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gfuds

Table of contents
Procedure
Abstract
Required_Reading
Keywords
Declarations
Brief_I/O
Detailed_Input
Detailed_Output
Parameters
Exceptions
Files
Particulars
Examples
Restrictions
Literature_References
Author_and_Institution
Version

Procedure

     GFUDS ( GF, user defined scalar )

     SUBROUTINE GFUDS ( UDFUNS, UDQDEC, RELATE, REFVAL,
    .                   ADJUST, STEP,   CNFINE,
    .                   MW,     NW,     WORK,   RESULT  )

Abstract

     Perform a GF search on a user defined scalar quantity.

Required_Reading

     GF
     SPK
     TIME
     WINDOWS

Keywords

     EPHEMERIS
     EVENT
     SEARCH
     WINDOW

Declarations

     IMPLICIT NONE

     INCLUDE               'gf.inc'
     INCLUDE               'zzgf.inc'
     INCLUDE               'zzholdd.inc'

     INTEGER               LBCELL
     PARAMETER           ( LBCELL = -5 )

     EXTERNAL              UDQDEC
     EXTERNAL              UDFUNS

     CHARACTER*(*)         RELATE
     DOUBLE PRECISION      REFVAL
     DOUBLE PRECISION      ADJUST
     DOUBLE PRECISION      STEP
     DOUBLE PRECISION      CNFINE ( LBCELL : * )
     INTEGER               MW
     INTEGER               NW
     DOUBLE PRECISION      WORK   ( LBCELL : MW, NW )
     DOUBLE PRECISION      RESULT ( LBCELL : * )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     LBCELL     P   SPICE Cell lower bound.
     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.
     CNFINE     I   SPICE window to which the search is confined.
     MW         I   Size of workspace windows.
     NW         I   Number of workspace windows.
     WORK       O   Array containing workspace windows.
     RESULT    I-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 calling sequence for
              UDFUNS is:

                 CALL UDFUNS ( ET, 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 calling
              sequence of UDQDEC is:

                 CALL UDQDEC ( UDFUNS, ET, 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 .TRUE.
                          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 CNVTOL for
              details.

              STEP has units of TDB 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.

              CNFINE must be initialized by the caller via the
              SPICELIB routine SSIZED.

              Certain computations can expand the time window over
              which UDFUNS and UDQDEC require data. See $Particulars
              for details.

     MW       is a parameter specifying the length of the SPICE
              windows in the workspace array WORK (see description
              below) used by this routine.

              MW should be set to a number at least twice as large
              as the maximum number of intervals required by any
              workspace window. 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 MW must be set according to
              the actual workspace requirement. A rule of thumb
              for the number of intervals NINTVLS 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

              MW should then be set to

                 2 * NINTVLS

     NW       is a parameter specifying the number of SPICE windows
              in the workspace array WORK (see description below)
              used by this routine. (The reason this dimension is
              an input argument is that this allows run-time
              error checking to be performed.)

              NW must be at least as large as the parameter NWUDS.

     RESULT   is a double precision SPICE window which will contain
              the search results. 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.

              RESULT must be initialized by the caller via the
              SPICELIB routine SSIZED.

              If RESULT is non-empty on input, its contents will be
              discarded before GFUDS conducts its search.

Detailed_Output

     WORK     is an array used to store workspace windows.

              This array should be declared by the caller as shown:

                  DOUBLE PRECISION     WORK ( LBCELL : MW,  NW )

              WORK need not be initialized by the caller.

              WORK is modified by this routine. The caller should
              re-initialize this array before attempting to use it for
              any other purpose.

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

              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.

Parameters

     LBCELL   is the integer value defining the lower bound for
              SPICE Cell arrays (a SPICE window is a kind of cell).

     CNVTOL   is the convergence tolerance used for finding
              endpoints of the intervals comprising the result
              window. CNVTOL is also used for finding intermediate
              results; in particular, CNVTOL is used for finding the
              windows on which the range rate is increasing
              or decreasing. CNVTOL is used to determine when binary
              searches for roots should terminate: when a root is
              bracketed within an interval of length 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.

     See INCLUDE file gf.inc for declarations and descriptions of
     parameters used throughout the GF system.

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.

     3)  If the workspace window size MW is less than 2 or not an even
         value, the error SPICE(INVALIDDIMENSION) is signaled.

     4)  If the number of workspace windows NW is too small for the
         required search, an error is signaled by a routine in the call
         tree of this routine.

