| <!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/impl_mat.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>impl_mat.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> |
| <span id="2">2</span> |
| <span id="3">3</span> |
| <span id="4">4</span> |
| <span id="5">5</span> |
| <span id="6">6</span> |
| <span id="7">7</span> |
| <span id="8">8</span> |
| <span id="9">9</span> |
| <span id="10">10</span> |
| <span id="11">11</span> |
| <span id="12">12</span> |
| <span id="13">13</span> |
| <span id="14">14</span> |
| <span id="15">15</span> |
| <span id="16">16</span> |
| <span id="17">17</span> |
| <span id="18">18</span> |
| <span id="19">19</span> |
| <span id="20">20</span> |
| <span id="21">21</span> |
| <span id="22">22</span> |
| <span id="23">23</span> |
| <span id="24">24</span> |
| <span id="25">25</span> |
| <span id="26">26</span> |
| <span id="27">27</span> |
| <span id="28">28</span> |
| <span id="29">29</span> |
| <span id="30">30</span> |
| <span id="31">31</span> |
| <span id="32">32</span> |
| <span id="33">33</span> |
| <span id="34">34</span> |
| <span id="35">35</span> |
| <span id="36">36</span> |
| <span id="37">37</span> |
| <span id="38">38</span> |
| <span id="39">39</span> |
| <span id="40">40</span> |
| <span id="41">41</span> |
| <span id="42">42</span> |
| <span id="43">43</span> |
| <span id="44">44</span> |
| <span id="45">45</span> |
| <span id="46">46</span> |
| <span id="47">47</span> |
| <span id="48">48</span> |
| <span id="49">49</span> |
| <span id="50">50</span> |
| <span id="51">51</span> |
| <span id="52">52</span> |
| <span id="53">53</span> |
| <span id="54">54</span> |
| <span id="55">55</span> |
| <span id="56">56</span> |
| <span id="57">57</span> |
| <span id="58">58</span> |
| <span id="59">59</span> |
| <span id="60">60</span> |
| <span id="61">61</span> |
| <span id="62">62</span> |
| <span id="63">63</span> |
| <span id="64">64</span> |
| <span id="65">65</span> |
| <span id="66">66</span> |
| <span id="67">67</span> |
| <span id="68">68</span> |
| <span id="69">69</span> |
| <span id="70">70</span> |
| <span id="71">71</span> |
| <span id="72">72</span> |
| <span id="73">73</span> |
| <span id="74">74</span> |
| <span id="75">75</span> |
| <span id="76">76</span> |
| <span id="77">77</span> |
| <span id="78">78</span> |
| <span id="79">79</span> |
| <span id="80">80</span> |
| <span id="81">81</span> |
| <span id="82">82</span> |
| <span id="83">83</span> |
| <span id="84">84</span> |
| <span id="85">85</span> |
| <span id="86">86</span> |
| <span id="87">87</span> |
| <span id="88">88</span> |
| <span id="89">89</span> |
| <span id="90">90</span> |
| <span id="91">91</span> |
| <span id="92">92</span> |
| <span id="93">93</span> |
| <span id="94">94</span> |
| <span id="95">95</span> |
| <span id="96">96</span> |
| <span id="97">97</span> |
| <span id="98">98</span> |
| <span id="99">99</span> |
| <span id="100">100</span> |
| <span id="101">101</span> |
| <span id="102">102</span> |
| <span id="103">103</span> |
| <span id="104">104</span> |
| <span id="105">105</span> |
| <span id="106">106</span> |
| <span id="107">107</span> |
| <span id="108">108</span> |
| <span id="109">109</span> |
| <span id="110">110</span> |
| <span id="111">111</span> |
| <span id="112">112</span> |
| <span id="113">113</span> |
| <span id="114">114</span> |
| <span id="115">115</span> |
| <span id="116">116</span> |
| <span id="117">117</span> |
| <span id="118">118</span> |
| <span id="119">119</span> |
| <span id="120">120</span> |
| <span id="121">121</span> |
| <span id="122">122</span> |
| <span id="123">123</span> |
| <span id="124">124</span> |
| <span id="125">125</span> |
| <span id="126">126</span> |
| <span id="127">127</span> |
| <span id="128">128</span> |
| <span id="129">129</span> |
| <span id="130">130</span> |
| <span id="131">131</span> |
| <span id="132">132</span> |
| <span id="133">133</span> |
| <span id="134">134</span> |
| <span id="135">135</span> |
| <span id="136">136</span> |
| <span id="137">137</span> |
| <span id="138">138</span> |
| <span id="139">139</span> |
| <span id="140">140</span> |
| <span id="141">141</span> |
| <span id="142">142</span> |
| <span id="143">143</span> |
| <span id="144">144</span> |
| <span id="145">145</span> |
| <span id="146">146</span> |
| <span id="147">147</span> |
| <span id="148">148</span> |
| <span id="149">149</span> |
| <span id="150">150</span> |
| <span id="151">151</span> |
| <span id="152">152</span> |
| <span id="153">153</span> |
| <span id="154">154</span> |
| <span id="155">155</span> |
| <span id="156">156</span> |
| <span id="157">157</span> |
| <span id="158">158</span> |
| <span id="159">159</span> |
| <span id="160">160</span> |
| <span id="161">161</span> |
| <span id="162">162</span> |
| <span id="163">163</span> |
| <span id="164">164</span> |
| <span id="165">165</span> |
| <span id="166">166</span> |
| <span id="167">167</span> |
| <span id="168">168</span> |
| <span id="169">169</span> |
| <span id="170">170</span> |
| <span id="171">171</span> |
| <span id="172">172</span> |
| <span id="173">173</span> |
| <span id="174">174</span> |
| <span id="175">175</span> |
| <span id="176">176</span> |
| <span id="177">177</span> |
| <span id="178">178</span> |
| <span id="179">179</span> |
| <span id="180">180</span> |
| <span id="181">181</span> |
| <span id="182">182</span> |
| <span id="183">183</span> |
| <span id="184">184</span> |
| <span id="185">185</span> |
| <span id="186">186</span> |
| <span id="187">187</span> |
| <span id="188">188</span> |
| <span id="189">189</span> |
| <span id="190">190</span> |
| <span id="191">191</span> |
| <span id="192">192</span> |
| <span id="193">193</span> |
| <span id="194">194</span> |
| <span id="195">195</span> |
| <span id="196">196</span> |
| <span id="197">197</span> |
| <span id="198">198</span> |
| <span id="199">199</span> |
| <span id="200">200</span> |
| <span id="201">201</span> |
| <span id="202">202</span> |
| <span id="203">203</span> |
| <span id="204">204</span> |
| <span id="205">205</span> |
| <span id="206">206</span> |
| <span id="207">207</span> |
| <span id="208">208</span> |
| <span id="209">209</span> |
| <span id="210">210</span> |
| <span id="211">211</span> |
| <span id="212">212</span> |
| <span id="213">213</span> |
| <span id="214">214</span> |
| <span id="215">215</span> |
| <span id="216">216</span> |
| <span id="217">217</span> |
| <span id="218">218</span> |
| <span id="219">219</span> |
| <span id="220">220</span> |
| <span id="221">221</span> |
| <span id="222">222</span> |
| <span id="223">223</span> |
| <span id="224">224</span> |
| <span id="225">225</span> |
| <span id="226">226</span> |
| <span id="227">227</span> |
| <span id="228">228</span> |
| <span id="229">229</span> |
| <span id="230">230</span> |
| <span id="231">231</span> |
| <span id="232">232</span> |
| <span id="233">233</span> |
| <span id="234">234</span> |
| <span id="235">235</span> |
| <span id="236">236</span> |
| <span id="237">237</span> |
| <span id="238">238</span> |
| <span id="239">239</span> |
| <span id="240">240</span> |
| <span id="241">241</span> |
| <span id="242">242</span> |
| <span id="243">243</span> |
| <span id="244">244</span> |
| <span id="245">245</span> |
| <span id="246">246</span> |
| <span id="247">247</span> |
| <span id="248">248</span> |
| <span id="249">249</span> |
| <span id="250">250</span> |
| <span id="251">251</span> |
| <span id="252">252</span> |
| <span id="253">253</span> |
| <span id="254">254</span> |
| <span id="255">255</span> |
| <span id="256">256</span> |
| <span id="257">257</span> |
| <span id="258">258</span> |
| <span id="259">259</span> |
| <span id="260">260</span> |
| <span id="261">261</span> |
| <span id="262">262</span> |
| <span id="263">263</span> |
| <span id="264">264</span> |
| <span id="265">265</span> |
