| <!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/matrix/decomposition/householder.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>householder.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="kw">use </span>matrix::{Matrix, BaseMatrix, BaseMatrixMut, Column, ColumnMut}; |
| <span class="kw">use </span>vector::Vector; |
| <span class="kw">use </span>utils; |
| |
| <span class="kw">use </span>libnum::Float; |
| |
| <span class="doccomment">/// An efficient representation of a Householder reflection, |
| /// also known as Householder matrix or elementary reflector. |
| /// |
| /// Mathematically, it has the form |
| /// H := I - τ v vᵀ, |
| /// with τ = 2 / (vᵀv). |
| /// |
| /// Given a vector `x`, it is possible to choose `v` such that |
| /// Hx = a e1, |
| /// where a is a constant and e1 is the standard unit vector |
| /// whose elements are zero except the first, which is 1. |
| /// |
| /// The implementation here is largely based upon the contents |
| /// of Chapter 5.1 (Householder and Givens Transformations) |
| /// in Matrix Computations, 4th Ed, Golub and Van Loan, |
| /// but with modifications that among other things makes |
| /// the implementation compliant with LAPACK. |
| </span><span class="kw">pub struct </span>HouseholderReflection<T> { |
| v: Vector<T>, |
| tau: T |
| } |
| |
| <span class="kw">impl</span><T: Float> HouseholderReflection<T> { |
| <span class="doccomment">/// Compute the Householder reflection which will zero out |
| /// all elements in the vector `x` except the first. |
| </span><span class="kw">pub fn </span>compute(x: Vector<T>) -> HouseholderReflection<T> { |
| <span class="comment">// The following code is loosely based on notes in |
| // Applied Numerical Linear Algebra by Demmel, |
| // Matrix Computations 4th Ed by Golub & Van Loan, |
| // as well as LAPACK documentation. |
| // |
| // From Demmel, we have that we can choose the vector |
| // v = [ x1 + sign(x1) norm(x) ] |
| // [ x[2:] ] |
| // as our Householder vector (the choice of sign in v(1) avoids |
| // cancellation issues which would lead to reduced accuracy in |
| // certain corner cases). However, we must divide v by |
| // v1 so that the first element of v is 1. Propagating these |
| // changes into τ leads to the below code. |
| // Note that if x[2:] == 0 (norm is identically zero), |
| // we explicitly set τ = 0 since x is already a multiple of |
| // the unit vector e1 (and we avoid potential division by zero). |
| </span><span class="kw">let </span>m = x.size(); |
| |
| <span class="kw">if </span>m > <span class="number">0 </span>{ |
| <span class="kw">let </span>sigma = utils::dot(<span class="kw-2">&</span>x.data()[<span class="number">1 </span>..], <span class="kw-2">&</span>x.data()[<span class="number">1 </span>..]); |
| <span class="kw">let </span>x0 = x[<span class="number">0</span>]; |
| <span class="kw">let </span>tau; |
| <span class="kw">let </span><span class="kw-2">mut </span>v = x; |
| |
| <span class="kw">if </span>sigma == T::zero() { |
| <span class="comment">// The vector is already a multiple of e1, the unit vector for which |
| // 1 is the first element and all other elements are zero. |
| </span>tau = T::zero(); |
| } <span class="kw">else </span>{ |
| <span class="kw">let </span>x_norm = T::sqrt(x0 * x0 + sigma); |
| <span class="comment">// This choice avoids accuracy issues related |
| // to cancellation |
| // (see e.g. Demmel, Applied Numerical Linear Algebra). |
| </span><span class="kw">let </span>v0 = <span class="kw">if </span>x0 > T::zero() { x0 + x_norm } |
| <span class="kw">else </span>{ x0 - x_norm }; |
| |
| <span class="comment">// Normalize the Householder vector v so that |
| // its first element is 1. |
| </span><span class="kw">let </span>two = T::from(<span class="number">2</span>).unwrap(); |
| tau = two * v0 * v0 / (v0 * v0 + sigma); |
| v[<span class="number">0</span>] = v0; |
| v = v / v0; |
| } |
| |
| HouseholderReflection { |
| v: v, |
| tau: tau |
| } |
| } <span class="kw">else </span>{ |
| <span class="comment">// x is an empty vector, so just use it as the |
