<!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 `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/nalgebra-0.32.1/src/base/matrix.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>matrix.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Regular-1f7d512b176f0f72.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Bold-124a1ca42af929b6.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../../../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../../../static.files/rustdoc-6827029ac823cab7.css" id="mainThemeStyle"><link rel="stylesheet" id="themeStyle" href="../../../static.files/light-ebce58d0a40c3431.css"><link rel="stylesheet" disabled href="../../../static.files/dark-f23faae4a2daf9a6.css"><link rel="stylesheet" disabled href="../../../static.files/ayu-8af5e100b21cd173.css"><script id="default-settings" ></script><script src="../../../static.files/storage-d43fa987303ecbbb.js"></script><script defer src="../../../static.files/source-script-5cf2e01a42cc9858.js"></script><script defer src="../../../source-files.js"></script><script defer src="../../../static.files/main-c55e1eb52e1886b4.js"></script><noscript><link rel="stylesheet" href="../../../static.files/noscript-13285aec31fa243e.css"></noscript><link rel="icon" href="https://nalgebra.org/img/favicon.ico"></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"></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../../nalgebra/index.html"><img class="rust-logo" src="../../../static.files/rust-logo-151179464ae7ed46.svg" alt="logo"></a><form class="search-form"><span></span><input class="search-input" name="search" aria-label="Run search in the documentation" 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="../../../static.files/wheel-5ec35bf9ca753509.svg"></a></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><a href="#1" id="1">1</a>
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<a href="#938" id="938">938</a>
<a href="#939" id="939">939</a>
<a href="#940" id="940">940</a>
<a href="#941" id="941">941</a>
<a href="#942" id="942">942</a>
<a href="#943" id="943">943</a>
<a href="#944" id="944">944</a>
<a href="#945" id="945">945</a>
<a href="#946" id="946">946</a>
<a href="#947" id="947">947</a>
<a href="#948" id="948">948</a>
<a href="#949" id="949">949</a>
<a href="#950" id="950">950</a>
<a href="#951" id="951">951</a>
<a href="#952" id="952">952</a>
<a href="#953" id="953">953</a>
<a href="#954" id="954">954</a>
<a href="#955" id="955">955</a>
<a href="#956" id="956">956</a>
<a href="#957" id="957">957</a>
<a href="#958" id="958">958</a>
<a href="#959" id="959">959</a>
<a href="#960" id="960">960</a>
<a href="#961" id="961">961</a>
<a href="#962" id="962">962</a>
<a href="#963" id="963">963</a>
<a href="#964" id="964">964</a>
<a href="#965" id="965">965</a>
<a href="#966" id="966">966</a>
<a href="#967" id="967">967</a>
<a href="#968" id="968">968</a>
<a href="#969" id="969">969</a>
<a href="#970" id="970">970</a>
<a href="#971" id="971">971</a>
<a href="#972" id="972">972</a>
<a href="#973" id="973">973</a>
<a href="#974" id="974">974</a>
<a href="#975" id="975">975</a>
<a href="#976" id="976">976</a>
<a href="#977" id="977">977</a>
<a href="#978" id="978">978</a>
<a href="#979" id="979">979</a>
<a href="#980" id="980">980</a>
<a href="#981" id="981">981</a>
<a href="#982" id="982">982</a>
<a href="#983" id="983">983</a>
<a href="#984" id="984">984</a>
<a href="#985" id="985">985</a>
<a href="#986" id="986">986</a>
<a href="#987" id="987">987</a>
<a href="#988" id="988">988</a>
<a href="#989" id="989">989</a>
<a href="#990" id="990">990</a>
<a href="#991" id="991">991</a>
<a href="#992" id="992">992</a>
<a href="#993" id="993">993</a>
<a href="#994" id="994">994</a>
<a href="#995" id="995">995</a>
<a href="#996" id="996">996</a>
<a href="#997" id="997">997</a>
<a href="#998" id="998">998</a>
<a href="#999" id="999">999</a>
<a href="#1000" id="1000">1000</a>
<a href="#1001" id="1001">1001</a>
<a href="#1002" id="1002">1002</a>
<a href="#1003" id="1003">1003</a>
<a href="#1004" id="1004">1004</a>
<a href="#1005" id="1005">1005</a>
<a href="#1006" id="1006">1006</a>
<a href="#1007" id="1007">1007</a>
<a href="#1008" id="1008">1008</a>
<a href="#1009" id="1009">1009</a>
<a href="#1010" id="1010">1010</a>
<a href="#1011" id="1011">1011</a>
<a href="#1012" id="1012">1012</a>
<a href="#1013" id="1013">1013</a>
<a href="#1014" id="1014">1014</a>
<a href="#1015" id="1015">1015</a>
<a href="#1016" id="1016">1016</a>
<a href="#1017" id="1017">1017</a>
<a href="#1018" id="1018">1018</a>
<a href="#1019" id="1019">1019</a>
<a href="#1020" id="1020">1020</a>
<a href="#1021" id="1021">1021</a>
<a href="#1022" id="1022">1022</a>
<a href="#1023" id="1023">1023</a>
<a href="#1024" id="1024">1024</a>
<a href="#1025" id="1025">1025</a>
<a href="#1026" id="1026">1026</a>
<a href="#1027" id="1027">1027</a>
<a href="#1028" id="1028">1028</a>
<a href="#1029" id="1029">1029</a>
<a href="#1030" id="1030">1030</a>
<a href="#1031" id="1031">1031</a>
<a href="#1032" id="1032">1032</a>
<a href="#1033" id="1033">1033</a>
<a href="#1034" id="1034">1034</a>
<a href="#1035" id="1035">1035</a>
<a href="#1036" id="1036">1036</a>
<a href="#1037" id="1037">1037</a>
<a href="#1038" id="1038">1038</a>
<a href="#1039" id="1039">1039</a>
<a href="#1040" id="1040">1040</a>
<a href="#1041" id="1041">1041</a>
<a href="#1042" id="1042">1042</a>
<a href="#1043" id="1043">1043</a>
<a href="#1044" id="1044">1044</a>
<a href="#1045" id="1045">1045</a>
<a href="#1046" id="1046">1046</a>
<a href="#1047" id="1047">1047</a>
<a href="#1048" id="1048">1048</a>
<a href="#1049" id="1049">1049</a>
<a href="#1050" id="1050">1050</a>
<a href="#1051" id="1051">1051</a>
<a href="#1052" id="1052">1052</a>
<a href="#1053" id="1053">1053</a>
<a href="#1054" id="1054">1054</a>
<a href="#1055" id="1055">1055</a>
<a href="#1056" id="1056">1056</a>
<a href="#1057" id="1057">1057</a>
<a href="#1058" id="1058">1058</a>
<a href="#1059" id="1059">1059</a>
<a href="#1060" id="1060">1060</a>
<a href="#1061" id="1061">1061</a>
<a href="#1062" id="1062">1062</a>
<a href="#1063" id="1063">1063</a>
<a href="#1064" id="1064">1064</a>
<a href="#1065" id="1065">1065</a>
<a href="#1066" id="1066">1066</a>
<a href="#1067" id="1067">1067</a>
<a href="#1068" id="1068">1068</a>
<a href="#1069" id="1069">1069</a>
<a href="#1070" id="1070">1070</a>
<a href="#1071" id="1071">1071</a>
<a href="#1072" id="1072">1072</a>
<a href="#1073" id="1073">1073</a>
<a href="#1074" id="1074">1074</a>
<a href="#1075" id="1075">1075</a>
<a href="#1076" id="1076">1076</a>
<a href="#1077" id="1077">1077</a>
<a href="#1078" id="1078">1078</a>
<a href="#1079" id="1079">1079</a>
<a href="#1080" id="1080">1080</a>
<a href="#1081" id="1081">1081</a>
<a href="#1082" id="1082">1082</a>
<a href="#1083" id="1083">1083</a>
<a href="#1084" id="1084">1084</a>
<a href="#1085" id="1085">1085</a>
<a href="#1086" id="1086">1086</a>
<a href="#1087" id="1087">1087</a>
<a href="#1088" id="1088">1088</a>
<a href="#1089" id="1089">1089</a>
<a href="#1090" id="1090">1090</a>
<a href="#1091" id="1091">1091</a>
<a href="#1092" id="1092">1092</a>
<a href="#1093" id="1093">1093</a>
<a href="#1094" id="1094">1094</a>
<a href="#1095" id="1095">1095</a>
<a href="#1096" id="1096">1096</a>
<a href="#1097" id="1097">1097</a>
<a href="#1098" id="1098">1098</a>
<a href="#1099" id="1099">1099</a>
<a href="#1100" id="1100">1100</a>
<a href="#1101" id="1101">1101</a>
<a href="#1102" id="1102">1102</a>
<a href="#1103" id="1103">1103</a>
<a href="#1104" id="1104">1104</a>
<a href="#1105" id="1105">1105</a>
<a href="#1106" id="1106">1106</a>
<a href="#1107" id="1107">1107</a>
<a href="#1108" id="1108">1108</a>
<a href="#1109" id="1109">1109</a>
<a href="#1110" id="1110">1110</a>
<a href="#1111" id="1111">1111</a>
<a href="#1112" id="1112">1112</a>
<a href="#1113" id="1113">1113</a>
<a href="#1114" id="1114">1114</a>
<a href="#1115" id="1115">1115</a>
<a href="#1116" id="1116">1116</a>
<a href="#1117" id="1117">1117</a>
<a href="#1118" id="1118">1118</a>
<a href="#1119" id="1119">1119</a>
<a href="#1120" id="1120">1120</a>
<a href="#1121" id="1121">1121</a>
<a href="#1122" id="1122">1122</a>
<a href="#1123" id="1123">1123</a>
<a href="#1124" id="1124">1124</a>
<a href="#1125" id="1125">1125</a>
<a href="#1126" id="1126">1126</a>
<a href="#1127" id="1127">1127</a>
<a href="#1128" id="1128">1128</a>
<a href="#1129" id="1129">1129</a>
<a href="#1130" id="1130">1130</a>
<a href="#1131" id="1131">1131</a>
<a href="#1132" id="1132">1132</a>
<a href="#1133" id="1133">1133</a>
<a href="#1134" id="1134">1134</a>
<a href="#1135" id="1135">1135</a>
<a href="#1136" id="1136">1136</a>
<a href="#1137" id="1137">1137</a>
<a href="#1138" id="1138">1138</a>
<a href="#1139" id="1139">1139</a>
<a href="#1140" id="1140">1140</a>
<a href="#1141" id="1141">1141</a>
<a href="#1142" id="1142">1142</a>
<a href="#1143" id="1143">1143</a>
<a href="#1144" id="1144">1144</a>
<a href="#1145" id="1145">1145</a>
<a href="#1146" id="1146">1146</a>
<a href="#1147" id="1147">1147</a>
<a href="#1148" id="1148">1148</a>
<a href="#1149" id="1149">1149</a>
<a href="#1150" id="1150">1150</a>
<a href="#1151" id="1151">1151</a>
<a href="#1152" id="1152">1152</a>
<a href="#1153" id="1153">1153</a>
<a href="#1154" id="1154">1154</a>
<a href="#1155" id="1155">1155</a>
<a href="#1156" id="1156">1156</a>
<a href="#1157" id="1157">1157</a>
<a href="#1158" id="1158">1158</a>
<a href="#1159" id="1159">1159</a>
<a href="#1160" id="1160">1160</a>
<a href="#1161" id="1161">1161</a>
<a href="#1162" id="1162">1162</a>
<a href="#1163" id="1163">1163</a>
<a href="#1164" id="1164">1164</a>
<a href="#1165" id="1165">1165</a>
<a href="#1166" id="1166">1166</a>
<a href="#1167" id="1167">1167</a>
<a href="#1168" id="1168">1168</a>
<a href="#1169" id="1169">1169</a>
<a href="#1170" id="1170">1170</a>
<a href="#1171" id="1171">1171</a>
<a href="#1172" id="1172">1172</a>
<a href="#1173" id="1173">1173</a>
<a href="#1174" id="1174">1174</a>
<a href="#1175" id="1175">1175</a>
<a href="#1176" id="1176">1176</a>
<a href="#1177" id="1177">1177</a>
<a href="#1178" id="1178">1178</a>
<a href="#1179" id="1179">1179</a>
<a href="#1180" id="1180">1180</a>
<a href="#1181" id="1181">1181</a>
<a href="#1182" id="1182">1182</a>
<a href="#1183" id="1183">1183</a>
<a href="#1184" id="1184">1184</a>
<a href="#1185" id="1185">1185</a>
<a href="#1186" id="1186">1186</a>
<a href="#1187" id="1187">1187</a>
<a href="#1188" id="1188">1188</a>
<a href="#1189" id="1189">1189</a>
<a href="#1190" id="1190">1190</a>
<a href="#1191" id="1191">1191</a>
<a href="#1192" id="1192">1192</a>
<a href="#1193" id="1193">1193</a>
<a href="#1194" id="1194">1194</a>
<a href="#1195" id="1195">1195</a>
<a href="#1196" id="1196">1196</a>
<a href="#1197" id="1197">1197</a>
<a href="#1198" id="1198">1198</a>
<a href="#1199" id="1199">1199</a>
<a href="#1200" id="1200">1200</a>
<a href="#1201" id="1201">1201</a>
<a href="#1202" id="1202">1202</a>
<a href="#1203" id="1203">1203</a>
<a href="#1204" id="1204">1204</a>
<a href="#1205" id="1205">1205</a>
<a href="#1206" id="1206">1206</a>
<a href="#1207" id="1207">1207</a>
<a href="#1208" id="1208">1208</a>
<a href="#1209" id="1209">1209</a>
<a href="#1210" id="1210">1210</a>
<a href="#1211" id="1211">1211</a>
<a href="#1212" id="1212">1212</a>
<a href="#1213" id="1213">1213</a>
<a href="#1214" id="1214">1214</a>
<a href="#1215" id="1215">1215</a>
<a href="#1216" id="1216">1216</a>
<a href="#1217" id="1217">1217</a>
<a href="#1218" id="1218">1218</a>
<a href="#1219" id="1219">1219</a>
<a href="#1220" id="1220">1220</a>
<a href="#1221" id="1221">1221</a>
<a href="#1222" id="1222">1222</a>
<a href="#1223" id="1223">1223</a>
<a href="#1224" id="1224">1224</a>
<a href="#1225" id="1225">1225</a>
<a href="#1226" id="1226">1226</a>
<a href="#1227" id="1227">1227</a>
<a href="#1228" id="1228">1228</a>
<a href="#1229" id="1229">1229</a>
<a href="#1230" id="1230">1230</a>
<a href="#1231" id="1231">1231</a>
<a href="#1232" id="1232">1232</a>
<a href="#1233" id="1233">1233</a>
<a href="#1234" id="1234">1234</a>
<a href="#1235" id="1235">1235</a>
<a href="#1236" id="1236">1236</a>
<a href="#1237" id="1237">1237</a>
<a href="#1238" id="1238">1238</a>
<a href="#1239" id="1239">1239</a>
<a href="#1240" id="1240">1240</a>
<a href="#1241" id="1241">1241</a>
<a href="#1242" id="1242">1242</a>
<a href="#1243" id="1243">1243</a>
<a href="#1244" id="1244">1244</a>
<a href="#1245" id="1245">1245</a>
<a href="#1246" id="1246">1246</a>
<a href="#1247" id="1247">1247</a>
<a href="#1248" id="1248">1248</a>
<a href="#1249" id="1249">1249</a>
<a href="#1250" id="1250">1250</a>
<a href="#1251" id="1251">1251</a>
<a href="#1252" id="1252">1252</a>
<a href="#1253" id="1253">1253</a>
<a href="#1254" id="1254">1254</a>
<a href="#1255" id="1255">1255</a>
<a href="#1256" id="1256">1256</a>
<a href="#1257" id="1257">1257</a>
<a href="#1258" id="1258">1258</a>
<a href="#1259" id="1259">1259</a>
<a href="#1260" id="1260">1260</a>
<a href="#1261" id="1261">1261</a>
<a href="#1262" id="1262">1262</a>
<a href="#1263" id="1263">1263</a>
<a href="#1264" id="1264">1264</a>
<a href="#1265" id="1265">1265</a>
<a href="#1266" id="1266">1266</a>
<a href="#1267" id="1267">1267</a>
<a href="#1268" id="1268">1268</a>
<a href="#1269" id="1269">1269</a>
<a href="#1270" id="1270">1270</a>
<a href="#1271" id="1271">1271</a>
<a href="#1272" id="1272">1272</a>
<a href="#1273" id="1273">1273</a>
<a href="#1274" id="1274">1274</a>
<a href="#1275" id="1275">1275</a>
<a href="#1276" id="1276">1276</a>
<a href="#1277" id="1277">1277</a>
<a href="#1278" id="1278">1278</a>
<a href="#1279" id="1279">1279</a>
<a href="#1280" id="1280">1280</a>
<a href="#1281" id="1281">1281</a>
<a href="#1282" id="1282">1282</a>
<a href="#1283" id="1283">1283</a>
<a href="#1284" id="1284">1284</a>
<a href="#1285" id="1285">1285</a>
<a href="#1286" id="1286">1286</a>
<a href="#1287" id="1287">1287</a>
<a href="#1288" id="1288">1288</a>
<a href="#1289" id="1289">1289</a>
<a href="#1290" id="1290">1290</a>
<a href="#1291" id="1291">1291</a>
<a href="#1292" id="1292">1292</a>
<a href="#1293" id="1293">1293</a>
<a href="#1294" id="1294">1294</a>
<a href="#1295" id="1295">1295</a>
<a href="#1296" id="1296">1296</a>
<a href="#1297" id="1297">1297</a>
<a href="#1298" id="1298">1298</a>
<a href="#1299" id="1299">1299</a>
<a href="#1300" id="1300">1300</a>
<a href="#1301" id="1301">1301</a>
<a href="#1302" id="1302">1302</a>
<a href="#1303" id="1303">1303</a>
<a href="#1304" id="1304">1304</a>
<a href="#1305" id="1305">1305</a>
<a href="#1306" id="1306">1306</a>
<a href="#1307" id="1307">1307</a>
<a href="#1308" id="1308">1308</a>
<a href="#1309" id="1309">1309</a>
<a href="#1310" id="1310">1310</a>
<a href="#1311" id="1311">1311</a>
<a href="#1312" id="1312">1312</a>
<a href="#1313" id="1313">1313</a>
<a href="#1314" id="1314">1314</a>
<a href="#1315" id="1315">1315</a>
<a href="#1316" id="1316">1316</a>
<a href="#1317" id="1317">1317</a>
<a href="#1318" id="1318">1318</a>
<a href="#1319" id="1319">1319</a>
<a href="#1320" id="1320">1320</a>
<a href="#1321" id="1321">1321</a>
<a href="#1322" id="1322">1322</a>
<a href="#1323" id="1323">1323</a>
<a href="#1324" id="1324">1324</a>
<a href="#1325" id="1325">1325</a>
<a href="#1326" id="1326">1326</a>
<a href="#1327" id="1327">1327</a>
<a href="#1328" id="1328">1328</a>
<a href="#1329" id="1329">1329</a>
<a href="#1330" id="1330">1330</a>
<a href="#1331" id="1331">1331</a>
<a href="#1332" id="1332">1332</a>
<a href="#1333" id="1333">1333</a>
<a href="#1334" id="1334">1334</a>
<a href="#1335" id="1335">1335</a>
<a href="#1336" id="1336">1336</a>
<a href="#1337" id="1337">1337</a>
<a href="#1338" id="1338">1338</a>
<a href="#1339" id="1339">1339</a>
<a href="#1340" id="1340">1340</a>
<a href="#1341" id="1341">1341</a>
<a href="#1342" id="1342">1342</a>
<a href="#1343" id="1343">1343</a>
<a href="#1344" id="1344">1344</a>
<a href="#1345" id="1345">1345</a>
<a href="#1346" id="1346">1346</a>
<a href="#1347" id="1347">1347</a>
<a href="#1348" id="1348">1348</a>
<a href="#1349" id="1349">1349</a>
<a href="#1350" id="1350">1350</a>
<a href="#1351" id="1351">1351</a>
<a href="#1352" id="1352">1352</a>
<a href="#1353" id="1353">1353</a>
<a href="#1354" id="1354">1354</a>
<a href="#1355" id="1355">1355</a>
<a href="#1356" id="1356">1356</a>
<a href="#1357" id="1357">1357</a>
<a href="#1358" id="1358">1358</a>
<a href="#1359" id="1359">1359</a>
<a href="#1360" id="1360">1360</a>
<a href="#1361" id="1361">1361</a>
<a href="#1362" id="1362">1362</a>
<a href="#1363" id="1363">1363</a>
<a href="#1364" id="1364">1364</a>
