Index Page gfuds_c

A B C D E F G H I J K L M N O P Q R S T U V W X

Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input | Detailed_Output Parameters Exceptions Files Particulars Examples | Restrictions Literature_References Author_and_Institution Version Index_Entries

#### Procedure

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

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

                                                       SpiceDouble       et,
                                                       SpiceBoolean    * isdecr ),

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

#### Abstract

       Perform a GF search on a user defined scalar quantity.

#### Required_Reading

       GF
       WINDOWS

#### Keywords

       EVENT
       GEOMETRY
       SEARCH
       WINDOW

#### Brief_I/O

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

#### Detailed_Input

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

                     udfuns ( et, &value )

                  where:

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

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

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

                     udqdec ( udfuns, et, &isdecr )

                  where:

                     udfuns   the name of the scalar function as defined above.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                  `step' has units of TDB seconds.

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

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

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

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

#### Detailed_Output

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

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

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

#### Parameters

       None.

#### Exceptions

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

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

       2)  Due to numerical errors, in particular,

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

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

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

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

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

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

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

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

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

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

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

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

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

#### Files

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

       If the user defined function requires access to ephemeris data:

          - SPK data: ephemeris data for any body over the
            time period defined by the confinement window must be
            loaded. If aberration corrections are used, the states of
            target and observer relative to the solar system barycenter
            must be calculable from the available ephemeris data.
            Typically ephemeris data are made available by loading one
            or more SPK files via furnsh_c.

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

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

#### Particulars

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

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

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

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

          d (udfuns)
          --         < 0
          dt

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

       void gfdecr ( SpiceDouble et, SpiceBoolean * isdecr )
          {

          SpiceDouble         dt = h, double precision interval size;

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

          return;
          }

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

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

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

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

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

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

       Step Size
       =========

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

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

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

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

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

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

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

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

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

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

          gfstol_c( tolerance value in seconds )

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

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

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

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

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

#### Examples

       The numerical results shown for these examples may differ across
       platforms. The results depend on the SPICE kernels used as
       input, the compiler and supporting libraries, and the machine
       specific arithmetic implementation.

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

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

             KPL/MK

             File name: standard.tm

             This meta-kernel is intended to support operation of SPICE
             example programs. The kernels shown here should not be
             assumed to contain adequate or correct versions of data
             required by SPICE-based user applications.

             In order for an application to use this meta-kernel, the
             kernels referenced here must be present in the user's
             current working directory.

             \begindata

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

             \begintext

       Code:

          #include <stdio.h>
          #include <stdlib.h>
          #include <string.h>

          #include "SpiceUsr.h"
          #include "SpiceZfc.h"

          #define       MAXWIN    20000
          #define       TIMFMT    "YYYY-MON-DD HR:MN:SC.###"
          #define       TIMLEN    41
          #define       NLOOPS    7

          void    gfq     ( SpiceDouble et, SpiceDouble * value );
          void    gfdecrx ( void ( * udfuns ) ( SpiceDouble    et,
                                                SpiceDouble  * value ),
                            SpiceDouble    et,
                            SpiceBoolean * isdecr );

          doublereal dvnorm_(doublereal *state);

          int main( int argc, char **argv )
             {

             /.
             Create the needed windows. Note, one interval
             consists of two values, so the total number
             of cell values to allocate is twice
             the number of intervals.
             ./
             SPICEDOUBLE_CELL ( result, 2*MAXWIN );
             SPICEDOUBLE_CELL ( cnfine, 2        );

             SpiceDouble       begtim;
             SpiceDouble       endtim;
             SpiceDouble       step;
             SpiceDouble       adjust;
             SpiceDouble       refval;
             SpiceDouble       beg;
             SpiceDouble       end;

             SpiceChar         begstr [ TIMLEN ];
             SpiceChar         endstr [ TIMLEN ];

             SpiceInt          count;
             SpiceInt          i;
             SpiceInt          j;

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

             printf( "Compile date %s, %s\n\n", __DATE__, __TIME__ );

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

             /.
             Store the time bounds of our search interval in the `cnfine'
             confinement window.
             ./
             str2et_c( "2007 JAN 01", &begtim );
             str2et_c( "2007 APR 01", &endtim );

             wninsd_c ( begtim, endtim, &cnfine );

             /.
             Search using a step size of 1 day (in units of seconds). The reference
             value is .3365 km/s. We're not using the adjustment feature, so
             we set `adjust' to zero.
             ./
             step   = spd_c();
             adjust = 0.;
             refval = .3365;

             for ( j = 0;  j < NLOOPS;  j++ )
                {

                printf ( "Relation condition: %s \n",  relate[j] );

                /.
                Perform the search. The SPICE window `result' contains
                the set of times when the condition is met.
                ./

                gfuds_c ( gfq,
                          gfdecrx,
                          relate[j],
                          refval,
                          adjust,
                          step,
                          MAXWIN,
                          &cnfine,
                          &result );

                count = wncard_c( &result );

                /.
                Display the results.
                ./
                if (count == 0 )
                   {
                   printf ( "Result window is empty.\n\n" );
                   }
                else
                   {
                   for ( i = 0;  i < count;  i++ )
                      {

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

                      timout_c ( beg, TIMFMT, TIMLEN, begstr );
                      timout_c ( end, TIMFMT, TIMLEN, endstr );

                      printf ( "Start time, drdt = %s \n", begstr );
                      printf ( "Stop time,  drdt = %s \n", endstr );

                      }

                   }

                printf("\n");

                }

             kclear_c();
             return( 0 );
             }

          /.
          The user defined functions required by GFUDS.

             gfq     for udfuns
             gfdecrx for udqdec
          ./

          /.
          -Procedure Procedure gfq
          ./

          void gfq ( SpiceDouble et, SpiceDouble * value )

          /.
          -Abstract

             User defined geometric quantity function. In this case,
             the range rate from the sun to the Moon at TDB time `et'.

          ./
             {

             /. Initialization ./
             SpiceInt             targ   = 301;
             SpiceInt             obs    = 10;

             SpiceChar          * ref    = "J2000";
             SpiceChar          * abcorr = "NONE";

             SpiceDouble          state [6];
             SpiceDouble          lt;

             /.
             Retrieve the vector from the Sun to the Moon in the J2000
             frame, without aberration correction.
             ./
             spkez_c ( targ, et, ref, abcorr, obs, state, &lt );

             /.
             Calculate the scalar range rate corresponding the
            `state' vector.
             ./

             *value = dvnorm_( state );

             return;
             }

          /.
          -Procedure gfdecrx
          ./

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

          /.
          -Abstract

             User defined function to detect if the function derivative
             is negative (the function is decreasing) at TDB time `et'.
          ./
             {

             SpiceDouble         dt = 10.;

             /.
             Determine if "udfuns" is decreasing at `et'.

             uddc_c   - the GF function to determine if
                        the derivative of the user defined
                        function is negative at `et'.

             uddf_c   - the SPICE function to numerically calculate the
                        derivative of "udfuns" at `et' for the
                        interval [et-dt, et+dt].
             ./

             uddc_c( udfuns, et, dt, isdecr );

             return;
             }

       The program outputs:

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

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

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

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

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

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

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

#### Restrictions

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

#### Literature_References

       None.

#### Author_and_Institution

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

#### Version

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

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

          Header was updated to discuss use of gfstol_c.

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

          Improved header detail describing convergence tolerance.

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

#### Index_Entries

       GF user defined scalar function search

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

    Wed Apr  5 17:54:36 2017