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<p>Hi Paul,</p>
<p>your cost function<br>
</p>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif""> </span><b><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#834310" lang="EN-US">f</span></b><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <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:p></o:p></span></pre>
<p>hasn't changed, since sqrt(x^2)=abs(x). What I meant before is
replacing</p>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif""> </span><b><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#834310" lang="EN-US">f</span></b><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">abs</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"></span><span style="color:#4A55DB"></span><span style="color:black">;</span> <o:p></o:p></span></pre>
<p>by<br>
</p>
<p><span
style="font-size:11.0pt;font-family:"Monospaced","serif"">
</span><b><span
style="font-size:11.0pt;font-family:"Monospaced","serif";color:#834310"
lang="EN-US">f</span></b><span
style="font-size:11.0pt;font-family:"Monospaced","serif""
lang="EN-US"> <span style="color:#5C5C5C">=</span> <span
style="color:#32B9B9"></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:p></o:p></span></p>
in order to make it differentiable. When using a non-differentiable
cost function together with numderivative, it seems logical that
tweaking the step size could artificially help convergence.<br>
<br>
S.<br>
<br>
<br>
<div class="moz-cite-prefix">Le 16/01/2017 à 10:30, Carrico, Paul a
écrit :<br>
</div>
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<div class="WordSection1">
<p class="MsoNormal"><span lang="EN-US">Hi 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">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: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">For my needs the mean
flags are :<o:p></o:p></span></p>
<pre style="margin-left:36.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo3"><!--[if !supportLists]--><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";mso-fareast-language:EN-US" lang="EN-US"><span style="mso-list:Ignore">-<span style="font:7.0pt "Times New Roman""> </span></span></span><!--[endif]--><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";mso-fareast-language:EN-US" lang="EN-US">Step h in numderivative </span><span style="font-size:11.0pt;font-family:Wingdings;mso-fareast-language:EN-US" lang="EN-US">à</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";mso-fareast-language:EN-US" lang="EN-US"> usefull reading as “EE 221 Numerical Computing" Scott Hudson<o:p></o:p></span></pre>
<p class="MsoListParagraph"
style="text-indent:-18.0pt;mso-list:l0 level1 lfo3"><!--[if !supportLists]--><span
lang="EN-US"><span style="mso-list:Ignore">-<span
style="font:7.0pt "Times New Roman"">
</span></span></span><!--[endif]--><span lang="EN-US">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:p></o:p></span></p>
<pre style="margin-left:36.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo3"><!--[if !supportLists]--><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";mso-fareast-language:EN-US" lang="EN-US"><span style="mso-list:Ignore">-<span style="font:7.0pt "Times New Roman""> </span></span></span><!--[endif]--><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";mso-fareast-language:EN-US" lang="EN-US">Ditto for Nelder-Mead and ‘-tolfunrelative’ & ‘-tolxrelative’<o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";mso-fareast-language:EN-US" lang="EN-US"><o:p> </o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";mso-fareast-language:EN-US" lang="EN-US">Now it works fine :-)<o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";mso-fareast-language:EN-US" lang="EN-US"><o:p> </o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";mso-fareast-language:EN-US" lang="EN-US">Thanks all for the support<o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";mso-fareast-language:EN-US" lang="EN-US"><o:p> </o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";mso-fareast-language:EN-US" lang="EN-US">Paul<o:p></o:p></span></pre>
<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>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#32B9B9" lang="EN-US">mode</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="EN-US">(</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:rosybrown" lang="EN-US">0</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="EN-US">)</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#32B9B9" lang="EN-US">clear</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p> </o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#32B9B9" lang="EN-US">global</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:rosybrown">count_use</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">count_use</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">0</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p> </o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">// ****</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#B01813" lang="EN-US">function</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <b><span style="color:#834310">f</span></b><span style="color:#5C5C5C">=</span><u><span style="color:black">lineaire</span></u><span style="color:#4A55DB">(</span><b><span style="color:#834310">x</span></b><span style="color:black">, </span><b><span style="color:#834310">a2</span></b><span style="color:black">, </span><b><span style="color:#834310">b2</span></b><span style="color:#4A55DB">)</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <b><span style="color:#834310">f</span></b> <span style="color:#5C5C5C">=</span> <b><span style="color:#834310">a2</span></b><span style="color:#5C5C5C">*</span><b><span style="color:#834310">x</span></b><span style="color:#5C5C5C">+</span><b><span style="color:#834310">b2</span></b><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#B01813" lang="EN-US">endfunction</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p> </o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">// ****</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#B01813" lang="EN-US">function</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <b><span style="color:#834310">g</span></b><span style="color:#5C5C5C">=</span><u><span style="color:black">racine</span></u><span style="color:#4A55DB">(</span><b><span style="color:#834310">x</span></b><span style="color:black">, </span><b><span style="color:#834310">a1</span></b><span style="color:black">, </span><b><span style="color:#834310">b1</span></b><span style="color:#4A55DB">)</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <b><span style="color:#834310">g</span></b> <span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">sqrt</span><span style="color:#4A55DB">(</span><b><span style="color:#834310">a1</span></b><span style="color:#5C5C5C">*</span><b><span style="color:#834310">x</span></b><span style="color:#4A55DB">)</span> <span style="color:#5C5C5C">+</span> <b><span style="color:#834310">b1</span></b><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#B01813" lang="EN-US">endfunction</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p> </o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">// ****</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#B01813" lang="EN-US">function</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <b><span style="color:#834310">f</span></b><span style="color:#5C5C5C">=</span><u><span style="color:black">target</span></u><span style="color:#4A55DB">(</span><b><span style="color:#834310">x</span></b><span style="color:black">, </span><b><span style="color:#834310">a1</span></b><span style="color:black">, </span><b><span style="color:#834310">b1</span></b><span style="color:black">, </span><b><span style="color:#834310">a2</span></b><span style="color:black">, </span><b><span style="color:#834310">b2</span></b><span style="color:#4A55DB">)</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> </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><b><span style="color:#834310">x</span></b><span style="color:black">,</span><b><span style="color:#834310">a2</span></b><span style="color:black">,</span><b><span style="color:#834310">b2</span></b><span style="color:#4A55DB">)</span><span style="color:black">;</span><o:p></o:p></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><b><span style="color:#834310">x</span></b><span style="color:black">,</span><b><span