<a href="#1365" id="1365">1365</a>
<a href="#1366" id="1366">1366</a>
<a href="#1367" id="1367">1367</a>
<a href="#1368" id="1368">1368</a>
<a href="#1369" id="1369">1369</a>
<a href="#1370" id="1370">1370</a>
<a href="#1371" id="1371">1371</a>
<a href="#1372" id="1372">1372</a>
<a href="#1373" id="1373">1373</a>
<a href="#1374" id="1374">1374</a>
<a href="#1375" id="1375">1375</a>
<a href="#1376" id="1376">1376</a>
<a href="#1377" id="1377">1377</a>
<a href="#1378" id="1378">1378</a>
<a href="#1379" id="1379">1379</a>
<a href="#1380" id="1380">1380</a>
<a href="#1381" id="1381">1381</a>
<a href="#1382" id="1382">1382</a>
<a href="#1383" id="1383">1383</a>
<a href="#1384" id="1384">1384</a>
<a href="#1385" id="1385">1385</a>
<a href="#1386" id="1386">1386</a>
<a href="#1387" id="1387">1387</a>
<a href="#1388" id="1388">1388</a>
<a href="#1389" id="1389">1389</a>
<a href="#1390" id="1390">1390</a>
<a href="#1391" id="1391">1391</a>
<a href="#1392" id="1392">1392</a>
<a href="#1393" id="1393">1393</a>
<a href="#1394" id="1394">1394</a>
<a href="#1395" id="1395">1395</a>
<a href="#1396" id="1396">1396</a>
<a href="#1397" id="1397">1397</a>
<a href="#1398" id="1398">1398</a>
<a href="#1399" id="1399">1399</a>
<a href="#1400" id="1400">1400</a>
<a href="#1401" id="1401">1401</a>
<a href="#1402" id="1402">1402</a>
<a href="#1403" id="1403">1403</a>
<a href="#1404" id="1404">1404</a>
<a href="#1405" id="1405">1405</a>
<a href="#1406" id="1406">1406</a>
<a href="#1407" id="1407">1407</a>
<a href="#1408" id="1408">1408</a>
<a href="#1409" id="1409">1409</a>
<a href="#1410" id="1410">1410</a>
<a href="#1411" id="1411">1411</a>
<a href="#1412" id="1412">1412</a>
<a href="#1413" id="1413">1413</a>
<a href="#1414" id="1414">1414</a>
<a href="#1415" id="1415">1415</a>
<a href="#1416" id="1416">1416</a>
<a href="#1417" id="1417">1417</a>
<a href="#1418" id="1418">1418</a>
<a href="#1419" id="1419">1419</a>
<a href="#1420" id="1420">1420</a>
<a href="#1421" id="1421">1421</a>
<a href="#1422" id="1422">1422</a>
<a href="#1423" id="1423">1423</a>
<a href="#1424" id="1424">1424</a>
<a href="#1425" id="1425">1425</a>
<a href="#1426" id="1426">1426</a>
<a href="#1427" id="1427">1427</a>
<a href="#1428" id="1428">1428</a>
<a href="#1429" id="1429">1429</a>
<a href="#1430" id="1430">1430</a>
<a href="#1431" id="1431">1431</a>
<a href="#1432" id="1432">1432</a>
<a href="#1433" id="1433">1433</a>
<a href="#1434" id="1434">1434</a>
<a href="#1435" id="1435">1435</a>
<a href="#1436" id="1436">1436</a>
<a href="#1437" id="1437">1437</a>
<a href="#1438" id="1438">1438</a>
<a href="#1439" id="1439">1439</a>
<a href="#1440" id="1440">1440</a>
<a href="#1441" id="1441">1441</a>
<a href="#1442" id="1442">1442</a>
<a href="#1443" id="1443">1443</a>
<a href="#1444" id="1444">1444</a>
<a href="#1445" id="1445">1445</a>
<a href="#1446" id="1446">1446</a>
<a href="#1447" id="1447">1447</a>
<a href="#1448" id="1448">1448</a>
<a href="#1449" id="1449">1449</a>
<a href="#1450" id="1450">1450</a>
<a href="#1451" id="1451">1451</a>
<a href="#1452" id="1452">1452</a>
<a href="#1453" id="1453">1453</a>
<a href="#1454" id="1454">1454</a>
<a href="#1455" id="1455">1455</a>
<a href="#1456" id="1456">1456</a>
<a href="#1457" id="1457">1457</a>
<a href="#1458" id="1458">1458</a>
<a href="#1459" id="1459">1459</a>
<a href="#1460" id="1460">1460</a>
<a href="#1461" id="1461">1461</a>
<a href="#1462" id="1462">1462</a>
<a href="#1463" id="1463">1463</a>
<a href="#1464" id="1464">1464</a>
<a href="#1465" id="1465">1465</a>
<a href="#1466" id="1466">1466</a>
<a href="#1467" id="1467">1467</a>
<a href="#1468" id="1468">1468</a>
<a href="#1469" id="1469">1469</a>
<a href="#1470" id="1470">1470</a>
<a href="#1471" id="1471">1471</a>
<a href="#1472" id="1472">1472</a>
<a href="#1473" id="1473">1473</a>
<a href="#1474" id="1474">1474</a>
<a href="#1475" id="1475">1475</a>
<a href="#1476" id="1476">1476</a>
<a href="#1477" id="1477">1477</a>
<a href="#1478" id="1478">1478</a>
<a href="#1479" id="1479">1479</a>
<a href="#1480" id="1480">1480</a>
<a href="#1481" id="1481">1481</a>
<a href="#1482" id="1482">1482</a>
<a href="#1483" id="1483">1483</a>
<a href="#1484" id="1484">1484</a>
<a href="#1485" id="1485">1485</a>
<a href="#1486" id="1486">1486</a>
<a href="#1487" id="1487">1487</a>
<a href="#1488" id="1488">1488</a>
<a href="#1489" id="1489">1489</a>
<a href="#1490" id="1490">1490</a>
<a href="#1491" id="1491">1491</a>
<a href="#1492" id="1492">1492</a>
<a href="#1493" id="1493">1493</a>
<a href="#1494" id="1494">1494</a>
<a href="#1495" id="1495">1495</a>
<a href="#1496" id="1496">1496</a>
<a href="#1497" id="1497">1497</a>
<a href="#1498" id="1498">1498</a>
<a href="#1499" id="1499">1499</a>
<a href="#1500" id="1500">1500</a>
<a href="#1501" id="1501">1501</a>
<a href="#1502" id="1502">1502</a>
<a href="#1503" id="1503">1503</a>
<a href="#1504" id="1504">1504</a>
<a href="#1505" id="1505">1505</a>
<a href="#1506" id="1506">1506</a>
<a href="#1507" id="1507">1507</a>
<a href="#1508" id="1508">1508</a>
<a href="#1509" id="1509">1509</a>
<a href="#1510" id="1510">1510</a>
<a href="#1511" id="1511">1511</a>
<a href="#1512" id="1512">1512</a>
<a href="#1513" id="1513">1513</a>
<a href="#1514" id="1514">1514</a>
<a href="#1515" id="1515">1515</a>
<a href="#1516" id="1516">1516</a>
<a href="#1517" id="1517">1517</a>
<a href="#1518" id="1518">1518</a>
<a href="#1519" id="1519">1519</a>
<a href="#1520" id="1520">1520</a>
<a href="#1521" id="1521">1521</a>
<a href="#1522" id="1522">1522</a>
<a href="#1523" id="1523">1523</a>
<a href="#1524" id="1524">1524</a>
<a href="#1525" id="1525">1525</a>
<a href="#1526" id="1526">1526</a>
<a href="#1527" id="1527">1527</a>
<a href="#1528" id="1528">1528</a>
<a href="#1529" id="1529">1529</a>
<a href="#1530" id="1530">1530</a>
<a href="#1531" id="1531">1531</a>
<a href="#1532" id="1532">1532</a>
<a href="#1533" id="1533">1533</a>
<a href="#1534" id="1534">1534</a>
<a href="#1535" id="1535">1535</a>
<a href="#1536" id="1536">1536</a>
<a href="#1537" id="1537">1537</a>
<a href="#1538" id="1538">1538</a>
<a href="#1539" id="1539">1539</a>
<a href="#1540" id="1540">1540</a>
<a href="#1541" id="1541">1541</a>
<a href="#1542" id="1542">1542</a>
<a href="#1543" id="1543">1543</a>
<a href="#1544" id="1544">1544</a>
<a href="#1545" id="1545">1545</a>
<a href="#1546" id="1546">1546</a>
<a href="#1547" id="1547">1547</a>
<a href="#1548" id="1548">1548</a>
<a href="#1549" id="1549">1549</a>
<a href="#1550" id="1550">1550</a>
<a href="#1551" id="1551">1551</a>
<a href="#1552" id="1552">1552</a>
<a href="#1553" id="1553">1553</a>
<a href="#1554" id="1554">1554</a>
<a href="#1555" id="1555">1555</a>
<a href="#1556" id="1556">1556</a>
<a href="#1557" id="1557">1557</a>
<a href="#1558" id="1558">1558</a>
<a href="#1559" id="1559">1559</a>
<a href="#1560" id="1560">1560</a>
<a href="#1561" id="1561">1561</a>
<a href="#1562" id="1562">1562</a>
<a href="#1563" id="1563">1563</a>
<a href="#1564" id="1564">1564</a>
<a href="#1565" id="1565">1565</a>
<a href="#1566" id="1566">1566</a>
<a href="#1567" id="1567">1567</a>
<a href="#1568" id="1568">1568</a>
<a href="#1569" id="1569">1569</a>
<a href="#1570" id="1570">1570</a>
<a href="#1571" id="1571">1571</a>
<a href="#1572" id="1572">1572</a>
<a href="#1573" id="1573">1573</a>
<a href="#1574" id="1574">1574</a>
<a href="#1575" id="1575">1575</a>
<a href="#1576" id="1576">1576</a>
<a href="#1577" id="1577">1577</a>
<a href="#1578" id="1578">1578</a>
<a href="#1579" id="1579">1579</a>
<a href="#1580" id="1580">1580</a>
<a href="#1581" id="1581">1581</a>
<a href="#1582" id="1582">1582</a>
<a href="#1583" id="1583">1583</a>
<a href="#1584" id="1584">1584</a>
<a href="#1585" id="1585">1585</a>
<a href="#1586" id="1586">1586</a>
<a href="#1587" id="1587">1587</a>
<a href="#1588" id="1588">1588</a>
<a href="#1589" id="1589">1589</a>
<a href="#1590" id="1590">1590</a>
<a href="#1591" id="1591">1591</a>
<a href="#1592" id="1592">1592</a>
<a href="#1593" id="1593">1593</a>
<a href="#1594" id="1594">1594</a>
<a href="#1595" id="1595">1595</a>
<a href="#1596" id="1596">1596</a>
<a href="#1597" id="1597">1597</a>
<a href="#1598" id="1598">1598</a>
<a href="#1599" id="1599">1599</a>
<a href="#1600" id="1600">1600</a>
<a href="#1601" id="1601">1601</a>
<a href="#1602" id="1602">1602</a>
<a href="#1603" id="1603">1603</a>
<a href="#1604" id="1604">1604</a>
<a href="#1605" id="1605">1605</a>
<a href="#1606" id="1606">1606</a>
<a href="#1607" id="1607">1607</a>
<a href="#1608" id="1608">1608</a>
<a href="#1609" id="1609">1609</a>
<a href="#1610" id="1610">1610</a>
<a href="#1611" id="1611">1611</a>
<a href="#1612" id="1612">1612</a>
<a href="#1613" id="1613">1613</a>
<a href="#1614" id="1614">1614</a>
<a href="#1615" id="1615">1615</a>
<a href="#1616" id="1616">1616</a>
<a href="#1617" id="1617">1617</a>
<a href="#1618" id="1618">1618</a>
<a href="#1619" id="1619">1619</a>
<a href="#1620" id="1620">1620</a>
<a href="#1621" id="1621">1621</a>
<a href="#1622" id="1622">1622</a>
<a href="#1623" id="1623">1623</a>
<a href="#1624" id="1624">1624</a>
<a href="#1625" id="1625">1625</a>
<a href="#1626" id="1626">1626</a>
<a href="#1627" id="1627">1627</a>
<a href="#1628" id="1628">1628</a>
<a href="#1629" id="1629">1629</a>
<a href="#1630" id="1630">1630</a>
<a href="#1631" id="1631">1631</a>
<a href="#1632" id="1632">1632</a>
<a href="#1633" id="1633">1633</a>
<a href="#1634" id="1634">1634</a>
<a href="#1635" id="1635">1635</a>
<a href="#1636" id="1636">1636</a>
<a href="#1637" id="1637">1637</a>
<a href="#1638" id="1638">1638</a>
<a href="#1639" id="1639">1639</a>
<a href="#1640" id="1640">1640</a>
<a href="#1641" id="1641">1641</a>
<a href="#1642" id="1642">1642</a>
<a href="#1643" id="1643">1643</a>
<a href="#1644" id="1644">1644</a>
<a href="#1645" id="1645">1645</a>
<a href="#1646" id="1646">1646</a>
<a href="#1647" id="1647">1647</a>
<a href="#1648" id="1648">1648</a>
<a href="#1649" id="1649">1649</a>
<a href="#1650" id="1650">1650</a>
<a href="#1651" id="1651">1651</a>
<a href="#1652" id="1652">1652</a>
<a href="#1653" id="1653">1653</a>
<a href="#1654" id="1654">1654</a>
<a href="#1655" id="1655">1655</a>
<a href="#1656" id="1656">1656</a>
<a href="#1657" id="1657">1657</a>
<a href="#1658" id="1658">1658</a>
<a href="#1659" id="1659">1659</a>
<a href="#1660" id="1660">1660</a>
<a href="#1661" id="1661">1661</a>
<a href="#1662" id="1662">1662</a>
<a href="#1663" id="1663">1663</a>
<a href="#1664" id="1664">1664</a>
<a href="#1665" id="1665">1665</a>
<a href="#1666" id="1666">1666</a>
<a href="#1667" id="1667">1667</a>
<a href="#1668" id="1668">1668</a>
<a href="#1669" id="1669">1669</a>
<a href="#1670" id="1670">1670</a>
<a href="#1671" id="1671">1671</a>
<a href="#1672" id="1672">1672</a>
<a href="#1673" id="1673">1673</a>
<a href="#1674" id="1674">1674</a>
<a href="#1675" id="1675">1675</a>
<a href="#1676" id="1676">1676</a>
<a href="#1677" id="1677">1677</a>
<a href="#1678" id="1678">1678</a>
<a href="#1679" id="1679">1679</a>
<a href="#1680" id="1680">1680</a>
<a href="#1681" id="1681">1681</a>
<a href="#1682" id="1682">1682</a>
<a href="#1683" id="1683">1683</a>
<a href="#1684" id="1684">1684</a>
<a href="#1685" id="1685">1685</a>
<a href="#1686" id="1686">1686</a>
<a href="#1687" id="1687">1687</a>
<a href="#1688" id="1688">1688</a>
<a href="#1689" id="1689">1689</a>
<a href="#1690" id="1690">1690</a>
<a href="#1691" id="1691">1691</a>
<a href="#1692" id="1692">1692</a>
<a href="#1693" id="1693">1693</a>
<a href="#1694" id="1694">1694</a>
<a href="#1695" id="1695">1695</a>
<a href="#1696" id="1696">1696</a>
<a href="#1697" id="1697">1697</a>
<a href="#1698" id="1698">1698</a>
<a href="#1699" id="1699">1699</a>
<a href="#1700" id="1700">1700</a>
<a href="#1701" id="1701">1701</a>
<a href="#1702" id="1702">1702</a>
<a href="#1703" id="1703">1703</a>
<a href="#1704" id="1704">1704</a>
<a href="#1705" id="1705">1705</a>
<a href="#1706" id="1706">1706</a>
<a href="#1707" id="1707">1707</a>
<a href="#1708" id="1708">1708</a>
<a href="#1709" id="1709">1709</a>
<a href="#1710" id="1710">1710</a>
<a href="#1711" id="1711">1711</a>
<a href="#1712" id="1712">1712</a>
<a href="#1713" id="1713">1713</a>
<a href="#1714" id="1714">1714</a>
<a href="#1715" id="1715">1715</a>
<a href="#1716" id="1716">1716</a>
<a href="#1717" id="1717">1717</a>
<a href="#1718" id="1718">1718</a>
<a href="#1719" id="1719">1719</a>
<a href="#1720" id="1720">1720</a>
<a href="#1721" id="1721">1721</a>
<a href="#1722" id="1722">1722</a>
<a href="#1723" id="1723">1723</a>
<a href="#1724" id="1724">1724</a>
<a href="#1725" id="1725">1725</a>
<a href="#1726" id="1726">1726</a>
<a href="#1727" id="1727">1727</a>
<a href="#1728" id="1728">1728</a>
<a href="#1729" id="1729">1729</a>
<a href="#1730" id="1730">1730</a>
<a href="#1731" id="1731">1731</a>
<a href="#1732" id="1732">1732</a>
<a href="#1733" id="1733">1733</a>
<a href="#1734" id="1734">1734</a>
<a href="#1735" id="1735">1735</a>
<a href="#1736" id="1736">1736</a>
<a href="#1737" id="1737">1737</a>
<a href="#1738" id="1738">1738</a>
<a href="#1739" id="1739">1739</a>
<a href="#1740" id="1740">1740</a>
<a href="#1741" id="1741">1741</a>
<a href="#1742" id="1742">1742</a>
<a href="#1743" id="1743">1743</a>
<a href="#1744" id="1744">1744</a>
<a href="#1745" id="1745">1745</a>
<a href="#1746" id="1746">1746</a>
<a href="#1747" id="1747">1747</a>
<a href="#1748" id="1748">1748</a>
<a href="#1749" id="1749">1749</a>
<a href="#1750" id="1750">1750</a>
<a href="#1751" id="1751">1751</a>
<a href="#1752" id="1752">1752</a>
<a href="#1753" id="1753">1753</a>
<a href="#1754" id="1754">1754</a>
<a href="#1755" id="1755">1755</a>
<a href="#1756" id="1756">1756</a>
<a href="#1757" id="1757">1757</a>
<a href="#1758" id="1758">1758</a>
<a href="#1759" id="1759">1759</a>
<a href="#1760" id="1760">1760</a>
<a href="#1761" id="1761">1761</a>
<a href="#1762" id="1762">1762</a>
<a href="#1763" id="1763">1763</a>
<a href="#1764" id="1764">1764</a>
<a href="#1765" id="1765">1765</a>
<a href="#1766" id="1766">1766</a>
<a href="#1767" id="1767">1767</a>
<a href="#1768" id="1768">1768</a>
<a href="#1769" id="1769">1769</a>
<a href="#1770" id="1770">1770</a>
<a href="#1771" id="1771">1771</a>
<a href="#1772" id="1772">1772</a>
<a href="#1773" id="1773">1773</a>
<a href="#1774" id="1774">1774</a>
<a href="#1775" id="1775">1775</a>
<a href="#1776" id="1776">1776</a>
<a href="#1777" id="1777">1777</a>
<a href="#1778" id="1778">1778</a>
<a href="#1779" id="1779">1779</a>
<a href="#1780" id="1780">1780</a>
<a href="#1781" id="1781">1781</a>
<a href="#1782" id="1782">1782</a>
<a href="#1783" id="1783">1783</a>
<a href="#1784" id="1784">1784</a>
<a href="#1785" id="1785">1785</a>
<a href="#1786" id="1786">1786</a>
<a href="#1787" id="1787">1787</a>
<a href="#1788" id="1788">1788</a>
<a href="#1789" id="1789">1789</a>
<a href="#1790" id="1790">1790</a>
<a href="#1791" id="1791">1791</a>
<a href="#1792" id="1792">1792</a>
<a href="#1793" id="1793">1793</a>
<a href="#1794" id="1794">1794</a>
<a href="#1795" id="1795">1795</a>
<a href="#1796" id="1796">1796</a>
<a href="#1797" id="1797">1797</a>
<a href="#1798" id="1798">1798</a>
<a href="#1799" id="1799">1799</a>
<a href="#1800" id="1800">1800</a>
<a href="#1801" id="1801">1801</a>
<a href="#1802" id="1802">1802</a>
<a href="#1803" id="1803">1803</a>
<a href="#1804" id="1804">1804</a>
<a href="#1805" id="1805">1805</a>
<a href="#1806" id="1806">1806</a>
<a href="#1807" id="1807">1807</a>
<a href="#1808" id="1808">1808</a>
<a href="#1809" id="1809">1809</a>
<a href="#1810" id="1810">1810</a>
<a href="#1811" id="1811">1811</a>
<a href="#1812" id="1812">1812</a>
<a href="#1813" id="1813">1813</a>
<a href="#1814" id="1814">1814</a>
<a href="#1815" id="1815">1815</a>
<a href="#1816" id="1816">1816</a>
<a href="#1817" id="1817">1817</a>
<a href="#1818" id="1818">1818</a>
<a href="#1819" id="1819">1819</a>
<a href="#1820" id="1820">1820</a>
<a href="#1821" id="1821">1821</a>
<a href="#1822" id="1822">1822</a>
<a href="#1823" id="1823">1823</a>
<a href="#1824" id="1824">1824</a>
<a href="#1825" id="1825">1825</a>
<a href="#1826" id="1826">1826</a>
<a href="#1827" id="1827">1827</a>
<a href="#1828" id="1828">1828</a>
<a href="#1829" id="1829">1829</a>
<a href="#1830" id="1830">1830</a>
<a href="#1831" id="1831">1831</a>
<a href="#1832" id="1832">1832</a>
<a href="#1833" id="1833">1833</a>
<a href="#1834" id="1834">1834</a>
<a href="#1835" id="1835">1835</a>
<a href="#1836" id="1836">1836</a>
<a href="#1837" id="1837">1837</a>
<a href="#1838" id="1838">1838</a>
<a href="#1839" id="1839">1839</a>
<a href="#1840" id="1840">1840</a>
