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cspice_gfpa

Table of contents
Abstract
I/O
Parameters
Examples
Particulars
Exceptions
Files
Restrictions
Required_Reading
Literature_References
Author_and_Institution
Version
Index_Entries


Abstract


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

I/O


   Given:

      target   the scalar string naming the target body.

               help, target
                  STRING = Scalar

               Optionally, you may supply the integer ID code for the object
               as an integer string. 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    the string name of the illuminating body.

               help, illmn
                  STRING = Scalar

               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   the scalar string indicating the aberration corrections to apply
               to the state evaluations to account for one-way light time and
               stellar aberration.

               help, abcorr
                  STRING = Scalar

               This routine accepts only reception mode aberration
               corrections. See the Aberration Correction Required
               Reading (abcorr.req) for a detailed description of
               the aberration correction options. For convenience,
               the appropriate aberration options are listed below:

                  'NONE'     Apply no correction.

                  '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   the scalar string naming the observing body.

               help, obsrvr
                  STRING = Scalar

               Optionally, you may supply the ID code of the object as an
               integer string. 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   the scalar string describing the constraint relational operator
               on the phase angle.

               help, relate
                  STRING = Scalar

               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.

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

               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   the scalar double precision reference value used together with
               `relate' argument to define an equality or inequality to satisfy
               by the phase angle.

               help, refval
                  DOUBLE = Scalar

               See the discussion of `relate' above for further information.

               The units of `refval' are radians

      adjust   a scalar 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, cspice_gfdist finds
               times when the observer-target vector coordinate is within
               `adjust' radians of the specified extreme value.

               help, adjust
                  DOUBLE = Scalar

               For `relate' set to 'ABSMAX', the result window contains
               time intervals when the observer-target vector coordinate has
               values between ABSMAX - adjust and ABSMAX.

               For `relate' set to 'ABSMIN', the result window contains
               time intervals when the phase angle has values between ABSMIN
               and ABSMIN + adjust.

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

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

               help, step
                  DOUBLE = Scalar

               `step' must be short enough for a search using this step size
               to locate the time intervals where coordinate function of the
               observer-target vector 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.

               `step' has units of seconds.

      nintvls  a scalar integer value specifying the number of intervals in the
               internal workspace array used by this routine.

               help, nintvls
                  LONG = Scalar

               `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 scalar double precision window that confines the time period
               over which the specified search is conducted.

               help, cnfine
                  STRUCT = cspice_celld(2*N)

               `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.

   the call:

      cspice_gfpa, target, illmn, abcorr,  obsrvr, relate, refval,           $
                   adjust, step,  nintvls, cnfine, result

   returns:

      result   the scalar double precision window of intervals, contained
               within the confinement window `cnfine', on which the specified
               constraint is satisfied.

               help, result
                  STRUCT = cspice_celld(2*R)

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

               `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 constraint
               is satisfied.

               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
               constraint, `result' will be returned with a
               cardinality of zero.

Parameters


   SPICE_GF_CNVTOL

               is the default convergence tolerance used for finding
               endpoints of the intervals comprising the result
               window. SPICE_GF_CNVTOL is also used for finding
               intermediate results; in particular, SPICE_GF_CNVTOL is
               used for finding the windows on which the specified
               illumination angle is increasing or decreasing.
               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.

               The calling program can reset the convergence
               tolerance; see the -Particulars section below for
               further information.

   See Icy include file IcyGF.pro for declarations and descriptions of
   parameters used throughout the GF subsystem.

Examples


   Any numerical results shown for this example may differ between
   platforms as the results depend on the SPICE kernels used as input
   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.


      PRO gfpa_ex1

         MAXWIN  =  5000L
         TIMFMT  = 'YYYY-MON-DD HR:MN:SC.###'
         TIMLEN  =  41

         relate = [ '=', '<', '>', 'LOCMIN', 'ABSMIN', 'LOCMAX', 'ABSMAX' ]

         ;;
         ;; Load kernels.
         ;;
         cspice_furnsh, 'gfpa_ex1.tm'

         ;;
         ;; Store the time bounds of our search interval in
         ;; the cnfine confinement window.
         ;;
         cspice_str2et, [ '2006 DEC 01', '2007 JAN 31'], et

         ;;
         ;; 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.
         ;;
         target  = 'MOON'
         illmn   = 'SUN'
         abcorr  = 'LT+S'
         obsrvr  = 'EARTH'
         refval  = 0.57598845D
         adjust  = 0.D
         step    = cspice_spd()
         nintvls = MAXWIN

         cnfine = cspice_celld( 2 )
         cspice_wninsd, et[0], et[1], cnfine

         result = cspice_celld( MAXWIN*2)

         for j=0, 6 do begin

            print, 'Relation condition: ',  relate[j]

            ;;
            ;; Perform the search. The SPICE window 'result' contains
            ;; the set of times when the condition is met.
            ;;
            cspice_gfpa, target, illmn, abcorr,  obsrvr, relate[j], refval,  $
                         adjust, step,  nintvls, cnfine, result

            ;;
            ;; List the beginning and ending times in each interval
            ;; if 'result' contains data.
            ;;
            count = cspice_wncard( result )

            if ( count eq 0 ) then begin

               print, 'Result window is empty.'