| // Householder vector |
| </span>HouseholderReflection { |
| v: x, |
| tau: T::zero() |
| } |
| } |
| } |
| |
| <span class="doccomment">/// Left-multiplies the given matrix by this Householder reflection. |
| /// |
| /// More precisely, let `H` denote this Householder reflection matrix, |
| /// and let `A` be a dimensionally compatible matrix. Then |
| /// this function computes the product `HA` and stores the result |
| /// back in `A`. |
| /// |
| /// The user must provide a buffer of size `A.cols()` which is used |
| /// to store intermediate results. |
| </span><span class="kw">pub fn </span>buffered_left_multiply_into<M>(<span class="kw-2">&</span><span class="self">self</span>, matrix: <span class="kw-2">&mut </span>M, buffer: <span class="kw-2">&mut </span>[T]) |
| <span class="kw">where </span>M: BaseMatrixMut<T> |
| { |
| <span class="kw">use </span>internal_utils::{transpose_gemv, ger}; |
| <span class="macro">assert!</span>(buffer.len() == matrix.cols()); |
| |
| <span class="comment">// Recall that the Householder reflection is represented by |
| // H = I - τ v vᵀ, |
| // |
| // which means that the product HA can be computed as |
| // |
| // HA = A - (τ v) (vᵀ A) = A - (τ v) (Aᵀ v)ᵀ, |
| // |
| // which constitutes a (transposed) matrix-vector product` |
| // u = Aᵀ v and a rank-1 update A <- A - τ v uᵀ |
| // |
| // Performing both the matrix-vector product and the |
| // rank-1 update can actually be performed without |
| // allocating any additional memory, but this would access |
| // the data in the matrix column-by-column, which is inefficient. |
| // Instead, we will use the provided buffer to hold the result of the |
| // matrix-vector product. |
| </span><span class="kw">let </span><span class="kw-2">ref </span>v = <span class="self">self</span>.v.data(); |
| <span class="kw">let </span><span class="kw-2">mut </span>u = buffer; |
| |
| <span class="comment">// u = A^T v |
| </span>transpose_gemv(matrix, v, u); |
| |
| <span class="comment">// A <- A - τ v uᵀ |
| </span>ger(matrix, - <span class="self">self</span>.tau, v, u); |
| } |
| |
| <span class="kw">pub fn </span>as_vector(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="kw-2">&</span>Vector<T> { |
| <span class="kw-2">&</span><span class="self">self</span>.v |
| } |
| |
| <span class="kw">pub fn </span>into_vector(<span class="self">self</span>) -> Vector<T> { |
| <span class="self">self</span>.v |
| } |
| |
| <span class="kw">pub fn </span>from_parameters(v: Vector<T>, tau: T) -> HouseholderReflection<T> { |
| HouseholderReflection { |
| v: v, |
| tau: tau |
| } |
| } |
| |
| <span class="kw">pub fn </span>tau(<span class="kw-2">&</span><span class="self">self</span>) -> T { |
| <span class="self">self</span>.tau |
| } |
| |
| <span class="kw">pub fn </span>store_in_col(<span class="kw-2">&</span><span class="self">self</span>, col: <span class="kw-2">&mut </span>ColumnMut<T>) { |
| <span class="kw">let </span>m = col.rows(); |
| <span class="macro">assert!</span>(m == <span class="self">self</span>.v.size()); |
| |
| <span class="kw">if </span>m > <span class="number">0 </span>{ |
| <span class="comment">// The first element is implicitly 1, so make sure we don't |
| // touch it |
| </span><span class="kw">let </span><span class="kw-2">mut </span>slice_after_first = col.sub_slice_mut([<span class="number">1</span>, <span class="number">0</span>], m - <span class="number">1</span>, <span class="number">1</span>); |
| <span class="kw">let </span><span class="kw-2">mut </span>col_after_first = slice_after_first.col_mut(<span class="number">0</span>); |
| col_after_first.clone_from_slice(<span class="kw-2">&</span><span class="self">self</span>.as_vector().data()[<span class="number">1</span>..]); |
| } |
| } |
| } |
| |
| <span class="doccomment">/// An efficient representation for a composition of |
| /// Householder transformations. |
| /// |
| /// This means that `HouseholderComposition` represents |
| /// an operator `Q` of the form |
| /// |
| /// ```text |
| /// Q = Q_1 * Q_2 * ... * Q_p |
| /// ``` |
| /// |
| /// as explained in the documentation for |
