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      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
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      <title lang="eng">
        <p>   Genfit Functions   ...  plotG ...  xd(L,H,N)   </p>
      </title>
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          <e type="operand">vy</e>
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          <e type="operand">size</e>
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          <e type="operand">1</e>
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          <e type="operand">vy</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="2">el</e>
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          <e type="operand">2</e>
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          <e type="operand">i</e>
          <e type="function" preserve="true" args="2">el</e>
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          <e type="operand">size</e>
          <e type="operand">color</e>
          <e type="function" preserve="true" args="5">augment</e>
          <e type="function" preserve="true" args="2">stack</e>
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          <e type="function" preserve="true" args="3">for</e>
          <e type="operand">plot</e>
          <e type="operand">4</e>
          <e type="operand">1</e>
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          <e type="operator" args="2">:</e>
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      <math optimize="2">
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          <e type="operand">L</e>
          <e type="operand">H</e>
          <e type="operand">N</e>
          <e type="function" args="3">xd</e>
          <e type="operand">U</e>
          <e type="operand">0</e>
          <e type="operator" args="2">:</e>
          <e type="operand">dx</e>
          <e type="operand">H</e>
          <e type="operand">L</e>
          <e type="operator" args="2">-</e>
          <e type="operand">N</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
          <e type="operand">i</e>
          <e type="operand">1</e>
          <e type="operand">N</e>
          <e type="operand">1</e>
          <e type="operator" args="2">+</e>
          <e type="function" preserve="true" args="2">range</e>
          <e type="operand">U</e>
          <e type="operand">i</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operand">L</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
          <e type="operand">dx</e>
          <e type="operand">i</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">:</e>
          <e type="function" preserve="true" args="3">for</e>
          <e type="operand">U</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">line</e>
          <e type="operand">3</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="5">line</e>
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      <text lang="eng">
        <p>Module xd(L,H,N) is a discretiserfor use in-situ  [user spec's]: range [L,H], density [N].</p>
      </text>
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          <p>Applicable parts are: Optimiz "numeric"</p>
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          <e type="operand" style="string">vx-&gt; raw initial vector fit</e>
          <e type="operand">i</e>
          <e type="operand">1</e>
          <e type="operand">X</e>
          <e type="function" preserve="true" args="1">length</e>
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          <e type="operand" style="string">M-&gt; Cholesky GradientMatrix</e>
          <e type="operand">j</e>
          <e type="operand">1</e>
          <e type="operand">k</e>
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          <e type="operand">1</e>
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          <e type="operand">M</e>
          <e type="operand">i</e>
          <e type="operand">j</e>
          <e type="function" preserve="true" args="3">el</e>
          <e type="operand">X</e>
          <e type="operand">i</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operand">β</e>
          <e type="function" args="2">φ</e>
          <e type="operand">j</e>
          <e type="operand">1</e>
          <e type="operator" args="2">+</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="function" preserve="true" args="1">eval</e>
          <e type="operator" args="2">:</e>
          <e type="function" preserve="true" args="3">for</e>
          <e type="function" preserve="true" args="3">for</e>
          <e type="operand" style="string">CholeskySolver LeastSquares</e>
          <e type="operand">Φ</e>
          <e type="operand">M</e>
          <e type="function" preserve="true" args="1">transpose</e>
          <e type="operand">M</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
          <e type="operand">d</e>
          <e type="operand">M</e>
          <e type="function" preserve="true" args="1">transpose</e>
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          <e type="operand">vx</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
          <e type="operand">Δβ</e>
          <e type="operand">Φ</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">^</e>
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          <e type="operand">d</e>
          <e type="operator" args="2">*</e>
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          <e type="operand">b</e>
          <e type="operand">β</e>
          <e type="operand">Δβ</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">:</e>
          <e type="operand">13</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="15">line</e>
