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2024-03-29T10:35:03Z
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AndraschkoBot: fixed links to namespace ApCoCoA
2020-10-07T08:38:27Z
<p>fixed links to namespace ApCoCoA</p>
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<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <see>Num.SavGol</see></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <see><ins class="diffchange diffchange-inline">ApCoCoA-1:Num.SavGol|</ins>Num.SavGol</see></div></td></tr>
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AndraschkoBot: Bot: Category moved
2020-10-02T16:35:33Z
<p>Bot: Category moved</p>
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AndraschkoBot
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S schuster: New page: <command> <title>Num.NumericalDerivative</title> <short_description>Compute numerical derivatives of arbitrarily spaced data using local polynomial regression.</short_description> <synt...
2013-05-17T10:22:22Z
<p>New page: <command> <title>Num.NumericalDerivative</title> <short_description>Compute numerical derivatives of arbitrarily spaced data using local polynomial regression.</short_description> <synt...</p>
<p><b>New page</b></p><div><command><br />
<title>Num.NumericalDerivative</title><br />
<br />
<short_description>Compute numerical derivatives of arbitrarily spaced data using local polynomial regression.</short_description><br />
<syntax><br />
NumericalDerivative(Points: MAT, MaxDiffOrd:INT, Nl:INT, Nr:INT, Deg:INT)<br />
<br />
</syntax><br />
<br />
<description><br />
This command computes numerical derivatives of given data series.<br />
<par/><br />
Matrix <tt>Points</tt> is considered to consist of two columns, ie., is considered to be of type <tt>Mat([[X_1,Y_1],...,[X_k, Y_k]])</tt>.<br />
<par/><br />
The polynomial degree <tt>Deg</tt> must be less than the window size <tt>Nl+Nr+1</tt>. The derivatives are computed up to order <tt>MaxDiffOrd</tt>.<br />
The resulting matrix has <tt>Nl+Nr</tt> rows less than Points and has <tt>MaxDiffOrd+1</tt> columns.<br />
<itemize><br />
<item>@param <em>Points</em> The data points for which numerical derivatives are computed.</item><br />
<item>@param <em>MaxDiffOrd</em> The order up to which derivatives are computed.</item><br />
<item>@param <em>Nl</em> Number of left data points to be considered.</item><br />
<item>@param <em>Nr</em> Number of right data points to be considered.</item><br />
<item>@param <em>Deg</em> Maximum degree of the interpolation polynomal. Must be greater or equal MaxOrd.<br />
</item><br />
<item>@return A matrix that represents the derivatives of Points up to order <tt>MaxDiffOrd</tt>.</item><br />
</itemize><br />
<br />
<br />
<example><br />
Points := Mat([[ I^2/800, Fn.CosN(I^2/800, 10) ] | I In 0..40 ]);<br />
<br />
MaxDiffOrd := 3;<br />
Nl := 4;<br />
Nr := 4;<br />
Deg := 3;<br />
Mode := 0; -- Mode is currently not used!<br />
StepWidth := 0.5;<br />
<br />
Result := Num.NumericalDerivative(Points, MaxDiffOrd, Nl, Nr, Deg);<br />
Dec(Result, 2); <br />
<br />
-- (Result) --<br />
Mat([<br />
[<quote>0.99</quote>, <quote>0.02</quote>, <quote>0.99</quote>, <quote>0.03</quote>]<br />
[<quote>0.99</quote>, <quote>0.03</quote>, <quote>0.99</quote>, <quote>0.05</quote>]<br />
[...]<br />
<br />
</example><br />
</description><br />
<br />
<seealso><br />
<see>Num.SavGol</see><br />
</seealso><br />
<types><br />
<type>apcocoaserver</type><br />
<type>points</type><br />
</types><br />
<key>NumericalDerivation</key><br />
<key>Num.NumericalDerivation</key><br />
<key>numerical.NumericalDerivation</key><br />
<wiki-category>Package_numerical</wiki-category><br />
</command></div>
S schuster