| /// [HouseholderQr](struct.HouseholderQr.html). |
| </span><span class="attribute">#[derive(Debug, Clone)] |
| </span><span class="kw">pub struct </span>HouseholderComposition<<span class="lifetime">'a</span>, T> <span class="kw">where </span>T: <span class="lifetime">'a </span>{ |
| storage: <span class="kw-2">&</span><span class="lifetime">'a </span>Matrix<T>, |
| tau: <span class="kw-2">&</span><span class="lifetime">'a </span>[T] |
| } |
| |
| <span class="doccomment">/// Instantiates a HouseholderComposition with the given |
| /// storage and vector of tau values. |
| /// |
| /// Note: This function is deliberately not exported to |
| /// the public API. This means that users cannot create |
| /// a HouseholderComposition by themselves, which is desirable |
| /// because we want to have the freedom to change details |
| /// of the internal representation if necessary. |
| </span><span class="kw">pub fn </span>create_composition<<span class="lifetime">'a</span>, T>(storage: <span class="kw-2">&</span><span class="lifetime">'a </span>Matrix<T>, tau: <span class="kw-2">&</span><span class="lifetime">'a </span>[T]) |
| -> HouseholderComposition<<span class="lifetime">'a</span>, T> |
| { |
| HouseholderComposition { |
| storage: storage, |
| tau: tau |
| } |
| } |
| |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, T> HouseholderComposition<<span class="lifetime">'a</span>, T> <span class="kw">where </span>T: Float { |
| <span class="doccomment">/// Given a matrix `A` of compatible dimensions, computes |
| /// the product `A <- QA`, storing the result in `A`. |
| </span><span class="kw">pub fn </span>left_multiply_into<X>(<span class="kw-2">&</span><span class="self">self</span>, matrix: <span class="kw-2">&mut </span>X) |
| <span class="kw">where </span>X: BaseMatrixMut<T> |
| { |
| <span class="kw">use </span>std::cmp::min; |
| |
| <span class="kw">let </span>m = <span class="self">self</span>.storage.rows(); |
| <span class="kw">let </span>n = <span class="self">self</span>.storage.cols(); |
| <span class="kw">let </span>p = min(m, n); |
| <span class="kw">let </span>q = matrix.cols(); |
| |
| <span class="macro">assert!</span>(matrix.rows() == m, <span class="string">"Matrix does not have compatible dimensions."</span>); |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>house_buffer = Vec::with_capacity(m); |
| <span class="kw">let </span><span class="kw-2">mut </span>multiply_buffer = <span class="macro">vec!</span>[T::zero(); q]; |
| <span class="kw">for </span>j <span class="kw">in </span>(<span class="number">0 </span>.. p).rev() { |
| house_buffer.resize(m - j, T::zero()); |
| <span class="kw">let </span>storage_block = <span class="self">self</span>.storage.sub_slice([j, j], m - j, n - j); |
| <span class="kw">let </span><span class="kw-2">mut </span>matrix_block = matrix.sub_slice_mut([j, <span class="number">0</span>], m - j, q); |
| <span class="kw">let </span>house = load_house_from_col(<span class="kw-2">&</span>storage_block.col(<span class="number">0</span>), |
| <span class="self">self</span>.tau[j], house_buffer); |
| house.buffered_left_multiply_into(<span class="kw-2">&mut </span>matrix_block, |
| <span class="kw-2">&mut </span>multiply_buffer); |
| house_buffer = house.into_vector().into_vec(); |
| } |
| } |
| |
| <span class="doccomment">/// Computes the first k columns of the implicitly |
| /// stored matrix `Q`. |
| /// |
| /// # Panics |
| /// - `k` must be less than or equal to `m`, the number |
| /// of rows of `Q`. |
| </span><span class="kw">pub fn </span>first_k_columns(<span class="kw-2">&</span><span class="self">self</span>, k: usize) -> Matrix<T> { |
| <span class="kw">use </span>std::cmp::min; |
| <span class="kw">let </span>m = <span class="self">self</span>.storage.rows(); |
| <span class="kw">let </span>n = <span class="self">self</span>.storage.cols(); |
| <span class="kw">let </span>p = min(m, n); |
| |
| <span class="macro">assert!</span>(k <= <span class="self">self</span>.storage.rows(), |
| <span class="string">"k cannot exceed m, the number of rows of Q"</span>); |
| |
