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<div class="moz-cite-prefix">Like this (I have simplified your
script a little bit) for n=1000 there is a x60 speedup with
Cardan's formulas:<br>
</div>
<pre style="font-family:Monospaced;font-style:normal;font-size:14.0;"><span style="color:rgb(50,185,185);">clear</span>
<span style="color:rgb(0,0,0);">n</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(188,143,143);">1000</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">S11</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(50,185,185);">rand</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">n</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(188,143,143);">1</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">S22</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(50,185,185);">rand</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">n</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(188,143,143);">1</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">S33</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(50,185,185);">rand</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">n</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(188,143,143);">1</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">S12</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(50,185,185);">rand</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">n</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(188,143,143);">1</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">S23</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(50,185,185);">rand</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">n</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(188,143,143);">1</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">S13</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(50,185,185);">rand</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">n</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(188,143,143);">1</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">princ</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(50,185,185);">zeros</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">n</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(188,143,143);">3</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(100,174,100);font-style:italic;">// with a loop</span>
<span style="color:rgb(50,185,185);">tic</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">princ1</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(50,185,185);">zeros</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">n</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(188,143,143);">3</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(160,32,240);">for</span> <span style="color:rgb(0,0,0);">i</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(188,143,143);">1</span> <span style="color:rgb(255,170,0);">:</span> <span style="color:rgb(0,0,0);">n</span>
<span style="color:rgb(0,0,0);">S</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(74,85,219);">[</span><span style="color:rgb(0,0,0);">S11</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">i</span><span style="color:rgb(74,85,219);">)</span> <span style="color:rgb(0,0,0);">S12</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">i</span><span style="color:rgb(74,85,219);">)</span> <span style="color:rgb(0,0,0);">S13</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">i</span><span style="color:rgb(74,85,219);">)</span>
<span style="color:rgb(0,0,0);">S12</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">i</span><span style="color:rgb(74,85,219);">)</span> <span style="color:rgb(0,0,0);">S22</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">i</span><span style="color:rgb(74,85,219);">)</span> <span style="color:rgb(0,0,0);">S23</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">i</span><span style="color:rgb(74,85,219);">)</span>
<span style="color:rgb(0,0,0);">S13</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">i</span><span style="color:rgb(74,85,219);">)</span> <span style="color:rgb(0,0,0);">S23</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">i</span><span style="color:rgb(74,85,219);">)</span> <span style="color:rgb(0,0,0);">S33</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">i</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(74,85,219);">]</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">princ1</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">i</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(255,170,0);">:</span><span style="color:rgb(74,85,219);">)</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(50,185,185);">gsort</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(50,185,185);">spec</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">S</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(92,92,92);">'</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(160,32,240);">end</span>
<span style="color:rgb(0,0,0);">duration1</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(50,185,185);">toc</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span> <span style="color:rgb(50,185,185);">printf</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(188,143,143);">"</span><span style="color:rgb(188,143,143);">Duration 1 = %g\n</span><span style="color:rgb(188,143,143);">"</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(0,0,0);">duration1</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(100,174,100);font-style:italic;">// using Cardan formulas</span>
<span style="color:rgb(50,185,185);">tic</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(100,174,100);font-style:italic;">// characteristic polynomial is poly([d c b a],</span><span style="color:rgb(100,174,100);font-style:italic;">"</span><span style="color:rgb(100,174,100);font-style:italic;">x</span><span style="color:rgb(100,174,100);font-style:italic;">"</span><span style="color:rgb(100,174,100);font-style:italic;">,</span><span style="color:rgb(100,174,100);font-style:italic;">"</span><span style="color:rgb(100,174,100);font-style:italic;">coeff</span><span style="color:rgb(100,174,100);font-style:italic;">"</span><span style="color:rgb(100,174,100);font-style:italic;">)</span>
<span style="color:rgb(0,0,0);">S13sq</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(0,0,0);">S13</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(0,0,0);">S13</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">S12sq</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(0,0,0);">S12</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(0,0,0);">S12</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">S23sq</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(0,0,0);">S23</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(0,0,0);">S23</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);"><span style="color:rgb(100,174,100);font-style:italic;">//a=1; (not used)</span>
