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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

   void gfuds_c (  void             ( * udfuns ) ( SpiceDouble       et,
                                                   SpiceDouble     * value ),

                   void             ( * udqdec ) ( void ( * udfuns )
                                                        ( SpiceDouble   et,
                                                          SpiceDouble * value ),

                                                   SpiceDouble       et,
                                                   SpiceBoolean    * isdecr ),

                   ConstSpiceChar     * relate,
                   SpiceDouble          refval,
                   SpiceDouble          adjust,
                   SpiceDouble          step,
                   SpiceInt             nintvls,
                   SpiceCell          * cnfine,
                   SpiceCell          * result )

Abstract

   Perform a GF search on a user defined scalar quantity.

Required_Reading

   GF
   WINDOWS

Keywords

   EVENT
   GEOMETRY
   SEARCH
   WINDOW


Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   udfuns     I   Name of the routine that computes the scalar quantity
                  of interest at some time.
   udqdec     I   Name of the routine that computes whether the
                  scalar quantity is decreasing.
   relate     I   Operator that either looks for an extreme value
                  (max, min, local, absolute) or compares the
                  geometric quantity value and a number.
   refval     I   Value used as reference for scalar quantity
                  condition.
   adjust     I   Allowed variation for absolute extremal
                  geometric conditions.
   step       I   Step size used for locating extrema and roots.
   nintvls    I   Workspace window interval count
   cnfine    I-O  SPICE window to which the search is restricted.
   result     O   SPICE window containing results.

Detailed_Input

   udfuns     the name of the external routine that returns the
              value of the scalar quantity of interest at time `et'.
              The calling sequence for "udfuns" is:

                 udfuns ( et, &value )

              where:

                 et      an input double precision value
                         representing the TDB ephemeris seconds time
                         at which to determine the scalar value.

                 value   is the value of the geometric quantity
                         at `et'.

   udqdec     the name of the external routine that determines if
              the scalar quantity calculated by "udfuns" is decreasing.
              The calling sequence for "udqdec" is:

                 udqdec ( udfuns, et, &isdecr )

              where:

                 udfuns   the name of the scalar function as defined above.

                 et       an input double precision value representing
                          the TDB ephemeris seconds time at at which
                          to determine the time derivative of `udfuns'.

                 isdecr   a logical variable indicating whether
                          or not the scalar value returned by udfuns
                          is decreasing. `isdecr' returns true if the
                          time derivative of "udfuns" at `et' is negative.

   relate     the scalar string comparison operator indicating
              the numeric constraint of interest. Values are:

                 ">"       value of scalar quantity greater than some
                           reference (refval).

                 "="       value of scalar quantity equal to some
                           reference (refval).

                 "<"       value of scalar quantity less than some
                           reference (refval).

                 "ABSMAX"  The scalar quantity is at an absolute
                           maximum.

                 "ABSMIN"  The scalar quantity is at an absolute
                            minimum.

                 "LOCMAX"  The scalar quantity is at a local
                           maximum.

                 "LOCMIN"  The scalar quantity is at a local
                           minimum.

              The caller may indicate that the region of interest
              is the set of time intervals where the quantity is
              within a specified distance of an absolute extremum.
              The argument `adjust' (described below) is used to
              specified this distance.

              Local extrema are considered to exist only in the
              interiors of the intervals comprising the confinement
              window:  a local extremum cannot exist at a boundary
              point of the confinement window.

              `relate' is insensitive to case, leading and
              trailing blanks.

   refval    is the reference value used to define an equality or
              inequality to  satisfied by the scalar quantity.
              The units of refval are those of the scalar quantity.

   adjust     the amount by which the quantity is allowed to vary
              from an absolute extremum.

              If the search is for an absolute minimum is performed,
              the resulting window contains time intervals when the
              geometric quantity value has values between ABSMIN and
              ABSMIN + adjust.

              If the search is for an absolute maximum, the
              corresponding range is between ABSMAX - adjust and
              ABSMAX.

