<!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/linalg/udu.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>udu.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(feature = <span class="string">"serde-serialize-no-std"</span>)]
</span><span class="kw">use </span>serde::{Deserialize, Serialize};
<span class="kw">use </span><span class="kw">crate</span>::allocator::Allocator;
<span class="kw">use </span><span class="kw">crate</span>::base::{Const, DefaultAllocator, OMatrix, OVector};
<span class="kw">use </span><span class="kw">crate</span>::dimension::Dim;
<span class="kw">use </span>simba::scalar::RealField;
<span class="doccomment">/// UDU factorization.
</span><span class="attr">#[cfg_attr(feature = <span class="string">"serde-serialize-no-std"</span>, derive(Serialize, Deserialize))]
#[cfg_attr(
feature = <span class="string">"serde-serialize-no-std"</span>,
serde(bound(serialize = <span class="string">"OVector<T, D>: Serialize, OMatrix<T, D, D>: Serialize"</span>))
)]
#[cfg_attr(
feature = <span class="string">"serde-serialize-no-std"</span>,
serde(bound(
deserialize = <span class="string">"OVector<T, D>: Deserialize<'de>, OMatrix<T, D, D>: Deserialize<'de>"
</span>))
)]
#[derive(Clone, Debug)]
</span><span class="kw">pub struct </span>UDU<T: RealField, D: Dim>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D> + Allocator<T, D, D>,
{
<span class="doccomment">/// The upper triangular matrix resulting from the factorization
</span><span class="kw">pub </span>u: OMatrix<T, D, D>,
<span class="doccomment">/// The diagonal matrix resulting from the factorization
</span><span class="kw">pub </span>d: OVector<T, D>,
}
<span class="kw">impl</span><T: RealField, D: Dim> Copy <span class="kw">for </span>UDU<T, D>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D> + Allocator<T, D, D>,
OVector<T, D>: Copy,
OMatrix<T, D, D>: Copy,
{
}
<span class="kw">impl</span><T: RealField, D: Dim> UDU<T, D>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D> + Allocator<T, D, D>,
{
<span class="doccomment">/// Computes the UDU^T factorization.
///
/// The input matrix `p` is assumed to be symmetric and this decomposition will only read
/// the upper-triangular part of `p`.
///
/// Ref.: "Optimal control and estimation-Dover Publications", Robert F. Stengel, (1994) page 360
</span><span class="kw">pub fn </span>new(p: OMatrix<T, D, D>) -> <span class="prelude-ty">Option</span><<span class="self">Self</span>> {
<span class="kw">let </span>n = p.ncols();
<span class="kw">let </span>n_dim = p.shape_generic().<span class="number">1</span>;
<span class="kw">let </span><span class="kw-2">mut </span>d = OVector::zeros_generic(n_dim, Const::<<span class="number">1</span>>);
<span class="kw">let </span><span class="kw-2">mut </span>u = OMatrix::zeros_generic(n_dim, n_dim);
d[n - <span class="number">1</span>] = p[(n - <span class="number">1</span>, n - <span class="number">1</span>)].clone();
<span class="kw">if </span>d[n - <span class="number">1</span>].is_zero() {
<span class="kw">return </span><span class="prelude-val">None</span>;
}
u.column_mut(n - <span class="number">1</span>)
.axpy(T::one() / d[n - <span class="number">1</span>].clone(), <span class="kw-2">&</span>p.column(n - <span class="number">1</span>), T::zero());
<span class="kw">for </span>j <span class="kw">in </span>(<span class="number">0</span>..n - <span class="number">1</span>).rev() {
<span class="kw">let </span><span class="kw-2">mut </span>d_j = d[j].clone();
<span class="kw">for </span>k <span class="kw">in </span>j + <span class="number">1</span>..n {
d_j += d[k].clone() * u[(j, k)].clone().powi(<span class="number">2</span>);
}
d[j] = p[(j, j)].clone() - d_j;
<span class="kw">if </span>d[j].is_zero() {
<span class="kw">return </span><span class="prelude-val">None</span>;
}
<span class="kw">for </span>i <span class="kw">in </span>(<span class="number">0</span>..=j).rev() {
<span class="kw">let </span><span class="kw-2">mut </span>u_ij = u[(i, j)].clone();
<span class="kw">for </span>k <span class="kw">in </span>j + <span class="number">1</span>..n {
u_ij += d[k].clone() * u[(j, k)].clone() * u[(i, k)].clone();
}
u[(i, j)] = (p[(i, j)].clone() - u_ij) / d[j].clone();
}
u[(j, j)] = T::one();
}
<span class="prelude-val">Some</span>(<span class="self">Self </span>{ u, d })
}
<span class="doccomment">/// Returns the diagonal elements as a matrix
</span><span class="attr">#[must_use]
</span><span class="kw">pub fn </span>d_matrix(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, D, D> {
OMatrix::from_diagonal(<span class="kw-2">&</span><span class="self">self</span>.d)
}
}
</code></pre></div>
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