b</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(92,92,92);">-</span><span style="color:rgb(0,0,0);">S11</span><span style="color:rgb(92,92,92);">-</span><span style="color:rgb(0,0,0);">S22</span><span style="color:rgb(92,92,92);">-</span><span style="color:rgb(0,0,0);">S33</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">c</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(0,0,0);">S11</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(0,0,0);">S22</span><span style="color:rgb(92,92,92);">+</span><span style="color:rgb(0,0,0);">S11</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(0,0,0);">S33</span><span style="color:rgb(92,92,92);">+</span><span style="color:rgb(0,0,0);">S22</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(0,0,0);">S33</span><span style="color:rgb(92,92,92);">-</span><span style="color:rgb(0,0,0);">S23sq</span><span style="color:rgb(92,92,92);">-</span><span style="color:rgb(0,0,0);">S13sq</span><span style="color:rgb(92,92,92);">-</span><span style="color:rgb(0,0,0);">S12sq</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">d</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(0,0,0);">S11</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(0,0,0);">S23sq</span><span style="color:rgb(92,92,92);">+</span><span style="color:rgb(0,0,0);">S22</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(0,0,0);">S13sq</span><span style="color:rgb(92,92,92);">+</span><span style="color:rgb(0,0,0);">S12sq</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(0,0,0);">S33</span> <span style="color:rgb(92,92,92);">-</span> <span style="color:rgb(0,0,0);">S11</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(0,0,0);">S22</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(0,0,0);">S33</span><span style="color:rgb(92,92,92);">-</span><span style="color:rgb(188,143,143);">2</span><span style="color:rgb(92,92,92);">*</span><span style="color:rgb(0,0,0);">S13</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(0,0,0);">S12</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(0,0,0);">S23</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">b2</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(0,0,0);">b</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(0,0,0);">b</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">p</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(92,92,92);">-</span><span style="color:rgb(0,0,0);">b2</span><span style="color:rgb(92,92,92);">/</span><span style="color:rgb(188,143,143);">3</span><span style="color:rgb(92,92,92);">+</span><span style="color:rgb(0,0,0);">c</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">q</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(0,0,0);">b</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(188,143,143);">2</span><span style="color:rgb(92,92,92);">*</span><span style="color:rgb(0,0,0);">b2</span><span style="color:rgb(92,92,92);">-</span><span style="color:rgb(188,143,143);">9</span><span style="color:rgb(92,92,92);">*</span><span style="color:rgb(0,0,0);">c</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(92,92,92);">/</span><span style="color:rgb(188,143,143);">27</span><span style="color:rgb(92,92,92);">+</span><span style="color:rgb(0,0,0);">d</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(100,174,100);font-style:italic;">//delta=-(4*p.*p.*p+27*q.*q) (not used since matrix is symetric =</span><span style="color:rgb(100,174,100);font-style:italic;">></span><span style="color:rgb(100,174,100);font-style:italic;"> real eigenvalues)</span>
<span style="color:rgb(0,0,0);">princ2</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(50,185,185);">zeros</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">n</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(188,143,143);">3</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">theta</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(50,185,185);">acos</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(188,143,143);">1.5</span><span style="color:rgb(92,92,92);">*</span><span style="color:rgb(0,0,0);">q</span><span style="color:rgb(92,92,92);">./</span><span style="color:rgb(0,0,0);">p</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(50,185,185);">sqrt</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(92,92,92);">-</span><span style="color:rgb(188,143,143);">3.</span><span style="color:rgb(92,92,92);">/</span><span style="color:rgb(0,0,0);">p</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(92,92,92);">/</span><span style="color:rgb(188,143,143);">3</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(160,32,240);">for</span> <span style="color:rgb(0,0,0);">k</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(188,143,143);">0</span><span style="color:rgb(255,170,0);">:</span><span style="color:rgb(188,143,143);">2</span>
<span style="color:rgb(0,0,0);">princ2</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(255,170,0);">:</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(0,0,0);">k</span><span style="color:rgb(92,92,92);">+</span><span style="color:rgb(188,143,143);">1</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(188,143,143);">2</span><span style="color:rgb(92,92,92);">*</span><span style="color:rgb(50,185,185);">sqrt</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(92,92,92);">-</span><span style="color:rgb(0,0,0);">p</span><span style="color:rgb(92,92,92);">/</span><span style="color:rgb(188,143,143);">3</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(50,185,185);">cos</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">theta</span><span style="color:rgb(92,92,92);">+</span><span style="color:rgb(188,143,143);">2</span><span style="color:rgb(92,92,92);">*</span><span style="color:rgb(0,0,0);">k</span><span style="color:rgb(92,92,92);">*</span><span style="color:rgb(218,112,214);">%pi</span><span style="color:rgb(92,92,92);">/</span><span style="color:rgb(188,143,143);">3</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(92,92,92);">-</span><span style="color:rgb(0,0,0);">b</span><span style="color:rgb(92,92,92);">/</span><span style="color:rgb(188,143,143);">3</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(160,32,240);">end</span>
<span style="color:rgb(0,0,0);">princ2</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(50,185,185);">gsort</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">princ2</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(188,143,143);">"</span><span style="color:rgb(188,143,143);">c</span><span style="color:rgb(188,143,143);">"</span><span style="color:rgb(74,85,219);">)</span>
<span style="color:rgb(0,0,0);">duration2</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(50,185,185);">toc</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span> <span style="color:rgb(50,185,185);">printf</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(188,143,143);">"</span><span style="color:rgb(188,143,143);">Duration 2 = %g\n</span><span style="color:rgb(188,143,143);">"</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(0,0,0);">duration2</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(50,185,185);">disp</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(50,185,185);">norm</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">princ1</span><span style="color:rgb(92,92,92);">-</span><span style="color:rgb(0,0,0);">princ2</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(218,112,214);">%inf</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(74,85,219);">)</span>
<span style="color:rgb(50,185,185);">disp</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">duration1</span><span style="color:rgb(92,92,92);">/</span><span style="color:rgb(0,0,0);">duration2</span><span style="color:rgb(74,85,219);">)</span></pre>
S.
