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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="Source of the Rust file `/root/.cargo/git/checkouts/rulinalg-309246e5a94bf5cf/1ed8b93/src/norm/mod.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>mod.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../../normalize.css"><link rel="stylesheet" href="../../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../../ayu.css" disabled><link rel="stylesheet" href="../../../dark.css" disabled><link rel="stylesheet" href="../../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../../storage.js"></script><script defer src="../../../source-script.js"></script><script defer src="../../../source-files.js"></script><script defer src="../../../main.js"></script><noscript><link rel="stylesheet" href="../../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../../favicon.svg"></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"><a class="sidebar-logo" href="../../../rulinalg/index.html"><div class="logo-container"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></div></a></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../../rulinalg/index.html"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></a><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" 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="../../../wheel.svg"></a></div></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><span id="1">1</span>
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</pre><pre class="rust"><code><span class="doccomment">//! The norm module
//!
//! This module contains implementations of various linear algebra norms.
//! The implementations are contained within the `VectorNorm` and
//! `MatrixNorm` traits. This module also contains `VectorMetric` and
//! `MatrixMetric` traits which are used to compute the metric distance.
//!
//! These traits can be used directly by importing implementors from
//! this module. In most cases it will be easier to use the `norm` and
//! `metric` functions which exist for both vectors and matrices. These
//! functions take generic arguments for the norm to be used.
//!
//! In general you should use the least generic norm that fits your purpose.
//! For example you would choose to use a `Euclidean` norm instead of an
//! `Lp(2.0)` norm - despite them being mathematically equivalent.
//!
//! # Defining your own norm
//!
//! Note that these traits enforce no requirements on the norm. It is up
//! to the user to ensure that they define a norm correctly.
//!
//! To define your own norm you need to implement the `MatrixNorm`
//! and/or the `VectorNorm` on your own struct. When you have defined
//! a norm you get the _induced metric_ for free. This means that any
//! object which implements the `VectorNorm` or `MatrixNorm` will
//! automatically implement the `VectorMetric` and `MatrixMetric` traits
//! respectively. This induced metric will compute the norm of the
//! difference between the vectors or matrices.
</span><span class="kw">use </span>matrix::BaseMatrix;
<span class="kw">use </span>vector::Vector;
<span class="kw">use </span>utils;
<span class="kw">use </span>std::ops::Sub;
<span class="kw">use </span>libnum::Float;
<span class="doccomment">/// Trait for vector norms
</span><span class="kw">pub trait </span>VectorNorm&lt;T&gt; {
<span class="doccomment">/// Computes the vector norm.
</span><span class="kw">fn </span>norm(<span class="kw-2">&amp;</span><span class="self">self</span>, v: <span class="kw-2">&amp;</span>Vector&lt;T&gt;) -&gt; T;
}
<span class="doccomment">/// Trait for vector metrics.
</span><span class="kw">pub trait </span>VectorMetric&lt;T&gt; {
<span class="doccomment">/// Computes the metric distance between two vectors.
</span><span class="kw">fn </span>metric(<span class="kw-2">&amp;</span><span class="self">self</span>, v1: <span class="kw-2">&amp;</span>Vector&lt;T&gt;, v2: <span class="kw-2">&amp;</span>Vector&lt;T&gt;) -&gt; T;
}
<span class="doccomment">/// Trait for matrix norms.
</span><span class="kw">pub trait </span>MatrixNorm&lt;T, M: BaseMatrix&lt;T&gt;&gt; {
<span class="doccomment">/// Computes the matrix norm.
</span><span class="kw">fn </span>norm(<span class="kw-2">&amp;</span><span class="self">self</span>, m: <span class="kw-2">&amp;</span>M) -&gt; T;
}
<span class="doccomment">/// Trait for matrix metrics.
</span><span class="kw">pub trait </span>MatrixMetric&lt;<span class="lifetime">&#39;a</span>, <span class="lifetime">&#39;b</span>, T, M1: <span class="lifetime">&#39;a </span>+ BaseMatrix&lt;T&gt;, M2: <span class="lifetime">&#39;b </span>+ BaseMatrix&lt;T&gt;&gt; {
<span class="doccomment">/// Computes the metric distance between two matrices.
