| <!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/qr.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>qr.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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| <span id="523">523</span> |
| <span id="524">524</span> |
| <span id="525">525</span> |
| <span id="526">526</span> |
| <span id="527">527</span> |
| <span id="528">528</span> |
| <span id="529">529</span> |
| <span id="530">530</span> |
| <span id="531">531</span> |
| <span id="532">532</span> |
| <span id="533">533</span> |
| <span id="534">534</span> |
| <span id="535">535</span> |
| <span id="536">536</span> |
| <span id="537">537</span> |
| <span id="538">538</span> |
| <span id="539">539</span> |
| <span id="540">540</span> |
| <span id="541">541</span> |
| <span id="542">542</span> |
| <span id="543">543</span> |
| <span id="544">544</span> |
| <span id="545">545</span> |
| <span id="546">546</span> |
| <span id="547">547</span> |
| <span id="548">548</span> |
| <span id="549">549</span> |
| <span id="550">550</span> |
| <span id="551">551</span> |
| <span id="552">552</span> |
| <span id="553">553</span> |
| <span id="554">554</span> |
| <span id="555">555</span> |
| <span id="556">556</span> |
| <span id="557">557</span> |
| <span id="558">558</span> |
| <span id="559">559</span> |
| <span id="560">560</span> |
| <span id="561">561</span> |
| <span id="562">562</span> |
| <span id="563">563</span> |
| <span id="564">564</span> |
| <span id="565">565</span> |
| <span id="566">566</span> |
| <span id="567">567</span> |
| <span id="568">568</span> |
| <span id="569">569</span> |
| <span id="570">570</span> |
| <span id="571">571</span> |
| <span id="572">572</span> |
| <span id="573">573</span> |
| <span id="574">574</span> |
| <span id="575">575</span> |
| <span id="576">576</span> |
| <span id="577">577</span> |
| </pre><pre class="rust"><code><span class="kw">use </span>matrix::{Matrix, MatrixSlice, BaseMatrix, BaseMatrixMut}; |
| <span class="kw">use </span>vector::Vector; |
| <span class="kw">use </span>error::{Error, ErrorKind}; |
| <span class="kw">use </span>matrix::decomposition::{ |
| Decomposition, |
| HouseholderReflection, |
| HouseholderComposition |
| }; |
| <span class="kw">use </span>matrix::decomposition::householder; |
| |
| <span class="kw">use </span>std::any::Any; |
| |
| <span class="kw">use </span>libnum::Float; |
| |
| <span class="doccomment">/// The result of unpacking a QR decomposition. |
| /// |
| /// Let `A` denote the `m x n` matrix given by `A = QR`. |
| /// Then `Q` is an `m x m` orthogonal matrix, and `R` |
| /// is an `m x n` upper trapezoidal matrix . |
| /// |
| /// More precisely, if `m > n`, then we have the decomposition |
| /// |
| /// ```text |
| /// A = QR = Q [ R1 ] |
| /// [ 0 ] |
| /// ``` |
| /// where `R1` is an `n x n` upper triangular matrix. |
| /// On the other hand, if `m < n`, we have |
| /// |
| /// ```text |
| /// A = QR = Q [ R1 R2 ] |
| /// ``` |
| /// |
| /// where `R1` is an `m x m` upper triangular matrix and |
| /// `R2` is an `m x (n - m)` general matrix. |
| /// |
| /// To actually compute the QR decomposition, see |
| /// [Householder QR](struct.HouseholderQr.html). |
| </span><span class="attribute">#[derive(Debug, Clone)] |
| </span><span class="kw">pub struct </span>QR<T> { |
| <span class="doccomment">/// The orthogonal matrix `Q` in the decomposition `A = QR`. |
| </span><span class="kw">pub </span>q: Matrix<T>, |
| <span class="doccomment">/// The upper-trapezoidal matrix `R` in the decomposition `A = QR`. |
| </span><span class="kw">pub </span>r: Matrix<T> |
| } |
| |
| <span class="doccomment">/// The result of computing a *thin* (or *reduced*) QR decomposition. |
| /// |
| /// Let `A` denote the `m x n` matrix given by `A = QR`. |
| /// Then `Q` is an `m x m` orthogonal matrix, and `R` |
