| <!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/cholesky.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>cholesky.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="522">522</span> |
| <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> |
| <span id="578">578</span> |
| <span id="579">579</span> |
| <span id="580">580</span> |
| <span id="581">581</span> |
| <span id="582">582</span> |
| <span id="583">583</span> |
| <span id="584">584</span> |
| <span id="585">585</span> |
| <span id="586">586</span> |
| <span id="587">587</span> |
| <span id="588">588</span> |
| <span id="589">589</span> |
| <span id="590">590</span> |
| <span id="591">591</span> |
| <span id="592">592</span> |
| <span id="593">593</span> |
| <span id="594">594</span> |
| </pre><pre class="rust"><code><span class="kw">use </span>matrix::{Matrix, BaseMatrix}; |
| <span class="kw">use </span>error::{Error, ErrorKind}; |
| <span class="kw">use </span>matrix::decomposition::Decomposition; |
| <span class="kw">use </span>matrix::forward_substitution; |
| <span class="kw">use </span>vector::Vector; |
| <span class="kw">use </span>utils::dot; |
| |
| <span class="kw">use </span>std::any::Any; |
| |
| <span class="kw">use </span>libnum::{Zero, Float}; |
| |
| <span class="doccomment">/// Cholesky decomposition. |
| /// |
| /// Given a square, symmetric positive definite matrix A, |
| /// there exists an invertible lower triangular matrix L |
| /// such that |
| /// |
| /// A = L L<sup>T</sup>. |
| /// |
| /// This is called the Cholesky decomposition of A. |
| /// For not too ill-conditioned A, the computation |
| /// of the decomposition is very robust, and it takes about |
| /// half the effort of an LU decomposition with partial pivoting. |
| /// |
| /// # Applications |
| /// The Cholesky decomposition can be thought of as a specialized |
| /// LU decomposition for symmetric positive definite matrices, |
| /// and so its applications are similar to that of LU. |
| /// |
| /// The following example shows how to compute the Cholesky |
| /// decomposition of a given matrix. In this example, we also |
| /// unpack the decomposition to retrieve the L matrix, |
| /// but in many practical applications we are not so concerned |
| /// with the factor itself. Instead, we may wish to |
| /// solve linear systems or compute the determinant or the |
| /// inverse of a symmetric positive definite matrix. |
| /// In this case, see the next subsections. |
| /// |
| /// ``` |
| /// # #[macro_use] extern crate rulinalg; fn main() { |
| /// use rulinalg::matrix::decomposition::Cholesky; |
| /// |
| /// // Need to import Decomposition if we want to unpack |
| /// use rulinalg::matrix::decomposition::Decomposition; |
| /// |
| /// let x = matrix![ 1.0, 3.0, 1.0; |
| /// 3.0, 13.0, 11.0; |
| /// 1.0, 11.0, 21.0 ]; |
| /// let cholesky = Cholesky::decompose(x) |
| /// .expect("Matrix is SPD."); |
| /// |
| /// // Obtain the matrix factor L |
| /// let l = cholesky.unpack(); |
| /// |
| /// assert_matrix_eq!(l, matrix![1.0, 0.0, 0.0; |
| /// 3.0, 2.0, 0.0; |
| /// 1.0, 4.0, 2.0], comp = float); |
| /// # } |
| /// ``` |
| /// |
| /// ## Solving linear systems |
| /// After having decomposed the matrix, one may efficiently |
| /// solve linear systems for different right-hand sides. |
| /// |
| /// ``` |
| /// # #[macro_use] extern crate rulinalg; fn main() { |
| /// # use rulinalg::matrix::decomposition::Cholesky; |
| /// # let x = matrix![ 1.0, 3.0, 1.0; |
| /// # 3.0, 13.0, 11.0; |
| /// # 1.0, 11.0, 21.0 ]; |
| /// # let cholesky = Cholesky::decompose(x).unwrap(); |
| /// let b1 = vector![ 3.0, 2.0, 1.0]; |
| /// let b2 = vector![-2.0, 1.0, 0.0]; |
| /// let y1 = cholesky.solve(b1).expect("Matrix is invertible."); |
| /// let y2 = cholesky.solve(b2).expect("Matrix is invertible."); |
| /// assert_vector_eq!(y1, vector![ 23.25, -7.75, 3.0 ]); |
| /// assert_vector_eq!(y2, vector![-22.25, 7.75, -3.00 ]); |
| /// # } |
| /// ``` |
| /// |
| /// ## Computing the inverse of a matrix |
| /// |
| /// While computing the inverse explicitly is rarely |
