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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">I’m wondering if there’s a way to speed up the following code using both “numderivative” and “integrate” ?<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">I tried to replace the loops by vectors, but it fails …
<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">Of course this basic example has been put in place in order to test the code – I’m working with test results with more than 200 000 measurements.<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 any help and/or suggestions.<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">Regards<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">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";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:black;mso-fareast-language:FR">PATH</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">get_absolute_file_path</span><span style="color:#4A55DB">(</span><span style="color:rosybrown">"test_signal.sce"</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">// here we generate a sin signal just for testing</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">Gamma_ampl</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>
<i><span style="color:#64AE64">// in [g]</span></i><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">Frequency</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:rosybrown">100</span><span style="color:black">;</span>
<i><span style="color:#64AE64">// in [Hz]</span></i><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">Omega</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:rosybrown">2</span> <span style="color:#5C5C5C">
*</span> <span style="color:orchid">%pi</span> <span style="color:#5C5C5C">*</span>
<span style="color:black">Frequency;</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">Number_of_periods</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><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">t</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">0</span>
<span style="color:#FFAA00">:</span> <span style="color:#4A55DB">(</span><span style="color:rosybrown">1</span><span style="color:#5C5C5C">/</span><span style="color:#4A55DB">(</span><span style="color:rosybrown">20</span>
<span style="color:#5C5C5C">*</span> <span style="color:black">Frequency</span><span style="color:#4A55DB">))</span>
<span style="color:#FFAA00">:</span> <span style="color:#4A55DB">(</span><span style="color:black">Number_of_periods</span>
<span style="color:#5C5C5C">/</span> <span style="color:black">Frequency</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">Acceleration</span><span style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:black">Gamma_ampl</span> <span style="color:#5C5C5C">
*</span><span style="color:#32B9B9">sin</span><span style="color:#4A55DB">(</span><span style="color:black">Omega</span>
<span style="color:#5C5C5C">*</span> <span style="color:black">t</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">Signal</span><span style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <span style="color:#4A55DB">[</span><span style="color:black">t</span>
<span style="color:black">;</span> <span style="color:black">Acceleration</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"><o:p> </o:p></span></p>
<p class="MsoNormal"><u><span style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">scf</span></u><span style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">()</span><span style="font-family:"Monospaced","serif";mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><u><span style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">plot</span></u><span style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><span style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">t,Acceleration,</span><span style="font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">'g'</span><span style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">)</span><span style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">;</span><span 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">xtitle</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">'Ref
curve - accelerogram'</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";color:rosybrown;mso-fareast-language:FR">'t'</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";color:rosybrown;mso-fareast-language:FR">'$\gamma
\mbox{[m/s$^{2}$]}$'</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:#32B9B9;mso-fareast-language:FR">xs2png</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">gcf</span></u><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";color:rosybrown;mso-fareast-language:FR">'Accelerogram.png'</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";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">// signal first derivation : y' = (Omega * Gamma_ampl)*cos(Omega * t)</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">Acceleration_prime</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:black">Omega</span>
<span style="color:#5C5C5C">*</span> <span style="color:black">Gamma_ampl</span><span style="color:#4A55DB">)</span>
<span style="color:#5C5C5C">*</span> <span style="color:#32B9B9">cos</span><span style="color:#4A55DB">(</span><span style="color:black">Omega</span>
<span style="color:#5C5C5C">*</span> <span style="color:black">t</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">// calculation of the jerk -> numerical derivative</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:#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">y</span></b><span style="color:#5C5C5C">=</span><u><span style="color:black">Gamma_function</span></u><span style="color:#4A55DB">(</span><b><span style="color:#834310">x</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">
<b><span style="color:#834310">y</span></b> <span style="color:#5C5C5C">=</span> <u>
<span style="color:#AE5CB0">interpln</span></u><span style="color:#4A55DB">(</span><span style="color:black">Signal,</span><b><span style="color:#834310">x</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";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:#32B9B9">size</span><span style="color:#4A55DB">(</span><span style="color:black">t,</span><span style="color:rosybrown">'*'</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">Numl_Gamma_derrivative</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:rosybrown">2</span><span style="color:black">,n</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">Numl_Gamma_derrivative</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">1</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";color:#FFAA00;mso-fareast-language:FR">:</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">
<span style="color:#5C5C5C">=</span> <span style="color:black">t;</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"><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">tic</span></u><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:#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">Numl_Gamma_derrivative</span><span style="color:#4A55DB">(</span><span style="color:rosybrown">2</span><span style="color:black">,i</span><span style="color:#4A55DB">)</span>