<a href="#1841" id="1841">1841</a>
<a href="#1842" id="1842">1842</a>
<a href="#1843" id="1843">1843</a>
<a href="#1844" id="1844">1844</a>
<a href="#1845" id="1845">1845</a>
<a href="#1846" id="1846">1846</a>
<a href="#1847" id="1847">1847</a>
<a href="#1848" id="1848">1848</a>
<a href="#1849" id="1849">1849</a>
<a href="#1850" id="1850">1850</a>
<a href="#1851" id="1851">1851</a>
<a href="#1852" id="1852">1852</a>
<a href="#1853" id="1853">1853</a>
<a href="#1854" id="1854">1854</a>
<a href="#1855" id="1855">1855</a>
<a href="#1856" id="1856">1856</a>
<a href="#1857" id="1857">1857</a>
<a href="#1858" id="1858">1858</a>
<a href="#1859" id="1859">1859</a>
<a href="#1860" id="1860">1860</a>
<a href="#1861" id="1861">1861</a>
<a href="#1862" id="1862">1862</a>
<a href="#1863" id="1863">1863</a>
<a href="#1864" id="1864">1864</a>
<a href="#1865" id="1865">1865</a>
<a href="#1866" id="1866">1866</a>
<a href="#1867" id="1867">1867</a>
<a href="#1868" id="1868">1868</a>
<a href="#1869" id="1869">1869</a>
<a href="#1870" id="1870">1870</a>
<a href="#1871" id="1871">1871</a>
<a href="#1872" id="1872">1872</a>
<a href="#1873" id="1873">1873</a>
<a href="#1874" id="1874">1874</a>
<a href="#1875" id="1875">1875</a>
<a href="#1876" id="1876">1876</a>
<a href="#1877" id="1877">1877</a>
<a href="#1878" id="1878">1878</a>
<a href="#1879" id="1879">1879</a>
<a href="#1880" id="1880">1880</a>
<a href="#1881" id="1881">1881</a>
<a href="#1882" id="1882">1882</a>
<a href="#1883" id="1883">1883</a>
<a href="#1884" id="1884">1884</a>
<a href="#1885" id="1885">1885</a>
<a href="#1886" id="1886">1886</a>
<a href="#1887" id="1887">1887</a>
<a href="#1888" id="1888">1888</a>
<a href="#1889" id="1889">1889</a>
<a href="#1890" id="1890">1890</a>
<a href="#1891" id="1891">1891</a>
<a href="#1892" id="1892">1892</a>
<a href="#1893" id="1893">1893</a>
<a href="#1894" id="1894">1894</a>
<a href="#1895" id="1895">1895</a>
<a href="#1896" id="1896">1896</a>
<a href="#1897" id="1897">1897</a>
<a href="#1898" id="1898">1898</a>
<a href="#1899" id="1899">1899</a>
<a href="#1900" id="1900">1900</a>
<a href="#1901" id="1901">1901</a>
<a href="#1902" id="1902">1902</a>
<a href="#1903" id="1903">1903</a>
<a href="#1904" id="1904">1904</a>
<a href="#1905" id="1905">1905</a>
<a href="#1906" id="1906">1906</a>
<a href="#1907" id="1907">1907</a>
<a href="#1908" id="1908">1908</a>
<a href="#1909" id="1909">1909</a>
<a href="#1910" id="1910">1910</a>
<a href="#1911" id="1911">1911</a>
<a href="#1912" id="1912">1912</a>
<a href="#1913" id="1913">1913</a>
<a href="#1914" id="1914">1914</a>
<a href="#1915" id="1915">1915</a>
<a href="#1916" id="1916">1916</a>
<a href="#1917" id="1917">1917</a>
<a href="#1918" id="1918">1918</a>
<a href="#1919" id="1919">1919</a>
<a href="#1920" id="1920">1920</a>
<a href="#1921" id="1921">1921</a>
<a href="#1922" id="1922">1922</a>
<a href="#1923" id="1923">1923</a>
<a href="#1924" id="1924">1924</a>
<a href="#1925" id="1925">1925</a>
<a href="#1926" id="1926">1926</a>
<a href="#1927" id="1927">1927</a>
<a href="#1928" id="1928">1928</a>
<a href="#1929" id="1929">1929</a>
<a href="#1930" id="1930">1930</a>
<a href="#1931" id="1931">1931</a>
<a href="#1932" id="1932">1932</a>
<a href="#1933" id="1933">1933</a>
<a href="#1934" id="1934">1934</a>
<a href="#1935" id="1935">1935</a>
<a href="#1936" id="1936">1936</a>
<a href="#1937" id="1937">1937</a>
<a href="#1938" id="1938">1938</a>
<a href="#1939" id="1939">1939</a>
<a href="#1940" id="1940">1940</a>
<a href="#1941" id="1941">1941</a>
<a href="#1942" id="1942">1942</a>
<a href="#1943" id="1943">1943</a>
<a href="#1944" id="1944">1944</a>
<a href="#1945" id="1945">1945</a>
<a href="#1946" id="1946">1946</a>
<a href="#1947" id="1947">1947</a>
<a href="#1948" id="1948">1948</a>
<a href="#1949" id="1949">1949</a>
<a href="#1950" id="1950">1950</a>
<a href="#1951" id="1951">1951</a>
<a href="#1952" id="1952">1952</a>
<a href="#1953" id="1953">1953</a>
<a href="#1954" id="1954">1954</a>
<a href="#1955" id="1955">1955</a>
<a href="#1956" id="1956">1956</a>
<a href="#1957" id="1957">1957</a>
<a href="#1958" id="1958">1958</a>
<a href="#1959" id="1959">1959</a>
<a href="#1960" id="1960">1960</a>
<a href="#1961" id="1961">1961</a>
<a href="#1962" id="1962">1962</a>
<a href="#1963" id="1963">1963</a>
<a href="#1964" id="1964">1964</a>
<a href="#1965" id="1965">1965</a>
<a href="#1966" id="1966">1966</a>
<a href="#1967" id="1967">1967</a>
<a href="#1968" id="1968">1968</a>
<a href="#1969" id="1969">1969</a>
<a href="#1970" id="1970">1970</a>
<a href="#1971" id="1971">1971</a>
<a href="#1972" id="1972">1972</a>
<a href="#1973" id="1973">1973</a>
<a href="#1974" id="1974">1974</a>
<a href="#1975" id="1975">1975</a>
<a href="#1976" id="1976">1976</a>
<a href="#1977" id="1977">1977</a>
<a href="#1978" id="1978">1978</a>
<a href="#1979" id="1979">1979</a>
<a href="#1980" id="1980">1980</a>
<a href="#1981" id="1981">1981</a>
<a href="#1982" id="1982">1982</a>
<a href="#1983" id="1983">1983</a>
<a href="#1984" id="1984">1984</a>
<a href="#1985" id="1985">1985</a>
<a href="#1986" id="1986">1986</a>
<a href="#1987" id="1987">1987</a>
<a href="#1988" id="1988">1988</a>
<a href="#1989" id="1989">1989</a>
<a href="#1990" id="1990">1990</a>
<a href="#1991" id="1991">1991</a>
<a href="#1992" id="1992">1992</a>
<a href="#1993" id="1993">1993</a>
<a href="#1994" id="1994">1994</a>
<a href="#1995" id="1995">1995</a>
<a href="#1996" id="1996">1996</a>
<a href="#1997" id="1997">1997</a>
<a href="#1998" id="1998">1998</a>
<a href="#1999" id="1999">1999</a>
<a href="#2000" id="2000">2000</a>
<a href="#2001" id="2001">2001</a>
<a href="#2002" id="2002">2002</a>
<a href="#2003" id="2003">2003</a>
<a href="#2004" id="2004">2004</a>
<a href="#2005" id="2005">2005</a>
<a href="#2006" id="2006">2006</a>
<a href="#2007" id="2007">2007</a>
<a href="#2008" id="2008">2008</a>
<a href="#2009" id="2009">2009</a>
<a href="#2010" id="2010">2010</a>
<a href="#2011" id="2011">2011</a>
<a href="#2012" id="2012">2012</a>
<a href="#2013" id="2013">2013</a>
<a href="#2014" id="2014">2014</a>
<a href="#2015" id="2015">2015</a>
<a href="#2016" id="2016">2016</a>
<a href="#2017" id="2017">2017</a>
<a href="#2018" id="2018">2018</a>
<a href="#2019" id="2019">2019</a>
<a href="#2020" id="2020">2020</a>
<a href="#2021" id="2021">2021</a>
<a href="#2022" id="2022">2022</a>
<a href="#2023" id="2023">2023</a>
<a href="#2024" id="2024">2024</a>
<a href="#2025" id="2025">2025</a>
<a href="#2026" id="2026">2026</a>
<a href="#2027" id="2027">2027</a>
<a href="#2028" id="2028">2028</a>
<a href="#2029" id="2029">2029</a>
<a href="#2030" id="2030">2030</a>
<a href="#2031" id="2031">2031</a>
<a href="#2032" id="2032">2032</a>
<a href="#2033" id="2033">2033</a>
<a href="#2034" id="2034">2034</a>
<a href="#2035" id="2035">2035</a>
<a href="#2036" id="2036">2036</a>
<a href="#2037" id="2037">2037</a>
<a href="#2038" id="2038">2038</a>
<a href="#2039" id="2039">2039</a>
<a href="#2040" id="2040">2040</a>
<a href="#2041" id="2041">2041</a>
<a href="#2042" id="2042">2042</a>
<a href="#2043" id="2043">2043</a>
<a href="#2044" id="2044">2044</a>
<a href="#2045" id="2045">2045</a>
<a href="#2046" id="2046">2046</a>
<a href="#2047" id="2047">2047</a>
<a href="#2048" id="2048">2048</a>
<a href="#2049" id="2049">2049</a>
<a href="#2050" id="2050">2050</a>
<a href="#2051" id="2051">2051</a>
<a href="#2052" id="2052">2052</a>
<a href="#2053" id="2053">2053</a>
<a href="#2054" id="2054">2054</a>
<a href="#2055" id="2055">2055</a>
<a href="#2056" id="2056">2056</a>
<a href="#2057" id="2057">2057</a>
<a href="#2058" id="2058">2058</a>
<a href="#2059" id="2059">2059</a>
<a href="#2060" id="2060">2060</a>
<a href="#2061" id="2061">2061</a>
<a href="#2062" id="2062">2062</a>
<a href="#2063" id="2063">2063</a>
<a href="#2064" id="2064">2064</a>
<a href="#2065" id="2065">2065</a>
<a href="#2066" id="2066">2066</a>
<a href="#2067" id="2067">2067</a>
<a href="#2068" id="2068">2068</a>
<a href="#2069" id="2069">2069</a>
<a href="#2070" id="2070">2070</a>
<a href="#2071" id="2071">2071</a>
<a href="#2072" id="2072">2072</a>
<a href="#2073" id="2073">2073</a>
<a href="#2074" id="2074">2074</a>
<a href="#2075" id="2075">2075</a>
<a href="#2076" id="2076">2076</a>
<a href="#2077" id="2077">2077</a>
<a href="#2078" id="2078">2078</a>
<a href="#2079" id="2079">2079</a>
<a href="#2080" id="2080">2080</a>
<a href="#2081" id="2081">2081</a>
<a href="#2082" id="2082">2082</a>
<a href="#2083" id="2083">2083</a>
<a href="#2084" id="2084">2084</a>
<a href="#2085" id="2085">2085</a>
<a href="#2086" id="2086">2086</a>
<a href="#2087" id="2087">2087</a>
<a href="#2088" id="2088">2088</a>
<a href="#2089" id="2089">2089</a>
<a href="#2090" id="2090">2090</a>
<a href="#2091" id="2091">2091</a>
<a href="#2092" id="2092">2092</a>
<a href="#2093" id="2093">2093</a>
<a href="#2094" id="2094">2094</a>
<a href="#2095" id="2095">2095</a>
<a href="#2096" id="2096">2096</a>
<a href="#2097" id="2097">2097</a>
<a href="#2098" id="2098">2098</a>
<a href="#2099" id="2099">2099</a>
<a href="#2100" id="2100">2100</a>
<a href="#2101" id="2101">2101</a>
<a href="#2102" id="2102">2102</a>
<a href="#2103" id="2103">2103</a>
<a href="#2104" id="2104">2104</a>
<a href="#2105" id="2105">2105</a>
<a href="#2106" id="2106">2106</a>
<a href="#2107" id="2107">2107</a>
<a href="#2108" id="2108">2108</a>
<a href="#2109" id="2109">2109</a>
<a href="#2110" id="2110">2110</a>
<a href="#2111" id="2111">2111</a>
<a href="#2112" id="2112">2112</a>
<a href="#2113" id="2113">2113</a>
<a href="#2114" id="2114">2114</a>
<a href="#2115" id="2115">2115</a>
<a href="#2116" id="2116">2116</a>
<a href="#2117" id="2117">2117</a>
<a href="#2118" id="2118">2118</a>
<a href="#2119" id="2119">2119</a>
<a href="#2120" id="2120">2120</a>
<a href="#2121" id="2121">2121</a>
<a href="#2122" id="2122">2122</a>
<a href="#2123" id="2123">2123</a>
<a href="#2124" id="2124">2124</a>
<a href="#2125" id="2125">2125</a>
<a href="#2126" id="2126">2126</a>
<a href="#2127" id="2127">2127</a>
<a href="#2128" id="2128">2128</a>
<a href="#2129" id="2129">2129</a>
<a href="#2130" id="2130">2130</a>
<a href="#2131" id="2131">2131</a>
<a href="#2132" id="2132">2132</a>
<a href="#2133" id="2133">2133</a>
<a href="#2134" id="2134">2134</a>
<a href="#2135" id="2135">2135</a>
<a href="#2136" id="2136">2136</a>
<a href="#2137" id="2137">2137</a>
<a href="#2138" id="2138">2138</a>
<a href="#2139" id="2139">2139</a>
<a href="#2140" id="2140">2140</a>
<a href="#2141" id="2141">2141</a>
<a href="#2142" id="2142">2142</a>
<a href="#2143" id="2143">2143</a>
<a href="#2144" id="2144">2144</a>
<a href="#2145" id="2145">2145</a>
<a href="#2146" id="2146">2146</a>
<a href="#2147" id="2147">2147</a>
<a href="#2148" id="2148">2148</a>
<a href="#2149" id="2149">2149</a>
<a href="#2150" id="2150">2150</a>
<a href="#2151" id="2151">2151</a>
<a href="#2152" id="2152">2152</a>
<a href="#2153" id="2153">2153</a>
<a href="#2154" id="2154">2154</a>
<a href="#2155" id="2155">2155</a>
<a href="#2156" id="2156">2156</a>
<a href="#2157" id="2157">2157</a>
<a href="#2158" id="2158">2158</a>
<a href="#2159" id="2159">2159</a>
<a href="#2160" id="2160">2160</a>
<a href="#2161" id="2161">2161</a>
<a href="#2162" id="2162">2162</a>
<a href="#2163" id="2163">2163</a>
<a href="#2164" id="2164">2164</a>
<a href="#2165" id="2165">2165</a>
<a href="#2166" id="2166">2166</a>
<a href="#2167" id="2167">2167</a>
<a href="#2168" id="2168">2168</a>
<a href="#2169" id="2169">2169</a>
<a href="#2170" id="2170">2170</a>
<a href="#2171" id="2171">2171</a>
<a href="#2172" id="2172">2172</a>
<a href="#2173" id="2173">2173</a>
<a href="#2174" id="2174">2174</a>
<a href="#2175" id="2175">2175</a>
<a href="#2176" id="2176">2176</a>
<a href="#2177" id="2177">2177</a>
<a href="#2178" id="2178">2178</a>
<a href="#2179" id="2179">2179</a>
<a href="#2180" id="2180">2180</a>
<a href="#2181" id="2181">2181</a>
<a href="#2182" id="2182">2182</a>
<a href="#2183" id="2183">2183</a>
<a href="#2184" id="2184">2184</a>
<a href="#2185" id="2185">2185</a>
<a href="#2186" id="2186">2186</a>
<a href="#2187" id="2187">2187</a>
<a href="#2188" id="2188">2188</a>
<a href="#2189" id="2189">2189</a>
<a href="#2190" id="2190">2190</a>
<a href="#2191" id="2191">2191</a>
<a href="#2192" id="2192">2192</a>
<a href="#2193" id="2193">2193</a>
<a href="#2194" id="2194">2194</a>
<a href="#2195" id="2195">2195</a>
<a href="#2196" id="2196">2196</a>
<a href="#2197" id="2197">2197</a>
<a href="#2198" id="2198">2198</a>
<a href="#2199" id="2199">2199</a>
<a href="#2200" id="2200">2200</a>
<a href="#2201" id="2201">2201</a>
<a href="#2202" id="2202">2202</a>
<a href="#2203" id="2203">2203</a>
<a href="#2204" id="2204">2204</a>
<a href="#2205" id="2205">2205</a>
<a href="#2206" id="2206">2206</a>
<a href="#2207" id="2207">2207</a>
<a href="#2208" id="2208">2208</a>
<a href="#2209" id="2209">2209</a>
<a href="#2210" id="2210">2210</a>
<a href="#2211" id="2211">2211</a>
<a href="#2212" id="2212">2212</a>
<a href="#2213" id="2213">2213</a>
<a href="#2214" id="2214">2214</a>
<a href="#2215" id="2215">2215</a>
<a href="#2216" id="2216">2216</a>
<a href="#2217" id="2217">2217</a>
<a href="#2218" id="2218">2218</a>
<a href="#2219" id="2219">2219</a>
<a href="#2220" id="2220">2220</a>
<a href="#2221" id="2221">2221</a>
<a href="#2222" id="2222">2222</a>
<a href="#2223" id="2223">2223</a>
<a href="#2224" id="2224">2224</a>
<a href="#2225" id="2225">2225</a>
<a href="#2226" id="2226">2226</a>
<a href="#2227" id="2227">2227</a>
<a href="#2228" id="2228">2228</a>
<a href="#2229" id="2229">2229</a>
<a href="#2230" id="2230">2230</a>
<a href="#2231" id="2231">2231</a>
<a href="#2232" id="2232">2232</a>
<a href="#2233" id="2233">2233</a>
<a href="#2234" id="2234">2234</a>
<a href="#2235" id="2235">2235</a>
<a href="#2236" id="2236">2236</a>
<a href="#2237" id="2237">2237</a>
<a href="#2238" id="2238">2238</a>
<a href="#2239" id="2239">2239</a>
<a href="#2240" id="2240">2240</a>
<a href="#2241" id="2241">2241</a>
<a href="#2242" id="2242">2242</a>
<a href="#2243" id="2243">2243</a>
<a href="#2244" id="2244">2244</a>
<a href="#2245" id="2245">2245</a>
<a href="#2246" id="2246">2246</a>
</pre><pre class="rust"><code><span class="kw">use </span>num::{One, Zero};
<span class="kw">use </span>approx::{AbsDiffEq, RelativeEq, UlpsEq};
<span class="kw">use </span>std::any::TypeId;
<span class="kw">use </span>std::cmp::Ordering;
<span class="kw">use </span>std::fmt;
<span class="kw">use </span>std::hash::{Hash, Hasher};
<span class="kw">use </span>std::marker::PhantomData;
<span class="kw">use </span>std::mem;
<span class="attr">#[cfg(feature = <span class="string">"serde-serialize-no-std"</span>)]
</span><span class="kw">use </span>serde::{Deserialize, Deserializer, Serialize, Serializer};
<span class="attr">#[cfg(feature = <span class="string">"rkyv-serialize-no-std"</span>)]
</span><span class="kw">use </span><span class="kw">super</span>::rkyv_wrappers::CustomPhantom;
<span class="attr">#[cfg(feature = <span class="string">"rkyv-serialize-no-std"</span>)]
</span><span class="kw">use </span>rkyv::{with::With, Archive, Archived};
<span class="kw">use </span>simba::scalar::{ClosedAdd, ClosedMul, ClosedSub, Field, SupersetOf};
<span class="kw">use </span>simba::simd::SimdPartialOrd;
<span class="kw">use </span><span class="kw">crate</span>::base::allocator::{Allocator, SameShapeAllocator, SameShapeC, SameShapeR};
<span class="kw">use </span><span class="kw">crate</span>::base::constraint::{DimEq, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
<span class="kw">use </span><span class="kw">crate</span>::base::dimension::{Dim, DimAdd, DimSum, IsNotStaticOne, U1, U2, U3};
<span class="kw">use </span><span class="kw">crate</span>::base::iter::{
ColumnIter, ColumnIterMut, MatrixIter, MatrixIterMut, RowIter, RowIterMut,
};
<span class="kw">use </span><span class="kw">crate</span>::base::storage::{Owned, RawStorage, RawStorageMut, SameShapeStorage};
<span class="kw">use </span><span class="kw">crate</span>::base::{Const, DefaultAllocator, OMatrix, OVector, Scalar, Unit};
<span class="kw">use crate</span>::{ArrayStorage, SMatrix, SimdComplexField, Storage, UninitMatrix};
<span class="kw">use </span><span class="kw">crate</span>::storage::IsContiguous;
<span class="kw">use </span><span class="kw">crate</span>::uninit::{Init, InitStatus, Uninit};
<span class="attr">#[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"alloc"</span>))]
</span><span class="kw">use crate</span>::{DMatrix, DVector, Dyn, RowDVector, VecStorage};
<span class="kw">use </span>std::mem::MaybeUninit;
<span class="doccomment">/// A square matrix.