style="color:#834310">a1</span></b><span style="color:black">,</span><b><span style="color:#834310">b1</span></b><span style="color:#4A55DB">)</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif""> </span><b><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#834310" lang="EN-US">f</span></b><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <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:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p> </o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#32B9B9">global</span> <span style="color:rosybrown">count_use</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <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:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#B01813" lang="EN-US">endfunction</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p> </o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">// Cost function: </span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#B01813" lang="EN-US">function</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#4A55DB">[</span><b><span style="color:#834310">f</span></b><span style="color:black">, </span><b><span style="color:#834310">g</span></b><span style="color:black">, </span><b><span style="color:#834310">ind</span></b><span style="color:#4A55DB">]</span><span style="color:#5C5C5C">=</span><u><span style="color:black">cost</span></u><span style="color:#4A55DB">(</span><b><span style="color:#834310">x</span></b><span style="color:black">, </span><b><span style="color:#834310">ind</span></b><span style="color:black">, </span><b><span style="color:#834310">a1</span></b><span style="color:black">, </span><b><span style="color:#834310">b1</span></b><span style="color:black">, </span><b><span style="color:#834310">a2</span></b><span style="color:black">, </span><b><span style="color:#834310">b2</span></b><span style="color:#4A55DB">)</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <b><span style="color:#834310">f</span></b> <span style="color:#5C5C5C">=</span> <u><span style="color:black">target</span></u><span style="color:#4A55DB">(</span><b><span style="color:#834310">x</span></b><span style="color:#4A55DB">)</span><span style="color:black">;</span> <o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <i><span style="color:#64AE64">// g = numderivative(target, x.',order = 4); </span></i><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <b><span style="color:#834310">g</span></b> <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> <b><span style="color:#834310">x</span></b><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> <i><span style="color:#64AE64">// 1E-3 => see EE 221 "Numerical Computing" Scott Hudson </span></i><o:p></o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">// Study of the influence of h on the number of target function calculation & the fopt accuracy:</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">// (epsg = %eps here)</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">// h = 1.e-1 => number = 220 & fopt = 2.242026e-05</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">// h = 1.e-2 => number = 195 & fopt = 2.267564e-07</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">// h = 1.e-3 => number = 170 & fopt = 2.189495e-09 ++++++</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">// h = 1.e-4 => number = 190 & fopt = 1.941203e-11</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">// h = 1.e-5 => number = 215 & fopt = 2.131628e-13</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">// h = 1.e-6 => number = 235 & fopt = 0.</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">// h = 1.e-7 => number = 255 & fopt = 7.105427e-15</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64">// h = 1.e-8 => number = 275 & fopt = 0.</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif""><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p> </o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#B01813" lang="EN-US">endfunction</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p> </o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">// *************************</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">// optimisation with optim</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">initial_parameters</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:#4A55DB">[</span><span style="color:rosybrown">10</span><span style="color:#4A55DB">]</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">lower_bounds</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <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:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">upper_bounds</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <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:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">nocf</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">1000</span><span style="color:black">;</span> <i><span style="color:#64AE64">// number max of call of f</span></i><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">niter</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">1000</span><span style="color:black">;</span> <i><span style="color:#64AE64">// number max of iterations</span></i><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">a1</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">30</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">b1</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">2.5</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">a2</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">1</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">b2</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">2</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p> </o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">epsg</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">1e-5</span><span style="color:black">;</span> <i><span style="color:#64AE64">// gradient norm threshold (%eps by defaut) --> lead to err = 1 !!!</span></i><o:p></o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">//epsg = %eps; // lead to Err = 13</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">epsf</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">0</span><span style="color:black">;</span> <i><span style="color:#64AE64">//threshold controlling decreasing of f (epsf = 0 by defaut)</span></i><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p> </o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">costf</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <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:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="EN-US">[</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">fopt,</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <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:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#32B9B9" lang="EN-US">printf</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="EN-US">(</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:rosybrown" lang="EN-US">"Optimized value : %g\n"</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">,xopt</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="EN-US">)</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">;</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#32B9B9" lang="EN-US">printf</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="EN-US">(</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:rosybrown" lang="EN-US">"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" lang="EN-US">,fopt</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="EN-US">)</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">;</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#32B9B9" lang="EN-US">printf</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="EN-US">(</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:rosybrown" lang="EN-US">'Number of calculations = %d !!!