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.