﻿<?xml version="1.0" encoding="utf-8" standalone="yes"?>
<?application progid="SMath Studio" version="0.95"?>
<regions>
  <settings>
    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <fractions>decimal</fractions>
    </calculation>
    <pageModel active="true" printAreas="true" simpleEqualsOnly="false">
      <paper id="9" orientation="Portrait" width="827" height="1169" />
      <margins left="39" right="39" top="39" bottom="39" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
    </pageModel>
    <dependences>
      <assembly name="SMath Studio" version="0.95" guid="a37cba83-b69c-4c71-9992-55ff666763bd" />
      <assembly name="Text Region" version="1.8.4594.45" guid="485d28c5-349a-48b6-93be-12a35a1c1e39" />
      <assembly name="Math Region" version="0.95" guid="02f1ab51-215b-466e-a74d-5d8b1cf85e8d" />
    </dependences>
  </settings>
  <region id="0" left="126" top="18" width="444" height="41" color="#000000" bgColor="#ff8000" fontSize="20">
    <text lang="eng">
      <p>Optimisation type effects:</p>
    </text>
  </region>
  <region id="1" left="36" top="63" width="155" height="46" border="true" color="#000000" bgColor="#80ff80" fontSize="10">
    <math>
      <input>
        <e type="operand">v.i</e>
        <e type="operand">1</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">/</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="5">mat</e>
        <e type="bracket">(</e>
        <e type="function" preserve="true" args="1">transpose</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="2" left="252" top="63" width="109" height="62" border="true" color="#000000" bgColor="#ffff80" fontSize="10">
    <math>
      <input>
        <e type="operand">v.i</e>
      </input>
      <result action="numeric">
        <e type="operand">0.5774</e>
        <e type="operand">0.5774</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.5774</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
      </result>
    </math>
  </region>
  <region id="3" left="414" top="63" width="228" height="86" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="function" args="2">axb3</e>
        <e type="operand">a</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">b</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">*</e>
        <e type="operand">a</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">b</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
        <e type="operand">a</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">b</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">*</e>
        <e type="operand">a</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">b</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
        <e type="operand">a</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">b</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">*</e>
        <e type="operand">a</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">b</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="4" left="414" top="162" width="163" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">vixvf</e>
        <e type="operand">v.i</e>
        <e type="operand">v.f</e>
        <e type="function" args="2">axb3</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="5" left="36" top="180" width="122" height="43" border="true" color="#000000" bgColor="#80ff80" fontSize="10">
    <math>
      <input>
        <e type="operand">v.f</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operand">1</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="5">mat</e>
        <e type="bracket">(</e>
        <e type="function" preserve="true" args="1">transpose</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="6" left="252" top="180" width="68" height="62" border="true" color="#000000" bgColor="#ffff80" fontSize="10">
    <math>
      <input>
        <e type="operand">v.f</e>
      </input>
      <result action="numeric">
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
      </result>
    </math>
  </region>
  <region id="7" left="414" top="216" width="124" height="62" color="#804000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">vixvf</e>
      </input>
      <result action="numeric">
        <e type="operand">0.5774</e>
        <e type="operand">0.5774</e>
        <e type="operand">0</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
      </result>
    </math>
  </region>
  <region id="8" left="36" top="261" width="109" height="61" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">λ</e>
        <e type="operand">v.f</e>
        <e type="function" preserve="true" args="1">norme</e>
        <e type="operand">v.i</e>
        <e type="function" preserve="true" args="1">norme</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="9" left="252" top="279" width="41" height="24" color="#804000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">λ</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
      </result>
    </math>
  </region>
  <region id="10" left="414" top="297" width="168" height="26" color="#804000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">vixvf</e>
        <e type="function" preserve="true" args="1">norme</e>
      </input>
      <result action="numeric">
        <e type="operand">0.8165</e>
      </result>
    </math>
  </region>
  <region id="11" left="36" top="333" width="133" height="43" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">p</e>
        <e type="operand">vixvf</e>
        <e type="operand">vixvf</e>
        <e type="function" preserve="true" args="1">norme</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="12" left="414" top="333" width="91" height="62" color="#804000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">p</e>
      </input>
      <result action="numeric">
        <e type="operand">0.7071</e>
        <e type="operand">0.7071</e>
        <e type="operand">0</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
      </result>
    </math>
  </region>
  <region id="13" left="36" top="405" width="247" height="61" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">θ</e>
        <e type="operand">v.f</e>
        <e type="operand">v.i</e>
        <e type="operator" args="2">*</e>
        <e type="operand">v.f</e>
        <e type="function" preserve="true" args="1">norme</e>
        <e type="operand">v.i</e>
        <e type="function" preserve="true" args="1">norme</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">/</e>
        <e type="function" preserve="true" args="1">acos</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="14" left="414" top="405" width="113" height="24" color="#804000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">θ</e>
      </input>
      <contract>
        <e type="operand" style="unit">°</e>
      </contract>
      <result action="numeric">
        <e type="operand">125.2644</e>
      </result>
    </math>
  </region>
  <region id="15" left="36" top="486" width="193" height="24" color="#000000" bgColor="#ff8040" fontSize="10">
    <text lang="eng">
      <p>Numerical optimisation</p>
    </text>
  </region>
  <region id="16" left="36" top="504" width="548" height="88" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">R</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="1">identity</e>
        <e type="operand">θ</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operand">0</e>
        <e type="operand">p</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="1">-</e>
        <e type="operand">p</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">p</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">0</e>
        <e type="operand">p</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="1">-</e>
        <e type="operand">p</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="1">-</e>
        <e type="operand">p</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">0</e>