| /// the best solution to any given problem, it is sometimes |
| /// necessary. In this case, it is easily accessible |
| /// through the `inverse()` method on `Cholesky`. |
| /// |
| /// # Computing the determinant of a matrix |
| /// |
| /// As with LU decomposition, the `Cholesky` decomposition |
| /// exposes a method `det` for computing the determinant |
| /// of the decomposed matrix. This is a very cheap operation. |
| </span><span class="attribute">#[derive(Clone, Debug)] |
| </span><span class="kw">pub struct </span>Cholesky<T> { |
| l: Matrix<T> |
| } |
| |
| <span class="kw">impl</span><T> Cholesky<T> <span class="kw">where </span>T: <span class="lifetime">'static </span>+ Float { |
| <span class="doccomment">/// Computes the Cholesky decomposition A = L L<sup>T</sup> |
| /// for the given square, symmetric positive definite matrix. |
| /// |
| /// Note that the implementation cannot reliably and efficiently |
| /// verify that the matrix truly is symmetric positive definite matrix, |
| /// so it is the responsibility of the user to make sure that this is |
| /// the case. In particular, if the input matrix is not SPD, |
| /// the returned decomposition may not be a valid decomposition |
| /// for the input matrix. |
| /// |
| /// # Errors |
| /// - A diagonal entry is effectively zero to working precision. |
| /// - A diagonal entry is negative. |
| /// |
| /// # Panics |
| /// |
| /// - The matrix must be square. |
| </span><span class="kw">pub fn </span>decompose(matrix: Matrix<T>) -> <span class="prelude-ty">Result</span><<span class="self">Self</span>, Error> { |
| <span class="macro">assert!</span>(matrix.rows() == matrix.cols(), |
| <span class="string">"Matrix must be square for Cholesky decomposition."</span>); |
| <span class="kw">let </span>n = matrix.rows(); |
| |
| <span class="comment">// The implementation here is based on the |
| // "Gaxpy-Rich Cholesky Factorization" |
| // from Chapter 4.2.5 in |
| // Matrix Computations, 4th Edition, |
| // (Golub and Van Loan). |
| |
| // We consume the matrix we're given, and overwrite its |
| // lower diagonal part with the L factor. However, |
| // we ignore the strictly upper triangular part of the matrix, |
| // because this saves us a few operations. |
| // When the decomposition is unpacked, we will completely zero |
| // the upper triangular part. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>a = matrix; |
| |
| <span class="kw">for </span>j <span class="kw">in </span><span class="number">0 </span>.. n { |
| <span class="kw">if </span>j > <span class="number">0 </span>{ |
| <span class="comment">// This is essentially a GAXPY operation y = y - Bx |
| // where B is the [j .. n, 0 .. j] submatrix of A, |
| // x is the [ j, 0 .. j ] submatrix of A, |
| // and y is the [ j .. n, j ] submatrix of A |
| </span><span class="kw">for </span>k <span class="kw">in </span>j .. n { |
| <span class="kw">let </span>kj_dot = { |
| <span class="kw">let </span>j_row = a.row(j).raw_slice(); |
| <span class="kw">let </span>k_row = a.row(k).raw_slice(); |
| dot(<span class="kw-2">&</span>k_row[<span class="number">0 </span>.. j], <span class="kw-2">&</span>j_row[<span class="number">0 </span>.. j]) |
| }; |
| a[[k, j]] = a[[k, j]] - kj_dot; |
| } |
| } |
| |
| <span class="kw">let </span>diagonal = a[[j, j]]; |
| <span class="kw">if </span>diagonal.abs() < T::epsilon() { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(Error::new(ErrorKind::DecompFailure, |
| <span class="string">"Matrix is singular to working precision."</span>)); |
| } <span class="kw">else if </span>diagonal < T::zero() { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(Error::new(ErrorKind::DecompFailure, |
| <span class="string">"Diagonal entries of matrix are not all positive."</span>)); |
| } |
| |
| <span class="kw">let </span>divisor = diagonal.sqrt(); |
| <span class="kw">for </span>k <span class="kw">in </span>j .. n { |
| a[[k, j]] = a[[k, j]] / divisor; |
| } |
| } |
| |
| <span class="prelude-val">Ok</span>(Cholesky { |
| l: a |
| }) |
| } |
| |