            endif else begin

               for i= 0L, (count - 1L ) do begin

                  ;;
                  ;; Fetch the endpoints of the Ith interval
                  ;; of the result window.
                  ;;
                  cspice_wnfetd, result, i, left, right
                  cspice_timout, [left, right], TIMFMT, TIMLEN, timstr

                  phaseq = cspice_phaseq( left,  target,                     $
                                          illmn, obsrvr, abcorr )
                  print, 'Start time = ', timstr[0], phaseq

                  phaseq = cspice_phaseq( right, target,                     $
                                          illmn, obsrvr, abcorr )
                  print, 'Stop time  = ', timstr[1], phaseq

               endfor

            endelse
            print, ' '


         endfor

         ;;
         ;; It's always good form to unload kernels after use,
         ;; particularly in IDL due to data persistence.
         ;;
         cspice_kclear

      END


      When this program was executed on a Mac/Intel/IDL8.x/64-bit
      platform, the output was:


      Relation condition: =
      Start time = 2006-DEC-02 13:31:34.414      0.57598845
      Stop time  = 2006-DEC-02 13:31:34.414      0.57598845
      Start time = 2006-DEC-07 14:07:55.470      0.57598845
      Stop time  = 2006-DEC-07 14:07:55.470      0.57598845
      Start time = 2006-DEC-31 23:59:59.997      0.57598845
      Stop time  = 2006-DEC-31 23:59:59.997      0.57598845
      Start time = 2007-JAN-06 08:16:25.512      0.57598845
      Stop time  = 2007-JAN-06 08:16:25.512      0.57598845
      Start time = 2007-JAN-30 11:41:32.557      0.57598845
      Stop time  = 2007-JAN-30 11:41:32.557      0.57598845

      Relation condition: <
      Start time = 2006-DEC-02 13:31:34.414      0.57598845
      Stop time  = 2006-DEC-07 14:07:55.470      0.57598845
      Start time = 2006-DEC-31 23:59:59.997      0.57598845
      Stop time  = 2007-JAN-06 08:16:25.512      0.57598845
      Start time = 2007-JAN-30 11:41:32.557      0.57598845
      Stop time  = 2007-JAN-31 00:00:00.000      0.46827909

      Relation condition: >
      Start time = 2006-DEC-01 00:00:00.000      0.94071497
      Stop time  = 2006-DEC-02 13:31:34.414      0.57598845
      Start time = 2006-DEC-07 14:07:55.470      0.57598845
      Stop time  = 2006-DEC-31 23:59:59.997      0.57598845
      Start time = 2007-JAN-06 08:16:25.512      0.57598845
      Stop time  = 2007-JAN-30 11:41:32.557      0.57598845

      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       3.0550629
      Stop time  = 2006-DEC-20 14:09:10.392       3.0550629
      Start time = 2007-JAN-19 04:27:54.600       3.0746039
      Stop time  = 2007-JAN-19 04:27:54.600       3.0746039

      Relation condition: ABSMAX
      Start time = 2007-JAN-19 04:27:54.600       3.0746039
      Stop time  = 2007-JAN-19 04:27:54.600       3.0746039


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.

   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 IcyGF.pro).

   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 cspice_gfstol, e.g.

      cspice_gfstol, tolerance value

   Call cspice_gfstol 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.

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 cspice_wncond.

   3)  If the number of intervals `nintvls' is less than 1, the error
       SPICE(VALUEOUTOFRANGE) is signaled by a routine in the call
       tree of this routine.

   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 input arguments, `target', `illmn', `abcorr',
       `obsrvr', `relate', `refval', `adjust', `step', `nintvls',
       `cnfine' or `result', is undefined, an error is signaled by
       the IDL error handling system.

   16) If any of the input arguments, `target', `illmn', `abcorr',
       `obsrvr', `relate', `refval', `adjust', `step', `nintvls',
       `cnfine' or `result', is not of the expected type, or it does
       not have the expected dimensions and size, an error is
       signaled by the Icy interface.

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
      cspice_furnsh.

   -  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.

Restrictions


   1)  The kernel files to be used by this routine must be loaded
       (normally using the Icy routine cspice_furnsh) before this
       routine is called.

Required_Reading


   ICY.REQ
   ABCORR.REQ
   GF.REQ
   NAIF_IDS.REQ
   SPK.REQ
   CK.REQ
   TIME.REQ
   WINDOWS.REQ

Literature_References


   None.

Author_and_Institution


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

Version


   -Icy Version 1.0.2, 03-NOV-2021 (JDR)

       Updated header to describe use of expanded confinement window.

       Edited the header to comply with NAIF standard.

       Added -Parameters, -Exceptions, -Files, -Restrictions,
       -Literature_References and -Author_and_Institution sections.

       Removed reference to the routine's corresponding CSPICE header from
       -Abstract section.

       Added arguments' type and size information in the -I/O section.

   -Icy Version 1.0.1, 09-MAY-2016 (EDW)

       Eliminated typo in example code; no change to functionality.

   -Icy Version 1.0.0, 15-JUL-2014 (EDW)

Index_Entries


   GF phase angle search



Fri Dec 31 18:43:05 2021