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<p>Hi Paul,<br /><br />You should be careful when using the square root function as it is not differentiable at 0 (cf the attached file which illustrates this point in your case). This will leads to issues and prevent optim from "really" (in a sound way) converging towards the solution.</p>
<p>To address the issue, you can</p>
<p>- reformulate your objective function so that it is smooth near the solution (you will still have an issue at 0 where g is not differentiable though),</p>
<p>- use order 0 methods (still, some of them might fail on non-smooth optimisation problems as the minimum might be very "narrow")</p>
<p>- dig into non-smooth optimisation (see e.g. http://napsu.karmitsa.fi/nso/)<br /><br />Regards,<br /><br />Pierre</p>
<p><br /></p>
<p>Le 16.01.2017 10:30, Carrico, Paul a écrit :</p>
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<p class="MsoNormal"><span>Hi all<!-- o ignored --></span></p>
<p class="MsoNormal"><span><!-- o ignored --> </span></p>
<p class="MsoNormal"><span>After performing tests (and modifying the target function as it should have been done first), I can better understand how to use ‘optim’ and ‘Neldermead’ procedures.<!-- o ignored --></span></p>
<p class="MsoNormal"><span><!-- o ignored --> </span></p>
<p class="MsoNormal"><span>For my needs the mean flags are :<!-- o ignored --></span></p>
<pre style="margin-left: 36.0pt; text-indent: -18.0pt; mso-list: l0 level1 lfo3;"><span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-fareast-language: EN-US;"><span style="mso-list: Ignore;">-<span style="font: 7.0pt 'Times New Roman';"> </span></span></span><span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-fareast-language: EN-US;">Step h in numderivative </span><span style="font-size: 11.0pt; font-family: Wingdings; mso-fareast-language: EN-US;">à</span><span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-fareast-language: EN-US;"> usefull reading as “EE 221 Numerical Computing" Scott Hudson<!-- o ignored --></span></pre>
<p class="MsoListParagraph" style="text-indent: -18.0pt; mso-list: l0 level1 lfo3;"><span><span style="mso-list: Ignore;">-<span style="font: 7.0pt 'Times New Roman';"> </span></span></span><span>The threshold epsg in optim (%eps is the default value – such high accuracy is not necessary for my application – furthermore using a value such as 1e-5 leads to err=1 that is correct for checking)<!-- o ignored --></span></p>
<pre style="margin-left: 36.0pt; text-indent: -18.0pt; mso-list: l0 level1 lfo3;"><span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-fareast-language: EN-US;"><span style="mso-list: Ignore;">-<span style="font: 7.0pt 'Times New Roman';"> </span></span></span><span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-fareast-language: EN-US;">Ditto for Nelder-Mead and ‘-tolfunrelative’ & ‘-tolxrelative’<!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-fareast-language: EN-US;"><!-- o ignored --> </span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-fareast-language: EN-US;">Now it works fine :-)<!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-fareast-language: EN-US;"><!-- o ignored --> </span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-fareast-language: EN-US;">Thanks all for the support<!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-fareast-language: EN-US;"><!-- o ignored --> </span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-fareast-language: EN-US;">Paul<!-- o ignored --></span></pre>
<p class="MsoNormal"><span><!-- o ignored --> </span></p>
<p class="MsoNormal"><span>#####################################################################<!-- o ignored --></span></p>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #32b9b9;">mode</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">(</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: rosybrown;">0</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">)</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #32b9b9;">clear</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --> </span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #32b9b9;">global</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: rosybrown;">count_use</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">count_use</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">0</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --> </span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// ****</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #b01813;">function</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <strong><span style="color: #834310;">f</span></strong><span style="color: #5c5c5c;">=</span><u><span style="color: black;">lineaire</span></u><span style="color: #4a55db;">(</span><strong><span style="color: #834310;">x</span></strong><span style="color: black;">, </span><strong><span style="color: #834310;">a2</span></strong><span style="color: black;">, </span><strong><span style="color: #834310;">b2</span></strong><span style="color: #4a55db;">)</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <strong><span style="color: #834310;">f</span></strong> <span style="color: #5c5c5c;">=</span> <strong><span style="color: #834310;">a2</span></strong><span style="color: #5c5c5c;">*</span><strong><span style="color: #834310;">x</span></strong><span style="color: #5c5c5c;">+</span><strong><span style="color: #834310;">b2</span></strong><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #b01813;">endfunction</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --> </span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// ****</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #b01813;">function</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <strong><span style="color: #834310;">g</span></strong><span style="color: #5c5c5c;">=</span><u><span style="color: black;">racine</span></u><span style="color: #4a55db;">(</span><strong><span style="color: #834310;">x</span></strong><span style="color: black;">, </span><strong><span style="color: #834310;">a1</span></strong><span style="color: black;">, </span><strong><span style="color: #834310;">b1</span></strong><span style="color: #4a55db;">)</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <strong><span style="color: #834310;">g</span></strong> <span style="color: #5c5c5c;">=</span> <span style="color: #32b9b9;">sqrt</span><span style="color: #4a55db;">(</span><strong><span style="color: #834310;">a1</span></strong><span style="color: #5c5c5c;">*</span><strong><span style="color: #834310;">x</span></strong><span style="color: #4a55db;">)</span> <span style="color: #5c5c5c;">+</span> <strong><span style="color: #834310;">b1</span></strong><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #b01813;">endfunction</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --> </span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// ****</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #b01813;">function</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <strong><span style="color: #834310;">f</span></strong><span style="color: #5c5c5c;">=</span><u><span style="color: black;">target</span></u><span style="color: #4a55db;">(</span><strong><span style="color: #834310;">x</span></strong><span style="color: black;">, </span><strong><span style="color: #834310;">a1</span></strong><span style="color: black;">, </span><strong><span style="color: #834310;">b1</span></strong><span style="color: black;">, </span><strong><span style="color: #834310;">a2</span></strong><span style="color: black;">, </span><strong><span style="color: #834310;">b2</span></strong><span style="color: #4a55db;">)</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> </span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">val_lin</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <u><span style="color: black;">lineaire</span></u><span style="color: #4a55db;">(</span><strong><span style="color: #834310;">x</span></strong><span style="color: black;">,</span><strong><span style="color: #834310;">a2</span></strong><span style="color: black;">,</span><strong><span style="color: #834310;">b2</span></strong><span style="color: #4a55db;">)</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: black;">val_rac</span> <span style="color: #5c5c5c;">=</span> <u><span style="color: black;">racine</span></u><span style="color: #4a55db;">(</span><strong><span style="color: #834310;">x</span></strong><span style="color: black;">,</span><strong><span style="color: #834310;">a1</span></strong><span style="color: black;">,</span><strong><span style="color: #834310;">b1</span></strong><span style="color: #4a55db;">)</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> </span><strong><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #834310;">f</span></strong><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: #32b9b9;">sqrt</span><span style="color: #4a55db;">((</span><span style="color: black;">val_lin</span> <span style="color: #5c5c5c;">-</span> <span style="color: black;">val_rac</span><span style="color: #4a55db;">)</span><span style="color: #5c5c5c;">^</span><span style="color: rosybrown;">2</span><span style="color: #4a55db;">)</span><span style="color: black;">;</span> <!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --> </span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #32b9b9;">global</span> <span style="color: rosybrown;">count_use</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: black;">count_use</span> <span style="color: #5c5c5c;">=</span> <span style="color: black;">count_use</span> <span style="color: #5c5c5c;">+</span><span style="color: rosybrown;">1</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #b01813;">endfunction</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --> </span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// Cost function: </span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #b01813;">function</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #4a55db;">[</span><strong><span style="color: #834310;">f</span></strong><span style="color: black;">, </span><strong><span style="color: #834310;">g</span></strong><span style="color: black;">, </span><strong><span style="color: #834310;">ind</span></strong><span style="color: #4a55db;">]</span><span style="color: #5c5c5c;">=</span><u><span style="color: black;">cost</span></u><span style="color: #4a55db;">(</span><strong><span style="color: #834310;">x</span></strong><span style="color: black;">, </span><strong><span style="color: #834310;">ind</span></strong><span style="color: black;">, </span><strong><span style="color: #834310;">a1</span></strong><span style="color: black;">, </span><strong><span style="color: #834310;">b1</span></strong><span style="color: black;">, </span><strong><span style="color: #834310;">a2</span></strong><span style="color: black;">, </span><strong><span style="color: #834310;">b2</span></strong><span style="color: #4a55db;">)</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <strong><span style="color: #834310;">f</span></strong> <span style="color: #5c5c5c;">=</span> <u><span style="color: black;">target</span></u><span style="color: #4a55db;">(</span><strong><span style="color: #834310;">x</span></strong><span style="color: #4a55db;">)</span><span style="color: black;">;</span> <!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <em><span style="color: #64ae64;">// g = numderivative(target, x.',order = 4); </span></em><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <strong><span style="color: #834310;">g</span></strong> <span style="color: #5c5c5c;">=</span> <u><span style="color: #ae5cb0;">numderivative</span></u><span style="color: #4a55db;">(</span><u><span style="color: black;">target</span></u><span style="color: black;">,</span> <strong><span style="color: #834310;">x</span></strong><span style="color: #5c5c5c;">.'</span><span style="color: black;">,</span><span style="color: rosybrown;">1e-3</span><span style="color: black;">,</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> <em><span style="color: #64ae64;">// 1E-3 => see EE 221 "Numerical Computing" Scott Hudson </span></em><!-- o ignored --></span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// Study of the influence of h on the number of target function calculation & the fopt accuracy:</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// (epsg = %eps here)</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// h = 1.e-1 => number = 220 & fopt = 2.242026e-05</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// h = 1.e-2 => number = 195 & fopt = 2.267564e-07</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// h = 1.e-3 => number = 170 & fopt = 2.189495e-09 ++++++</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// h = 1.e-4 => number = 190 & fopt = 1.941203e-11</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// h = 1.e-5 => number = 215 & fopt = 2.131628e-13</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// h = 1.e-6 => number = 235 & fopt = 0.</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// h = 1.e-7 => number = 255 & fopt = 7.105427e-15</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// h = 1.e-8 => number = 275 & fopt = 0.</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --> </span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #b01813;">endfunction</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --> </span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// *************************</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// optimisation with optim</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">initial_parameters</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: #4a55db;">[</span><span style="color: rosybrown;">10</span><span style="color: #4a55db;">]</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">lower_bounds</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: #4a55db;">[</span><span style="color: rosybrown;">0</span><span style="color: #4a55db;">]</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">upper_bounds</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: #4a55db;">[</span><span style="color: rosybrown;">1000</span><span style="color: #4a55db;">]</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">nocf</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">1000</span><span style="color: black;">;</span> <em><span style="color: #64ae64;">// number max of call of f</span></em><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">niter</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">1000</span><span style="color: black;">;</span> <em><span style="color: #64ae64;">// number max of iterations</span></em><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">a1</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">30</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">b1</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">2.5</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">a2</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">1</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">b2</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">2</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --> </span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">epsg</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">1e-5</span><span style="color: black;">;</span> <em><span style="color: #64ae64;">// gradient norm threshold (%eps by defaut) --> lead to err = 1 !!!