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Index Page gfpa_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

       gfpa_c ( GF, phase angle search )

       void gfpa_c ( ConstSpiceChar     * target,
                     ConstSpiceChar     * illmn,
                     ConstSpiceChar     * abcorr,
                     ConstSpiceChar     * obsrvr,
                     ConstSpiceChar     * relate,
                     SpiceDouble          refval,
                     SpiceDouble          adjust,
                     SpiceDouble          step,
                     SpiceInt             nintvls,
                     SpiceCell          * cnfine,
                     SpiceCell          * result     )

#### Abstract

       Determine time intervals for which a specified constraint
       on the phase angle between an illumination source, a target,
       and observer body centers is met.

#### Required_Reading

       GF
       NAIF_IDS
       SPK
       TIME
       WINDOWS

#### Keywords

       EPHEMERIS
       EVENT
       GEOMETRY
       SEARCH
       WINDOW

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       SPICE_GF_CNVTOL
                  P   Default convergence tolerance.
       target     I   Name of the target body.
       illmn      I   Name of the illuminating body.
       abcorr     I   Aberration correction flag.
       obsrvr     I   Name of the observing body.
       relate     I   Relational operator.
       refval     I   Reference value.
       adjust     I   Adjustment value for absolute extrema searches.
       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

       target      is the name of a target body. Optionally, you may supply
                   a string containing the integer ID code for the object.
                   For example both "MOON" and "301" are legitimate strings
                   that indicate the Moon is the target body.

                   Case and leading or trailing blanks are not significant
                   in the string `target'.

       illmn       is the name of the illuminating body. This will normally
                   be "SUN" but the algorithm can use any ephemeris object.

                   Case and leading or trailing blanks are not significant
                   in the string `illmn'.

       abcorr      is the description of the aberration corrections to apply
                   to the state evaluations to account for one-way light
                   time and stellar aberration.

                   This routine accepts only reception mode aberration
                   corrections. See the header of spkezr_c for a detailed
                   description of the aberration correction options. For
                   convenience, the allowed aberration options are listed
                   below:

                      "NONE"     Apply no correction. Returns the "true"
                                 geometric state.

                      "LT"       "Reception" case: correct for
                                 one-way light time using a Newtonian
                                 formulation.

                      "LT+S"     "Reception" case: correct for
                                 one-way light time and stellar
                                 aberration using a Newtonian
                                 formulation.

                      "CN"       "Reception" case: converged
                                 Newtonian light time correction.

                     "CN+S"      "Reception" case: converged
                                 Newtonian light time and stellar
                                 aberration corrections.

                   Case and leading or trailing blanks are not significant
                   in the string `abcorr'.

       obsrvr      is the name of an observing body. Optionally, you may
                   supply a string containing the integer ID code for the
                   object. For example both "MOON" and "301" are legitimate
                   strings that indicate the Moon is the observer.

                   Case and leading or trailing blanks are not significant
                   in the string `obsrvr'.

       relate      is a relational operator used to define a constraint on a
                   specified phase angle. The result window found by this
                   routine indicates the time intervals where the constraint
                   is satisfied. Supported values of `relate' and
                   corresponding meanings are shown below:

                      ">"        The phase angle value is greater than the
                                 reference value `refval'.

                      "="        The phase angle value is equal to the
                                 reference value `refval'.

                      "<"        The phase angle value is less than the
                                 reference value `refval'.

                      "ABSMAX"   The phase angle value is at an absolute
                                 maximum.

                      "ABSMIN"   The phase angle value is at an absolute
                                 minimum.

                      "LOCMAX"   The phase angle value is at a local
                                 maximum.

                      "LOCMIN"   The phase angle value is at a local
                                 minimum.

                   `relate' may be used to specify an "adjusted" absolute
                   extremum constraint: this requires the phase angle to be
                   within a specified offset relative to an absolute
                   extremum. The argument `adjust' (described below) is used
                   to specify this offset.

                   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.

                   Case and leading or trailing blanks are not
                   significant in the string `relate'.

       refval      is the double precision reference value used together
                   with the argument `relate' to define an equality or
                   inequality to be satisfied by the phase angle. See the
                   discussion of `relate' above for further information.

