<!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 of the Rust file `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/nalgebra-0.32.1/src/base/norm.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>norm.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Regular-1f7d512b176f0f72.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Bold-124a1ca42af929b6.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../../../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../../../static.files/rustdoc-6827029ac823cab7.css" id="mainThemeStyle"><link rel="stylesheet" id="themeStyle" href="../../../static.files/light-ebce58d0a40c3431.css"><link rel="stylesheet" disabled href="../../../static.files/dark-f23faae4a2daf9a6.css"><link rel="stylesheet" disabled href="../../../static.files/ayu-8af5e100b21cd173.css"><script id="default-settings" ></script><script src="../../../static.files/storage-d43fa987303ecbbb.js"></script><script defer src="../../../static.files/source-script-5cf2e01a42cc9858.js"></script><script defer src="../../../source-files.js"></script><script defer src="../../../static.files/main-c55e1eb52e1886b4.js"></script><noscript><link rel="stylesheet" href="../../../static.files/noscript-13285aec31fa243e.css"></noscript><link rel="icon" href="https://nalgebra.org/img/favicon.ico"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../../nalgebra/index.html"><img class="rust-logo" src="../../../static.files/rust-logo-151179464ae7ed46.svg" alt="logo"></a><form class="search-form"><span></span><input class="search-input" name="search" aria-label="Run search in the documentation" 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="../../../static.files/wheel-5ec35bf9ca753509.svg"></a></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><a href="#1" id="1">1</a>
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</pre><pre class="rust"><code><span class="attr">#[cfg(all(feature = <span class="string">"alloc"</span>, not(feature = <span class="string">"std"</span>)))]
</span><span class="kw">use </span>alloc::vec::Vec;
<span class="kw">use </span>num::Zero;
<span class="kw">use </span>std::ops::Neg;
<span class="kw">use </span><span class="kw">crate</span>::allocator::Allocator;
<span class="kw">use </span><span class="kw">crate</span>::base::{DefaultAllocator, Dim, DimName, Matrix, Normed, OMatrix, OVector};
<span class="kw">use </span><span class="kw">crate</span>::constraint::{SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
<span class="kw">use </span><span class="kw">crate</span>::storage::{Storage, StorageMut};
<span class="kw">use crate</span>::{ComplexField, Scalar, SimdComplexField, Unit};
<span class="kw">use </span>simba::scalar::ClosedNeg;
<span class="kw">use </span>simba::simd::{SimdOption, SimdPartialOrd, SimdValue};
<span class="comment">// TODO: this should be be a trait on alga?
</span><span class="doccomment">/// A trait for abstract matrix norms.
///
/// This may be moved to the alga crate in the future.
</span><span class="kw">pub trait </span>Norm<T: SimdComplexField> {
<span class="doccomment">/// Apply this norm to the given matrix.
</span><span class="kw">fn </span>norm<R, C, S>(<span class="kw-2">&</span><span class="self">self</span>, m: <span class="kw-2">&</span>Matrix<T, R, C, S>) -> T::SimdRealField
<span class="kw">where
</span>R: Dim,
C: Dim,
S: Storage<T, R, C>;
<span class="doccomment">/// Use the metric induced by this norm to compute the metric distance between the two given matrices.
</span><span class="kw">fn </span>metric_distance<R1, C1, S1, R2, C2, S2>(
<span class="kw-2">&</span><span class="self">self</span>,
m1: <span class="kw-2">&</span>Matrix<T, R1, C1, S1>,
m2: <span class="kw-2">&</span>Matrix<T, R2, C2, S2>,
) -> T::SimdRealField
<span class="kw">where
</span>R1: Dim,
C1: Dim,
S1: Storage<T, R1, C1>,
R2: Dim,
C2: Dim,
S2: Storage<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>;
}
<span class="doccomment">/// Euclidean norm.
</span><span class="attr">#[derive(Copy, Clone, Debug)]
</span><span class="kw">pub struct </span>EuclideanNorm;
<span class="doccomment">/// Lp norm.
</span><span class="attr">#[derive(Copy, Clone, Debug)]
</span><span class="kw">pub struct </span>LpNorm(<span class="kw">pub </span>i32);
<span class="doccomment">/// L-infinite norm aka. Chebytchev norm aka. uniform norm aka. suppremum norm.