| /// is an `m x n` upper trapezoidal matrix. |
| /// |
| /// If `m > n`, we may write |
| /// |
| /// ```text |
| /// A = QR = [ Q1 Q2 ] [ R1 ] = Q1 R1 |
| /// [ 0 ] |
| /// ``` |
| /// |
| /// where `Q1` is an `m x n` matrix with orthogonal columns, |
| /// and `R1` is an `n x n` upper triangular matrix. |
| /// For some applications, the remaining (m - n) columns |
| /// of the full `Q` matrix are not needed, in which case |
| /// the thin QR decomposition is substantially cheaper if |
| /// `m >> n`. |
| /// |
| /// If `m <= n`, then the thin QR decomposition coincides with |
| /// the usual decomposition. See [QR](struct.QR.html) for details. |
| /// |
| /// To actually compute the QR decomposition, see |
| /// [Householder QR](struct.HouseholderQr.html). |
| </span><span class="attribute">#[derive(Debug, Clone)] |
| </span><span class="kw">pub struct </span>ThinQR<T> { |
| <span class="doccomment">/// The matrix `Q1` in the decomposition `A = Q1 R1`. |
| </span><span class="kw">pub </span>q1: Matrix<T>, |
| <span class="doccomment">/// The upper-triangular matrix `R1` in the decomposition `A = Q1 R1`. |
| </span><span class="kw">pub </span>r1: Matrix<T> |
| } |
| |
| <span class="doccomment">/// QR decomposition based on Householder reflections. |
| /// |
| /// For any `m x n` matrix `A`, there exist an `m x m` |
| /// orthogonal matrix `Q` and an `m x n` upper trapezoidal |
| /// (triangular) matrix `R` such that |
| /// |
| /// ```text |
| /// A = QR. |
| /// ``` |
| /// |
| /// `HouseholderQr` holds the result of a QR decomposition |
| /// procedure based on Householder reflections. The full |
| /// factors `Q` and `R` can be acquired by calling `unpack()`. |
| /// However, it turns out that the orthogonal factor `Q` |
| /// can be represented much more efficiently than as a |
| /// full `m x m` matrix. For this purpose, the [q()](#method.q) |
| /// method provides access to an instance of |
| /// [HouseholderComposition](struct.HouseholderComposition.html) |
| /// which allows the efficient application of the (implicit) |
| /// `Q` matrix. |
| /// |
| /// For some applications, it is sufficient to compute a |
| /// *thin* (or *reduced*) QR decomposition. The thin QR decomposition |
| /// can be obtained by calling [unpack_thin()](#method.unpack_thin) |
| /// on the decomposition object. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// # #[macro_use] extern crate rulinalg; fn main() { |
| /// use rulinalg::matrix::Matrix; |
| /// use rulinalg::matrix::decomposition::{ |
| /// Decomposition, HouseholderQr, QR |
| /// }; |
| /// |
| /// let a = matrix![ 3.0, 2.0; |
| /// -5.0, 1.0; |
| /// 4.0, -2.0 ]; |
| /// let identity = Matrix::identity(3); |
| /// |
| /// let qr = HouseholderQr::decompose(a.clone()); |
| /// let QR { q, r } = qr.unpack(); |
| /// |
| /// // Check that `Q` is orthogonal |
| /// assert_matrix_eq!(&q * q.transpose(), identity, comp = float); |
| /// assert_matrix_eq!(q.transpose() * &q, identity, comp = float); |
| /// |
| /// // Check that `A = QR` |
| /// assert_matrix_eq!(q * r, a, comp = float); |
| /// # } |
| /// ``` |
| /// |
| /// # Internal storage format |
| /// Upon decomposition, the `HouseholderQr` struct takes ownership |
| /// of the matrix and repurposes its storage to compactly |
| /// store the factors `Q` and `R`. |
| /// In addition, a vector `tau` of size `min(m, n)` |
| /// holds auxiliary information about the Householder reflectors |
| /// which together constitute the `Q` matrix. |
| /// |
| /// Specifically, given an input matrix `A`, |
| /// the upper triangular factor `R` is stored in `A_ij` for |
| /// `j >= i`. The orthogonal factor `Q` is implicitly stored |
| /// as the composition of `p := min(m, n)` Householder reflectors |
| /// `Q_i`, such that |
| /// |
| /// ```text |