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          <p>Vector gradient ... Optimiz Symbolic </p>
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          <e type="operand">1</e>
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          <e type="operand" style="string">stack f(x,β) &amp; PD </e>
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          <e type="operand">4</e>
          <e type="operand">1</e>
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          <e type="function" preserve="true" args="3">for</e>
          <e type="operand">V</e>
          <e type="operand">3</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="5">line</e>
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        <e type="operand">9.65</e>
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        <e type="operand">24</e>
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        <e type="operand">48.06</e>
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        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">β</e>
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        <e type="operand">x</e>
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      <p bold="true">&lt;= Model function</p>
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        <e type="operand" style="string">in φ(x,β,f,n) -&gt; set 'n' to last index</e>
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      <p bold="true">&lt;= Gradient Vector Function</p>
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        <e type="operand">β</e>
        <e type="operand">126.04</e>
        <e type="operand">126.48</e>
        <e type="operator" args="1">-</e>
        <e type="operand">9.91</e>
        <e type="operand">27.79</e>
        <e type="operand">666.2</e>
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      <p bold="true">&lt;= ..... initial β ............ iterate manually .....&lt;= &lt;= re-inject the last 'β'</p>
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        <e type="operand">5</e>
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        <p>Genfit coeff's of fit</p>
      </description>
      <input>
        <e type="operand">β</e>
        <e type="operand">XY</e>
        <e type="operand">f</e>
        <e type="operand">φ</e>
        <e type="operand">β</e>
        <e type="function" args="4">βNlin</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="20" left="279" top="1188" width="250" height="24" border="true" color="#000000" bgColor="#ebebeb" fontSize="10">
    <text lang="eng">
      <p>re-inject to iterate manually</p>
    </text>
  </region>
  <region id="21" left="9" top="1224" width="130" height="83" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="6">
      <description active="true" position="Top" lang="eng">
        <p>range/populate</p>
      </description>
      <input>
        <e type="operand">L</e>
        <e type="operand">5</e>
        <e type="operator" args="2">:</e>
        <e type="operand">H</e>
        <e type="operand">500</e>
        <e type="operator" args="2">:</e>
        <e type="operand">N</e>
        <e type="operand">199</e>
        <e type="operator" args="2">:</e>
        <e type="operand">U</e>
        <e type="operand">L</e>
        <e type="operand">H</e>
        <e type="operand">N</e>
        <e type="function" args="3">xd</e>
        <e type="operator" args="2">:</e>
        <e type="operand">4</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="6">line</e>
      </input>
    </math>
  </region>
  <region id="22" left="333" top="1242" width="113" height="99" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">β</e>
      </input>
      <result action="numeric">
        <e type="operand">126.29</e>
        <e type="operand">126.73</e>
        <e type="operator" args="1">-</e>
        <e type="operand">10.31</e>
        <e type="operand">27.7</e>
        <e type="operand">669.18</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="7">mat</e>
      </result>
    </math>
  </region>
  <region id="23" left="432" top="1323" width="275" height="24" color="#000000" bgColor="#ebebeb" fontSize="10">
    <text lang="eng">
      <p bold="true">Collect initial &amp; successive 'β'</p>
    </text>
  </region>
  <region id="24" left="9" top="1332" width="244" height="75" border="true" color="#000000" bgColor="#ffff80" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">FIT</e>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">U</e>
        <e type="function" preserve="true" args="1">rows</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">FIT</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">U</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">β</e>
        <e type="function" args="2">f</e>
        <e type="function" preserve="true" args="1">eval</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">FIT</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="25" left="432" top="1350" width="331" height="102" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math fractionType="fraction">
      <input>
        <e type="operand">β</e>
        <e type="operand">125</e>
        <e type="operand">126</e>
        <e type="operator" args="1">-</e>
        <e type="operand">20</e>
        <e type="operand">30</e>
        <e type="operand">800</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="7">mat</e>
        <e type="operand">124.91</e>
        <e type="operand">125.25</e>
        <e type="operator" args="1">-</e>
        <e type="operand">17.03</e>
        <e type="operand">27.48</e>
        <e type="operand">924.96</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="7">mat</e>
