ApCoCoA-1:Num.NumericalDerivative
Num.NumericalDerivative
Compute numerical derivatives of arbitrarily spaced data using local polynomial regression.
Syntax
NumericalDerivative(Points: MAT, MaxDiffOrd:INT, Nl:INT, Nr:INT, Deg:INT)
Description
This command computes numerical derivatives of given data series.
Matrix Points is considered to consist of two columns, ie., is considered to be of type Mat([[X_1,Y_1],...,[X_k, Y_k]]).
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 columns.
@param Points The data points for which numerical derivatives are computed.
@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.
Example
Points := Mat([[ I^2/800, Fn.CosN(I^2/800, 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.NumericalDerivative(Points, MaxDiffOrd, Nl, Nr, Deg); Dec(Result, 2); -- (Result) -- Mat([ [<quote>0.99</quote>, <quote>0.02</quote>, <quote>0.99</quote>, <quote>0.03</quote>] [<quote>0.99</quote>, <quote>0.03</quote>, <quote>0.99</quote>, <quote>0.05</quote>] [...]
See also
