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functions in spline.i - s

 
 
 
spline


             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  
SEE ALSO: interp,   tspline  
 
 
 
sprime


             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