| gfudb_c |
|
Table of contents
Procedure
gfudb_c ( GF, user defined boolean )
void gfudb_c ( void ( * udfuns ) ( SpiceDouble et,
SpiceDouble * value ),
void ( * udfunb ) ( void ( * udfuns )
( SpiceDouble et,
SpiceDouble * value ),
SpiceDouble et,
SpiceBoolean * xbool ),
SpiceDouble step,
SpiceCell * cnfine,
SpiceCell * result )
AbstractPerform a GF search on a user defined boolean quantity. Required_ReadingGF WINDOWS KeywordsEVENT GEOMETRY SEARCH WINDOW Brief_I/O
VARIABLE I/O DESCRIPTION
-------- --- --------------------------------------------------
SPICE_GF_CNVTOL
P Convergence tolerance.
udfuns I Name of the routine that computes a scalar
quantity corresponding to an `et'.
udfunb I Name of the routine returning the boolean value
corresponding to an `et'.
step I Constant step size in seconds for finding geometric
events.
cnfine I-O SPICE window to which the search is restricted.
result O SPICE window containing results.
Detailed_Input
udfuns is the routine that returns the value of the scalar
quantity of interest at time `et'. The prototype of
`udfuns' is:
void ( * udfuns ) ( SpiceDouble et,
SpiceDouble * value )
where:
et a double precision value representing
ephemeris time, expressed as seconds past
J2000 TDB at which to evaluate `udfuns'.
value is the value of the scalar quantity
at `et'.
udfunb is the user defined routine returning a boolean value for
an epoch `et'. The prototype of `udfunb' is:
void ( * udfunb ) ( void ( * udfuns )
( SpiceDouble et,
SpiceDouble * value ),
SpiceDouble et,
SpiceBoolean * xbool )
where:
udfuns the name of the scalar function as
defined above.
et a double precision value representing
ephemeris time, expressed as seconds past
J2000 TDB, at which to evaluate `udfunb'.
xbool the boolean value at `et'.
gfudb_c will correctly operate only for boolean functions
with true conditions defining non zero measure time
intervals.
Note, `udfunb' need not call `udfuns'. The use of `udfuns' is
determined by the needs of the calculation and the user's
design.
step is the step size to be used in the search. `step' must be
shorter than any interval, within the confinement window,
over which the user defined boolean function is met. In
other words, `step' must be shorter than the shortest time
interval for which the boolean function is true; `step'
must also be shorter than the shortest time interval
between two boolean function true events occurring within
the confinement window (see below). However, `step' must
not be *too* short, or the search will take an
unreasonable amount of time.
The choice of `step' affects the completeness but not
the precision of solutions found by this routine; the
precision is controlled by the convergence tolerance.
See the discussion of the parameter SPICE_GF_CNVTOL for
details.
`step' has units of TDB seconds.
cnfine is a SPICE window that confines the time period over
which the specified search is conducted. `cnfine' may
consist of a single interval or a collection of
intervals.
In some cases the confinement window can be used to
greatly reduce the time period that must be searched
for the desired solution. See the -Particulars section
below for further discussion.
See the -Examples section below for a code example
that shows how to create a confinement window.
In some cases the observer's state may be computed at
times outside of `cnfine' by as much as 2 seconds. See
-Particulars for details.
`cnfine' must be declared as a double precision SpiceCell.
CSPICE provides the following macro, which declares and
initializes the cell
SPICEDOUBLE_CELL ( cnfine, CNFINESZ );
where CNFINESZ is the maximum capacity of `cnfine'.
Detailed_Output
cnfine is the input confinement window, updated if necessary so the
control area of its data array indicates the window's size
and cardinality. The window data are unchanged.
result is a SPICE window containing the time intervals within
the confinement window, during which the specified
boolean quantity is SPICETRUE.
`result' must be declared and initialized with sufficient
size to capture the full set of time intervals within the
search region on which the specified condition is satisfied.
If `result' is non-empty on input, its contents will be
discarded before gfudb_c conducts its search.
The endpoints of the time intervals comprising `result' are
interpreted as seconds past J2000 TDB.
If no times within the confinement window satisfy the
search criteria, `result' will be returned with a
cardinality of zero.
`result' must be declared as a double precision SpiceCell.
CSPICE provides the following macro, which declares and
initializes the cell
SPICEDOUBLE_CELL ( result, RESULTSZ );
where RESULTSZ is the maximum capacity of `result'.
Parameters
SPICE_GF_CNVTOL
is the convergence tolerance used for finding endpoints
of the intervals comprising the result window.
SPICE_GF_CNVTOL is used to determine when binary
searches for roots should terminate: when a root is
bracketed within an interval of length SPICE_GF_CNVTOL,
the root is considered to have been found.