| /// Q = Q_1 * Q_2 * ... * Q_p. |
| /// ``` |
| /// |
| /// Each such Householder reflection `Q_i` corresponds to a |
| /// transformation of the form (using MATLAB-like colon notation) |
| /// |
| /// ```text |
| /// Q_i [1:(i-1), 1:(i-1)] = I |
| /// Q_i [i:m, i:m] = I - τ_i * v_i * transpose(v_i) |
| /// ``` |
| /// |
| /// where `I` denotes the identity matrix of appropriate size, |
| /// `v_i` is the *Householder vector* normalized in such a way that |
| /// its first element is implicitly `1` (and thus does not need to |
| /// be stored) and `τ_i` is an appropriate scale factor. Each vector |
| /// `v_i` has length `m - i + 1`, and since the first element does not |
| /// need to be stored, each `v_i` can be stored in column `i` of |
| /// the matrix `A`. |
| /// |
| /// The scale factors `τ_i` are stored in a separate vector. |
| /// |
| /// This storage scheme should be compatible with LAPACK, although |
| /// this has yet to be put to the test. For the same reason, |
| /// the internal storage is not exposed in the public API at this point. |
| </span><span class="attribute">#[derive(Debug, Clone)] |
| </span><span class="kw">pub struct </span>HouseholderQr<T> { |
| qr: Matrix<T>, |
| tau: Vec<T> |
| } |
| |
| <span class="kw">impl</span><T> HouseholderQr<T> <span class="kw">where </span>T: Float { |
| <span class="doccomment">/// Decomposes the given matrix into implicitly stored factors |
| /// `Q` and `R` as described in the struct documentation. |
| </span><span class="kw">pub fn </span>decompose(matrix: Matrix<T>) -> HouseholderQr<T> { |
| <span class="kw">use </span>std::cmp::min; |
| |
| <span class="comment">// The implementation here is based on |
| // Algorithm 5.2.1 (Householder QR) from |
| // Matrix Computations, 4th Ed, |
| // by Golub & Van Loan |
| </span><span class="kw">let </span>m = matrix.rows(); |
| <span class="kw">let </span>n = matrix.cols(); |
| <span class="kw">let </span>p = min(m, n); |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>qr = matrix; |
| <span class="kw">let </span><span class="kw-2">mut </span>tau = <span class="macro">vec!</span>[T::zero(); p]; |
| |
| <span class="comment">// In order to avoid frequently allocating new vectors |
| // to hold the householder reflections, we allocate a single |
| // buffer which we can reuse for every iteration. We also |
| // need one as work space when applying the Householder |
| // transformations. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>buffer = <span class="macro">vec!</span>[T::zero(); m]; |
| <span class="kw">let </span><span class="kw-2">mut </span>multiply_buffer = <span class="macro">vec!</span>[T::zero(); n]; |
| |
| <span class="kw">for </span>j <span class="kw">in </span><span class="number">0 </span>.. p { |
| <span class="kw">let </span><span class="kw-2">mut </span>bottom_right = qr.sub_slice_mut([j, j], m - j, n - j); |
| |
| <span class="comment">// The householder vector which we will hold in the buffer |
| // gets shorter for each iteration, so we truncate the buffer |
| // to the appropriate length. |
| </span>buffer.truncate(m - j); |
| multiply_buffer.truncate(bottom_right.cols()); |
| bottom_right.col(<span class="number">0</span>).clone_into_slice(<span class="kw-2">&mut </span>buffer); |
| |
| <span class="kw">let </span>house = HouseholderReflection::compute(Vector::new(buffer)); |
| house.buffered_left_multiply_into(<span class="kw-2">&mut </span>bottom_right, |
| <span class="kw-2">&mut </span>multiply_buffer); |
| house.store_in_col(<span class="kw-2">&mut </span>bottom_right.col_mut(<span class="number">0</span>)); |
| tau[j] = house.tau(); |
| buffer = house.into_vector().into_vec(); |
| } |
| HouseholderQr { |
| qr: qr, |
| tau: tau |
| } |
| } |
| |
| <span class="doccomment">/// Returns the orthogonal factor `Q` as an instance of a |
