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.\"
.IX Title "Math::Derivative 3pm"
.TH Math::Derivative 3pm "2017-11-09" "perl v5.26.1" "User Contributed Perl Documentation"
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.SH "NAME"
Math::Derivative \- Numeric 1st and 2nd order differentiation
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\&    use Math::Derivative qw(:all);
\&
\&    @dydx = forwarddiff(\e@x, \e@y);
\&
\&    @dydx = centraldiff(\e@x, \e@y);
\&
\&    @dydx = Derivative1(\e@x, \e@y);     # A synonym for centraldiff()
\&
\&    @d2ydx2 = Derivative2(\e@x, \e@y, $yd0, $ydn);
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
This Perl package exports functions that numerically approximate first
and second order differentiation on vectors of data. The accuracy of
the approximation will depend upon the differences between the
successive values in the X array.
.SS "\s-1FUNCTIONS\s0"
.IX Subsection "FUNCTIONS"
The functions may be imported by name or by using the tag \*(L":all\*(R".
.PP
\fI\fIforwarddiff()\fI\fR
.IX Subsection "forwarddiff()"
.PP
.Vb 1
\&    @dydx = forwarddiff(\e@x, \e@y);
.Ve
.PP
Take the references to two arrays containing the x and y ordinates of
the data, and return an array of approximate first derivatives at the
given x ordinates, using the forward difference approximation.
.PP
The last term is actually formed using a backward difference formula,
there being no array item to subtract from at the end of the array.
If you want to use derivatives strictly formed from the forward
difference formula, use only the values from [0 .. #y\-1], e.g.:
.PP
.Vb 1
\&    @dydx = (forwarddiff(\e@x, \e@y))[0 .. $#y\-1];
.Ve
.PP
or, more simply,
.PP
.Vb 2
\&    @dydx = forwarddiff(\e@x, \e@y);
\&    pop @dydx;
.Ve
.PP
\fI\fIcentraldiff()\fI\fR
.IX Subsection "centraldiff()"
.PP
.Vb 1
\&    @dydx = centraldiff(\e@x, \e@y);
.Ve
.PP
Take the references to two arrays containing the x and y ordinates of
the data, and return an array of approximate first derivatives at the
given x ordinates.
.PP
The algorithm used three data points to calculate the derivative, except
at the end points, where by necessity the forward difference algorithm
is used instead. If you want to use derivatives strictly formed from
the central difference formula, use only the values from [1 .. #y\-1],
e.g.:
.PP
.Vb 1
\&    @dydx = (centraldiff(\e@x, \e@y))[1 .. $#y\-1];
.Ve
.PP
\fI\fIDerivative2()\fI\fR
.IX Subsection "Derivative2()"
.PP
.Vb 1
\&    @d2ydx2 = Derivative2(\e@x, \e@y);
.Ve
.PP
or
.PP
.Vb 1
\&    @d2ydx2 = Derivative2(\e@x, \e@y, $yp0, $ypn);
.Ve
.PP
Take references to two arrays containing the x and y ordinates of the
data and return an array of approximate second derivatives at the given
x ordinates.
.PP
You may optionally give values to use as the first derivatives at the
start and end points of the data. If you don't, first derivative values
will be assumed to be zero.
.PP
\fI\fIDerivative1()\fI\fR
.IX Subsection "Derivative1()"
.PP
A synonym for \fIcentraldiff()\fR.
.SH "REFERENCES"
.IX Header "REFERENCES"
<http://www.holoborodko.com/pavel/numerical\-methods/numerical\-derivative/central\-differences/>
.PP
<http://www.robots.ox.ac.uk/~sjrob/Teaching/EngComp/ecl6.pdf>
.SH "AUTHOR"
.IX Header "AUTHOR"
John A.R. Williams \fBJ.A.R.Williams@aston.ac.uk\fR
.PP
John M. Gamble \fBjgamble@cpan.org\fR (current maintainer)