| <span class="doccomment">/// Computes the determinant of the decomposed matrix. |
| /// |
| /// Note that the determinant of an empty matrix is considered |
| /// to be equal to 1. |
| </span><span class="kw">pub fn </span>det(<span class="kw-2">&</span><span class="self">self</span>) -> T { |
| <span class="kw">let </span>l_det = <span class="self">self</span>.l.diag() |
| .cloned() |
| .fold(T::one(), |a, b| a * b); |
| l_det * l_det |
| } |
| |
| <span class="doccomment">/// Solves the linear system Ax = b. |
| /// |
| /// Here A is the decomposed matrix and b is the |
| /// supplied vector. |
| /// |
| /// # Errors |
| /// If the matrix is sufficiently ill-conditioned, |
| /// it is possible that the solution cannot be obtained. |
| /// |
| /// # Panics |
| /// - The supplied right-hand side vector must be |
| /// dimensionally compatible with the supplied matrix. |
| </span><span class="kw">pub fn </span>solve(<span class="kw-2">&</span><span class="self">self</span>, b: Vector<T>) -> <span class="prelude-ty">Result</span><Vector<T>, Error> { |
| <span class="macro">assert!</span>(<span class="self">self</span>.l.rows() == b.size(), |
| <span class="string">"RHS vector and coefficient matrix must be |
| dimensionally compatible."</span>); |
| <span class="comment">// Solve Ly = b |
| </span><span class="kw">let </span>y = forward_substitution(<span class="kw-2">&</span><span class="self">self</span>.l, b)<span class="question-mark">?</span>; |
| <span class="comment">// Solve L^T x = y |
| </span>transpose_back_substitution(<span class="kw-2">&</span><span class="self">self</span>.l, y) |
| } |
| |
| <span class="doccomment">/// Computes the inverse of the decomposed matrix. |
| /// |
| /// # Errors |
| /// If the matrix is sufficiently ill-conditioned, |
| /// it is possible that the inverse cannot be obtained. |
| </span><span class="kw">pub fn </span>inverse(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Result</span><Matrix<T>, Error> { |
| <span class="kw">let </span>n = <span class="self">self</span>.l.rows(); |
| <span class="kw">let </span><span class="kw-2">mut </span>inv = Matrix::zeros(n, n); |
| <span class="kw">let </span><span class="kw-2">mut </span>e = Vector::zeros(n); |
| |
| <span class="comment">// Note: this is essentially the same as |
| // PartialPivLu::inverse(), and consequently |
| // the data access patterns here can also be |
| // improved by way of using BLAS-3 calls. |
| // Please see that function's implementation |
| // for more details. |
| |
| // Solve for each column of the inverse matrix |
| </span><span class="kw">for </span>i <span class="kw">in </span><span class="number">0 </span>.. n { |
| e[i] = T::one(); |
| <span class="kw">let </span>col = <span class="self">self</span>.solve(e)<span class="question-mark">?</span>; |
| |
| <span class="kw">for </span>j <span class="kw">in </span><span class="number">0 </span>.. n { |
| inv[[j, i]] = col[j]; |
| } |
| |
| e = col.apply(<span class="kw-2">&</span>|<span class="kw">_</span>| T::zero()); |
| } |
| |
| <span class="prelude-val">Ok</span>(inv) |
| } |
| } |
| |
| <span class="kw">impl</span><T: Zero> Decomposition <span class="kw">for </span>Cholesky<T> { |
| <span class="kw">type </span>Factors = Matrix<T>; |
| |
| <span class="kw">fn </span>unpack(<span class="self">self</span>) -> Matrix<T> { |
| <span class="kw">use </span>internal_utils::nullify_upper_triangular_part; |
| <span class="kw">let </span><span class="kw-2">mut </span>l = <span class="self">self</span>.l; |
| nullify_upper_triangular_part(<span class="kw-2">&mut </span>l); |
| l |
| } |
| } |
| |
| |
| <span class="kw">impl</span><T> Matrix<T> |
| <span class="kw">where </span>T: Any + Float |
| { |
| <span class="doccomment">/// Cholesky decomposition |
| /// |
| /// Returns the cholesky decomposition of a positive definite matrix. |
| /// |
| /// *NOTE*: This function is deprecated, and will be removed in a |
| /// future release. Please see |
| /// [Cholesky](decomposition/struct.Cholesky.html) for its |
| /// replacement. |
| /// |