</span><span class="attr">#[derive(Copy, Clone, Debug)]
</span><span class="kw">pub struct </span>UniformNorm;
<span class="kw">impl</span><T: SimdComplexField> Norm<T> <span class="kw">for </span>EuclideanNorm {
<span class="attr">#[inline]
</span><span class="kw">fn </span>norm<R, C, S>(<span class="kw-2">&</span><span class="self">self</span>, m: <span class="kw-2">&</span>Matrix<T, R, C, S>) -> T::SimdRealField
<span class="kw">where
</span>R: Dim,
C: Dim,
S: Storage<T, R, C>,
{
m.norm_squared().simd_sqrt()
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>metric_distance<R1, C1, S1, R2, C2, S2>(
<span class="kw-2">&</span><span class="self">self</span>,
m1: <span class="kw-2">&</span>Matrix<T, R1, C1, S1>,
m2: <span class="kw-2">&</span>Matrix<T, R2, C2, S2>,
) -> T::SimdRealField
<span class="kw">where
</span>R1: Dim,
C1: Dim,
S1: Storage<T, R1, C1>,
R2: Dim,
C2: Dim,
S2: Storage<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,
{
m1.zip_fold(m2, T::SimdRealField::zero(), |acc, a, b| {
<span class="kw">let </span>diff = a - b;
acc + diff.simd_modulus_squared()
})
.simd_sqrt()
}
}
<span class="kw">impl</span><T: SimdComplexField> Norm<T> <span class="kw">for </span>LpNorm {
<span class="attr">#[inline]
</span><span class="kw">fn </span>norm<R, C, S>(<span class="kw-2">&</span><span class="self">self</span>, m: <span class="kw-2">&</span>Matrix<T, R, C, S>) -> T::SimdRealField
<span class="kw">where
</span>R: Dim,
C: Dim,
S: Storage<T, R, C>,
{
m.fold(T::SimdRealField::zero(), |a, b| {
a + b.simd_modulus().simd_powi(<span class="self">self</span>.<span class="number">0</span>)
})
.simd_powf(<span class="kw">crate</span>::convert(<span class="number">1.0 </span>/ (<span class="self">self</span>.<span class="number">0 </span><span class="kw">as </span>f64)))
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>metric_distance<R1, C1, S1, R2, C2, S2>(
<span class="kw-2">&</span><span class="self">self</span>,
m1: <span class="kw-2">&</span>Matrix<T, R1, C1, S1>,
m2: <span class="kw-2">&</span>Matrix<T, R2, C2, S2>,
) -> T::SimdRealField
<span class="kw">where
</span>R1: Dim,
C1: Dim,
S1: Storage<T, R1, C1>,
R2: Dim,
C2: Dim,
S2: Storage<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,
{
m1.zip_fold(m2, T::SimdRealField::zero(), |acc, a, b| {
<span class="kw">let </span>diff = a - b;
acc + diff.simd_modulus().simd_powi(<span class="self">self</span>.<span class="number">0</span>)
})
.simd_powf(<span class="kw">crate</span>::convert(<span class="number">1.0 </span>/ (<span class="self">self</span>.<span class="number">0 </span><span class="kw">as </span>f64)))
}
}
<span class="kw">impl</span><T: SimdComplexField> Norm<T> <span class="kw">for </span>UniformNorm {
<span class="attr">#[inline]
</span><span class="kw">fn </span>norm<R, C, S>(<span class="kw-2">&</span><span class="self">self</span>, m: <span class="kw-2">&</span>Matrix<T, R, C, S>) -> T::SimdRealField
<span class="kw">where
</span>R: Dim,
C: Dim,
S: Storage<T, R, C>,
{
<span class="comment">// NOTE: we don't use `m.amax()` here because for the complex
// numbers this will return the max norm1 instead of the modulus.