| <span id="266">266</span> |
| <span id="267">267</span> |
| <span id="268">268</span> |
| <span id="269">269</span> |
| <span id="270">270</span> |
| <span id="271">271</span> |
| <span id="272">272</span> |
| <span id="273">273</span> |
| <span id="274">274</span> |
| <span id="275">275</span> |
| <span id="276">276</span> |
| <span id="277">277</span> |
| <span id="278">278</span> |
| <span id="279">279</span> |
| <span id="280">280</span> |
| <span id="281">281</span> |
| <span id="282">282</span> |
| <span id="283">283</span> |
| <span id="284">284</span> |
| <span id="285">285</span> |
| <span id="286">286</span> |
| <span id="287">287</span> |
| <span id="288">288</span> |
| <span id="289">289</span> |
| <span id="290">290</span> |
| <span id="291">291</span> |
| <span id="292">292</span> |
| <span id="293">293</span> |
| <span id="294">294</span> |
| <span id="295">295</span> |
| <span id="296">296</span> |
| <span id="297">297</span> |
| <span id="298">298</span> |
| <span id="299">299</span> |
| <span id="300">300</span> |
| <span id="301">301</span> |
| <span id="302">302</span> |
| <span id="303">303</span> |
| <span id="304">304</span> |
| <span id="305">305</span> |
| <span id="306">306</span> |
| <span id="307">307</span> |
| <span id="308">308</span> |
| <span id="309">309</span> |
| <span id="310">310</span> |
| <span id="311">311</span> |
| <span id="312">312</span> |
| <span id="313">313</span> |
| <span id="314">314</span> |
| <span id="315">315</span> |
| <span id="316">316</span> |
| <span id="317">317</span> |
| <span id="318">318</span> |
| <span id="319">319</span> |
| <span id="320">320</span> |
| <span id="321">321</span> |
| <span id="322">322</span> |
| <span id="323">323</span> |
| <span id="324">324</span> |
| <span id="325">325</span> |
| <span id="326">326</span> |
| <span id="327">327</span> |
| <span id="328">328</span> |
| <span id="329">329</span> |
| <span id="330">330</span> |
| <span id="331">331</span> |
| <span id="332">332</span> |
| <span id="333">333</span> |
| <span id="334">334</span> |
| <span id="335">335</span> |
| <span id="336">336</span> |
| <span id="337">337</span> |
| <span id="338">338</span> |
| <span id="339">339</span> |
| <span id="340">340</span> |
| <span id="341">341</span> |
| <span id="342">342</span> |
| <span id="343">343</span> |
| <span id="344">344</span> |
| <span id="345">345</span> |
| <span id="346">346</span> |
| <span id="347">347</span> |
| <span id="348">348</span> |
| <span id="349">349</span> |
| <span id="350">350</span> |
| <span id="351">351</span> |
| <span id="352">352</span> |
| <span id="353">353</span> |
| <span id="354">354</span> |
| <span id="355">355</span> |
| <span id="356">356</span> |
| <span id="357">357</span> |
| <span id="358">358</span> |
| <span id="359">359</span> |
| <span id="360">360</span> |
| <span id="361">361</span> |
| <span id="362">362</span> |
| <span id="363">363</span> |
| <span id="364">364</span> |
| <span id="365">365</span> |
| <span id="366">366</span> |
| <span id="367">367</span> |
| <span id="368">368</span> |
| <span id="369">369</span> |
| <span id="370">370</span> |
| <span id="371">371</span> |
| <span id="372">372</span> |
| <span id="373">373</span> |
| <span id="374">374</span> |
| <span id="375">375</span> |
| <span id="376">376</span> |
| <span id="377">377</span> |
| <span id="378">378</span> |
| <span id="379">379</span> |
| <span id="380">380</span> |
| <span id="381">381</span> |
| <span id="382">382</span> |
| <span id="383">383</span> |
| <span id="384">384</span> |
| <span id="385">385</span> |
| <span id="386">386</span> |
| <span id="387">387</span> |
| <span id="388">388</span> |
| <span id="389">389</span> |
| <span id="390">390</span> |
| <span id="391">391</span> |
| <span id="392">392</span> |
| <span id="393">393</span> |
| <span id="394">394</span> |
| <span id="395">395</span> |
| <span id="396">396</span> |
| <span id="397">397</span> |
| <span id="398">398</span> |
| <span id="399">399</span> |
| <span id="400">400</span> |
| <span id="401">401</span> |
| <span id="402">402</span> |
| <span id="403">403</span> |
| <span id="404">404</span> |
| <span id="405">405</span> |
| <span id="406">406</span> |
| <span id="407">407</span> |
| <span id="408">408</span> |
| <span id="409">409</span> |
| <span id="410">410</span> |
| <span id="411">411</span> |
| <span id="412">412</span> |
| <span id="413">413</span> |
| <span id="414">414</span> |
| <span id="415">415</span> |
| <span id="416">416</span> |
| <span id="417">417</span> |
| <span id="418">418</span> |
| <span id="419">419</span> |
| <span id="420">420</span> |
| <span id="421">421</span> |
| <span id="422">422</span> |
| <span id="423">423</span> |
| <span id="424">424</span> |
| <span id="425">425</span> |
| <span id="426">426</span> |
| <span id="427">427</span> |
| <span id="428">428</span> |
| <span id="429">429</span> |
| <span id="430">430</span> |
| <span id="431">431</span> |
| <span id="432">432</span> |
| <span id="433">433</span> |
| <span id="434">434</span> |
| <span id="435">435</span> |
| <span id="436">436</span> |
| <span id="437">437</span> |
| <span id="438">438</span> |
| <span id="439">439</span> |
| <span id="440">440</span> |
| <span id="441">441</span> |
| <span id="442">442</span> |
| <span id="443">443</span> |
| <span id="444">444</span> |
| <span id="445">445</span> |
| <span id="446">446</span> |
| <span id="447">447</span> |
| <span id="448">448</span> |
| <span id="449">449</span> |
| <span id="450">450</span> |
| <span id="451">451</span> |
| <span id="452">452</span> |
| <span id="453">453</span> |
| <span id="454">454</span> |
| <span id="455">455</span> |
| <span id="456">456</span> |
| <span id="457">457</span> |
| <span id="458">458</span> |
| <span id="459">459</span> |
| <span id="460">460</span> |
| <span id="461">461</span> |
| <span id="462">462</span> |
| <span id="463">463</span> |
| <span id="464">464</span> |
| <span id="465">465</span> |
| <span id="466">466</span> |
| <span id="467">467</span> |
| <span id="468">468</span> |
| <span id="469">469</span> |
| <span id="470">470</span> |
| <span id="471">471</span> |
| <span id="472">472</span> |
| <span id="473">473</span> |
| <span id="474">474</span> |
| <span id="475">475</span> |
| <span id="476">476</span> |
| <span id="477">477</span> |
| <span id="478">478</span> |
| <span id="479">479</span> |
| <span id="480">480</span> |
| <span id="481">481</span> |
| <span id="482">482</span> |
| <span id="483">483</span> |
| <span id="484">484</span> |
| <span id="485">485</span> |
| <span id="486">486</span> |
| <span id="487">487</span> |
| <span id="488">488</span> |
| <span id="489">489</span> |
| <span id="490">490</span> |
| <span id="491">491</span> |
| <span id="492">492</span> |
| <span id="493">493</span> |
| <span id="494">494</span> |
| <span id="495">495</span> |
| <span id="496">496</span> |
| <span id="497">497</span> |
| <span id="498">498</span> |
| <span id="499">499</span> |
| <span id="500">500</span> |
| <span id="501">501</span> |
| <span id="502">502</span> |
| <span id="503">503</span> |
| <span id="504">504</span> |
| <span id="505">505</span> |
| <span id="506">506</span> |
| <span id="507">507</span> |
| <span id="508">508</span> |
| <span id="509">509</span> |
| <span id="510">510</span> |
| <span id="511">511</span> |
| <span id="512">512</span> |
| <span id="513">513</span> |
| <span id="514">514</span> |
| <span id="515">515</span> |
| <span id="516">516</span> |
| <span id="517">517</span> |
| <span id="518">518</span> |
| <span id="519">519</span> |
| <span id="520">520</span> |
| <span id="521">521</span> |
| <span id="522">522</span> |
| <span id="523">523</span> |
| <span id="524">524</span> |
| <span id="525">525</span> |
| <span id="526">526</span> |
| <span id="527">527</span> |
| <span id="528">528</span> |
