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<p class="MsoNormal"><span lang="EN-US">Dear All<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">May I ask you advices in order to use vectorization instead of the loop? All the trials I did have failed – the problem I’m confront to comes from the S matrix<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Thanks for your feedback<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Paul<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">########################################################<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">clc</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">mode</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">0</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">clear</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:#B01813;mso-fareast-language:FR">function</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<b><span style="color:#834310">V</span></b><span style="color:#5C5C5C">=</span><u><span style="color:black">eigen_val</span></u><span style="color:#4A55DB">(</span><b><span style="color:#834310">S11</span></b><span style="color:black">,
</span><b><span style="color:#834310">S12</span></b><span style="color:black">, </span>
<b><span style="color:#834310">S13</span></b><span style="color:black">, </span><b><span style="color:#834310">S22</span></b><span style="color:black">,
</span><b><span style="color:#834310">S23</span></b><span style="color:black">, </span>
<b><span style="color:#834310">S33</span></b><span style="color:#4A55DB">)</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:black">S_u</span> <span style="color:#5C5C5C">=</span> <span style="color:#4A55DB">
[</span><span style="color:rosybrown">0</span> <b><span style="color:#834310">S12</span></b>
<b><span style="color:#834310">S13</span></b> <span style="color:black">;</span> <span style="color:rosybrown">
0</span> <span style="color:rosybrown">0</span> <b><span style="color:#834310">S23</span></b>
<span style="color:black">;</span> <span style="color:rosybrown">0.</span> <span style="color:rosybrown">
0.</span> <span style="color:rosybrown">0.</span><span style="color:#4A55DB">]</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:black">S_d</span> <span style="color:#5C5C5C">=</span> <span style="color:#4A55DB">
[</span><b><span style="color:#834310">S11</span></b> <span style="color:black">;</span>
<b><span style="color:#834310">S22</span></b> <span style="color:black">;</span> <b>
<span style="color:#834310">S33</span></b><span style="color:#4A55DB">]</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:black">S</span> <span style="color:#5C5C5C">=</span> <span style="color:black">
S_u</span> <span style="color:#5C5C5C">+</span> <span style="color:black">S_u</span><span style="color:#5C5C5C">'</span>
<span style="color:#5C5C5C">+</span> <span style="color:#32B9B9">diag</span><span style="color:#4A55DB">(</span><span style="color:black">S_d</span><span style="color:#4A55DB">)</span><span style="color:black">;</span>
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"> <b><span style="color:#834310">V</span></b>
<span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">gsort</span><span style="color:#4A55DB">(</span><span style="color:#32B9B9">spec</span><span style="color:#4A55DB">(</span><span style="color:black">S</span><span style="color:#4A55DB">)</span><span style="color:black">,</span><span style="color:rosybrown">'lr'</span><span style="color:black">,</span><span style="color:rosybrown">'d'</span><span style="color:#4A55DB">)</span><span style="color:#5C5C5C">'</span><span style="color:black">;</span>
<span style="color:#32B9B9">clear</span> <span style="color:rosybrown">S</span><span style="color:black">;</span>
<span style="color:#32B9B9">clear</span> <span style="color:rosybrown">S_u</span><span style="color:black">;</span>
<span style="color:#32B9B9">clear</span> <span style="color:rosybrown">S_d</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:#B01813;mso-fareast-language:FR">endfunction</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">n</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:rosybrown">10</span><span style="color:black">;</span>
<span style="color:black">m</span> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">