<span style="color:#5C5C5C">=</span> <u><span style="color:#AE5CB0">numderivative</span></u><span style="color:#4A55DB">(</span><u><span style="color:black">Gamma_function</span></u><span style="color:black">,</span>
<span style="color:black">Numl_Gamma_derrivative</span><span style="color:#4A55DB">(</span><span style="color:rosybrown">1</span><span style="color:black">,i</span><span style="color:#4A55DB">)</span><span style="color:black">,</span><span style="color:rosybrown">1e-3</span><span style="color:black">,order</span><span style="color:#5C5C5C">=</span><span style="color:rosybrown">4</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">Numederivative_duration</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <u><span style="color:#AE5CB0">toc</span></u><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"><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">scf</span></u><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"><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">plot</span></u><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">Numl_Gamma_derrivative</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">1</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";color:#FFAA00;mso-fareast-language:FR">:</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">,Numl_Gamma_derrivative</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">2</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";color:#FFAA00;mso-fareast-language:FR">:</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";color:rosybrown;mso-fareast-language:FR">'b'</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"><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">plot</span></u><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">t,Acceleration_prime,</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">'ro'</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">xtitle</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">'Jerk
- numerical derivation vs derivative formula'</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";color:rosybrown;mso-fareast-language:FR">'t'</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";color:rosybrown;mso-fareast-language:FR">'$\mbox{J
[m/s}^{3}\mbox{]}$'</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"><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">legend</span></u><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">'Numerical'</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";color:rosybrown;mso-fareast-language:FR">'Reference'</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">,opt</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">=</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">1</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:#32B9B9;mso-fareast-language:FR">xs2png</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">gcf</span></u><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";color:rosybrown;mso-fareast-language:FR">'Jerk.png'</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";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">// calculation of the speed</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">Speed_ref</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:black">Gamma_ampl</span>
<span style="color:#5C5C5C">/</span> <span style="color:black">Omega</span><span style="color:#4A55DB">)</span>
<span style="color:#5C5C5C">*</span> <span style="color:#4A55DB">(</span><span style="color:rosybrown">1</span>
<span style="color:#5C5C5C">-</span> <span style="color:#32B9B9">cos</span><span style="color:#4A55DB">(</span><span style="color:black">Omega</span>
<span style="color:#5C5C5C">*</span> <span style="color:black">t</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:black;mso-fareast-language:FR">Speed_num_integration</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:rosybrown">2</span><span style="color:black">,n</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">Speed_num_integration</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">1</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";color:#FFAA00;mso-fareast-language:FR">:</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">
<span style="color:#5C5C5C">=</span> <span style="color:black">t;</span><o:p></o:p></span></p>
<p class="MsoNormal"><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">tic</span></u><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">Speed_num_integration</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">2</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";color:#FFAA00;mso-fareast-language:FR">:</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">
<span style="color:#5C5C5C">=</span> <u><span style="color:#AE5CB0">integrate</span></u><span style="color:#4A55DB">(</span><span style="color:rosybrown">'Gamma_function'</span><span style="color:black">,</span><span style="color:rosybrown">'x'</span><span style="color:black">,</span><span style="color:rosybrown">0</span><span style="color:black">,t</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">First_integrate_duration</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <u><span style="color:#AE5CB0">toc</span></u><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"><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">scf</span></u><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"><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">plot</span></u><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">Speed_num_integration</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">1</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";color:#FFAA00;mso-fareast-language:FR">:</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">,Speed_num_integration</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">2</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";color:#FFAA00;mso-fareast-language:FR">:</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";color:rosybrown;mso-fareast-language:FR">'m'</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"><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">plot</span></u><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">t,Speed_ref,</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">'cd'</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">xtitle</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">'Speed
- numerical integration vs antiderivative formula'</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";color:rosybrown;mso-fareast-language:FR">'t'</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";color:rosybrown;mso-fareast-language:FR">'v