| /// # 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 l = m.cholesky(); |
| /// # } |
| /// ``` |
| /// |
| /// # Panics |
| /// |
| /// - The matrix is not square. |
| /// |
| /// # Failures |
| /// |
| /// - Matrix is not positive definite. |
| </span><span class="attribute">#[deprecated] |
| </span><span class="kw">pub fn </span>cholesky(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Result</span><Matrix<T>, Error> { |
| <span class="macro">assert!</span>(<span class="self">self</span>.rows == <span class="self">self</span>.cols, |
| <span class="string">"Matrix must be square for Cholesky decomposition."</span>); |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>new_data = Vec::<T>::with_capacity(<span class="self">self</span>.rows() * <span class="self">self</span>.cols()); |
| |
| <span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..<span class="self">self</span>.rows() { |
| |
| <span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..<span class="self">self</span>.cols() { |
| |
| <span class="kw">if </span>j > i { |
| new_data.push(T::zero()); |
| <span class="kw">continue</span>; |
| } |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>sum = T::zero(); |
| <span class="kw">for </span>k <span class="kw">in </span><span class="number">0</span>..j { |
| sum = sum + (new_data[i * <span class="self">self</span>.cols() + k] * new_data[j * <span class="self">self</span>.cols() + k]); |
| } |
| |
| <span class="kw">if </span>j == i { |
| new_data.push((<span class="self">self</span>[[i, i]] - sum).sqrt()); |
| } <span class="kw">else </span>{ |
| <span class="kw">let </span>p = (<span class="self">self</span>[[i, j]] - sum) / new_data[j * <span class="self">self</span>.cols + j]; |
| |
| <span class="kw">if </span>!p.is_finite() { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(Error::new(ErrorKind::DecompFailure, |
| <span class="string">"Matrix is not positive definite."</span>)); |
| } <span class="kw">else </span>{ |
| |
| } |
| new_data.push(p); |
| } |
| } |
| } |
| |
| <span class="prelude-val">Ok</span>(Matrix { |
| rows: <span class="self">self</span>.rows(), |
| cols: <span class="self">self</span>.cols(), |
| data: new_data, |
| }) |
| } |
| } |
| |
| <span class="doccomment">/// Solves the square system L^T x = b, |
| /// where L is lower triangular |
| </span><span class="kw">fn </span>transpose_back_substitution<T>(l: <span class="kw-2">&</span>Matrix<T>, b: Vector<T>) |
| -> <span class="prelude-ty">Result</span><Vector<T>, Error> <span class="kw">where </span>T: Float { |
| <span class="macro">assert!</span>(l.rows() == l.cols(), <span class="string">"Matrix L must be square."</span>); |
| <span class="macro">assert!</span>(l.rows() == b.size(), <span class="string">"L and b must be dimensionally compatible."</span>); |
| <span class="kw">let </span>n = l.rows(); |
| <span class="kw">let </span><span class="kw-2">mut </span>x = b; |
| |
| <span class="kw">for </span>i <span class="kw">in </span>(<span class="number">0 </span>.. n).rev() { |
| <span class="kw">let </span>row = l.row(i).raw_slice(); |
| <span class="kw">let </span>diagonal = l[[i, i]]; |
| <span class="kw">if </span>diagonal.abs() < T::epsilon() { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(Error::new(ErrorKind::DivByZero, |
| <span class="string">"Matrix L is singular to working precision."</span>)); |
| } |
| |
| x[i] = x[i] / diagonal; |
| |
| <span class="comment">// Apply the BLAS-1 operation |
| // y <- y + α x |
| // where α = - x[i], |
| // y = x[0 .. i] |
| // and x = l[i, 0 .. i] |
| // TODO: Hopefully we'll have a more systematic way |
| // of applying optimized BLAS-like operations in the future. |
| // In this case, we should replace this loop with a call |
| // to the appropriate function. |
| </span><span class="kw">for </span>j <span class="kw">in </span><span class="number">0 </span>.. i { |
| x[j] = x[j] - x[i] * row[j]; |
| } |
| } |
| |
| <span class="prelude-val">Ok</span>(x) |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>tests { |