| /// [HouseholderComposition](struct.HouseholderComposition.html) |
| /// operator. |
| </span><span class="kw">pub fn </span>q(<span class="kw-2">&</span><span class="self">self</span>) -> HouseholderComposition<T> { |
| householder::create_composition(<span class="kw-2">&</span><span class="self">self</span>.qr, <span class="kw-2">&</span><span class="self">self</span>.tau) |
| } |
| |
| <span class="doccomment">/// Computes the *thin* (or reduced) QR decomposition. |
| /// |
| /// If `m <= n`, the thin QR decomposition coincides with the |
| /// usual QR decomposition. See [ThinQR](struct.ThinQR.html) |
| /// for details. |
| /// |
| /// # Examples |
| /// ``` |
| /// # #[macro_use] extern crate rulinalg; fn main() { |
| /// # use rulinalg::matrix::Matrix; |
| /// # let x: Matrix<f64> = matrix![]; |
| /// use rulinalg::matrix::decomposition::{HouseholderQr, ThinQR}; |
| /// let x = matrix![3.0, 2.0; |
| /// 1.0, 2.0; |
| /// 4.0, 5.0]; |
| /// let ThinQR { q1, r1 } = HouseholderQr::decompose(x).unpack_thin(); |
| /// # } |
| /// ``` |
| </span><span class="kw">pub fn </span>unpack_thin(<span class="self">self</span>) -> ThinQR<T> { |
| <span class="comment">// Note: currently, there is no need to take ownership of |
| // `self`. However, it is actually possible to compute the |
| // rectangular Q1 factor in-place, but it is not currently |
| // done. By taking `self` now, we can make this change in |
| // the future without breaking changes. |
| </span><span class="kw">let </span>m = <span class="self">self</span>.qr.rows(); |
| <span class="kw">let </span>n = <span class="self">self</span>.qr.cols(); |
| |
| <span class="kw">if </span>m <= n { |
| <span class="comment">// If m <= n, Thin QR coincides with regular QR |
| </span><span class="kw">let </span>qr = <span class="self">self</span>.unpack(); |
| ThinQR { |
| q1: qr.q, |
| r1: qr.r |
| } |
| } <span class="kw">else </span>{ |
| <span class="kw">let </span>composition = householder::create_composition(<span class="kw-2">&</span><span class="self">self</span>.qr, <span class="kw-2">&</span><span class="self">self</span>.tau); |
| <span class="kw">let </span>q1 = composition.first_k_columns(n); |
| <span class="kw">let </span>r1 = extract_r1(<span class="kw-2">&</span><span class="self">self</span>.qr); |
| ThinQR { |
| q1: q1, |
| r1: r1 |
| } |
| } |
| } |
| } |
| |
| <span class="kw">impl</span><T: Float> Decomposition <span class="kw">for </span>HouseholderQr<T> { |
| <span class="kw">type </span>Factors = QR<T>; |
| <span class="kw">fn </span>unpack(<span class="self">self</span>) -> QR<T> { |
| <span class="kw">use </span>internal_utils; |
| <span class="kw">let </span>q = assemble_q(<span class="kw-2">&</span><span class="self">self</span>.qr, <span class="kw-2">&</span><span class="self">self</span>.tau); |
| <span class="kw">let </span><span class="kw-2">mut </span>r = <span class="self">self</span>.qr; |
| internal_utils::nullify_lower_triangular_part(<span class="kw-2">&mut </span>r); |
| QR { |
| q: q, |
| r: r |
| } |
| } |
| } |
| |
| <span class="kw">fn </span>assemble_q<T: Float>(qr: <span class="kw-2">&</span>Matrix<T>, tau: <span class="kw-2">&</span>Vec<T>) -> Matrix<T> { |
| <span class="kw">let </span>m = qr.rows(); |
| <span class="kw">let </span>q_operator = householder::create_composition(qr, tau); |
| q_operator.first_k_columns(m) |
| } |
| |
| <span class="kw">fn </span>extract_r1<T: Float>(qr: <span class="kw-2">&</span>Matrix<T>) -> Matrix<T> { |
| <span class="kw">let </span>m = qr.rows(); |
| <span class="kw">let </span>n = qr.cols(); |
| <span class="kw">let </span><span class="kw-2">mut </span>data = Vec::<T>::with_capacity(m * n); |
| |
| <span class="macro">assert!</span>(m > n, <span class="string">"We only want to extract r1 if m > n!"</span>); |
| |