</span><span class="kw">pub type </span>SquareMatrix<T, D, S> = Matrix<T, D, D, S>;
<span class="doccomment">/// A matrix with one column and `D` rows.
</span><span class="kw">pub type </span>Vector<T, D, S> = Matrix<T, D, U1, S>;
<span class="doccomment">/// A matrix with one row and `D` columns .
</span><span class="kw">pub type </span>RowVector<T, D, S> = Matrix<T, U1, D, S>;
<span class="doccomment">/// The type of the result of a matrix sum.
</span><span class="kw">pub type </span>MatrixSum<T, R1, C1, R2, C2> =
Matrix<T, SameShapeR<R1, R2>, SameShapeC<C1, C2>, SameShapeStorage<T, R1, C1, R2, C2>>;
<span class="doccomment">/// The type of the result of a matrix sum.
</span><span class="kw">pub type </span>VectorSum<T, R1, R2> =
Matrix<T, SameShapeR<R1, R2>, U1, SameShapeStorage<T, R1, U1, R2, U1>>;
<span class="doccomment">/// The type of the result of a matrix cross product.
</span><span class="kw">pub type </span>MatrixCross<T, R1, C1, R2, C2> =
Matrix<T, SameShapeR<R1, R2>, SameShapeC<C1, C2>, SameShapeStorage<T, R1, C1, R2, C2>>;
<span class="doccomment">/// The most generic column-major matrix (and vector) type.
///
/// # Methods summary
/// Because `Matrix` is the most generic types used as a common representation of all matrices and
/// vectors of **nalgebra** this documentation page contains every single matrix/vector-related
/// method. In order to make browsing this page simpler, the next subsections contain direct links
/// to groups of methods related to a specific topic.
///
/// #### Vector and matrix construction
/// - [Constructors of statically-sized vectors or statically-sized matrices](#constructors-of-statically-sized-vectors-or-statically-sized-matrices)
/// (`Vector3`, `Matrix3x6`…)
/// - [Constructors of fully dynamic matrices](#constructors-of-fully-dynamic-matrices) (`DMatrix`)
/// - [Constructors of dynamic vectors and matrices with a dynamic number of rows](#constructors-of-dynamic-vectors-and-matrices-with-a-dynamic-number-of-rows)
/// (`DVector`, `MatrixXx3`…)
/// - [Constructors of matrices with a dynamic number of columns](#constructors-of-matrices-with-a-dynamic-number-of-columns)
/// (`Matrix2xX`…)
/// - [Generic constructors](#generic-constructors)
/// (For code generic wrt. the vectors or matrices dimensions.)
///
/// #### Computer graphics utilities for transformations
/// - [2D transformations as a Matrix3 <span style="float:right;">`new_rotation`…</span>](#2d-transformations-as-a-matrix3)
/// - [3D transformations as a Matrix4 <span style="float:right;">`new_rotation`, `new_perspective`, `look_at_rh`…</span>](#3d-transformations-as-a-matrix4)
/// - [Translation and scaling in any dimension <span style="float:right;">`new_scaling`, `new_translation`…</span>](#translation-and-scaling-in-any-dimension)
/// - [Append/prepend translation and scaling <span style="float:right;">`append_scaling`, `prepend_translation_mut`…</span>](#appendprepend-translation-and-scaling)
/// - [Transformation of vectors and points <span style="float:right;">`transform_vector`, `transform_point`…</span>](#transformation-of-vectors-and-points)
///
/// #### Common math operations
/// - [Componentwise operations <span style="float:right;">`component_mul`, `component_div`, `inf`…</span>](#componentwise-operations)
/// - [Special multiplications <span style="float:right;">`tr_mul`, `ad_mul`, `kronecker`…</span>](#special-multiplications)
/// - [Dot/scalar product <span style="float:right;">`dot`, `dotc`, `tr_dot`…</span>](#dotscalar-product)
/// - [Cross product <span style="float:right;">`cross`, `perp`…</span>](#cross-product)
/// - [Magnitude and norms <span style="float:right;">`norm`, `normalize`, `metric_distance`…</span>](#magnitude-and-norms)
/// - [In-place normalization <span style="float:right;">`normalize_mut`, `try_normalize_mut`…</span>](#in-place-normalization)
/// - [Interpolation <span style="float:right;">`lerp`, `slerp`…</span>](#interpolation)
/// - [BLAS functions <span style="float:right;">`gemv`, `gemm`, `syger`…</span>](#blas-functions)
/// - [Swizzling <span style="float:right;">`xx`, `yxz`…</span>](#swizzling)
/// - [Triangular matrix extraction <span style="float:right;">`upper_triangle`, `lower_triangle`</span>](#triangular-matrix-extraction)
///
/// #### Statistics
/// - [Common operations <span style="float:right;">`row_sum`, `column_mean`, `variance`…</span>](#common-statistics-operations)
/// - [Find the min and max components <span style="float:right;">`min`, `max`, `amin`, `amax`, `camin`, `cmax`…</span>](#find-the-min-and-max-components)
/// - [Find the min and max components (vector-specific methods) <span style="float:right;">`argmin`, `argmax`, `icamin`, `icamax`…</span>](#find-the-min-and-max-components-vector-specific-methods)
///
/// #### Iteration, map, and fold
/// - [Iteration on components, rows, and columns <span style="float:right;">`iter`, `column_iter`…</span>](#iteration-on-components-rows-and-columns)
/// - [Parallel iterators using rayon <span style="float:right;">`par_column_iter`, `par_column_iter_mut`…</span>](#parallel-iterators-using-rayon)
/// - [Elementwise mapping and folding <span style="float:right;">`map`, `fold`, `zip_map`…</span>](#elementwise-mapping-and-folding)
/// - [Folding or columns and rows <span style="float:right;">`compress_rows`, `compress_columns`…</span>](#folding-on-columns-and-rows)
///
/// #### Vector and matrix views
/// - [Creating matrix views from `&[T]` <span style="float:right;">`from_slice`, `from_slice_with_strides`…</span>](#creating-matrix-views-from-t)
/// - [Creating mutable matrix views from `&mut [T]` <span style="float:right;">`from_slice_mut`, `from_slice_with_strides_mut`…</span>](#creating-mutable-matrix-views-from-mut-t)
/// - [Views based on index and length <span style="float:right;">`row`, `columns`, `view`…</span>](#views-based-on-index-and-length)
/// - [Mutable views based on index and length <span style="float:right;">`row_mut`, `columns_mut`, `view_mut`…</span>](#mutable-views-based-on-index-and-length)
/// - [Views based on ranges <span style="float:right;">`rows_range`, `columns_range`…</span>](#views-based-on-ranges)
/// - [Mutable views based on ranges <span style="float:right;">`rows_range_mut`, `columns_range_mut`…</span>](#mutable-views-based-on-ranges)
///
/// #### In-place modification of a single matrix or vector
/// - [In-place filling <span style="float:right;">`fill`, `fill_diagonal`, `fill_with_identity`…</span>](#in-place-filling)
/// - [In-place swapping <span style="float:right;">`swap`, `swap_columns`…</span>](#in-place-swapping)
/// - [Set rows, columns, and diagonal <span style="float:right;">`set_column`, `set_diagonal`…</span>](#set-rows-columns-and-diagonal)
///
/// #### Vector and matrix size modification
/// - [Rows and columns insertion <span style="float:right;">`insert_row`, `insert_column`…</span>](#rows-and-columns-insertion)
/// - [Rows and columns removal <span style="float:right;">`remove_row`, `remove column`…</span>](#rows-and-columns-removal)
/// - [Rows and columns extraction <span style="float:right;">`select_rows`, `select_columns`…</span>](#rows-and-columns-extraction)
/// - [Resizing and reshaping <span style="float:right;">`resize`, `reshape_generic`…</span>](#resizing-and-reshaping)
/// - [In-place resizing <span style="float:right;">`resize_mut`, `resize_vertically_mut`…</span>](#in-place-resizing)
///
/// #### Matrix decomposition
/// - [Rectangular matrix decomposition <span style="float:right;">`qr`, `lu`, `svd`…</span>](#rectangular-matrix-decomposition)
/// - [Square matrix decomposition <span style="float:right;">`cholesky`, `symmetric_eigen`…</span>](#square-matrix-decomposition)
///
/// #### Vector basis computation
/// - [Basis and orthogonalization <span style="float:right;">`orthonormal_subspace_basis`, `orthonormalize`…</span>](#basis-and-orthogonalization)
///
/// # Type parameters
/// The generic `Matrix` type has four type parameters:
/// - `T`: for the matrix components scalar type.
/// - `R`: for the matrix number of rows.
/// - `C`: for the matrix number of columns.
/// - `S`: for the matrix data storage, i.e., the buffer that actually contains the matrix
/// components.
///
/// The matrix dimensions parameters `R` and `C` can either be:
/// - type-level unsigned integer constants (e.g. `U1`, `U124`) from the `nalgebra::` root module.
/// All numbers from 0 to 127 are defined that way.
/// - type-level unsigned integer constants (e.g. `U1024`, `U10000`) from the `typenum::` crate.
/// Using those, you will not get error messages as nice as for numbers smaller than 128 defined on
/// the `nalgebra::` module.
/// - the special value `Dyn` from the `nalgebra::` root module. This indicates that the
/// specified dimension is not known at compile-time. Note that this will generally imply that the
/// matrix data storage `S` performs a dynamic allocation and contains extra metadata for the
/// matrix shape.
///
/// Note that mixing `Dyn` with type-level unsigned integers is allowed. Actually, a
/// dynamically-sized column vector should be represented as a `Matrix<T, Dyn, U1, S>` (given
/// some concrete types for `T` and a compatible data storage type `S`).
</span><span class="attr">#[repr(C)]
#[derive(Clone, Copy)]
#[cfg_attr(
feature = <span class="string">"rkyv-serialize-no-std"</span>,
derive(Archive, rkyv::Serialize, rkyv::Deserialize),
archive(
<span class="kw">as </span>= <span class="string">"Matrix<T::Archived, R, C, S::Archived>"</span>,
bound(archive = <span class="string">"
T: Archive,
S: Archive,
With<PhantomData<(T, R, C)>, CustomPhantom<(Archived<T>, R, C)>>: Archive<Archived = PhantomData<(Archived<T>, R, C)>>
"</span>)
)
)]
#[cfg_attr(feature = <span class="string">"rkyv-serialize"</span>, derive(bytecheck::CheckBytes))]
#[cfg_attr(feature = <span class="string">"cuda"</span>, derive(cust_core::DeviceCopy))]
</span><span class="kw">pub struct </span>Matrix<T, R, C, S> {
<span class="doccomment">/// The data storage that contains all the matrix components. Disappointed?
///
/// Well, if you came here to see how you can access the matrix components,
/// you may be in luck: you can access the individual components of all vectors with compile-time
/// dimensions <= 6 using field notation like this:
/// `vec.x`, `vec.y`, `vec.z`, `vec.w`, `vec.a`, `vec.b`. Reference and assignation work too:
/// ```
/// # use nalgebra::Vector3;
/// let mut vec = Vector3::new(1.0, 2.0, 3.0);
/// vec.x = 10.0;
/// vec.y += 30.0;
/// assert_eq!(vec.x, 10.0);
/// assert_eq!(vec.y + 100.0, 132.0);
/// ```
/// Similarly, for matrices with compile-time dimensions <= 6, you can use field notation
/// like this: `mat.m11`, `mat.m42`, etc. The first digit identifies the row to address
/// and the second digit identifies the column to address. So `mat.m13` identifies the component
/// at the first row and third column (note that the count of rows and columns start at 1 instead
/// of 0 here. This is so we match the mathematical notation).
///
/// For all matrices and vectors, independently from their size, individual components can
/// be accessed and modified using indexing: `vec[20]`, `mat[(20, 19)]`. Here the indexing
/// starts at 0 as you would expect.
</span><span class="kw">pub </span>data: S,
<span class="comment">// NOTE: the fact that this field is private is important because
// this prevents the user from constructing a matrix with
// dimensions R, C that don't match the dimension of the
// storage S. Instead they have to use the unsafe function
// from_data_statically_unchecked.
// Note that it would probably make sense to just have
// the type `Matrix<S>`, and have `T, R, C` be associated-types
// of the `RawStorage` trait. However, because we don't have
// specialization, this is not possible because these `T, R, C`
// allows us to desambiguate a lot of configurations.
</span><span class="attr">#[cfg_attr(feature = <span class="string">"rkyv-serialize-no-std"</span>, with(CustomPhantom<(T::Archived, R, C)>))]
</span>_phantoms: PhantomData<(T, R, C)>,
}
<span class="kw">impl</span><T, R: Dim, C: Dim, S: fmt::Debug> fmt::Debug <span class="kw">for </span>Matrix<T, R, C, S> {
<span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, formatter: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> <span class="prelude-ty">Result</span><(), fmt::Error> {
<span class="self">self</span>.data.fmt(formatter)
}
}
<span class="kw">impl</span><T, R, C, S> Default <span class="kw">for </span>Matrix<T, R, C, S>
<span class="kw">where
</span>T: Scalar,
R: Dim,
C: Dim,
S: Default,
{
<span class="kw">fn </span>default() -> <span class="self">Self </span>{
Matrix {
data: Default::default(),
_phantoms: PhantomData,
}
}
}
<span class="attr">#[cfg(feature = <span class="string">"serde-serialize-no-std"</span>)]
</span><span class="kw">impl</span><T, R, C, S> Serialize <span class="kw">for </span>Matrix<T, R, C, S>
<span class="kw">where
</span>T: Scalar,
R: Dim,
C: Dim,
S: Serialize,
{
<span class="kw">fn </span>serialize<Ser>(<span class="kw-2">&</span><span class="self">self</span>, serializer: Ser) -> <span class="prelude-ty">Result</span><Ser::Ok, Ser::Error>
<span class="kw">where
</span>Ser: Serializer,
{
<span class="self">self</span>.data.serialize(serializer)
}
}
<span class="attr">#[cfg(feature = <span class="string">"serde-serialize-no-std"</span>)]
</span><span class="kw">impl</span><<span class="lifetime">'de</span>, T, R, C, S> Deserialize<<span class="lifetime">'de</span>> <span class="kw">for </span>Matrix<T, R, C, S>
<span class="kw">where
</span>T: Scalar,
R: Dim,
C: Dim,
S: Deserialize<<span class="lifetime">'de</span>>,
{
<span class="kw">fn </span>deserialize<D>(deserializer: D) -> <span class="prelude-ty">Result</span><<span class="self">Self</span>, D::Error>
<span class="kw">where
</span>D: Deserializer<<span class="lifetime">'de</span>>,
{
S::deserialize(deserializer).map(|x| Matrix {
data: x,
_phantoms: PhantomData,
})
}
}
<span class="attr">#[cfg(feature = <span class="string">"compare"</span>)]
</span><span class="kw">impl</span><T: Scalar, R: Dim, C: Dim, S: RawStorage<T, R, C>> matrixcompare_core::Matrix<T>
<span class="kw">for </span>Matrix<T, R, C, S>
{
<span class="kw">fn </span>rows(<span class="kw-2">&</span><span class="self">self</span>) -> usize {
<span class="self">self</span>.nrows()
}
<span class="kw">fn </span>cols(<span class="kw-2">&</span><span class="self">self</span>) -> usize {
<span class="self">self</span>.ncols()
}
<span class="kw">fn </span>access(<span class="kw-2">&</span><span class="self">self</span>) -> matrixcompare_core::Access<<span class="lifetime">'_</span>, T> {
matrixcompare_core::Access::Dense(<span class="self">self</span>)
}
}
<span class="attr">#[cfg(feature = <span class="string">"compare"</span>)]
</span><span class="kw">impl</span><T: Scalar, R: Dim, C: Dim, S: RawStorage<T, R, C>> matrixcompare_core::DenseAccess<T>
<span class="kw">for </span>Matrix<T, R, C, S>
{
<span class="kw">fn </span>fetch_single(<span class="kw-2">&</span><span class="self">self</span>, row: usize, col: usize) -> T {
<span class="self">self</span>.index((row, col)).clone()
}
}
<span class="attr">#[cfg(feature = <span class="string">"bytemuck"</span>)]
</span><span class="kw">unsafe impl</span><T: Scalar, R: Dim, C: Dim, S: RawStorage<T, R, C>> bytemuck::Zeroable
<span class="kw">for </span>Matrix<T, R, C, S>
<span class="kw">where
</span>S: bytemuck::Zeroable,
{
}
<span class="attr">#[cfg(feature = <span class="string">"bytemuck"</span>)]
</span><span class="kw">unsafe impl</span><T: Scalar, R: Dim, C: Dim, S: RawStorage<T, R, C>> bytemuck::Pod <span class="kw">for </span>Matrix<T, R, C, S>
<span class="kw">where
</span>S: bytemuck::Pod,
<span class="self">Self</span>: Copy,
{
}
<span class="kw">impl</span><T, R, C, S> Matrix<T, R, C, S> {
<span class="doccomment">/// Creates a new matrix with the given data without statically checking that the matrix
/// dimension matches the storage dimension.
</span><span class="attr">#[inline(always)]
</span><span class="kw">pub const unsafe fn </span>from_data_statically_unchecked(data: S) -> Matrix<T, R, C, S> {
Matrix {
data,
_phantoms: PhantomData,
}
}
}
<span class="kw">impl</span><T, <span class="kw">const </span>R: usize, <span class="kw">const </span>C: usize> SMatrix<T, R, C> {
<span class="doccomment">/// Creates a new statically-allocated matrix from the given [`ArrayStorage`].
