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This article is about a function from ApCoCoA-1.


Compute numerical derivatives of equally spaced data using local polynomial regression.


SavGol(Points: MAT, MaxDiffOrd:INT, Nl:INT, Nr:INT, Deg:INT, Mode, StepWidth:RAT)


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This command computes numerical derivatives of given data series assuming that the data points are equally spaced.

Each data series is considered as a column of the matrix Points. It is assumed that the spacing StepWidth is the same for all columns. The polynomial degree Deg must be less than the window size Nl+Nr+1. The derivatives are computed up to order MaxDiffOrd.

The resulting matrix has Nl+Nr rows less than Points and has MaxDiffOrd+1 times more columns as Points. The first MaxDiffOrd+1 columns correspond to the 0-th, 1-st,...,MaxDiffOrd-th derivatives of the first column of Points, and so on.

  • @param Points The data points for which numerical derivatives are computed, each data series is considered as a column.

  • @param MaxDiffOrd The order up to which derivatives are computed.

  • @param Nl Number of left data points to be considered.

  • @param Nr Number of right data points to be considered.

  • @param Deg Maximum degree of the interpolation polynomal. Must be greater or equal MaxOrd.

  • @return A matrix that represents the derivatives of Points up to order MaxDiffOrd.


Points := Mat([[ Fn.SinN(I/2, 10), Fn.CosN(I/2, 10) ] | I In 0..40 ]);

MaxDiffOrd := 3;
Nl := 4;
Nr := 4;
Deg := 3;
Mode := 0; -- Mode is currently not used!
StepWidth := 0.5;

Result := Num.SavGol(Points, MaxDiffOrd, Nl, Nr, Deg, Mode, StepWidth);
Dec(Result, 2); ]])

-- (Result) --
  [<quote>0.84</quote>, <quote>0.40</quote>, <quote>0.63</quote>, <quote>0.31</quote>, <quote>0.38</quote>, <quote>0.87</quote>, <quote>0.29</quote>, <quote>0.69</quote>]
  [<quote>0.55</quote>, <quote>0.77</quote>, <quote>0.41</quote>, <quote>0.61</quote>, <quote>0.74</quote>, <quote>0.57</quote>, <quote>0.56</quote>, <quote>0.45</quote>]

See also