</span>m.fold(T::SimdRealField::zero(), |acc, a| {
acc.simd_max(a.simd_modulus())
})
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>metric_distance<R1, C1, S1, R2, C2, S2>(
<span class="kw-2">&</span><span class="self">self</span>,
m1: <span class="kw-2">&</span>Matrix<T, R1, C1, S1>,
m2: <span class="kw-2">&</span>Matrix<T, R2, C2, S2>,
) -> T::SimdRealField
<span class="kw">where
</span>R1: Dim,
C1: Dim,
S1: Storage<T, R1, C1>,
R2: Dim,
C2: Dim,
S2: Storage<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,
{
m1.zip_fold(m2, T::SimdRealField::zero(), |acc, a, b| {
<span class="kw">let </span>val = (a - b).simd_modulus();
acc.simd_max(val)
})
}
}
<span class="doccomment">/// # Magnitude and norms
</span><span class="kw">impl</span><T: Scalar, R: Dim, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S> {
<span class="doccomment">/// The squared L2 norm of this vector.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>norm_squared(<span class="kw-2">&</span><span class="self">self</span>) -> T::SimdRealField
<span class="kw">where
</span>T: SimdComplexField,
{
<span class="kw">let </span><span class="kw-2">mut </span>res = T::SimdRealField::zero();
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..<span class="self">self</span>.ncols() {
<span class="kw">let </span>col = <span class="self">self</span>.column(i);
res += col.dotc(<span class="kw-2">&</span>col).simd_real()
}
res
}
<span class="doccomment">/// The L2 norm of this matrix.
///
/// Use `.apply_norm` to apply a custom norm.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>norm(<span class="kw-2">&</span><span class="self">self</span>) -> T::SimdRealField
<span class="kw">where
</span>T: SimdComplexField,
{
<span class="self">self</span>.norm_squared().simd_sqrt()
}
<span class="doccomment">/// Compute the distance between `self` and `rhs` using the metric induced by the euclidean norm.
///
/// Use `.apply_metric_distance` to apply a custom norm.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>metric_distance<R2, C2, S2>(<span class="kw-2">&</span><span class="self">self</span>, rhs: <span class="kw-2">&</span>Matrix<T, R2, C2, S2>) -> T::SimdRealField
<span class="kw">where
</span>T: SimdComplexField,
R2: Dim,
C2: Dim,
S2: Storage<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
<span class="self">self</span>.apply_metric_distance(rhs, <span class="kw-2">&</span>EuclideanNorm)
}
<span class="doccomment">/// Uses the given `norm` to compute the norm of `self`.
///
/// # Example
///
/// ```
/// # use nalgebra::{Vector3, UniformNorm, LpNorm, EuclideanNorm};
///
/// let v = Vector3::new(1.0, 2.0, 3.0);
/// assert_eq!(v.apply_norm(&UniformNorm), 3.0);
/// assert_eq!(v.apply_norm(&LpNorm(1)), 6.0);
/// assert_eq!(v.apply_norm(&EuclideanNorm), v.norm());
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>apply_norm(<span class="kw-2">&</span><span class="self">self</span>, norm: <span class="kw-2">&</span><span class="kw">impl </span>Norm<T>) -> T::SimdRealField
<span class="kw">where
</span>T: SimdComplexField,
{
norm.norm(<span class="self">self</span>)
}
<span class="doccomment">/// Uses the metric induced by the given `norm` to compute the metric distance between `self` and `rhs`.
///
/// # Example
///
/// ```
/// # use nalgebra::{Vector3, UniformNorm, LpNorm, EuclideanNorm};
///
/// let v1 = Vector3::new(1.0, 2.0, 3.0);
/// let v2 = Vector3::new(10.0, 20.0, 30.0);
///
/// assert_eq!(v1.apply_metric_distance(&v2, &UniformNorm), 27.0);
/// assert_eq!(v1.apply_metric_distance(&v2, &LpNorm(1)), 27.0 + 18.0 + 9.0);
/// assert_eq!(v1.apply_metric_distance(&v2, &EuclideanNorm), (v1 - v2).norm());
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>apply_metric_distance<R2, C2, S2>(
<span class="kw-2">&</span><span class="self">self</span>,
rhs: <span class="kw-2">&</span>Matrix<T, R2, C2, S2>,
norm: <span class="kw-2">&</span><span class="kw">impl </span>Norm<T>,
) -> T::SimdRealField
<span class="kw">where
</span>T: SimdComplexField,
R2: Dim,
C2: Dim,
S2: Storage<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
norm.metric_distance(<span class="self">self</span>, rhs)
}
<span class="doccomment">/// A synonym for the norm of this matrix.
///
/// Aka the length.