</span><span class="kw">fn </span>metric(<span class="kw-2">&amp;</span><span class="self">self</span>, m1: <span class="kw-2">&amp;</span><span class="lifetime">&#39;a </span>M1, m2: <span class="kw-2">&amp;</span><span class="lifetime">&#39;b </span>M2) -&gt; T;
}
<span class="doccomment">/// The induced vector metric
///
/// Given a norm `N`, the induced vector metric `M` computes
/// the metric distance, `d`, between two vectors `v1` and `v2`
/// as follows:
///
/// `d = M(v1, v2) = N(v1 - v2)`
</span><span class="kw">impl</span>&lt;U, T&gt; VectorMetric&lt;T&gt; <span class="kw">for </span>U
<span class="kw">where </span>U: VectorNorm&lt;T&gt;, T: Copy + Sub&lt;T, Output=T&gt; {
<span class="kw">fn </span>metric(<span class="kw-2">&amp;</span><span class="self">self</span>, v1: <span class="kw-2">&amp;</span>Vector&lt;T&gt;, v2: <span class="kw-2">&amp;</span>Vector&lt;T&gt;) -&gt; T {
<span class="self">self</span>.norm(<span class="kw-2">&amp;</span>(v1 - v2))
}
}
<span class="doccomment">/// The induced matrix metric
///
/// Given a norm `N`, the induced matrix metric `M` computes
/// the metric distance, `d`, between two matrices `m1` and `m2`
/// as follows:
///
/// `d = M(m1, m2) = N(m1 - m2)`
</span><span class="kw">impl</span>&lt;<span class="lifetime">&#39;a</span>, <span class="lifetime">&#39;b</span>, U, T, M1, M2&gt; MatrixMetric&lt;<span class="lifetime">&#39;a</span>, <span class="lifetime">&#39;b</span>, T, M1, M2&gt; <span class="kw">for </span>U
<span class="kw">where </span>U: MatrixNorm&lt;T, ::matrix::Matrix&lt;T&gt;&gt;,
M1: <span class="lifetime">&#39;a </span>+ BaseMatrix&lt;T&gt;,
M2: <span class="lifetime">&#39;b </span>+ BaseMatrix&lt;T&gt;,
<span class="kw-2">&amp;</span><span class="lifetime">&#39;a </span>M1: Sub&lt;<span class="kw-2">&amp;</span><span class="lifetime">&#39;b </span>M2, Output=::matrix::Matrix&lt;T&gt;&gt; {
<span class="kw">fn </span>metric(<span class="kw-2">&amp;</span><span class="self">self</span>, m1: <span class="kw-2">&amp;</span><span class="lifetime">&#39;a </span>M1, m2: <span class="kw-2">&amp;</span><span class="lifetime">&#39;b </span>M2) -&gt; T {
<span class="self">self</span>.norm(<span class="kw-2">&amp;</span>(m1 - m2))
}
}
<span class="doccomment">/// The Euclidean norm
///
/// The Euclidean norm computes the square-root
/// of the sum of squares.
///
/// `||v|| = SQRT(SUM(v_i * v_i))`
</span><span class="attribute">#[derive(Debug)]
</span><span class="kw">pub struct </span>Euclidean;
<span class="kw">impl</span>&lt;T: Float&gt; VectorNorm&lt;T&gt; <span class="kw">for </span>Euclidean {
<span class="kw">fn </span>norm(<span class="kw-2">&amp;</span><span class="self">self</span>, v: <span class="kw-2">&amp;</span>Vector&lt;T&gt;) -&gt; T {
utils::dot(v.data(), v.data()).sqrt()
}
}
<span class="kw">impl</span>&lt;T: Float, M: BaseMatrix&lt;T&gt;&gt; MatrixNorm&lt;T, M&gt; <span class="kw">for </span>Euclidean {
<span class="kw">fn </span>norm(<span class="kw-2">&amp;</span><span class="self">self</span>, m: <span class="kw-2">&amp;</span>M) -&gt; T {
<span class="kw">let </span><span class="kw-2">mut </span>s = T::zero();
<span class="kw">for </span>row <span class="kw">in </span>m.row_iter() {
s = s + utils::dot(row.raw_slice(), row.raw_slice());
}
s.sqrt()
}
}
<span class="doccomment">/// The Lp norm
///
/// The
/// [Lp norm](https://en.wikipedia.org/wiki/Norm_(mathematics)#p-norm)
/// computes the `p`th root of the sum of elements
/// to the `p`th power.
///
/// The Lp norm requires `p` to be greater than
/// or equal `1`.
///
/// We use an enum for this norm to allow us to explicitly handle
/// special cases at compile time. For example, we have an `Infinity`
/// variant which handles the special case when the `Lp` norm is a
/// supremum over absolute values. The `Integer` variant gives us a
/// performance boost when `p` is an integer.
