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CSPLINE

CSPLINE

## Purpose

Function to evaluate a natural cubic spline at specified data points

## Explanation

Combines the Numerical Recipes functions SPL_INIT and SPL_INTERP

## Calling Sequence

result = cspline( x, y, t, [ DERIV = ])

## Inputs

x - vector of spline node positions, must be monotonic increasing or
decreasing
y - vector of node values
t - x-positions at which to evaluate the spline, scalar or vector
INPUT-OUTPUT KEYWORD:
DERIV - values of the second derivatives of the interpolating function
at the node points. This is an intermediate step in the
computation of the natural spline that requires only the X and
Y vectors. If repeated interpolation is to be applied to
the same (X,Y) pair, then some computation time can be saved
by supplying the DERIV keyword on each call. On the first call
DERIV will be computed and returned on output.

## Output

the values for positions t are returned as the function value
If any of the input variables are double precision, then the output will
also be double precision; otherwise the output is floating point.

## Example

The following uses the example vectors from the SPL_INTERP documentation
IDL> x = (findgen(21)/20.0)*2.0*!PI ;X vector
IDL> y = sin(x) ;Y vector
IDL> t = (findgen(11)/11.0)*!PI ;Values at which to interpolate
IDL> cgplot,x,y,psym=1 ;Plot original grid
IDL> cgplot, /over, t,cspline(x,y,t),psym=2 ;Overplot interpolated values

## Method

The "Numerical Recipes" implementation of the natural cubic spline is
used, by calling the intrinsic IDL functions SPL_INIT and SPL_INTERP.

## History

version 1 D. Lindler May, 1989
version 2 W. Landsman April, 1997
Rewrite using the intrinsic SPL_INIT & SPL_INTERP functions
Converted to IDL V5.0 W. Landsman September 1997
Work for monotonic decreasing X vector W. Landsman February 1999

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