| <span class="comment">// Let Q_k = Q[:, 1:k], the first k rows of Q |
| </span><span class="kw">let </span><span class="kw-2">mut </span>q_k = Matrix::from_fn(m, k, |row, col| { |
| <span class="kw">if </span>row == col { T::one()} |
| <span class="kw">else </span>{ T::zero() } |
| }); |
| |
| <span class="comment">// This is almost identical to left_multiply_into, |
| // but we can use the sparsity of the identity matrix |
| // to reduce the number of operations |
| // (note the size of the "q_k_block") |
| </span><span class="kw">let </span><span class="kw-2">mut </span>buffer = Vec::with_capacity(m); |
| <span class="kw">let </span><span class="kw-2">mut </span>multiply_buffer = Vec::with_capacity(k); |
| <span class="kw">for </span>j <span class="kw">in </span>(<span class="number">0 </span>.. min(p, k)).rev() { |
| buffer.resize(m - j, T::zero()); |
| multiply_buffer.resize(k - j, T::zero()); |
| <span class="kw">let </span>storage_block = <span class="self">self</span>.storage.sub_slice([j, j], m - j, n - j); |
| <span class="kw">let </span><span class="kw-2">mut </span>q_k_block = q_k.sub_slice_mut([j, j], m - j, k - j); |
| <span class="kw">let </span>house = load_house_from_col(<span class="kw-2">&</span>storage_block.col(<span class="number">0</span>), |
| <span class="self">self</span>.tau[j], buffer); |
| house.buffered_left_multiply_into(<span class="kw-2">&mut </span>q_k_block, |
| <span class="kw-2">&mut </span>multiply_buffer); |
| buffer = house.into_vector().into_vec(); |
| } |
| q_k |
| } |
| } |
| |
| <span class="kw">fn </span>load_house_from_col<T: Float>(col: <span class="kw-2">&</span>Column<T>, tau: T, buffer: Vec<T>) |
| -> HouseholderReflection<T> { |
| <span class="kw">let </span><span class="kw-2">mut </span>v = buffer; |
| |
| col.clone_into_slice(<span class="kw-2">&mut </span>v); |
| |
| <span class="comment">// First element is implicitly 1 regardless of |
| // whatever is stored in the column. |
| </span><span class="kw">if let </span><span class="prelude-val">Some</span>(first_element) = v.get_mut(<span class="number">0</span>) { |
| <span class="kw-2">*</span>first_element = T::one(); |
| } |
| |
| HouseholderReflection::from_parameters(Vector::new(v), tau) |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>tests { |
| <span class="kw">use </span>vector::Vector; |
| <span class="kw">use </span>matrix::{Matrix, BaseMatrix}; |
| <span class="kw">use </span><span class="kw">super</span>::HouseholderReflection; |
| <span class="kw">use </span><span class="kw">super</span>::create_composition; |
| |
| <span class="kw">pub fn </span>house_as_matrix(house: HouseholderReflection<f64>) |
| -> Matrix<f64> |
| { |
| <span class="kw">let </span>m = house.v.size(); |
| <span class="kw">let </span>v = Matrix::new(m, <span class="number">1</span>, house.v.into_vec()); |
| <span class="kw">let </span>v_t = v.transpose(); |
| Matrix::identity(m) - v * v_t * house.tau |
| } |
| |
| <span class="kw">fn </span>verify_house(x: Vector<f64>, house: HouseholderReflection<f64>) { |
| <span class="kw">let </span>m = x.size(); |
| <span class="macro">assert!</span>(m > <span class="number">0</span>); |
| |
| <span class="kw">let </span>house = house_as_matrix(house); |
| <span class="kw">let </span>y = house.clone() * x.clone(); |
| |
| <span class="comment">// Check that y[1 ..] is approximately zero |
| </span><span class="kw">let </span>z = Vector::new(y.data().iter().skip(<span class="number">1</span>).cloned().collect::<Vec<<span class="kw">_</span>>>()); |
| <span class="macro">assert_vector_eq!</span>(z, Vector::zeros(m - <span class="number">1</span>), comp = float, eps = <span class="number">1e-12</span>); |
| |
| <span class="comment">// Check that applying the Householder transformation again |
| // recovers the original vector (since H = H^T = inv(H)) |
| </span><span class="kw">let </span>w = house * y; |
| <span class="macro">assert_vector_eq!</span>(x, w, comp = float); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>compute_empty_vector() { |
| <span class="kw">let </span>x: Vector<f64> = <span class="macro">vector!</span>[]; |