///
/// This method exists primarily as a workaround for the fact that `from_data` can not
/// work in `const fn` contexts.
</span><span class="attr">#[inline(always)]
</span><span class="kw">pub const fn </span>from_array_storage(storage: ArrayStorage<T, R, C>) -> <span class="self">Self </span>{
<span class="comment">// This is sound because the row and column types are exactly the same as that of the
// storage, so there can be no mismatch
</span><span class="kw">unsafe </span>{ <span class="self">Self</span>::from_data_statically_unchecked(storage) }
}
}
<span class="comment">// TODO: Consider removing/deprecating `from_vec_storage` once we are able to make
// `from_data` const fn compatible
</span><span class="attr">#[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"alloc"</span>))]
</span><span class="kw">impl</span><T> DMatrix<T> {
<span class="doccomment">/// Creates a new heap-allocated matrix from the given [`VecStorage`].
///
/// This method exists primarily as a workaround for the fact that `from_data` can not
/// work in `const fn` contexts.
</span><span class="kw">pub const fn </span>from_vec_storage(storage: VecStorage<T, Dyn, Dyn>) -> <span class="self">Self </span>{
<span class="comment">// This is sound because the dimensions of the matrix and the storage are guaranteed
// to be the same
</span><span class="kw">unsafe </span>{ <span class="self">Self</span>::from_data_statically_unchecked(storage) }
}
}
<span class="comment">// TODO: Consider removing/deprecating `from_vec_storage` once we are able to make
// `from_data` const fn compatible
</span><span class="attr">#[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"alloc"</span>))]
</span><span class="kw">impl</span><T> DVector<T> {
<span class="doccomment">/// Creates a new heap-allocated matrix from the given [`VecStorage`].
///
/// This method exists primarily as a workaround for the fact that `from_data` can not
/// work in `const fn` contexts.
</span><span class="kw">pub const fn </span>from_vec_storage(storage: VecStorage<T, Dyn, U1>) -> <span class="self">Self </span>{
<span class="comment">// This is sound because the dimensions of the matrix and the storage are guaranteed
// to be the same
</span><span class="kw">unsafe </span>{ <span class="self">Self</span>::from_data_statically_unchecked(storage) }
}
}
<span class="comment">// TODO: Consider removing/deprecating `from_vec_storage` once we are able to make
// `from_data` const fn compatible
</span><span class="attr">#[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"alloc"</span>))]
</span><span class="kw">impl</span><T> RowDVector<T> {
<span class="doccomment">/// Creates a new heap-allocated matrix from the given [`VecStorage`].
///
/// This method exists primarily as a workaround for the fact that `from_data` can not
/// work in `const fn` contexts.
</span><span class="kw">pub const fn </span>from_vec_storage(storage: VecStorage<T, U1, Dyn>) -> <span class="self">Self </span>{
<span class="comment">// This is sound because the dimensions of the matrix and the storage are guaranteed
// to be the same
</span><span class="kw">unsafe </span>{ <span class="self">Self</span>::from_data_statically_unchecked(storage) }
}
}
<span class="kw">impl</span><T, R: Dim, C: Dim> UninitMatrix<T, R, C>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, R, C>,
{
<span class="doccomment">/// Assumes a matrix's entries to be initialized. This operation should be near zero-cost.
///
/// # Safety
/// The user must make sure that every single entry of the buffer has been initialized,
/// or Undefined Behavior will immediately occur.
</span><span class="attr">#[inline(always)]
</span><span class="kw">pub unsafe fn </span>assume_init(<span class="self">self</span>) -> OMatrix<T, R, C> {
OMatrix::from_data(<DefaultAllocator <span class="kw">as </span>Allocator<T, R, C>>::assume_init(
<span class="self">self</span>.data,
))
}
}
<span class="kw">impl</span><T, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S> {
<span class="doccomment">/// Creates a new matrix with the given data.
</span><span class="attr">#[inline(always)]
</span><span class="kw">pub fn </span>from_data(data: S) -> <span class="self">Self </span>{
<span class="kw">unsafe </span>{ <span class="self">Self</span>::from_data_statically_unchecked(data) }
}
<span class="doccomment">/// The shape of this matrix returned as the tuple (number of rows, number of columns).
///
/// # Example
/// ```
/// # use nalgebra::Matrix3x4;
/// let mat = Matrix3x4::<f32>::zeros();
/// assert_eq!(mat.shape(), (3, 4));
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>shape(<span class="kw-2">&</span><span class="self">self</span>) -> (usize, usize) {
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape_generic();
(nrows.value(), ncols.value())
}
<span class="doccomment">/// The shape of this matrix wrapped into their representative types (`Const` or `Dyn`).
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>shape_generic(<span class="kw-2">&</span><span class="self">self</span>) -> (R, C) {
<span class="self">self</span>.data.shape()
}
<span class="doccomment">/// The number of rows of this matrix.
///
/// # Example
/// ```
/// # use nalgebra::Matrix3x4;
/// let mat = Matrix3x4::<f32>::zeros();
/// assert_eq!(mat.nrows(), 3);
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>nrows(<span class="kw-2">&</span><span class="self">self</span>) -> usize {
<span class="self">self</span>.shape().<span class="number">0
</span>}
<span class="doccomment">/// The number of columns of this matrix.
///
/// # Example
/// ```
/// # use nalgebra::Matrix3x4;
/// let mat = Matrix3x4::<f32>::zeros();
/// assert_eq!(mat.ncols(), 4);
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>ncols(<span class="kw-2">&</span><span class="self">self</span>) -> usize {
<span class="self">self</span>.shape().<span class="number">1
</span>}
<span class="doccomment">/// The strides (row stride, column stride) of this matrix.
///
/// # Example
/// ```
/// # use nalgebra::DMatrix;
/// let mat = DMatrix::<f32>::zeros(10, 10);
/// let view = mat.view_with_steps((0, 0), (5, 3), (1, 2));
/// // The column strides is the number of steps (here 2) multiplied by the corresponding dimension.
/// assert_eq!(mat.strides(), (1, 10));
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>strides(<span class="kw-2">&</span><span class="self">self</span>) -> (usize, usize) {
<span class="kw">let </span>(srows, scols) = <span class="self">self</span>.data.strides();
(srows.value(), scols.value())
}
<span class="doccomment">/// Computes the row and column coordinates of the i-th element of this matrix seen as a
/// vector.
///
/// # Example
/// ```
/// # use nalgebra::Matrix2;
/// let m = Matrix2::new(1, 2,
/// 3, 4);
/// let i = m.vector_to_matrix_index(3);
/// assert_eq!(i, (1, 1));
/// assert_eq!(m[i], m[3]);
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>vector_to_matrix_index(<span class="kw-2">&</span><span class="self">self</span>, i: usize) -> (usize, usize) {
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape();
<span class="comment">// Two most common uses that should be optimized by the compiler for statically-sized
// matrices.
</span><span class="kw">if </span>nrows == <span class="number">1 </span>{
(<span class="number">0</span>, i)
} <span class="kw">else if </span>ncols == <span class="number">1 </span>{
(i, <span class="number">0</span>)
} <span class="kw">else </span>{
(i % nrows, i / nrows)
}
}
<span class="doccomment">/// Returns a pointer to the start of the matrix.
///
/// If the matrix is not empty, this pointer is guaranteed to be aligned
/// and non-null.
///
/// # Example
/// ```
/// # use nalgebra::Matrix2;
/// let m = Matrix2::new(1, 2,
/// 3, 4);
/// let ptr = m.as_ptr();
/// assert_eq!(unsafe { *ptr }, m[0]);
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>as_ptr(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="kw-2">*const </span>T {
<span class="self">self</span>.data.ptr()
}
<span class="doccomment">/// Tests whether `self` and `rhs` are equal up to a given epsilon.
///
/// See `relative_eq` from the `RelativeEq` trait for more details.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>relative_eq<R2, C2, SB>(
<span class="kw-2">&</span><span class="self">self</span>,
other: <span class="kw-2">&</span>Matrix<T, R2, C2, SB>,
eps: T::Epsilon,
max_relative: T::Epsilon,
) -> bool
<span class="kw">where
</span>T: RelativeEq,
R2: Dim,
C2: Dim,
SB: Storage<T, R2, C2>,
T::Epsilon: Clone,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
<span class="macro">assert!</span>(<span class="self">self</span>.shape() == other.shape());
<span class="self">self</span>.iter()
.zip(other.iter())
.all(|(a, b)| a.relative_eq(b, eps.clone(), max_relative.clone()))
}
<span class="doccomment">/// Tests whether `self` and `rhs` are exactly equal.
</span><span class="attr">#[inline]
#[must_use]
#[allow(clippy::should_implement_trait)]
</span><span class="kw">pub fn </span>eq<R2, C2, SB>(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span>Matrix<T, R2, C2, SB>) -> bool
<span class="kw">where
</span>T: PartialEq,
R2: Dim,
C2: Dim,
SB: RawStorage<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
<span class="macro">assert!</span>(<span class="self">self</span>.shape() == other.shape());
<span class="self">self</span>.iter().zip(other.iter()).all(|(a, b)| <span class="kw-2">*</span>a == <span class="kw-2">*</span>b)
}
<span class="doccomment">/// Moves this matrix into one that owns its data.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>into_owned(<span class="self">self</span>) -> OMatrix<T, R, C>
<span class="kw">where
</span>T: Scalar,
S: Storage<T, R, C>,
DefaultAllocator: Allocator<T, R, C>,
{
Matrix::from_data(<span class="self">self</span>.data.into_owned())
}
<span class="comment">// TODO: this could probably benefit from specialization.
// XXX: bad name.
</span><span class="doccomment">/// Moves this matrix into one that owns its data. The actual type of the result depends on
/// matrix storage combination rules for addition.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>into_owned_sum<R2, C2>(<span class="self">self</span>) -> MatrixSum<T, R, C, R2, C2>
<span class="kw">where
</span>T: Scalar,
S: Storage<T, R, C>,
R2: Dim,
C2: Dim,
DefaultAllocator: SameShapeAllocator<T, R, C, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
<span class="kw">if </span>TypeId::of::<SameShapeStorage<T, R, C, R2, C2>>() == TypeId::of::<Owned<T, R, C>>() {
<span class="comment">// We can just return `self.into_owned()`.
</span><span class="kw">unsafe </span>{
<span class="comment">// TODO: check that those copies are optimized away by the compiler.
</span><span class="kw">let </span>owned = <span class="self">self</span>.into_owned();
<span class="kw">let </span>res = mem::transmute_copy(<span class="kw-2">&</span>owned);
mem::forget(owned);
res
}
} <span class="kw">else </span>{
<span class="self">self</span>.clone_owned_sum()
}
}
<span class="doccomment">/// Clones this matrix to one that owns its data.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>clone_owned(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, R, C>
<span class="kw">where
</span>T: Scalar,
S: Storage<T, R, C>,
DefaultAllocator: Allocator<T, R, C>,
{
Matrix::from_data(<span class="self">self</span>.data.clone_owned())
}
<span class="doccomment">/// Clones this matrix into one that owns its data. The actual type of the result depends on
/// matrix storage combination rules for addition.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>clone_owned_sum<R2, C2>(<span class="kw-2">&</span><span class="self">self</span>) -> MatrixSum<T, R, C, R2, C2>
<span class="kw">where
</span>T: Scalar,
S: Storage<T, R, C>,
R2: Dim,
C2: Dim,
DefaultAllocator: SameShapeAllocator<T, R, C, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape();
<span class="kw">let </span>nrows: SameShapeR<R, R2> = Dim::from_usize(nrows);
<span class="kw">let </span>ncols: SameShapeC<C, C2> = Dim::from_usize(ncols);
<span class="kw">let </span><span class="kw-2">mut </span>res = Matrix::uninit(nrows, ncols);
<span class="kw">unsafe </span>{
<span class="comment">// TODO: use copy_from?
</span><span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..res.ncols() {
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..res.nrows() {
<span class="kw-2">*</span>res.get_unchecked_mut((i, j)) =
MaybeUninit::new(<span class="self">self</span>.get_unchecked((i, j)).clone());
}
}
<span class="comment">// SAFETY: the output has been initialized above.
</span>res.assume_init()
}
}
<span class="doccomment">/// Transposes `self` and store the result into `out`.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>transpose_to_uninit<Status, R2, C2, SB>(
<span class="kw-2">&</span><span class="self">self</span>,
_status: Status,
out: <span class="kw-2">&mut </span>Matrix<Status::Value, R2, C2, SB>,
) <span class="kw">where
</span>Status: InitStatus<T>,
T: Scalar,
R2: Dim,
C2: Dim,
SB: RawStorageMut<Status::Value, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape();
<span class="macro">assert!</span>(
(ncols, nrows) == out.shape(),
<span class="string">"Incompatible shape for transposition."
</span>);
<span class="comment">// TODO: optimize that.
</span><span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..nrows {
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..ncols {
<span class="comment">// Safety: the indices are in range.
</span><span class="kw">unsafe </span>{
Status::init(
out.get_unchecked_mut((j, i)),
<span class="self">self</span>.get_unchecked((i, j)).clone(),
);
}
}
}
}
<span class="doccomment">/// Transposes `self` and store the result into `out`.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>transpose_to<R2, C2, SB>(<span class="kw-2">&</span><span class="self">self</span>, out: <span class="kw-2">&mut </span>Matrix<T, R2, C2, SB>)
<span class="kw">where
</span>T: Scalar,
R2: Dim,
C2: Dim,
SB: RawStorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,
{
<span class="self">self</span>.transpose_to_uninit(Init, out)
}
<span class="doccomment">/// Transposes `self`.
</span><span class="attr">#[inline]
#[must_use = <span class="string">"Did you mean to use transpose_mut()?"</span>]
</span><span class="kw">pub fn </span>transpose(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, C, R>
<span class="kw">where
</span>T: Scalar,
DefaultAllocator: Allocator<T, C, R>,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape_generic();
<span class="kw">let </span><span class="kw-2">mut </span>res = Matrix::uninit(ncols, nrows);
<span class="self">self</span>.transpose_to_uninit(Uninit, <span class="kw-2">&mut </span>res);
<span class="comment">// Safety: res is now fully initialized.
</span><span class="kw">unsafe </span>{ res.assume_init() }
}
}
<span class="doccomment">/// # Elementwise mapping and folding
</span><span class="kw">impl</span><T, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S> {
<span class="doccomment">/// Returns a matrix containing the result of `f` applied to each of its entries.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>map<T2: Scalar, F: FnMut(T) -> T2>(<span class="kw-2">&</span><span class="self">self</span>, <span class="kw-2">mut </span>f: F) -> OMatrix<T2, R, C>
<span class="kw">where
</span>T: Scalar,
DefaultAllocator: Allocator<T2, R, C>,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape_generic();
<span class="kw">let </span><span class="kw-2">mut </span>res = Matrix::uninit(nrows, ncols);
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..ncols.value() {
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..nrows.value() {
<span class="comment">// Safety: all indices are in range.
</span><span class="kw">unsafe </span>{
<span class="kw">let </span>a = <span class="self">self</span>.data.get_unchecked(i, j).clone();
<span class="kw-2">*</span>res.data.get_unchecked_mut(i, j) = MaybeUninit::new(f(a));
}
}
}
<span class="comment">// Safety: res is now fully initialized.
</span><span class="kw">unsafe </span>{ res.assume_init() }
}
<span class="doccomment">/// Cast the components of `self` to another type.
///
/// # Example
/// ```
/// # use nalgebra::Vector3;
/// let q = Vector3::new(1.0f64, 2.0, 3.0);
/// let q2 = q.cast::<f32>();
/// assert_eq!(q2, Vector3::new(1.0f32, 2.0, 3.0));
/// ```
</span><span class="kw">pub fn </span>cast<T2: Scalar>(<span class="self">self</span>) -> OMatrix<T2, R, C>
<span class="kw">where
</span>T: Scalar,
OMatrix<T2, R, C>: SupersetOf<<span class="self">Self</span>>,
DefaultAllocator: Allocator<T2, R, C>,
{
<span class="kw">crate</span>::convert(<span class="self">self</span>)
}
<span class="doccomment">/// Attempts to cast the components of `self` to another type.
///
/// # Example
/// ```
/// # use nalgebra::Vector3;
/// let q = Vector3::new(1.0f64, 2.0, 3.0);
/// let q2 = q.try_cast::<i32>();
/// assert_eq!(q2, Some(Vector3::new(1, 2, 3)));
/// ```
</span><span class="kw">pub fn </span>try_cast<T2: Scalar>(<span class="self">self</span>) -> <span class="prelude-ty">Option</span><OMatrix<T2, R, C>>
<span class="kw">where
</span>T: Scalar,
<span class="self">Self</span>: SupersetOf<OMatrix<T2, R, C>>,
DefaultAllocator: Allocator<T2, R, C>,
{
<span class="kw">crate</span>::try_convert(<span class="self">self</span>)
}
<span class="doccomment">/// Similar to `self.iter().fold(init, f)` except that `init` is replaced by a closure.
///
/// The initialization closure is given the first component of this matrix:
/// - If the matrix has no component (0 rows or 0 columns) then `init_f` is called with `None`
/// and its return value is the value returned by this method.
/// - If the matrix has has least one component, then `init_f` is called with the first component
/// to compute the initial value. Folding then continues on all the remaining components of the matrix.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>fold_with<T2>(
<span class="kw-2">&</span><span class="self">self</span>,
init_f: <span class="kw">impl </span>FnOnce(<span class="prelude-ty">Option</span><<span class="kw-2">&</span>T>) -> T2,
f: <span class="kw">impl </span>FnMut(T2, <span class="kw-2">&</span>T) -> T2,
) -> T2
<span class="kw">where
</span>T: Scalar,
{
<span class="kw">let </span><span class="kw-2">mut </span>it = <span class="self">self</span>.iter();
<span class="kw">let </span>init = init_f(it.next());
it.fold(init, f)
}
<span class="doccomment">/// Returns a matrix containing the result of `f` applied to each of its entries. Unlike `map`,
/// `f` also gets passed the row and column index, i.e. `f(row, col, value)`.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>map_with_location<T2: Scalar, F: FnMut(usize, usize, T) -> T2>(
<span class="kw-2">&</span><span class="self">self</span>,
<span class="kw-2">mut </span>f: F,
) -> OMatrix<T2, R, C>
<span class="kw">where
</span>T: Scalar,
DefaultAllocator: Allocator<T2, R, C>,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape_generic();
<span class="kw">let </span><span class="kw-2">mut </span>res = Matrix::uninit(nrows, ncols);
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..ncols.value() {
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..nrows.value() {
<span class="comment">// Safety: all indices are in range.
</span><span class="kw">unsafe </span>{
<span class="kw">let </span>a = <span class="self">self</span>.data.get_unchecked(i, j).clone();
<span class="kw-2">*</span>res.data.get_unchecked_mut(i, j) = MaybeUninit::new(f(i, j, a));
}
}
}
<span class="comment">// Safety: res is now fully initialized.
</span><span class="kw">unsafe </span>{ res.assume_init() }
}
<span class="doccomment">/// Returns a matrix containing the result of `f` applied to each entries of `self` and
/// `rhs`.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>zip_map<T2, N3, S2, F>(<span class="kw-2">&</span><span class="self">self</span>, rhs: <span class="kw-2">&</span>Matrix<T2, R, C, S2>, <span class="kw-2">mut </span>f: F) -> OMatrix<N3, R, C>
<span class="kw">where
</span>T: Scalar,
T2: Scalar,
N3: Scalar,
S2: RawStorage<T2, R, C>,
F: FnMut(T, T2) -> N3,
DefaultAllocator: Allocator<N3, R, C>,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape_generic();
<span class="kw">let </span><span class="kw-2">mut </span>res = Matrix::uninit(nrows, ncols);
<span class="macro">assert_eq!</span>(
(nrows.value(), ncols.value()),
rhs.shape(),
<span class="string">"Matrix simultaneous traversal error: dimension mismatch."
</span>);
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..ncols.value() {
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..nrows.value() {
<span class="comment">// Safety: all indices are in range.
</span><span class="kw">unsafe </span>{
<span class="kw">let </span>a = <span class="self">self</span>.data.get_unchecked(i, j).clone();
<span class="kw">let </span>b = rhs.data.get_unchecked(i, j).clone();
<span class="kw-2">*</span>res.data.get_unchecked_mut(i, j) = MaybeUninit::new(f(a, b))
}
}
}
<span class="comment">// Safety: res is now fully initialized.
