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    <identity>
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      <revision>46</revision>
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    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <fractions>decimal</fractions>
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    <pageModel active="true" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <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>
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  <region id="0" left="18" top="18" width="163" height="26" color="#000000" bgColor="#ffff80" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="operand">B</e>
        <e type="function" preserve="true" args="2">al_convr1dinv</e>
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    </math>
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  <region id="1" left="18" top="36" width="211" height="26" color="#000000" bgColor="#ffff80" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="operand">m</e>
        <e type="operand">B</e>
        <e type="operand">n</e>
        <e type="function" preserve="true" args="4">al_convr1dinv</e>
      </input>
    </math>
  </region>
  <region id="2" left="18" top="72" width="202" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Part of plugin</p>
    </text>
    <text lang="ger">
      <p>Bestandteil des Plugins</p>
    </text>
  </region>
  <region id="3" left="243" top="72" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin Alglib.sm">Alglib</p>
    </text>
  </region>
  <region id="4" left="18" top="108" width="697" height="88" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>real one-dimensional deconvolution of two vectors A and B. 
The four-argument version does not provide any advantage over the two-argument 
version, except of being a direct map of the internal alglib call.
(http://www.alglib.net/translator/man/manual.cpp.html#sub_convr1d)</p>
    </text>
    <text lang="ger">
      <p>Reelle eindimensionale Faltung. der beiden Vektoren A und B. 
Ergebnis ist ein Vektor der Länge LängeA+LängeB-1. 
Die Version mit vier Argumenten bietet keine Vorteile gegenüber derjenigen mit zwei 
Argumenten, außer dass sie den internen Aufruf 1:1 abbildet.
(http://www.alglib.net/translator/man/manual.cpp.html#sub_convr1d)</p>
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  <region id="5" left="18" top="198" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
      </input>
    </math>
  </region>
  <region id="6" left="108" top="198" width="167" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>vector with m numbers</p>
    </text>
    <text lang="ger">
      <p>Vektor mit m Zahlen</p>
    </text>
  </region>
  <region id="7" left="18" top="234" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">B</e>
      </input>
    </math>
  </region>
  <region id="8" left="108" top="234" width="167" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>vector with n numbers</p>
    </text>
    <text lang="ger">
      <p>Vektor mit n Zahlen</p>
    </text>
  </region>
  <region id="9" left="18" top="270" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">m</e>
      </input>
    </math>
  </region>
  <region id="10" left="108" top="270" width="208" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>number of elements in A</p>
    </text>
    <text lang="ger">
      <p>Anzahl der Elemente in A</p>
    </text>
  </region>
  <region id="11" left="18" top="306" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">n</e>
      </input>
    </math>
  </region>
  <region id="12" left="108" top="306" width="208" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>number of elements in B</p>
    </text>
    <text lang="ger">
      <p>Anzahl der Elemente in B</p>
    </text>
  </region>
  <region id="13" left="18" top="342" width="82" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>result</p>
    </text>
    <text lang="ger">
      <p>Ergebnis </p>
    </text>
  </region>
  <region id="14" left="108" top="342" width="363" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>vector C such that C*B=A, having m-n+1 elements</p>
    </text>
    <text lang="ger">
      <p>Vektor C mit m-n+1 Elementen, so dass C*B=A</p>
    </text>
  </region>
  <region id="15" top="378" color="#000000" bgColor="#ffffff">
    <area collapsed="false">
      <title lang="eng">
        <p>Example</p>
      </title>
      <title lang="ger">
        <p>Beispiel</p>
      </title>
    </area>
    <region id="16" left="18" top="396" width="694" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p>The example shows the approximation of the first derivative by central difference and 
it's inverse (integration by trapezoidal rule)</p>
      </text>
      <text lang="ger">
        <p>Das Beispiel zeigt die numerische Ableitung mit dem zentralen Differenzenquotienten
und ihre Umkehrung (Integration mit der Trapezregel)</p>
      </text>
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    <region id="17" left="27" top="441" width="60" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">m</e>
          <e type="operand">100</e>
          <e type="operator" args="2">:</e>
        </input>
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    <region id="18" left="99" top="441" width="76" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">dx</e>
          <e type="operand">2</e>
          <e type="operand">π</e>
          <e type="operator" args="2">*</e>
          <e type="operand">m</e>
          <e type="operand">1</e>