[m/s]'</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"><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">legend</span></u><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">'Numerical'</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";color:rosybrown;mso-fareast-language:FR">'Reference'</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">,opt</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">=</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">1</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:#32B9B9;mso-fareast-language:FR">xs2png</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">gcf</span></u><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";color:rosybrown;mso-fareast-language:FR">'Speed.png'</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";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">// calculation of the displacement</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">Displ_ref</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:black">Gamma_ampl</span>
<span style="color:#5C5C5C">/</span> <span style="color:black">Omega</span><span style="color:#4A55DB">)</span>
<span style="color:#5C5C5C">*</span> <span style="color:#4A55DB">(</span><span style="color:black">t</span>
<span style="color:#5C5C5C">-</span> <span style="color:#4A55DB">(</span><span style="color:#32B9B9">sin</span><span style="color:#4A55DB">(</span><span style="color:black">Omega</span>
<span style="color:#5C5C5C">*</span> <span style="color:black">t</span><span style="color:#4A55DB">)</span><span style="color:#5C5C5C">/</span><span style="color:black">Omega</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:#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">y</span></b><span style="color:#5C5C5C">=</span><u><span style="color:black">Speed_function</span></u><span style="color:#4A55DB">(</span><b><span style="color:#834310">x</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">
<b><span style="color:#834310">y</span></b> <span style="color:#5C5C5C">=</span> <u>
<span style="color:#AE5CB0">interpln</span></u><span style="color:#4A55DB">(</span><span style="color:black">Speed_num_integration,</span><b><span style="color:#834310">x</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";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">Displ_num_integration</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:rosybrown">2</span><span style="color:black">,n</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">Displ_num_integration</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">1</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";color:#FFAA00;mso-fareast-language:FR">:</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">
<span style="color:#5C5C5C">=</span> <span style="color:black">t;</span><o:p></o:p></span></p>
<p class="MsoNormal"><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">tic</span></u><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">Displ_num_integration</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">2</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";color:#FFAA00;mso-fareast-language:FR">:</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">
<span style="color:#5C5C5C">=</span> <u><span style="color:#AE5CB0">integrate</span></u><span style="color:#4A55DB">(</span><span style="color:rosybrown">'Speed_function'</span><span style="color:black">,</span><span style="color:rosybrown">'x'</span><span style="color:black">,</span><span style="color:rosybrown">0</span><span style="color:black">,t</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">Second_integrate_duration</span><span lang="EN-US" style="font-family:"Monospaced","serif";mso-fareast-language:FR">
<span style="color:#5C5C5C">=</span> <u><span style="color:#AE5CB0">toc</span></u><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"><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">scf</span></u><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"><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">plot</span></u><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">Displ_num_integration</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">1</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";color:#FFAA00;mso-fareast-language:FR">:</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">,Displ_num_integration</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">2</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";color:#FFAA00;mso-fareast-language:FR">:</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";color:rosybrown;mso-fareast-language:FR">'r'</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"><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">plot</span></u><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">t,Displ_ref,</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">'b>'</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:#32B9B9;mso-fareast-language:FR">xtitle</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">'Displacement
- numerical integration vs antiderivative formula'</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";color:rosybrown;mso-fareast-language:FR">'t'</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";color:rosybrown;mso-fareast-language:FR">'$\delta
\mbox{ [m]}$'</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"><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">legend</span></u><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">'Numerical'</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";color:rosybrown;mso-fareast-language:FR">'Reference'</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">,opt</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:#5C5C5C;mso-fareast-language:FR">=</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:rosybrown;mso-fareast-language:FR">4</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:#32B9B9;mso-fareast-language:FR">xs2png</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:#4A55DB;mso-fareast-language:FR">(</span><u><span lang="EN-US" style="font-family:"Monospaced","serif";color:#AE5CB0;mso-fareast-language:FR">gcf</span></u><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";color:rosybrown;mso-fareast-language:FR">'Displacements.png'</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";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">// information's</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">printf</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">"The
duration for Numederivative = %g\n"</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">,Numederivative_duration</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:#32B9B9;mso-fareast-language:FR">printf</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">"The
duration for 1rst integration = %g\n"</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">,First_integrate_duration</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:#32B9B9;mso-fareast-language:FR">printf</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">"The
duration for 2nd integration = %g\n"</span><span lang="EN-US" style="font-family:"Monospaced","serif";color:black;mso-fareast-language:FR">,Second_integrate_duration</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"><o:p></o:p></p>
<p><b><i><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:gray">EXPORT CONTROL :
<br>
</span></i></b><b><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:black">Cet email ne contient pas de données techniques<br>
This email does not contain technical data</span></b><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
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