\n'</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">,count_use</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="EN-US">)</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">;</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p> </o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p> </o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64">// Curves definition</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif""><o:p></o:p></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:p></o:p></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:p></o:p></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:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif""><o:p> </o:p></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:p></o:p></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:p></o:p></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:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">f</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <u><span style="color:#AE5CB0">gcf</span></u><span style="color:#4A55DB">()</span><span style="color:black">;</span> <o:p></o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">//f </span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">f</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">figure_size</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <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:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">f</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">background</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <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:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">a</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <u><span style="color:#AE5CB0">gca</span></u><span style="color:#4A55DB">()</span><span style="color:black">;</span> <o:p></o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">//a </span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">a</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">font_size</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">2</span><span style="color:black">;</span> <o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">a</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">x_label</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">text</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">"X axis"</span> <span style="color:black">;</span> <o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">a</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">x_location</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">=</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:rosybrown" lang="EN-US">"bottom"</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">;</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">a</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">x_label</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">font_angle</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">=</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:rosybrown" lang="EN-US">0</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">;</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">a</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">x_label</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">font_size</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">4</span><span style="color:black">;</span> <o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">a</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">y_label</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">text</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">"Y axis"</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">a</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">y_location</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">=</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:rosybrown" lang="EN-US">"left"</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">;</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">a</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">y_label</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">font_angle</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">=-</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:rosybrown" lang="EN-US">90</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">;</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">a</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">Y_label</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">font_size</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">4</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">a</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">title</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">text</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">"Title"</span><span style="color:black">;</span> <o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">a</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">title</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">font_size</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">5</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">a</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">line_style</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">1</span><span style="color:black">;</span> <o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p> </o:p></span></pre>
<pre><i><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#64AE64" lang="EN-US">// Curves plot</span></i><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><u><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AE5CB0" lang="EN-US">plot</span></u><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="EN-US">(</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">x,plot_lin</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="EN-US">)</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">;</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">e1</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <u><span style="color:#AE5CB0">gce</span></u><span style="color:#4A55DB">()</span><span style="color:black">;</span> <o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">p1</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <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:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">p1</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">thickness</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">1</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">p1</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">line_style</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">1</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">p1</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">foreground</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">3</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p> </o:p></span></pre>
<pre><u><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AE5CB0" lang="EN-US">plot</span></u><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="EN-US">(</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">x,plot_raci</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="EN-US">)</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">;</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">e2</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <u><span style="color:#AE5CB0">gce</span></u><span style="color:#4A55DB">()</span><span style="color:black">;</span> <o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">p2</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <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:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">p2</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">thickness</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">1</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:black" lang="EN-US">p2</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="EN-US">.</span><span style="font-size:11.0pt;font-family:"Monospaced","serif";color:#AAAAAA" lang="EN-US">line_style</span><span style="font-size:11.0pt;font-family:"Monospaced","serif"" lang="EN-US"> <span style="color:#5C5C5C">=</span> <span style="color:rosybrown">1</span><span style="color:black">;</span><o:p></o:p></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:p></o:p></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:p></o:p></span></pre>
<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 :
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style="font-size:10.0pt;font-family:"Arial","sans-serif";color:black">Cet
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This email does not contain technical data</span></b><o:p></o:p></p>
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