</span></em><!-- o ignored --></span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">//epsg = %eps; // lead to Err = 13</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">epsf</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">0</span><span style="color: black;">;</span> <em><span style="color: #64ae64;">//threshold controlling decreasing of f (epsf = 0 by defaut)</span></em><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --> </span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">costf</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: #32b9b9;">list</span> <span style="color: #4a55db;">(</span><u><span style="color: black;">cost</span></u><span style="color: black;">,</span> <span style="color: black;">a1,</span> <span style="color: black;">b1,</span> <span style="color: black;">a2,</span> <span style="color: black;">b2</span><span style="color: #4a55db;">)</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">[</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">fopt,</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: black;">xopt,</span> <span style="color: black;">gopt,</span> <span style="color: black;">work,</span> <span style="color: black;">iters,</span> <span style="color: black;">evals,</span> <span style="color: black;">err</span><span style="color: #4a55db;">]</span> <span style="color: #5c5c5c;">=</span> <span style="color: #32b9b9;">optim</span><span style="color: #4a55db;">(</span><span style="color: black;">costf,</span><span style="color: rosybrown;">'b'</span><span style="color: black;">,lower_bounds,upper_bounds,initial_parameters,</span><span style="color: rosybrown;">'qn'</span><span style="color: black;">,</span><span style="color: rosybrown;">'ar'</span><span style="color: black;">,nocf,niter,epsg,epsf</span><span style="color: #4a55db;">)</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #32b9b9;">printf</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">(</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: rosybrown;">"Optimized value : %g\n"</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">,xopt</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">)</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">;</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #32b9b9;">printf</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">(</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: rosybrown;">"min cost function value (should be as closed as possible to 0) ; %e\n"</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">,fopt</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">)</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">;</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #32b9b9;">printf</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">(</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: rosybrown;">'Number of calculations = %d !!!\n'</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">,count_use</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">)</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">;</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --> </span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --> </span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// Curves definition</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">x</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <u><span style="color: #ae5cb0;">linspace</span></u><span style="color: #4a55db;">(</span><span style="color: rosybrown;">0</span><span style="color: black;">,</span><span style="color: rosybrown;">50</span><span style="color: black;">,</span><span style="color: rosybrown;">1000</span><span style="color: #4a55db;">)</span><span style="color: #5c5c5c;">'</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">plot_raci</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <u><span style="color: black;">racine</span></u><span style="color: #4a55db;">(</span><span style="color: black;">x,a1,b1</span><span style="color: #4a55db;">)</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">plot_lin</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <u><span style="color: black;">lineaire</span></u><span style="color: #4a55db;">(</span><span style="color: black;">x,a2,b2</span><span style="color: #4a55db;">)</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --> </span></pre>
<pre><u><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #ae5cb0;">scf</span></u><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">(</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: rosybrown;">1</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">)</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">;</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #32b9b9;">drawlater</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">()</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">;</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #32b9b9;">xgrid</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">(</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: rosybrown;">3</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">)</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">;</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">f</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <u><span style="color: #ae5cb0;">gcf</span></u><span style="color: #4a55db;">()</span><span style="color: black;">;</span> <!-- o ignored --></span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">//f </span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">f</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">figure_size</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: #4a55db;">[</span><span style="color: rosybrown;">1000</span><span style="color: black;">,</span> <span style="color: rosybrown;">1000</span><span style="color: #4a55db;">]</span><span style="color: black;">;</span> <!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">f</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">background</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: #32b9b9;">color</span><span style="color: #4a55db;">(</span><span style="color: rosybrown;">255</span><span style="color: black;">,</span><span style="color: rosybrown;">255</span><span style="color: black;">,</span><span style="color: rosybrown;">255</span><span style="color: #4a55db;">)</span><span style="color: black;">;</span> <!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">a</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <u><span style="color: #ae5cb0;">gca</span></u><span style="color: #4a55db;">()</span><span style="color: black;">;</span> <!