| <span class="kw">for </span>(i, row) <span class="kw">in </span>qr.row_iter().take(n).enumerate() { |
| <span class="kw">for _ in </span><span class="number">0 </span>.. i { |
| data.push(T::zero()); |
| } |
| |
| <span class="kw">for </span>element <span class="kw">in </span>row.raw_slice().iter().skip(i).cloned() { |
| data.push(element); |
| } |
| } |
| Matrix::new(n, n, data) |
| } |
| |
| <span class="kw">impl</span><T> Matrix<T> |
| <span class="kw">where </span>T: Any + Float |
| { |
| <span class="doccomment">/// Compute the QR decomposition of the matrix. |
| /// |
| /// Returns the tuple (Q,R). |
| /// |
| /// Note: this function is deprecated in favor of |
| /// [HouseholderQr](./decomposition/struct.HouseholderQr.html) |
| /// and will be removed in a future release. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// # #[macro_use] extern crate rulinalg; fn main() { |
| /// use rulinalg::matrix::Matrix; |
| /// |
| /// let m = matrix![1.0, 0.5, 0.5; |
| /// 0.5, 1.0, 0.5; |
| /// 0.5, 0.5, 1.0]; |
| /// |
| /// let (q, r) = m.qr_decomp().unwrap(); |
| /// # } |
| /// ``` |
| /// |
| /// # Failures |
| /// |
| /// - Cannot compute the QR decomposition. |
| </span><span class="attribute">#[deprecated] |
| </span><span class="kw">pub fn </span>qr_decomp(<span class="self">self</span>) -> <span class="prelude-ty">Result</span><(Matrix<T>, Matrix<T>), Error> { |
| <span class="kw">let </span>m = <span class="self">self</span>.rows(); |
| <span class="kw">let </span>n = <span class="self">self</span>.cols(); |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>q = Matrix::<T>::identity(m); |
| <span class="kw">let </span><span class="kw-2">mut </span>r = <span class="self">self</span>; |
| |
| <span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..(n - ((m == n) <span class="kw">as </span>usize)) { |
| <span class="kw">let </span>holder_transform: <span class="prelude-ty">Result</span><Matrix<T>, Error>; |
| { |
| <span class="kw">let </span>lower_slice = MatrixSlice::from_matrix(<span class="kw-2">&</span>r, [i, i], m - i, <span class="number">1</span>); |
| holder_transform = |
| Matrix::make_householder(<span class="kw-2">&</span>lower_slice.iter().cloned().collect::<Vec<<span class="kw">_</span>>>()); |
| } |
| |
| <span class="kw">if </span>!holder_transform.is_ok() { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(Error::new(ErrorKind::DecompFailure, |
| <span class="string">"Cannot compute QR decomposition."</span>)); |
| } <span class="kw">else </span>{ |
| <span class="kw">let </span><span class="kw-2">mut </span>holder_data = holder_transform.unwrap().into_vec(); |
| |
| <span class="comment">// This bit is inefficient |
| // using for now as we'll swap to lapack eventually. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>h_full_data = Vec::with_capacity(m * m); |
| |
| <span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..m { |
| <span class="kw">let </span><span class="kw-2">mut </span>row_data: Vec<T>; |
| <span class="kw">if </span>j < i { |
| row_data = <span class="macro">vec!</span>[T::zero(); m]; |
| row_data[j] = T::one(); |
| h_full_data.extend(row_data); |
| } <span class="kw">else </span>{ |
| row_data = <span class="macro">vec!</span>[T::zero(); i]; |
| h_full_data.extend(row_data); |
| h_full_data.extend(holder_data.drain(..m - i)); |
| } |
| } |
| |
| <span class="kw">let </span>h = Matrix::new(m, m, h_full_data); |
| |
| q = q * <span class="kw-2">&</span>h; |
| r = h * <span class="kw-2">&</span>r; |
| } |
| } |
| |
| <span class="prelude-val">Ok</span>((q, r)) |
| } |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>tests { |
| <span class="kw">use </span><span class="kw">super</span>::HouseholderQr; |
| <span class="kw">use super</span>::{QR, ThinQR}; |
| |
| <span class="kw">use </span>matrix::{Matrix, BaseMatrix}; |