</span><span class="kw">unsafe </span>{ res.assume_init() }
}
<span class="doccomment">/// Returns a matrix containing the result of `f` applied to each entries of `self` and
/// `b`, and `c`.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>zip_zip_map<T2, N3, N4, S2, S3, F>(
<span class="kw-2">&</span><span class="self">self</span>,
b: <span class="kw-2">&</span>Matrix<T2, R, C, S2>,
c: <span class="kw-2">&</span>Matrix<N3, R, C, S3>,
<span class="kw-2">mut </span>f: F,
) -> OMatrix<N4, R, C>
<span class="kw">where
</span>T: Scalar,
T2: Scalar,
N3: Scalar,
N4: Scalar,
S2: RawStorage<T2, R, C>,
S3: RawStorage<N3, R, C>,
F: FnMut(T, T2, N3) -> N4,
DefaultAllocator: Allocator<N4, R, C>,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape_generic();
<span class="kw">let </span><span class="kw-2">mut </span>res = Matrix::uninit(nrows, ncols);
<span class="macro">assert_eq!</span>(
(nrows.value(), ncols.value()),
b.shape(),
<span class="string">"Matrix simultaneous traversal error: dimension mismatch."
</span>);
<span class="macro">assert_eq!</span>(
(nrows.value(), ncols.value()),
c.shape(),
<span class="string">"Matrix simultaneous traversal error: dimension mismatch."
</span>);
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..ncols.value() {
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..nrows.value() {
<span class="comment">// Safety: all indices are in range.
</span><span class="kw">unsafe </span>{
<span class="kw">let </span>a = <span class="self">self</span>.data.get_unchecked(i, j).clone();
<span class="kw">let </span>b = b.data.get_unchecked(i, j).clone();
<span class="kw">let </span>c = c.data.get_unchecked(i, j).clone();
<span class="kw-2">*</span>res.data.get_unchecked_mut(i, j) = MaybeUninit::new(f(a, b, c))
}
}
}
<span class="comment">// Safety: res is now fully initialized.
</span><span class="kw">unsafe </span>{ res.assume_init() }
}
<span class="doccomment">/// Folds a function `f` on each entry of `self`.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>fold<Acc>(<span class="kw-2">&</span><span class="self">self</span>, init: Acc, <span class="kw-2">mut </span>f: <span class="kw">impl </span>FnMut(Acc, T) -> Acc) -> Acc
<span class="kw">where
</span>T: Scalar,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape_generic();
<span class="kw">let </span><span class="kw-2">mut </span>res = init;
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..ncols.value() {
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..nrows.value() {
<span class="comment">// Safety: all indices are in range.
</span><span class="kw">unsafe </span>{
<span class="kw">let </span>a = <span class="self">self</span>.data.get_unchecked(i, j).clone();
res = f(res, a)
}
}
}
res
}
<span class="doccomment">/// Folds a function `f` on each pairs of entries from `self` and `rhs`.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>zip_fold<T2, R2, C2, S2, Acc>(
<span class="kw-2">&</span><span class="self">self</span>,
rhs: <span class="kw-2">&</span>Matrix<T2, R2, C2, S2>,
init: Acc,
<span class="kw-2">mut </span>f: <span class="kw">impl </span>FnMut(Acc, T, T2) -> Acc,
) -> Acc
<span class="kw">where
</span>T: Scalar,
T2: Scalar,
R2: Dim,
C2: Dim,
S2: RawStorage<T2, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape_generic();
<span class="kw">let </span><span class="kw-2">mut </span>res = init;
<span class="macro">assert_eq!</span>(
(nrows.value(), ncols.value()),
rhs.shape(),
<span class="string">"Matrix simultaneous traversal error: dimension mismatch."
</span>);
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..ncols.value() {
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..nrows.value() {
<span class="kw">unsafe </span>{
<span class="kw">let </span>a = <span class="self">self</span>.data.get_unchecked(i, j).clone();
<span class="kw">let </span>b = rhs.data.get_unchecked(i, j).clone();
res = f(res, a, b)
}
}
}
res
}
<span class="doccomment">/// Applies a closure `f` to modify each component of `self`.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>apply<F: FnMut(<span class="kw-2">&mut </span>T)>(<span class="kw-2">&mut </span><span class="self">self</span>, <span class="kw-2">mut </span>f: F)
<span class="kw">where
</span>S: RawStorageMut<T, R, C>,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape();
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..ncols {
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..nrows {
<span class="kw">unsafe </span>{
<span class="kw">let </span>e = <span class="self">self</span>.data.get_unchecked_mut(i, j);
f(e)
}
}
}
}
<span class="doccomment">/// Replaces each component of `self` by the result of a closure `f` applied on its components
/// joined with the components from `rhs`.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>zip_apply<T2, R2, C2, S2>(
<span class="kw-2">&mut </span><span class="self">self</span>,
rhs: <span class="kw-2">&</span>Matrix<T2, R2, C2, S2>,
<span class="kw-2">mut </span>f: <span class="kw">impl </span>FnMut(<span class="kw-2">&mut </span>T, T2),
) <span class="kw">where
</span>S: RawStorageMut<T, R, C>,
T2: Scalar,
R2: Dim,
C2: Dim,
S2: RawStorage<T2, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape();
<span class="macro">assert_eq!</span>(
(nrows, ncols),
rhs.shape(),
<span class="string">"Matrix simultaneous traversal error: dimension mismatch."
</span>);
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..ncols {
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..nrows {
<span class="kw">unsafe </span>{
<span class="kw">let </span>e = <span class="self">self</span>.data.get_unchecked_mut(i, j);
<span class="kw">let </span>rhs = rhs.get_unchecked((i, j)).clone();
f(e, rhs)
}
}
}
}
<span class="doccomment">/// Replaces each component of `self` by the result of a closure `f` applied on its components
/// joined with the components from `b` and `c`.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>zip_zip_apply<T2, R2, C2, S2, N3, R3, C3, S3>(
<span class="kw-2">&mut </span><span class="self">self</span>,
b: <span class="kw-2">&</span>Matrix<T2, R2, C2, S2>,
c: <span class="kw-2">&</span>Matrix<N3, R3, C3, S3>,
<span class="kw-2">mut </span>f: <span class="kw">impl </span>FnMut(<span class="kw-2">&mut </span>T, T2, N3),
) <span class="kw">where
</span>S: RawStorageMut<T, R, C>,
T2: Scalar,
R2: Dim,
C2: Dim,
S2: RawStorage<T2, R2, C2>,
N3: Scalar,
R3: Dim,
C3: Dim,
S3: RawStorage<N3, R3, C3>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape();
<span class="macro">assert_eq!</span>(
(nrows, ncols),
b.shape(),
<span class="string">"Matrix simultaneous traversal error: dimension mismatch."
</span>);
<span class="macro">assert_eq!</span>(
(nrows, ncols),
c.shape(),
<span class="string">"Matrix simultaneous traversal error: dimension mismatch."
</span>);
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..ncols {
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..nrows {
<span class="kw">unsafe </span>{
<span class="kw">let </span>e = <span class="self">self</span>.data.get_unchecked_mut(i, j);
<span class="kw">let </span>b = b.get_unchecked((i, j)).clone();
<span class="kw">let </span>c = c.get_unchecked((i, j)).clone();
f(e, b, c)
}
}
}
}
}
<span class="doccomment">/// # Iteration on components, rows, and columns
</span><span class="kw">impl</span><T, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S> {
<span class="doccomment">/// Iterates through this matrix coordinates in column-major order.
///
/// # Example
/// ```
/// # use nalgebra::Matrix2x3;
/// let mat = Matrix2x3::new(11, 12, 13,
/// 21, 22, 23);
/// let mut it = mat.iter();
/// assert_eq!(*it.next().unwrap(), 11);
/// assert_eq!(*it.next().unwrap(), 21);
/// assert_eq!(*it.next().unwrap(), 12);
/// assert_eq!(*it.next().unwrap(), 22);
/// assert_eq!(*it.next().unwrap(), 13);
/// assert_eq!(*it.next().unwrap(), 23);
/// assert!(it.next().is_none());
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>iter(<span class="kw-2">&</span><span class="self">self</span>) -> MatrixIter<<span class="lifetime">'_</span>, T, R, C, S> {
MatrixIter::new(<span class="kw-2">&</span><span class="self">self</span>.data)
}
<span class="doccomment">/// Iterate through the rows of this matrix.
///
/// # Example
/// ```
/// # use nalgebra::Matrix2x3;
/// let mut a = Matrix2x3::new(1, 2, 3,
/// 4, 5, 6);
/// for (i, row) in a.row_iter().enumerate() {
/// assert_eq!(row, a.row(i))
/// }
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>row_iter(<span class="kw-2">&</span><span class="self">self</span>) -> RowIter<<span class="lifetime">'_</span>, T, R, C, S> {
RowIter::new(<span class="self">self</span>)
}
<span class="doccomment">/// Iterate through the columns of this matrix.
///
/// # Example
/// ```
/// # use nalgebra::Matrix2x3;
/// let mut a = Matrix2x3::new(1, 2, 3,
/// 4, 5, 6);
/// for (i, column) in a.column_iter().enumerate() {
/// assert_eq!(column, a.column(i))
/// }
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>column_iter(<span class="kw-2">&</span><span class="self">self</span>) -> ColumnIter<<span class="lifetime">'_</span>, T, R, C, S> {
ColumnIter::new(<span class="self">self</span>)
}
<span class="doccomment">/// Mutably iterates through this matrix coordinates.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>iter_mut(<span class="kw-2">&mut </span><span class="self">self</span>) -> MatrixIterMut<<span class="lifetime">'_</span>, T, R, C, S>
<span class="kw">where
</span>S: RawStorageMut<T, R, C>,
{
MatrixIterMut::new(<span class="kw-2">&mut </span><span class="self">self</span>.data)
}
<span class="doccomment">/// Mutably iterates through this matrix rows.
///
/// # Example
/// ```
/// # use nalgebra::Matrix2x3;
/// let mut a = Matrix2x3::new(1, 2, 3,
/// 4, 5, 6);
/// for (i, mut row) in a.row_iter_mut().enumerate() {
/// row *= (i + 1) * 10;
/// }
///
/// let expected = Matrix2x3::new(10, 20, 30,
/// 80, 100, 120);
/// assert_eq!(a, expected);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>row_iter_mut(<span class="kw-2">&mut </span><span class="self">self</span>) -> RowIterMut<<span class="lifetime">'_</span>, T, R, C, S>
<span class="kw">where
</span>S: RawStorageMut<T, R, C>,
{
RowIterMut::new(<span class="self">self</span>)
}
<span class="doccomment">/// Mutably iterates through this matrix columns.
///
/// # Example
/// ```
/// # use nalgebra::Matrix2x3;
/// let mut a = Matrix2x3::new(1, 2, 3,
/// 4, 5, 6);
/// for (i, mut col) in a.column_iter_mut().enumerate() {
/// col *= (i + 1) * 10;
/// }
///
/// let expected = Matrix2x3::new(10, 40, 90,
/// 40, 100, 180);
/// assert_eq!(a, expected);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>column_iter_mut(<span class="kw-2">&mut </span><span class="self">self</span>) -> ColumnIterMut<<span class="lifetime">'_</span>, T, R, C, S>
<span class="kw">where
</span>S: RawStorageMut<T, R, C>,
{
ColumnIterMut::new(<span class="self">self</span>)
}
}
<span class="kw">impl</span><T, R: Dim, C: Dim, S: RawStorageMut<T, R, C>> Matrix<T, R, C, S> {
<span class="doccomment">/// Returns a mutable pointer to the start of the matrix.
///
/// If the matrix is not empty, this pointer is guaranteed to be aligned
/// and non-null.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>as_mut_ptr(<span class="kw-2">&mut </span><span class="self">self</span>) -> <span class="kw-2">*mut </span>T {
<span class="self">self</span>.data.ptr_mut()
}
<span class="doccomment">/// Swaps two entries without bound-checking.
</span><span class="attr">#[inline]
</span><span class="kw">pub unsafe fn </span>swap_unchecked(<span class="kw-2">&mut </span><span class="self">self</span>, row_cols1: (usize, usize), row_cols2: (usize, usize)) {
<span class="macro">debug_assert!</span>(row_cols1.<span class="number">0 </span>< <span class="self">self</span>.nrows() && row_cols1.<span class="number">1 </span>< <span class="self">self</span>.ncols());
<span class="macro">debug_assert!</span>(row_cols2.<span class="number">0 </span>< <span class="self">self</span>.nrows() && row_cols2.<span class="number">1 </span>< <span class="self">self</span>.ncols());
<span class="self">self</span>.data.swap_unchecked(row_cols1, row_cols2)
}
<span class="doccomment">/// Swaps two entries.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>swap(<span class="kw-2">&mut </span><span class="self">self</span>, row_cols1: (usize, usize), row_cols2: (usize, usize)) {
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape();
<span class="macro">assert!</span>(
row_cols1.<span class="number">0 </span>< nrows && row_cols1.<span class="number">1 </span>< ncols,
<span class="string">"Matrix elements swap index out of bounds."
</span>);
<span class="macro">assert!</span>(
row_cols2.<span class="number">0 </span>< nrows && row_cols2.<span class="number">1 </span>< ncols,
<span class="string">"Matrix elements swap index out of bounds."
</span>);
<span class="kw">unsafe </span>{ <span class="self">self</span>.swap_unchecked(row_cols1, row_cols2) }
}
<span class="doccomment">/// Fills this matrix with the content of a slice. Both must hold the same number of elements.
///
/// The components of the slice are assumed to be ordered in column-major order.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>copy_from_slice(<span class="kw-2">&mut </span><span class="self">self</span>, slice: <span class="kw-2">&</span>[T])
<span class="kw">where
</span>T: Scalar,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape();
<span class="macro">assert!</span>(
nrows * ncols == slice.len(),
<span class="string">"The slice must contain the same number of elements as the matrix."
</span>);
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..ncols {
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..nrows {
<span class="kw">unsafe </span>{
<span class="kw-2">*</span><span class="self">self</span>.get_unchecked_mut((i, j)) = slice.get_unchecked(i + j * nrows).clone();
}
}
}
}
<span class="doccomment">/// Fills this matrix with the content of another one. Both must have the same shape.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>copy_from<R2, C2, SB>(<span class="kw-2">&mut </span><span class="self">self</span>, other: <span class="kw-2">&</span>Matrix<T, R2, C2, SB>)
<span class="kw">where
</span>T: Scalar,
R2: Dim,
C2: Dim,
SB: RawStorage<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
<span class="macro">assert!</span>(
<span class="self">self</span>.shape() == other.shape(),
<span class="string">"Unable to copy from a matrix with a different shape."
</span>);
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..<span class="self">self</span>.ncols() {
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..<span class="self">self</span>.nrows() {
<span class="kw">unsafe </span>{
<span class="kw-2">*</span><span class="self">self</span>.get_unchecked_mut((i, j)) = other.get_unchecked((i, j)).clone();
}
}
}
}
<span class="doccomment">/// Fills this matrix with the content of the transpose another one.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>tr_copy_from<R2, C2, SB>(<span class="kw-2">&mut </span><span class="self">self</span>, other: <span class="kw-2">&</span>Matrix<T, R2, C2, SB>)
<span class="kw">where
</span>T: Scalar,
R2: Dim,
C2: Dim,
SB: RawStorage<T, R2, C2>,
ShapeConstraint: DimEq<R, C2> + SameNumberOfColumns<C, R2>,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape();
<span class="macro">assert!</span>(
(ncols, nrows) == other.shape(),
<span class="string">"Unable to copy from a matrix with incompatible shape."
</span>);
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..ncols {
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..nrows {
<span class="kw">unsafe </span>{
<span class="kw-2">*</span><span class="self">self</span>.get_unchecked_mut((i, j)) = other.get_unchecked((j, i)).clone();
}
}
}
}
<span class="comment">// TODO: rename `apply` to `apply_mut` and `apply_into` to `apply`?
</span><span class="doccomment">/// Returns `self` with each of its components replaced by the result of a closure `f` applied on it.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>apply_into<F: FnMut(<span class="kw-2">&mut </span>T)>(<span class="kw-2">mut </span><span class="self">self</span>, f: F) -> <span class="self">Self </span>{
<span class="self">self</span>.apply(f);
<span class="self">self
</span>}
}
<span class="kw">impl</span><T, D: Dim, S: RawStorage<T, D>> Vector<T, D, S> {
<span class="doccomment">/// Gets a reference to the i-th element of this column vector without bound checking.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub unsafe fn </span>vget_unchecked(<span class="kw-2">&</span><span class="self">self</span>, i: usize) -> <span class="kw-2">&</span>T {
<span class="macro">debug_assert!</span>(i < <span class="self">self</span>.nrows(), <span class="string">"Vector index out of bounds."</span>);
<span class="kw">let </span>i = i * <span class="self">self</span>.strides().<span class="number">0</span>;
<span class="self">self</span>.data.get_unchecked_linear(i)
}
}
<span class="kw">impl</span><T, D: Dim, S: RawStorageMut<T, D>> Vector<T, D, S> {
<span class="doccomment">/// Gets a mutable reference to the i-th element of this column vector without bound checking.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub unsafe fn </span>vget_unchecked_mut(<span class="kw-2">&mut </span><span class="self">self</span>, i: usize) -> <span class="kw-2">&mut </span>T {
<span class="macro">debug_assert!</span>(i < <span class="self">self</span>.nrows(), <span class="string">"Vector index out of bounds."</span>);
<span class="kw">let </span>i = i * <span class="self">self</span>.strides().<span class="number">0</span>;
<span class="self">self</span>.data.get_unchecked_linear_mut(i)
}
}
<span class="kw">impl</span><T, R: Dim, C: Dim, S: RawStorage<T, R, C> + IsContiguous> Matrix<T, R, C, S> {
<span class="doccomment">/// Extracts a slice containing the entire matrix entries ordered column-by-columns.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>as_slice(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="kw-2">&</span>[T] {
<span class="comment">// Safety: this is OK thanks to the IsContiguous trait.
</span><span class="kw">unsafe </span>{ <span class="self">self</span>.data.as_slice_unchecked() }
}
}
<span class="kw">impl</span><T, R: Dim, C: Dim, S: RawStorageMut<T, R, C> + IsContiguous> Matrix<T, R, C, S> {
<span class="doccomment">/// Extracts a mutable slice containing the entire matrix entries ordered column-by-columns.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>as_mut_slice(<span class="kw-2">&mut </span><span class="self">self</span>) -> <span class="kw-2">&mut </span>[T] {
<span class="comment">// Safety: this is OK thanks to the IsContiguous trait.
</span><span class="kw">unsafe </span>{ <span class="self">self</span>.data.as_mut_slice_unchecked() }
}
}
<span class="kw">impl</span><T: Scalar, D: Dim, S: RawStorageMut<T, D, D>> Matrix<T, D, D, S> {
<span class="doccomment">/// Transposes the square matrix `self` in-place.
</span><span class="kw">pub fn </span>transpose_mut(<span class="kw-2">&mut </span><span class="self">self</span>) {
<span class="macro">assert!</span>(
<span class="self">self</span>.is_square(),
<span class="string">"Unable to transpose a non-square matrix in-place."
</span>);
<span class="kw">let </span>dim = <span class="self">self</span>.shape().<span class="number">0</span>;
<span class="kw">for </span>i <span class="kw">in </span><span class="number">1</span>..dim {
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..i {
<span class="kw">unsafe </span>{ <span class="self">self</span>.swap_unchecked((i, j), (j, i)) }
}
}
}
}
<span class="kw">impl</span><T: SimdComplexField, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S> {
<span class="doccomment">/// Takes the adjoint (aka. conjugate-transpose) of `self` and store the result into `out`.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>adjoint_to_uninit<Status, R2, C2, SB>(
<span class="kw-2">&</span><span class="self">self</span>,
_status: Status,
out: <span class="kw-2">&mut </span>Matrix<Status::Value, R2, C2, SB>,
) <span class="kw">where
</span>Status: InitStatus<T>,
R2: Dim,
C2: Dim,
SB: RawStorageMut<Status::Value, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape();
<span class="macro">assert!</span>(
(ncols, nrows) == out.shape(),
<span class="string">"Incompatible shape for transpose-copy."
</span>);
<span class="comment">// TODO: optimize that.