              `adjust' is not used for searches for local extrema,
              equality or inequality conditions and must have value
              zero for such searches.

   step       the double precision time step size to use in
              the search.

              `step' must be short enough to for a search using this
              step size to locate the time intervals where the
              scalar quantity function is monotone increasing or
              decreasing. However, `step' must not be *too* short,
              or the search will take an

              The choice of `step' affects the completeness but not
              the precision of solutions found by this routine; the
              precision is controlled by the convergence tolerance.
              See the discussion of the parameter SPICE_GF_CNVTOL for
              details.

              `step' has units of TDB seconds.

   nintvls    an integer value specifying the number of intervals in the
              the internal workspace array used by this routine. `nintvls'
              should be at least as large as the number of intervals
              within the search region on which the specified observer-target
              vector coordinate function is monotone increasing or decreasing.
              It does no harm to pick a value of `nintvls' larger than the
              minimum required to execute the specified search, but if chosen
              too small, the search will fail.

   cnfine     a double precision SPICE window that confines the time
              period over which the specified search is conducted.
              cnfine may consist of a single interval or a collection
              of intervals.

              In some cases the confinement window can be used to
              greatly reduce the time period that must be searched
              for the desired solution. See the Particulars section
              below for further discussion.

              See the Examples section below for a code example
              that shows how to create a confinement window.

Detailed_Output

   cnfine     is the input confinement window, updated if necessary
              so the control area of its data array indicates the
              window's size and cardinality. The window data are
              unchanged.

   result     is a SPICE window representing the set of time
              intervals, within the confinement period, when the
              specified geometric event occurs.

              If `result' is non-empty on input, its contents
              will be discarded before gfuds_c conducts its
              search.

Parameters

   None.

Exceptions

   1)  In order for this routine to produce correct results,
       the step size must be appropriate for the problem at hand.
       Step sizes that are too large may cause this routine to miss
       roots; step sizes that are too small may cause this routine
       to run unacceptably slowly and in some cases, find spurious
       roots.

       This routine does not diagnose invalid step sizes, except
       that if the step size is non-positive, an error is signaled
       by a routine in the call tree of this routine.

   2)  Due to numerical errors, in particular,

          - Truncation error in time values
          - Finite tolerance value
          - Errors in computed geometric quantities

       it is *normal* for the condition of interest to not always be
       satisfied near the endpoints of the intervals comprising the
       result window.

       The result window may need to be contracted slightly by the
       caller to achieve desired results. The SPICE window routine
       wncond_c can be used to contract the result window.

   3)  If an error (typically cell overflow) occurs while performing
       window arithmetic, the error will be diagnosed by a routine
       in the call tree of this routine.

   4)  If the relational operator `relate' is not recognized, an
       error is signaled by a routine in the call tree of this
       routine.

   5)  If `adjust' is negative, the error SPICE(VALUEOUTOFRANGE) will
       signal from a routine in the call tree of this routine.

       A non-zero value for `adjust' when `relate' has any value other than
       "ABSMIN" or "ABSMAX" causes the error SPICE(INVALIDVALUE) to
       signal from a routine in the call tree of this routine.

   6)  If required ephemerides or other kernel data are not
       available, an error is signaled by a routine in the call tree
       of this routine.

   7)  If the workspace interval count is less than 1, the error
       SPICE(VALUEOUTOFRANGE) will be signaled.

   8)  If the required amount of workspace memory cannot be
       allocated, the error SPICE(MALLOCFAILURE) will be
       signaled.

   9)  If any input string argument pointer is null, the error
       SPICE(NULLPOINTER) will be signaled.

   10) If any input string argument is empty, the error
       SPICE(EMPTYSTRING) will be signaled.

   11) If either input cell has type other than SpiceDouble,
       the error SPICE(TYPEMISMATCH) is signaled.

Files

   Appropriate kernels must be loaded by the calling program before
   this routine is called.