| <span class="kw">use </span>matrix::decomposition::Decomposition; |
| |
| <span class="kw">use </span>testsupport::is_upper_triangular; |
| |
| <span class="kw">fn </span>verify_qr(x: Matrix<f64>, qr: QR<f64>) { |
| <span class="kw">let </span>m = x.rows(); |
| <span class="kw">let </span>QR { <span class="kw-2">ref </span>q, <span class="kw-2">ref </span>r } = qr; |
| |
| <span class="macro">assert_matrix_eq!</span>(q * r, x, comp = float, ulp = <span class="number">100</span>); |
| <span class="macro">assert!</span>(is_upper_triangular(r)); |
| |
| <span class="comment">// check orthogonality |
| </span><span class="macro">assert_matrix_eq!</span>(q.transpose() * q, Matrix::identity(m), |
| comp = float, ulp = <span class="number">100</span>); |
| <span class="macro">assert_matrix_eq!</span>(q * q.transpose(), Matrix::identity(m), |
| comp = float, ulp = <span class="number">100</span>); |
| } |
| |
| <span class="kw">fn </span>verify_thin_qr(x: Matrix<f64>, qr: ThinQR<f64>) { |
| <span class="kw">use </span>std::cmp::min; |
| |
| <span class="kw">let </span>m = x.rows(); |
| <span class="kw">let </span>n = x.cols(); |
| <span class="kw">let </span>ThinQR { <span class="kw-2">ref </span>q1, <span class="kw-2">ref </span>r1 } = qr; |
| |
| <span class="macro">assert_matrix_eq!</span>(q1 * r1, x, comp = float, ulp = <span class="number">100</span>); |
| <span class="macro">assert!</span>(is_upper_triangular(r1)); |
| |
| <span class="comment">// Check that q1 has orthogonal columns |
| </span><span class="macro">assert_matrix_eq!</span>(q1.transpose() * q1, Matrix::identity(min(m, n)), |
| comp = float, ulp = <span class="number">100</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">pub fn </span>householder_qr_unpack_reconstruction() { |
| { |
| <span class="comment">// 1x1 |
| </span><span class="kw">let </span>x = <span class="macro">matrix!</span>[<span class="number">1.0</span>]; |
| <span class="kw">let </span>qr = HouseholderQr::decompose(x.clone()).unpack(); |
| verify_qr(x, qr); |
| } |
| |
| { |
| <span class="comment">// 1x2 |
| </span><span class="kw">let </span>x = <span class="macro">matrix!</span>[<span class="number">1.0</span>, <span class="number">2.0</span>]; |
| <span class="kw">let </span>qr = HouseholderQr::decompose(x.clone()).unpack(); |
| verify_qr(x, qr); |
| } |
| |
| { |
| <span class="comment">// 2x1 |
| </span><span class="kw">let </span>x = <span class="macro">matrix!</span>[<span class="number">1.0</span>; |
| <span class="number">2.0</span>]; |
| <span class="kw">let </span>qr = HouseholderQr::decompose(x.clone()).unpack(); |
| verify_qr(x, qr); |
| } |
| |
| { |
| <span class="comment">// 2x2 |
| </span><span class="kw">let </span>x = <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="number">4.0</span>]; |
| <span class="kw">let </span>qr = HouseholderQr::decompose(x.clone()).unpack(); |
| verify_qr(x, qr); |
| } |
| |
| { |
| <span class="comment">// 3x2 |
| </span><span class="kw">let </span>x = <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="number">4.0</span>; |
| <span class="number">4.0</span>, <span class="number">5.0</span>]; |
| <span class="kw">let </span>qr = HouseholderQr::decompose(x.clone()).unpack(); |
| verify_qr(x, qr); |
| } |
| |
| { |
| <span class="comment">// 2x3 |
| </span><span class="kw">let </span>x = <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="number">4.0</span>, <span class="number">5.0</span>, <span class="number">6.0</span>]; |
| <span class="kw">let </span>qr = HouseholderQr::decompose(x.clone()).unpack(); |
| verify_qr(x, qr); |
| } |
| |
| { |
| <span class="comment">// 3x3 |
| </span><span class="kw">let </span>x = <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="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="kw">let </span>qr = HouseholderQr::decompose(x.clone()).unpack(); |