     5)  If the size of the SPICE window RESULT is less than 2 or not
         an even value, the error SPICE(INVALIDDIMENSION) is signaled.

     6)  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.

     7)  If the window count NW is less than NWUDS, the error
         SPICE(INVALIDDIMENSION) is signaled.

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

     9)  If the relational operator RELATE is not recognized, an
         error is signaled by a routine in the call tree of this
         routine.

     10) If ADJUST is negative, an error is signaled by a routine in
         the call tree of this routine.

     11) 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.

     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.

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.

     -  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 determines the truth of the expression

        d (UDFUNS)
        --         < 0
        dt

     using the library routine UDDF to numerically calculate the
     derivative of UDFUNS using a three-point estimation.
     Please see the $Examples section for an example of GFDECR use.

           SUBROUTINE GFDECR ( UDFUNS, ET, ISDECR )
           IMPLICIT NONE

           EXTERNAL              UDFUNS
           EXTERNAL              UDDF

           DOUBLE PRECISION      ET
           LOGICAL               ISDECR

           DOUBLE PRECISION      DT

           DT =  h, double precision interval size

           CALL UDDC ( UDFUNS, ET, DT, ISDECR )

           END

     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 CNVTOL (defined
     in gf.inc).

     The value of 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
     CNVTOL value by calling the routine GFSTOL, e.g.

        CALL GFSTOL( tolerance value )

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

     Setting the tolerance tighter than 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 or SPKEZ, 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
              IMPLICIT NONE

        C
        C     Include GF parameter declarations:
        C
              INCLUDE 'gf.inc'

        C
        C     User defined external routines
        C
              EXTERNAL     GFQ
              EXTERNAL     GFDECR

        C
        C     SPICELIB functions
        C
              DOUBLE PRECISION      SPD
              DOUBLE PRECISION      DVNORM
              INTEGER               WNCARD

        C
        C     Local parameters
        C
              INTEGER               LBCELL
              PARAMETER           ( LBCELL = -5 )

        C
        C     Use the parameter MAXWIN for both the result window size
        C     and the workspace size.
        C
              INTEGER               MAXWIN
              PARAMETER           ( MAXWIN = 20000 )

        C
        C     Length of strings:
        C
              INTEGER               TIMLEN
              PARAMETER           ( TIMLEN = 26 )

              INTEGER               NLOOPS
              PARAMETER           ( NLOOPS = 7 )

        C
        C     Local variables
        C
              CHARACTER*(TIMLEN)    TIMSTR
              CHARACTER*(TIMLEN)    RELATE (NLOOPS)

              DOUBLE PRECISION      ADJUST
              DOUBLE PRECISION      CNFINE ( LBCELL : 2 )
              DOUBLE PRECISION      DRDT
              DOUBLE PRECISION      ET0
              DOUBLE PRECISION      ET1
              DOUBLE PRECISION      FINISH
              DOUBLE PRECISION      LT
              DOUBLE PRECISION      POS    ( 6 )
              DOUBLE PRECISION      REFVAL
              DOUBLE PRECISION      RESULT ( LBCELL : MAXWIN )
              DOUBLE PRECISION      START
              DOUBLE PRECISION      STEP
              DOUBLE PRECISION      WORK   ( LBCELL : MAXWIN, NWUDS )

              INTEGER               I
              INTEGER               J

        C
        C     Saved variables
        C
        C     The confinement, workspace and result windows CNFINE,
        C     WORK and RESULT are saved because this practice helps to
        C     prevent stack overflow.
        C
              SAVE                  CNFINE
              SAVE                  RESULT
              SAVE                  WORK

              DATA                  RELATE / '=',
             .                               '<',
             .                               '>',
             .                               'LOCMIN',
             .                               'ABSMIN',
             .                               'LOCMAX',
             .                               'ABSMAX'  /

        C
        C     Load kernels.
        C
              CALL FURNSH ( 'gfuds_ex1.tm' )

        C
        C     Initialize windows.
        C
              CALL SSIZED ( MAXWIN, RESULT )
              CALL SSIZED ( 2,      CNFINE )

              CALL SCARDD ( 0,      CNFINE )

        C
        C     Store the time bounds of our search interval in
        C     the confinement window.
        C
              CALL STR2ET ( '2007 JAN 1', ET0 )
              CALL STR2ET ( '2007 APR 1', ET1 )

              CALL WNINSD ( ET0, ET1, CNFINE )

        C
        C     Search using a step size of 1 day (in units of seconds).
        C     The reference value is .3365 km/s - a range rate value
        C     known to exist during the confinement window. We're not
        C     using the adjustment feature, so we set ADJUST to zero.
        C
              STEP   = SPD()
              REFVAL = .3365D0
              ADJUST = 0.D0

              DO J=1, NLOOPS

                 WRITE(*,*) 'Relation condition: ', RELATE(J)

        C
        C        Perform the search. The SPICE window RESULT contains
        C        the set of times when the condition is met.
        C
                 CALL GFUDS ( GFQ,    GFDECR, RELATE(J),
             .                REFVAL, ADJUST,      STEP, CNFINE,
             .                MAXWIN,  NWUDS,      WORK, RESULT )


        C
        C        Display the results.
        C
                 IF ( WNCARD(RESULT) .EQ. 0 ) THEN

                    WRITE (*, '(A)') 'Result window is empty.'

                 ELSE

                    DO I = 1, WNCARD(RESULT)

        C
        C              Fetch the endpoints of the Ith interval
        C              of the result window.
        C
                       CALL WNFETD ( RESULT, I, START, FINISH )

                       CALL SPKEZR ( 'MOON',  START, 'J2000', 'NONE',
             .                       'SUN', POS,   LT               )
                       DRDT = DVNORM(POS)

                       CALL TIMOUT ( START,
             .                       'YYYY-MON-DD HR:MN:SC.###',
             .                       TIMSTR                     )

                       WRITE (*, '(A,F16.9)' ) 'Start time, drdt = '//
             .                                 TIMSTR, DRDT

                       CALL SPKEZR ( 'MOON',  FINISH, 'J2000', 'NONE',
             .                       'SUN', POS,     LT              )
                       DRDT = DVNORM(POS)

                       CALL TIMOUT ( FINISH,
             .                       'YYYY-MON-DD HR:MN:SC.###',
             .                       TIMSTR                    )

                       WRITE (*, '(A,F16.9)' ) 'Stop time,  drdt = '//
             .                              TIMSTR, DRDT
                    END DO

                 END IF

                 WRITE(*,*) ' '

              END DO

              END



        C-Procedure GFQ

              SUBROUTINE GFQ ( ET, VALUE )
              IMPLICIT NONE

        C- Abstract
        C
        C     User defined geometric quantity function. In this case,
        C     the range from the sun to the Moon at TDB time ET.
        C

              DOUBLE PRECISION      ET
              DOUBLE PRECISION      VALUE

        C
        C     Local variables.
        C
              INTEGER               TARG
              INTEGER               OBS

              CHARACTER*(12)        REF
              CHARACTER*(12)        ABCORR

              DOUBLE PRECISION      STATE ( 6 )
              DOUBLE PRECISION      LT
              DOUBLE PRECISION      DVNORM

        C
        C     Initialization. Retrieve the vector from the Sun to
        C     the Moon in the J2000 frame, without aberration
        C     correction.
        C
              TARG   = 301
              REF    = 'J2000'
              ABCORR = 'NONE'
              OBS    = 10

              CALL SPKEZ ( TARG, ET, REF, ABCORR, OBS, STATE, LT )

        C
        C     Calculate the scalar range rate corresponding the
        C     STATE vector.
        C
              VALUE = DVNORM( STATE )

              END




        C-Procedure GFDECR

              SUBROUTINE GFDECR ( UDFUNS, ET, ISDECR )
              IMPLICIT NONE

        C- Abstract
        C
        C     User defined function to detect if the function
        C     derivative is negative (the function is decreasing)
        C     at TDB time ET.
        C

              EXTERNAL              UDFUNS
              EXTERNAL              UDDF

              DOUBLE PRECISION      ET
              LOGICAL               ISDECR

              DOUBLE PRECISION      DT

              DT = 1.D0

        C
        C     Determine if GFQ is decreasing at ET.
        C
        C     UDDC - the default GF function to determine if
        C                the derivative of the user defined
        C                function is negative at ET.
        C
        C     UDFUNS - the user defined scalar quantity function.
        C
              CALL UDDC ( UDFUNS, ET, DT, ISDECR )

              END


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


         Relation condition: =
        Start time, drdt = 2007-JAN-02 00:35:19.574       0.336500000
        Stop time,  drdt = 2007-JAN-02 00:35:19.574       0.336500000
        Start time, drdt = 2007-JAN-19 22:04:54.899       0.336500000
        Stop time,  drdt = 2007-JAN-19 22:04:54.899       0.336500000
        Start time, drdt = 2007-FEB-01 23:30:13.428       0.336500000
        Stop time,  drdt = 2007-FEB-01 23:30:13.428       0.336500000
        Start time, drdt = 2007-FEB-17 11:10:46.540       0.336500000
        Stop time,  drdt = 2007-FEB-17 11:10:46.540       0.336500000
        Start time, drdt = 2007-MAR-04 15:50:19.929       0.336500000
        Stop time,  drdt = 2007-MAR-04 15:50:19.929       0.336500000
        Start time, drdt = 2007-MAR-18 09:59:05.959       0.336500000
        Stop time,  drdt = 2007-MAR-18 09:59:05.959       0.336500000

         Relation condition: <
        Start time, drdt = 2007-JAN-02 00:35:19.574       0.336500000
        Stop time,  drdt = 2007-JAN-19 22:04:54.899       0.336500000
        Start time, drdt = 2007-FEB-01 23:30:13.428       0.336500000
        Stop time,  drdt = 2007-FEB-17 11:10:46.540       0.336500000
        Start time, drdt = 2007-MAR-04 15:50:19.929       0.336500000
        Stop time,  drdt = 2007-MAR-18 09:59:05.959       0.336500000

         Relation condition: >
        Start time, drdt = 2007-JAN-01 00:00:00.000       0.515522367
        Stop time,  drdt = 2007-JAN-02 00:35:19.574       0.336500000
        Start time, drdt = 2007-JAN-19 22:04:54.899       0.336500000
        Stop time,  drdt = 2007-FEB-01 23:30:13.428       0.336500000
        Start time, drdt = 2007-FEB-17 11:10:46.540       0.336500000
        Stop time,  drdt = 2007-MAR-04 15:50:19.929       0.336500000
        Start time, drdt = 2007-MAR-18 09:59:05.959       0.336500000
        Stop time,  drdt = 2007-APR-01 00:00:00.000       0.793546222

         Relation condition: LOCMIN
        Start time, drdt = 2007-JAN-11 07:03:58.988      -0.803382743
        Stop time,  drdt = 2007-JAN-11 07:03:58.988      -0.803382743
        Start time, drdt = 2007-FEB-10 06:26:15.438      -0.575837623
        Stop time,  drdt = 2007-FEB-10 06:26:15.438      -0.575837623
        Start time, drdt = 2007-MAR-12 03:28:36.404      -0.441800446
        Stop time,  drdt = 2007-MAR-12 03:28:36.404      -0.441800446

         Relation condition: ABSMIN
        Start time, drdt = 2007-JAN-11 07:03:58.988      -0.803382743
        Stop time,  drdt = 2007-JAN-11 07:03:58.988      -0.803382743

         Relation condition: LOCMAX
        Start time, drdt = 2007-JAN-26 02:27:33.767       1.154648992
        Stop time,  drdt = 2007-JAN-26 02:27:33.767       1.154648992
        Start time, drdt = 2007-FEB-24 09:35:07.816       1.347132236
        Stop time,  drdt = 2007-FEB-24 09:35:07.816       1.347132236
        Start time, drdt = 2007-MAR-25 17:26:56.150       1.428141707
        Stop time,  drdt = 2007-MAR-25 17:26:56.150       1.428141707

         Relation condition: ABSMAX
        Start time, drdt = 2007-MAR-25 17:26:56.150       1.428141707
        Stop time,  drdt = 2007-MAR-25 17:26:56.150       1.428141707

Restrictions

     1)  Any kernel files required by this routine must be loaded
         (normally via the SPICELIB routine FURNSH) 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

    SPICELIB Version 1.1.1, 21-OCT-2021 (JDR) (NJB)

        Edited the header to comply with NAIF standard.

        Updated description of WORK and RESULT arguments in $Brief_I/O,
        $Detailed_Input and $Detailed_Output.

        Added SAVE statements for CNFINE, WORK and RESULT variables in
        code example.

        Updated header to describe use of expanded confinement window.

    SPICELIB Version 1.1.0, 15-JUL-2014 (EDW)

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

        Edit to comments to correct search description.

        Implemented use of ZZHOLDD to allow user to alter convergence
        tolerance.

        Removed the STEP > 0 error check. The GFSSTP call includes
        the check.

        Removed ZZGFREF call. That call now occurs in ZZGFRELX. Update
        to ZZGFRELX argument list to reflect this change in
        functionality.

        Added RETURN() check.

    SPICELIB Version 1.0.0, 16-FEB-2010 (EDW) (NJB)
Fri Dec 31 18:36:26 2021