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Index Page gfuds_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

       gfuds_c ( GF, user defined scalar )

       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
       --------  ---  --------------------------------------------------
       SPICE_GF_CNVTOL
                  P   Convergence tolerance.
       udfuns     I   Name of the routine that computes a scalar
                      quantity corresponding to an `et'.
       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 confined.
       result     O   SPICE window containing results.

#### Detailed_Input

       udfuns      is the routine that returns the value of the scalar
                   quantity of interest at time `et'. The prototype of
                   `udfuns' is:

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

                   where:

                      et      is a double precision value representing
                              ephemeris time, expressed as seconds past
                              J2000 TDB, at which to determine the scalar
                              value.

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

       udqdec      is the name of the routine that determines if the scalar
                   quantity calculated by `udfuns' is decreasing. The prototype
                   of `udqdec' is:

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

                  where:

                      udfuns   is the name of the scalar function as defined
                               above.

                      et       is a double precision value representing
                               ephemeris time, expressed as seconds past
                               J2000 TDB, at which to determine the time
                               derivative of `udfuns'.

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

       relate      is 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      is 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        is 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 unreasonable amount of time.

                   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     is an integer parameter specifying the number of intervals
                   that can be accommodated by each of the dynamically allocated
                   workspace windows used internally by this routine.

                   In many cases, it's not necessary to compute an accurate
                   estimate of how many intervals are needed; rather, the user
                   can pick a size considerably larger than what's really
                   required.

                   However, since excessively large arrays can prevent
                   applications from compiling, linking, or running properly,
                   sometimes `nintvls' must be set according to the actual
                   workspace requirement. A rule of thumb for the number of
                   intervals needed is

                      nintvls  =  2*n  +  ( m / step )

                   where

                      n      is the number of intervals in the confinement
                             window.

                      m      is the measure of the confinement window, in units
                             of seconds.

                      step   is the search step size in seconds.

       cnfine      is a 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.

                   In some cases the observer's state may be computed at
                   times outside of `cnfine' by as much as 2 seconds. See
                   -Particulars for details.

                   `cnfine' must be declared as a double precision SpiceCell.

                   CSPICE provides the following macro, which declares and
                   initializes the cell

                      SPICEDOUBLE_CELL        ( cnfine, CNFINESZ );

                   where CNFINESZ is the maximum capacity of `cnfine'.

#### 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 containing the time intervals within
                   the confinement window, during which the specified
                   condition on the scalar quantity is met.

                   `result' must be declared and initialized with sufficient
                   size to capture the full set of time intervals within the
                   search region on which the specified condition is satisfied.

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

                   The endpoints of the time intervals comprising `result' are
                   interpreted as seconds past J2000 TDB.

                   If the search is for local extrema, or for absolute
                   extrema with `adjust' set to zero, then normally each
                   interval of `result' will be a singleton: the left and
                   right endpoints of each interval will be identical.

                   If no times within the confinement window satisfy the
                   search criteria, `result' will be returned with a
                   cardinality of zero.

                   `result' must be declared as a double precision SpiceCell.

                   CSPICE provides the following macro, which declares and
                   initializes the cell

                      SPICEDOUBLE_CELL        ( result, RESULTSZ );

                   where RESULTSZ is the maximum capacity of `result'.

#### 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. One technique to handle such a situation,
           slightly contract `result' using the window routine wncond_c.

       3)  If the number of intervals `nintvls' is less than 1, the error
           SPICE(VALUEOUTOFRANGE) is signaled.

       4)  If the size of the SPICE window `result' is less than 2 or not
           an even value, the error SPICE(INVALIDDIMENSION) is signaled
           by a routine in the call tree of this routine.

       5)  If `result' has insufficient capacity to contain the
           number of intervals on which the specified condition
           is met, an error is signaled by a routine in the call
           tree of this routine.