///
/// This function is simply implemented as a call to `norm()`
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>magnitude(<span class="kw-2">&</span><span class="self">self</span>) -> T::SimdRealField
<span class="kw">where
</span>T: SimdComplexField,
{
<span class="self">self</span>.norm()
}
<span class="doccomment">/// A synonym for the squared norm of this matrix.
///
/// Aka the squared length.
///
/// This function is simply implemented as a call to `norm_squared()`
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>magnitude_squared(<span class="kw-2">&</span><span class="self">self</span>) -> T::SimdRealField
<span class="kw">where
</span>T: SimdComplexField,
{
<span class="self">self</span>.norm_squared()
}
<span class="doccomment">/// Sets the magnitude of this vector.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>set_magnitude(<span class="kw-2">&mut </span><span class="self">self</span>, magnitude: T::SimdRealField)
<span class="kw">where
</span>T: SimdComplexField,
S: StorageMut<T, R, C>,
{
<span class="kw">let </span>n = <span class="self">self</span>.norm();
<span class="self">self</span>.scale_mut(magnitude / n)
}
<span class="doccomment">/// Returns a normalized version of this matrix.
</span><span class="attr">#[inline]
#[must_use = <span class="string">"Did you mean to use normalize_mut()?"</span>]
</span><span class="kw">pub fn </span>normalize(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, R, C>
<span class="kw">where
</span>T: SimdComplexField,
DefaultAllocator: Allocator<T, R, C>,
{
<span class="self">self</span>.unscale(<span class="self">self</span>.norm())
}
<span class="doccomment">/// The Lp norm of this matrix.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>lp_norm(<span class="kw-2">&</span><span class="self">self</span>, p: i32) -> T::SimdRealField
<span class="kw">where
</span>T: SimdComplexField,
{
<span class="self">self</span>.apply_norm(<span class="kw-2">&</span>LpNorm(p))
}
<span class="doccomment">/// Attempts to normalize `self`.
///
/// The components of this matrix can be SIMD types.
</span><span class="attr">#[inline]
#[must_use = <span class="string">"Did you mean to use simd_try_normalize_mut()?"</span>]
</span><span class="kw">pub fn </span>simd_try_normalize(<span class="kw-2">&</span><span class="self">self</span>, min_norm: T::SimdRealField) -> SimdOption<OMatrix<T, R, C>>
<span class="kw">where
</span>T: SimdComplexField,
T::Element: Scalar,
DefaultAllocator: Allocator<T, R, C> + Allocator<T::Element, R, C>,
{
<span class="kw">let </span>n = <span class="self">self</span>.norm();
<span class="kw">let </span>le = n.clone().simd_le(min_norm);
<span class="kw">let </span>val = <span class="self">self</span>.unscale(n);
SimdOption::new(val, le)
}
<span class="doccomment">/// Sets the magnitude of this vector unless it is smaller than `min_magnitude`.
///
/// If `self.magnitude()` is smaller than `min_magnitude`, it will be left unchanged.
/// Otherwise this is equivalent to: `*self = self.normalize() * magnitude.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>try_set_magnitude(<span class="kw-2">&mut </span><span class="self">self</span>, magnitude: T::RealField, min_magnitude: T::RealField)
<span class="kw">where
</span>T: ComplexField,
S: StorageMut<T, R, C>,
{
<span class="kw">let </span>n = <span class="self">self</span>.norm();
<span class="kw">if </span>n > min_magnitude {
<span class="self">self</span>.scale_mut(magnitude / n)
}
}
<span class="doccomment">/// Returns a new vector with the same magnitude as `self` clamped between `0.0` and `max`.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>cap_magnitude(<span class="kw-2">&</span><span class="self">self</span>, max: T::RealField) -> OMatrix<T, R, C>
<span class="kw">where
</span>T: ComplexField,
DefaultAllocator: Allocator<T, R, C>,
{
<span class="kw">let </span>n = <span class="self">self</span>.norm();
<span class="kw">if </span>n > max {
<span class="self">self</span>.scale(max / n)
} <span class="kw">else </span>{
<span class="self">self</span>.clone_owned()
}
}
<span class="doccomment">/// Returns a new vector with the same magnitude as `self` clamped between `0.0` and `max`.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>simd_cap_magnitude(<span class="kw-2">&</span><span class="self">self</span>, max: T::SimdRealField) -> OMatrix<T, R, C>
<span class="kw">where
</span>T: SimdComplexField,
T::Element: Scalar,
DefaultAllocator: Allocator<T, R, C> + Allocator<T::Element, R, C>,
{
<span class="kw">let </span>n = <span class="self">self</span>.norm();
<span class="kw">let </span>scaled = <span class="self">self</span>.scale(max.clone() / n.clone());
<span class="kw">let </span>use_scaled = n.simd_gt(max);
scaled.select(use_scaled, <span class="self">self</span>.clone_owned())
}
<span class="doccomment">/// Returns a normalized version of this matrix unless its norm as smaller or equal to `eps`.