| verify_qr(x, qr); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>householder_qr_unpack_square_reconstruction_corner_cases() { |
| { |
| <span class="kw">let </span>x = <span class="macro">matrix!</span>[-<span class="number">1.0</span>, <span class="number">0.0</span>; |
| <span class="number">0.0</span>, <span class="number">1.0</span>]; |
| <span class="kw">let </span>qr = HouseholderQr::decompose(x.clone()).unpack(); |
| verify_qr(x, qr); |
| } |
| |
| { |
| <span class="kw">let </span>x = <span class="macro">matrix!</span>[<span class="number">1.0</span>, <span class="number">0.0</span>, <span class="number">0.0</span>; |
| <span class="number">0.0</span>, <span class="number">1.0</span>, <span class="number">0.0</span>; |
| <span class="number">0.0</span>, <span class="number">0.0</span>, -<span class="number">1.0</span>]; |
| <span class="kw">let </span>qr = HouseholderQr::decompose(x.clone()).unpack(); |
| verify_qr(x, qr); |
| } |
| |
| { |
| <span class="kw">let </span>x = <span class="macro">matrix!</span>[<span class="number">1.0</span>, <span class="number">0.0</span>, <span class="number">0.0</span>; |
| <span class="number">0.0</span>, -<span class="number">1.0</span>, <span class="number">0.0</span>; |
| <span class="number">0.0</span>, <span class="number">0.0</span>, -<span class="number">1.0</span>]; |
| <span class="kw">let </span>qr = HouseholderQr::decompose(x.clone()).unpack(); |
| verify_qr(x, qr); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>householder_qr_unpack_thin_reconstruction() { |
| { |
| <span class="comment">// 1x1 |
| </span><span class="kw">let </span>x = <span class="macro">matrix!</span>[<span class="number">1.0</span>]; |
| <span class="kw">let </span>qr = HouseholderQr::decompose(x.clone()).unpack_thin(); |
| verify_thin_qr(x, qr); |
| } |
| |
| { |
| <span class="comment">// 1x2 |
| </span><span class="kw">let </span>x = <span class="macro">matrix!</span>[<span class="number">1.0</span>, <span class="number">2.0</span>]; |
| <span class="kw">let </span>qr = HouseholderQr::decompose(x.clone()).unpack_thin(); |
| verify_thin_qr(x, qr); |
| } |
| |
| { |
| <span class="comment">// 2x1 |
| </span><span class="kw">let </span>x = <span class="macro">matrix!</span>[<span class="number">1.0</span>; |
| <span class="number">2.0</span>]; |
| <span class="kw">let </span>qr = HouseholderQr::decompose(x.clone()).unpack_thin(); |
| verify_thin_qr(x, qr); |
| } |
| |
| { |
| <span class="comment">// 2x2 |
| </span><span class="kw">let </span>x = <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="number">4.0</span>]; |
| <span class="kw">let </span>qr = HouseholderQr::decompose(x.clone()).unpack_thin(); |
| verify_thin_qr(x, qr); |
| } |
| |
| { |
| <span class="comment">// 3x2 |
| </span><span class="kw">let </span>x = <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="number">4.0</span>; |
| <span class="number">4.0</span>, <span class="number">5.0</span>]; |
| <span class="kw">let </span>qr = HouseholderQr::decompose(x.clone()).unpack_thin(); |
| verify_thin_qr(x, qr); |
| } |
| |
| { |
| <span class="comment">// 2x3 |
| </span><span class="kw">let </span>x = <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="number">4.0</span>, <span class="number">5.0</span>, <span class="number">6.0</span>]; |
| <span class="kw">let </span>qr = HouseholderQr::decompose(x.clone()).unpack_thin(); |
| verify_thin_qr(x, qr); |
| } |
| |
| { |
| <span class="comment">// 3x3 |
| </span><span class="kw">let </span>x = <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="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="kw">let </span>qr = HouseholderQr::decompose(x.clone()).unpack_thin(); |
| verify_thin_qr(x, qr); |
| } |
| } |
| } |
| </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> |