| <span id="529">529</span> |
| <span id="530">530</span> |
| <span id="531">531</span> |
| <span id="532">532</span> |
| <span id="533">533</span> |
| <span id="534">534</span> |
| <span id="535">535</span> |
| <span id="536">536</span> |
| <span id="537">537</span> |
| <span id="538">538</span> |
| <span id="539">539</span> |
| <span id="540">540</span> |
| <span id="541">541</span> |
| <span id="542">542</span> |
| <span id="543">543</span> |
| <span id="544">544</span> |
| <span id="545">545</span> |
| <span id="546">546</span> |
| <span id="547">547</span> |
| <span id="548">548</span> |
| <span id="549">549</span> |
| <span id="550">550</span> |
| <span id="551">551</span> |
| <span id="552">552</span> |
| <span id="553">553</span> |
| <span id="554">554</span> |
| <span id="555">555</span> |
| <span id="556">556</span> |
| <span id="557">557</span> |
| <span id="558">558</span> |
| <span id="559">559</span> |
| <span id="560">560</span> |
| <span id="561">561</span> |
| <span id="562">562</span> |
| <span id="563">563</span> |
| <span id="564">564</span> |
| <span id="565">565</span> |
| <span id="566">566</span> |
| <span id="567">567</span> |
| <span id="568">568</span> |
| <span id="569">569</span> |
| <span id="570">570</span> |
| <span id="571">571</span> |
| <span id="572">572</span> |
| <span id="573">573</span> |
| <span id="574">574</span> |
| <span id="575">575</span> |
| <span id="576">576</span> |
| <span id="577">577</span> |
| <span id="578">578</span> |
| <span id="579">579</span> |
| <span id="580">580</span> |
| <span id="581">581</span> |
| <span id="582">582</span> |
| <span id="583">583</span> |
| <span id="584">584</span> |
| <span id="585">585</span> |
| <span id="586">586</span> |
| <span id="587">587</span> |
| <span id="588">588</span> |
| <span id="589">589</span> |
| <span id="590">590</span> |
| <span id="591">591</span> |
| <span id="592">592</span> |
| <span id="593">593</span> |
| <span id="594">594</span> |
| <span id="595">595</span> |
| <span id="596">596</span> |
| <span id="597">597</span> |
| <span id="598">598</span> |
| <span id="599">599</span> |
| <span id="600">600</span> |
| <span id="601">601</span> |
| <span id="602">602</span> |
| <span id="603">603</span> |
| <span id="604">604</span> |
| <span id="605">605</span> |
| <span id="606">606</span> |
| <span id="607">607</span> |
| <span id="608">608</span> |
| <span id="609">609</span> |
| <span id="610">610</span> |
| <span id="611">611</span> |
| <span id="612">612</span> |
| <span id="613">613</span> |
| <span id="614">614</span> |
| <span id="615">615</span> |
| <span id="616">616</span> |
| <span id="617">617</span> |
| <span id="618">618</span> |
| <span id="619">619</span> |
| <span id="620">620</span> |
| <span id="621">621</span> |
| <span id="622">622</span> |
| <span id="623">623</span> |
| <span id="624">624</span> |
| <span id="625">625</span> |
| <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> |
| <span id="631">631</span> |
| <span id="632">632</span> |
| <span id="633">633</span> |
| <span id="634">634</span> |
| <span id="635">635</span> |
| <span id="636">636</span> |
| <span id="637">637</span> |
| <span id="638">638</span> |
| <span id="639">639</span> |
| <span id="640">640</span> |
| <span id="641">641</span> |
| <span id="642">642</span> |
| <span id="643">643</span> |
| <span id="644">644</span> |
| <span id="645">645</span> |
| <span id="646">646</span> |
| <span id="647">647</span> |
| <span id="648">648</span> |
| <span id="649">649</span> |
| <span id="650">650</span> |
| <span id="651">651</span> |
| <span id="652">652</span> |
| <span id="653">653</span> |
| <span id="654">654</span> |
| <span id="655">655</span> |
| <span id="656">656</span> |
| <span id="657">657</span> |
| <span id="658">658</span> |
| <span id="659">659</span> |
| <span id="660">660</span> |
| <span id="661">661</span> |
| <span id="662">662</span> |
| <span id="663">663</span> |
| <span id="664">664</span> |
| <span id="665">665</span> |
| <span id="666">666</span> |
| <span id="667">667</span> |
| <span id="668">668</span> |
| <span id="669">669</span> |
| <span id="670">670</span> |
| <span id="671">671</span> |
| <span id="672">672</span> |
| <span id="673">673</span> |
| <span id="674">674</span> |
| <span id="675">675</span> |
| <span id="676">676</span> |
| <span id="677">677</span> |
| <span id="678">678</span> |
| <span id="679">679</span> |
| <span id="680">680</span> |
| <span id="681">681</span> |
| <span id="682">682</span> |
| <span id="683">683</span> |
| <span id="684">684</span> |
| <span id="685">685</span> |
| <span id="686">686</span> |
| <span id="687">687</span> |
| <span id="688">688</span> |
| <span id="689">689</span> |
| <span id="690">690</span> |
| <span id="691">691</span> |
| <span id="692">692</span> |
| <span id="693">693</span> |
| <span id="694">694</span> |
| <span id="695">695</span> |
| <span id="696">696</span> |
| <span id="697">697</span> |
| <span id="698">698</span> |
| <span id="699">699</span> |
| <span id="700">700</span> |
| <span id="701">701</span> |
| <span id="702">702</span> |
| <span id="703">703</span> |
| <span id="704">704</span> |
| <span id="705">705</span> |
| <span id="706">706</span> |
| <span id="707">707</span> |
| <span id="708">708</span> |
| <span id="709">709</span> |
| <span id="710">710</span> |
| <span id="711">711</span> |
| <span id="712">712</span> |
| <span id="713">713</span> |
| <span id="714">714</span> |
| <span id="715">715</span> |
| <span id="716">716</span> |
| <span id="717">717</span> |
| <span id="718">718</span> |
| <span id="719">719</span> |
| <span id="720">720</span> |
| <span id="721">721</span> |
| <span id="722">722</span> |
| <span id="723">723</span> |
| <span id="724">724</span> |
| <span id="725">725</span> |
| <span id="726">726</span> |
| <span id="727">727</span> |
| <span id="728">728</span> |
| <span id="729">729</span> |
| <span id="730">730</span> |
| <span id="731">731</span> |
| <span id="732">732</span> |
| <span id="733">733</span> |
| <span id="734">734</span> |
| <span id="735">735</span> |
| <span id="736">736</span> |
| <span id="737">737</span> |
| <span id="738">738</span> |
| <span id="739">739</span> |
| <span id="740">740</span> |
| <span id="741">741</span> |
| <span id="742">742</span> |
| <span id="743">743</span> |
| <span id="744">744</span> |
| <span id="745">745</span> |
| <span id="746">746</span> |
| <span id="747">747</span> |
| <span id="748">748</span> |
| <span id="749">749</span> |
| <span id="750">750</span> |
| <span id="751">751</span> |
| <span id="752">752</span> |
| <span id="753">753</span> |
| <span id="754">754</span> |
| <span id="755">755</span> |
| <span id="756">756</span> |
| <span id="757">757</span> |
| <span id="758">758</span> |
| <span id="759">759</span> |
| <span id="760">760</span> |
| <span id="761">761</span> |
| <span id="762">762</span> |
| <span id="763">763</span> |
| <span id="764">764</span> |
| <span id="765">765</span> |
| <span id="766">766</span> |
| <span id="767">767</span> |
| <span id="768">768</span> |
| <span id="769">769</span> |
| <span id="770">770</span> |
| <span id="771">771</span> |
| <span id="772">772</span> |
| <span id="773">773</span> |
| <span id="774">774</span> |
| <span id="775">775</span> |
| <span id="776">776</span> |
| <span id="777">777</span> |
| <span id="778">778</span> |
| <span id="779">779</span> |
| <span id="780">780</span> |
| <span id="781">781</span> |
| <span id="782">782</span> |
| <span id="783">783</span> |
| </pre><pre class="rust"><code><span class="kw">use </span>std::any::Any; |
| <span class="kw">use </span>std::fmt; |
| <span class="kw">use </span>libnum::{One, Zero, Float, FromPrimitive}; |
| |
| <span class="kw">use super</span>::{Matrix}; |
| <span class="kw">use super</span>::{Axes}; |
| <span class="kw">use </span><span class="kw">super</span>::base::BaseMatrix; |
