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.