function cspline,xx, yy, tt, Deriv = deriv ;+ ; NAME: ; 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 ;- ;-------------------------------------------------------------------------- On_error,2 compile_opt idl2 if N_params() LT 3 then begin print,'Syntax: result = cspline( x, y, t, [ DERIV = ] )' return,-1 endif n = N_elements(xx) if xx[n-1] LT xx[0] then begin ;Descending order? xrev = reverse(xx) yrev = reverse(yy) if N_elements(Deriv) NE n then begin if min( xx - xx[1:*]) LT 0 then \$ message,'ERROR - Input vector not monotonic' deriv = spl_init( xrev, yrev) endif return, spl_interp( xrev, yrev, deriv, tt) endif if N_elements(Deriv) NE n then deriv = spl_init( xx, yy) return, spl_interp( xx, yy, deriv, tt) end