| <span class="kw">use </span>error::{Error, ErrorKind}; |
| <span class="kw">use </span>vector::Vector; |
| <span class="kw">use </span>matrix::decomposition::PartialPivLu; |
| |
| <span class="kw">impl</span><T> Matrix<T> { |
| <span class="doccomment">/// Constructor for Matrix struct. |
| /// |
| /// Requires both the row and column dimensions. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use rulinalg::matrix::{Matrix, BaseMatrix}; |
| /// |
| /// let mat = Matrix::new(2,2, vec![1.0, 2.0, 3.0, 4.0]); |
| /// |
| /// assert_eq!(mat.rows(), 2); |
| /// assert_eq!(mat.cols(), 2); |
| /// ``` |
| /// |
| /// # Panics |
| /// |
| /// - The input data does not match the given dimensions. |
| </span><span class="kw">pub fn </span>new<U: Into<Vec<T>>>(rows: usize, cols: usize, data: U) -> Matrix<T> { |
| <span class="kw">let </span>our_data = data.into(); |
| |
| <span class="macro">assert!</span>(cols * rows == our_data.len(), |
| <span class="string">"Data does not match given dimensions."</span>); |
| Matrix { |
| cols: cols, |
| rows: rows, |
| data: our_data, |
| } |
| } |
| |
| <span class="doccomment">/// Constructor for Matrix struct that takes a function `f` |
| /// and constructs a new matrix such that `A_ij = f(j, i)`, |
| /// where `i` is the row index and `j` the column index. |
| /// |
| /// Requires both the row and column dimensions |
| /// as well as a generating function. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use rulinalg::matrix::{Matrix, BaseMatrix}; |
| /// |
| /// // Let's assume you have an array of "things" for |
| /// // which you want to generate a distance matrix: |
| /// let things: [i32; 3] = [1, 2, 3]; |
| /// let distances: Matrix<f64> = Matrix::from_fn(things.len(), things.len(), |col, row| { |
| /// (things[col] - things[row]).abs().into() |
| /// }); |
| /// |
| /// assert_eq!(distances.rows(), 3); |
| /// assert_eq!(distances.cols(), 3); |
| /// assert_eq!(distances.data(), &vec![ |
| /// 0.0, 1.0, 2.0, |
| /// 1.0, 0.0, 1.0, |
| /// 2.0, 1.0, 0.0, |
| /// ]); |
| /// ``` |
| /// # Warning |
| /// |
| /// _This function will be changed in a future release so that `A_ij = f(i, j)` - to be consistent |
| /// with the rest of the library._ |
| </span><span class="kw">pub fn </span>from_fn<F>(rows: usize, cols: usize, <span class="kw-2">mut </span>f: F) -> Matrix<T> |
| <span class="kw">where </span>F: FnMut(usize, usize) -> T |
| { |
| <span class="kw">let </span><span class="kw-2">mut </span>data = Vec::with_capacity(rows * cols); |
| <span class="kw">for </span>row <span class="kw">in </span><span class="number">0</span>..rows { |
| <span class="kw">for </span>col <span class="kw">in </span><span class="number">0</span>..cols { |
| data.push(f(col, row)); |
| } |
| } |
| Matrix::new(rows, cols, data) |
| } |
| |
| <span class="doccomment">/// Returns a non-mutable reference to the underlying data. |
| </span><span class="kw">pub fn </span>data(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="kw-2">&</span>Vec<T> { |
| <span class="kw-2">&</span><span class="self">self</span>.data |
| } |
| |
| <span class="doccomment">/// Returns a mutable slice of the underlying data. |
| </span><span class="kw">pub fn </span>mut_data(<span class="kw-2">&mut </span><span class="self">self</span>) -> <span class="kw-2">&mut </span>[T] { |
| <span class="kw-2">&mut </span><span class="self">self</span>.data |
| } |
| |
| <span class="doccomment">/// Consumes the Matrix and returns the Vec of data. |
| </span><span class="kw">pub fn </span>into_vec(<span class="self">self</span>) -> Vec<T> { |
| <span class="self">self</span>.data |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + Zero> Matrix<T> { |
| <span class="doccomment">/// Constructs matrix of all zeros. |
| /// |
| /// Requires both the row and the column dimensions. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use rulinalg::matrix::Matrix; |
| /// |
| /// let mat = Matrix::<f64>::zeros(2,3); |
| /// ``` |
| </span><span class="kw">pub fn </span>zeros(rows: usize, cols: usize) -> Matrix<T> { |
| Matrix { |
| cols: cols, |
| rows: rows, |
| data: <span class="macro">vec!</span>[T::zero(); cols<span class="kw-2">*</span>rows], |
| } |
| } |
| |
| <span class="doccomment">/// Constructs matrix with given diagonal. |
| /// |
| /// Requires slice of diagonal elements. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use rulinalg::matrix::Matrix; |
| /// |
| /// let mat = Matrix::from_diag(&vec![1.0,2.0,3.0,4.0]); |
| /// ``` |
| </span><span class="kw">pub fn </span>from_diag(diag: <span class="kw-2">&</span>[T]) -> Matrix<T> { |
| <span class="kw">let </span>size = diag.len(); |
| <span class="kw">let </span><span class="kw-2">mut </span>data = <span class="macro">vec!</span>[T::zero(); size * size]; |
| |
| <span class="kw">for </span>(i, item) <span class="kw">in </span>diag.into_iter().enumerate().take(size) { |
| data[i * (size + <span class="number">1</span>)] = item.clone(); |
| } |
| |
| Matrix { |
| cols: size, |
| rows: size, |
| data: data, |
| } |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + One> Matrix<T> { |
| <span class="doccomment">/// Constructs matrix of all ones. |
| /// |
| /// Requires both the row and the column dimensions. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use rulinalg::matrix::Matrix; |
| /// |
| /// let mat = Matrix::<f64>::ones(2,3); |
| /// ``` |
| </span><span class="kw">pub fn </span>ones(rows: usize, cols: usize) -> Matrix<T> { |
| Matrix { |
| cols: cols, |
| rows: rows, |
| data: <span class="macro">vec!</span>[T::one(); cols<span class="kw-2">*</span>rows], |
| } |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + Zero + One> Matrix<T> { |
| <span class="doccomment">/// Constructs the identity matrix. |
| /// |
| /// Requires the size of the matrix. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use rulinalg::matrix::Matrix; |
| /// |
| /// let I = Matrix::<f64>::identity(4); |
| /// ``` |
| </span><span class="kw">pub fn </span>identity(size: usize) -> Matrix<T> { |
| <span class="kw">let </span><span class="kw-2">mut </span>data = <span class="macro">vec!</span>[T::zero(); size * size]; |
| |
| <span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..size { |
| data[(i * (size + <span class="number">1</span>)) <span class="kw">as </span>usize] = T::one(); |
| } |
| |
| Matrix { |
| cols: size, |
| rows: size, |
| data: data, |
| } |
| } |
| } |
| |
| <span class="kw">impl</span><T: Float + FromPrimitive> Matrix<T> { |
| <span class="doccomment">/// The mean of the matrix along the specified axis. |
| /// |
| /// - Axis Row - Arithmetic mean of rows. |
| /// - Axis Col - Arithmetic mean of columns. |
| /// |
| /// Calling `mean()` on an empty matrix will return an empty matrix. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// # #[macro_use] extern crate rulinalg; fn main() { |
| /// use rulinalg::matrix::{Matrix, Axes}; |
| /// |
| /// let a = matrix![1.0, 2.0; |
| /// 3.0, 4.0]; |
| /// |
| /// let c = a.mean(Axes::Row); |
| /// assert_eq!(c, vector![2.0, 3.0]); |
| /// |
| /// let d = a.mean(Axes::Col); |
| /// assert_eq!(d, vector![1.5, 3.5]); |
| /// # } |
| /// ``` |
| </span><span class="kw">pub fn </span>mean(<span class="kw-2">&</span><span class="self">self</span>, axis: Axes) -> Vector<T> { |
| <span class="kw">if </span><span class="self">self</span>.data.len() == <span class="number">0 </span>{ |
| <span class="comment">// If the matrix is empty, there are no means to calculate. |
| </span><span class="kw">return </span>Vector::new(<span class="macro">vec!</span>[]); |
| } |
| |
| <span class="kw">let </span>m: Vector<T>; |
| <span class="kw">let </span>n: T; |
| <span class="kw">match </span>axis { |
| Axes::Row => { |
| m = <span class="self">self</span>.sum_rows(); |
| n = FromPrimitive::from_usize(<span class="self">self</span>.rows).unwrap(); |
