| <!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/svd.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>svd.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, MatrixSlice, MatrixSliceMut}; |
| <span class="kw">use </span>error::{Error, ErrorKind}; |
| |
| <span class="kw">use </span>std::any::Any; |
| <span class="kw">use </span>std::cmp; |
| |
| <span class="kw">use </span>libnum::{Float, Signed}; |
| |
| <span class="doccomment">/// Ensures that all singular values in the given singular value decomposition |
| /// are non-negative, making necessary corrections to the singular vectors. |
| /// |
| /// The SVD is represented by matrices `(b, u, v)`, where `b` is the diagonal matrix |
| /// containing the singular values, `u` is the matrix of left singular vectors |
| /// and v is the matrix of right singular vectors. |
| </span><span class="kw">fn </span>correct_svd_signs<T>(<span class="kw-2">mut </span>b: Matrix<T>, |
| <span class="kw-2">mut </span>u: Matrix<T>, |
| <span class="kw-2">mut </span>v: Matrix<T>) |
| -> (Matrix<T>, Matrix<T>, Matrix<T>) |
| <span class="kw">where </span>T: Any + Float + Signed |
| { |
| |
| <span class="comment">// When correcting the signs of the singular vectors, we can choose |
| // to correct EITHER u or v. We make the choice depending on which matrix has the |
| // least number of rows. Later we will need to multiply all elements in columns by |
| // -1, which might be significantly faster in corner cases if we pick the matrix |
| // with the least amount of rows. |
| </span>{ |
| <span class="kw">let </span><span class="kw-2">ref mut </span>shortest_matrix = <span class="kw">if </span>u.rows() <= v.rows() { <span class="kw-2">&mut </span>u } <span class="kw">else </span>{ <span class="kw-2">&mut </span>v }; |
| <span class="kw">let </span>column_length = shortest_matrix.rows(); |
| <span class="kw">let </span>num_singular_values = cmp::min(b.rows(), b.cols()); |
| |
| <span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..num_singular_values { |
| <span class="kw">if </span>b[[i, i]] < T::zero() { |
| <span class="comment">// Swap sign of singular value and column in u |
| </span>b[[i, i]] = b[[i, i]].abs(); |
| |
| <span class="comment">// Access the column as a slice and flip sign |
| </span><span class="kw">let </span><span class="kw-2">mut </span>column = shortest_matrix.sub_slice_mut([<span class="number">0</span>, i], column_length, <span class="number">1</span>); |
| column <span class="kw-2">*</span>= -T::one(); |
| } |
| } |
| } |
| (b, u, v) |
| } |
| |
| <span class="kw">fn </span>sort_svd<T>(<span class="kw-2">mut </span>b: Matrix<T>, |
| <span class="kw-2">mut </span>u: Matrix<T>, |
| <span class="kw-2">mut </span>v: Matrix<T>) |
| -> (Matrix<T>, Matrix<T>, Matrix<T>) |
| <span class="kw">where </span>T: Any + Float + Signed |
| { |
| |
| <span class="macro">assert!</span>(u.cols() == b.cols() && b.cols() == v.cols()); |
| |
| <span class="comment">// This unfortunately incurs two allocations since we have no (simple) |
| // way to iterate over a matrix diagonal, only to copy it into a new Vector |
| </span><span class="kw">let </span><span class="kw-2">mut </span>indexed_sorted_values: Vec<<span class="kw">_</span>> = b.diag().cloned().enumerate().collect(); |
| |
| <span class="comment">// Sorting a vector of indices simultaneously with the singular values |
| // gives us a mapping between old and new (final) column indices. |
| </span>indexed_sorted_values.sort_by(|<span class="kw-2">&</span>(<span class="kw">_</span>, <span class="kw-2">ref </span>x), <span class="kw-2">&</span>(<span class="kw">_</span>, <span class="kw-2">ref </span>y)| { |