</span><span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..nrows {
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..ncols {
<span class="comment">// Safety: all indices are in range.
</span><span class="kw">unsafe </span>{
Status::init(
out.get_unchecked_mut((j, i)),
<span class="self">self</span>.get_unchecked((i, j)).clone().simd_conjugate(),
);
}
}
}
}
<span class="doccomment">/// Takes the adjoint (aka. conjugate-transpose) of `self` and store the result into `out`.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>adjoint_to<R2, C2, SB>(<span class="kw-2">&</span><span class="self">self</span>, out: <span class="kw-2">&mut </span>Matrix<T, R2, C2, SB>)
<span class="kw">where
</span>R2: Dim,
C2: Dim,
SB: RawStorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,
{
<span class="self">self</span>.adjoint_to_uninit(Init, out)
}
<span class="doccomment">/// The adjoint (aka. conjugate-transpose) of `self`.
</span><span class="attr">#[inline]
#[must_use = <span class="string">"Did you mean to use adjoint_mut()?"</span>]
</span><span class="kw">pub fn </span>adjoint(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, C, R>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, C, R>,
{
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape_generic();
<span class="kw">let </span><span class="kw-2">mut </span>res = Matrix::uninit(ncols, nrows);
<span class="self">self</span>.adjoint_to_uninit(Uninit, <span class="kw-2">&mut </span>res);
<span class="comment">// Safety: res is now fully initialized.
</span><span class="kw">unsafe </span>{ res.assume_init() }
}
<span class="doccomment">/// Takes the conjugate and transposes `self` and store the result into `out`.
</span><span class="attr">#[deprecated(note = <span class="string">"Renamed `self.adjoint_to(out)`."</span>)]
#[inline]
</span><span class="kw">pub fn </span>conjugate_transpose_to<R2, C2, SB>(<span class="kw-2">&</span><span class="self">self</span>, out: <span class="kw-2">&mut </span>Matrix<T, R2, C2, SB>)
<span class="kw">where
</span>R2: Dim,
C2: Dim,
SB: RawStorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,
{
<span class="self">self</span>.adjoint_to(out)
}
<span class="doccomment">/// The conjugate transposition of `self`.
</span><span class="attr">#[deprecated(note = <span class="string">"Renamed `self.adjoint()`."</span>)]
#[inline]
</span><span class="kw">pub fn </span>conjugate_transpose(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, C, R>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, C, R>,
{
<span class="self">self</span>.adjoint()
}
<span class="doccomment">/// The conjugate of `self`.
</span><span class="attr">#[inline]
#[must_use = <span class="string">"Did you mean to use conjugate_mut()?"</span>]
</span><span class="kw">pub fn </span>conjugate(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, R, C>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, R, C>,
{
<span class="self">self</span>.map(|e| e.simd_conjugate())
}
<span class="doccomment">/// Divides each component of the complex matrix `self` by the given real.
</span><span class="attr">#[inline]
#[must_use = <span class="string">"Did you mean to use unscale_mut()?"</span>]
</span><span class="kw">pub fn </span>unscale(<span class="kw-2">&</span><span class="self">self</span>, real: T::SimdRealField) -> OMatrix<T, R, C>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, R, C>,
{
<span class="self">self</span>.map(|e| e.simd_unscale(real.clone()))
}
<span class="doccomment">/// Multiplies each component of the complex matrix `self` by the given real.
</span><span class="attr">#[inline]
#[must_use = <span class="string">"Did you mean to use scale_mut()?"</span>]
</span><span class="kw">pub fn </span>scale(<span class="kw-2">&</span><span class="self">self</span>, real: T::SimdRealField) -> OMatrix<T, R, C>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, R, C>,
{
<span class="self">self</span>.map(|e| e.simd_scale(real.clone()))
}
}
<span class="kw">impl</span><T: SimdComplexField, R: Dim, C: Dim, S: RawStorageMut<T, R, C>> Matrix<T, R, C, S> {
<span class="doccomment">/// The conjugate of the complex matrix `self` computed in-place.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>conjugate_mut(<span class="kw-2">&mut </span><span class="self">self</span>) {
<span class="self">self</span>.apply(|e| <span class="kw-2">*</span>e = e.clone().simd_conjugate())
}
<span class="doccomment">/// Divides each component of the complex matrix `self` by the given real.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>unscale_mut(<span class="kw-2">&mut </span><span class="self">self</span>, real: T::SimdRealField) {
<span class="self">self</span>.apply(|e| <span class="kw-2">*</span>e = e.clone().simd_unscale(real.clone()))
}
<span class="doccomment">/// Multiplies each component of the complex matrix `self` by the given real.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>scale_mut(<span class="kw-2">&mut </span><span class="self">self</span>, real: T::SimdRealField) {
<span class="self">self</span>.apply(|e| <span class="kw-2">*</span>e = e.clone().simd_scale(real.clone()))
}
}
<span class="kw">impl</span><T: SimdComplexField, D: Dim, S: RawStorageMut<T, D, D>> Matrix<T, D, D, S> {
<span class="doccomment">/// Sets `self` to its adjoint.
</span><span class="attr">#[deprecated(note = <span class="string">"Renamed to `self.adjoint_mut()`."</span>)]
</span><span class="kw">pub fn </span>conjugate_transform_mut(<span class="kw-2">&mut </span><span class="self">self</span>) {
<span class="self">self</span>.adjoint_mut()
}
<span class="doccomment">/// Sets `self` to its adjoint (aka. conjugate-transpose).
</span><span class="kw">pub fn </span>adjoint_mut(<span class="kw-2">&mut </span><span class="self">self</span>) {
<span class="macro">assert!</span>(
<span class="self">self</span>.is_square(),
<span class="string">"Unable to transpose a non-square matrix in-place."
</span>);
<span class="kw">let </span>dim = <span class="self">self</span>.shape().<span class="number">0</span>;
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..dim {
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..i {
<span class="kw">unsafe </span>{
<span class="kw">let </span>ref_ij = <span class="self">self</span>.get_unchecked((i, j)).clone();
<span class="kw">let </span>ref_ji = <span class="self">self</span>.get_unchecked((j, i)).clone();
<span class="kw">let </span>conj_ij = ref_ij.simd_conjugate();
<span class="kw">let </span>conj_ji = ref_ji.simd_conjugate();
<span class="kw-2">*</span><span class="self">self</span>.get_unchecked_mut((i, j)) = conj_ji;
<span class="kw-2">*</span><span class="self">self</span>.get_unchecked_mut((j, i)) = conj_ij;
}
}
{
<span class="kw">let </span>diag = <span class="kw">unsafe </span>{ <span class="self">self</span>.get_unchecked_mut((i, i)) };
<span class="kw-2">*</span>diag = diag.clone().simd_conjugate();
}
}
}
}
<span class="kw">impl</span><T: Scalar, D: Dim, S: RawStorage<T, D, D>> SquareMatrix<T, D, S> {
<span class="doccomment">/// The diagonal of this matrix.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>diagonal(<span class="kw-2">&</span><span class="self">self</span>) -> OVector<T, D>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D>,
{
<span class="self">self</span>.map_diagonal(|e| e)
}
<span class="doccomment">/// Apply the given function to this matrix's diagonal and returns it.
///
/// This is a more efficient version of `self.diagonal().map(f)` since this
/// allocates only once.
</span><span class="attr">#[must_use]
</span><span class="kw">pub fn </span>map_diagonal<T2: Scalar>(<span class="kw-2">&</span><span class="self">self</span>, <span class="kw-2">mut </span>f: <span class="kw">impl </span>FnMut(T) -> T2) -> OVector<T2, D>
<span class="kw">where
</span>DefaultAllocator: Allocator<T2, D>,
{
<span class="macro">assert!</span>(
<span class="self">self</span>.is_square(),
<span class="string">"Unable to get the diagonal of a non-square matrix."
</span>);
<span class="kw">let </span>dim = <span class="self">self</span>.shape_generic().<span class="number">0</span>;
<span class="kw">let </span><span class="kw-2">mut </span>res = Matrix::uninit(dim, Const::<<span class="number">1</span>>);
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..dim.value() {
<span class="comment">// Safety: all indices are in range.
</span><span class="kw">unsafe </span>{
<span class="kw-2">*</span>res.vget_unchecked_mut(i) =
MaybeUninit::new(f(<span class="self">self</span>.get_unchecked((i, i)).clone()));
}
}
<span class="comment">// Safety: res is now fully initialized.
</span><span class="kw">unsafe </span>{ res.assume_init() }
}
<span class="doccomment">/// Computes a trace of a square matrix, i.e., the sum of its diagonal elements.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>trace(<span class="kw-2">&</span><span class="self">self</span>) -> T
<span class="kw">where
</span>T: Scalar + Zero + ClosedAdd,
{
<span class="macro">assert!</span>(
<span class="self">self</span>.is_square(),
<span class="string">"Cannot compute the trace of non-square matrix."
</span>);
<span class="kw">let </span>dim = <span class="self">self</span>.shape_generic().<span class="number">0</span>;
<span class="kw">let </span><span class="kw-2">mut </span>res = T::zero();
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..dim.value() {
res += <span class="kw">unsafe </span>{ <span class="self">self</span>.get_unchecked((i, i)).clone() };
}
res
}
}
<span class="kw">impl</span><T: SimdComplexField, D: Dim, S: Storage<T, D, D>> SquareMatrix<T, D, S> {
<span class="doccomment">/// The symmetric part of `self`, i.e., `0.5 * (self + self.transpose())`.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>symmetric_part(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, D, D>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D, D>,
{
<span class="macro">assert!</span>(
<span class="self">self</span>.is_square(),
<span class="string">"Cannot compute the symmetric part of a non-square matrix."
</span>);
<span class="kw">let </span><span class="kw-2">mut </span>tr = <span class="self">self</span>.transpose();
tr += <span class="self">self</span>;
tr <span class="kw-2">*</span>= <span class="kw">crate</span>::convert::<<span class="kw">_</span>, T>(<span class="number">0.5</span>);
tr
}
<span class="doccomment">/// The hermitian part of `self`, i.e., `0.5 * (self + self.adjoint())`.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>hermitian_part(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, D, D>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D, D>,
{
<span class="macro">assert!</span>(
<span class="self">self</span>.is_square(),
<span class="string">"Cannot compute the hermitian part of a non-square matrix."
</span>);
<span class="kw">let </span><span class="kw-2">mut </span>tr = <span class="self">self</span>.adjoint();
tr += <span class="self">self</span>;
tr <span class="kw-2">*</span>= <span class="kw">crate</span>::convert::<<span class="kw">_</span>, T>(<span class="number">0.5</span>);
tr
}
}
<span class="kw">impl</span><T: Scalar + Zero + One, D: DimAdd<U1> + IsNotStaticOne, S: RawStorage<T, D, D>>
Matrix<T, D, D, S>
{
<span class="doccomment">/// Yields the homogeneous matrix for this matrix, i.e., appending an additional dimension and
/// and setting the diagonal element to `1`.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>to_homogeneous(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, DimSum<D, U1>, DimSum<D, U1>>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, DimSum<D, U1>, DimSum<D, U1>>,
{
<span class="macro">assert!</span>(
<span class="self">self</span>.is_square(),
<span class="string">"Only square matrices can currently be transformed to homogeneous coordinates."
</span>);
<span class="kw">let </span>dim = DimSum::<D, U1>::from_usize(<span class="self">self</span>.nrows() + <span class="number">1</span>);
<span class="kw">let </span><span class="kw-2">mut </span>res = OMatrix::identity_generic(dim, dim);
res.generic_view_mut::<D, D>((<span class="number">0</span>, <span class="number">0</span>), <span class="self">self</span>.shape_generic())
.copy_from(<span class="self">self</span>);
res
}
}
<span class="kw">impl</span><T: Scalar + Zero, D: DimAdd<U1>, S: RawStorage<T, D>> Vector<T, D, S> {
<span class="doccomment">/// Computes the coordinates in projective space of this vector, i.e., appends a `0` to its
/// coordinates.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>to_homogeneous(<span class="kw-2">&</span><span class="self">self</span>) -> OVector<T, DimSum<D, U1>>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, DimSum<D, U1>>,
{
<span class="self">self</span>.push(T::zero())
}
<span class="doccomment">/// Constructs a vector from coordinates in projective space, i.e., removes a `0` at the end of
/// `self`. Returns `None` if this last component is not zero.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>from_homogeneous<SB>(v: Vector<T, DimSum<D, U1>, SB>) -> <span class="prelude-ty">Option</span><OVector<T, D>>
<span class="kw">where
</span>SB: RawStorage<T, DimSum<D, U1>>,
DefaultAllocator: Allocator<T, D>,
{
<span class="kw">if </span>v[v.len() - <span class="number">1</span>].is_zero() {
<span class="kw">let </span>nrows = D::from_usize(v.len() - <span class="number">1</span>);
<span class="prelude-val">Some</span>(v.generic_view((<span class="number">0</span>, <span class="number">0</span>), (nrows, Const::<<span class="number">1</span>>)).into_owned())
} <span class="kw">else </span>{
<span class="prelude-val">None
</span>}
}
}
<span class="kw">impl</span><T: Scalar, D: DimAdd<U1>, S: RawStorage<T, D>> Vector<T, D, S> {
<span class="doccomment">/// Constructs a new vector of higher dimension by appending `element` to the end of `self`.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>push(<span class="kw-2">&</span><span class="self">self</span>, element: T) -> OVector<T, DimSum<D, U1>>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, DimSum<D, U1>>,
{
<span class="kw">let </span>len = <span class="self">self</span>.len();
<span class="kw">let </span>hnrows = DimSum::<D, U1>::from_usize(len + <span class="number">1</span>);
<span class="kw">let </span><span class="kw-2">mut </span>res = Matrix::uninit(hnrows, Const::<<span class="number">1</span>>);
<span class="comment">// This is basically a copy_from except that we warp the copied
// values into MaybeUninit.
</span>res.generic_view_mut((<span class="number">0</span>, <span class="number">0</span>), <span class="self">self</span>.shape_generic())
.zip_apply(<span class="self">self</span>, |out, e| <span class="kw-2">*</span>out = MaybeUninit::new(e));
res[(len, <span class="number">0</span>)] = MaybeUninit::new(element);
<span class="comment">// Safety: res has been fully initialized.
</span><span class="kw">unsafe </span>{ res.assume_init() }
}
}
<span class="kw">impl</span><T, R: Dim, C: Dim, S> AbsDiffEq <span class="kw">for </span>Matrix<T, R, C, S>
<span class="kw">where
</span>T: Scalar + AbsDiffEq,
S: RawStorage<T, R, C>,
T::Epsilon: Clone,
{
<span class="kw">type </span>Epsilon = T::Epsilon;
<span class="attr">#[inline]
</span><span class="kw">fn </span>default_epsilon() -> <span class="self">Self</span>::Epsilon {
T::default_epsilon()
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>abs_diff_eq(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>, epsilon: <span class="self">Self</span>::Epsilon) -> bool {
<span class="self">self</span>.iter()
.zip(other.iter())
.all(|(a, b)| a.abs_diff_eq(b, epsilon.clone()))
}
}
<span class="kw">impl</span><T, R: Dim, C: Dim, S> RelativeEq <span class="kw">for </span>Matrix<T, R, C, S>
<span class="kw">where
</span>T: Scalar + RelativeEq,
S: Storage<T, R, C>,
T::Epsilon: Clone,
{
<span class="attr">#[inline]
</span><span class="kw">fn </span>default_max_relative() -> <span class="self">Self</span>::Epsilon {
T::default_max_relative()
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>relative_eq(
<span class="kw-2">&</span><span class="self">self</span>,
other: <span class="kw-2">&</span><span class="self">Self</span>,
epsilon: <span class="self">Self</span>::Epsilon,
max_relative: <span class="self">Self</span>::Epsilon,
) -> bool {
<span class="self">self</span>.relative_eq(other, epsilon, max_relative)
}
}
<span class="kw">impl</span><T, R: Dim, C: Dim, S> UlpsEq <span class="kw">for </span>Matrix<T, R, C, S>
<span class="kw">where
</span>T: Scalar + UlpsEq,
S: RawStorage<T, R, C>,
T::Epsilon: Clone,
{
<span class="attr">#[inline]
</span><span class="kw">fn </span>default_max_ulps() -> u32 {
T::default_max_ulps()
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>ulps_eq(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>, epsilon: <span class="self">Self</span>::Epsilon, max_ulps: u32) -> bool {
<span class="macro">assert!</span>(<span class="self">self</span>.shape() == other.shape());
<span class="self">self</span>.iter()
.zip(other.iter())
.all(|(a, b)| a.ulps_eq(b, epsilon.clone(), max_ulps))
}
}
<span class="kw">impl</span><T, R: Dim, C: Dim, S> PartialOrd <span class="kw">for </span>Matrix<T, R, C, S>
<span class="kw">where
</span>T: Scalar + PartialOrd,
S: RawStorage<T, R, C>,
{
<span class="attr">#[inline]
</span><span class="kw">fn </span>partial_cmp(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="prelude-ty">Option</span><Ordering> {
<span class="kw">if </span><span class="self">self</span>.shape() != other.shape() {
<span class="kw">return </span><span class="prelude-val">None</span>;
}
<span class="kw">if </span><span class="self">self</span>.nrows() == <span class="number">0 </span>|| <span class="self">self</span>.ncols() == <span class="number">0 </span>{
<span class="kw">return </span><span class="prelude-val">Some</span>(Ordering::Equal);
}
<span class="kw">let </span><span class="kw-2">mut </span>first_ord = <span class="kw">unsafe </span>{
<span class="self">self</span>.data
.get_unchecked_linear(<span class="number">0</span>)
.partial_cmp(other.data.get_unchecked_linear(<span class="number">0</span>))
};
<span class="kw">if let </span><span class="prelude-val">Some</span>(first_ord) = first_ord.as_mut() {
<span class="kw">let </span><span class="kw-2">mut </span>it = <span class="self">self</span>.iter().zip(other.iter());
<span class="kw">let _ </span>= it.next(); <span class="comment">// Drop the first elements (we already tested it).
</span><span class="kw">for </span>(left, right) <span class="kw">in </span>it {
<span class="kw">if let </span><span class="prelude-val">Some</span>(ord) = left.partial_cmp(right) {
<span class="kw">match </span>ord {
Ordering::Equal => { <span class="comment">/* Does not change anything. */ </span>}
Ordering::Less => {
<span class="kw">if </span><span class="kw-2">*</span>first_ord == Ordering::Greater {
<span class="kw">return </span><span class="prelude-val">None</span>;
}
<span class="kw-2">*</span>first_ord = ord
}
Ordering::Greater => {
<span class="kw">if </span><span class="kw-2">*</span>first_ord == Ordering::Less {
<span class="kw">return </span><span class="prelude-val">None</span>;
}
<span class="kw-2">*</span>first_ord = ord
}
}
} <span class="kw">else </span>{
<span class="kw">return </span><span class="prelude-val">None</span>;
}
}
}
first_ord
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>lt(<span class="kw-2">&</span><span class="self">self</span>, right: <span class="kw-2">&</span><span class="self">Self</span>) -> bool {
<span class="macro">assert_eq!</span>(
<span class="self">self</span>.shape(),
right.shape(),
<span class="string">"Matrix comparison error: dimensions mismatch."
</span>);
<span class="self">self</span>.iter().zip(right.iter()).all(|(a, b)| a.lt(b))
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>le(<span class="kw-2">&</span><span class="self">self</span>, right: <span class="kw-2">&</span><span class="self">Self</span>) -> bool {
<span class="macro">assert_eq!</span>(
<span class="self">self</span>.shape(),
right.shape(),
<span class="string">"Matrix comparison error: dimensions mismatch."
</span>);
<span class="self">self</span>.iter().zip(right.iter()).all(|(a, b)| a.le(b))
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>gt(<span class="kw-2">&</span><span class="self">self</span>, right: <span class="kw-2">&</span><span class="self">Self</span>) -> bool {
<span class="macro">assert_eq!</span>(
<span class="self">self</span>.shape(),
right.shape(),
<span class="string">"Matrix comparison error: dimensions mismatch."
</span>);
<span class="self">self</span>.iter().zip(right.iter()).all(|(a, b)| a.gt(b))
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>ge(<span class="kw-2">&</span><span class="self">self</span>, right: <span class="kw-2">&</span><span class="self">Self</span>) -> bool {
<span class="macro">assert_eq!</span>(
<span class="self">self</span>.shape(),
right.shape(),
<span class="string">"Matrix comparison error: dimensions mismatch."