The accuracy, as opposed to precision, of roots found by
this routine depends on the accuracy of the input data.
In most cases, the accuracy of solutions will be
inferior to their precision.
SPICE_GF_CNVTOL is declared in the header file
SpiceGF.h.
Exceptions
1) In order for this routine to produce correct results,
the step size must be appropriate for the problem at hand.
Step sizes that are too large may cause this routine to miss
roots; step sizes that are too small may cause this routine
to run unacceptably slowly and in some cases, find spurious
roots.
This routine does not diagnose invalid step sizes, except that
if the step size is non-positive, an error is signaled by a
routine in the call tree of this routine.
2) Due to numerical errors, in particular,
- truncation error in time values
- finite tolerance value
- errors in computed geometric quantities
it is *normal* for the condition of interest to not always be
satisfied near the endpoints of the intervals comprising the
`result' window. One technique to handle such a situation,
slightly contract `result' using the window routine wncond_c.
3) If an error (typically cell overflow) occurs while performing
window arithmetic, the error is signaled by a routine
in the call tree of this routine.
4) If the size of the SPICE window `result' is less than 2 or not
an even value, the error SPICE(INVALIDDIMENSION) is signaled
by a routine in the call tree of this routine.
5) If `result' has insufficient capacity to contain the number of
intervals on which the specified condition is met, an error is
signaled by a routine in the call tree of this routine.
6) If 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 any the `cnfine' or `result' cell arguments has a 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 boolean function requires access to ephemeris data:
- SPK data: ephemeris data for any body over the
time period defined by the confinement window must be
loaded. If aberration corrections are used, the states of
target and observer relative to the solar system barycenter
must be calculable from the available ephemeris data.
Typically ephemeris data are made available by loading one
or more SPK files via furnsh_c.
- If non-inertial reference frames are used, then PCK
files, frame kernels, C-kernels, and SCLK kernels may be
needed.
- Certain computations can expand the time window over which
`udfuns' and `udfunb' 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.
ParticularsThis routine determines a set of one or more time intervals within the confinement window when the boolean function evaluates to true. 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. udfuns Default Template ======================= The boolean function includes an argument for an input scalar function. Use of a scalar function during the evaluation of the boolean function is not required. SPICE provides a no-op scalar routine, udf_c, as a dummy argument for instances when the boolean function does not need to call the scalar function. The Search Process ================== The search for boolean events is treated as a search for state transitions: times are sought when the boolean function value changes from true to false or vice versa. Step Size ========= 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 boolean function will be sampled. Starting at the left endpoint of the interval, samples of the boolean function will be taken at each step. If a state change is detected, a root has been bracketed; at that point, the "root"--the time at which the state change occurs---is found by a refinement process, for example, via binary search. Note that the optimal choice of step size depends on the lengths of the intervals over which the boolean function is constant: the step size should be shorter than the shortest such interval and the shortest separation between the intervals, within the confinement window. Having some knowledge of the relative geometry of the targets and observer can be a valuable aid in picking a reasonable step size. In general, the user can compensate for lack of such knowledge by picking a very short step size; the cost is increased computation time. Note that the step size is not related to the precision with which the endpoints of the intervals of the result window are computed. That precision level is controlled by the convergence tolerance. Convergence Tolerance ===================== Once a root has been bracketed, a refinement process is used to narrow down the time interval within which the root must lie. This refinement process terminates when the location of the root has been determined to within an error margin called the "convergence tolerance." The default convergence tolerance used by this routine is set by the parameter SPICE_GF_CNVTOL (defined in SpiceGF.h). The value of SPICE_GF_CNVTOL is set to a "tight" value so that the tolerance doesn't become the limiting factor in the accuracy of solutions found by this routine. In general the accuracy of input data will be the limiting factor. The user may change the convergence tolerance from the default SPICE_GF_CNVTOL value by calling the routine gfstol_c, e.g. gfstol_c ( tolerance value ); Call gfstol_c prior to calling this routine. All subsequent searches will use the updated tolerance value. Setting the tolerance tighter than SPICE_GF_CNVTOL is unlikely to be useful, since the results are unlikely to be more accurate. Making the tolerance looser will speed up searches somewhat, since a few convergence steps will be omitted. However, in most cases, the step size is likely to have a much greater effect on processing time than would the convergence tolerance. The Confinement Window ====================== The simplest use of the confinement window is to specify a time interval within which a solution is sought. The confinement window also can be used to restrict a search to a time window over which required data are known to be available. In some cases, the confinement window can 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. See the "CASCADE" example program in gf.req for a demonstration. 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. Computation of observer-target states by spkezr_c or spkez_c, using stellar aberration corrections, requires the state of the observer, relative to the solar system barycenter, to be computed at times offset from the input time by +/- 1 second. If the input time ET is used by `udfuns' or `udfunb' to compute such a state, the window over which the observer state is computed is expanded by 1 second. 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 possible expansion of the search window when 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 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.