   If the user defined function requires access to ephemeris data:

      - SPK data: ephemeris data for any body over the
        time period defined by the confinement window must be
        loaded. 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.
        Typically ephemeris data are made available by loading one
        or more SPK files via furnsh_c.

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

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

Particulars

   This routine determines a set of one or more time intervals
   within the confinement window when the scalar function
   satisfies a caller-specified constraint. The resulting set of
   intervals is returned as a SPICE window.

   Below we discuss in greater detail aspects of this routine's
   solution process that are relevant to correct and efficient
   use of this routine in user applications.

   udqdec Default Template
   =======================

   The user must supply a routine to determine whether sign of the
   time derivative of udfuns is positive or negative at `et'. For
   cases where udfuns is numerically well behaved, the user
   may find it convenient to use a routine based on the below
   template. uddc_c determines the truth of the expression

      d (udfuns)
      --         < 0
      dt

   using the library routine uddf_c to numerically calculate the
   derivative of udfuns using a three-point estimation. Use
   of gfdecr requires only changing the "udfuns" argument
   to that of the user provided scalar function passed to gfuds_c
   and defining the differential interval size, `dt'. Please see
   the Examples section for an example of gfdecr use.

   void gfdecr ( SpiceDouble et, SpiceBoolean * isdecr )
      {

      SpiceDouble         dt = h, double precision interval size;

      uddc_c( udfuns, uddf_c, et, dt, isdecr );

      return;
      }

   Below we discuss in greater detail aspects of this routine's
   solution process that are relevant to correct and efficient
   use of this routine in user applications.


   The Search Process
   ==================

   Regardless of the type of constraint selected by the caller, this
   routine starts the search for solutions by determining the time
   periods, within the confinement window, over which the specified
   scalar function is monotone increasing and monotone
   decreasing. Each of these time periods is represented by a SPICE
   window. Having found these windows, all of the quantity
   function's local extrema within the confinement window are known.
   Absolute extrema then can be found very easily.

   Within any interval of these "monotone" windows, there will be at
   most one solution of any equality constraint. Since the boundary
   of the solution set for any inequality constraint is contained in
   the union of

      - the set of points where an equality constraint is met
      - the boundary points of the confinement window

   the solutions of both equality and inequality constraints can be
   found easily once the monotone windows have been found.


   Step Size
   =========

   The monotone windows (described above) are found using a two-step
   search process. Each interval of the confinement window is
   searched as follows: first, the input step size is used to
   determine the time separation at which the sign of the rate of
   change of quantity function will be sampled. Starting at
   the left endpoint of an interval, samples will be taken at each
   step. If a change of sign is found, a root has been bracketed; at
   that point, the time at which the time derivative of the quantity
   function is zero can be found by a refinement process, for
   example, using a binary search.

   Note that the optimal choice of step size depends on the lengths
   of the intervals over which the quantity function is monotone:
   the step size should be shorter than the shortest of these
   intervals (within the confinement window).

   The optimal step size is *not* necessarily related to the lengths
   of the intervals comprising the result window. For example, if
   the shortest monotone interval has length 10 days, and if the
   shortest result window interval has length 5 minutes, a step size
   of 9.9 days is still adequate to find all of the intervals in the
   result window. In situations like this, the technique of using
   monotone windows yields a dramatic efficiency improvement over a
   state-based search that simply tests at each step whether the
   specified constraint is satisfied. The latter type of search can
   miss solution intervals if the step size is longer than the
   shortest solution interval.

   Having some knowledge of the relative geometry of the targets and
   observer can be a valuable aid in picking a reasonable step size.
   In general, the user can compensate for lack of such knowledge by
   picking a very short step size; the cost is increased computation
   time.

   Note that the step size is not related to the precision with which
   the endpoints of the intervals of the result window are computed.
   That precision level is controlled by the convergence tolerance.