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">Le 18/01/2019 à 15:21, Stéphane
Mottelet a écrit :<br>
</div>
<blockquote type="cite"
cite="mid:b998d5cc-8701-1586-d2e1-98f46e6b793c@utc.fr">
<meta http-equiv="Content-Type" content="text/html;
charset=windows-1252">
<div class="moz-cite-prefix">Hello Paul,</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">If you stick to 3x3, you can
vectorize the Cardan formulas applied to the characteristic
polynomial of each individual matrix.</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">S.<br>
</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">Le 15/01/2019 à 09:56, Carrico, Paul
a écrit :<br>
</div>
<blockquote type="cite"
cite="mid:3A6B7233274DB449A2A0053A47684F953FF1B02B@BGS-EX01.auxitrol.ad">
<p class="MsoNormal"><span
style="font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR"
lang="EN-US">clc</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR"
lang="EN-US">mode</span><span
style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR"
lang="EN-US">(</span><span
style="font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR"
lang="EN-US">0</span><span
style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR"
lang="EN-US">)</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR"
lang="EN-US">clear</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-family:"Monospaced","serif";color:#B01813;mso-fareast-language:FR"
lang="EN-US">function</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";color:#B01813;mso-fareast-language:FR"
lang="EN-US">endfunction</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR"
lang="EN-US">n</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR"
lang="EN-US">S11</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR"
lang="EN-US">S22</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR"
lang="EN-US">S33</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR"
lang="EN-US">S12</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR"
lang="EN-US">S23</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR"
lang="EN-US">S13</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR"
lang="EN-US">princ</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><i><span
style="font-family:"Monospaced","serif";color:#64AE64;mso-fareast-language:FR"
lang="EN-US">// with a loop</span></i><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR"
lang="EN-US">tic</span><span
style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR"
lang="EN-US">()</span><span
style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR"
lang="EN-US">;</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR"
lang="EN-US">princ1</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";color:#A020F0;mso-fareast-language:FR"
lang="EN-US">for</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";color:#A020F0;mso-fareast-language:FR"
lang="EN-US">end</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR"
lang="EN-US">duration1</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><i><span
style="font-family:"Monospaced","serif";color:#64AE64;mso-fareast-language:FR"
lang="EN-US">// using a function</span></i><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR"
lang="EN-US">tic</span><span
style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR"
lang="EN-US">()</span><span
style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR"
lang="EN-US">;</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR"
lang="EN-US">princ2</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";color:#A020F0;mso-fareast-language:FR"
lang="EN-US">for</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";color:#A020F0;mso-fareast-language:FR"
lang="EN-US">end</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR"
lang="EN-US">duration2</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-family:"Monospaced","serif";color:#32B9B9;mso-fareast-language:FR"
lang="EN-US">isequal</span><span
style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR"
lang="EN-US">(</span><span
style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR"
lang="EN-US">princ1,princ2</span><span
style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR"
lang="EN-US">)</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><i><span
style="font-family:"Monospaced","serif";color:#64AE64;mso-fareast-language:FR"
lang="EN-US">// using vectorization (in combination with
the function ?)</span></i><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR"
lang="EN-US">i</span><span
style="font-family:"Monospaced","serif";mso-fareast-language:FR"
lang="EN-US"> <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 style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">S</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <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></span></pre>
</blockquote>
<p><br>
</p>
<pre class="moz-signature" cols="72">--
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
<a class="moz-txt-link-freetext" href="https://antispam.utc.fr/proxy/1/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/www.utc.fr/~mottelet" moz-do-not-send="true">http://www.utc.fr/~mottelet</a></pre>
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</blockquote>
<p><br>
</p>
<pre class="moz-signature" cols="72">--
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
<a class="moz-txt-link-freetext" href="http://www.utc.fr/~mottelet">http://www.utc.fr/~mottelet</a></pre>
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