NAME¶
Math::Spline - Cubic Spline Interpolation of data
SYNOPSIS¶
use Math::Spline;
$spline = Math::Spline->new(\@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 = Math::Spline->new(\@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.