1) Calculate the time intervals when the position of the moon relative
to the earth in the IAU_EARTH frame has a positive value in for
the Z position component, with also a positive value for the Vz
velocity component.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: gfudb_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
--------- --------
de418.bsp Planetary ephemeris
pck00008.tpc Planet orientation and
radii
naif0009.tls Leapseconds
\begindata
KERNELS_TO_LOAD = ( 'de418.bsp',
'pck00008.tpc',
'naif0009.tls' )
\begintext
End of meta-kernel
Example code begins here.
/.
Program gfudb_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"
#define MAXWIN 20000
#define TIMFMT "YYYY-MON-DD HR:MN:SC.###"
#define TIMLEN 41
#define NLOOPS 7
void gfq ( void ( * udfunc ) ( SpiceDouble et,
SpiceDouble * value ),
SpiceDouble et,
SpiceBoolean * xbool );
int main( )
{
/.
Create the needed windows. Note, one interval
consists of two values, so the total number
of cell values to allocate is twice
the number of intervals.
./
SPICEDOUBLE_CELL ( result, 2*MAXWIN );
SPICEDOUBLE_CELL ( cnfine, 2 );
SpiceDouble begtim;
SpiceDouble endtim;
SpiceDouble left;
SpiceDouble right;
SpiceDouble step;
SpiceDouble lt;
SpiceDouble state [6];
SpiceChar begstr [ TIMLEN ];
SpiceChar endstr [ TIMLEN ];
SpiceInt count;
SpiceInt i;
/.
Load kernels.
./
furnsh_c( "gfudb_ex1.tm" );
/.
Store the time bounds of our search interval in the 'cnfine'
confinement window.
./
str2et_c ( "Jan 1 2011", &begtim );
str2et_c ( "Apr 1 2011", &endtim );
wninsd_c ( begtim, endtim, &cnfine );
/.
The moon orbit about the earth-moon barycenter is
twenty-eight days. The event condition occurs
during (very) approximately a quarter of the orbit. Use
a step of five days.
./
step = 5.0 * spd_c();
gfudb_c ( udf_c,
gfq,
step,
&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, &left, &right );
printf ( "Interval %d\n", (int)i );
timout_c ( left, TIMFMT, TIMLEN, begstr );
printf ( " Interval start: %s \n", begstr );
spkez_c ( 301, left, "IAU_EARTH", "NONE", 399, state, <);
printf ( " Z= %.12g \n", state[2] );
printf ( " Vz= %.12g \n", state[5] );
timout_c ( right, TIMFMT, TIMLEN, endstr );
printf ( " Interval end : %s \n", endstr );
spkez_c ( 301, right, "IAU_EARTH", "NONE", 399, state, <);
printf ( " Z= %.12g \n", state[2] );
printf ( " Vz= %.12g \n\n", state[5] );
}
}
kclear_c();
return( 0 );
}
/.
The user defined functions required by gfudb_c.
udf_c for udfuns
gfq for udfunb
./
/.
-Procedure Procedure gfq
./
void gfq ( void ( * udfuns ) ( SpiceDouble et,
SpiceDouble * value ),
SpiceDouble et,
SpiceBoolean * xbool )
/.
-Abstract
User defined geometric boolean function:
Z >= 0 with dZ/dt > 0.
./
{
/.
Initialization. Retrieve the vector from the earth to
the moon in the IAU_EARTH frame, without aberration
correction.
./
SpiceInt targ = 301;
SpiceInt obs = 399;
SpiceChar * ref = "IAU_EARTH";
SpiceChar * abcorr = "NONE";
SpiceDouble state [6];
SpiceDouble lt;
/.
Evaluate the state of TARG from OBS at ET with
correction ABCORR.
./
spkez_c ( targ, et, ref, abcorr, obs, state, < );
/.
Calculate the boolean value.
./
*xbool = (state[2] >= 0.0) && (state[5] > 0.0);
return;
}
When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:
Interval 0
Interval start: 2011-JAN-09 15:24:23.416
Z= -1.12510406325e-07
Vz= 0.396984084546
Interval end : 2011-JAN-16 16:08:28.564
Z= 156247.488042
Vz= 4.0992339731e-13
Interval 1
Interval start: 2011-FEB-05 23:17:57.359
Z= -1.24675068491e-07
Vz= 0.396781282843
Interval end : 2011-FEB-13 01:38:28.426
Z= 157016.055001
Vz= 1.73745783386e-13
Interval 2
Interval start: 2011-MAR-05 06:08:17.668
Z= -7.77218360781e-08
Vz= 0.393990253634
Interval end : 2011-MAR-12 10:27:45.189
Z= 157503.773777
Vz= -2.97863513368e-13
2) Calculate the time intervals when the Z component of the earth
to moon position vector in the IAU_EARTH frame has value
between -1000 km and 1000 km (e.g. above and below the equatorial
plane).