///
/// The components of this matrix cannot be SIMD types (see `simd_try_normalize`) instead.
</span><span class="attr">#[inline]
#[must_use = <span class="string">"Did you mean to use try_normalize_mut()?"</span>]
</span><span class="kw">pub fn </span>try_normalize(<span class="kw-2">&</span><span class="self">self</span>, min_norm: T::RealField) -> <span class="prelude-ty">Option</span><OMatrix<T, R, C>>
<span class="kw">where
</span>T: ComplexField,
DefaultAllocator: Allocator<T, R, C>,
{
<span class="kw">let </span>n = <span class="self">self</span>.norm();
<span class="kw">if </span>n <= min_norm {
<span class="prelude-val">None
</span>} <span class="kw">else </span>{
<span class="prelude-val">Some</span>(<span class="self">self</span>.unscale(n))
}
}
}
<span class="doccomment">/// # In-place normalization
</span><span class="kw">impl</span><T: Scalar, R: Dim, C: Dim, S: StorageMut<T, R, C>> Matrix<T, R, C, S> {
<span class="doccomment">/// Normalizes this matrix in-place and returns its norm.
///
/// The components of the matrix cannot be SIMD types (see `simd_try_normalize_mut` instead).
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>normalize_mut(<span class="kw-2">&mut </span><span class="self">self</span>) -> T::SimdRealField
<span class="kw">where
</span>T: SimdComplexField,
{
<span class="kw">let </span>n = <span class="self">self</span>.norm();
<span class="self">self</span>.unscale_mut(n.clone());
n
}
<span class="doccomment">/// Normalizes this matrix in-place and return its norm.
///
/// The components of the matrix can be SIMD types.
</span><span class="attr">#[inline]
#[must_use = <span class="string">"Did you mean to use simd_try_normalize_mut()?"</span>]
</span><span class="kw">pub fn </span>simd_try_normalize_mut(
<span class="kw-2">&mut </span><span class="self">self</span>,
min_norm: T::SimdRealField,
) -> SimdOption<T::SimdRealField>
<span class="kw">where
</span>T: SimdComplexField,
T::Element: Scalar,
DefaultAllocator: Allocator<T, R, C> + Allocator<T::Element, R, C>,
{
<span class="kw">let </span>n = <span class="self">self</span>.norm();
<span class="kw">let </span>le = n.clone().simd_le(min_norm);
<span class="self">self</span>.apply(|e| <span class="kw-2">*</span>e = e.clone().simd_unscale(n.clone()).select(le, e.clone()));
SimdOption::new(n, le)
}
<span class="doccomment">/// Normalizes this matrix in-place or does nothing if its norm is smaller or equal to `eps`.
