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Index Page uddf_c

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Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input | Detailed_Output Parameters Exceptions Files Particulars Examples | Restrictions Literature_References Author_and_Institution Version Index_Entries

#### Procedure

       uddf_c ( First derivative of a function, df(x)/dx )

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

#### Abstract

       Calculate the first derivative of a caller-specified scalar
       function using a three-point estimation.

#### Required_Reading

       None.

#### Keywords

       DERIVATIVE
       MATH

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       udfunc     I   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           is a scalar double precision value at which to determine
                   the derivative of `udfunc'.

                   For many SPICE uses, `x' will represent ephemeris time,
                   expressed as seconds past J2000 TDB.

       dx          is a scalar double precision value representing half the
                   interval in units of `x' separating the evaluation
                   values of `udfunc'; the evaluations occur at (x + dx)
                   and (x - dx).

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

#### Detailed_Output

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

                   Functionally:

                               d udfunc ( y )  |
                      deriv = ---------------- |
                                     dy        | y=x

#### Parameters

       None.

#### Exceptions

       1)  If `dx' has a value of zero, an error is signaled by a routine
           in the call tree of this routine.

#### Files

       If the evaluation of `udfunc' requires SPICE kernel data, the
       appropriate kernels must be loaded before calling this routine.

       -  SPK data: the calling application must load ephemeris data
          for the targets, observer, and any intermediate objects in
          a chain connecting the targets and observer for the time
          used in the evaluation. If aberration corrections are
          used, the states of target and observer relative to the
          solar system barycenter must be calculable from the
          available ephemeris data.

       -  If non-inertial reference frames are used, then PCK
          files, frame kernels, C-kernels, and SCLK kernels may be
          needed.

       Such kernel data are normally loaded once per program run, NOT
       every time this routine is called.

#### Particulars

       This routine provides a simple interface to numerically calculate
       the first derivative of a scalar quantity function, `udfunc'.
       `udfunc' is expected to be "well behaved" across at the evaluation
       interval [ x - dx, x + dx ]. This means a linear approximation to
       the function over the interval is sufficiently accurate to
       calculate the approximate derivative at `x'.

       The routine qderiv_c performs the differentiation using a three
       point estimation. See the header of the SPICE routine qderiv_c for
       details of the discrete derivative computation performed by this
       routine.

#### Examples

       The numerical results shown for this example 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.

       1) Calculate the time derivative of the light time corresponding
          to the apparent position of Mercury relative to the Moon at
          time "JAN 1 2009."

          Use the meta-kernel shown below to load the required SPICE
          kernels.

             KPL/MK

             File name: uddf_ex1.tm

             This meta-kernel is intended to support operation of SPICE
             example programs. The kernels shown here should not be
             assumed to contain adequate or correct versions of data
             required by SPICE-based user applications.

             In order for an application to use this meta-kernel, the
             kernels referenced here must be present in the user's
             current working directory.

             The names and contents of the kernels referenced
             by this meta-kernel are as follows:

                File name                     Contents
                ---------                     --------
                de421.bsp                     Planetary ephemeris
                naif0009.tls                  Leapseconds

             \begindata

                KERNELS_TO_LOAD = ( 'de421.bsp',
                                    'naif0009.tls'  )

             \begintext

             End of meta-kernel

          Example code begins here.

          /.
             Program uddf_ex1
          ./

          #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 ( "uddf_ex1.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;
          }

          When this program was executed on a Mac/Intel/cc/64-bit
          platform, the output was:

             -0.000135670941

#### Restrictions

       1)  The function `udfunc' must exist everywhere within [x - dx, x + dx].

#### Literature_References

       None.

#### Author_and_Institution

       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)
       E.D. Wright         (JPL)

#### Version

       -CSPICE Version 1.0.1, 05-AUG-2021 (JDR)

           Edited the header to comply with NAIF standard. Renamed example's
           meta-kernel.

           Added the -Exceptions, -Particulars and -Files sections.

       -CSPICE Version 1.0.0, 31-MAR-2010 (EDW) (NJB)

#### Index_Entries

       first derivative of a user-defined scalar function

#### Link to routine uddf_c source file uddf_c.c

    Fri Dec 31 18:41:14 2021