///
/// You should avoid matching directly against this enum as it is likely
/// to grow.
</span><span class="attribute">#[derive(Debug)]
</span><span class="kw">pub enum </span>Lp&lt;T: Float&gt; {
<span class="doccomment">/// The L-infinity norm (supremum)
</span>Infinity,
<span class="doccomment">/// The Lp norm where p is an integer
</span>Integer(i32),
<span class="doccomment">/// The Lp norm where p is a float
</span>Float(T)
}
<span class="kw">impl</span>&lt;T: Float&gt; VectorNorm&lt;T&gt; <span class="kw">for </span>Lp&lt;T&gt; {
<span class="kw">fn </span>norm(<span class="kw-2">&amp;</span><span class="self">self</span>, v: <span class="kw-2">&amp;</span>Vector&lt;T&gt;) -&gt; T {
<span class="kw">match </span><span class="kw-2">*</span><span class="self">self </span>{
Lp::Infinity =&gt; {
<span class="comment">// Compute supremum
</span><span class="kw">let </span><span class="kw-2">mut </span>abs_sup = T::zero();
<span class="kw">for </span>d <span class="kw">in </span>v.iter().map(|d| d.abs()) {
<span class="kw">if </span>d &gt; abs_sup {
abs_sup = d;
}
}
abs_sup
},
Lp::Integer(p) =&gt; {
<span class="macro">assert!</span>(p &gt;= <span class="number">1</span>, <span class="string">&quot;p value in Lp norm must be &gt;= 1&quot;</span>);
<span class="comment">// Compute standard lp norm
</span><span class="kw">let </span><span class="kw-2">mut </span>s = T::zero();
<span class="kw">for </span>x <span class="kw">in </span>v {
s = s + x.abs().powi(p);
}
s.powf(T::from(p).expect(<span class="string">&quot;Could not cast i32 to float&quot;</span>).recip())
},
Lp::Float(p) =&gt; {
<span class="macro">assert!</span>(p &gt;= T::one(), <span class="string">&quot;p value in Lp norm must be &gt;= 1&quot;</span>);
<span class="comment">// Compute standard lp norm
</span><span class="kw">let </span><span class="kw-2">mut </span>s = T::zero();
<span class="kw">for </span>x <span class="kw">in </span>v {
s = s + x.abs().powf(p);
}
s.powf(p.recip())
}
}
}
}
<span class="kw">impl</span>&lt;T: Float, M: BaseMatrix&lt;T&gt;&gt; MatrixNorm&lt;T, M&gt; <span class="kw">for </span>Lp&lt;T&gt; {
<span class="kw">fn </span>norm(<span class="kw-2">&amp;</span><span class="self">self</span>, m: <span class="kw-2">&amp;</span>M) -&gt; T {
<span class="kw">match </span><span class="kw-2">*</span><span class="self">self </span>{
Lp::Infinity =&gt; {
<span class="comment">// Compute supremum
</span><span class="kw">let </span><span class="kw-2">mut </span>abs_sup = T::zero();
<span class="kw">for </span>d <span class="kw">in </span>m.iter().map(|d| d.abs()) {
<span class="kw">if </span>d &gt; abs_sup {
abs_sup = d;
}
}
abs_sup
},
Lp::Integer(p) =&gt; {
<span class="macro">assert!</span>(p &gt;= <span class="number">1</span>, <span class="string">&quot;p value in Lp norm must be &gt;= 1&quot;</span>);
<span class="comment">// Compute standard lp norm
</span><span class="kw">let </span><span class="kw-2">mut </span>s = T::zero();
<span class="kw">for </span>x <span class="kw">in </span>m.iter() {
s = s + x.abs().powi(p);
}
s.powf(T::from(p).expect(<span class="string">&quot;Could not cast i32 to float&quot;</span>).recip())
},
Lp::Float(p) =&gt; {
<span class="macro">assert!</span>(p &gt;= T::one(), <span class="string">&quot;p value in Lp norm must be &gt;= 1&quot;</span>);
<span class="comment">// Compute standard lp norm
</span><span class="kw">let </span><span class="kw-2">mut </span>s = T::zero();
<span class="kw">for </span>x <span class="kw">in </span>m.iter() {
s = s + x.abs().powf(p);
}
s.powf(p.recip())
}
}
}
}
<span class="attribute">#[cfg(test)]
</span><span class="kw">mod </span>tests {
<span class="kw">use </span>libnum::Float;
<span class="kw">use </span>std::f64;
<span class="kw">use super</span>::<span class="kw-2">*</span>;
<span class="kw">use </span>vector::Vector;
<span class="kw">use </span>matrix::{Matrix, MatrixSlice};
<span class="attribute">#[test]
