﻿<?xml version="1.0" encoding="utf-8" standalone="yes"?>
<?application progid="SMath Studio Desktop" version="0.97.5346.24640"?>
<regions>
  <settings>
    <identity>
      <id>13d63a35-e90c-4534-a911-6ac439702245</id>
      <revision>16</revision>
    </identity>
    <calculation>
      <precision>6</precision>
      <exponentialThreshold>9</exponentialThreshold>
      <fractions>decimal</fractions>
    </calculation>
    <pageModel active="true" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <paper id="1" orientation="Portrait" width="850" height="1100" />
      <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>
      <backgrounds />
    </pageModel>
    <dependences>
      <assembly name="SMath Studio Desktop" version="0.97.5346.24640" guid="a37cba83-b69c-4c71-9992-55ff666763bd" />
      <assembly name="Special Functions" version="1.11.5346.31403" guid="2814e667-4e12-48b1-8d51-194e480eabc5" />
      <assembly name="Math Region" version="0.97.5346.24640" guid="02f1ab51-215b-466e-a74d-5d8b1cf85e8d" />
      <assembly name="Plot Region" version="1.9.5346.32570" guid="c451c2b5-798b-4f08-b9ec-b90963d1ddaa" />
    </dependences>
  </settings>
  <region id="0" left="18" top="18" width="595" height="140" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math decimalPlaces="4" exponentialThreshold="3">
      <input>
        <e type="operand">vx</e>
        <e type="operand">vy</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">c</e>
        <e type="function" args="5">plotG</e>
        <e type="operand">a</e>
        <e type="operand" style="string">char</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">b</e>
        <e type="operand">size</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">c</e>
        <e type="operand" style="string">color</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">1</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="5">mat</e>
        <e type="operand">n</e>
        <e type="operand">vx</e>
        <e type="function" preserve="true" args="1">length</e>
        <e type="operator" args="2">:</e>
        <e type="operand">plot</e>
        <e type="operand">vx</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">vy</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">c</e>
        <e type="function" preserve="true" args="5">augment</e>
        <e type="operator" args="2">:</e>
        <e type="operand">i</e>
        <e type="operand">2</e>
        <e type="operand">n</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">plot</e>
        <e type="operand">plot</e>
        <e type="operand">vx</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">vy</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">c</e>
        <e type="function" preserve="true" args="5">augment</e>
        <e type="function" preserve="true" args="2">stack</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">plot</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="7">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="1" left="18" top="180" width="62" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math fractionType="auto">
      <input>
        <e type="operand">X</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operand">1</e>
        <e type="operand">4</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="2" left="90" top="180" width="53" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math fractionType="auto">
      <input>
        <e type="operand">Y</e>
        <e type="operand">4</e>
        <e type="operand">1</e>
        <e type="operand">3</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="3" left="153" top="180" width="85" height="71" color="#000000" bgColor="#fff5eb" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">φ</e>
        <e type="operand">1</e>
        <e type="operand">x</e>
        <e type="operand">x</e>
        <e type="operand">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="18" top="279" width="217" height="165" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <description active="true" position="Top" lang="eng">
        <p>Cholesky linear solver ...it solves for the linear combination in Legendre LS</p>
      </description>
      <input>
        <e type="operand">j</e>
        <e type="operand">1</e>
        <e type="operand">X</e>
        <e type="function" preserve="true" args="1">length</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">x</e>
        <e type="function" args="1">φ</e>
        <e type="function" preserve="true" args="1">length</e>
        <e type="function" preserve="true" args="2">range</e>
        <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="function" args="1">φ</e>
        <e type="operand">j</e>
        <e type="function" preserve="true" args="2">el</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">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>
        <e type="operand">Y</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
        <e type="operand">b</e>
        <e type="operand">Φ</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="function" preserve="true" args="1">eval</e>
        <e type="operand">d</e>
        <e type="operator" args="2">*</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="5" left="270" top="441" width="115" height="26" color="#000000" bgColor="#ffff80" fontSize="10">
    <math optimize="0" decimalPlaces="4">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">fit</e>
        <e type="operand">b</e>
        <e type="operand">x</e>
        <e type="function" args="1">φ</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="6" left="270" top="468" width="258" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">XY</e>
        <e type="operand">X</e>
        <e type="operand">Y</e>
        <e type="operand" style="string">+</e>
        <e type="operand">14</e>
        <e type="operand" style="string">red</e>
        <e type="function" args="5">plotG</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="7" left="18" top="540" width="240" height="158" color="#000000" bgColor="#ebebeb" fontSize="10">
    <plot type="2d" render="lines" scale_x="2.51670571529257" scale_y="3.79749833583241" scale_z="9.55718576560347" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-46" transpose_y="-53" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">fit</e>
        <e type="operand">XY</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </input>
    </plot>
  </region>
  <region id="8" left="288" top="540" width="121" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <description active="true" position="Top" lang="eng">
        <p>Choleski</p>
      </description>
      <input>
        <e type="operand">b</e>
      </input>
      <result action="numeric">
        <e type="operand">2.066667</e>
        <e type="operand">1.5</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.433333</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="9" left="450" top="540" width="124" height="92" color="#000000" bgColor="#ffffff" fontSize="10">
    <math fractionType="auto">
      <description active="true" position="Top" lang="eng">
        <p>sanity check</p>
      </description>
      <input>
        <e type="operand">X</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" args="1">fit</e>
        <e type="operand">X</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" args="1">fit</e>
        <e type="operand">X</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" args="1">fit</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
      </input>
      <result action="numeric">
        <e type="operand">4</e>
        <e type="operand">1</e>
        <e type="operand">3</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
      </result>
    </math>
  </region>
</regions>