                   The units of `refval' are radians.

       adjust      is a double precision value used to modify searches for
                   absolute extrema: when `relate' is set to "ABSMAX" or
                   "ABSMIN" and `adjust' is set to a positive value, gfpa_c
                   finds times when the phase angle is within `adjust' radians
                   of the specified extreme value.

                   If `adjust' is non-zero and a search for an absolute
                   minimum `min' is performed, the result window contains
                   time intervals when the phase angle has values between
                    `min' and min+adjust.

                   If the search is for an absolute maximum `max', the
                   corresponding range is from max-adjust to `max'.

                   `adjust' is not used for searches for local extrema,
                   equality or inequality conditions.

       step        is the step size to be used in the search. `step' must
                   be shorter than any maximal time interval on which the
                   specified phase angle function is monotone increasing or
                   decreasing. That is, if the confinement window is
                   partitioned into alternating intervals on which the
                   phase angle function is either monotone increasing or
                   decreasing, `step' must be shorter than any of these
                   intervals.

                   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 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.

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

                   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 the SPICE window of intervals, contained within the
                   confinement window `cnfine', on which the specified phase
                   angle constraint is satisfied.

                   `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 gfpa_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

       SPICE_GF_CNVTOL

                   is the convergence tolerance used for finding endpoints
                   of the intervals comprising the result window.
                   SPICE_GF_CNVTOL is used to determine when binary
                   searches for roots should terminate: when a root is
                   bracketed within an interval of length SPICE_GF_CNVTOL,
                   the root is considered to have been found.

                   The accuracy, as opposed to precision, of roots found by
                   this routine depends on the accuracy of the input data.
                   In most cases, the accuracy of solutions will be
                   inferior to their precision.

                   SPICE_GF_CNVTOL is declared in the header file
                   SpiceGF.h.

#### 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 result window, `result', is not at least 2 and an even value,
           the error SPICE(INVALIDDIMENSION) is signaled by a routine in
           the call tree of this routine is signaled.

       5)  If `result' has insufficient capacity to contain the
           number of intervals on which the specified angle 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 `adjust' has a non-zero value 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 any of the input body names, `target', `illmn', `obsrvr', do
           not map to NAIF ID codes, an error is signaled by a routine
           in the call tree of this routine.

       11) If the input body names, `target', `illmn', `obsrvr', are not
           distinct, an error is signaled by a routine in the call
           tree of this routine.

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

       13) If the aberration correction specifier contains an
           unrecognized value, an error is signaled by a routine in the
           call tree of this routine.

       14) If a transmit mode aberration correction is requested, an
           error is signaled by a routine in the call tree of this
           routine.

       15) If any of the `target', `illmn', `abcorr', `obsrvr' or
           `relate' input string pointers is null, the error
           SPICE(NULLPOINTER) is signaled.

       16) If any of the `target', `illmn', `abcorr', `obsrvr' or
           `relate' input strings has zero length, the error
           SPICE(EMPTYSTRING) is signaled.

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

       18) 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 SPK and PCK kernels must be loaded by the calling
       program before this routine is called.

       The following data are required:

       -  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 that cover the
          time period specified by the window `cnfine'. 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 using
          furnsh_c.

       -  In some cases the observer's state may be computed at times
          outside of `cnfine' by as much as 2 seconds; data required to
          compute this state must be provided by loaded kernels. See
          -Particulars for details.

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

#### Particulars

                          illmn      OBS
          illmn as seen      *       /
          from TARG at       |      /
          et - lt.           |     /
                            >|..../< phase angle
                             |   /
                           . |  /
                         .   | /
                        .     *     TARG as seen from OBS
                  SEP   .   TARG    at `et'
                         .  /
                           /
                          *

       This routine determines if the caller-specified constraint
       condition on the geometric event (phase angle) is satisfied for
       any time intervals within the confinement window `cnfine'. If one
       or more such time intervals exist, those intervals are added
       to the `result' window.

       This routine provides a simpler, but less flexible interface
       than does the routine gfevnt_c for conducting searches for
       illuminator-target-observer phase angle value events.
       Applications that require support for progress reporting,
       interrupt handling, non-default step or refinement functions
       should call gfevnt_c rather than this routine.