| } |
| Axes::Col => { |
| m = <span class="self">self</span>.sum_cols(); |
| n = FromPrimitive::from_usize(<span class="self">self</span>.cols).unwrap(); |
| } |
| } |
| m / n |
| } |
| |
| <span class="doccomment">/// The variance of the matrix along the specified axis. |
| /// |
| /// - Axis Row - Sample variance of rows. |
| /// - Axis Col - Sample variance of columns. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// # #[macro_use] extern crate rulinalg; fn main() { |
| /// use rulinalg::matrix::{Matrix, Axes}; |
| /// |
| /// let a = matrix![1.0, 2.0; |
| /// 3.0, 4.0]; |
| /// |
| /// let c = a.variance(Axes::Row).unwrap(); |
| /// assert_eq!(c, vector![2.0, 2.0]); |
| /// |
| /// let d = a.variance(Axes::Col).unwrap(); |
| /// assert_eq!(d, vector![0.5, 0.5]); |
| /// # } |
| /// ``` |
| /// |
| /// # Failures |
| /// |
| /// - There are one or fewer row/columns in the working axis. |
| </span><span class="kw">pub fn </span>variance(<span class="kw-2">&</span><span class="self">self</span>, axis: Axes) -> <span class="prelude-ty">Result</span><Vector<T>, Error> { |
| <span class="kw">let </span>mean = <span class="self">self</span>.mean(axis); |
| |
| <span class="kw">let </span>n: usize; |
| <span class="kw">let </span>m: usize; |
| |
| <span class="kw">match </span>axis { |
| Axes::Row => { |
| n = <span class="self">self</span>.rows; |
| m = <span class="self">self</span>.cols; |
| } |
| Axes::Col => { |
| n = <span class="self">self</span>.cols; |
| m = <span class="self">self</span>.rows; |
| } |
| } |
| |
| <span class="kw">if </span>n < <span class="number">2 </span>{ |
| <span class="kw">return </span><span class="prelude-val">Err</span>(Error::new(ErrorKind::InvalidArg, |
| <span class="string">"There must be at least two rows or columns in the working \ |
| axis."</span>)); |
| } |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>variance = Vector::zeros(m); |
| |
| <span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..n { |
| <span class="kw">let </span><span class="kw-2">mut </span>t = Vec::<T>::with_capacity(m); |
| |
| <span class="kw">unsafe </span>{ |
| t.set_len(m); |
| |
| <span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..m { |
| t[j] = <span class="kw">match </span>axis { |
| Axes::Row => <span class="kw-2">*</span><span class="self">self</span>.data.get_unchecked(i * m + j), |
| Axes::Col => <span class="kw-2">*</span><span class="self">self</span>.data.get_unchecked(j * n + i), |
| } |
| |
| } |
| } |
| |
| <span class="kw">let </span>diff = Vector::new(t) - <span class="kw-2">&</span>mean; |
| |
| variance = variance + diff.elemul(<span class="kw-2">&</span>diff); |
| } |
| |
| <span class="kw">let </span>var_size: T = FromPrimitive::from_usize(n - <span class="number">1</span>).unwrap(); |
| <span class="prelude-val">Ok</span>(variance / var_size) |
| } |
| } |
| |
| <span class="kw">impl</span><T: Any + Float> Matrix<T> { |
| <span class="doccomment">/// Solves the equation `Ax = y`. |
| /// |
| /// Requires a Vector `y` as input. |
| /// |
| /// The method performs an LU decomposition internally, |
| /// consuming the matrix in the process. If solving |
| /// the same system for multiple right-hand sides |
| /// is desired, see |
| /// [PartialPivLu](decomposition/struct.PartialPivLu.html). |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// # #[macro_use] extern crate rulinalg; fn main() { |
| /// use rulinalg::matrix::Matrix; |
| /// use rulinalg::vector::Vector; |
| /// |
| /// let a = matrix![2.0, 3.0; |
| /// 1.0, 2.0]; |
| /// let y = vector![13.0, 8.0]; |
| /// |
| /// let x = a.solve(y).unwrap(); |
| /// |
| /// assert_eq!(x, vector![2.0, 3.0]); |
| /// # } |
| /// ``` |
| /// |
| /// # Panics |
| /// |
| /// - The matrix column count and vector size are different. |
| /// - The matrix is not square. |
| /// |
| /// # Failures |
| /// |
| /// - The matrix cannot be decomposed into an LUP form to solve. |
| /// - There is no valid solution as the matrix is singular. |
| </span><span class="kw">pub fn </span>solve(<span class="self">self</span>, y: Vector<T>) -> <span class="prelude-ty">Result</span><Vector<T>, Error> { |
| PartialPivLu::decompose(<span class="self">self</span>)<span class="question-mark">?</span>.solve(y) |
| } |
| |
| <span class="doccomment">/// Computes the inverse of the matrix. |
| /// |
| /// Internally performs an LU decomposition. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// # #[macro_use] extern crate rulinalg; fn main() { |
| /// use rulinalg::matrix::Matrix; |
| /// |
| /// let a = matrix![2., 3.; |
| /// 1., 2.]; |
| /// let inv = a.clone().inverse().expect("This matrix should have an inverse!"); |
| /// |
| /// let I = a * inv; |
| /// |
| /// assert_matrix_eq!(I, matrix![1.0, 0.0; 0.0, 1.0]); |
| /// # } |
| /// ``` |
| /// |
| /// # Panics |
| /// |
| /// - The matrix is not square. |
| /// |
| /// # Failures |
| /// |
| /// - The matrix could not be LUP decomposed. |
| /// - The matrix has zero determinant. |
| </span><span class="kw">pub fn </span>inverse(<span class="self">self</span>) -> <span class="prelude-ty">Result</span><Matrix<T>, Error> { |
| PartialPivLu::decompose(<span class="self">self</span>)<span class="question-mark">?</span>.inverse() |
| } |
| |
| <span class="doccomment">/// Computes the determinant of the matrix. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// # #[macro_use] extern crate rulinalg; fn main() { |
| /// let a = matrix![1.0, 2.0, 0.0; |
| /// 0.0, 3.0, 4.0; |
| /// 5.0, 1.0, 2.0]; |
| /// |
| /// let det = a.det(); |
| /// # } |
| /// ``` |
| /// |
| /// # Panics |
| /// |
| /// - The matrix is not square. |
| </span><span class="kw">pub fn </span>det(<span class="self">self</span>) -> T { |
| <span class="macro">assert!</span>(<span class="self">self</span>.rows == <span class="self">self</span>.cols, <span class="string">"Matrix is not square."</span>); |
| |
| <span class="kw">let </span>n = <span class="self">self</span>.cols; |
| |
| <span class="kw">if </span><span class="self">self</span>.is_diag() { |
| <span class="self">self</span>.diag().cloned().fold(T::one(), |d, entry| d * entry) |
| } <span class="kw">else if </span>n == <span class="number">2 </span>{ |
| (<span class="self">self</span>[[<span class="number">0</span>, <span class="number">0</span>]] * <span class="self">self</span>[[<span class="number">1</span>, <span class="number">1</span>]]) - (<span class="self">self</span>[[<span class="number">0</span>, <span class="number">1</span>]] * <span class="self">self</span>[[<span class="number">1</span>, <span class="number">0</span>]]) |
| } <span class="kw">else if </span>n == <span class="number">3 </span>{ |
| (<span class="self">self</span>[[<span class="number">0</span>, <span class="number">0</span>]] * <span class="self">self</span>[[<span class="number">1</span>, <span class="number">1</span>]] * <span class="self">self</span>[[<span class="number">2</span>, <span class="number">2</span>]]) + |
| (<span class="self">self</span>[[<span class="number">0</span>, <span class="number">1</span>]] * <span class="self">self</span>[[<span class="number">1</span>, <span class="number">2</span>]] * <span class="self">self</span>[[<span class="number">2</span>, <span class="number">0</span>]]) + |
| (<span class="self">self</span>[[<span class="number">0</span>, <span class="number">2</span>]] * <span class="self">self</span>[[<span class="number">1</span>, <span class="number">0</span>]] * <span class="self">self</span>[[<span class="number">2</span>, <span class="number">1</span>]]) - |
| (<span class="self">self</span>[[<span class="number">0</span>, <span class="number">0</span>]] * <span class="self">self</span>[[<span class="number">1</span>, <span class="number">2</span>]] * <span class="self">self</span>[[<span class="number">2</span>, <span class="number">1</span>]]) - |
