| <!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/permutation_matrix.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>permutation_matrix.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> |
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| <span id="611">611</span> |
| <span id="612">612</span> |
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| <span id="620">620</span> |
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| <span id="622">622</span> |
| <span id="623">623</span> |
| <span id="624">624</span> |
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| <span id="626">626</span> |
| <span id="627">627</span> |
| <span id="628">628</span> |
| <span id="629">629</span> |
| <span id="630">630</span> |
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| <span id="658">658</span> |
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| <span id="663">663</span> |
| <span id="664">664</span> |
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| <span id="669">669</span> |
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| <span id="674">674</span> |
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| <span id="768">768</span> |
| <span id="769">769</span> |
| <span id="770">770</span> |
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| <span id="790">790</span> |
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| <span id="792">792</span> |
| <span id="793">793</span> |
| <span id="794">794</span> |
| <span id="795">795</span> |
| <span id="796">796</span> |
| <span id="797">797</span> |
| <span id="798">798</span> |
| <span id="799">799</span> |
| <span id="800">800</span> |
| <span id="801">801</span> |
| <span id="802">802</span> |
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| <span id="806">806</span> |
| <span id="807">807</span> |
| <span id="808">808</span> |
| <span id="809">809</span> |
| <span id="810">810</span> |
| <span id="811">811</span> |
| <span id="812">812</span> |
| <span id="813">813</span> |
| <span id="814">814</span> |
| <span id="815">815</span> |
| <span id="816">816</span> |
| <span id="817">817</span> |
| <span id="818">818</span> |
| <span id="819">819</span> |
| <span id="820">820</span> |
| <span id="821">821</span> |
| <span id="822">822</span> |
| <span id="823">823</span> |
| <span id="824">824</span> |
| <span id="825">825</span> |
| <span id="826">826</span> |
| <span id="827">827</span> |
| <span id="828">828</span> |
| <span id="829">829</span> |
| <span id="830">830</span> |
| <span id="831">831</span> |
| <span id="832">832</span> |
| <span id="833">833</span> |
| <span id="834">834</span> |
| <span id="835">835</span> |
| <span id="836">836</span> |
| <span id="837">837</span> |
| <span id="838">838</span> |
| <span id="839">839</span> |
| <span id="840">840</span> |
| <span id="841">841</span> |
| <span id="842">842</span> |
| <span id="843">843</span> |
| <span id="844">844</span> |
| <span id="845">845</span> |
| <span id="846">846</span> |
| <span id="847">847</span> |
| <span id="848">848</span> |
| <span id="849">849</span> |
| <span id="850">850</span> |
| <span id="851">851</span> |
| <span id="852">852</span> |
| <span id="853">853</span> |
| <span id="854">854</span> |
| <span id="855">855</span> |
| <span id="856">856</span> |
| <span id="857">857</span> |
| <span id="858">858</span> |
| <span id="859">859</span> |
| <span id="860">860</span> |
| <span id="861">861</span> |
| <span id="862">862</span> |
| <span id="863">863</span> |
| <span id="864">864</span> |
| <span id="865">865</span> |
| <span id="866">866</span> |
| <span id="867">867</span> |
| <span id="868">868</span> |
| <span id="869">869</span> |
| <span id="870">870</span> |
| <span id="871">871</span> |
| <span id="872">872</span> |
| <span id="873">873</span> |
| <span id="874">874</span> |
| <span id="875">875</span> |
| <span id="876">876</span> |
| <span id="877">877</span> |
| <span id="878">878</span> |
| <span id="879">879</span> |
| <span id="880">880</span> |
| <span id="881">881</span> |
| <span id="882">882</span> |
| <span id="883">883</span> |
| <span id="884">884</span> |
| <span id="885">885</span> |
| </pre><pre class="rust"><code><span class="kw">use </span>std; |
| |
| <span class="kw">use </span>matrix::{Matrix, BaseMatrix, BaseMatrixMut}; |
| <span class="kw">use </span>vector::Vector; |
| <span class="kw">use </span>error::{Error, ErrorKind}; |
| |
| <span class="kw">use </span>libnum::Num; |
| |
| <span class="doccomment">/// An efficient implementation of a permutation matrix. |
| /// |
| /// # Examples |
| /// ``` |
| /// # #[macro_use] extern crate rulinalg; fn main() { |
| /// use rulinalg::matrix::PermutationMatrix; |
| /// |
| /// let ref x = matrix![1, 2, 3; |
| /// 4, 5, 6; |
| /// 7, 8, 9]; |
| /// |
| /// // Swap the two first rows of x by left-multiplying a permutation matrix |
| /// let expected = matrix![4, 5, 6; |
| /// 1, 2, 3; |
| /// 7, 8, 9]; |
| /// let mut p = PermutationMatrix::identity(3); |
| /// p.swap_rows(0, 1); |
| /// assert_eq!(expected, p * x); |
| /// |
| /// // Swap the two last columns of x by right-multiplying a permutation matrix |
| /// let expected = matrix![1, 3, 2; |
| /// 4, 6, 5; |
| /// 7, 9, 8]; |
| /// let mut p = PermutationMatrix::identity(3); |
| /// p.swap_rows(1, 2); |
| /// assert_eq!(expected, x * p); |
| /// |
| /// // One can also construct the same permutation matrix directly |
| /// // from an array representation. |
| /// let ref p = PermutationMatrix::from_array(vec![0, 2, 1]).unwrap(); |
| /// assert_eq!(expected, x * p); |
| /// |
| /// // One may also obtain a full matrix representation of the permutation |
| /// assert_eq!(p.as_matrix(), matrix![1, 0, 0; |
| /// 0, 0, 1; |
| /// 0, 1, 0]); |
| /// |
| /// // The inverse of a permutation matrix can efficiently be obtained |
| /// let p_inv = p.inverse(); |
| /// |
| /// // And permutations can be composed through multiplication |
| /// assert_eq!(p * p_inv, PermutationMatrix::identity(3)); |
| /// # } |
| /// ``` |
| /// |
| /// # Rationale and complexity |
| /// |
| /// A [permutation matrix](https://en.wikipedia.org/wiki/Permutation_matrix) |
| /// is a very special kind of matrix. It is essentially a matrix representation |
| /// of the more general concept of a permutation. That is, an `n` x `n` permutation |
| /// matrix corresponds to a permutation of ordered sets whose cardinality is `n`. |
| /// In particular, given an `m` x `n` matrix `A` and an `m` x `m` permutation |
| /// matrix `P`, the action of left-multiplying `A` by `P`, `PA`, corresponds |
| /// to permuting the rows of `A` by the given permutation represented by `P`. |
| /// Conversely, right-multiplication corresponds to column permutation. |