</span>);
<span class="self">self</span>.iter().zip(right.iter()).all(|(a, b)| a.ge(b))
}
}
<span class="kw">impl</span><T, R: Dim, C: Dim, S> Eq <span class="kw">for </span>Matrix<T, R, C, S>
<span class="kw">where
</span>T: Scalar + Eq,
S: RawStorage<T, R, C>,
{
}
<span class="kw">impl</span><T, R, R2, C, C2, S, S2> PartialEq<Matrix<T, R2, C2, S2>> <span class="kw">for </span>Matrix<T, R, C, S>
<span class="kw">where
</span>T: Scalar + PartialEq,
C: Dim,
C2: Dim,
R: Dim,
R2: Dim,
S: RawStorage<T, R, C>,
S2: RawStorage<T, R2, C2>,
{
<span class="attr">#[inline]
</span><span class="kw">fn </span>eq(<span class="kw-2">&</span><span class="self">self</span>, right: <span class="kw-2">&</span>Matrix<T, R2, C2, S2>) -> bool {
<span class="self">self</span>.shape() == right.shape() && <span class="self">self</span>.iter().zip(right.iter()).all(|(l, r)| l == r)
}
}
<span class="macro">macro_rules! </span>impl_fmt {
(<span class="macro-nonterminal">$</span><span class="kw">trait</span>: <span class="macro-nonterminal">path</span>, <span class="macro-nonterminal">$fmt_str_without_precision</span>: expr, <span class="macro-nonterminal">$fmt_str_with_precision</span>: expr) => {
<span class="kw">impl</span><T, R: Dim, C: Dim, S> <span class="macro-nonterminal">$</span><span class="kw">trait for </span><span class="macro-nonterminal">Matrix</span><T, R, C, S>
<span class="kw">where
</span>T: Scalar + <span class="macro-nonterminal">$</span><span class="kw">trait</span>,
<span class="macro-nonterminal">S</span>: RawStorage<T, R, C>,
{
<span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result {
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="kw">fn </span>val_width<T: Scalar + <span class="macro-nonterminal">$</span><span class="kw">trait</span>>(<span class="macro-nonterminal">val</span>: <span class="kw-2">&</span>T, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> usize {
<span class="kw">match </span>f.precision() {
<span class="prelude-val">Some</span>(precision) => <span class="macro">format!</span>(<span class="macro-nonterminal">$fmt_str_with_precision</span>, val, precision)
.chars()
.count(),
<span class="prelude-val">None </span>=> <span class="macro">format!</span>(<span class="macro-nonterminal">$fmt_str_without_precision</span>, val).chars().count(),
}
}
<span class="attr">#[cfg(not(feature = <span class="string">"std"</span>))]
</span><span class="kw">fn </span>val_width<T: Scalar + <span class="macro-nonterminal">$</span><span class="kw">trait</span>>(<span class="kw">_</span>: <span class="kw-2">&</span><span class="macro-nonterminal">T</span>, <span class="kw">_</span>: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> usize {
<span class="number">4
</span>}
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape();
<span class="kw">if </span>nrows == <span class="number">0 </span>|| ncols == <span class="number">0 </span>{
<span class="kw">return </span><span class="macro">write!</span>(f, <span class="string">"[ ]"</span>);
}
<span class="kw">let </span><span class="kw-2">mut </span>max_length = <span class="number">0</span>;
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..nrows {
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..ncols {
max_length = <span class="kw">crate</span>::max(max_length, val_width(<span class="kw-2">&</span><span class="self">self</span>[(i, j)], f));
}
}
<span class="kw">let </span>max_length_with_space = max_length + <span class="number">1</span>;
<span class="macro">writeln!</span>(f)<span class="question-mark">?</span>;
<span class="macro">writeln!</span>(
f,
<span class="string">" ┌ {:>width$} ┐"</span>,
<span class="string">""</span>,
width = max_length_with_space * ncols - <span class="number">1
</span>)<span class="question-mark">?</span>;
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..nrows {
<span class="macro">write!</span>(f, <span class="string">" │"</span>)<span class="question-mark">?</span>;
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..ncols {
<span class="kw">let </span>number_length = val_width(<span class="kw-2">&</span><span class="self">self</span>[(i, j)], f) + <span class="number">1</span>;
<span class="kw">let </span>pad = max_length_with_space - number_length;
<span class="macro">write!</span>(f, <span class="string">" {:>thepad$}"</span>, <span class="string">""</span>, thepad = pad)<span class="question-mark">?</span>;
<span class="kw">match </span>f.precision() {
<span class="prelude-val">Some</span>(precision) => {
<span class="macro">write!</span>(f, <span class="macro-nonterminal">$fmt_str_with_precision</span>, (<span class="kw-2">*</span><span class="self">self</span>)[(i, j)], precision)<span class="question-mark">?
</span>}
<span class="prelude-val">None </span>=> <span class="macro">write!</span>(f, <span class="macro-nonterminal">$fmt_str_without_precision</span>, (<span class="kw-2">*</span><span class="self">self</span>)[(i, j)])<span class="question-mark">?</span>,
}
}
<span class="macro">writeln!</span>(f, <span class="string">" │"</span>)<span class="question-mark">?</span>;
}
<span class="macro">writeln!</span>(
f,
<span class="string">" └ {:>width$} ┘"</span>,
<span class="string">""</span>,
width = max_length_with_space * ncols - <span class="number">1
</span>)<span class="question-mark">?</span>;
<span class="macro">writeln!</span>(f)
}
}
};
}
<span class="macro">impl_fmt!</span>(fmt::Display, <span class="string">"{}"</span>, <span class="string">"{:.1$}"</span>);
<span class="macro">impl_fmt!</span>(fmt::LowerExp, <span class="string">"{:e}"</span>, <span class="string">"{:.1$e}"</span>);
<span class="macro">impl_fmt!</span>(fmt::UpperExp, <span class="string">"{:E}"</span>, <span class="string">"{:.1$E}"</span>);
<span class="macro">impl_fmt!</span>(fmt::Octal, <span class="string">"{:o}"</span>, <span class="string">"{:1$o}"</span>);
<span class="macro">impl_fmt!</span>(fmt::LowerHex, <span class="string">"{:x}"</span>, <span class="string">"{:1$x}"</span>);
<span class="macro">impl_fmt!</span>(fmt::UpperHex, <span class="string">"{:X}"</span>, <span class="string">"{:1$X}"</span>);
<span class="macro">impl_fmt!</span>(fmt::Binary, <span class="string">"{:b}"</span>, <span class="string">"{:.1$b}"</span>);
<span class="macro">impl_fmt!</span>(fmt::Pointer, <span class="string">"{:p}"</span>, <span class="string">"{:.1$p}"</span>);
<span class="attr">#[cfg(test)]
</span><span class="kw">mod </span>tests {
<span class="attr">#[test]
</span><span class="kw">fn </span>empty_display() {
<span class="kw">let </span>vec: Vec<f64> = Vec::new();
<span class="kw">let </span>dvector = <span class="kw">crate</span>::DVector::from_vec(vec);
<span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{}"</span>, dvector), <span class="string">"[ ]"</span>)
}
<span class="attr">#[test]
</span><span class="kw">fn </span>lower_exp() {
<span class="kw">let </span>test = <span class="kw">crate</span>::Matrix2::new(<span class="number">1e6</span>, <span class="number">2e5</span>, <span class="number">2e-5</span>, <span class="number">1.</span>);
<span class="macro">assert_eq!</span>(
<span class="macro">format!</span>(<span class="string">"{:e}"</span>, test),
<span class="string">r"
┌ ┐
│ 1e6 2e5 │
│ 2e-5 1e0 │
└ ┘
"
</span>)
}
}
<span class="doccomment">/// # Cross product
</span><span class="kw">impl</span><T: Scalar + ClosedAdd + ClosedSub + ClosedMul, R: Dim, C: Dim, S: RawStorage<T, R, C>>
Matrix<T, R, C, S>
{
<span class="doccomment">/// The perpendicular product between two 2D column vectors, i.e. `a.x * b.y - a.y * b.x`.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>perp<R2, C2, SB>(<span class="kw-2">&</span><span class="self">self</span>, b: <span class="kw-2">&</span>Matrix<T, R2, C2, SB>) -> T
<span class="kw">where
</span>R2: Dim,
C2: Dim,
SB: RawStorage<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, U2>
+ SameNumberOfColumns<C, U1>
+ SameNumberOfRows<R2, U2>
+ SameNumberOfColumns<C2, U1>,
{
<span class="kw">let </span>shape = <span class="self">self</span>.shape();
<span class="macro">assert_eq!</span>(
shape,
b.shape(),
<span class="string">"2D vector perpendicular product dimension mismatch."
</span>);
<span class="macro">assert_eq!</span>(
shape,
(<span class="number">2</span>, <span class="number">1</span>),
<span class="string">"2D perpendicular product requires (2, 1) vectors {:?}"</span>,
shape
);
<span class="comment">// SAFETY: assertion above ensures correct shape
</span><span class="kw">let </span>ax = <span class="kw">unsafe </span>{ <span class="self">self</span>.get_unchecked((<span class="number">0</span>, <span class="number">0</span>)).clone() };
<span class="kw">let </span>ay = <span class="kw">unsafe </span>{ <span class="self">self</span>.get_unchecked((<span class="number">1</span>, <span class="number">0</span>)).clone() };
<span class="kw">let </span>bx = <span class="kw">unsafe </span>{ b.get_unchecked((<span class="number">0</span>, <span class="number">0</span>)).clone() };
<span class="kw">let </span>by = <span class="kw">unsafe </span>{ b.get_unchecked((<span class="number">1</span>, <span class="number">0</span>)).clone() };
ax * by - ay * bx
}
<span class="comment">// TODO: use specialization instead of an assertion.
</span><span class="doccomment">/// The 3D cross product between two vectors.
///
/// Panics if the shape is not 3D vector. In the future, this will be implemented only for
/// dynamically-sized matrices and statically-sized 3D matrices.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>cross<R2, C2, SB>(<span class="kw-2">&</span><span class="self">self</span>, b: <span class="kw-2">&</span>Matrix<T, R2, C2, SB>) -> MatrixCross<T, R, C, R2, C2>
<span class="kw">where
</span>R2: Dim,
C2: Dim,
SB: RawStorage<T, R2, C2>,
DefaultAllocator: SameShapeAllocator<T, R, C, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
<span class="kw">let </span>shape = <span class="self">self</span>.shape();
<span class="macro">assert_eq!</span>(shape, b.shape(), <span class="string">"Vector cross product dimension mismatch."</span>);
<span class="macro">assert!</span>(
shape == (<span class="number">3</span>, <span class="number">1</span>) || shape == (<span class="number">1</span>, <span class="number">3</span>),
<span class="string">"Vector cross product dimension mismatch: must be (3, 1) or (1, 3) but found {:?}."</span>,
shape
);
<span class="kw">if </span>shape.<span class="number">0 </span>== <span class="number">3 </span>{
<span class="kw">unsafe </span>{
<span class="kw">let </span><span class="kw-2">mut </span>res = Matrix::uninit(Dim::from_usize(<span class="number">3</span>), Dim::from_usize(<span class="number">1</span>));
<span class="kw">let </span>ax = <span class="self">self</span>.get_unchecked((<span class="number">0</span>, <span class="number">0</span>));
<span class="kw">let </span>ay = <span class="self">self</span>.get_unchecked((<span class="number">1</span>, <span class="number">0</span>));
<span class="kw">let </span>az = <span class="self">self</span>.get_unchecked((<span class="number">2</span>, <span class="number">0</span>));
<span class="kw">let </span>bx = b.get_unchecked((<span class="number">0</span>, <span class="number">0</span>));
<span class="kw">let </span>by = b.get_unchecked((<span class="number">1</span>, <span class="number">0</span>));
<span class="kw">let </span>bz = b.get_unchecked((<span class="number">2</span>, <span class="number">0</span>));
<span class="kw-2">*</span>res.get_unchecked_mut((<span class="number">0</span>, <span class="number">0</span>)) =
MaybeUninit::new(ay.clone() * bz.clone() - az.clone() * by.clone());
<span class="kw-2">*</span>res.get_unchecked_mut((<span class="number">1</span>, <span class="number">0</span>)) =
MaybeUninit::new(az.clone() * bx.clone() - ax.clone() * bz.clone());
<span class="kw-2">*</span>res.get_unchecked_mut((<span class="number">2</span>, <span class="number">0</span>)) =
MaybeUninit::new(ax.clone() * by.clone() - ay.clone() * bx.clone());
<span class="comment">// Safety: res is now fully initialized.
</span>res.assume_init()
}
} <span class="kw">else </span>{
<span class="kw">unsafe </span>{
<span class="kw">let </span><span class="kw-2">mut </span>res = Matrix::uninit(Dim::from_usize(<span class="number">1</span>), Dim::from_usize(<span class="number">3</span>));
<span class="kw">let </span>ax = <span class="self">self</span>.get_unchecked((<span class="number">0</span>, <span class="number">0</span>));
<span class="kw">let </span>ay = <span class="self">self</span>.get_unchecked((<span class="number">0</span>, <span class="number">1</span>));
<span class="kw">let </span>az = <span class="self">self</span>.get_unchecked((<span class="number">0</span>, <span class="number">2</span>));
<span class="kw">let </span>bx = b.get_unchecked((<span class="number">0</span>, <span class="number">0</span>));
<span class="kw">let </span>by = b.get_unchecked((<span class="number">0</span>, <span class="number">1</span>));
<span class="kw">let </span>bz = b.get_unchecked((<span class="number">0</span>, <span class="number">2</span>));
<span class="kw-2">*</span>res.get_unchecked_mut((<span class="number">0</span>, <span class="number">0</span>)) =
MaybeUninit::new(ay.clone() * bz.clone() - az.clone() * by.clone());
<span class="kw-2">*</span>res.get_unchecked_mut((<span class="number">0</span>, <span class="number">1</span>)) =
MaybeUninit::new(az.clone() * bx.clone() - ax.clone() * bz.clone());
<span class="kw-2">*</span>res.get_unchecked_mut((<span class="number">0</span>, <span class="number">2</span>)) =
MaybeUninit::new(ax.clone() * by.clone() - ay.clone() * bx.clone());
<span class="comment">// Safety: res is now fully initialized.
</span>res.assume_init()
}
}
}
}
<span class="kw">impl</span><T: Scalar + Field, S: RawStorage<T, U3>> Vector<T, U3, S> {
<span class="doccomment">/// Computes the matrix `M` such that for all vector `v` we have `M * v == self.cross(&v)`.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>cross_matrix(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, U3, U3> {
OMatrix::<T, U3, U3>::new(
T::zero(),
-<span class="self">self</span>[<span class="number">2</span>].clone(),
<span class="self">self</span>[<span class="number">1</span>].clone(),
<span class="self">self</span>[<span class="number">2</span>].clone(),
T::zero(),
-<span class="self">self</span>[<span class="number">0</span>].clone(),
-<span class="self">self</span>[<span class="number">1</span>].clone(),
<span class="self">self</span>[<span class="number">0</span>].clone(),
T::zero(),
)
}
}
<span class="kw">impl</span><T: SimdComplexField, R: Dim, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S> {
<span class="doccomment">/// The smallest angle between two vectors.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>angle<R2: Dim, C2: Dim, SB>(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span>Matrix<T, R2, C2, SB>) -> T::SimdRealField
<span class="kw">where
</span>SB: Storage<T, R2, C2>,
ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,
{
<span class="kw">let </span>prod = <span class="self">self</span>.dotc(other);
<span class="kw">let </span>n1 = <span class="self">self</span>.norm();
<span class="kw">let </span>n2 = other.norm();
<span class="kw">if </span>n1.is_zero() || n2.is_zero() {
T::SimdRealField::zero()
} <span class="kw">else </span>{
<span class="kw">let </span>cang = prod.simd_real() / (n1 * n2);
cang.simd_clamp(-T::SimdRealField::one(), T::SimdRealField::one())
.simd_acos()
}
}
}
<span class="kw">impl</span><T, R: Dim, C: Dim, S> AbsDiffEq <span class="kw">for </span>Unit<Matrix<T, R, C, S>>
<span class="kw">where
</span>T: Scalar + AbsDiffEq,
S: RawStorage<T, R, C>,
T::Epsilon: Clone,
{
<span class="kw">type </span>Epsilon = T::Epsilon;
<span class="attr">#[inline]
</span><span class="kw">fn </span>default_epsilon() -> <span class="self">Self</span>::Epsilon {
T::default_epsilon()
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>abs_diff_eq(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>, epsilon: <span class="self">Self</span>::Epsilon) -> bool {
<span class="self">self</span>.as_ref().abs_diff_eq(other.as_ref(), epsilon)
}
}
<span class="kw">impl</span><T, R: Dim, C: Dim, S> RelativeEq <span class="kw">for </span>Unit<Matrix<T, R, C, S>>
<span class="kw">where
</span>T: Scalar + RelativeEq,
S: Storage<T, R, C>,
T::Epsilon: Clone,
{
<span class="attr">#[inline]
</span><span class="kw">fn </span>default_max_relative() -> <span class="self">Self</span>::Epsilon {
T::default_max_relative()
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>relative_eq(
<span class="kw-2">&</span><span class="self">self</span>,
other: <span class="kw-2">&</span><span class="self">Self</span>,
epsilon: <span class="self">Self</span>::Epsilon,
max_relative: <span class="self">Self</span>::Epsilon,
) -> bool {
<span class="self">self</span>.as_ref()
.relative_eq(other.as_ref(), epsilon, max_relative)
}
}
<span class="kw">impl</span><T, R: Dim, C: Dim, S> UlpsEq <span class="kw">for </span>Unit<Matrix<T, R, C, S>>
<span class="kw">where
</span>T: Scalar + UlpsEq,
S: RawStorage<T, R, C>,
T::Epsilon: Clone,
{
<span class="attr">#[inline]
</span><span class="kw">fn </span>default_max_ulps() -> u32 {
T::default_max_ulps()
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>ulps_eq(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>, epsilon: <span class="self">Self</span>::Epsilon, max_ulps: u32) -> bool {
<span class="self">self</span>.as_ref().ulps_eq(other.as_ref(), epsilon, max_ulps)
}
}
<span class="kw">impl</span><T, R, C, S> Hash <span class="kw">for </span>Matrix<T, R, C, S>
<span class="kw">where
</span>T: Scalar + Hash,
R: Dim,
C: Dim,
S: RawStorage<T, R, C>,
{
<span class="kw">fn </span>hash<H: Hasher>(<span class="kw-2">&</span><span class="self">self</span>, state: <span class="kw-2">&mut </span>H) {
<span class="kw">let </span>(nrows, ncols) = <span class="self">self</span>.shape();
(nrows, ncols).hash(state);
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..ncols {
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..nrows {
<span class="kw">unsafe </span>{
<span class="self">self</span>.get_unchecked((i, j)).hash(state);
}
}
}
}
}
<span class="kw">impl</span><T, D, S> Unit<Vector<T, D, S>>
<span class="kw">where
</span>T: Scalar,
D: Dim,
S: RawStorage<T, D, U1>,
{
<span class="doccomment">/// Cast the components of `self` to another type.
///
/// # Example
/// ```
/// # use nalgebra::Vector3;
/// let v = Vector3::<f64>::y_axis();
/// let v2 = v.cast::<f32>();
/// assert_eq!(v2, Vector3::<f32>::y_axis());
/// ```
</span><span class="kw">pub fn </span>cast<T2: Scalar>(<span class="self">self</span>) -> Unit<OVector<T2, D>>
<span class="kw">where
</span>T: Scalar,
OVector<T2, D>: SupersetOf<Vector<T, D, S>>,
DefaultAllocator: Allocator<T2, D, U1>,
{
Unit::new_unchecked(<span class="kw">crate</span>::convert_ref(<span class="self">self</span>.as_ref()))
}
}
</code></pre></div>
</section></div></main><div id="rustdoc-vars" data-root-path="../../../" data-static-root-path="../../../static.files/" data-current-crate="nalgebra" data-themes="" data-resource-suffix="" data-rustdoc-version="1.67.1 (d5a82bbd2 2023-02-07)" data-search-js="search-444266647c4dba98.js" data-settings-js="settings-bebeae96e00e4617.js" data-settings-css="settings-af96d9e2fc13e081.css" ></div></body></html>