1Math::Derivative(3)   User Contributed Perl Documentation  Math::Derivative(3)
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NAME

6       Math::Derivative - Numeric 1st and 2nd order differentiation
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SYNOPSIS

9           use Math::Derivative qw(:all);
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11           @dydx = forwarddiff(\@x, \@y);
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13           @dydx = centraldiff(\@x, \@y);
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15           @dydx = Derivative1(\@x, \@y);     # A synonym for centraldiff()
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17           @d2ydx2 = Derivative2(\@x, \@y, $yd0, $ydn);
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DESCRIPTION

20       This Perl package exports functions that numerically approximate first
21       and second order differentiation on vectors of data. The accuracy of
22       the approximation will depend upon the differences between the
23       successive values in the X array.
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25   FUNCTIONS
26       The functions may be imported by name or by using the tag ":all".
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28       forwarddiff()
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30           @dydx = forwarddiff(\@x, \@y);
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32       Take the references to two arrays containing the x and y ordinates of
33       the data, and return an array of approximate first derivatives at the
34       given x ordinates, using the forward difference approximation.
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36       The last term is actually formed using a backward difference formula,
37       there being no array item to subtract from at the end of the array.  If
38       you want to use derivatives strictly formed from the forward difference
39       formula, use only the values from [0 .. #y-1], e.g.:
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41           @dydx = (forwarddiff(\@x, \@y))[0 .. $#y-1];
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43       or, more simply,
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45           @dydx = forwarddiff(\@x, \@y);
46           pop @dydx;
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48       centraldiff()
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50           @dydx = centraldiff(\@x, \@y);
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52       Take the references to two arrays containing the x and y ordinates of
53       the data, and return an array of approximate first derivatives at the
54       given x ordinates.
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56       The algorithm used three data points to calculate the derivative,
57       except at the end points, where by necessity the forward difference
58       algorithm is used instead. If you want to use derivatives strictly
59       formed from the central difference formula, use only the values from [1
60       .. #y-1], e.g.:
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62           @dydx = (centraldiff(\@x, \@y))[1 .. $#y-1];
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64       Derivative2()
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66           @d2ydx2 = Derivative2(\@x, \@y);
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68       or
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70           @d2ydx2 = Derivative2(\@x, \@y, $yp0, $ypn);
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72       Take references to two arrays containing the x and y ordinates of the
73       data and return an array of approximate second derivatives at the given
74       x ordinates.
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76       You may optionally give values to use as the first derivatives at the
77       start and end points of the data. If you don't, first derivative values
78       will be assumed to be zero.
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80       Derivative1()
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82       A synonym for centraldiff().
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REFERENCES

85       <http://www.holoborodko.com/pavel/numerical-methods/numerical-derivative/central-differences/>
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87       <http://www.robots.ox.ac.uk/~sjrob/Teaching/EngComp/ecl6.pdf>
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AUTHOR

90       John A.R. Williams J.A.R.Williams@aston.ac.uk
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92       John M. Gamble jgamble@cpan.org (current maintainer)
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96perl v5.34.0                      2022-01-21               Math::Derivative(3)