   Convergence Tolerance
   =====================

   As described above, the root-finding process used by this routine
   involves first bracketing roots and then using a search process to
   locate them.  "Roots" include times when extrema are attained and
   times when the geometric quantity function is equal to a reference
   value or adjusted extremum. All endpoints of the intervals comprising
   the result window are either endpoints of intervals of the confinement
   window or roots.

   Once a root has been bracketed, a refinement process is used to
   narrow down the time interval within which the root must lie.
   This refinement process terminates when the location of the root
   has been determined to within an error margin called the
   "convergence tolerance." The convergence tolerance used by this
   routine is set via the parameter SPICE_GF_CNVTOL.

   The value of SPICE_GF_CNVTOL is set to a "tight" value so that the
   tolerance doesn't limit the accuracy of solutions found by this
   routine. In general the accuracy of input data will be the limiting
   factor.

   The user may change the convergence tolerance from the default
   SPICE_GF_CNVTOL value by calling the routine gfstol_c, e.g.

      gfstol_c( tolerance value in seconds )

   Call gfstol_c prior to calling this routine. All subsequent
   searches will use the updated tolerance value.

   Searches over time windows of long duration may require use of
   larger tolerance values than the default: the tolerance must be
   large enough so that it, when added to or subtracted from the
   confinement window's lower and upper bounds, yields distinct time
   values.

   Setting the tolerance tighter than SPICE_GF_CNVTOL is unlikely to be
   useful, since the results are unlikely to be more accurate.
   Making the tolerance looser will speed up searches somewhat,
   since a few convergence steps will be omitted. However, in most
   cases, the step size is likely to have a much greater effect
   on processing time than would the convergence tolerance.


   The Confinement Window
   ======================

   The simplest use of the confinement window is to specify a time
   interval within which a solution is sought. However, the
   confinement window can, in some cases, be used to make searches
   more efficient. Sometimes it's possible to do an efficient search
   to reduce the size of the time period over which a relatively
   slow search of interest must be performed.

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.

   Conduct a search on the range rate of the vector from the Sun
   to the Moon. Define a function to calculate the value.

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

         KPL/MK

         File name: standard.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.


         \begindata

            KERNELS_TO_LOAD = ( 'de414.bsp',
                                'pck00008.tpc',
                                'naif0009.tls'  )

         \begintext

   Code:

      #include <stdio.h>
      #include <stdlib.h>
      #include <string.h>
   
      #include "SpiceUsr.h"
      #include "SpiceZfc.h"
   
   
      #define       MAXWIN    20000
      #define       TIMFMT    "YYYY-MON-DD HR:MN:SC.###"
      #define       TIMLEN    41
      #define       NLOOPS    7
   
      void    gfq     ( SpiceDouble et, SpiceDouble * value );
      void    gfdecrx ( void ( * udfuns ) ( SpiceDouble    et,
                                            SpiceDouble  * value ),
                        SpiceDouble    et,
                        SpiceBoolean * isdecr );
   
      doublereal dvnorm_(doublereal *state);
   
   
      int main( int argc, char **argv )
         {
   
         /.
         Create the needed windows. Note, one interval
         consists of two values, so the total number
         of cell values to allocate is twice
         the number of intervals.
         ./
         SPICEDOUBLE_CELL ( result, 2*MAXWIN );
         SPICEDOUBLE_CELL ( cnfine, 2        );
   
         SpiceDouble       begtim;
         SpiceDouble       endtim;
         SpiceDouble       step;
         SpiceDouble       adjust;
         SpiceDouble       refval;
         SpiceDouble       beg;
         SpiceDouble       end;
   
         SpiceChar         begstr [ TIMLEN ];
         SpiceChar         endstr [ TIMLEN ];
   
         SpiceInt          count;
         SpiceInt          i;
         SpiceInt          j;
   
         ConstSpiceChar * relate [NLOOPS] = { "=",
                                              "<",
                                              ">",
                                              "LOCMIN",
                                              "ABSMIN",
                                              "LOCMAX",
                                              "ABSMAX"
                                            };
   
         printf( "Compile date %s, %s\n\n", __DATE__, __TIME__ );
   