| (<span class="self">self</span>[[<span class="number">0</span>, <span class="number">1</span>]] * <span class="self">self</span>[[<span class="number">1</span>, <span class="number">0</span>]] * <span class="self">self</span>[[<span class="number">2</span>, <span class="number">2</span>]]) - |
| (<span class="self">self</span>[[<span class="number">0</span>, <span class="number">2</span>]] * <span class="self">self</span>[[<span class="number">1</span>, <span class="number">1</span>]] * <span class="self">self</span>[[<span class="number">2</span>, <span class="number">0</span>]]) |
| } <span class="kw">else </span>{ |
| PartialPivLu::decompose(<span class="self">self</span>).map(|lu| lu.det()) |
| .unwrap_or(T::zero()) |
| } |
| } |
| } |
| |
| <span class="kw">impl</span><T: fmt::Display> fmt::Display <span class="kw">for </span>Matrix<T> { |
| <span class="doccomment">/// Formats the Matrix for display. |
| </span><span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter) -> <span class="prelude-ty">Result</span><(), fmt::Error> { |
| <span class="kw">let </span><span class="kw-2">mut </span>max_datum_width = <span class="number">0</span>; |
| <span class="kw">for </span>datum <span class="kw">in </span><span class="kw-2">&</span><span class="self">self</span>.data { |
| <span class="kw">let </span>datum_width = <span class="kw">match </span>f.precision() { |
| <span class="prelude-val">Some</span>(places) => <span class="macro">format!</span>(<span class="string">"{:.1$}"</span>, datum, places).len(), |
| <span class="prelude-val">None </span>=> <span class="macro">format!</span>(<span class="string">"{}"</span>, datum).len(), |
| }; |
| <span class="kw">if </span>datum_width > max_datum_width { |
| max_datum_width = datum_width; |
| } |
| } |
| <span class="kw">let </span>width = max_datum_width; |
| |
| <span class="kw">fn </span>write_row<T>(f: <span class="kw-2">&mut </span>fmt::Formatter, |
| row: <span class="kw-2">&</span>[T], |
| left_delimiter: <span class="kw-2">&</span>str, |
| right_delimiter: <span class="kw-2">&</span>str, |
| width: usize) |
| -> <span class="prelude-ty">Result</span><(), fmt::Error> |
| <span class="kw">where </span>T: fmt::Display |
| { |
| <span class="macro">try!</span>(<span class="macro">write!</span>(f, <span class="string">"{}"</span>, left_delimiter)); |
| <span class="kw">for </span>(index, datum) <span class="kw">in </span>row.iter().enumerate() { |
| <span class="kw">match </span>f.precision() { |
| <span class="prelude-val">Some</span>(places) => { |
| <span class="macro">try!</span>(<span class="macro">write!</span>(f, <span class="string">"{:1$.2$}"</span>, datum, width, places)); |
| } |
| <span class="prelude-val">None </span>=> { |
| <span class="macro">try!</span>(<span class="macro">write!</span>(f, <span class="string">"{:1$}"</span>, datum, width)); |
| } |
| } |
| <span class="kw">if </span>index < row.len() - <span class="number">1 </span>{ |
| <span class="macro">try!</span>(<span class="macro">write!</span>(f, <span class="string">" "</span>)); |
| } |
| } |
| <span class="macro">write!</span>(f, <span class="string">"{}"</span>, right_delimiter) |
| } |
| |
| <span class="kw">match </span><span class="self">self</span>.rows { |
| <span class="number">1 </span>=> write_row(f, <span class="kw-2">&</span><span class="self">self</span>.data, <span class="string">"["</span>, <span class="string">"]"</span>, width), |
| <span class="kw">_ </span>=> { |
| <span class="macro">try!</span>(write_row(f, |
| <span class="kw-2">&</span><span class="self">self</span>.data[<span class="number">0</span>..<span class="self">self</span>.cols], |
| <span class="string">"⎡"</span>, <span class="comment">// \u{23a1} LEFT SQUARE BRACKET UPPER CORNER |
| </span><span class="string">"⎤"</span>, <span class="comment">// \u{23a4} RIGHT SQUARE BRACKET UPPER CORNER |
| </span>width)); |
| <span class="macro">try!</span>(f.write_str(<span class="string">"\n"</span>)); |
| <span class="kw">for </span>row_index <span class="kw">in </span><span class="number">1</span>..<span class="self">self</span>.rows - <span class="number">1 </span>{ |
| <span class="macro">try!</span>(write_row(f, |
| <span class="kw-2">&</span><span class="self">self</span>.data[row_index * <span class="self">self</span>.cols..(row_index + <span class="number">1</span>) * <span class="self">self</span>.cols], |
| <span class="string">"⎢"</span>, <span class="comment">// \u{23a2} LEFT SQUARE BRACKET EXTENSION |
| </span><span class="string">"⎥"</span>, <span class="comment">// \u{23a5} RIGHT SQUARE BRACKET EXTENSION |
| </span>width)); |
| <span class="macro">try!</span>(f.write_str(<span class="string">"\n"</span>)); |
| } |
| write_row(f, |
| <span class="kw-2">&</span><span class="self">self</span>.data[(<span class="self">self</span>.rows - <span class="number">1</span>) * <span class="self">self</span>.cols..<span class="self">self</span>.rows * <span class="self">self</span>.cols], |
| <span class="string">"⎣"</span>, <span class="comment">// \u{23a3} LEFT SQUARE BRACKET LOWER CORNER |
| </span><span class="string">"⎦"</span>, <span class="comment">// \u{23a6} RIGHT SQUARE BRACKET LOWER CORNER |
| </span>width) |
| } |
| } |
| |
| } |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>tests { |
| <span class="kw">use </span>matrix::{Axes, BaseMatrix, Matrix}; |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_new_mat() { |
| <span class="kw">let </span>a = <span class="macro">vec!</span>[<span class="number">2.0</span>; <span class="number">9</span>]; |
| <span class="kw">let </span>b = Matrix::new(<span class="number">3</span>, <span class="number">3</span>, a); |
| |
| <span class="macro">assert_eq!</span>(b.rows(), <span class="number">3</span>); |
| <span class="macro">assert_eq!</span>(b.cols(), <span class="number">3</span>); |
| <span class="macro">assert_eq!</span>(b.into_vec(), <span class="macro">vec!</span>[<span class="number">2.0</span>; <span class="number">9</span>]); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>test_new_mat_bad_data() { |
| <span class="kw">let </span>a = <span class="macro">vec!</span>[<span class="number">2.0</span>; <span class="number">7</span>]; |
| <span class="kw">let _ </span>= Matrix::new(<span class="number">3</span>, <span class="number">3</span>, a); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_new_mat_from_fn() { |
| <span class="kw">let </span><span class="kw-2">mut </span>counter = <span class="number">0</span>; |
| <span class="kw">let </span>m: Matrix<usize> = Matrix::from_fn(<span class="number">3</span>, <span class="number">2</span>, |<span class="kw">_</span>, <span class="kw">_</span>| { |
| <span class="kw">let </span>value = counter; |
| counter += <span class="number">1</span>; |
| value |
| }); |
| <span class="macro">assert!</span>(m.rows() == <span class="number">3</span>); |
| <span class="macro">assert!</span>(m.cols() == <span class="number">2</span>); |
| <span class="macro">assert!</span>(m.data == <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>, <span class="number">4</span>, <span class="number">5</span>]); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_equality() { |
| <span class="comment">// well, "PartialEq", at least |
| </span><span class="kw">let </span>a = <span class="macro">matrix!</span>[<span class="number">1.</span>, <span class="number">2.</span>, <span class="number">3.</span>; |
| <span class="number">4.</span>, <span class="number">5.</span>, <span class="number">6.</span>]; |
| <span class="kw">let </span>a_redux = a.clone(); |
| <span class="macro">assert_eq!</span>(a, a_redux); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_new_from_slice() { |
| <span class="kw">let </span>data_vec: Vec<u32> = <span class="macro">vec!</span>[<span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">4</span>, <span class="number">5</span>, <span class="number">6</span>]; |