       6)  If an error (typically cell overflow) occurs during
           window arithmetic, the error is signaled by a routine
           in the call tree of this routine.

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

       8)  If `adjust' is negative, an error is signaled by a routine in
           the call tree of this routine.

       9)  If a non-zero value is provided for `adjust' when `relate' has any
           value other than "ABSMIN" or "ABSMAX", an error is signaled by
           a routine in the call tree of this routine.

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

       11) If the `relate' input string pointer is null, the error
           SPICE(NULLPOINTER) is signaled.

       12) If the `relate' input string has zero length, the error
           SPICE(EMPTYSTRING) is signaled.

       13) If any the `cnfine' or `result' cell arguments has a type
           other than SpiceDouble, the error SPICE(TYPEMISMATCH) is
           signaled.

       14) If memory cannot be allocated to create the temporary variable
           required for the execution of the underlying Fortran routine,
           the error SPICE(MALLOCFAILED) is signaled.

#### Files

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

       If the scalar 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.

       -  Certain computations can expand the time window over which
          `udfuns' and `udqdec' require data; such data must be provided by
          loaded kernels. See -Particulars for details.

       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.

       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.
       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, et, dt, isdecr );

             return;
          }

       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
       =====================

       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 default convergence tolerance
       used by this routine is set by the parameter SPICE_GF_CNVTOL (defined
       in SpiceGF.h).

       The value of SPICE_GF_CNVTOL is set to a "tight" value so that the
       tolerance doesn't become the limiting factor in 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 );

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

       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.

       Certain user-defined computations may expand the window over
       which computations are performed. Here "expansion" of a window by
       an amount "T" means that the left endpoint of each interval
       comprising the window is shifted left by T, the right endpoint of
       each interval is shifted right by T, and any overlapping
       intervals are merged. Note that the input window `cnfine' itself is
       not modified.

       If a search uses an equality constraint, the time window over
       which the functions `udfuns' and `udqdec' are called is expanded by 1
       second.

       Computation of observer-target states by spkezr_c or spkez_c, using
       stellar aberration corrections, requires the state of the
       observer, relative to the solar system barycenter, to be computed
       at times offset from the input time by +/- 1 second. If the input
       time `et' is used by `udfuns' or `udqdec' to compute such a state, the
       window over which the observer state is computed is expanded by
       1 second.

       The window expansions described above are additive: if both
       conditions apply, the window expansion amount is the sum of the
       individual amounts.

       When light time corrections are used in the computation of
       observer-target states, expansion of the search window also
       affects the set of times at which the light time-corrected states
       of the targets are computed.

       In addition to the possible expansion of the search window that
       occurs when both an equality constraint and stellar aberration
       corrections are used, round-off error should be taken into
       account when the need for data availability is analyzed.

#### 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) 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: gfuds_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
                ---------                     --------
                de414.bsp                     Planetary ephemeris
                pck00008.tpc                  Planet orientation and
                                              radii
                naif0009.tls                  Leapseconds

             \begindata

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

             \begintext

             End of meta-kernel

          Example code begins here.

          /.
             Program gfuds_ex1
          ./
          #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( )
             {

             /.
             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( "gfuds_ex1.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'.
             ./

             uddc_c( udfuns, et, dt, isdecr );

             return;
             }

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

          Compile date Mar 20 2018, 17:48:10

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

#### Version

       -CSPICE Version 1.1.0, 03-NOV-2021 (JDR) (EDW) (NJB)

           Added use of ALLOC_CHECK_INTRA to check net null effect on
           alloc count.

           Updated header to describe use of expanded confinement window.

           Edited the header to comply with NAIF standard.

           Updated the description of "nintvls", "cnfine" and "result"
           arguments.

           Added entries #4, #5 and #14 in -Exceptions sections, and
           replaced old entry #5 by new entries #8 and #9.

       -CSPICE Version 1.0.1, 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

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

    Fri Dec 31 18:41:07 2021