| <span class="kw">use </span>matrix::Matrix; |
| <span class="kw">use </span>matrix::decomposition::Decomposition; |
| <span class="kw">use </span>vector::Vector; |
| |
| <span class="kw">use </span><span class="kw">super</span>::Cholesky; |
| <span class="kw">use </span><span class="kw">super</span>::transpose_back_substitution; |
| |
| <span class="kw">use </span>quickcheck::TestResult; |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| #[allow(deprecated)] |
| </span><span class="kw">fn </span>test_non_square_cholesky() { |
| <span class="kw">let </span>a = Matrix::<f64>::ones(<span class="number">2</span>, <span class="number">3</span>); |
| |
| <span class="kw">let _ </span>= a.cholesky(); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>cholesky_unpack_empty() { |
| <span class="kw">let </span>x: Matrix<f64> = <span class="macro">matrix!</span>[]; |
| <span class="kw">let </span>l = Cholesky::decompose(x.clone()) |
| .unwrap() |
| .unpack(); |
| <span class="macro">assert_matrix_eq!</span>(l, x); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>cholesky_unpack_1x1() { |
| <span class="kw">let </span>x = <span class="macro">matrix!</span>[ <span class="number">4.0 </span>]; |
| <span class="kw">let </span>expected = <span class="macro">matrix!</span>[ <span class="number">2.0 </span>]; |
| <span class="kw">let </span>l = Cholesky::decompose(x) |
| .unwrap() |
| .unpack(); |
| <span class="macro">assert_matrix_eq!</span>(l, expected, comp = float); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>cholesky_unpack_2x2() { |
| { |
| <span class="kw">let </span>x = <span class="macro">matrix!</span>[ <span class="number">9.0</span>, -<span class="number">6.0</span>; |
| -<span class="number">6.0</span>, <span class="number">20.0</span>]; |
| <span class="kw">let </span>expected = <span class="macro">matrix!</span>[ <span class="number">3.0</span>, <span class="number">0.0</span>; |
| -<span class="number">2.0</span>, <span class="number">4.0</span>]; |
| |
| <span class="kw">let </span>l = Cholesky::decompose(x) |
| .unwrap() |
| .unpack(); |
| <span class="macro">assert_matrix_eq!</span>(l, expected, comp = float); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>cholesky_singular_fails() { |
| { |
| <span class="kw">let </span>x = <span class="macro">matrix!</span>[<span class="number">0.0</span>]; |
| <span class="macro">assert!</span>(Cholesky::decompose(x).is_err()); |
| } |
| |
| { |
| <span class="kw">let </span>x = <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">1.0</span>]; |
| <span class="macro">assert!</span>(Cholesky::decompose(x).is_err()); |
| } |
| |
| { |
| <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="macro">assert!</span>(Cholesky::decompose(x).is_err()); |
| } |
| |
| { |
| <span class="kw">let </span>x = <span class="macro">matrix!</span>[<span class="number">1.0</span>, <span class="number">3.0</span>, <span class="number">5.0</span>; |
| <span class="number">3.0</span>, <span class="number">9.0</span>, <span class="number">15.0</span>; |
| <span class="number">5.0</span>, <span class="number">15.0</span>, <span class="number">65.0</span>]; |
| <span class="macro">assert!</span>(Cholesky::decompose(x).is_err()); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>cholesky_det_empty() { |
| <span class="kw">let </span>x: Matrix<f64> = <span class="macro">matrix!</span>[]; |
| <span class="kw">let </span>cholesky = Cholesky::decompose(x).unwrap(); |
| <span class="macro">assert_eq!</span>(cholesky.det(), <span class="number">1.0</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>cholesky_det() { |
| { |
| <span class="kw">let </span>x = <span class="macro">matrix!</span>[<span class="number">1.0</span>]; |
| <span class="kw">let </span>cholesky = Cholesky::decompose(x).unwrap(); |
| <span class="macro">assert_scalar_eq!</span>(cholesky.det(), <span class="number">1.0</span>, comp = float); |
| } |
| |
| { |
| <span class="kw">let </span>x = <span class="macro">matrix!</span>[<span class="number">1.0</span>, <span class="number">3.0</span>, <span class="number">5.0</span>; |
