<!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/balancing.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>balancing.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="doccomment">//! Functions for balancing a matrix.
</span><span class="kw">use </span>simba::scalar::RealField;
<span class="kw">use </span>std::ops::{DivAssign, MulAssign};
<span class="kw">use </span><span class="kw">crate</span>::allocator::Allocator;
<span class="kw">use </span><span class="kw">crate</span>::base::dimension::Dim;
<span class="kw">use </span><span class="kw">crate</span>::base::{Const, DefaultAllocator, OMatrix, OVector};
<span class="doccomment">/// Applies in-place a modified Parlett and Reinsch matrix balancing with 2-norm to the matrix and returns
/// the corresponding diagonal transformation.
///
/// See <https://arxiv.org/pdf/1401.5766.pdf>
</span><span class="kw">pub fn </span>balance_parlett_reinsch<T: RealField, D: Dim>(matrix: <span class="kw-2">&mut </span>OMatrix<T, D, D>) -> OVector<T, D>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
{
<span class="macro">assert!</span>(matrix.is_square(), <span class="string">"Unable to balance a non-square matrix."</span>);
<span class="kw">let </span>dim = matrix.shape_generic().<span class="number">0</span>;
<span class="kw">let </span>radix: T = <span class="kw">crate</span>::convert(<span class="number">2.0f64</span>);
<span class="kw">let </span><span class="kw-2">mut </span>d = OVector::from_element_generic(dim, Const::<<span class="number">1</span>>, T::one());
<span class="kw">let </span><span class="kw-2">mut </span>converged = <span class="bool-val">false</span>;
<span class="kw">while </span>!converged {
converged = <span class="bool-val">true</span>;
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..dim.value() {
<span class="kw">let </span><span class="kw-2">mut </span>n_col = matrix.column(i).norm_squared();
<span class="kw">let </span><span class="kw-2">mut </span>n_row = matrix.row(i).norm_squared();
<span class="kw">let </span><span class="kw-2">mut </span>f = T::one();
<span class="kw">let </span>s = n_col.clone() + n_row.clone();
n_col = n_col.sqrt();
n_row = n_row.sqrt();
<span class="kw">if </span>n_col.clone().is_zero() || n_row.clone().is_zero() {
<span class="kw">continue</span>;
}
<span class="kw">while </span>n_col.clone() < n_row.clone() / radix.clone() {
n_col <span class="kw-2">*</span>= radix.clone();
n_row /= radix.clone();
f <span class="kw-2">*</span>= radix.clone();
}
<span class="kw">while </span>n_col.clone() >= n_row.clone() * radix.clone() {
n_col /= radix.clone();
n_row <span class="kw-2">*</span>= radix.clone();
f /= radix.clone();
}
<span class="kw">let </span>eps: T = <span class="kw">crate</span>::convert(<span class="number">0.95</span>);
<span class="attr">#[allow(clippy::suspicious_operation_groupings)]
</span><span class="kw">if </span>n_col.clone() * n_col + n_row.clone() * n_row < eps * s {
converged = <span class="bool-val">false</span>;
d[i] <span class="kw-2">*</span>= f.clone();
matrix.column_mut(i).mul_assign(f.clone());
matrix.row_mut(i).div_assign(f.clone());
}
}
}
d
}
<span class="doccomment">/// Computes in-place `D * m * D.inverse()`, where `D` is the matrix with diagonal `d`.
</span><span class="kw">pub fn </span>unbalance<T: RealField, D: Dim>(m: <span class="kw-2">&mut </span>OMatrix<T, D, D>, d: <span class="kw-2">&</span>OVector<T, D>)
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
{
<span class="macro">assert!</span>(m.is_square(), <span class="string">"Unable to unbalance a non-square matrix."</span>);
<span class="macro">assert_eq!</span>(m.nrows(), d.len(), <span class="string">"Unbalancing: mismatched dimensions."</span>);
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..d.len() {
<span class="kw">let </span><span class="kw-2">mut </span>col = m.column_mut(j);
<span class="kw">let </span>denom = T::one() / d[j].clone();
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..d.len() {
col[i] <span class="kw-2">*</span>= d[i].clone() * denom.clone();
}
}
}
</code></pre></div>
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