">Self</span> <span class="kw">as</span> <span class="ident">VectorSpace</span><span class="op">></span>::<span class="ident">Field</span><span class="op">></span>
{
<span class="doccomment">/// The vector space dimension.</span>
<span class="kw">fn</span> <span class="ident">dimension</span>() <span class="op">-</span><span class="op">></span> <span class="ident">usize</span>;
<span class="doccomment">/// Applies the given closule to each element of this vector space's canonical basis. Stops if</span>
<span class="doccomment">/// `f` returns `false`.</span>
<span class="comment">// XXX: return an iterator instead when `-> impl Iterator` will be supported by Rust.</span>
<span class="kw">fn</span> <span class="ident">canonical_basis</span><span class="op"><</span><span class="ident">F</span>: <span class="ident">FnMut</span>(<span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span><span class="op">></span>(<span class="kw-2">mut</span> <span class="ident">f</span>: <span class="ident">F</span>) {
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="number">0</span>..<span class="self">Self</span>::<span class="ident">dimension</span>() {
<span class="kw">if</span> <span class="op">!</span><span class="ident">f</span>(<span class="kw-2">&</span><span class="self">Self</span>::<span class="ident">canonical_basis_element</span>(<span class="ident">i</span>)) {
<span class="kw">break</span>;
}
}
}
<span class="doccomment">/// The i-the canonical basis element.</span>
<span class="kw">fn</span> <span class="ident">canonical_basis_element</span>(<span class="ident">i</span>: <span class="ident">usize</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>;
<span class="doccomment">/// The dot product between two vectors.</span>
<span class="kw">fn</span> <span class="ident">dot</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>::<span class="ident">Field</span>;
<span class="doccomment">/// Same as `&self[i]` but without bound-checking.</span>
<span class="kw">unsafe</span> <span class="kw">fn</span> <span class="ident">component_unchecked</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">i</span>: <span class="ident">usize</span>) <span class="op">-</span><span class="op">></span> <span class="kw-2">&</span><span class="self">Self</span>::<span class="ident">Field</span>;
<span class="doccomment">/// Same as `&mut self[i]` but without bound-checking.</span>
<span class="kw">unsafe</span> <span class="kw">fn</span> <span class="ident">component_unchecked_mut</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">i</span>: <span class="ident">usize</span>) <span class="op">-</span><span class="op">></span> <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">Self</span>::<span class="ident">Field</span>;
}
<span class="doccomment">/// A finite-dimensional vector space equipped with an inner product that must coincide</span>
<span class="doccomment">/// with the dot product.</span>
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">FiniteDimInnerSpace</span>:
<span class="ident">InnerSpace</span> <span class="op">+</span> <span class="ident">FiniteDimVectorSpace</span><span class="op"><</span><span class="ident">Field</span> <span class="op">=</span> <span class="op"><</span><span class="self">Self</span> <span class="kw">as</span> <span class="ident">NormedSpace</span><span class="op">></span>::<span class="ident">ComplexField</span><span class="op">></span>
{
<span class="doccomment">/// Orthonormalizes the given family of vectors. The largest free family of vectors is moved at</span>
<span class="doccomment">/// the beginning of the array and its size is returned. Vectors at an indices larger or equal to</span>
<span class="doccomment">/// this length can be modified to an arbitrary value.</span>
<span class="kw">fn</span> <span class="ident">orthonormalize</span>(<span class="ident">vs</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> [<span class="self">Self</span>]) <span class="op">-</span><span class="op">></span> <span class="ident">usize</span>;
<span class="doccomment">/// Applies the given closure to each element of the orthonormal basis of the subspace</span>
<span class="doccomment">/// orthogonal to free family of vectors `vs`. If `vs` is not a free family, the result is</span>
<span class="doccomment">/// unspecified.</span>
<span class="comment">// XXX: return an iterator instead when `-> impl Iterator` will be supported by Rust.</span>
<span class="kw">fn</span> <span class="ident">orthonormal_subspace_basis</span><span class="op"><</span><span class="ident">F</span>: <span class="ident">FnMut</span>(<span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span><span class="op">></span>(<span class="ident">vs</span>: <span class="kw-2">&</span>[<span class="self">Self</span>], <span class="ident">f</span>: <span class="ident">F</span>);
}
<span class="doccomment">/// A set points associated with a vector space and a transitive and free additive group action</span>
