functions in spline.i - s

    dydx= spline(y, x)  


  -or-   yp= spline(dydx, y, x, xp)  
  -or-   yp= spline(y, x, xp)  
computes the cubic spline curve passing through the points (X, Y).  
With two arguments, Y and X, spline returns the derivatives DYDX at  
the points, an array of the same length as X and Y.  The DYDX values  
are chosen so that the piecewise cubic function returned by the four  
argument call will have a continuous second derivative.  
The X array must be strictly monotonic; it may either increase or  
decrease.  
The values Y and the derivatives DYDX uniquely determine a piecewise  
cubic function, whose value is returned in the four argument form.  
In this form, spline is analogous to the piecewise linear interpolator  
interp; usually you will regard it as a continuous function of its  
fourth argument, XP.  The first argument, DYDX, will normally have  
been computed by a previous call to the two argument spline function.  
However, this need not be the case; another DYDX will generate a  
piecewise cubic function with continuous first derivative, but a  
discontinuous second derivative.  For XP outside the extreme values  
of X, spline is linear (if DYDX1 or DYDX0 keywords were specified,  
the function will NOT have continuous second derivative at the  
endpoint).  
The XP array may have any dimensionality; the result YP will have  
the same dimensions as XP.  
If you only want the spline evaluated at a single set of XP, use the  
three argument form.  This is equivalent to:  
     yp= spline(spline(y,x), y, x, xp)  
The keywords DYDX1 and DYDX0 can be used to set the values of the  
returned DYDX(1) and DYDX(0) -- the first and last values of the  
slope, respectively.  If either is not specified or nil, the slope at  
that end will be chosen so that the second derivative is zero there.  
The function tspline (tensioned spline) gives an interpolation  
function which lies between spline and interp, at the cost of  
requiring you to specify another parameter (the tension).  
Interpreted function, defined at i/spline.i   line 10  

    ypprime= sprime(dydx, y, x, xp)  


computes the derivative of the cubic spline curve passing through the  
points (X, Y) at the points XP.  
The DYDX values will have been computed by a previous call to SPLINE,  
and are chosen so that the piecewise cubic function returned by the four  
argument call will have a continuous second derivative.  
The X array must be strictly monotonic; it may either increase or  
decrease.  
Interpreted function, defined at i/spline.i   line 309