| <span class="kw">let </span>house = HouseholderReflection::compute(x.clone()); |
| <span class="macro">assert_scalar_eq!</span>(house.tau, <span class="number">0.0</span>); |
| <span class="macro">assert_vector_eq!</span>(house.v, x.clone()); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>compute_single_element_vector() { |
| <span class="kw">let </span>x = <span class="macro">vector!</span>[<span class="number">2.0</span>]; |
| <span class="kw">let </span>house = HouseholderReflection::compute(x.clone()); |
| <span class="macro">assert_scalar_eq!</span>(house.tau, <span class="number">0.0</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>compute_examples() { |
| { |
| <span class="kw">let </span>x = <span class="macro">vector!</span>[<span class="number">1.0</span>, <span class="number">0.0</span>, <span class="number">0.0</span>]; |
| <span class="kw">let </span>house = HouseholderReflection::compute(x.clone()); |
| verify_house(x, house); |
| } |
| |
| { |
| <span class="kw">let </span>x = <span class="macro">vector!</span>[-<span class="number">1.0</span>, <span class="number">0.0</span>, <span class="number">0.0</span>]; |
| <span class="kw">let </span>house = HouseholderReflection::compute(x.clone()); |
| verify_house(x, house); |
| } |
| |
| { |
| <span class="kw">let </span>x = <span class="macro">vector!</span>[<span class="number">3.0</span>, -<span class="number">2.0</span>, <span class="number">5.0</span>]; |
| <span class="kw">let </span>house = HouseholderReflection::compute(x.clone()); |
| verify_house(x, house); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>householder_reflection_left_multiply() { |
| <span class="kw">let </span><span class="kw-2">mut </span>x = <span class="macro">matrix!</span>[ <span class="number">0.0</span>, <span class="number">1.0</span>, <span class="number">2.0</span>, <span class="number">3.0</span>; |
| <span class="number">4.0</span>, <span class="number">5.0</span>, <span class="number">6.0</span>, <span class="number">7.0</span>; |
| <span class="number">8.0</span>, <span class="number">9.0</span>, <span class="number">10.0</span>, <span class="number">11.0</span>; |
| <span class="number">12.0</span>, <span class="number">13.0</span>, <span class="number">14.0</span>, <span class="number">15.0 </span>]; |
| |
| <span class="comment">// The provided data is rather rubbish, but |
| // the result should still hold |
| </span><span class="kw">let </span>h = HouseholderReflection { |
| tau: <span class="number">0.06666666666666667</span>, |
| v: <span class="macro">vector!</span>[<span class="number">1.0</span>, <span class="number">2.0</span>, <span class="number">3.0</span>, <span class="number">4.0</span>] |
| }; |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>buffer = <span class="macro">vec!</span>[<span class="number">0.0</span>; <span class="number">4</span>]; |
| |
| h.buffered_left_multiply_into(<span class="kw-2">&mut </span>x, <span class="kw-2">&mut </span>buffer); |
| |
| <span class="kw">let </span>expected = <span class="macro">matrix!</span>[ -<span class="number">5.3333</span>, -<span class="number">5.0000</span>, -<span class="number">4.6667</span>, -<span class="number">4.3333</span>; |
| -<span class="number">6.6667</span>, -<span class="number">7.0000</span>, -<span class="number">7.3333</span>, -<span class="number">7.6667</span>; |
| -<span class="number">8.0000</span>, -<span class="number">9.0000</span>,-<span class="number">10.0000</span>, -<span class="number">11.0000</span>; |
| -<span class="number">9.3333</span>, -<span class="number">11.0000</span>,-<span class="number">12.6667</span>, -<span class="number">14.3333</span>]; |
| <span class="macro">assert_matrix_eq!</span>(x, expected, comp = abs, tol = <span class="number">1e-3</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>householder_composition_left_multiply() { |
| <span class="kw">let </span>storage = <span class="macro">matrix!</span>[ <span class="number">5.0</span>, <span class="number">3.0</span>, <span class="number">2.0</span>; |