<span class="doccomment">/// (the translation).</span>
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">AffineSpace</span>:
<span class="ident">Sized</span>
<span class="op">+</span> <span class="ident">Clone</span>
<span class="op">+</span> <span class="ident">PartialEq</span>
<span class="op">+</span> <span class="ident">Sub</span><span class="op"><</span><span class="self">Self</span>, <span class="ident">Output</span> <span class="op">=</span> <span class="op"><</span><span class="self">Self</span> <span class="kw">as</span> <span class="ident">AffineSpace</span><span class="op">></span>::<span class="ident">Translation</span><span class="op">></span>
<span class="op">+</span> <span class="ident">ClosedAdd</span><span class="op"><</span><span class="op"><</span><span class="self">Self</span> <span class="kw">as</span> <span class="ident">AffineSpace</span><span class="op">></span>::<span class="ident">Translation</span><span class="op">></span>
{
<span class="doccomment">/// The associated vector space.</span>
<span class="kw">type</span> <span class="ident">Translation</span>: <span class="ident">VectorSpace</span>;
<span class="doccomment">/// Same as `*self + *t`. Applies the additive group action of this affine space's associated</span>
<span class="doccomment">/// vector space on `self`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">translate_by</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">t</span>: <span class="kw-2">&</span><span class="self">Self</span>::<span class="ident">Translation</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="self">self</span>.<span class="ident">clone</span>() <span class="op">+</span> <span class="ident">t</span>.<span class="ident">clone</span>()
}
<span class="doccomment">/// Same as `*self - *other`. Returns the unique element `v` of the associated vector space</span>
<span class="doccomment">/// such that `self = right + v`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">subtract</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">right</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>::<span class="ident">Translation</span> {
<span class="self">self</span>.<span class="ident">clone</span>() <span class="op">-</span> <span class="ident">right</span>.<span class="ident">clone</span>()
}
}
<span class="doccomment">/// The finite-dimensional affine space based on the field of reals.</span>
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">EuclideanSpace</span>: <span class="ident">AffineSpace</span><span class="op"><</span><span class="ident">Translation</span> <span class="op">=</span> <span class="op"><</span><span class="self">Self</span> <span class="kw">as</span> <span class="ident">EuclideanSpace</span><span class="op">></span>::<span class="ident">Coordinates</span><span class="op">></span> <span class="op">+</span>
<span class="comment">// Equivalent to `.scale_by`.</span>
<span class="ident">ClosedMul</span><span class="op"><</span><span class="op"><</span><span class="self">Self</span> <span class="kw">as</span> <span class="ident">EuclideanSpace</span><span class="op">></span>::<span class="ident">RealField</span><span class="op">></span> <span class="op">+</span>
<span class="comment">// Equivalent to `.scale_by`.</span>
<span class="ident">ClosedDiv</span><span class="op"><</span><span class="op"><</span><span class="self">Self</span> <span class="kw">as</span> <span class="ident">EuclideanSpace</span><span class="op">></span>::<span class="ident">RealField</span><span class="op">></span> <span class="op">+</span>
<span class="comment">// Equivalent to `.scale_by(-1.0)`.</span>
<span class="ident">Neg</span><span class="op"><</span><span class="ident">Output</span> <span class="op">=</span> <span class="self">Self</span><span class="op">></span> {
<span class="doccomment">/// The underlying finite vector space.</span>
<span class="kw">type</span> <span class="ident">Coordinates</span>: <span class="ident">FiniteDimInnerSpace</span><span class="op"><</span><span class="ident">RealField</span> <span class="op">=</span> <span class="self">Self</span>::<span class="ident">RealField</span>, <span class="ident">ComplexField</span> <span class="op">=</span> <span class="self">Self</span>::<span class="ident">RealField</span><span class="op">></span> <span class="op">+</span>
<span class="comment">// XXX: the following bounds should not be necessary but the compiler does not</span>
<span class="comment">// seem to be able to find them (from supertraits of VectorSpace)… Also, it won't</span>
<span class="comment">// find them even if we add ClosedMul instead of Mul and MulAssign separately…</span>
<span class="ident">Add</span><span class="op"><</span><span class="self">Self</span>::<span class="ident">Coordinates</span>, <span class="ident">Output</span> <span class="op">=</span> <span class="self">Self</span>::<span class="ident">Coordinates</span><span class="op">></span> <span class="op">+</span>
<span class="ident">AddAssign</span><span class="op"><</span><span class="self">Self</span>::<span class="ident">Coordinates</span><span class="op">></span> <span class="op">+</span>
<span class="ident">Sub</span><span class="op"><</span><span class="self">Self</span>::<span class="ident">Coordinates</span>, <span class="ident">Output</span> <span class="op">=</span> <span class="self">Self</span>::<span class="ident">Coordinates</span><span class="op">></span> <span class="op">+</span>
<span class="ident">SubAssign</span><span class="op"><</span><span class="self">Self</span>::<span class="ident">Coordinates</span><span class="op">></span> <span class="op">+</span>
<span class="ident">Mul</span><span class="op"><</span><span class="self">Self</span>::<span class="ident">RealField</span>, <span class="ident">Output</span> <span class="op">=</span> <span class="self">Self</span>::<span class="ident">Coordinates</span><span class="op">></span> <span class="op">+</span>
<span class="ident">MulAssign</span><span class="op"><</span><span class="self">Self</span>::<span class="ident">RealField</span><span class="op">></span> <span class="op">+</span>
<span class="ident">Div</span><span class="op"><</span><span class="self">Self</span>::<span class="ident">RealField</span>, <span class="ident">Output</span> <span class="op">=</span> <span class="self">Self</span>::<span class="ident">Coordinates</span><span class="op">></span> <span class="op">+</span>
<span class="ident">DivAssign</span><span class="op"><</span><span class="self">Self</span>::<span class="ident">RealField</span><span class="op">></span> <span class="op">+</span>
<span class="ident">Neg</span><span class="op"><</span><span class="ident">Output</span> <span class="op">=</span> <span class="self">Self</span>::<span class="ident">Coordinates</span><span class="op">></span>;
<span class="comment">// XXX: we can't write the following =( :</span>
<span class="comment">// type Vector: FiniteDimInnerSpace<Field = Self::RealField> + InnerSpace<RealField = Self::RealField>;</span>
<span class="comment">// The compiler won't recognize that VectorSpace::Field = Self::RealField.</span>
<span class="comment">// Though it will work if only one bound is used… looks like a compiler bug.</span>
<span class="doccomment">/// The underlying reals.</span>
<span class="kw">type</span> <span class="ident">RealField</span>: <span class="ident">RealField</span>;
<span class="doccomment">/// The preferred origin of this euclidean space.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Theoretically, an euclidean space has no clearly defined origin. Though it is almost always</span>
<span class="doccomment">/// useful to have some reference point to express all the others as translations of it.</span>
<span class="kw">fn</span> <span class="ident">origin</span>() <span class="op">-</span><span class="op">></span> <span class="self">Self</span>;
<span class="doccomment">/// Multiplies the distance of this point to `Self::origin()` by `s`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Same as self * s.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">scale_by</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">s</span>: <span class="self">Self</span>::<span class="ident">RealField</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="self">Self</span>::<span class="ident">from_coordinates</span>(<span class="self">self</span>.<span class="ident">coordinates</span>() <span class="op">*</span> <span class="ident">s</span>)
}
<span class="comment">// FIXME: take self by-value?</span>
<span class="doccomment">/// The coordinates of this point, i.e., the translation from the origin.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">coordinates</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>::<span class="ident">Coordinates</span> {
<span class="self">self</span>.<span class="ident">subtract</span>(<span class="kw-2">&</span><span class="self">Self</span>::<span class="ident">origin</span>())
}
<span class="doccomment">/// Builds a point from its coordinates relative to the origin.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">from_coordinates</span>(<span class="ident">coords</span>: <span class="self">Self</span>::<span class="ident">Coordinates</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="self">Self</span>::<span class="ident">origin</span>().<span class="ident">translate_by</span>(<span class="kw-2">&</span><span class="ident">coords</span>)
}
<span class="doccomment">/// The distance between two points.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">distance_squared</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">b</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>::<span class="ident">RealField</span> {
<span class="self">self</span>.<span class="ident">subtract</span>(<span class="ident">b</span>).<span class="ident">norm_squared</span>()