1</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">S11</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">rand</span><span style="color:#4A55DB">(</span><span style="color:black">n,m</span><span style="color:#4A55DB">)</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">S22</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">rand</span><span style="color:#4A55DB">(</span><span style="color:black">n,m</span><span style="color:#4A55DB">)</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">S33</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">rand</span><span style="color:#4A55DB">(</span><span style="color:black">n,m</span><span style="color:#4A55DB">)</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">S12</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">rand</span><span style="color:#4A55DB">(</span><span style="color:black">n,m</span><span style="color:#4A55DB">)</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">S23</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">rand</span><span style="color:#4A55DB">(</span><span style="color:black">n,m</span><span style="color:#4A55DB">)</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">S13</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">rand</span><span style="color:#4A55DB">(</span><span style="color:black">n,m</span><span style="color:#4A55DB">)</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">princ</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">zeros</span><span style="color:#4A55DB">(</span><span style="color:black">n,</span><span style="color:rosybrown">3</span><span style="color:#4A55DB">)</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p> </o:p></span></p>
<p class="MsoNormal"><i><span lang="EN-US" style="font-family:"Monospaced","serif";color:#64AE64;mso-fareast-language:FR">// with a loop</span></i><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">tic</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">()</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">;</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">princ1</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">zeros</span><span style="color:#4A55DB">(</span><span style="color:black">n,</span><span style="color:rosybrown">3</span><span style="color:#5C5C5C">*</span><span style="color:black">m</span><span style="color:#4A55DB">)</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:#A020F0;mso-fareast-language:FR">for</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:black">i</span> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">
1</span> <span style="color:#FFAA00">:</span> <span style="color:black">n</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:black">S_u</span> <span style="color:#5C5C5C">=</span> <span style="color:#4A55DB">
[</span><span style="color:rosybrown">0</span> <span style="color:black">S12</span><span style="color:#4A55DB">(</span><span style="color:black">i,m</span><span style="color:#4A55DB">)</span>
<span style="color:black">S13</span><span style="color:#4A55DB">(</span><span style="color:black">i,m</span><span style="color:#4A55DB">)</span>
<span style="color:black">;</span> <span style="color:rosybrown">0</span> <span style="color:rosybrown">
0</span> <span style="color:black">S23</span><span style="color:#4A55DB">(</span><span style="color:black">i,m</span><span style="color:#4A55DB">)</span>
<span style="color:black">;</span> <span style="color:rosybrown">0.</span> <span style="color:rosybrown">
0.</span> <span style="color:rosybrown">0.</span><span style="color:#4A55DB">]</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:black">S_d</span> <span style="color:#5C5C5C">=</span> <span style="color:#4A55DB">
[</span><span style="color:black">S11</span><span style="color:#4A55DB">(</span><span style="color:black">i,m</span><span style="color:#4A55DB">)</span>
<span style="color:black">;</span> <span style="color:black">S22</span><span style="color:#4A55DB">(</span><span style="color:black">i,</span><span style="color:rosybrown">1</span><span style="color:#4A55DB">)</span>
<span style="color:black">;</span> <span style="color:black">S33</span><span style="color:#4A55DB">(</span><span style="color:black">i,m</span><span style="color:#4A55DB">)]</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:black">S</span> <span style="color:#5C5C5C">=</span> <span style="color:black">
S_u</span> <span style="color:#5C5C5C">+</span> <span style="color:black">S_u</span><span style="color:#5C5C5C">'</span>
<span style="color:#5C5C5C">+</span> <span style="color:#32B9B9">diag</span><span style="color:#4A55DB">(</span><span style="color:black">S_d</span><span style="color:#4A55DB">)</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:black">princ1</span><span style="color:#4A55DB">(</span><span style="color:black">i,</span><span style="color:#FFAA00">:</span><span style="color:#4A55DB">)</span>
<span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">gsort</span><span style="color:#4A55DB">(</span><span style="color:#32B9B9">spec</span><span style="color:#4A55DB">(</span><span style="color:black">S</span><span style="color:#4A55DB">)</span><span style="color:black">,</span><span style="color:rosybrown">'lr'</span><span style="color:black">,</span><span style="color:rosybrown">'d'</span><span style="color:#4A55DB">)</span><span style="color:#5C5C5C">'</span><span style="color:black">;</span>