| /// More precisely, given another permutation matrix `Q` of size `n` x `n`, |
| /// then `AQ` is the corresponding permutation of the columns of `A`. |
| /// |
| /// Due to their unique structure, permutation matrices can be much more |
| /// efficiently represented and applied than general matrices. Recall that |
| /// for general matrices `X` and `Y` of size `m` x `m` and `n` x `n` respectively, |
| /// the storage of `X` requires O(`m`<sup>2</sup>) memory and the storage of |
| /// `Y` requires O(`n`<sup>2</sup>) memory. Ignoring for the moment the existence |
| /// of Strassen's matrix multiplication algorithm and more theoretical alternatives, |
| /// the multiplication `XA` requires O(`m`<sup>2</sup>`n`) operations, and |
| /// the multiplication `AY` requires O(`m``n`<sup>2</sup>) operations. |
| /// |
| /// By contrast, the storage of `P` requires only O(`m`) memory, and |
| /// the storage of `K` requires O(`n`) memory. Moreover, the products |
| /// `PA` and `AK` both require merely O(`mn`) operations. |
| /// |
| /// # Representation |
| /// A permutation of an ordered set of cardinality *n* is a map of the form |
| /// |
| /// ```text |
| /// p: { 1, ..., n } -> { 1, ..., n }. |
| /// ``` |
| /// |
| /// That is, for any index `i`, the permutation `p` sends `i` to some |
| /// index `j = p(i)`, and hence the map may be represented as an array of integers |
| /// of length *n*. |
| /// |
| /// By convention, an instance of `PermutationMatrix` represents row permutations. |
| /// That is, the indices referred to above correspond to *row indices*, |
| /// and the internal representation of a `PermutationMatrix` is an array |
| /// describing how the permutation sends a row index `i` to a new row index |
| /// `j` in the permuted matrix. Because of this internal representation, one can only |
| /// efficiently swap *rows* of a `PermutationMatrix`. |
| /// However, keep in mind that while this API only lets one swap individual rows |
| /// of the permutation matrix itself, the right-multiplication of a general |
| /// matrix with a permutation matrix will permute the columns of the general matrix, |
| /// and so in practice this restriction is insignificant. |
| /// |
| </span><span class="attribute">#[derive(Debug, PartialEq, Eq, Clone)] |
| </span><span class="kw">pub struct </span>PermutationMatrix<T> { |
| <span class="comment">// A permutation matrix of dimensions NxN is represented as a permutation of the rows |
| // of an NxM matrix for any M. |
| </span>perm: Vec<usize>, |
| |
| <span class="comment">// Currently, we need to let PermutationMatrix be generic over T, |
| // because BaseMatrixMut is. |
| </span>marker: std::marker::PhantomData<T> |
| } |
| |
| <span class="doccomment">/// Parity is the fact of being even or odd. |
| </span><span class="attribute">#[derive(Debug, Copy, Clone, PartialEq, Eq)] |
| </span><span class="kw">pub enum </span>Parity { |
| <span class="doccomment">/// Even parity. |
| </span>Even, |
| <span class="doccomment">/// Odd parity. |
| </span>Odd |
| } |
| |
| <span class="kw">impl</span><T> PermutationMatrix<T> { |
| <span class="doccomment">/// The identity permutation. |
| </span><span class="kw">pub fn </span>identity(n: usize) -> <span class="self">Self </span>{ |
| PermutationMatrix { |
| perm: (<span class="number">0 </span>.. n).collect(), |
| marker: std::marker::PhantomData |
| } |
| } |
| |
| <span class="doccomment">/// Swaps rows i and j in the permutation matrix. |
| </span><span class="kw">pub fn </span>swap_rows(<span class="kw-2">&mut </span><span class="self">self</span>, i: usize, j: usize) { |
| <span class="self">self</span>.perm.swap(i, j); |
| } |
| |
| <span class="doccomment">/// The inverse of the permutation matrix. |
| </span><span class="kw">pub fn </span>inverse(<span class="kw-2">&</span><span class="self">self</span>) -> PermutationMatrix<T> { |
| <span class="kw">let </span><span class="kw-2">mut </span>inv: Vec<usize> = <span class="macro">vec!</span>[<span class="number">0</span>; <span class="self">self</span>.size()]; |
| |
| <span class="kw">for </span>(source, target) <span class="kw">in </span><span class="self">self</span>.perm.iter().cloned().enumerate() { |
| inv[target] = source; |
| } |
| |
| PermutationMatrix { |
| perm: inv, |
| marker: std::marker::PhantomData |
| } |
| } |
| |
| <span class="doccomment">/// The size of the permutation matrix. |
| /// |
| /// A permutation matrix is a square matrix, so `size()` is equal |
| /// to both the number of rows, as well as the number of columns. |
| </span><span class="kw">pub fn </span>size(<span class="kw-2">&</span><span class="self">self</span>) -> usize { |
| <span class="self">self</span>.perm.len() |
| } |
| |
| <span class="doccomment">/// Constructs a `PermutationMatrix` from an array. |
| /// |
| /// # Errors |
| /// The supplied N-length array must satisfy the following: |
| /// |
| /// - Each element must be in the half-open range [0, N). |
| /// - Each element must be unique. |
| </span><span class="kw">pub fn </span>from_array<A: Into<Vec<usize>>>(array: A) -> <span class="prelude-ty">Result</span><PermutationMatrix<T>, Error> { |
| <span class="kw">let </span>p = PermutationMatrix { |
| perm: array.into(), |
| marker: std::marker::PhantomData |
| }; |
| validate_permutation(<span class="kw-2">&</span>p.perm).map(|<span class="kw">_</span>| p) |
| } |
| |
| <span class="doccomment">/// Constructs a `PermutationMatrix` from an array, without checking the validity of |
| /// the supplied permutation. |
| /// |
| /// # Safety |
| /// The supplied N-length array must satisfy the following: |
| /// |
| /// - Each element must be in the half-open range [0, N). |
| /// - Each element must be unique. |
| /// |
| /// Note that while this function *itself* is technically safe |
| /// regardless of the input array, passing an incorrect permutation matrix |
| /// may cause undefined behavior in other methods of `PermutationMatrix`. |
| /// As such, it may be difficult to debug. The user is strongly |
| /// encouraged to use the safe function `from_array`, which for |
| /// most real world applications only incurs a minor |
| /// or even insignificant performance hit as a result of the |
| /// extra validation. |
| </span><span class="kw">pub unsafe fn </span>from_array_unchecked<A: Into<Vec<usize>>>(array: A) -> PermutationMatrix<T> { |
| <span class="kw">let </span>p = PermutationMatrix { |
| perm: array.into(), |
| marker: std::marker::PhantomData |
| }; |
| p |
| } |
| |
| <span class="doccomment">/// Maps the given row index into the resulting row index in the permuted matrix. |
| /// |
| /// More specifically, if the permutation sends row `i` to `j`, then |
| /// `map_row(i)` returns `j`. |
| /// |
| /// # Examples |
| /// |