</span><span class="kw">fn </span>test_euclidean_vector_norm() {
<span class="kw">let </span>v = <span class="macro">vector!</span>[<span class="number">3.0</span>, <span class="number">4.0</span>];
<span class="macro">assert_scalar_eq!</span>(VectorNorm::norm(<span class="kw-2">&amp;</span>Euclidean, <span class="kw-2">&amp;</span>v), <span class="number">5.0</span>, comp = float);
}
<span class="attribute">#[test]
</span><span class="kw">fn </span>test_euclidean_matrix_norm() {
<span class="kw">let </span>m = <span class="macro">matrix!</span>[<span class="number">3.0</span>, <span class="number">4.0</span>;
<span class="number">1.0</span>, <span class="number">3.0</span>];
<span class="macro">assert_scalar_eq!</span>(MatrixNorm::norm(<span class="kw-2">&amp;</span>Euclidean, <span class="kw-2">&amp;</span>m), <span class="number">35.0</span>.sqrt(), comp = float);
}
<span class="attribute">#[test]
</span><span class="kw">fn </span>test_euclidean_matrix_slice_norm() {
<span class="kw">let </span>m = <span class="macro">matrix!</span>[<span class="number">3.0</span>, <span class="number">4.0</span>;
<span class="number">1.0</span>, <span class="number">3.0</span>];
<span class="kw">let </span>slice = MatrixSlice::from_matrix(<span class="kw-2">&amp;</span>m, [<span class="number">0</span>,<span class="number">0</span>], <span class="number">1</span>, <span class="number">2</span>);
<span class="macro">assert_scalar_eq!</span>(MatrixNorm::norm(<span class="kw-2">&amp;</span>Euclidean, <span class="kw-2">&amp;</span>slice), <span class="number">5.0</span>, comp = float);
}
<span class="attribute">#[test]
</span><span class="kw">fn </span>test_euclidean_vector_metric() {
<span class="kw">let </span>v = <span class="macro">vector!</span>[<span class="number">3.0</span>, <span class="number">4.0</span>];
<span class="macro">assert_scalar_eq!</span>(VectorMetric::metric(<span class="kw-2">&amp;</span>Euclidean, <span class="kw-2">&amp;</span>v, <span class="kw-2">&amp;</span>v), <span class="number">0.0</span>, comp = float);
<span class="kw">let </span>v1 = <span class="macro">vector!</span>[<span class="number">0.0</span>, <span class="number">0.0</span>];
<span class="macro">assert_scalar_eq!</span>(VectorMetric::metric(<span class="kw-2">&amp;</span>Euclidean, <span class="kw-2">&amp;</span>v, <span class="kw-2">&amp;</span>v1), <span class="number">5.0</span>, comp = float);
<span class="kw">let </span>v2 = <span class="macro">vector!</span>[<span class="number">4.0</span>, <span class="number">3.0</span>];
<span class="macro">assert_scalar_eq!</span>(VectorMetric::metric(<span class="kw-2">&amp;</span>Euclidean, <span class="kw-2">&amp;</span>v, <span class="kw-2">&amp;</span>v2), <span class="number">2.0</span>.sqrt(), comp = float);
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>test_euclidean_vector_metric_bad_dim() {
<span class="kw">let </span>v = <span class="macro">vector!</span>[<span class="number">3.0</span>, <span class="number">4.0</span>];
<span class="kw">let </span>v2 = <span class="macro">vector!</span>[<span class="number">1.0</span>, <span class="number">2.0</span>, <span class="number">3.0</span>];
VectorMetric::metric(<span class="kw-2">&amp;</span>Euclidean, <span class="kw-2">&amp;</span>v, <span class="kw-2">&amp;</span>v2);
}
<span class="attribute">#[test]
</span><span class="kw">fn </span>test_euclidean_matrix_metric() {
<span class="kw">let </span>m = <span class="macro">matrix!</span>[<span class="number">3.0</span>, <span class="number">4.0</span>;
<span class="number">1.0</span>, <span class="number">3.0</span>];
<span class="macro">assert_scalar_eq!</span>(MatrixMetric::metric(<span class="kw-2">&amp;</span>Euclidean, <span class="kw-2">&amp;</span>m, <span class="kw-2">&amp;</span>m), <span class="number">0.0</span>, comp = float);
<span class="kw">let </span>m1 = Matrix::zeros(<span class="number">2</span>, <span class="number">2</span>);