| <span class="kw">let </span>data_slice: <span class="kw-2">&</span>[u32] = <span class="kw-2">&</span>data_vec[..]; |
| <span class="kw">let </span>from_vec = Matrix::new(<span class="number">3</span>, <span class="number">2</span>, data_vec.clone()); |
| <span class="kw">let </span>from_slice = Matrix::new(<span class="number">3</span>, <span class="number">2</span>, data_slice); |
| <span class="macro">assert_eq!</span>(from_vec, from_slice); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_display_formatting() { |
| <span class="kw">let </span>first_matrix = <span class="macro">matrix!</span>[<span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>; |
| <span class="number">4</span>, <span class="number">5</span>, <span class="number">6</span>]; |
| <span class="kw">let </span>first_expectation = <span class="string">"⎡1 2 3⎤\n⎣4 5 6⎦"</span>; |
| <span class="macro">assert_eq!</span>(first_expectation, <span class="macro">format!</span>(<span class="string">"{}"</span>, first_matrix)); |
| |
| <span class="kw">let </span>second_matrix = <span class="macro">matrix!</span>[<span class="number">3.14</span>, <span class="number">2.718</span>, <span class="number">1.414</span>; |
| <span class="number">2.503</span>, <span class="number">4.669</span>, <span class="number">1.202</span>; |
| <span class="number">1.618</span>, <span class="number">0.5772</span>, <span class="number">1.3</span>; |
| <span class="number">2.68545</span>, <span class="number">1.282</span>, <span class="number">10000.</span>]; |
| <span class="kw">let </span>second_exp = <span class="string">"⎡ 3.14 2.718 1.414⎤\n⎢ 2.503 4.669 1.202⎥\n⎢ \ |
| 1.618 0.5772 1.3⎥\n⎣2.68545 1.282 10000⎦"</span>; |
| <span class="macro">assert_eq!</span>(second_exp, <span class="macro">format!</span>(<span class="string">"{}"</span>, second_matrix)); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_single_row_display_formatting() { |
| <span class="kw">let </span>one_row_matrix = <span class="macro">matrix!</span>[<span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">4</span>]; |
| <span class="macro">assert_eq!</span>(<span class="string">"[1 2 3 4]"</span>, <span class="macro">format!</span>(<span class="string">"{}"</span>, one_row_matrix)); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_display_formatting_precision() { |
| <span class="kw">let </span>our_matrix = <span class="macro">matrix!</span>[<span class="number">1.2</span>, <span class="number">1.23</span>, <span class="number">1.234</span>; |
| <span class="number">1.2345</span>, <span class="number">1.23456</span>, <span class="number">1.234567</span>]; |
| <span class="kw">let </span>expectations = <span class="macro">vec!</span>[<span class="string">"⎡1.2 1.2 1.2⎤\n⎣1.2 1.2 1.2⎦"</span>, |
| |
| <span class="string">"⎡1.20 1.23 1.23⎤\n⎣1.23 1.23 1.23⎦"</span>, |
| |
| <span class="string">"⎡1.200 1.230 1.234⎤\n⎣1.234 1.235 1.235⎦"</span>, |
| |
| <span class="string">"⎡1.2000 1.2300 1.2340⎤\n⎣1.2345 1.2346 1.2346⎦"</span>]; |
| |
| <span class="kw">for </span>(places, <span class="kw-2">&</span>expectation) <span class="kw">in </span>(<span class="number">1</span>..<span class="number">5</span>).zip(expectations.iter()) { |
| <span class="macro">assert_eq!</span>(expectation, <span class="macro">format!</span>(<span class="string">"{:.1$}"</span>, our_matrix, places)); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_matrix_index_mut() { |
| <span class="kw">let </span><span class="kw-2">mut </span>a = Matrix::ones(<span class="number">3</span>, <span class="number">3</span>) * <span class="number">2.0</span>; |
| |
| a[[<span class="number">0</span>, <span class="number">0</span>]] = <span class="number">13.0</span>; |
| |
| <span class="kw">for </span>i <span class="kw">in </span><span class="number">1</span>..<span class="number">9 </span>{ |
| <span class="macro">assert_eq!</span>(a.data()[i], <span class="number">2.0</span>); |
| } |
| |
| <span class="macro">assert_eq!</span>(a[[<span class="number">0</span>, <span class="number">0</span>]], <span class="number">13.0</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_matrix_select_rows() { |
| <span class="kw">let </span>a = Matrix::new(<span class="number">4</span>, <span class="number">2</span>, (<span class="number">0</span>..<span class="number">8</span>).collect::<Vec<usize>>()); |
| |
| <span class="kw">let </span>b = a.select_rows(<span class="kw-2">&</span>[<span class="number">0</span>, <span class="number">2</span>, <span class="number">3</span>]); |
| |
| <span class="macro">assert_eq!</span>(b.into_vec(), <span class="macro">vec!</span>[<span class="number">0</span>, <span class="number">1</span>, <span class="number">4</span>, <span class="number">5</span>, <span class="number">6</span>, <span class="number">7</span>]); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_matrix_select_cols() { |
| <span class="kw">let </span>a = Matrix::new(<span class="number">4</span>, <span class="number">2</span>, (<span class="number">0</span>..<span class="number">8</span>).collect::<Vec<usize>>()); |
| |
| <span class="kw">let </span>b = a.select_cols(<span class="kw-2">&</span>[<span class="number">1</span>]); |
| |
| <span class="macro">assert_eq!</span>(b.into_vec(), <span class="macro">vec!</span>[<span class="number">1</span>, <span class="number">3</span>, <span class="number">5</span>, <span class="number">7</span>]); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_matrix_select() { |
| <span class="kw">let </span>a = Matrix::new(<span class="number">4</span>, <span class="number">2</span>, (<span class="number">0</span>..<span class="number">8</span>).collect::<Vec<usize>>()); |
| |
| <span class="kw">let </span>b = a.select(<span class="kw-2">&</span>[<span class="number">0</span>, <span class="number">2</span>], <span class="kw-2">&</span>[<span class="number">1</span>]); |
| |
| <span class="macro">assert_eq!</span>(b.into_vec(), <span class="macro">vec!</span>[<span class="number">1</span>, <span class="number">5</span>]); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>matrix_diag() { |
| <span class="kw">let </span>a = <span class="macro">matrix!</span>[<span class="number">1.</span>, <span class="number">3.</span>, <span class="number">5.</span>; |
| <span class="number">2.</span>, <span class="number">4.</span>, <span class="number">7.</span>; |
| <span class="number">1.</span>, <span class="number">1.</span>, <span class="number">0.</span>]; |
| |
| <span class="kw">let </span>b = a.is_diag(); |
| |
| <span class="macro">assert!</span>(!b); |
| |
| <span class="kw">let </span>c = <span class="macro">matrix!</span>[<span class="number">1.</span>, <span class="number">0.</span>, <span class="number">0.</span>; |
| <span class="number">0.</span>, <span class="number">2.</span>, <span class="number">0.</span>; |
| <span class="number">0.</span>, <span class="number">0.</span>, <span class="number">3.</span>]; |
| <span class="kw">let </span>d = c.is_diag(); |
| |
| <span class="macro">assert!</span>(d); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>matrix_det() { |
| <span class="kw">let </span>a = <span class="macro">matrix!</span>[<span class="number">2.</span>, <span class="number">3.</span>; |
| <span class="number">1.</span>, <span class="number">2.</span>]; |
| <span class="kw">let </span>b = a.det(); |
| |
| <span class="macro">assert_eq!</span>(b, <span class="number">1.</span>); |
| |
| <span class="kw">let </span>c = <span class="macro">matrix!</span>[<span class="number">1.</span>, <span class="number">2.</span>, <span class="number">3.</span>; |
| <span class="number">4.</span>, <span class="number">5.</span>, <span class="number">6.</span>; |
| <span class="number">7.</span>, <span class="number">8.</span>, <span class="number">9.</span>]; |