        <e type="operand">3</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="11">mat</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">1</e>
        <e type="operand">θ</e>
        <e type="function" preserve="true" args="1">cos</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operand">p</e>
        <e type="operand">p</e>
        <e type="function" preserve="true" args="1">transpose</e>
        <e type="operator" args="2">*</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="1">identity</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="bracket">(</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="17" left="36" top="603" width="223" height="62" border="true" color="#000000" bgColor="#80ffff" fontSize="10">
    <math>
      <input>
        <e type="operand">R</e>
      </input>
      <result action="numeric">
        <e type="operand">0.2113</e>
        <e type="operand">0.7887</e>
        <e type="operand">0.5774</e>
        <e type="operand">0.7887</e>
        <e type="operand">0.2113</e>
        <e type="operand">0.5774</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.5774</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.5774</e>
        <e type="operand">0.5774</e>
        <e type="operator" args="1">-</e>
        <e type="operand">3</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="11">mat</e>
      </result>
    </math>
  </region>
  <region id="18" left="522" top="612" width="28" height="24" color="#000000" bgColor="#80ff80" fontSize="10">
    <text lang="eng">
      <p>OK</p>
    </text>
  </region>
  <region id="19" left="36" top="675" width="115" height="32" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">v.fver</e>
        <e type="operand">R</e>
        <e type="operand">v.i</e>
        <e type="operator" args="2">*</e>
        <e type="operand">λ</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="20" left="162" top="675" width="185" height="80" border="true" color="#000000" bgColor="#80ffff" fontSize="10">
    <math exponentialThreshold="15">
      <input>
        <e type="operand">v.fver</e>
      </input>
      <result action="numeric">
        <e type="operand">1.7496</e>
        <e type="operand">10</e>
        <e type="operand">15</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand">1.7496</e>
        <e type="operand">10</e>
        <e type="operand">15</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="1">-</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
      </result>
    </math>
  </region>
  <region id="21" left="405" top="675" width="115" height="32" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">v.iver</e>
        <e type="operand">R</e>
        <e type="operand">v.f</e>
        <e type="operator" args="2">*</e>
        <e type="operand">λ</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="22" left="540" top="675" width="133" height="62" border="true" color="#000000" bgColor="#80ffff" fontSize="10">
    <math exponentialThreshold="15">
      <input>
        <e type="operand">v.iver</e>
      </input>
      <result action="numeric">
        <e type="operand">0.5774</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.5774</e>
        <e type="operand">0.5774</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
      </result>
    </math>
  </region>
  <region id="23" left="36" top="783" width="201" height="24" color="#000000" bgColor="#ff8040" fontSize="10">
    <text lang="eng">
      <p>Symbolical optimisation</p>
    </text>
  </region>
  <region id="24" left="36" top="801" width="548" height="88" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">R</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="1">identity</e>
        <e type="operand">θ</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operand">0</e>
        <e type="operand">p</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="1">-</e>
        <e type="operand">p</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">p</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">0</e>
        <e type="operand">p</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="1">-</e>
        <e type="operand">p</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="1">-</e>
        <e type="operand">p</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">0</e>
        <e type="operand">3</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="11">mat</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">1</e>
        <e type="operand">θ</e>
        <e type="function" preserve="true" args="1">cos</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operand">p</e>
        <e type="operand">p</e>
        <e type="function" preserve="true" args="1">transpose</e>
        <e type="operator" args="2">*</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="1">identity</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="bracket">(</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="25" left="36" top="900" width="400" height="89" border="true" color="#000000" bgColor="#80ffff" fontSize="10">
    <math>
      <input>
        <e type="operand">R</e>
      </input>
      <result action="numeric">
        <e type="operand">0.2113</e>
        <e type="operand">0.7887</e>
        <e type="operand">4.4721</e>
        <e type="operand">10</e>
        <e type="operand">8</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operand">0.7887</e>
        <e type="operand">0.2113</e>
        <e type="operand">4.4721</e>
        <e type="operand">10</e>
        <e type="operand">8</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="1">-</e>
        <e type="operand">4.4721</e>
        <e type="operand">10</e>
        <e type="operand">8</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="1">-</e>
        <e type="operand">4.4721</e>
        <e type="operand">10</e>
        <e type="operand">8</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operand">0.5774</e>
        <e type="operator" args="1">-</e>
        <e type="operand">3</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="11">mat</e>
      </result>
    </math>
  </region>
  <region id="26" left="522" top="936" width="61" height="24" color="#000000" bgColor="#ff0000" fontSize="10">
    <text lang="eng">
      <p>KO !!!</p>
    </text>
  </region>
  <region id="27" left="36" top="999" width="115" height="32" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">v.fver</e>
        <e type="operand">R</e>
        <e type="operand">v.i</e>
        <e type="operator" args="2">*</e>
        <e type="operand">λ</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="28" left="162" top="999" width="133" height="62" border="true" color="#000000" bgColor="#80ffff" fontSize="10">
    <math exponentialThreshold="15">
      <input>
        <e type="operand">v.fver</e>
      </input>
      <result action="numeric">
        <e type="operand">0.3333</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.3333</e>
        <e type="operand">0.3333</e>
        <e type="operator" args="1">-</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
      </result>
    </math>
  </region>
  <region id="29" left="405" top="999" width="115" height="32" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">v.iver</e>
        <e type="operand">R</e>
        <e type="operand">v.f</e>
        <e type="operator" args="2">*</e>
        <e type="operand">λ</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="30" left="540" top="999" width="124" height="62" border="true" color="#000000" bgColor="#80ffff" fontSize="10">
    <math exponentialThreshold="15">
      <input>
        <e type="operand">v.iver</e>
      </input>
      <result action="numeric">
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">0.5774</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
      </result>
    </math>
  </region>
</regions>