| /// ```rust |
| /// use rulinalg::matrix::PermutationMatrix; |
| /// let mut p = PermutationMatrix::<u32>::identity(3); |
| /// p.swap_rows(1, 2); |
| /// assert_eq!(p.map_row(1), 2); |
| /// ``` |
| </span><span class="kw">pub fn </span>map_row(<span class="kw-2">&</span><span class="self">self</span>, row_index: usize) -> usize { |
| <span class="self">self</span>.perm[row_index] |
| } |
| |
| <span class="doccomment">/// Computes the parity of the permutation (even- or oddness). |
| </span><span class="kw">pub fn </span>parity(<span class="kw-2">mut </span><span class="self">self</span>) -> Parity { |
| <span class="comment">// As it happens, permute_by_swap effectively decomposes |
| // each disjoint cycle in the permutation into a series |
| // of transpositions. The result is that the whole permutation |
| // is effectively decomposed into a series of |
| // transpositions. |
| // Hence, if we start out by assuming that the permutation |
| // is even and simply flip this variable every time a swap |
| // (transposition) is performed, we'll have the result by |
| // the end of the procedure. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>is_even = <span class="bool-val">true</span>; |
| permute_by_swap(<span class="kw-2">&mut </span><span class="self">self</span>.perm, |<span class="kw">_</span>, <span class="kw">_</span>| is_even = !is_even); |
| |
| <span class="kw">if </span>is_even { |
| Parity::Even |
| } <span class="kw">else </span>{ |
| Parity::Odd |
| } |
| } |
| } |
| |
| <span class="kw">impl</span><T: Num> PermutationMatrix<T> { |
| <span class="doccomment">/// The permutation matrix in an equivalent full matrix representation. |
| </span><span class="kw">pub fn </span>as_matrix(<span class="kw-2">&</span><span class="self">self</span>) -> Matrix<T> { |
| Matrix::from_fn(<span class="self">self</span>.size(), <span class="self">self</span>.size(), |i, j| |
| <span class="kw">if </span><span class="self">self</span>.perm[i] == j { |
| T::one() |
| } <span class="kw">else </span>{ |
| T::zero() |
| } |
| ) |
| } |
| |
| <span class="doccomment">/// Computes the determinant of the permutation matrix. |
| /// |
| /// The determinant of a permutation matrix is always |
| /// +1 (if the permutation is even) or |
| /// -1 (if the permutation is odd). |
| </span><span class="kw">pub fn </span>det(<span class="self">self</span>) -> T { |
| <span class="kw">let </span>parity = <span class="self">self</span>.parity(); |
| <span class="kw">match </span>parity { |
| Parity::Even => T::one(), |
| Parity::Odd => T::zero() - T::one() |
| } |
| } |
| } |
| |
| <span class="kw">impl</span><T> PermutationMatrix<T> { |
| <span class="doccomment">/// Permutes the rows of the given matrix in-place. |
| /// |
| /// # Panics |
| /// |
| /// - The number of rows in the matrix is not equal to |
| /// the size of the permutation matrix. |
| </span><span class="kw">pub fn </span>permute_rows_in_place<M>(<span class="kw-2">mut </span><span class="self">self</span>, matrix: <span class="kw-2">&mut </span>M) <span class="kw">where </span>M: BaseMatrixMut<T> { |
| validate_permutation_left_mul_dimensions(<span class="kw-2">&</span><span class="self">self</span>, matrix); |
| permute_by_swap(<span class="kw-2">&mut </span><span class="self">self</span>.perm, |i, j| matrix.swap_rows(i, j)); |
| } |
| |
| <span class="doccomment">/// Permutes the columns of the given matrix in-place. |
| /// |
| /// # Panics |
| /// |
| /// - The number of columns in the matrix is not equal to |
| /// the size of the permutation matrix. |
| </span><span class="kw">pub fn </span>permute_cols_in_place<M>(<span class="kw-2">mut </span><span class="self">self</span>, matrix: <span class="kw-2">&mut </span>M) <span class="kw">where </span>M: BaseMatrixMut<T> { |
| validate_permutation_right_mul_dimensions(matrix, <span class="kw-2">&</span><span class="self">self</span>); |
| <span class="comment">// Note: it _may_ be possible to increase cache efficiency |
| // of this routine by swapping elements in each row individually |
| // (since matrices are row major), but this would mean augmenting |
| // permute_by_swap in such a way that the original permutation can |
| // be recovered, which includes a little bit of additional work. |
| // Moreover, it would mean having to work with signed indices |
| // instead of unsigned (although temporarily casting would be sufficient), |
| // which may or may not complicate matters. |
| // For now, it was deemed significantly simpler and probably good enough |
| // to just swap whole columns instead. |
| </span>permute_by_swap(<span class="kw-2">&mut </span><span class="self">self</span>.perm, |i, j| matrix.swap_cols(i, j)); |
| } |
| |
| <span class="doccomment">/// Permutes the elements of the given vector in-place. |
| /// |
| /// # Panics |
| /// |
| /// - The size of the vector is not equal to the size of |
| /// the permutation matrix. |
| </span><span class="kw">pub fn </span>permute_vector_in_place(<span class="kw-2">mut </span><span class="self">self</span>, vector: <span class="kw-2">&mut </span>Vector<T>) { |
| validate_permutation_vector_dimensions(<span class="kw-2">&</span><span class="self">self</span>, vector); |
| permute_by_swap(<span class="kw-2">&mut </span><span class="self">self</span>.perm, |i, j| vector.mut_data().swap(i, j)); |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone> PermutationMatrix<T> { |
| <span class="doccomment">/// Permutes the rows of the given `source_matrix` and stores the |
| /// result in `buffer`. |
| /// |
| /// # Panics |
| /// |
| /// - The number of rows in the source matrix is not equal to |
| /// the size of the permutation matrix. |
| /// - The dimensions of the source matrix and the buffer |
| /// are not identical. |
| </span><span class="kw">pub fn </span>permute_rows_into_buffer<X, Y>(<span class="kw-2">&</span><span class="self">self</span>, source_matrix: <span class="kw-2">&</span>X, buffer: <span class="kw-2">&mut </span>Y) |
| <span class="kw">where </span>X: BaseMatrix<T>, Y: BaseMatrixMut<T> { |
| <span class="macro">assert!</span>(source_matrix.rows() == buffer.rows() |
| && source_matrix.cols() == buffer.cols(), |
| <span class="string">"Source and target matrix must have equal dimensions."</span>); |
| validate_permutation_left_mul_dimensions(<span class="self">self</span>, source_matrix); |
| <span class="kw">for </span>(source_row, target_row_index) <span class="kw">in </span>source_matrix.row_iter() |
| .zip(<span class="self">self</span>.perm.iter() |
| .cloned()) { |
| buffer.row_mut(target_row_index) |
| .raw_slice_mut() |
| .clone_from_slice(source_row.raw_slice()); |
| } |
| } |
| |
| <span class="doccomment">/// Permutes the columns of the given `source_matrix` and stores the |