| <span class="kw">let </span>d = c.det(); |
| |
| <span class="macro">assert_eq!</span>(d, <span class="number">0.</span>); |
| |
| <span class="kw">let </span>e: Matrix<f64> = <span class="macro">matrix!</span>[<span class="number">1.</span>, <span class="number">2.</span>, <span class="number">3.</span>, <span class="number">4.</span>, <span class="number">5.</span>; |
| <span class="number">3.</span>, <span class="number">0.</span>, <span class="number">4.</span>, <span class="number">5.</span>, <span class="number">6.</span>; |
| <span class="number">2.</span>, <span class="number">1.</span>, <span class="number">2.</span>, <span class="number">3.</span>, <span class="number">4.</span>; |
| <span class="number">0.</span>, <span class="number">0.</span>, <span class="number">0.</span>, <span class="number">6.</span>, <span class="number">5.</span>; |
| <span class="number">0.</span>, <span class="number">0.</span>, <span class="number">0.</span>, <span class="number">5.</span>, <span class="number">6.</span>]; |
| |
| <span class="kw">let </span>f = e.det(); |
| |
| <span class="macro">assert_scalar_eq!</span>(f, <span class="number">99.0</span>, comp = float); |
| |
| <span class="kw">let </span>g: Matrix<f64> = <span class="macro">matrix!</span>[<span class="number">1.</span>, <span class="number">2.</span>, <span class="number">3.</span>, <span class="number">4.</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">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="kw">let </span>h = g.det(); |
| <span class="macro">assert_eq!</span>(h, <span class="number">0.</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>matrix_solve() { |
| <span class="kw">let </span>a = <span class="macro">matrix!</span>[<span class="number">2.</span>, <span class="number">3.</span>; |
| <span class="number">1.</span>, <span class="number">2.</span>]; |
| |
| <span class="kw">let </span>y = <span class="macro">vector!</span>[<span class="number">8.</span>, <span class="number">5.</span>]; |
| |
| <span class="kw">let </span>x = a.solve(y).unwrap(); |
| |
| <span class="macro">assert_eq!</span>(x.size(), <span class="number">2</span>); |
| |
| <span class="macro">assert_eq!</span>(x[<span class="number">0</span>], <span class="number">1.</span>); |
| <span class="macro">assert_eq!</span>(x[<span class="number">1</span>], <span class="number">2.</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>create_mat_zeros() { |
| <span class="kw">let </span>a = Matrix::<f32>::zeros(<span class="number">10</span>, <span class="number">10</span>); |
| |
| <span class="macro">assert_eq!</span>(a.rows(), <span class="number">10</span>); |
| <span class="macro">assert_eq!</span>(a.cols(), <span class="number">10</span>); |
| |
| <span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..<span class="number">10 </span>{ |
| <span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..<span class="number">10 </span>{ |
| <span class="macro">assert_eq!</span>(a[[i, j]], <span class="number">0.0</span>); |
| } |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>create_mat_identity() { |
| <span class="kw">let </span>a = Matrix::<f32>::identity(<span class="number">4</span>); |
| |
| <span class="macro">assert_eq!</span>(a.rows(), <span class="number">4</span>); |
| <span class="macro">assert_eq!</span>(a.cols(), <span class="number">4</span>); |
| |
| <span class="macro">assert_eq!</span>(a[[<span class="number">0</span>, <span class="number">0</span>]], <span class="number">1.0</span>); |
| <span class="macro">assert_eq!</span>(a[[<span class="number">1</span>, <span class="number">1</span>]], <span class="number">1.0</span>); |
| <span class="macro">assert_eq!</span>(a[[<span class="number">2</span>, <span class="number">2</span>]], <span class="number">1.0</span>); |
| <span class="macro">assert_eq!</span>(a[[<span class="number">3</span>, <span class="number">3</span>]], <span class="number">1.0</span>); |
| |
| <span class="macro">assert_eq!</span>(a[[<span class="number">0</span>, <span class="number">1</span>]], <span class="number">0.0</span>); |
| <span class="macro">assert_eq!</span>(a[[<span class="number">2</span>, <span class="number">1</span>]], <span class="number">0.0</span>); |
| <span class="macro">assert_eq!</span>(a[[<span class="number">3</span>, <span class="number">0</span>]], <span class="number">0.0</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>create_mat_diag() { |
| <span class="kw">let </span>a = Matrix::from_diag(<span class="kw-2">&</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="macro">assert_eq!</span>(a.rows(), <span class="number">4</span>); |
| <span class="macro">assert_eq!</span>(a.cols(), <span class="number">4</span>); |
| |
| <span class="macro">assert_eq!</span>(a[[<span class="number">0</span>, <span class="number">0</span>]], <span class="number">1.0</span>); |
| <span class="macro">assert_eq!</span>(a[[<span class="number">1</span>, <span class="number">1</span>]], <span class="number">2.0</span>); |
| <span class="macro">assert_eq!</span>(a[[<span class="number">2</span>, <span class="number">2</span>]], <span class="number">3.0</span>); |
| <span class="macro">assert_eq!</span>(a[[<span class="number">3</span>, <span class="number">3</span>]], <span class="number">4.0</span>); |
| |
| <span class="macro">assert_eq!</span>(a[[<span class="number">0</span>, <span class="number">1</span>]], <span class="number">0.0</span>); |
| <span class="macro">assert_eq!</span>(a[[<span class="number">2</span>, <span class="number">1</span>]], <span class="number">0.0</span>); |
| <span class="macro">assert_eq!</span>(a[[<span class="number">3</span>, <span class="number">0</span>]], <span class="number">0.0</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_empty_mean() { |
| <span class="kw">let </span>a: Matrix<f64> = <span class="macro">matrix!</span>[]; |
| |
| <span class="kw">let </span>c = a.mean(Axes::Row); |
| <span class="macro">assert_eq!</span>(<span class="kw-2">*</span>c.data(), <span class="macro">vec!</span>[]); |
| |
| <span class="kw">let </span>d = a.mean(Axes::Col); |
| <span class="macro">assert_eq!</span>(<span class="kw-2">*</span>d.data(), <span class="macro">vec!</span>[]); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_invalid_variance() { |
| <span class="comment">// Only one row |
| </span><span class="kw">let </span>a: Matrix<f32> = <span class="macro">matrix!</span>[<span class="number">1.0</span>, <span class="number">2.0</span>]; |
| |
| <span class="kw">let </span>a_row = a.variance(Axes::Row); |
| <span class="macro">assert!</span>(a_row.is_err()); |
| |
| <span class="kw">let </span>a_col = a.variance(Axes::Col).unwrap(); |
| <span class="macro">assert_eq!</span>(<span class="kw-2">*</span>a_col.data(), <span class="macro">vec!</span>[<span class="number">0.5</span>]); |
| |
| <span class="comment">// Only one column |
| </span><span class="kw">let </span>b: Matrix<f32> = <span class="macro">matrix!</span>[<span class="number">1.0</span>; <span class="number">2.0</span>]; |
| |
| <span class="kw">let </span>b_row = b.variance(Axes::Row).unwrap(); |
| <span class="macro">assert_eq!</span>(<span class="kw-2">*</span>b_row.data(), <span class="macro">vec!</span>[<span class="number">0.5</span>]); |
| |
| <span class="kw">let </span>b_col = b.variance(Axes::Col); |
| <span class="macro">assert!</span>(b_col.is_err()); |
| |
| <span class="comment">// Empty matrix |
| </span><span class="kw">let </span>d: Matrix<f32> = <span class="macro">matrix!</span>[]; |
| |
| <span class="kw">let </span>d_row = d.variance(Axes::Row); |
| <span class="macro">assert!</span>(d_row.is_err()); |
| |
| <span class="kw">let </span>d_col = d.variance(Axes::Col); |
| <span class="macro">assert!</span>(d_col.is_err()); |
| } |
| } |
| </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> |