| <span class="number">2.0</span>, <span class="number">1.0</span>, <span class="number">3.0</span>; |
| -<span class="number">2.0</span>, <span class="number">3.0</span>, -<span class="number">2.0</span>]; |
| <span class="kw">let </span>tau = <span class="macro">vec!</span>[<span class="number">2.0</span>/<span class="number">9.0</span>, <span class="number">1.0 </span>/ <span class="number">5.0</span>, <span class="number">2.0</span>]; |
| |
| <span class="comment">// `q` is a manually computed matrix representation |
| // of the Householder composition stored implicitly in |
| // `storage` and `tau. We leave it here to make writing |
| // further tests easier |
| // let q = matrix![7.0/9.0, -28.0/45.0, 4.0/45.0; |
| // -4.0/9.0, - 4.0/ 9.0, 7.0/ 9.0; |
| // 4.0/9.0, 29.0/45.0, 28.0/45.0]; |
| </span><span class="kw">let </span>composition = create_composition(<span class="kw-2">&</span>storage, <span class="kw-2">&</span>tau); |
| |
| { |
| <span class="comment">// Square |
| </span><span class="kw">let </span><span class="kw-2">mut </span>x = <span class="macro">matrix!</span>[<span class="number">4.0</span>, <span class="number">5.0</span>, -<span class="number">3.0</span>; |
| <span class="number">2.0</span>, -<span class="number">1.0</span>, -<span class="number">3.0</span>; |
| <span class="number">1.0</span>, <span class="number">3.0</span>, <span class="number">5.0</span>]; |
| composition.left_multiply_into(<span class="kw-2">&mut </span>x); |
| |
| <span class="kw">let </span>expected = <span class="macro">matrix!</span>[ <span class="number">88.0</span>/<span class="number">45.0</span>, <span class="number">43.0</span>/<span class="number">9.0</span>, -<span class="number">1.0</span>/<span class="number">45.0</span>; |
| -<span class="number">17.0</span>/ <span class="number">9.0</span>, <span class="number">5.0</span>/<span class="number">9.0</span>, <span class="number">59.0</span>/ <span class="number">9.0</span>; |
| <span class="number">166.0</span>/<span class="number">45.0</span>, <span class="number">31.0</span>/<span class="number">9.0</span>, -<span class="number">7.0</span>/<span class="number">45.0</span>]; |
| <span class="macro">assert_matrix_eq!</span>(x, expected, comp = float, eps = <span class="number">1e-15</span>); |
| } |
| |
| { |
| <span class="comment">// Tall |
| </span><span class="kw">let </span><span class="kw-2">mut </span>x = <span class="macro">matrix!</span>[ <span class="number">4.0</span>, <span class="number">5.0</span>; |
| <span class="number">3.0</span>, <span class="number">2.0</span>; |
| -<span class="number">1.0</span>,-<span class="number">2.0</span>]; |
| composition.left_multiply_into(<span class="kw-2">&mut </span>x); |
| <span class="kw">let </span>expected = <span class="macro">matrix!</span>[<span class="number">52.0</span>/<span class="number">45.0</span>, <span class="number">37.0</span>/<span class="number">15.0</span>; |
| -<span class="number">35.0</span>/ <span class="number">9.0</span>, -<span class="number">14.0</span>/ <span class="number">3.0</span>; |
| <span class="number">139.0</span>/<span class="number">45.0</span>, <span class="number">34.0</span>/<span class="number">15.0</span>]; |
| <span class="macro">assert_matrix_eq!</span>(x, expected, comp = float, eps = <span class="number">1e-15</span>); |
| } |
| |
| { |
| <span class="comment">// Short |
| </span><span class="kw">let </span><span class="kw-2">mut </span>x = <span class="macro">matrix!</span>[ <span class="number">4.0</span>, <span class="number">5.0</span>, <span class="number">2.0</span>, -<span class="number">5.0</span>; |
| <span class="number">3.0</span>, <span class="number">2.0</span>, <span class="number">1.0</span>, <span class="number">1.0</span>; |
| -<span class="number">1.0</span>, -<span class="number">2.0</span>, <span class="number">0.0</span>, -<span class="number">5.0</span>]; |
| composition.left_multiply_into(<span class="kw-2">&mut </span>x); |
| <span class="kw">let </span>expected = <span class="macro">matrix!</span>[<span class="number">52.0</span>/<span class="number">45.0</span>, <span class="number">37.0</span>/<span class="number">15.0</span>, <span class="number">14.0</span>/<span class="number">15.0</span>, -<span class="number">223.0</span>/<span class="number">45.0</span>; |
