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)
Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
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) -- Mat([ [<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>] [...]