Spline(3) User Contributed Perl Documentation Spline(3)NAMEMath::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
Derivative2, the low index of the interval in which to interpolate and
the x ordinate in that interval. Returned is the interpolated y
ordinate. 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)."\n";
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.
perl v5.14.0 1995-12-26 Spline(3)