<span class="macro">assert_scalar_eq!</span>(MatrixMetric::metric(<span class="kw-2">&amp;</span>Euclidean, <span class="kw-2">&amp;</span>m, <span class="kw-2">&amp;</span>m1), <span class="number">35.0</span>.sqrt(), comp = float);
<span class="kw">let </span>m2 = <span class="macro">matrix!</span>[<span class="number">2.0</span>, <span class="number">3.0</span>;
<span class="number">2.0</span>, <span class="number">4.0</span>];
<span class="macro">assert_scalar_eq!</span>(MatrixMetric::metric(<span class="kw-2">&amp;</span>Euclidean, <span class="kw-2">&amp;</span>m, <span class="kw-2">&amp;</span>m2), <span class="number">2.0</span>, comp = float);
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>test_euclidean_matrix_metric_bad_dim() {
<span class="kw">let </span>m = <span class="macro">matrix!</span>[<span class="number">3.0</span>, <span class="number">4.0</span>];
<span class="kw">let </span>m2 = <span class="macro">matrix!</span>[<span class="number">1.0</span>, <span class="number">2.0</span>, <span class="number">3.0</span>];
MatrixMetric::metric(<span class="kw-2">&amp;</span>Euclidean, <span class="kw-2">&amp;</span>m, <span class="kw-2">&amp;</span>m2);
}
<span class="attribute">#[test]
</span><span class="kw">fn </span>test_euclidean_matrix_slice_metric() {
<span class="kw">let </span>m = <span class="macro">matrix!</span>[
<span class="number">1.0</span>, <span class="number">1.0</span>, <span class="number">1.0</span>;
<span class="number">1.0</span>, <span class="number">1.0</span>, <span class="number">1.0</span>;
<span class="number">1.0</span>, <span class="number">1.0</span>, <span class="number">1.0
</span>];
<span class="kw">let </span>m2 = <span class="macro">matrix!</span>[
<span class="number">0.0</span>, <span class="number">0.0</span>, <span class="number">0.0</span>;
<span class="number">0.0</span>, <span class="number">0.0</span>, <span class="number">0.0</span>;
<span class="number">0.0</span>, <span class="number">0.0</span>, <span class="number">0.0
</span>];
<span class="kw">let </span>m_slice = MatrixSlice::from_matrix(
<span class="kw-2">&amp;</span>m, [<span class="number">0</span>; <span class="number">2</span>], <span class="number">1</span>, <span class="number">2
</span>);
<span class="kw">let </span>m2_slice = MatrixSlice::from_matrix(
<span class="kw-2">&amp;</span>m2, [<span class="number">0</span>; <span class="number">2</span>], <span class="number">1</span>, <span class="number">2
</span>);
<span class="macro">assert_scalar_eq!</span>(MatrixMetric::metric(<span class="kw-2">&amp;</span>Euclidean, <span class="kw-2">&amp;</span>m_slice, <span class="kw-2">&amp;</span>m2_slice), <span class="number">2.0</span>.sqrt(), comp = exact);
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>test_euclidean_matrix_slice_metric_bad_dim() {
<span class="kw">let </span>m = <span class="macro">matrix!</span>[<span class="number">3.0</span>, <span class="number">4.0</span>];
<span class="kw">let </span>m2 = <span class="macro">matrix!</span>[<span class="number">1.0</span>, <span class="number">2.0</span>, <span class="number">3.0</span>];
<span class="kw">let </span>m_slice = MatrixSlice::from_matrix(
<span class="kw-2">&amp;</span>m, [<span class="number">0</span>; <span class="number">2</span>], <span class="number">1</span>, <span class="number">1
</span>);
<span class="kw">let </span>m2_slice = MatrixSlice::from_matrix(
<span class="kw-2">&amp;</span>m2, [<span class="number">0</span>; <span class="number">2</span>], <span class="number">1</span>, <span class="number">2
</span>);
MatrixMetric::metric(<span class="kw-2">&amp;</span>Euclidean, <span class="kw-2">&amp;</span>m_slice, <span class="kw-2">&amp;</span>m2_slice);
}
<span class="attribute">#[test]
</span><span class="kw">fn </span>test_lp_vector_supremum() {
<span class="kw">let </span>v = <span class="macro">vector!</span>[-<span class="number">5.0</span>, <span class="number">3.0</span>];