}
<span class="doccomment">/// The distance between two points.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">distance</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">b</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>::<span class="ident">RealField</span> {
<span class="self">self</span>.<span class="ident">subtract</span>(<span class="ident">b</span>).<span class="ident">norm</span>()
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">N</span>: <span class="ident">Field</span> <span class="op">+</span> <span class="ident">num</span>::<span class="ident">NumAssign</span><span class="op">></span> <span class="ident">VectorSpace</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">N</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Field</span> <span class="op">=</span> <span class="ident">N</span>;
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">N</span>: <span class="ident">RealField</span><span class="op">></span> <span class="ident">NormedSpace</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">N</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">RealField</span> <span class="op">=</span> <span class="ident">N</span>;
<span class="kw">type</span> <span class="ident">ComplexField</span> <span class="op">=</span> <span class="ident">N</span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">norm_squared</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>::<span class="ident">RealField</span> {
<span class="self">self</span>.<span class="ident">norm_sqr</span>()
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">norm</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>::<span class="ident">RealField</span> {
<span class="self">self</span>.<span class="ident">norm_sqr</span>().<span class="ident">sqrt</span>()
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">normalize</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="kw-2">*</span><span class="self">self</span> <span class="op">/</span> <span class="self">self</span>.<span class="ident">norm</span>()
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">normalize_mut</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>::<span class="ident">RealField</span> {
<span class="kw">let</span> <span class="ident">norm</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">norm</span>();
<span class="kw-2">*</span><span class="self">self</span> <span class="op">/</span><span class="op">=</span> <span class="ident">norm</span>;
<span class="ident">norm</span>
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">try_normalize</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">eps</span>: <span class="self">Self</span>::<span class="ident">RealField</span>) <span class="op">-</span><span class="op">></span> <span class="prelude-ty">Option</span><span class="op"><</span><span class="self">Self</span><span class="op">></span> {
<span class="kw">let</span> <span class="ident">norm</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">norm_sqr</span>();
<span class="kw">if</span> <span class="ident">norm</span> <span class="op">></span> <span class="ident">eps</span> <span class="op">*</span> <span class="ident">eps</span> {
<span class="prelude-val">Some</span>(<span class="kw-2">*</span><span class="self">self</span> <span class="op">/</span> <span class="ident">norm</span>.<span class="ident">sqrt</span>())
} <span class="kw">else</span> {
<span class="prelude-val">None</span>
}
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">try_normalize_mut</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">eps</span>: <span class="self">Self</span>::<span class="ident">RealField</span>) <span class="op">-</span><span class="op">></span> <span class="prelude-ty">Option</span><span class="op"><</span><span class="self">Self</span>::<span class="ident">RealField</span><span class="op">></span> {
<span class="kw">let</span> <span class="ident">sq_norm</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">norm_sqr</span>();
<span class="kw">if</span> <span class="ident">sq_norm</span> <span class="op">></span> <span class="ident">eps</span> <span class="op">*</span> <span class="ident">eps</span> {
<span class="kw">let</span> <span class="ident">norm</span> <span class="op">=</span> <span class="ident">sq_norm</span>.<span class="ident">sqrt</span>();
<span class="kw-2">*</span><span class="self">self</span> <span class="op">/</span><span class="op">=</span> <span class="ident">norm</span>;
<span class="prelude-val">Some</span>(<span class="ident">norm</span>)
} <span class="kw">else</span> {
<span class="prelude-val">None</span>
}
}
}
<span class="comment">// Note: we can't implement FiniteDimVectorSpace for Complex because</span>
<span class="comment">// the `Complex` type does not implement Index.</span>
</pre></div>
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