        <e type="operand">125.82</e>
        <e type="operand">126.26</e>
        <e type="operator" args="1">-</e>
        <e type="operand">17.03</e>
        <e type="operand">27.51</e>
        <e type="operand">849.15</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="7">mat</e>
        <e type="operand">#</e>
        <e type="operand">126.29</e>
        <e type="operand">126.73</e>
        <e type="operator" args="1">-</e>
        <e type="operand">10.31</e>
        <e type="operand">27.7</e>
        <e type="operand">669.18</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="7">mat</e>
        <e type="operand">1</e>
        <e type="operand">5</e>
        <e type="function" preserve="true" args="7">mat</e>
        <e type="operator" args="2">≡</e>
      </input>
    </math>
  </region>
  <region id="26" left="9" top="1404" width="187" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">MyFit</e>
        <e type="operand">U</e>
        <e type="operand">FIT</e>
        <e type="function" preserve="true" args="2">augment</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="27" left="9" top="1431" width="292" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">data</e>
        <e type="operand">X</e>
        <e type="operand">Y</e>
        <e type="operand" style="string">.</e>
        <e type="operand">12</e>
        <e type="operand" style="string">black</e>
        <e type="function" args="5">plotG</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="28" left="9" top="1458" width="431" height="27" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Title</e>
        <e type="operand">200</e>
        <e type="operand">45</e>
        <e type="operand" style="string">Transmute fit to Kirby2</e>
        <e type="operand">12</e>
        <e type="operand" style="string">black</e>
        <e type="operand">1</e>
        <e type="operand">5</e>
        <e type="function" preserve="true" args="7">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="29" left="9" top="1485" width="509" height="194" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="0.0859103530751931" scale_y="0.0584132350505397" scale_z="0.00501830164745611" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-209" transpose_y="-70" transpose_z="0">
      <input>
        <e type="operand">data</e>
        <e type="operand">MyFit</e>
        <e type="operand">Title</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">sys</e>
      </input>
    </plot>
  </region>
  <region id="30" left="36" top="1809" width="103" height="99" color="#000000" bgColor="#ffffff" fontSize="10">
    <math fractionType="fraction">
      <input>
        <e type="operand">β</e>
        <e type="operand">126.29</e>
        <e type="operand">126.73</e>
        <e type="operator" args="1">-</e>
        <e type="operand">10.31</e>
        <e type="operand">27.7</e>
        <e type="operand">669.18</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="7">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="31" left="198" top="1809" width="235" height="93" border="true" color="#000000" bgColor="#ebffff" fontSize="10">
    <math fractionType="fraction">
      <description active="true" position="Top" lang="eng">
        <p>Check the export  for enough decimals </p>
      </description>
      <input>
        <e type="operand">x</e>
        <e type="operand">β</e>
        <e type="function" args="2">f</e>
        <e type="operand">β</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">β</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">1</e>
        <e type="operand">β</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">x</e>
        <e type="operand">β</e>
        <e type="operand">4</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">-</e>
        <e type="operand">β</e>
        <e type="operand">5</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">/</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="32" left="198" top="1935" width="295" height="77" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <math fractionType="fraction">
      <input>
        <e type="operand">Resd</e>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">Y</e>
        <e type="function" preserve="true" args="1">rows</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">resd</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">Y</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">X</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">β</e>
        <e type="function" args="2">f</e>
        <e type="function" preserve="true" args="1">eval</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">Y</e>
        <e type="operand">resd</e>
        <e type="function" preserve="true" args="2">augment</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="33" left="198" top="2016" width="156" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">u</e>
        <e type="operand">9.5</e>
        <e type="operand">x</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operand">x</e>
        <e type="operand">500</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">&amp;</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="34" left="198" top="2052" width="299" height="158" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="0.0965173961230158" scale_y="0.0457023316480934" scale_z="0.00441107004742447" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-111" transpose_y="-49" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="operand">β</e>
        <e type="function" args="2">f</e>
        <e type="operand">u</e>
        <e type="operator" args="2">*</e>
        <e type="operand">data</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </input>
    </plot>
  </region>
</regions>