///
/// If the normalization succeeded, returns the old norm of this matrix.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>try_normalize_mut(<span class="kw-2">&mut </span><span class="self">self</span>, min_norm: T::RealField) -> <span class="prelude-ty">Option</span><T::RealField>
<span class="kw">where
</span>T: ComplexField,
{
<span class="kw">let </span>n = <span class="self">self</span>.norm();
<span class="kw">if </span>n <= min_norm {
<span class="prelude-val">None
</span>} <span class="kw">else </span>{
<span class="self">self</span>.unscale_mut(n.clone());
<span class="prelude-val">Some</span>(n)
}
}
}
<span class="kw">impl</span><T: SimdComplexField, R: Dim, C: Dim> Normed <span class="kw">for </span>OMatrix<T, R, C>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, R, C>,
{
<span class="kw">type </span>Norm = T::SimdRealField;
<span class="attr">#[inline]
</span><span class="kw">fn </span>norm(<span class="kw-2">&</span><span class="self">self</span>) -> T::SimdRealField {
<span class="self">self</span>.norm()
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>norm_squared(<span class="kw-2">&</span><span class="self">self</span>) -> T::SimdRealField {
<span class="self">self</span>.norm_squared()
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>scale_mut(<span class="kw-2">&mut </span><span class="self">self</span>, n: <span class="self">Self</span>::Norm) {
<span class="self">self</span>.scale_mut(n)
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>unscale_mut(<span class="kw-2">&mut </span><span class="self">self</span>, n: <span class="self">Self</span>::Norm) {
<span class="self">self</span>.unscale_mut(n)
}
}
<span class="kw">impl</span><T: Scalar + ClosedNeg, R: Dim, C: Dim> Neg <span class="kw">for </span>Unit<OMatrix<T, R, C>>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, R, C>,
{
<span class="kw">type </span>Output = Unit<OMatrix<T, R, C>>;
<span class="attr">#[inline]
</span><span class="kw">fn </span>neg(<span class="self">self</span>) -> <span class="self">Self</span>::Output {
Unit::new_unchecked(-<span class="self">self</span>.value)
}
}
<span class="comment">// TODO: specialization will greatly simplify this implementation in the future.
// In particular:
// − use `x()` instead of `::canonical_basis_element`
// − use `::new(x, y, z)` instead of `::from_slice`
</span><span class="doccomment">/// # Basis and orthogonalization
</span><span class="kw">impl</span><T: ComplexField, D: DimName> OVector<T, D>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D>,
{
<span class="doccomment">/// The i-the canonical basis element.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>canonical_basis_element(i: usize) -> <span class="self">Self </span>{
<span class="kw">let </span><span class="kw-2">mut </span>res = <span class="self">Self</span>::zero();
res[i] = T::one();
res
}
<span class="doccomment">/// Orthonormalizes the given family of vectors. The largest free family of vectors is moved at
/// the beginning of the array and its size is returned. Vectors at an indices larger or equal to
/// this length can be modified to an arbitrary value.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>orthonormalize(vs: <span class="kw-2">&mut </span>[<span class="self">Self</span>]) -> usize {
<span class="kw">let </span><span class="kw-2">mut </span>nbasis_elements = <span class="number">0</span>;
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..vs.len() {
{
<span class="kw">let </span>(elt, basis) = vs[..i + <span class="number">1</span>].split_last_mut().unwrap();
<span class="kw">for </span>basis_element <span class="kw">in </span><span class="kw-2">&</span>basis[..nbasis_elements] {
<span class="kw-2">*</span>elt -= <span class="kw-2">&*</span>basis_element * elt.dot(basis_element)
}
}
<span class="kw">if </span>vs[i].try_normalize_mut(T::RealField::zero()).is_some() {
<span class="comment">// TODO: this will be efficient on dynamically-allocated vectors but for
// statically-allocated ones, `.clone_from` would be better.
</span>vs.swap(nbasis_elements, i);
nbasis_elements += <span class="number">1</span>;
<span class="comment">// All the other vectors will be dependent.
</span><span class="kw">if </span>nbasis_elements == D::dim() {
<span class="kw">break</span>;
}
}
}
nbasis_elements
}
<span class="doccomment">/// Applies the given closure to each element of the orthonormal basis of the subspace
/// orthogonal to free family of vectors `vs`. If `vs` is not a free family, the result is
/// unspecified.
</span><span class="comment">// TODO: return an iterator instead when `-> impl Iterator` will be supported by Rust.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>orthonormal_subspace_basis<F>(vs: <span class="kw-2">&</span>[<span class="self">Self</span>], <span class="kw-2">mut </span>f: F)
<span class="kw">where
</span>F: FnMut(<span class="kw-2">&</span><span class="self">Self</span>) -> bool,
{
<span class="comment">// TODO: is this necessary?
</span><span class="macro">assert!</span>(
vs.len() <= D::dim(),
<span class="string">"The given set of vectors has no chance of being a free family."
