functions in splinef.i -

             spline_coef  
 
    is the worker for the splinef, splined, and splinei functions.  
    If you need to compute both function and derivative or integral,  
    you will improve performance using spline_coef.  See the source  
    code for those functions for usage.  
    

             yp = splined(dydx, y, x, xp)  
         or yp = splined(x_y_dydx, xp)  
 
    returns the derivative of the piecewise cubic function specified  
    by DYDX, Y, X at the points XP.  Extrapolation beyond the extreme  
    endpoints of X is linear, so splined gives the final value of DYDX.  
    The return value dimensions are the same as the dimensions of XP.  
    
    In the second form, X_Y_DYDX is a 3-by-nknots array of [x,y,dydx]  
    values.  The values of X in either case must either increase or  
    decrease monotonically.  
    

             yp = splinef(dydx, y, x, xp)  
         or yp = splinef(x_y_dydx, xp)  
 
    returns piecewise cubic function specified by DYDX, Y, X at  
    the points XP.  Extrapolation beyond the extreme endpoints of X  
    is linear, with slope equal to the final value of DYDX.  The  
    return value dimensions are the same as the dimensions of XP.  
    
    In the second form, X_Y_DYDX is a 3-by-nknots array of [x,y,dydx]  
    values.  The values of X in either case must either increase or  
    decrease monotonically.  
    

             yp = splinei(dydx, y, x, xp)  
         or yp = splinei(x_y_dydx, xp)  
 
    returns the integral of the piecewise cubic function specified  
    by DYDX, Y, X at the points XP.  The integral is quadratic beyond  
    the extreme endpoints of X, and zero at X(1).  The dimensions of  
    the return value are the same as the dimensions of XP.  
    This is the cubic analog of the integ function.  
    
    In the second form, X_Y_DYDX is a 3-by-nknots array of [x,y,dydx]  
    values.  The values of X in either case must either increase or  
    decrease monotonically.  
    

             x_y_dydx = splinelsq(y, x, xfit)  
             ...  
             yp = splinef(x_y_dydx, xp)  
 
     performs a least squares fit to the data points (X, Y).  The input  
     XFIT are the abcissas of the piecewise cubic function with knot  
     points XFIT which is the least squares best fit to the data (X,Y).  
     The XFIT must be strictly increase or decrease.  
     Any points in XFIT with no data points in the intervals on  
     either side will be removed.  
     A weight= keyword of the same length as X and Y may be supplied in  
     order to weight the various data points differently; a typical  
     WEIGHT function is 1/sigma^2 where sigma are the standard deviations  
     associated with the Y values.  
     You can specify y0=, dydx0=, y1=, and dydx1= keywords to fix the  
     value of the function or its derivative at the first (0) or last (1)  
     endpoint.  Be sure there is at least one point in the final  
     interval so that the XFIT at the endpoint is not removed.  
     More generally, you can specify a constrain= keyword.  The value  
     of constrain is a hook function which will be called just before  
     the matrix solve.  Your constrain subroutine will be passed no  
     arguments, but it can access and modify the mat and rhs variables.