| x.partial_cmp(y) |
| .expect(<span class="string">"All singular values should be finite, and thus sortable."</span>) |
| .reverse() |
| }); |
| |
| <span class="comment">// Set the diagonal elements of the singular value matrix |
| </span><span class="kw">for </span>(i, <span class="kw-2">&</span>(<span class="kw">_</span>, value)) <span class="kw">in </span>indexed_sorted_values.iter().enumerate() { |
| b[[i, i]] = value; |
| } |
| |
| <span class="comment">// Assuming N columns, the simultaneous sorting of indices and singular values yields |
| // a set of N (i, j) pairs which correspond to columns which must be swapped. However, |
| // for any (i, j) in this set, there is also (j, i). Keeping both of these would make us |
| // swap the columns back and forth, so we must remove the duplicates. We can avoid |
| // any further sorting or hashsets or similar by noting that we can simply |
| // remove any (i, j) for which j >= i. This also removes (i, i) pairs, |
| // i.e. columns that don't need to be swapped. |
| </span><span class="kw">let </span>swappable_pairs = indexed_sorted_values.into_iter() |
| .enumerate() |
| .map(|(new_index, (old_index, <span class="kw">_</span>))| (old_index, new_index)) |
| .filter(|<span class="kw-2">&</span>(old_index, new_index)| old_index < new_index); |
| |
| <span class="kw">for </span>(old_index, new_index) <span class="kw">in </span>swappable_pairs { |
| u.swap_cols(old_index, new_index); |
| v.swap_cols(old_index, new_index); |
| } |
| |
| (b, u, v) |
| } |
| |
| <span class="kw">impl</span><T: Any + Float + Signed> Matrix<T> { |
| <span class="doccomment">/// Singular Value Decomposition |
| /// |
| /// Computes the SVD using the Golub-Reinsch algorithm. |
| /// |
| /// Returns Σ, U, V, such that `self` = U Σ V<sup>T</sup>. Σ is a diagonal matrix whose elements |
| /// correspond to the non-negative singular values of the matrix. The singular values are ordered in |
| /// non-increasing order. U and V have orthonormal columns, and each column represents the |
| /// left and right singular vectors for the corresponding singular value in Σ, respectively. |
| /// |
| /// If `self` has M rows and N columns, the dimensions of the returned matrices |
| /// are as follows. |
| /// |
| /// If M >= N: |
| /// |
| /// - `Σ`: N x N |
| /// - `U`: M x N |
| /// - `V`: N x N |
| /// |
| /// If M < N: |
| /// |
| /// - `Σ`: M x M |
| /// - `U`: M x M |
| /// - `V`: N x M |
| /// |
| /// Note: This version of the SVD is sometimes referred to as the 'economy SVD'. |
| /// |
| /// # Failures |
| /// |
| /// This function may fail in some cases. The current decomposition whilst being |
| /// efficient is fairly basic. Hopefully the algorithm can be made not to fail in the near future. |
| </span><span class="kw">pub fn </span>svd(<span class="self">self</span>) -> <span class="prelude-ty">Result</span><(Matrix<T>, Matrix<T>, Matrix<T>), Error> { |
| <span class="kw">let </span>(b, u, v) = <span class="macro">try!</span>(<span class="self">self</span>.svd_unordered()); |
| <span class="prelude-val">Ok</span>(sort_svd(b, u, v)) |
| } |
| |
| <span class="kw">fn </span>svd_unordered(<span class="self">self</span>) -> <span class="prelude-ty">Result</span><(Matrix<T>, Matrix<T>, Matrix<T>), Error> { |
| <span class="kw">let </span>(b, u, v) = <span class="macro">try!</span>(<span class="self">self</span>.svd_golub_reinsch()); |
| |
| <span class="comment">// The Golub-Reinsch implementation sometimes spits out negative singular values, |
| // so we need to correct these. |
| </span><span class="prelude-val">Ok</span>(correct_svd_signs(b, u, v)) |
| } |
| |
| <span class="kw">fn </span>svd_golub_reinsch(<span class="kw-2">mut </span><span class="self">self</span>) -> <span class="prelude-ty">Result</span><(Matrix<T>, Matrix<T>, Matrix<T>), Error> { |
| <span class="kw">let </span><span class="kw-2">mut </span>flipped = <span class="bool-val">false</span>; |
| |
| <span class="comment">// The algorithm assumes rows > cols. If this is not the case we transpose and fix later. |
| </span><span class="kw">if </span><span class="self">self</span>.cols > <span class="self">self</span>.rows { |
| <span class="self">self </span>= <span class="self">self</span>.transpose(); |
| flipped = <span class="bool-val">true</span>; |
| } |
| |
| <span class="kw">let </span>eps = T::from(<span class="number">3.0</span>).unwrap() * T::epsilon(); |
| <span class="kw">let </span>n = <span class="self">self</span>.cols; |
| |
| <span class="comment">// Get the bidiagonal decomposition |
| </span><span class="kw">let </span>(<span class="kw-2">mut </span>b, <span class="kw-2">mut </span>u, <span class="kw-2">mut </span>v) = <span class="macro">try!</span>(<span class="self">self</span>.bidiagonal_decomp() |
| .map_err(|<span class="kw">_</span>| Error::new(ErrorKind::DecompFailure, <span class="string">"Could not compute SVD."</span>))); |
| |
| <span class="kw">loop </span>{ |
| <span class="comment">// Values to count the size of lower diagonal block |
| </span><span class="kw">let </span><span class="kw-2">mut </span>q = <span class="number">0</span>; |
| <span class="kw">let </span><span class="kw-2">mut </span>on_lower = <span class="bool-val">true</span>; |
| |
| <span class="comment">// Values to count top block |
| </span><span class="kw">let </span><span class="kw-2">mut </span>p = <span class="number">0</span>; |
| <span class="kw">let </span><span class="kw-2">mut </span>on_middle = <span class="bool-val">false</span>; |
| |
| <span class="comment">// Iterate through and hard set the super diag if converged |
| </span><span class="kw">for </span>i <span class="kw">in </span>(<span class="number">0</span>..n - <span class="number">1</span>).rev() { |
| <span class="kw">let </span>(b_ii, b_sup_diag, diag_abs_sum): (T, T, T); |
| <span class="kw">unsafe </span>{ |
| b_ii = <span class="kw-2">*</span>b.get_unchecked([i, i]); |
| b_sup_diag = b.get_unchecked([i, i + <span class="number">1</span>]).abs(); |
| diag_abs_sum = eps * (b_ii.abs() + b.get_unchecked([i + <span class="number">1</span>, i + <span class="number">1</span>]).abs()); |
| } |
| <span class="kw">if </span>b_sup_diag <= diag_abs_sum { |
| <span class="comment">// Adjust q or p to define boundaries of sup-diagonal box |
| </span><span class="kw">if </span>on_lower { |
| q += <span class="number">1</span>; |
| } <span class="kw">else if </span>on_middle { |
| on_middle = <span class="bool-val">false</span>; |
| p = i + <span class="number">1</span>; |
| } |
| <span class="kw">unsafe </span>{ |
| <span class="kw-2">*</span>b.get_unchecked_mut([i, i + <span class="number">1</span>]) = T::zero(); |
| } |
| } <span class="kw">else </span>{ |
| <span class="kw">if </span>on_lower { |
| <span class="comment">// No longer on the lower diagonal |
| </span>on_middle = <span class="bool-val">true</span>; |
| on_lower = <span class="bool-val">false</span>; |
| } |
| } |
| } |
| |
| <span class="comment">// We have converged! |
| </span><span class="kw">if </span>q == n - <span class="number">1 </span>{ |
| <span class="kw">break</span>; |
| } |
| |
| <span class="comment">// Zero off diagonals if needed. |
| </span><span class="kw">for </span>i <span class="kw">in </span>p..n - q - <span class="number">1 </span>{ |
| <span class="kw">let </span>(b_ii, b_sup_diag): (T, T); |
| <span class="kw">unsafe </span>{ |
| b_ii = <span class="kw-2">*</span>b.get_unchecked([i, i]); |
| b_sup_diag = <span class="kw-2">*</span>b.get_unchecked([i, i + <span class="number">1</span>]); |
| } |
| |
| <span class="kw">if </span>b_ii.abs() < eps { |
| <span class="kw">let </span>(c, s) = Matrix::<T>::givens_rot(b_ii, b_sup_diag); |
| <span class="kw">let </span>givens = Matrix::new(<span class="number">2</span>, <span class="number">2</span>, <span class="macro">vec!</span>[c, s, -s, c]); |
| <span class="kw">let </span>b_i = MatrixSliceMut::from_matrix(<span class="kw-2">&mut </span>b, [i, i], <span class="number">1</span>, <span class="number">2</span>); |
| <span class="kw">let </span>zerod_line = <span class="kw-2">&</span>b_i * givens; |
| |
| b_i.set_to(zerod_line.as_slice()); |
| } |
| } |
| |
| <span class="comment">// Apply Golub-Kahan svd step |
| </span><span class="kw">unsafe </span>{ |
| <span class="macro">try!</span>(Matrix::<T>::golub_kahan_svd_step(<span class="kw-2">&mut </span>b, <span class="kw-2">&mut </span>u, <span class="kw-2">&mut </span>v, p, q) |
| .map_err(|<span class="kw">_</span>| Error::new(ErrorKind::DecompFailure, <span class="string">"Could not compute SVD."</span>))); |
| } |
| } |
| |
| <span class="kw">if </span>flipped { |
| <span class="prelude-val">Ok</span>((b.transpose(), v, u)) |
| } <span class="kw">else </span>{ |
| <span class="prelude-val">Ok</span>((b, u, v)) |
| } |
| |
| } |
| |
| <span class="doccomment">/// This function is unsafe as it makes assumptions about the dimensions |
| /// of the inputs matrices and does not check them. As a result if misused |
| /// this function can call `get_unchecked` on invalid indices. |
| </span><span class="kw">unsafe fn </span>golub_kahan_svd_step(b: <span class="kw-2">&mut </span>Matrix<T>, |
| u: <span class="kw-2">&mut </span>Matrix<T>, |
| v: <span class="kw-2">&mut </span>Matrix<T>, |
| p: usize, |
| q: usize) |
| -> <span class="prelude-ty">Result</span><(), Error> { |
| <span class="kw">let </span>n = b.rows(); |
| |
| <span class="comment">// C is the lower, right 2x2 square of aTa, where a is the |
| // middle block of b (between p and n-q). |
| // |
| // Computed as xTx + yTy, where y is the bottom 2x2 block of a |
| // and x are the two columns above it within a. |
| </span><span class="kw">let </span>c: Matrix<T>; |
| { |
| <span class="kw">let </span>y = MatrixSlice::from_matrix(<span class="kw-2">&</span>b, [n - q - <span class="number">2</span>, n - q - <span class="number">2</span>], <span class="number">2</span>, <span class="number">2</span>).into_matrix(); |
| <span class="kw">if </span>n - q - p - <span class="number">2 </span>> <span class="number">0 </span>{ |
| <span class="kw">let </span>x = MatrixSlice::from_matrix(<span class="kw-2">&</span>b, [p, n - q - <span class="number">2</span>], n - q - p - <span class="number">2</span>, <span class="number">2</span>); |
| c = x.into_matrix().transpose() * x + y.transpose() * y; |
| } <span class="kw">else </span>{ |
| c = y.transpose() * y; |
| } |
| } |
| |
| <span class="kw">let </span>c_eigs = <span class="macro">try!</span>(c.clone().eigenvalues()); |
| |
| <span class="comment">// Choose eigenvalue closes to c[1,1]. |
| </span><span class="kw">let </span>lambda: T; |
| <span class="kw">if </span>(c_eigs[<span class="number">0</span>] - <span class="kw-2">*</span>c.get_unchecked([<span class="number">1</span>, <span class="number">1</span>])).abs() < |
| (c_eigs[<span class="number">1</span>] - <span class="kw-2">*</span>c.get_unchecked([<span class="number">1</span>, <span class="number">1</span>])).abs() { |
| lambda = c_eigs[<span class="number">0</span>]; |
| } <span class="kw">else </span>{ |
| lambda = c_eigs[<span class="number">1</span>]; |
| } |
| |
| <span class="kw">let </span>b_pp = <span class="kw-2">*</span>b.get_unchecked([p, p]); |
| <span class="kw">let </span><span class="kw-2">mut </span>alpha = (b_pp * b_pp) - lambda; |
| <span class="kw">let </span><span class="kw-2">mut </span>beta = b_pp * <span class="kw-2">*</span>b.get_unchecked([p, p + <span class="number">1</span>]); |
| <span class="kw">for </span>k <span class="kw">in </span>p..n - q - <span class="number">1 </span>{ |
| <span class="comment">// Givens rot on columns k and k + 1 |
| </span><span class="kw">let </span>(c, s) = Matrix::<T>::givens_rot(alpha, beta); |
| <span class="kw">let </span>givens_mat = Matrix::new(<span class="number">2</span>, <span class="number">2</span>, <span class="macro">vec!</span>[c, s, -s, c]); |
| |
| { |
| <span class="comment">// Pick the rows from b to be zerod. |
| </span><span class="kw">let </span>b_block = MatrixSliceMut::from_matrix(b, |
| [k.saturating_sub(<span class="number">1</span>), k], |
| cmp::min(<span class="number">3</span>, n - k.saturating_sub(<span class="number">1</span>)), |
| <span class="number">2</span>); |
| <span class="kw">let </span>transformed = <span class="kw-2">&</span>b_block * <span class="kw-2">&</span>givens_mat; |
| b_block.set_to(transformed.as_slice()); |
| |
| <span class="kw">let </span>v_block = MatrixSliceMut::from_matrix(v, [<span class="number">0</span>, k], n, <span class="number">2</span>); |
| <span class="kw">let </span>transformed = <span class="kw-2">&</span>v_block * <span class="kw-2">&</span>givens_mat; |
| v_block.set_to(transformed.as_slice()); |
| } |
| |
| alpha = <span class="kw-2">*</span>b.get_unchecked([k, k]); |
| beta = <span class="kw-2">*</span>b.get_unchecked([k + <span class="number">1</span>, k]); |
| |
| <span class="kw">let </span>(c, s) = Matrix::<T>::givens_rot(alpha, beta); |
| <span class="kw">let </span>givens_mat = Matrix::new(<span class="number">2</span>, <span class="number">2</span>, <span class="macro">vec!</span>[c, -s, s, c]); |
| |
| { |
| <span class="comment">// Pick the columns from b to be zerod. |
| </span><span class="kw">let </span>b_block = MatrixSliceMut::from_matrix(b, [k, k], <span class="number">2</span>, cmp::min(<span class="number">3</span>, n - k)); |
| <span class="kw">let </span>transformed = <span class="kw-2">&</span>givens_mat * <span class="kw-2">&</span>b_block; |
| b_block.set_to(transformed.as_slice()); |
| |
| <span class="kw">let </span>m = u.rows(); |
| <span class="kw">let </span>u_block = MatrixSliceMut::from_matrix(u, [<span class="number">0</span>, k], m, <span class="number">2</span>); |
| <span class="kw">let </span>transformed = <span class="kw-2">&</span>u_block * givens_mat.transpose(); |
| u_block.set_to(transformed.as_slice()); |
| } |
| |
| <span class="kw">if </span>k + <span class="number">2 </span>< n - q { |
| alpha = <span class="kw-2">*</span>b.get_unchecked([k, k + <span class="number">1</span>]); |
| beta = <span class="kw-2">*</span>b.get_unchecked([k, k + <span class="number">2</span>]); |
| } |
| } |
| <span class="prelude-val">Ok</span>(()) |
| } |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>tests { |
| <span class="kw">use </span>matrix::{Matrix, BaseMatrix}; |
| <span class="kw">use </span>vector::Vector; |
| <span class="kw">use </span><span class="kw">super</span>::sort_svd; |
| |
| <span class="kw">fn </span>validate_svd(mat: <span class="kw-2">&</span>Matrix<f64>, b: <span class="kw-2">&</span>Matrix<f64>, u: <span class="kw-2">&</span>Matrix<f64>, v: <span class="kw-2">&</span>Matrix<f64>) { |
| <span class="comment">// b is diagonal (the singular values) |
| </span><span class="kw">for </span>(idx, row) <span class="kw">in </span>b.row_iter().enumerate() { |
| <span class="macro">assert!</span>(!row.iter().take(idx).any(|<span class="kw-2">&</span>x| x > <span class="number">1e-10</span>)); |
| <span class="macro">assert!</span>(!row.iter().skip(idx + <span class="number">1</span>).any(|<span class="kw-2">&</span>x| x > <span class="number">1e-10</span>)); |
| <span class="comment">// Assert non-negativity of diagonal elements |
| </span><span class="macro">assert!</span>(row[idx] >= <span class="number">0.0</span>); |
| } |
| |
| <span class="kw">let </span>recovered = u * b * v.transpose(); |
| |
| <span class="macro">assert_eq!</span>(recovered.rows(), mat.rows()); |
| <span class="macro">assert_eq!</span>(recovered.cols(), mat.cols()); |
| |
| <span class="macro">assert!</span>(!mat.data() |
| .iter() |
| .zip(recovered.data().iter()) |
| .any(|(<span class="kw-2">&</span>x, <span class="kw-2">&</span>y)| (x - y).abs() > <span class="number">1e-10</span>)); |
| |
| <span class="comment">// The transposition is due to the fact that there does not exist |
| // any column iterators at the moment, and we need to simultaneously iterate |
| // over the columns. Once they do exist, we should rewrite |
| // the below iterators to use iter_cols() or whatever instead. |
| </span><span class="kw">let </span><span class="kw-2">ref </span>u_transposed = u.transpose(); |
| <span class="kw">let </span><span class="kw-2">ref </span>v_transposed = v.transpose(); |
| <span class="kw">let </span><span class="kw-2">ref </span>mat_transposed = mat.transpose(); |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>singular_triplets = u_transposed.row_iter().zip(b.diag()).zip(v_transposed.row_iter()) |
| <span class="comment">// chained zipping results in nested tuple. Flatten it. |
| </span>.map(|((u_col, singular_value), v_col)| (Vector::new(u_col.raw_slice()), singular_value, Vector::new(v_col.raw_slice()))); |
| |
| <span class="macro">assert!</span>(singular_triplets.by_ref() |
| <span class="comment">// For a matrix M, each singular value σ and left and right singular vectors u and v respectively |
| // satisfy M v = σ u, so we take the difference |
| </span>.map(|(<span class="kw-2">ref </span>u, sigma, <span class="kw-2">ref </span>v)| mat * v - u * sigma) |
| .flat_map(|v| v.into_vec().into_iter()) |
| .all(|x| x.abs() < <span class="number">1e-10</span>)); |
| |
| <span class="macro">assert!</span>(singular_triplets.by_ref() |
| <span class="comment">// For a matrix M, each singular value σ and left and right singular vectors u and v respectively |
| // satisfy M_transposed u = σ v, so we take the difference |
| </span>.map(|(<span class="kw-2">ref </span>u, sigma, <span class="kw-2">ref </span>v)| mat_transposed * u - v * sigma) |
| .flat_map(|v| v.into_vec().into_iter()) |
| .all(|x| x.abs() < <span class="number">1e-10</span>)); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_sort_svd() { |
| <span class="kw">let </span>u = <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>b = <span class="macro">matrix!</span>[<span class="number">4.0</span>, <span class="number">0.0</span>, <span class="number">0.0</span>; |
| <span class="number">0.0</span>, <span class="number">8.0</span>, <span class="number">0.0</span>; |
| <span class="number">0.0</span>, <span class="number">0.0</span>, <span class="number">2.0</span>]; |
| <span class="kw">let </span>v = <span class="macro">matrix!</span>[<span class="number">21.0</span>, <span class="number">22.0</span>, <span class="number">23.0</span>; |
| <span class="number">24.0</span>, <span class="number">25.0</span>, <span class="number">26.0</span>; |
| <span class="number">27.0</span>, <span class="number">28.0</span>, <span class="number">29.0</span>]; |
| |
| <span class="kw">let </span>(b, u, v) = sort_svd(b, u, v); |
| |
| <span class="macro">assert_eq!</span>(b.data(), <span class="kw-2">&</span><span class="macro">vec!</span>[<span class="number">8.0</span>, <span class="number">0.0</span>, <span class="number">0.0</span>, <span class="number">0.0</span>, <span class="number">4.0</span>, <span class="number">0.0</span>, <span class="number">0.0</span>, <span class="number">0.0</span>, <span class="number">2.0</span>]); |
| <span class="macro">assert_eq!</span>(u.data(), <span class="kw-2">&</span><span class="macro">vec!</span>[<span class="number">2.0</span>, <span class="number">1.0</span>, <span class="number">3.0</span>, <span class="number">5.0</span>, <span class="number">4.0</span>, <span class="number">6.0</span>]); |
| <span class="macro">assert_eq!</span>(v.data(), |
| <span class="kw-2">&</span><span class="macro">vec!</span>[<span class="number">22.0</span>, <span class="number">21.0</span>, <span class="number">23.0</span>, <span class="number">25.0</span>, <span class="number">24.0</span>, <span class="number">26.0</span>, <span class="number">28.0</span>, <span class="number">27.0</span>, <span class="number">29.0</span>]); |
| |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_svd_tall_matrix() { |
| <span class="comment">// Note: This matrix is not arbitrary. It has been constructed specifically so that |
| // the "natural" order of the singular values it not sorted by default. |
| </span><span class="kw">let </span>mat = <span class="macro">matrix!</span>[<span class="number">3.61833700244349288</span>, -<span class="number">3.28382346228211697</span>, <span class="number">1.97968027781346501</span>, -<span class="number">0.41869628192662156</span>; |
| <span class="number">3.96046289599926427</span>, <span class="number">0.70730060716580723</span>, -<span class="number">2.80552479438772817</span>, -<span class="number">1.45283286109873933</span>; |
| <span class="number">1.44435028724617442</span>, <span class="number">1.27749196276785826</span>, -<span class="number">1.09858397535426366</span>, -<span class="number">0.03159619816434689</span>; |
| <span class="number">1.13455445826500667</span>, <span class="number">0.81521390274755756</span>, <span class="number">3.99123446373437263</span>, -<span class="number">2.83025703359666192</span>; |
| -<span class="number">3.30895752093770579</span>, -<span class="number">0.04979044289857298</span>, <span class="number">3.03248594516832792</span>, <span class="number">3.85962479743330977</span>]; |
| <span class="kw">let </span>(b, u, v) = mat.clone().svd().unwrap(); |
| |
| <span class="kw">let </span>expected_values = <span class="macro">vec!</span>[<span class="number">8.0</span>, <span class="number">6.0</span>, <span class="number">4.0</span>, <span class="number">2.0</span>]; |
| |
| validate_svd(<span class="kw-2">&</span>mat, <span class="kw-2">&</span>b, <span class="kw-2">&</span>u, <span class="kw-2">&</span>v); |
| |
| <span class="comment">// Assert the singular values are what we expect |
| </span><span class="macro">assert!</span>(expected_values.iter() |
| .zip(b.diag()) |
| .all(|(expected, actual)| (expected - actual).abs() < <span class="number">1e-14</span>)); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_svd_short_matrix() { |
| <span class="comment">// Note: This matrix is not arbitrary. It has been constructed specifically so that |
| // the "natural" order of the singular values it not sorted by default. |
| </span><span class="kw">let </span>mat = <span class="macro">matrix!</span>[<span class="number">3.61833700244349288</span>, <span class="number">3.96046289599926427</span>, <span class="number">1.44435028724617442</span>, <span class="number">1.13455445826500645</span>, -<span class="number">3.30895752093770579</span>; |
| -<span class="number">3.28382346228211697</span>, <span class="number">0.70730060716580723</span>, <span class="number">1.27749196276785826</span>, <span class="number">0.81521390274755756</span>, -<span class="number">0.04979044289857298</span>; |
| <span class="number">1.97968027781346545</span>, -<span class="number">2.80552479438772817</span>, -<span class="number">1.09858397535426366</span>, <span class="number">3.99123446373437263</span>, <span class="number">3.03248594516832792</span>; |
| -<span class="number">0.41869628192662156</span>, -<span class="number">1.45283286109873933</span>, -<span class="number">0.03159619816434689</span>, -<span class="number">2.83025703359666192</span>, <span class="number">3.85962479743330977</span>]; |
| <span class="kw">let </span>(b, u, v) = mat.clone().svd().unwrap(); |
| |
| <span class="kw">let </span>expected_values = <span class="macro">vec!</span>[<span class="number">8.0</span>, <span class="number">6.0</span>, <span class="number">4.0</span>, <span class="number">2.0</span>]; |
| |
| validate_svd(<span class="kw-2">&</span>mat, <span class="kw-2">&</span>b, <span class="kw-2">&</span>u, <span class="kw-2">&</span>v); |
| |
| <span class="comment">// Assert the singular values are what we expect |
| </span><span class="macro">assert!</span>(expected_values.iter() |
| .zip(b.diag()) |
| .all(|(expected, actual)| (expected - actual).abs() < <span class="number">1e-14</span>)); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_svd_square_matrix() { |
| <span class="kw">let </span>mat = <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">2.0</span>, <span class="number">4.0</span>, <span class="number">1.0</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">7.0</span>, <span class="number">1.0</span>, <span class="number">1.0</span>; |
| <span class="number">4.0</span>, <span class="number">2.0</span>, <span class="number">1.0</span>, -<span class="number">1.0</span>, <span class="number">3.0</span>; |
| <span class="number">5.0</span>, <span class="number">1.0</span>, <span class="number">1.0</span>, <span class="number">3.0</span>, <span class="number">2.0</span>]; |
| |
| <span class="kw">let </span>expected_values = <span class="macro">vec!</span>[<span class="number">12.1739747429271112</span>, |
| <span class="number">5.2681047320525831</span>, |
| <span class="number">4.4942269799769843</span>, |
| <span class="number">2.9279675877385123</span>, |
| <span class="number">2.8758200827412224</span>]; |
| |
| <span class="kw">let </span>(b, u, v) = mat.clone().svd().unwrap(); |
| validate_svd(<span class="kw-2">&</span>mat, <span class="kw-2">&</span>b, <span class="kw-2">&</span>u, <span class="kw-2">&</span>v); |
| |
| <span class="comment">// Assert the singular values are what we expect |
| </span><span class="macro">assert!</span>(expected_values.iter() |
| .zip(b.diag()) |
| .all(|(expected, actual)| (expected - actual).abs() < <span class="number">1e-12</span>)); |
| } |
| } |
| </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> |