       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
       phase angle 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 phase angle
       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 phase angle 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
       phase angle 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 phase angle 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 target,
       illumination source, 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" are both times when local extrema are
       attained and times when the geometric quantity function is equal
       to a reference value. 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 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 types of searches require the state of the observer,
       relative to the solar system barycenter, to be computed at times
       slightly outside the confinement window `cnfine'. The time window
       that is actually used is the result of "expanding" `cnfine' by a
       specified amount "T": each time interval of `cnfine' is expanded by
       shifting the interval's left endpoint to the left and the right
       endpoint to the right by T seconds. Any overlapping intervals are
       merged. (The input argument `cnfine' is not modified.)

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

       -  If a search uses an equality constraint, the time window
          over which the state of the observer is computed is expanded
          by 1 second at both ends of all of the time intervals
          comprising the window over which the search is conducted.

       -  If a search uses stellar aberration corrections, the time
          window over which the state of the observer is computed is
          expanded as described above.

       When light time corrections are used, expansion of the search
       window also affects the set of times at which the light time-
       corrected state of the target is computed.

       In addition to the possible 2 second 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) Determine the time windows from December 1, 2006 UTC to
          January 31, 2007 UTC for which the sun-moon-earth configuration
          phase angle satisfies the relation conditions with respect to a
          reference value of .57598845 radians (the phase angle at
          January 1, 2007 00:00:00.000 UTC, 33.001707 degrees). Also
          determine the time windows corresponding to the local maximum and
          minimum phase angles, and the absolute maximum and minimum phase
          angles during the search interval. The configuration defines the
          sun as the illuminator, the moon as the target, and the earth as
          the observer.

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

             KPL/MK

             File name: gfpa_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
                pck00009.tpc                  Planet orientation and
                                              radii
                naif0009.tls                  Leapseconds

             \begindata

                KERNELS_TO_LOAD = ( 'de421.bsp',
                                    'pck00009.tpc',
                                    'naif0009.tls'  )

             \begintext

             End of meta-kernel

          Example code begins here.

          /.
             Program gfpa_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          #define  TIMFMT  "YYYY MON DD HR:MN:SC.###"
          #define  NINTVL  5000
          #define  TIMLEN  41
          #define  NLOOPS  7

          int main()
             {

             /.
             Local variables
             ./
             SpiceChar               begstr [ TIMLEN ];
             SpiceChar               endstr [ TIMLEN ];

             SPICEDOUBLE_CELL      ( cnfine, 2 );
             SPICEDOUBLE_CELL      ( result, NINTVL*2 );

             SpiceDouble             adjust;
             SpiceDouble             et0;
             SpiceDouble             et1;
             SpiceDouble             phaseq;
             SpiceDouble             refval;
             SpiceDouble             start;
             SpiceDouble             step;
             SpiceDouble             stop;
             SpiceInt                i;
             SpiceInt                j;

             /.
             Define the values for target, observer, illuminator, and
             aberration correction.
             ./

             ConstSpiceChar * target = "moon";
             ConstSpiceChar * illmn  = "sun";
             ConstSpiceChar * abcorr = "lt+s";
             ConstSpiceChar * obsrvr = "earth";

             ConstSpiceChar * relate [NLOOPS] = { "=",
                                                  "<",
                                                  ">",
                                                  "LOCMIN",
                                                  "ABSMIN",
                                                  "LOCMAX",
                                                  "ABSMAX",
                                                };

             /.
             Load kernels.
             ./
             furnsh_c ( "gfpa_ex1.tm" );

             /.
             Store the time bounds of our search interval in
             the confinement window.
             ./
             str2et_c ( "2006 DEC 01", &et0 );
             str2et_c ( "2007 JAN 31", &et1 );

             wninsd_c ( et0, et1, &cnfine );

             /.
             Search using a step size of 1 day (in units of seconds).
             The reference value is 0.57598845 radians. We're not using the
             adjustment feature, so we set ADJUST to zero.
             ./
             step   = spd_c();
             refval = 0.57598845;
             adjust = 0.0;

             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.
                ./
                gfpa_c ( target,    illmn,   abcorr, obsrvr,
                         relate[j], refval,  adjust, step,
                         NINTVL,    &cnfine, &result        );