-- o ignored --></span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">//a </span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">a</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">font_size</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">2</span><span style="color: black;">;</span> <!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">a</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">x_label</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">text</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">"X axis"</span> <span style="color: black;">;</span> <!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">a</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">x_location</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">=</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: rosybrown;">"bottom"</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">;</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">a</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">x_label</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">font_angle</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">=</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: rosybrown;">0</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">;</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">a</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">x_label</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">font_size</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">4</span><span style="color: black;">;</span> <!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">a</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">y_label</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">text</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">"Y axis"</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">a</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">y_location</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">=</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: rosybrown;">"left"</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">;</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">a</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">y_label</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">font_angle</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">=-</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: rosybrown;">90</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">;</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">a</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">Y_label</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">font_size</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">4</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">a</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">title</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">text</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">"Title"</span><span style="color: black;">;</span> <!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">a</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">title</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">font_size</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">5</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">a</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">line_style</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">1</span><span style="color: black;">;</span> <!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --> </span></pre>
<pre><em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #64ae64;">// Curves plot</span></em><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><u><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #ae5cb0;">plot</span></u><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">(</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">x,plot_lin</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">)</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">;</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">e1</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <u><span style="color: #ae5cb0;">gce</span></u><span style="color: #4a55db;">()</span><span style="color: black;">;</span> <!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">p1</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: black;">e1</span><span style="color: #5c5c5c;">.</span><span style="color: #aaaaaa;">children</span><span style="color: black;">;</span> <!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">p1</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">thickness</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">1</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">p1</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">line_style</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">1</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">p1</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">foreground</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">3</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --> </span></pre>
<pre><u><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #ae5cb0;">plot</span></u><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">(</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">x,plot_raci</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">)</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">;</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">e2</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <u><span style="color: #ae5cb0;">gce</span></u><span style="color: #4a55db;">()</span><span style="color: black;">;</span> <!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">p2</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: black;">e2</span><span style="color: #5c5c5c;">.</span><span style="color: #aaaaaa;">children</span><span style="color: black;">;</span> <!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">p2</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">thickness</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">1</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">p2</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">line_style</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">1</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">p2</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #5c5c5c;">.</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #aaaaaa;">foreground</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"> <span style="color: #5c5c5c;">=</span> <span style="color: rosybrown;">2</span><span style="color: black;">;</span><!-- o ignored --></span></pre>
<pre><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #32b9b9;">drawnow</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: #4a55db;">()</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif'; color: black;">;</span><span style="font-size: 11.0pt; font-family: 'Monospaced','serif';"><!-- o ignored --></span></pre>
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<p><strong><em><span style="font-size: 10.0pt; font-family: 'Arial','sans-serif'; color: gray;">EXPORT CONTROL : <br /> </span></em></strong><strong><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></strong><!-- o ignored --></p>
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