| /// result in `buffer`. |
| /// |
| /// # Panics |
| /// |
| /// - The number of columns in the source matrix is not equal to |
| /// the size of the permutation matrix. |
| /// - The dimensions of the source matrix and the buffer |
| /// are not identical. |
| </span><span class="kw">pub fn </span>permute_cols_into_buffer<X, Y>(<span class="kw-2">&</span><span class="self">self</span>, source_matrix: <span class="kw-2">&</span>X, target_matrix: <span class="kw-2">&mut </span>Y) |
| <span class="kw">where </span>X: BaseMatrix<T>, Y: BaseMatrixMut<T> { |
| <span class="macro">assert!</span>(source_matrix.rows() == target_matrix.rows() |
| && source_matrix.cols() == target_matrix.cols(), |
| <span class="string">"Source and target matrix must have equal dimensions."</span>); |
| validate_permutation_right_mul_dimensions(source_matrix, <span class="self">self</span>); |
| |
| <span class="comment">// Permute columns in one row at a time for (presumably) better cache performance |
| </span><span class="kw">for </span>(row_index, source_row) <span class="kw">in </span>source_matrix.row_iter() |
| .map(|r| r.raw_slice()) |
| .enumerate() { |
| <span class="kw">let </span>target_row = target_matrix.row_mut(row_index).raw_slice_mut(); |
| <span class="kw">for </span>(source_element, target_col) <span class="kw">in </span>source_row.iter().zip(<span class="self">self</span>.perm.iter().cloned()) { |
| target_row[target_col] = source_element.clone(); |
| } |
| } |
| } |
| |
| <span class="doccomment">/// Permutes the elements of the given `source_vector` and stores the |
| /// result in `buffer`. |
| /// |
| /// # Panics |
| /// |
| /// - The size of the source vector is not equal to the |
| /// size of the permutation matrix. |
| /// - The dimensions of the source vector and the buffer |
| /// are not identical. |
| </span><span class="kw">pub fn </span>permute_vector_into_buffer( |
| <span class="kw-2">&</span><span class="self">self</span>, |
| source_vector: <span class="kw-2">&</span>Vector<T>, |
| buffer: <span class="kw-2">&mut </span>Vector<T> |
| ) { |
| <span class="macro">assert!</span>(source_vector.size() == buffer.size(), |
| <span class="string">"Source and target vector must have equal dimensions."</span>); |
| validate_permutation_vector_dimensions(<span class="self">self</span>, buffer); |
| <span class="kw">for </span>(source_element, target_index) <span class="kw">in </span>source_vector.data() |
| .iter() |
| .zip(<span class="self">self</span>.perm.iter().cloned()) { |
| buffer[target_index] = source_element.clone(); |
| } |
| } |
| |
| <span class="doccomment">/// Computes the composition of `self` with the given `source_perm` |
| /// and stores the result in `buffer`. |
| /// |
| /// # Panics |
| /// |
| /// - The size of the permutation matrix (self) is not equal to the |
| /// size of the source permutation matrix. |
| </span><span class="kw">pub fn </span>compose_into_buffer( |
| <span class="kw-2">&</span><span class="self">self</span>, |
| source_perm: <span class="kw-2">&</span>PermutationMatrix<T>, |
| buffer: <span class="kw-2">&mut </span>PermutationMatrix<T> |
| ) { |
| <span class="macro">assert!</span>(source_perm.size() == buffer.size(), |
| <span class="string">"Source and target permutation matrix must have equal dimensions."</span>); |
| <span class="kw">let </span>left = <span class="self">self</span>; |
| <span class="kw">let </span>right = source_perm; |
| <span class="kw">for </span>i <span class="kw">in </span><span class="number">0 </span>.. <span class="self">self</span>.perm.len() { |
| buffer.perm[i] = left.perm[right.perm[i]]; |
| } |
| } |
| } |
| |
| <span class="kw">impl</span><T> From<PermutationMatrix<T>> <span class="kw">for </span>Vec<usize> { |
| <span class="kw">fn </span>from(p: PermutationMatrix<T>) -> Vec<usize> { |
| p.perm |
| } |
| } |
| |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, T> Into<<span class="kw-2">&</span><span class="lifetime">'a </span>[usize]> <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'a </span>PermutationMatrix<T> { |
| <span class="kw">fn </span>into(<span class="self">self</span>) -> <span class="kw-2">&</span><span class="lifetime">'a </span>[usize] { |
| <span class="kw-2">&</span><span class="self">self</span>.perm |
| } |
| } |
| |
| <span class="kw">fn </span>validate_permutation_vector_dimensions<T>(p: <span class="kw-2">&</span>PermutationMatrix<T>, v: <span class="kw-2">&</span>Vector<T>) { |
| <span class="macro">assert!</span>(p.size() == v.size(), |
| <span class="string">"Permutation matrix and Vector dimensions are not compatible."</span>); |
| } |
| |
| |
| <span class="kw">fn </span>validate_permutation_left_mul_dimensions<T, M>(p: <span class="kw-2">&</span>PermutationMatrix<T>, rhs: <span class="kw-2">&</span>M) |
| <span class="kw">where </span>M: BaseMatrix<T> { |
| <span class="macro">assert!</span>(p.size() == rhs.rows(), |
| <span class="string">"Permutation matrix and right-hand side matrix dimensions |
| are not compatible."</span>); |
| } |
| |
| <span class="kw">fn </span>validate_permutation_right_mul_dimensions<T, M>(lhs: <span class="kw-2">&</span>M, p: <span class="kw-2">&</span>PermutationMatrix<T>) |
| <span class="kw">where </span>M: BaseMatrix<T> { |
| <span class="macro">assert!</span>(lhs.cols() == p.size(), |
| <span class="string">"Left-hand side matrix and permutation matrix dimensions |
| are not compatible."</span>); |
| } |
| |
| <span class="kw">fn </span>validate_permutation(perm: <span class="kw-2">&</span>[usize]) -> <span class="prelude-ty">Result</span><(), Error> { |
| <span class="comment">// Recall that a permutation array of size n is valid if: |
| // 1. All elements are in the range [0, n) |
| // 2. All elements are unique |
| |
| </span><span class="kw">let </span>n = perm.len(); |
| |
| <span class="comment">// Here we use a vector of boolean. If memory usage or performance |
| // is ever an issue, we could replace the vector with a bit vector |
| // (from e.g. the bit-vec crate), which would cut memory usage |
| // to 1/8, and likely improve performance due to more data |
| // fitting in cache. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>visited = <span class="macro">vec!</span>[<span class="bool-val">false</span>; n]; |
| <span class="kw">for </span>p <span class="kw">in </span>perm.iter().cloned() { |
| <span class="kw">if </span>p < n { |
| visited[p] = <span class="bool-val">true</span>; |
| } |
| <span class="kw">else </span>{ |
| <span class="kw">return </span><span class="prelude-val">Err</span>(Error::new(ErrorKind::InvalidPermutation, |
| <span class="string">"Supplied permutation array contains elements out of bounds."</span>)); |
| } |
| } |