| <span class="number">3.0</span>, <span class="number">18.0</span>, <span class="number">33.0</span>; |
| <span class="number">5.0</span>, <span class="number">33.0</span>, <span class="number">65.0</span>]; |
| <span class="kw">let </span>cholesky = Cholesky::decompose(x).unwrap(); |
| <span class="macro">assert_scalar_eq!</span>(cholesky.det(), <span class="number">36.0</span>, comp = float); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>cholesky_solve_examples() { |
| { |
| <span class="kw">let </span>a: Matrix<f64> = <span class="macro">matrix!</span>[]; |
| <span class="kw">let </span>b: Vector<f64> = <span class="macro">vector!</span>[]; |
| <span class="kw">let </span>expected: Vector<f64> = <span class="macro">vector!</span>[]; |
| <span class="kw">let </span>cholesky = Cholesky::decompose(a).unwrap(); |
| <span class="kw">let </span>x = cholesky.solve(b).unwrap(); |
| <span class="macro">assert_eq!</span>(x, expected); |
| } |
| |
| { |
| <span class="kw">let </span>a = <span class="macro">matrix!</span>[ <span class="number">1.0 </span>]; |
| <span class="kw">let </span>b = <span class="macro">vector!</span>[ <span class="number">4.0 </span>]; |
| <span class="kw">let </span>expected = <span class="macro">vector!</span>[ <span class="number">4.0 </span>]; |
| <span class="kw">let </span>cholesky = Cholesky::decompose(a).unwrap(); |
| <span class="kw">let </span>x = cholesky.solve(b).unwrap(); |
| <span class="macro">assert_vector_eq!</span>(x, expected, comp = float); |
| } |
| |
| { |
| <span class="kw">let </span>a = <span class="macro">matrix!</span>[ <span class="number">4.0</span>, <span class="number">6.0</span>; |
| <span class="number">6.0</span>, <span class="number">25.0</span>]; |
| <span class="kw">let </span>b = <span class="macro">vector!</span>[ <span class="number">2.0</span>, <span class="number">4.0</span>]; |
| <span class="kw">let </span>expected = <span class="macro">vector!</span>[ <span class="number">0.40625</span>, <span class="number">0.0625 </span>]; |
| <span class="kw">let </span>cholesky = Cholesky::decompose(a).unwrap(); |
| <span class="kw">let </span>x = cholesky.solve(b).unwrap(); |
| <span class="macro">assert_vector_eq!</span>(x, expected, comp = float); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>cholesky_inverse_examples() { |
| { |
| <span class="kw">let </span>a: Matrix<f64> = <span class="macro">matrix!</span>[]; |
| <span class="kw">let </span>expected: Matrix<f64> = <span class="macro">matrix!</span>[]; |
| <span class="kw">let </span>cholesky = Cholesky::decompose(a).unwrap(); |
| <span class="macro">assert_eq!</span>(cholesky.inverse().unwrap(), expected); |
| } |
| |
| { |
| <span class="kw">let </span>a = <span class="macro">matrix!</span>[ <span class="number">2.0 </span>]; |
| <span class="kw">let </span>expected = <span class="macro">matrix!</span>[ <span class="number">0.5 </span>]; |
| <span class="kw">let </span>cholesky = Cholesky::decompose(a).unwrap(); |
| <span class="macro">assert_matrix_eq!</span>(cholesky.inverse().unwrap(), expected, |
| comp = float); |
| } |
| |
| { |
| <span class="kw">let </span>a = <span class="macro">matrix!</span>[ <span class="number">4.0</span>, <span class="number">6.0</span>; |
| <span class="number">6.0</span>, <span class="number">25.0</span>]; |
| <span class="kw">let </span>expected = <span class="macro">matrix!</span>[ <span class="number">0.390625</span>, -<span class="number">0.09375</span>; |
| -<span class="number">0.093750 </span>, <span class="number">0.06250</span>]; |
| <span class="kw">let </span>cholesky = Cholesky::decompose(a).unwrap(); |
| <span class="macro">assert_matrix_eq!</span>(cholesky.inverse().unwrap(), expected, |
| comp = float); |
| } |
| |
| { |
| <span class="kw">let </span>a = <span class="macro">matrix!</span>[ <span class="number">9.0</span>, <span class="number">6.0</span>, <span class="number">3.0</span>; |
| <span class="number">6.0</span>, <span class="number">20.0</span>, <span class="number">10.0</span>; |