         /.
         Load kernels.
         ./
         furnsh_c( "standard.tm" );
   
         /.
         Store the time bounds of our search interval in the `cnfine'
         confinement window.
         ./
         str2et_c( "2007 JAN 01", &begtim );
         str2et_c( "2007 APR 01", &endtim );
   
         wninsd_c ( begtim, endtim, &cnfine );
   
         /.
         Search using a step size of 1 day (in units of seconds). The reference
         value is .3365 km/s. We're not using the adjustment feature, so
         we set `adjust' to zero.
         ./
         step   = spd_c();
         adjust = 0.;
         refval = .3365;
   
         for ( j = 0;  j < NLOOPS;  j++ )
            {
   
            printf ( "Relation condition: %s \n",  relate[j] );
   
            /.
            Perform the search. The SPICE window `result' contains
            the set of times when the condition is met.
            ./
   
            gfuds_c ( gfq,
                      gfdecrx,
                      relate[j],
                      refval,
                      adjust,
                      step,
                      MAXWIN,
                      &cnfine,
                      &result );
   
            count = wncard_c( &result );
   
            /.
            Display the results.
            ./
            if (count == 0 )
               {
               printf ( "Result window is empty.\n\n" );
               }
            else
               {
               for ( i = 0;  i < count;  i++ )
                  {
   
                  /.
                  Fetch the endpoints of the Ith interval
                  of the result window.
                  ./
                  wnfetd_c ( &result, i, &beg, &end );
   
                  timout_c ( beg, TIMFMT, TIMLEN, begstr );
                  timout_c ( end, TIMFMT, TIMLEN, endstr );
   
                  printf ( "Start time, drdt = %s \n", begstr );
                  printf ( "Stop time,  drdt = %s \n", endstr );
   
                  }
   
               }
   
            printf("\n");
   
            }
   
         kclear_c();
         return( 0 );
         }
   
   
   
      /.
      The user defined functions required by GFUDS.
   
         gfq     for udfuns
         gfdecrx for udqdec
      ./
   
   
   
      /.
      -Procedure Procedure gfq
      ./
   
      void gfq ( SpiceDouble et, SpiceDouble * value )
   
      /.
      -Abstract
   
         User defined geometric quantity function. In this case,
         the range rate from the sun to the Moon at TDB time `et'.
   
      ./
         {
   
         /. Initialization ./
         SpiceInt             targ   = 301;
         SpiceInt             obs    = 10;
   
         SpiceChar          * ref    = "J2000";
         SpiceChar          * abcorr = "NONE";
   
         SpiceDouble          state [6];
         SpiceDouble          lt;
   
         /.
         Retrieve the vector from the Sun to the Moon in the J2000
         frame, without aberration correction.
         ./
         spkez_c ( targ, et, ref, abcorr, obs, state, &lt );
   
         /.
         Calculate the scalar range rate corresponding the
        `state' vector.
         ./
   
         *value = dvnorm_( state );
   
         return;
         }
   
   
   
      /.
      -Procedure gfdecrx
      ./
   
      void gfdecrx ( void ( * udfuns ) ( SpiceDouble    et,
                                         SpiceDouble  * value ),
                     SpiceDouble    et,
                     SpiceBoolean * isdecr )
   
      /.
      -Abstract
   
         User defined function to detect if the function derivative
         is negative (the function is decreasing) at TDB time `et'.
      ./
         {
   
         SpiceDouble         dt = 10.;
   
         /.
         Determine if "udfuns" is decreasing at `et'.
   
         uddc_c   - the GF function to determine if
                    the derivative of the user defined
                    function is negative at `et'.
   
         uddf_c   - the SPICE function to numerically calculate the
                    derivative of "udfuns" at `et' for the
                    interval [et-dt, et+dt].
         ./
   
         uddc_c( udfuns, et, dt, isdecr );
   
         return;
         }


   The program outputs:

      Relation condition: =
      Start time, drdt = 2007-JAN-02 00:35:19.574
      Stop time,  drdt = 2007-JAN-02 00:35:19.574
      Start time, drdt = 2007-JAN-19 22:04:54.899
      Stop time,  drdt = 2007-JAN-19 22:04:54.899
      Start time, drdt = 2007-FEB-01 23:30:13.428
      Stop time,  drdt = 2007-FEB-01 23:30:13.428
      Start time, drdt = 2007-FEB-17 11:10:46.540
      Stop time,  drdt = 2007-FEB-17 11:10:46.540
      Start time, drdt = 2007-MAR-04 15:50:19.929
      Stop time,  drdt = 2007-MAR-04 15:50:19.929
      Start time, drdt = 2007-MAR-18 09:59:05.959
      Stop time,  drdt = 2007-MAR-18 09:59:05.959

      Relation condition: <
      Start time, drdt = 2007-JAN-02 00:35:19.574
      Stop time,  drdt = 2007-JAN-19 22:04:54.899
      Start time, drdt = 2007-FEB-01 23:30:13.428
      Stop time,  drdt = 2007-FEB-17 11:10:46.540
      Start time, drdt = 2007-MAR-04 15:50:19.929
      Stop time,  drdt = 2007-MAR-18 09:59:05.959

      Relation condition: >
      Start time, drdt = 2007-JAN-01 00:00:00.000
      Stop time,  drdt = 2007-JAN-02 00:35:19.574
      Start time, drdt = 2007-JAN-19 22:04:54.899
      Stop time,  drdt = 2007-FEB-01 23:30:13.428
      Start time, drdt = 2007-FEB-17 11:10:46.540
      Stop time,  drdt = 2007-MAR-04 15:50:19.929
      Start time, drdt = 2007-MAR-18 09:59:05.959
      Stop time,  drdt = 2007-APR-01 00:00:00.000

      Relation condition: LOCMIN
      Start time, drdt = 2007-JAN-11 07:03:58.988
      Stop time,  drdt = 2007-JAN-11 07:03:58.988
      Start time, drdt = 2007-FEB-10 06:26:15.439
      Stop time,  drdt = 2007-FEB-10 06:26:15.439
      Start time, drdt = 2007-MAR-12 03:28:36.404
      Stop time,  drdt = 2007-MAR-12 03:28:36.404

      Relation condition: ABSMIN
      Start time, drdt = 2007-JAN-11 07:03:58.988
      Stop time,  drdt = 2007-JAN-11 07:03:58.988

      Relation condition: LOCMAX
      Start time, drdt = 2007-JAN-26 02:27:33.766
      Stop time,  drdt = 2007-JAN-26 02:27:33.766
      Start time, drdt = 2007-FEB-24 09:35:07.816
      Stop time,  drdt = 2007-FEB-24 09:35:07.816
      Start time, drdt = 2007-MAR-25 17:26:56.150
      Stop time,  drdt = 2007-MAR-25 17:26:56.150

      Relation condition: ABSMAX
      Start time, drdt = 2007-MAR-25 17:26:56.150
      Stop time,  drdt = 2007-MAR-25 17:26:56.150

Restrictions

   1) Any kernel files required by this routine must be loaded
      before this routine is called.

Literature_References

   None.

Author_and_Institution

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

Version

   -CSPICE Version 1.1.0, 21-OCT-2013 (NJB)(EDW)

      Correction to description of UDQDEC to show UDFUNC as 
      an argument.

      Header was updated to discuss use of gfstol_c.

      Edit to comments to correct search description; eliminate
      typo in gfq Abstract, "range rate" instead of "range."

      Improved header detail describing convergence tolerance.

   -CSPICE Version 1.0.0, 22-FEB-2010 (EDW)

Index_Entries

   GF user defined scalar function search
Wed Apr  5 17:54:36 2017