<span style="color:#32B9B9">clear</span> <span style="color:rosybrown">S</span><span style="color:black">;</span>
<span style="color:#32B9B9">clear</span> <span style="color:rosybrown">S_u</span><span style="color:black">;</span>
<span style="color:#32B9B9">clear</span> <span style="color:rosybrown">S_d</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:#A020F0;mso-fareast-language:FR">end</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">duration1</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">toc</span><span style="color:#4A55DB">()</span><span style="color:black">;</span>
<span style="color:#32B9B9">printf</span><span style="color:#4A55DB">(</span><span style="color:rosybrown">"Duration 1 = %g\n"</span><span style="color:black">,duration1</span><span style="color:#4A55DB">)</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p> </o:p></span></p>
<p class="MsoNormal"><i><span lang="EN-US" style="font-family:"Monospaced","serif";color:#64AE64;mso-fareast-language:FR">// using a function</span></i><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">tic</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">()</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">;</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">princ2</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">zeros</span><span style="color:#4A55DB">(</span><span style="color:black">n,</span><span style="color:rosybrown">3</span><span style="color:#5C5C5C">*</span><span style="color:black">m</span><span style="color:#4A55DB">)</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:#A020F0;mso-fareast-language:FR">for</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:black">i</span> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">
1</span> <span style="color:#FFAA00">:</span> <span style="color:black">n</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:black">princ2</span><span style="color:#4A55DB">(</span><span style="color:black">i,</span><span style="color:#FFAA00">:</span><span style="color:#4A55DB">)</span>
<span style="color:#5C5C5C">=</span> <u><span style="color:black">eigen_val</span></u><span style="color:#4A55DB">(</span><span style="color:black">S11</span><span style="color:#4A55DB">(</span><span style="color:black">i,m</span><span style="color:#4A55DB">)</span><span style="color:black">,S12</span><span style="color:#4A55DB">(</span><span style="color:black">i,m</span><span style="color:#4A55DB">)</span><span style="color:black">,S13</span><span style="color:#4A55DB">(</span><span style="color:black">i,m</span><span style="color:#4A55DB">)</span><span style="color:black">,S22</span><span style="color:#4A55DB">(</span><span style="color:black">i,m</span><span style="color:#4A55DB">)</span><span style="color:black">,S23</span><span style="color:#4A55DB">(</span><span style="color:black">i,m</span><span style="color:#4A55DB">)</span><span style="color:black">,S33</span><span style="color:#4A55DB">(</span><span style="color:black">i,m</span><span style="color:#4A55DB">))</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:#A020F0;mso-fareast-language:FR">end</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">duration2</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">toc</span><span style="color:#4A55DB">()</span><span style="color:black">;</span>
<span style="color:#32B9B9">printf</span><span style="color:#4A55DB">(</span><span style="color:rosybrown">"Duration 2 = %g\n"</span><span style="color:black">,duration2</span><span style="color:#4A55DB">)</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR">isequal</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">princ1,princ2</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p> </o:p></span></p>
<p class="MsoNormal"><i><span lang="EN-US" style="font-family:"Monospaced","serif";color:#64AE64;mso-fareast-language:FR">// using vectorization (in combination with the function ?)</span></i><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">i</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#4A55DB">(</span><span style="color:rosybrown">1</span><span style="color:#FFAA00">:</span><span style="color:black">n</span><span style="color:#4A55DB">)</span><span style="color:#5C5C5C">'</span><span style="color:black">;</span><o:p></o:p></span></p>
<pre><span lang="EN-US" style="font-size:11.0pt;font-family:"Monospaced","serif";color:black">S</span><span lang="EN-US" style="font-size:11.0pt;font-family:"Monospaced","serif""> <span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">zeros</span><span style="color:#4A55DB">(</span><span style="color:rosybrown">3</span><span style="color:black">,</span><span style="color:rosybrown">3</span><span style="color:black">,n</span><span style="color:#4A55DB">)</span><o:p></o:p></span></pre>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
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