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<p class="MsoNormal"><span lang="EN-US" style="color:#1F497D;mso-fareast-language:EN-US">Hello,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:#1F497D;mso-fareast-language:EN-US">If the fixed point has to be optimized as well, it is possible to keep a linear treatment, although the solution that I have found is tedious:<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:#1F497D;mso-fareast-language:EN-US">First, notice that because of the fixed point and the set of xk is the same for the 3 lines, all Y coordinates are proportional, I mean
<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l0 level1 lfo2"><![if !supportLists]><span lang="EN-US" style="color:#1F497D;mso-fareast-language:EN-US"><span style="mso-list:Ignore">-<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="EN-US" style="color:#1F497D;mso-fareast-language:EN-US">y2(xk)=P2/P1*y1(xk)<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l0 level1 lfo2"><![if !supportLists]><span lang="EN-US" style="color:#1F497D;mso-fareast-language:EN-US"><span style="mso-list:Ignore">-<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="EN-US" style="color:#1F497D;mso-fareast-language:EN-US">y3(xk)=P3/P1*y1(xk)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:#1F497D;mso-fareast-language:EN-US">It is probably easy to fit the datasets y2 and y3 as a function of y1 to find r=P2/P1 and s=P3/P1. It might even be possible to use r=sum(y2)/sum(y1) and s= sum(y3)/sum(y1)…
but the exact solution of the least square method is r=sum(y2.*y1)/sum(y1.*y1), s= sum(y3.*y1)/sum(y1.*y1).<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:#1F497D;mso-fareast-language:EN-US">Then the full dataset of the 3 functions y1, y2/r and y3/s can be adjusted to the same function p1*x+A (e.g. using reglin)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:#1F497D;mso-fareast-language:EN-US">However, I did not write the code, yet… There might exist a more elegant solution…<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:#1F497D;mso-fareast-language:EN-US">I understand it is not in the focus of the initial question, but it may help anyway.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:#1F497D;mso-fareast-language:EN-US">Denis<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:#1F497D;mso-fareast-language:EN-US">NB: a more compact algorithm is to fit for i=1…3, yi/sum(yi.*y1)= f(x)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b><span lang="EN-US">De :</span></b><span lang="EN-US"> users <users-bounces@lists.scilab.org>
<b>De la part de</b> Rafael Guerra<br>
<b>Envoyé :</b> mardi 25 août 2020 01:47<br>
<b>À :</b> Heinz Nabielek <heinznabielek@me.com>; Users mailing list for Scilab <users@lists.scilab.org><br>
<b>Objet :</b> Re: [Scilab-users] errors (uncertainties) in non-linear least-squares fitting parameters<o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">In that case, the code can be simplified using backslash left matrix division:<o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><i><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced;color:#64AE64">// Fixed point (-4,0) solution:</span></i><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced;color:black">a</span><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced">
<span style="color:#5C5C5C">=</span> <span style="color:#4A55DB">(</span><span style="color:black">MW</span><span style="color:#5C5C5C">+</span><span style="color:rosybrown">4</span><span style="color:#4A55DB">)</span><span style="color:#5C5C5C">\</span><span style="color:black">Y;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced;color:black">b</span><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced">
<span style="color:#5C5C5C">=</span> <span style="color:black">a</span><span style="color:#5C5C5C">*</span><span style="color:rosybrown">4</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced;color:black">GG</span><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced;color:#5C5C5C">=</span><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced">
<span style="color:black">a</span><span style="color:#5C5C5C">'.*.</span><span style="color:black">xx</span><span style="color:#5C5C5C">'</span>
<span style="color:#5C5C5C">+</span> <span style="color:black">repmat</span><span style="color:#4A55DB">(</span><span style="color:black">b</span><span style="color:#5C5C5C">'</span><span style="color:black">,</span><span style="color:rosybrown">1</span><span style="color:black">,</span><span style="color:#32B9B9">size</span><span style="color:#4A55DB">(</span><span style="color:black">xx,</span><span style="color:rosybrown">1</span><span style="color:#4A55DB">))</span><span style="color:black">;</span><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced;color:black">plot</span><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced;color:#4A55DB">(</span><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced;color:black">xx,GG</span><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced;color:#5C5C5C">'</span><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced;color:black">,</span><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced;color:rosybrown">'LineWidth'</span><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced;color:black">,</span><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced;color:rosybrown">1</span><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced;color:#4A55DB">)</span><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced;color:black">;</span><span lang="EN-US" style="font-size:10.0pt;font-family:Monospaced"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:12.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><span lang="EN-US">Regards,<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-bottom:12.0pt"><span lang="EN-US" style="font-size:12.0pt">Rafael<o:p></o:p></span></p>
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