Derivative(3pm) User Contributed Perl Documentation Derivative(3pm)NAME
Math::Derivative - Numeric 1st and 2nd order differentiation
SYNOPSIS
use Math::Derivative qw(Derivative1 Derivative2);
@dydx=Derivative1(@x,@y);
@d2ydx2=Derivative2(@x,@y);
@d2ydx2=Derivative2(@x,@y,$yp0,$ypn);
DESCRIPTION
This Perl package exports functions for performing numerical first (Derivative1) and second Derivative2) order differentiation on vectors
of data. They both take references to two arrays containing the x and y ordinates of the data and return an array of the 1st or 2nd
derivative at the given x ordinates. Derivative2 may optionally be given values to use for the first dervivative at the start and end
points of the data - otherwiswe 'natural' values are used.
HISTORY
$Log: Derivative.pm,v $ Revision 1.1 1995/12/26 16:26:59 willijar Initial revision
BUGS
Let me know.
AUTHOR
John A.R. Williams <J.A.R.Williams@aston.ac.uk>
perl v5.12.3 2011-06-14 Derivative(3pm)
Check Out this Related Man Page
Spline(3pm) User Contributed Perl Documentation Spline(3pm)NAME
Math::Spline - Cubic Spline Interpolation of data
SYNOPSIS
require Math::Spline;
$spline=new Math::Spline(@x,@y)
$y_interp=$spline->evaluate($x);
use Math::Spline qw(spline linsearch binsearch);
use Math::Derivative qw(Derivative2);
@y2=Derivative2(@x,@y);
$index=binsearch(@x,$x);
$index=linsearch(@x,$x,$index);
$y_interp=spline(@x,@y,@y2,$index,$x);
DESCRIPTION
This package provides cubic spline interpolation of numeric data. The data is passed as references to two arrays containing the x and y
ordinates. It may be used as an exporter of the numerical functions or, more easily as a class module.
The Math::Spline class constructor new takes references to the arrays of x and y ordinates of the data. An interpolation is performed using
the evaluate method, which, when given an x ordinate returns the interpolate y ordinate at that value.
The spline function takes as arguments references to the x and y ordinate array, a reference to the 2nd derivatives (calculated using De-
rivative2, the low index of the interval in which to interpolate and the x ordinate in that interval. Returned is the interpolated y ordi-
nate. Two functions are provided to look up the appropriate index in the array of x data. For random calls binsearch can be used - give a
reference to the x ordinates and the x loopup value it returns the low index of the interval in the data in which the value lies. Where the
lookups are strictly in ascending sequence (e.g. if interpolating to produce a higher resolution data set to draw a curve) the linsearch
function may more efficiently be used. It performs like binsearch, but requires a third argument being the previous index value, which is
incremented if necessary.
NOTE
requires Math::Derivative module
EXAMPLE
require Math::Spline;
my @x=(1,3,8,10);
my @y=(1,2,3,4);
$spline=new Math::Spline(@x,@y);
print $spline->evaluate(5)."
";
produces the output
2.44
HISTORY
$Log: Spline.pm,v $ Revision 1.1 1995/12/26 17:28:17 willijar Initial revision
BUGS
Bug reports or constructive comments are welcome.
AUTHOR
John A.R. Williams <J.A.R.Williams@aston.ac.uk>
SEE ALSO
"Numerical Recipies: The Art of Scientific Computing" W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling. Cambridge University
Press. ISBN 0 521 30811 9.
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