</span>);
<span class="kw">match </span>D::dim() {
<span class="number">1 </span>=> {
<span class="kw">if </span>vs.is_empty() {
<span class="kw">let _ </span>= f(<span class="kw-2">&</span><span class="self">Self</span>::canonical_basis_element(<span class="number">0</span>));
}
}
<span class="number">2 </span>=> {
<span class="kw">if </span>vs.is_empty() {
<span class="kw">let _ </span>= f(<span class="kw-2">&</span><span class="self">Self</span>::canonical_basis_element(<span class="number">0</span>))
&& f(<span class="kw-2">&</span><span class="self">Self</span>::canonical_basis_element(<span class="number">1</span>));
} <span class="kw">else if </span>vs.len() == <span class="number">1 </span>{
<span class="kw">let </span>v = <span class="kw-2">&</span>vs[<span class="number">0</span>];
<span class="kw">let </span>res = <span class="self">Self</span>::from_column_slice(<span class="kw-2">&</span>[-v[<span class="number">1</span>].clone(), v[<span class="number">0</span>].clone()]);
<span class="kw">let _ </span>= f(<span class="kw-2">&</span>res.normalize());
}
<span class="comment">// Otherwise, nothing.
</span>}
<span class="number">3 </span>=> {
<span class="kw">if </span>vs.is_empty() {
<span class="kw">let _ </span>= f(<span class="kw-2">&</span><span class="self">Self</span>::canonical_basis_element(<span class="number">0</span>))
&& f(<span class="kw-2">&</span><span class="self">Self</span>::canonical_basis_element(<span class="number">1</span>))
&& f(<span class="kw-2">&</span><span class="self">Self</span>::canonical_basis_element(<span class="number">2</span>));
} <span class="kw">else if </span>vs.len() == <span class="number">1 </span>{
<span class="kw">let </span>v = <span class="kw-2">&</span>vs[<span class="number">0</span>];
<span class="kw">let </span><span class="kw-2">mut </span>a;
<span class="kw">if </span>v[<span class="number">0</span>].clone().norm1() > v[<span class="number">1</span>].clone().norm1() {
a = <span class="self">Self</span>::from_column_slice(<span class="kw-2">&</span>[v[<span class="number">2</span>].clone(), T::zero(), -v[<span class="number">0</span>].clone()]);
} <span class="kw">else </span>{
a = <span class="self">Self</span>::from_column_slice(<span class="kw-2">&</span>[T::zero(), -v[<span class="number">2</span>].clone(), v[<span class="number">1</span>].clone()]);
};
<span class="kw">let _ </span>= a.normalize_mut();
<span class="kw">if </span>f(<span class="kw-2">&</span>a.cross(v)) {
<span class="kw">let _ </span>= f(<span class="kw-2">&</span>a);
}
} <span class="kw">else if </span>vs.len() == <span class="number">2 </span>{
<span class="kw">let _ </span>= f(<span class="kw-2">&</span>vs[<span class="number">0</span>].cross(<span class="kw-2">&</span>vs[<span class="number">1</span>]).normalize());
}
}
<span class="kw">_ </span>=> {
<span class="attr">#[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"alloc"</span>))]
</span>{
<span class="comment">// XXX: use a GenericArray instead.
</span><span class="kw">let </span><span class="kw-2">mut </span>known_basis = Vec::new();
<span class="kw">for </span>v <span class="kw">in </span>vs.iter() {
known_basis.push(v.normalize())
}
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..D::dim() - vs.len() {
<span class="kw">let </span><span class="kw-2">mut </span>elt = <span class="self">Self</span>::canonical_basis_element(i);
<span class="kw">for </span>v <span class="kw">in </span><span class="kw-2">&</span>known_basis {
elt -= v * elt.dot(v)
}
<span class="kw">if let </span><span class="prelude-val">Some</span>(subsp_elt) = elt.try_normalize(T::RealField::zero()) {
<span class="kw">if </span>!f(<span class="kw-2">&</span>subsp_elt) {
<span class="kw">return</span>;
};
known_basis.push(subsp_elt);
}
}
}
<span class="attr">#[cfg(all(not(feature = <span class="string">"std"</span>), not(feature = <span class="string">"alloc"</span>)))]
</span>{
<span class="macro">panic!</span>(<span class="string">"Cannot compute the orthogonal subspace basis of a vector with a dimension greater than 3 \
if #![no_std] is enabled and the 'alloc' feature is not enabled."</span>)
}
}
}
}
}
</code></pre></div>
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