                /.
                Display the results.
                ./
                if ( wncard_c(&result) == 0 )
                   {
                   printf ( "Result window is empty.\n\n" );
                   }
                else
                   {

                   for ( i = 0;  i < wncard_c(&result);  i++ )
                      {

                      /.
                      Fetch the endpoints of the Ith interval
                      of the result window.
                      ./
                      wnfetd_c ( &result, i, &start, &stop );

                      phaseq = phaseq_c ( start, target, illmn, obsrvr, abcorr );

                      timout_c ( start, TIMFMT, TIMLEN, begstr );
                      printf ( "Start time = %s %16.9f\n", begstr, phaseq );

                      phaseq = phaseq_c ( stop, target, illmn, obsrvr, abcorr );

                      timout_c ( stop, TIMFMT, TIMLEN, endstr );
                      printf ( "Stop time  = %s %16.9f\n", endstr, phaseq );
                      }

                   printf("\n");

                   }

                }

             return ( 0 );
             }

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

          Relation condition: =
          Start time = 2006 DEC 02 13:31:34.414      0.575988450
          Stop time  = 2006 DEC 02 13:31:34.414      0.575988450
          Start time = 2006 DEC 07 14:07:55.470      0.575988450
          Stop time  = 2006 DEC 07 14:07:55.470      0.575988450
          Start time = 2006 DEC 31 23:59:59.997      0.575988450
          Stop time  = 2006 DEC 31 23:59:59.997      0.575988450
          Start time = 2007 JAN 06 08:16:25.512      0.575988450
          Stop time  = 2007 JAN 06 08:16:25.512      0.575988450
          Start time = 2007 JAN 30 11:41:32.557      0.575988450
          Stop time  = 2007 JAN 30 11:41:32.557      0.575988450

          Relation condition: <
          Start time = 2006 DEC 02 13:31:34.414      0.575988450
          Stop time  = 2006 DEC 07 14:07:55.470      0.575988450
          Start time = 2006 DEC 31 23:59:59.997      0.575988450
          Stop time  = 2007 JAN 06 08:16:25.512      0.575988450
          Start time = 2007 JAN 30 11:41:32.557      0.575988450
          Stop time  = 2007 JAN 31 00:00:00.000      0.468279091

          Relation condition: >
          Start time = 2006 DEC 01 00:00:00.000      0.940714974
          Stop time  = 2006 DEC 02 13:31:34.414      0.575988450
          Start time = 2006 DEC 07 14:07:55.470      0.575988450
          Stop time  = 2006 DEC 31 23:59:59.997      0.575988450
          Start time = 2007 JAN 06 08:16:25.512      0.575988450
          Stop time  = 2007 JAN 30 11:41:32.557      0.575988450

          Relation condition: LOCMIN
          Start time = 2006 DEC 05 00:16:50.317      0.086121423
          Stop time  = 2006 DEC 05 00:16:50.317      0.086121423
          Start time = 2007 JAN 03 14:18:31.977      0.079899769
          Stop time  = 2007 JAN 03 14:18:31.977      0.079899769

          Relation condition: ABSMIN
          Start time = 2007 JAN 03 14:18:31.977      0.079899769
          Stop time  = 2007 JAN 03 14:18:31.977      0.079899769

          Relation condition: LOCMAX
          Start time = 2006 DEC 20 14:09:10.392      3.055062862
          Stop time  = 2006 DEC 20 14:09:10.392      3.055062862
          Start time = 2007 JAN 19 04:27:54.600      3.074603891
          Stop time  = 2007 JAN 19 04:27:54.600      3.074603891

          Relation condition: ABSMAX
          Start time = 2007 JAN 19 04:27:54.600      3.074603891
          Stop time  = 2007 JAN 19 04:27:54.600      3.074603891

#### Restrictions

       1)  The kernel files to be used by this routine must be loaded
           (normally using the CSPICE routine furnsh_c) 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, 01-NOV-2021 (JDR) (EDW)

           Updated short error message for consistency within CSPICE wrapper
           interface: MALLOCFAILURE -> MALLOCFAILED.

           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.

           Replaced entry #8 by new entries #8 and #9, and added entry #11
           in -Exceptions section.

       -CSPICE Version 1.0.0, 15-JUL-2014 (EDW) (NJB)

#### Index_Entries

       GF phase angle search

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

    Fri Dec 31 18:41:07 2021