<span class="kw">let </span>sup = VectorNorm::norm(<span class="kw-2">&amp;</span>Lp::Infinity, <span class="kw-2">&amp;</span>v);
<span class="macro">assert_eq!</span>(sup, <span class="number">5.0</span>);
}
<span class="attribute">#[test]
</span><span class="kw">fn </span>test_lp_matrix_supremum() {
<span class="kw">let </span>m = <span class="macro">matrix!</span>[<span class="number">0.0</span>, -<span class="number">2.0</span>;
<span class="number">3.5</span>, <span class="number">1.0</span>];
<span class="kw">let </span>sup = MatrixNorm::norm(<span class="kw-2">&amp;</span>Lp::Infinity, <span class="kw-2">&amp;</span>m);
<span class="macro">assert_eq!</span>(sup, <span class="number">3.5</span>);
}
<span class="attribute">#[test]
</span><span class="kw">fn </span>test_lp_vector_one() {
<span class="kw">let </span>v = <span class="macro">vector!</span>[<span class="number">1.0</span>, <span class="number">2.0</span>, -<span class="number">2.0</span>];
<span class="macro">assert_eq!</span>(VectorNorm::norm(<span class="kw-2">&amp;</span>Lp::Integer(<span class="number">1</span>), <span class="kw-2">&amp;</span>v), <span class="number">5.0</span>);
}
<span class="attribute">#[test]
</span><span class="kw">fn </span>test_lp_matrix_one() {
<span class="kw">let </span>m = <span class="macro">matrix!</span>[<span class="number">1.0</span>, -<span class="number">2.0</span>;
<span class="number">0.5</span>, <span class="number">1.0</span>];
<span class="macro">assert_eq!</span>(MatrixNorm::norm(<span class="kw-2">&amp;</span>Lp::Integer(<span class="number">1</span>), <span class="kw-2">&amp;</span>m), <span class="number">4.5</span>);
}
<span class="attribute">#[test]
</span><span class="kw">fn </span>test_lp_vector_float() {
<span class="kw">let </span>v = <span class="macro">vector!</span>[<span class="number">1.0</span>, <span class="number">2.0</span>, -<span class="number">2.0</span>];
<span class="macro">assert_eq!</span>(VectorNorm::norm(<span class="kw-2">&amp;</span>Lp::Float(<span class="number">1.0</span>), <span class="kw-2">&amp;</span>v), <span class="number">5.0</span>);
}
<span class="attribute">#[test]
</span><span class="kw">fn </span>test_lp_matrix_float() {
<span class="kw">let </span>m = <span class="macro">matrix!</span>[<span class="number">1.0</span>, -<span class="number">2.0</span>;
<span class="number">0.5</span>, <span class="number">1.0</span>];
<span class="macro">assert_eq!</span>(MatrixNorm::norm(<span class="kw-2">&amp;</span>Lp::Float(<span class="number">1.0</span>), <span class="kw-2">&amp;</span>m), <span class="number">4.5</span>);
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>test_lp_vector_bad_p() {
<span class="kw">let </span>v = Vector::new(<span class="macro">vec!</span>[]);
VectorNorm::norm(<span class="kw-2">&amp;</span>Lp::Float(<span class="number">0.5</span>), <span class="kw-2">&amp;</span>v);
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>test_lp_matrix_bad_p() {
<span class="kw">let </span>m = <span class="macro">matrix!</span>[];
MatrixNorm::norm(<span class="kw-2">&amp;</span>Lp::Float(<span class="number">0.5</span>), <span class="kw-2">&amp;</span>m);
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>test_lp_vector_bad_int_p() {
<span class="kw">let </span>v: Vector&lt;f64&gt; = Vector::new(<span class="macro">vec!</span>[]);
VectorNorm::norm(<span class="kw-2">&amp;</span>Lp::Integer(<span class="number">0</span>), <span class="kw-2">&amp;</span>v);
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>test_lp_matrix_bad_int_p() {
<span class="kw">let </span>m: Matrix&lt;f64&gt; = <span class="macro">matrix!</span>[];
MatrixNorm::norm(<span class="kw-2">&amp;</span>Lp::Integer(<span class="number">0</span>), <span class="kw-2">&amp;</span>m);
}
}
</code></pre></div>
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