Procedure

   void uddf_c (  void             ( * udfunc ) ( SpiceDouble    et,
                                                  SpiceDouble  * value ),
                  SpiceDouble          x,
                  SpiceDouble          dx,
                  SpiceDouble        * deriv )

Abstract

   Routine to calculate the first derivative of a caller-specified
   function using a three-point estimation.

Required_Reading

   None.

Keywords

   DERIVATIVE

Brief_I/O

     Variable  I/O  Description
     --------  ---  --------------------------------------------------
     udfunc     I   Name of the routine that computes the scalar value
                    of interest.
     x          I   Independent variable of 'udfunc'
     dx         I   Interval from 'x' for derivative calculation
     deriv      O   Approximate derivative of 'udfunc' at 'x'

Detailed_Input

     udfunc     is an externally specified routine that returns the 
                value of the scalar quantity function of interest
                at x. 

                The prototype for 'udfunc' is

                    void   ( * udfunc ) ( SpiceDouble    et,
                                          SpiceDouble  * value )

                where: 
 
                    et      an input double precision value of the independent
                            variable the function at which to determine the
                            scalar value.  
 
                    value   the scalar double precision value of 'udfunc' 
                            at 'x'.

     x          a scalar double precision value representing the independent 
                variable at which to determine the derivative of 'udfunc'.

                For many SPICE uses, 'x' will represent the TDB ephemeris
                time.

     dx         a scalar double precision value representing half the 
                interval in units of X separating the evaluation
                epochs of UDFUNC; the evaluations occur at (x + dx)) 
                and (x - dx).

                'dx' may be negative but must be non-zero.
     

Detailed_Output

     deriv      the scalar double precision approximate value of the 
                first derivative of udfunc with respect to 'x'.

                Functionally:

                            d  udfunc ( x )
                   deriv =  --
                            dx

Parameters

   None.

Exceptions

   None.

Files

   None.

Particulars

   This routine provides a simple interface to numerically calculate
   the first derivative of a scalar quantity function.

Examples

   The numerical results shown for these examples may differ across
   platforms. The results depend on the SPICE kernels used as
   input, the compiler and supporting libraries, and the machine 
   specific arithmetic implementation. 


      #include <stdio.h>
      #include "SpiceUsr.h"

      void udfunc ( SpiceDouble et, SpiceDouble * value );
                   
      int main()
         {

         SpiceDouble       et;
         SpiceDouble       dt;
         SpiceDouble       deriv;

         /.
         Load leapsecond and SPK kernels. The name of the 
         meta kernel file shown here is fictitious; you 
         must supply the name of a file available 
         on your own computer system.
         ./

         furnsh_c ( "standard.tm" );

         /.
         Use a shift of one second off the epoch of interest.
         ./
         dt = 1.;

         /.
         Convert the epoch date string to ephemeris seconds.
         ./
         str2et_c ( "JAN 1 2009", &et );

         /.
         Calculate the derivative of UDFUNC at ET.
         ./
         uddf_c( udfunc, et, dt, &deriv );

         /.
         Output the calculated derivative.
         ./

         printf( "%18.12f\n", deriv );

         return ( 0 );
         }


      /.
      A scalar quantity function that returns the light-time
      between the Moon and Mercury at 'et'.
      ./

      void udfunc ( SpiceDouble et, SpiceDouble * value )
         {

         SpiceDouble          lt;
         SpiceDouble          pos[3];

         /.
         Evaluate the apparent position of Mercury with respect 
         to the Moon at 'et'.
         ./
         spkpos_c ( "MERCURY", et, "J2000", "LT+S", "MOON", pos, &lt );
         
         /.
         Return the light-time value as the scalar quantity.
         ./
         *value = lt;

         return;
         }

   The program outputs: 

      -0.000135670940

Restrictions

   'udfunc' must evaluate to real values at x + dx and x - dx.
   

Literature_References

   See qderiv.c header.

Author_and_Institution

   N.J. Bachman   (JPL)
   E.D. Wright    (JPL)

Version

   CSPICE Version 1.0.0  31-MAR-2010 (EDW) 

Index_Entries

   first derivative of a function

Link to routine uddf_c source file uddf_c.c