          <e type="operator" args="2">-</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
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    <region id="19" left="189" top="441" width="154" height="48" color="#000000" bgColor="#ffffff" fontSize="10">
      <math optimize="2">
        <input>
          <e type="operand">i</e>
          <e type="operand">0</e>
          <e type="operand">m</e>
          <e type="operand">1</e>
          <e type="operator" args="2">-</e>
          <e type="function" preserve="true" args="2">range</e>
          <e type="operand">y</e>
          <e type="operand">i</e>
          <e type="operand">1</e>
          <e type="operator" args="2">+</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operand">dx</e>
          <e type="operand">i</e>
          <e type="operator" args="2">*</e>
          <e type="function" preserve="true" args="1">sin</e>
          <e type="operator" args="2">:</e>
          <e type="function" preserve="true" args="3">for</e>
        </input>
      </math>
    </region>
    <region id="20" left="369" top="441" width="365" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p>y: original function, sine function, sampled
at m points </p>
      </text>
      <text lang="ger">
        <p>y: Ausgangsdaten, mit m Punkten abgetastete
       Simusfunktion   </p>
      </text>
    </region>
    <region id="21" left="27" top="495" width="61" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">f</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0</e>
          <e type="operand">1</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>
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      </math>
    </region>
    <region id="22" left="135" top="513" width="104" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">n</e>
          <e type="operand">f</e>
          <e type="function" preserve="true" args="1">length</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="23" left="369" top="513" width="37" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>y*f</p>
      </text>
    </region>
    <region id="24" left="405" top="513" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>=</p>
      </text>
    </region>
    <region id="25" left="423" top="513" width="111" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">y</e>
          <e type="operand">i</e>
          <e type="operand">1</e>
          <e type="operator" args="2">+</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operand">y</e>
          <e type="operand">i</e>
          <e type="operand">1</e>
          <e type="operator" args="2">-</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operator" args="2">-</e>
        </input>
      </math>
    </region>
    <region id="26" left="396" top="522" width="24" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>i </p>
      </text>
    </region>
    <region id="27" left="369" top="540" width="299" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p>the corresponding x step is 2 dx</p>
      </text>
      <text lang="ger">
        <p>Die zugehörige x-Differenz ist 2 dx</p>
      </text>
    </region>
    <region id="28" left="27" top="567" width="97" height="33" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">t.0</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="1">time</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="29" left="369" top="567" width="185" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p>timer reset</p>
      </text>
      <text lang="ger">
        <p>Start der Zeitmessung</p>
      </text>
    </region>
    <region id="30" left="27" top="594" width="211" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
      <math optimize="2">
        <input>
          <e type="operand">dy</e>
          <e type="operand">1</e>
          <e type="operand">2</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operand">y</e>
          <e type="operand">f</e>
          <e type="function" preserve="true" args="2">al_convr1d</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
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      </math>
    </region>
    <region id="31" left="369" top="594" width="311" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p>dy approximates the first derivative of y
using divided central differences</p>
      </text>
      <text lang="ger">
        <p>dy ist eine Approximation der ersten 
Ableitung von y mit dem zentralen 
Differenzenquotienten</p>
      </text>
    </region>
    <region id="32" left="18" top="648" width="421" height="128" color="#000000" bgColor="#ffffff" fontSize="10">
      <plot type="2d" render="lines" scale_x="2.24087831910315" scale_y="2.45302245280626" scale_z="1.11539612174276" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-160" transpose_y="2" transpose_z="0">
        <input>
          <e type="operand">dx</e>
          <e type="operand">0</e>
          <e type="operand">m</e>
          <e type="operand">1</e>
          <e type="operator" args="2">-</e>
          <e type="function" preserve="true" args="2">range</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">y</e>
          <e type="function" preserve="true" args="2">augment</e>
          <e type="operand">dx</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="operand">m</e>
          <e type="operand">n</e>
          <e type="operator" args="2">+</e>
          <e type="operand">3</e>
          <e type="operator" args="2">-</e>
          <e type="function" preserve="true" args="2">range</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">dy</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">sys</e>