| -<span class="number">35.0</span>/ <span class="number">9.0</span>, -<span class="number">14.0</span>/ <span class="number">3.0</span>, -<span class="number">4.0</span>/ <span class="number">3.0</span>, -<span class="number">19.0</span>/ <span class="number">9.0</span>; |
| <span class="number">139.0</span>/<span class="number">45.0</span>, <span class="number">34.0</span>/<span class="number">15.0</span>, <span class="number">23.0</span>/<span class="number">15.0</span>, -<span class="number">211.0</span>/<span class="number">45.0</span>]; |
| <span class="macro">assert_matrix_eq!</span>(x, expected, comp = float, eps = <span class="number">1e-15</span>); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>householder_composition_first_k_columns() { |
| <span class="kw">let </span>storage = <span class="macro">matrix!</span>[ <span class="number">5.0</span>, <span class="number">3.0</span>, <span class="number">2.0</span>; |
| <span class="number">2.0</span>, <span class="number">1.0</span>, <span class="number">3.0</span>; |
| -<span class="number">2.0</span>, <span class="number">3.0</span>, -<span class="number">2.0</span>]; |
| <span class="kw">let </span>tau = <span class="macro">vec!</span>[<span class="number">2.0</span>/<span class="number">9.0</span>, <span class="number">1.0 </span>/ <span class="number">5.0</span>, <span class="number">2.0</span>]; |
| <span class="kw">let </span>composition = create_composition(<span class="kw-2">&</span>storage, <span class="kw-2">&</span>tau); |
| |
| <span class="comment">// This corresponds to the following `Q` matrix |
| </span><span class="kw">let </span>q = <span class="macro">matrix!</span>[<span class="number">7.0</span>/<span class="number">9.0</span>, -<span class="number">28.0</span>/<span class="number">45.0</span>, <span class="number">4.0</span>/<span class="number">45.0</span>; |
| -<span class="number">4.0</span>/<span class="number">9.0</span>, - <span class="number">4.0</span>/ <span class="number">9.0</span>, <span class="number">7.0</span>/ <span class="number">9.0</span>; |
| <span class="number">4.0</span>/<span class="number">9.0</span>, <span class="number">29.0</span>/<span class="number">45.0</span>, <span class="number">28.0</span>/<span class="number">45.0</span>]; |
| { |
| <span class="comment">// First 0 columns |
| </span><span class="kw">let </span>q_k = composition.first_k_columns(<span class="number">0</span>); |
| <span class="macro">assert_eq!</span>(q_k.rows(), <span class="number">3</span>); |
| <span class="macro">assert_eq!</span>(q_k.cols(), <span class="number">0</span>); |
| } |
| |
| { |
| <span class="comment">// First column |
| </span><span class="kw">let </span>q_k = composition.first_k_columns(<span class="number">1</span>); |
| <span class="macro">assert_matrix_eq!</span>(q_k, q.sub_slice([<span class="number">0</span>, <span class="number">0</span>], <span class="number">3</span>, <span class="number">1</span>), |
| comp = float); |
| } |
| |
| { |
| <span class="comment">// First 2 columns |
| </span><span class="kw">let </span>q_k = composition.first_k_columns(<span class="number">2</span>); |
| <span class="macro">assert_matrix_eq!</span>(q_k, q.sub_slice([<span class="number">0</span>, <span class="number">0</span>], <span class="number">3</span>, <span class="number">2</span>), |
| comp = float); |
| } |
| |
| { |
| <span class="comment">// First 3 columns |
| </span><span class="kw">let </span>q_k = composition.first_k_columns(<span class="number">3</span>); |
| <span class="macro">assert_matrix_eq!</span>(q_k, q.sub_slice([<span class="number">0</span>, <span class="number">0</span>], <span class="number">3</span>, <span class="number">3</span>), |
| comp = float); |
| } |
| } |
| |
| |
| } |
| </code></pre></div> |
| </section></div></main><div id="rustdoc-vars" data-root-path="../../../../" data-current-crate="rulinalg" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |