SPL_INIT

The SPL_INIT function is called to establish the type of interpolating spline for a tabulated set of functional values X _i , Y _i = F ( X _i ). SPL_INIT returns the values of the 2nd derivative of the interpolating function at the points X _i .

It is important to realize that SPL_INIT should be called only once to process an entire tabulated function in arrays X and Y . Once this has been done, values of the interpolated function for any value of X can be obtained by calls (as many as desired) to the separate function SPL_INTERP.

SPL_INIT is based on the routine spline described in section 3.3 of Numerical Recipes in C: The Art of Scientific Computing (Second Edition), published by Cambridge University Press, and is used by permission.

Arguments

X

An n -element input vector that specifies the tabulate points in ascending order.

Y

An n -element input vector that specifies the values of the tabulated function F ( X _i ) corresponding to X _i .

Keywords

DOUBLE

Set this keyword to force the computation to be done in double-precision arithmetic.

YP0

The first derivative of the interpolating function at the point X ₀ . If YP0 is omitted, the second derivative at the boundary is set to zero, resulting in a "natural spline."

YPN_1

The first derivative of the interpolating function at the point X _n-1 . If YPN_1 is omitted, the second derivative at the boundary is set to zero, resulting in a "natural spline."

Example

X = (FINDGEN(21)/20.) * 2.0*!PI

Y = SIN(X)

PRINT, SPL_INIT(X, Y, YP0 = -1.1, YPN_1 = 0.0)

IDL prints:

23.1552 -6.51599 1.06983 -1.26115 -0.839544 -1.04023

-0.950336 -0.817987 -0.592022 -0.311726 2.31192e-05 0.311634

0.592347 0.816783 0.954825 1.02348 0.902068 1.02781

-0.198994 3.26597 -11.0260

PRINT, SPL_INIT(X, Y, YP0 = -1.1)

IDL prints:

23.1552 -6.51599 1.06983 -1.26115 -0.839544 -1.04023

-0.950336 -0.817988 -0.592020 -0.311732 4.41521e-05 0.311555

0.592640 0.815690 0.958905 1.00825 0.958905 0.815692

0.592635 0.311567 0.00000