        </input>
      </plot>
    </region>
    <region id="33" left="27" top="828" width="126" height="33" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">Δt</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="1">time</e>
          <e type="operand">t.0</e>
          <e type="operator" args="2">-</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="34" left="189" top="828" width="100" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">Δt</e>
        </input>
        <result action="numeric">
          <e type="operand">0.06</e>
          <e type="operand" style="unit">s</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region id="35" left="369" top="828" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p>timing</p>
      </text>
      <text lang="ger">
        <p>Zeitnahme</p>
      </text>
    </region>
    <region id="36" left="18" top="855" width="299" height="64" color="#000000" bgColor="#ffffff" fontSize="10">
      <math optimize="2">
        <input>
          <e type="operand">u</e>
          <e type="operand">2</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">*</e>
          <e type="operand">dy</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0.000001</e>
          <e type="operand">1</e>
          <e type="operand">3</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="5">mat</e>
          <e type="function" preserve="true" args="2">al_convr1dinv</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="37" left="369" top="855" width="307" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p>The inverse transformation fails with the
original filter, thus a small perturbation
has to be applied.</p>
      </text>
      <text lang="ger">
        <p>Die inverse Transformation mit dem 
originalen Filterkern gelingt nicht,
daher muss er leicht gestört werden.</p>
      </text>
    </region>
    <region id="38" left="18" top="918" width="421" height="128" color="#000000" bgColor="#ffffff" fontSize="10">
      <plot type="2d" render="lines" scale_x="2.24087831910315" scale_y="2.45302245280626" scale_z="1.11539612174276" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-160" transpose_y="2" transpose_z="0">
        <input>
          <e type="operand">dx</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="operand">m</e>
          <e type="operand">n</e>
          <e type="operator" args="2">+</e>
          <e type="operand">3</e>
          <e type="operator" args="2">-</e>
          <e type="function" preserve="true" args="2">range</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">dy</e>
          <e type="function" preserve="true" args="2">augment</e>
          <e type="operand">dx</e>
          <e type="operand">0</e>
          <e type="operand">m</e>
          <e type="operand">1</e>
          <e type="operator" args="2">-</e>
          <e type="function" preserve="true" args="2">range</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">u</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">sys</e>
        </input>
      </plot>
    </region>
    <region id="39" left="459" top="927" width="268" height="104" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p>The inverse transformation 
yields the original function,
thus effectively is an 
integration using trapezoidal
rule.</p>
      </text>
      <text lang="ger">
        <p>Die inverse Transformation 
liefert wieder das Original, 
stellt also effektiv eine 
Integration mit der Trapezregel
dar.
</p>
      </text>
    </region>
    <region id="40" left="27" top="1089" width="164" height="33" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">Δt.1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="1">time</e>
          <e type="operand">Δt</e>
          <e type="operator" args="2">-</e>
          <e type="operand">t.0</e>
          <e type="operator" args="2">-</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="41" left="207" top="1089" width="109" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">Δt.1</e>
        </input>
        <result action="numeric">
          <e type="operand">0.06</e>
          <e type="operand" style="unit">s</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region id="42" left="378" top="1089" width="90" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p>timing</p>
      </text>
      <text lang="ger">
        <p>Zeitnahme </p>
      </text>
    </region>
    <region id="43" top="1116" color="#000000" bgColor="#ffffff">
      <area terminator="true" />
    </region>
  </region>
  <region id="44" left="18" top="1152" width="111" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="al_convr1d.sm">al_convr1d()</p>
    </text>
  </region>
  <region id="45" left="18" top="1170" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin Alglib.sm">Alglib</p>
    </text>
  </region>
  <region id="46" left="18" top="1206" width="127" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p href="Function index.sm">Function index</p>
    </text>
    <text lang="ger">
      <p href="Function index.sm">Funktionsindex</p>
    </text>
  </region>
  <region id="47" left="18" top="1224" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p href="Handbook.sm">Contents</p>
    </text>
    <text lang="ger">
      <p href="Handbook.sm">Inhalt</p>
    </text>
  </region>
  <region id="48" left="18" top="1260" width="450" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p italic="true">$Author: mkraska $
$Date: 2013-08-13 01:21:04 +0200 (Di, 13. Aug 2013) $ </p>
    </text>
  </region>
</regions>