| <span class="number">3.0</span>, <span class="number">10.0</span>, <span class="number">14.0</span>]; |
| <span class="kw">let </span>expected = <span class="macro">matrix!</span>[<span class="number">0.1388888888888889</span>, -<span class="number">0.0416666666666667</span>, <span class="number">0.0 </span>; |
| -<span class="number">0.0416666666666667</span>, <span class="number">0.0902777777777778</span>, -<span class="number">0.0555555555555556</span>; |
| <span class="number">0.0</span>, -<span class="number">0.0555555555555556</span>, <span class="number">0.1111111111111111</span>]; |
| <span class="kw">let </span>cholesky = Cholesky::decompose(a).unwrap(); |
| <span class="macro">assert_matrix_eq!</span>(cholesky.inverse().unwrap(), expected, |
| comp = float); |
| } |
| } |
| |
| <span class="macro">quickcheck! </span>{ |
| <span class="kw">fn </span>property_cholesky_of_identity_is_identity(n: usize) -> TestResult { |
| <span class="kw">if </span>n > <span class="number">30 </span>{ |
| <span class="kw">return </span>TestResult::discard(); |
| } |
| |
| <span class="kw">let </span>x = Matrix::<f64>::identity(n); |
| <span class="kw">let </span>l = Cholesky::decompose(x.clone()).map(|c| c.unpack()); |
| <span class="kw">match </span>l { |
| <span class="prelude-val">Ok</span>(l) => { |
| <span class="macro">assert_matrix_eq!</span>(l, x, comp = float); |
| TestResult::passed() |
| }, |
| <span class="kw">_ </span>=> TestResult::failed() |
| } |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>transpose_back_substitution_examples() { |
| { |
| <span class="kw">let </span>l: Matrix<f64> = <span class="macro">matrix!</span>[]; |
| <span class="kw">let </span>b: Vector<f64> = <span class="macro">vector!</span>[]; |
| <span class="kw">let </span>expected: Vector<f64> = <span class="macro">vector!</span>[]; |
| <span class="kw">let </span>x = transpose_back_substitution(<span class="kw-2">&</span>l, b).unwrap(); |
| <span class="macro">assert_vector_eq!</span>(x, expected); |
| } |
| |
| { |
| <span class="kw">let </span>l = <span class="macro">matrix!</span>[<span class="number">2.0</span>]; |
| <span class="kw">let </span>b = <span class="macro">vector!</span>[<span class="number">2.0</span>]; |
| <span class="kw">let </span>expected = <span class="macro">vector!</span>[<span class="number">1.0</span>]; |
| <span class="kw">let </span>x = transpose_back_substitution(<span class="kw-2">&</span>l, b).unwrap(); |
| <span class="macro">assert_vector_eq!</span>(x, expected, comp = float); |
| } |
| |
| { |
| <span class="kw">let </span>l = <span class="macro">matrix!</span>[<span class="number">2.0</span>, <span class="number">0.0</span>; |
| <span class="number">3.0</span>, <span class="number">4.0</span>]; |
| <span class="kw">let </span>b = <span class="macro">vector!</span>[<span class="number">2.0</span>, <span class="number">1.0</span>]; |
| <span class="kw">let </span>expected = <span class="macro">vector!</span>[<span class="number">0.625</span>, <span class="number">0.25 </span>]; |
| <span class="kw">let </span>x = transpose_back_substitution(<span class="kw-2">&</span>l, b).unwrap(); |
| <span class="macro">assert_vector_eq!</span>(x, expected, comp = float); |
| } |
| |
| { |
| <span class="kw">let </span>l = <span class="macro">matrix!</span>[ <span class="number">2.0</span>, <span class="number">0.0</span>, <span class="number">0.0</span>; |
| <span class="number">5.0</span>, -<span class="number">1.0</span>, <span class="number">0.0</span>; |
| -<span class="number">2.0</span>, <span class="number">0.0</span>, <span class="number">1.0</span>]; |
| <span class="kw">let </span>b = <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="kw">let </span>expected = <span class="macro">vector!</span>[ <span class="number">7.5</span>, -<span class="number">2.0</span>, <span class="number">3.0 </span>]; |
| <span class="kw">let </span>x = transpose_back_substitution(<span class="kw-2">&</span>l, b).unwrap(); |
| <span class="macro">assert_vector_eq!</span>(x, expected, 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> |