| <span class="kw">let </span>all_unique = visited.iter().all(|x| x.clone()); |
| <span class="kw">if </span>all_unique { |
| <span class="prelude-val">Ok</span>(()) |
| } <span class="kw">else </span>{ |
| <span class="prelude-val">Err</span>(Error::new(ErrorKind::InvalidPermutation, |
| <span class="string">"Supplied permutation array contains duplicate elements."</span>)) |
| } |
| } |
| |
| <span class="doccomment">/// Applies the permutation by swapping elements in an abstract |
| /// container. |
| /// |
| /// The permutation is applied by calls to `swap(i, j)` for indices |
| /// `i` and `j`. |
| /// |
| /// # Complexity |
| /// |
| /// - O(1) memory usage. |
| /// - O(n) worst case number of calls to `swap`. |
| </span><span class="kw">fn </span>permute_by_swap<S>(perm: <span class="kw-2">&mut </span>[usize], <span class="kw-2">mut </span>swap: S) <span class="kw">where </span>S: FnMut(usize, usize) -> () { |
| <span class="comment">// Please see https://en.wikipedia.org/wiki/Cyclic_permutation |
| // for some explanation to the terminology used here. |
| // Some useful resources I found on the internet: |
| // |
| // https://blog.merovius.de/2014/08/12/applying-permutation-in-constant.html |
| // http://stackoverflow.com/questions/16501424/algorithm-to-apply-permutation-in-constant-memory-space |
| // |
| // A fundamental property of permutations on finite sets is that |
| // any such permutation can be decomposed into a collection of |
| // cycles on disjoint orbits. |
| // |
| // An observation is thus that given a permutation P, |
| // we can trace out the cycle that includes index i |
| // by starting at i and moving to P[i] recursively. |
| </span><span class="kw">for </span>i <span class="kw">in </span><span class="number">0 </span>.. perm.len() { |
| <span class="kw">let </span><span class="kw-2">mut </span>target = perm[i]; |
| <span class="kw">while </span>i != target { |
| <span class="comment">// When resolving a cycle, we resolve each index in the cycle |
| // by repeatedly moving the current item into the target position, |
| // and item in the target position into the current position. |
| // By repeating this until we hit the start index, |
| // we effectively resolve the entire cycle. |
| </span><span class="kw">let </span>new_target = perm[target]; |
| swap(i, target); |
| perm[target] = target; |
| target = new_target; |
| } |
| perm[i] = i; |
| } |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>tests { |
| <span class="kw">use </span>matrix::Matrix; |
| <span class="kw">use </span>vector::Vector; |
| <span class="kw">use super</span>::{PermutationMatrix, Parity}; |
| <span class="kw">use super</span>::{permute_by_swap, validate_permutation}; |
| |
| <span class="kw">use </span>itertools::Itertools; |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>swap_rows() { |
| <span class="kw">let </span><span class="kw-2">mut </span>p = PermutationMatrix::<u64>::identity(<span class="number">4</span>); |
| p.swap_rows(<span class="number">0</span>, <span class="number">3</span>); |
| p.swap_rows(<span class="number">1</span>, <span class="number">3</span>); |
| |
| <span class="kw">let </span>expected_permutation = PermutationMatrix::from_array(<span class="macro">vec!</span>[<span class="number">3</span>, <span class="number">0</span>, <span class="number">2</span>, <span class="number">1</span>]).unwrap(); |
| <span class="macro">assert_eq!</span>(p, expected_permutation); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>as_matrix() { |
| <span class="kw">let </span>p = PermutationMatrix::from_array(<span class="macro">vec!</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">3</span>]).unwrap(); |
| <span class="kw">let </span>expected_matrix: Matrix<u32> = <span class="macro">matrix!</span>[<span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">0</span>; |
| <span class="number">0</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>; |
| <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>; |
| <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>]; |
| |
| <span class="macro">assert_matrix_eq!</span>(expected_matrix, p.as_matrix()); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>from_array() { |
| <span class="kw">let </span>array = <span class="macro">vec!</span>[<span class="number">1</span>, <span class="number">0</span>, <span class="number">3</span>, <span class="number">2</span>]; |
| <span class="kw">let </span>p = PermutationMatrix::<u32>::from_array(array.clone()).unwrap(); |
| <span class="kw">let </span>p_as_array: Vec<usize> = p.into(); |
| <span class="macro">assert_eq!</span>(p_as_array, array); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>from_array_unchecked() { |
| <span class="kw">let </span>array = <span class="macro">vec!</span>[<span class="number">1</span>, <span class="number">0</span>, <span class="number">3</span>, <span class="number">2</span>]; |
| <span class="kw">let </span>p = <span class="kw">unsafe </span>{ PermutationMatrix::<u32>::from_array_unchecked(array.clone()) }; |
| <span class="kw">let </span>p_as_array: Vec<usize> = p.into(); |
| <span class="macro">assert_eq!</span>(p_as_array, array); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>from_array_invalid() { |
| <span class="macro">assert!</span>(PermutationMatrix::<u32>::from_array(<span class="macro">vec!</span>[<span class="number">0</span>, <span class="number">1</span>, <span class="number">3</span>]).is_err()); |
| <span class="macro">assert!</span>(PermutationMatrix::<u32>::from_array(<span class="macro">vec!</span>[<span class="number">0</span>, <span class="number">0</span>]).is_err()); |
| <span class="macro">assert!</span>(PermutationMatrix::<u32>::from_array(<span class="macro">vec!</span>[<span class="number">3</span>, <span class="number">0</span>, <span class="number">1</span>]).is_err()); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>vec_from_permutation() { |
| <span class="kw">let </span>source_vec = <span class="macro">vec!</span>[<span class="number">0</span>, <span class="number">2</span>, <span class="number">1</span>]; |
| <span class="kw">let </span>p = PermutationMatrix::<u32>::from_array(source_vec.clone()).unwrap(); |
| <span class="kw">let </span>vec = Vec::from(p); |
| <span class="macro">assert_eq!</span>(<span class="kw-2">&</span>source_vec, <span class="kw-2">&</span>vec); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>into_slice_ref() { |
| <span class="kw">let </span>source_vec = <span class="macro">vec!</span>[<span class="number">0</span>, <span class="number">2</span>, <span class="number">1</span>]; |
| <span class="kw">let </span><span class="kw-2">ref </span>p = PermutationMatrix::<u32>::from_array(source_vec.clone()).unwrap(); |
| <span class="kw">let </span>p_as_slice_ref: <span class="kw-2">&</span>[usize] = p.into(); |
| <span class="macro">assert_eq!</span>(source_vec.as_slice(), p_as_slice_ref); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>map_row() { |
| <span class="kw">let </span>p = PermutationMatrix::<u32>::from_array(<span class="macro">vec!</span>[<span class="number">0</span>, <span class="number">2</span>, <span class="number">1</span>]).unwrap(); |
| <span class="macro">assert_eq!</span>(p.map_row(<span class="number">0</span>), <span class="number">0</span>); |
| <span class="macro">assert_eq!</span>(p.map_row(<span class="number">1</span>), <span class="number">2</span>); |
| <span class="macro">assert_eq!</span>(p.map_row(<span class="number">2</span>), <span class="number">1</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>inverse() { |
| <span class="kw">let </span>p = PermutationMatrix::<u32>::from_array(<span class="macro">vec!</span>[<span class="number">1</span>, <span class="number">2</span>, <span class="number">0</span>]).unwrap(); |
| <span class="kw">let </span>expected_inverse = PermutationMatrix::<u32>::from_array(<span class="macro">vec!</span>[<span class="number">2</span>, <span class="number">0</span>, <span class="number">1</span>]).unwrap(); |
| <span class="macro">assert_eq!</span>(p.inverse(), expected_inverse); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>parity() { |
| { |
| <span class="kw">let </span>p = PermutationMatrix::<u32>::from_array(<span class="macro">vec!</span>[<span class="number">1</span>, <span class="number">0</span>, <span class="number">3</span>, <span class="number">2</span>]).unwrap(); |
| <span class="macro">assert_eq!</span>(p.parity(), Parity::Even); |
| } |
| |
| { |
| <span class="kw">let </span>p = PermutationMatrix::<u32>::from_array(<span class="macro">vec!</span>[<span class="number">4</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">5</span>]).unwrap(); |
| <span class="macro">assert_eq!</span>(p.parity(), Parity::Odd); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>det() { |
| { |
| <span class="kw">let </span>p = PermutationMatrix::<i32>::from_array(<span class="macro">vec!</span>[<span class="number">1</span>, <span class="number">0</span>, <span class="number">3</span>, <span class="number">2</span>]).unwrap(); |
| <span class="macro">assert_eq!</span>(p.det(), <span class="number">1</span>); |
| } |
| |
| { |
| <span class="kw">let </span>p = PermutationMatrix::<i32>::from_array(<span class="macro">vec!</span>[<span class="number">4</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">5</span>]).unwrap(); |
| <span class="macro">assert_eq!</span>(p.det(), -<span class="number">1</span>); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>permute_by_swap_on_empty_array() { |
| <span class="kw">let </span><span class="kw-2">mut </span>x = Vec::<char>::new(); |
| <span class="kw">let </span><span class="kw-2">mut </span>permutation_array = Vec::new(); |
| permute_by_swap(<span class="kw-2">&mut </span>permutation_array, |i, j| x.swap(i, j)); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>permute_by_swap_on_arbitrary_array() { |
| <span class="kw">let </span><span class="kw-2">mut </span>x = <span class="macro">vec!</span>[<span class="string">'a'</span>, <span class="string">'b'</span>, <span class="string">'c'</span>, <span class="string">'d'</span>]; |
| <span class="kw">let </span><span class="kw-2">mut </span>permutation_array = <span class="macro">vec!</span>[<span class="number">0</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">1</span>]; |
| |
| permute_by_swap(<span class="kw-2">&mut </span>permutation_array, |i, j| x.swap(i, j)); |
| <span class="macro">assert_eq!</span>(x, <span class="macro">vec!</span>[<span class="string">'a'</span>, <span class="string">'d'</span>, <span class="string">'b'</span>, <span class="string">'c'</span>]); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>permute_by_swap_identity_on_arbitrary_array() { |
| <span class="kw">let </span><span class="kw-2">mut </span>x = <span class="macro">vec!</span>[<span class="string">'a'</span>, <span class="string">'b'</span>, <span class="string">'c'</span>, <span class="string">'d'</span>]; |
| <span class="kw">let </span><span class="kw-2">mut </span>permutation_array = <span class="macro">vec!</span>[<span class="number">0</span>, <span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>]; |
| permute_by_swap(<span class="kw-2">&mut </span>permutation_array, |i, j| x.swap(i, j)); |
| <span class="macro">assert_eq!</span>(x, <span class="macro">vec!</span>[<span class="string">'a'</span>, <span class="string">'b'</span>, <span class="string">'c'</span>, <span class="string">'d'</span>]); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>compose_into_buffer() { |
| <span class="kw">let </span>p = PermutationMatrix::<u32>::from_array(<span class="macro">vec!</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">0</span>]).unwrap(); |
| <span class="kw">let </span>q = PermutationMatrix::<u32>::from_array(<span class="macro">vec!</span>[<span class="number">1</span>, <span class="number">0</span>, <span class="number">2</span>]).unwrap(); |
| <span class="kw">let </span>pq_expected = PermutationMatrix::<u32>::from_array(<span class="macro">vec!</span>[<span class="number">1</span>, <span class="number">2</span>, <span class="number">0</span>]).unwrap(); |
| <span class="kw">let </span>qp_expected = PermutationMatrix::<u32>::from_array(<span class="macro">vec!</span>[<span class="number">2</span>, <span class="number">0</span>, <span class="number">1</span>]).unwrap(); |
| |
| { |
| <span class="kw">let </span><span class="kw-2">mut </span>pq = PermutationMatrix::identity(<span class="number">3</span>); |
| p.compose_into_buffer(<span class="kw-2">&</span>q, <span class="kw-2">&mut </span>pq); |
| <span class="macro">assert_eq!</span>(pq, pq_expected); |
| } |
| |
| { |
| <span class="kw">let </span><span class="kw-2">mut </span>qp = PermutationMatrix::identity(<span class="number">3</span>); |
| q.compose_into_buffer(<span class="kw-2">&</span>p, <span class="kw-2">&mut </span>qp); |
| <span class="macro">assert_eq!</span>(qp, qp_expected); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>compose_regression() { |
| <span class="comment">// At some point during development, this example failed to |
| // give the expected results |
| </span><span class="kw">let </span>p = PermutationMatrix::<u32>::from_array(<span class="macro">vec!</span>[<span class="number">1</span>, <span class="number">2</span>, <span class="number">0</span>]).unwrap(); |
| <span class="kw">let </span>q = PermutationMatrix::<u32>::from_array(<span class="macro">vec!</span>[<span class="number">2</span>, <span class="number">0</span>, <span class="number">1</span>]).unwrap(); |
| <span class="kw">let </span>pq_expected = PermutationMatrix::<u32>::from_array(<span class="macro">vec!</span>[<span class="number">0</span>, <span class="number">1</span>, <span class="number">2</span>]).unwrap(); |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>pq = PermutationMatrix::identity(<span class="number">3</span>); |
| p.compose_into_buffer(<span class="kw-2">&</span>q, <span class="kw-2">&mut </span>pq); |
| <span class="macro">assert_eq!</span>(pq, pq_expected); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>permute_rows_into_buffer() { |
| <span class="kw">let </span>x = <span class="macro">matrix!</span>[ <span class="number">0</span>; |
| <span class="number">1</span>; |
| <span class="number">2</span>; |
| <span class="number">3</span>]; |
| <span class="kw">let </span>p = PermutationMatrix::from_array(<span class="macro">vec!</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">3</span>, <span class="number">0</span>]).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>output = Matrix::zeros(<span class="number">4</span>, <span class="number">1</span>); |
| p.permute_rows_into_buffer(<span class="kw-2">&</span>x, <span class="kw-2">&mut </span>output); |
| <span class="macro">assert_matrix_eq!</span>(output, <span class="macro">matrix!</span>[ <span class="number">3</span>; <span class="number">1</span>; <span class="number">0</span>; <span class="number">2</span>]); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>permute_rows_in_place() { |
| <span class="kw">let </span><span class="kw-2">mut </span>x = <span class="macro">matrix!</span>[ <span class="number">0</span>; |
| <span class="number">1</span>; |
| <span class="number">2</span>; |
| <span class="number">3</span>]; |
| <span class="kw">let </span>p = PermutationMatrix::from_array(<span class="macro">vec!</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">3</span>, <span class="number">0</span>]).unwrap(); |
| p.permute_rows_in_place(<span class="kw-2">&mut </span>x); |
| <span class="macro">assert_matrix_eq!</span>(x, <span class="macro">matrix!</span>[ <span class="number">3</span>; <span class="number">1</span>; <span class="number">0</span>; <span class="number">2</span>]); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>permute_cols_into_buffer() { |
| <span class="kw">let </span>x = <span class="macro">matrix!</span>[ <span class="number">0</span>, <span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>]; |
| <span class="kw">let </span>p = PermutationMatrix::from_array(<span class="macro">vec!</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">3</span>, <span class="number">0</span>]).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>output = Matrix::zeros(<span class="number">1</span>, <span class="number">4</span>); |
| p.permute_cols_into_buffer(<span class="kw-2">&</span>x, <span class="kw-2">&mut </span>output); |
| <span class="macro">assert_matrix_eq!</span>(output, <span class="macro">matrix!</span>[ <span class="number">3</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">2</span>]); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>permute_cols_in_place() { |
| <span class="kw">let </span><span class="kw-2">mut </span>x = <span class="macro">matrix!</span>[ <span class="number">0</span>, <span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>]; |
| <span class="kw">let </span>p = PermutationMatrix::from_array(<span class="macro">vec!</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">3</span>, <span class="number">0</span>]).unwrap(); |
| p.permute_cols_in_place(<span class="kw-2">&mut </span>x); |
| <span class="macro">assert_matrix_eq!</span>(x, <span class="macro">matrix!</span>[ <span class="number">3</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">2</span>]); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>permute_vector_into_buffer() { |
| <span class="kw">let </span>x = <span class="macro">vector!</span>[ <span class="number">0</span>, <span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>]; |
| <span class="kw">let </span>p = PermutationMatrix::from_array(<span class="macro">vec!</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">3</span>, <span class="number">0</span>]).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>output = Vector::zeros(<span class="number">4</span>); |
| p.permute_vector_into_buffer(<span class="kw-2">&</span>x, <span class="kw-2">&mut </span>output); |
| <span class="macro">assert_vector_eq!</span>(output, <span class="macro">vector!</span>[ <span class="number">3</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">2</span>]); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>permute_vector_in_place() { |
| <span class="kw">let </span><span class="kw-2">mut </span>x = <span class="macro">vector!</span>[ <span class="number">0</span>, <span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>]; |
| <span class="kw">let </span>p = PermutationMatrix::from_array(<span class="macro">vec!</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">3</span>, <span class="number">0</span>]).unwrap(); |
| p.permute_vector_in_place(<span class="kw-2">&mut </span>x); |
| <span class="macro">assert_vector_eq!</span>(x, <span class="macro">vector!</span>[ <span class="number">3</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">2</span>]); |
| } |
| |
| <span class="kw">use </span>quickcheck::{Arbitrary, Gen}; |
| |
| <span class="comment">// In order to write property tests for the validation of a permutation, |
| // we need to be able to generate arbitrary (valid) permutations. |
| </span><span class="attribute">#[derive(Debug, Clone, PartialEq, Eq)] |
| </span><span class="kw">struct </span>ValidPermutationArray(<span class="kw">pub </span>Vec<usize>); |
| |
| <span class="kw">impl </span>Arbitrary <span class="kw">for </span>ValidPermutationArray { |
| <span class="kw">fn </span>arbitrary<G: Gen>(g: <span class="kw-2">&mut </span>G) -> <span class="self">Self </span>{ |
| <span class="kw">let </span>upper_bound = g.size(); |
| <span class="kw">let </span><span class="kw-2">mut </span>array = (<span class="number">0 </span>.. upper_bound).collect::<Vec<usize>>(); |
| g.shuffle(<span class="kw-2">&mut </span>array); |
| ValidPermutationArray(array) |
| } |
| } |
| |
| <span class="comment">// We also want to be able to generate invalid permutations for |
| // the same reasons |
| </span><span class="attribute">#[derive(Debug, Clone, PartialEq, Eq)] |
| </span><span class="kw">struct </span>InvalidPermutationArray(<span class="kw">pub </span>Vec<usize>); |
| |
| <span class="kw">impl </span>Arbitrary <span class="kw">for </span>InvalidPermutationArray { |
| <span class="kw">fn </span>arbitrary<G: Gen>(g: <span class="kw-2">&mut </span>G) -> <span class="self">Self </span>{ |
| <span class="comment">// Take an arbitrary valid permutation and mutate it so that |
| // it is invalid |
| </span><span class="kw">let </span><span class="kw-2">mut </span>permutation_array = ValidPermutationArray::arbitrary(g).<span class="number">0</span>; |
| <span class="kw">let </span>n = permutation_array.len(); |
| |
| <span class="comment">// There are two essential sources of invalidity: |
| // 1. Duplicate elements |
| // 2. Indices out of bounds |
| // We want to have either or both |
| |
| </span><span class="kw">let </span>should_have_duplicates = g.gen::<bool>(); |
| <span class="kw">let </span>should_have_out_of_bounds = !should_have_duplicates || g.gen::<bool>(); |
| <span class="macro">assert!</span>(should_have_duplicates || should_have_out_of_bounds); |
| |
| <span class="kw">if </span>should_have_out_of_bounds { |
| <span class="kw">let </span>num_out_of_bounds_rounds = g.gen_range::<usize>(<span class="number">1</span>, n); |
| <span class="kw">for _ in </span><span class="number">0 </span>.. num_out_of_bounds_rounds { |
| <span class="kw">let </span>interior_index = g.gen_range::<usize>(<span class="number">0</span>, n); |
| <span class="kw">let </span>exterior_index = n + g.gen::<usize>(); |
| permutation_array[interior_index] = exterior_index; |
| } |
| } |
| |
| <span class="kw">if </span>should_have_duplicates { |
| <span class="kw">let </span>num_duplicates = g.gen_range::<usize>(<span class="number">1</span>, n); |
| <span class="kw">for _ in </span><span class="number">0 </span>.. num_duplicates { |
| <span class="kw">let </span>interior_index = g.gen_range::<usize>(<span class="number">0</span>, n); |
| <span class="kw">let </span>duplicate_value = permutation_array[interior_index]; |
| permutation_array.push(duplicate_value); |
| } |
| } |
| |
| <span class="comment">// The duplicates are placed at the end, so we perform |
| // an additional shuffle to end up with a more or less |
| // arbitrary invalid permutation |
| </span>g.shuffle(<span class="kw-2">&mut </span>permutation_array); |
| InvalidPermutationArray(permutation_array) |
| } |
| } |
| |
| <span class="kw">impl</span><T: Send + Clone + <span class="lifetime">'static</span>> Arbitrary <span class="kw">for </span>PermutationMatrix<T> { |
| <span class="kw">fn </span>arbitrary<G: Gen>(g: <span class="kw-2">&mut </span>G) -> <span class="self">Self </span>{ |
| <span class="kw">let </span>ValidPermutationArray(array) = ValidPermutationArray::arbitrary(g); |
| PermutationMatrix::from_array(array) |
| .expect(<span class="string">"The generated permutation array should always be valid."</span>) |
| } |
| } |
| |
| <span class="macro">quickcheck! </span>{ |
| <span class="kw">fn </span>property_validate_permutation_is_ok_for_valid_input(array: ValidPermutationArray) -> bool { |
| validate_permutation(<span class="kw-2">&</span>array.<span class="number">0</span>).is_ok() |
| } |
| } |
| |
| <span class="macro">quickcheck! </span>{ |
| <span class="kw">fn </span>property_validate_permutation_is_err_for_invalid_input(array: InvalidPermutationArray) -> bool { |
| validate_permutation(<span class="kw-2">&</span>array.<span class="number">0</span>).is_err() |
| } |
| } |
| |
| <span class="macro">quickcheck! </span>{ |
| <span class="kw">fn </span>property_identity_has_identity_array(size: usize) -> bool { |
| <span class="kw">let </span>p = PermutationMatrix::<u64>::identity(size); |
| <span class="kw">let </span>p_as_array: Vec<usize> = p.into(); |
| <span class="kw">let </span>expected = (<span class="number">0 </span>.. size).collect::<Vec<usize>>(); |
| p_as_array == expected |
| } |
| } |
| |
| <span class="macro">quickcheck! </span>{ |
| <span class="kw">fn </span>property_dim_is_equal_to_array_dimensions(array: ValidPermutationArray) -> bool { |
| <span class="kw">let </span>ValidPermutationArray(array) = array; |
| <span class="kw">let </span>n = array.len(); |
| <span class="kw">let </span>p = PermutationMatrix::<u32>::from_array(array).unwrap(); |
| p.size() == n |
| } |
| } |
| |
| <span class="macro">quickcheck! </span>{ |
| <span class="kw">fn </span>property_inverse_of_inverse_is_original(p: PermutationMatrix<u32>) -> bool { |
| p == p.inverse().inverse() |
| } |
| } |
| |
| <span class="macro">quickcheck! </span>{ |
| <span class="kw">fn </span>property_inverse_composes_to_identity(p: PermutationMatrix<u32>) -> bool { |
| <span class="comment">// Recall that P * P_inv = I and P_inv * P = I |
| </span><span class="kw">let </span>n = p.size(); |
| <span class="kw">let </span>pinv = p.inverse(); |
| <span class="kw">let </span><span class="kw-2">mut </span>p_pinv_composition = PermutationMatrix::identity(n); |
| <span class="kw">let </span><span class="kw-2">mut </span>pinv_p_composition = PermutationMatrix::identity(n); |
| p.compose_into_buffer(<span class="kw-2">&</span>pinv, <span class="kw-2">&mut </span>p_pinv_composition); |
| pinv.compose_into_buffer(<span class="kw-2">&</span>p, <span class="kw-2">&mut </span>pinv_p_composition); |
| <span class="macro">assert_eq!</span>(p_pinv_composition, PermutationMatrix::identity(n)); |
| <span class="macro">assert_eq!</span>(pinv_p_composition, PermutationMatrix::identity(n)); |
| <span class="bool-val">true |
| </span>} |
| } |
| |
| <span class="macro">quickcheck! </span>{ |
| <span class="kw">fn </span>property_identity_parity_is_even(n: usize) -> bool { |
| <span class="kw">let </span>p = PermutationMatrix::<u32>::identity(n); |
| p.parity() == Parity::Even |
| } |
| } |
| |
| <span class="macro">quickcheck! </span>{ |
| <span class="kw">fn </span>property_parity_agrees_with_parity_of_inversions(p: PermutationMatrix<u32>) -> bool { |
| <span class="kw">let </span>array: <span class="kw-2">&</span>[usize] = (<span class="kw-2">&</span>p).into(); |
| <span class="kw">let </span>num_inversions = array.iter().cloned().enumerate() |
| .cartesian_product(array.iter().cloned().enumerate()) |
| .filter(|<span class="kw-2">&</span>((i, permuted_i), (j, permuted_j))| |
| <span class="comment">// This is simply the definition of an inversion |
| </span>i < j && permuted_i > permuted_j |
| ) |
| .count(); |
| <span class="comment">// Recall that the parity of the number of inversions in the |
| // permutation is equal to the parity of the permutation |
| </span><span class="kw">let </span>parity = <span class="kw">if </span>num_inversions % <span class="number">2 </span>== <span class="number">0 </span>{ |
| Parity::Even |
| } <span class="kw">else </span>{ |
| Parity::Odd |
| }; |
| |
| parity == p.clone().parity() |
| } |
| } |
| } |
| </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> |