Use the meta-kernel from the first example.
Example code begins here.
/.
Program gfudb_ex2
./
#include <stdio.h>
#include "SpiceUsr.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 gfb ( void ( * udfuns ) ( SpiceDouble et,
SpiceDouble * value ),
SpiceDouble et,
SpiceBoolean * xbool );
int main( )
{
/.
Create the needed windows. Note, one interval
consists of two values, so the total number
of cell values to allocate is twice
the number of intervals.
./
SPICEDOUBLE_CELL ( result, 2*MAXWIN );
SPICEDOUBLE_CELL ( cnfine, 2 );
SpiceDouble begtim;
SpiceDouble endtim;
SpiceDouble left;
SpiceDouble right;
SpiceDouble step;
SpiceDouble lt;
SpiceDouble state [6];
SpiceChar begstr [ TIMLEN ];
SpiceChar endstr [ TIMLEN ];
SpiceInt count;
SpiceInt i;
/.
Load kernels.
./
furnsh_c( "gfudb_ex1.tm" );
/.
Store the time bounds of our search interval in the 'cnfine'
confinement window.
./
str2et_c ( "Jan 1 2011", &begtim );
str2et_c ( "Apr 1 2011", &endtim );
wninsd_c ( begtim, endtim, &cnfine );
/.
The duration of the event is approximately ninety minutes.
Use a step of one hour.
./
step = 60.*60.;
gfudb_c ( gfq,
gfb,
step,
&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, &left, &right );
printf ( "Interval %d\n", (int)i );
timout_c ( left, TIMFMT, TIMLEN, begstr );
printf ( " Interval start: %s \n", begstr );
spkez_c ( 301, left, "IAU_EARTH", "NONE", 399, state, <);
printf ( " Z= %.12g \n", state[2] );
timout_c ( right, TIMFMT, TIMLEN, endstr );
printf ( " Interval end : %s \n", endstr );
spkez_c ( 301, right, "IAU_EARTH", "NONE", 399, state, <);
printf ( " Z= %.12g \n", state[2] );
}
}
kclear_c();
return( 0 );
}
/.
The user defined functions required by gfudb_c.
gfq for udfuns
gfb for udfunb
./
/.
-Procedure Procedure gfq
./
void gfq ( SpiceDouble et,
SpiceDouble * value )
/.
-Abstract
User defined scalar function:
./
{
/.
Initialization. Retrieve the vector from the earth to
the moon in the IAU_EARTH frame, without aberration
correction.
./
SpiceInt targ = 301;
SpiceInt obs = 399;
SpiceChar * ref = "IAU_EARTH";
SpiceChar * abcorr = "NONE";
SpiceDouble pos [3];
SpiceDouble lt;
/.
Evaluate the state of TARG from OBS at ET with
correction ABCORR.
./
spkezp_c ( targ, et, ref, abcorr, obs, pos, < );
*value = pos[2];
return;
}
/.
-Procedure Procedure gfb
./
void gfb ( void ( * udfuns ) ( SpiceDouble et,
SpiceDouble * value ),
SpiceDouble et,
SpiceBoolean * xbool )
/.
-Abstract
User defined boolean function:
./
{
SpiceDouble value;
SpiceDouble lim1 = -1000.;
SpiceDouble lim2 = 1000.;
udfuns( et, &value );
/.
Calculate the boolean value.
./
*xbool = (value >= lim1) && (value <= lim2);
return;
}
When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:
Interval 0
Interval start: 2011-JAN-09 14:42:24.485
Z= -999.999999841
Interval end : 2011-JAN-09 16:06:22.503
Z= 999.999999876
Interval 1
Interval start: 2011-JAN-23 04:07:44.456
Z= 999.999999922
Interval end : 2011-JAN-23 05:23:06.244
Z= -1000.00000013
Interval 2
Interval start: 2011-FEB-05 22:35:57.157
Z= -1000.0000001
Interval end : 2011-FEB-05 23:59:57.749
Z= 999.999999843
Interval 3
Interval start: 2011-FEB-19 14:11:28.294
Z= 1000.0000001
Interval end : 2011-FEB-19 15:26:01.719
Z= -999.999999854
Interval 4
Interval start: 2011-MAR-05 05:25:59.562
Z= -1000.00000003
Interval end : 2011-MAR-05 06:50:35.862
Z= 1000.00000009
Interval 5
Interval start: 2011-MAR-19 01:30:19.166
Z= 999.99999983
Interval end : 2011-MAR-19 02:45:21.112
Z= -1000.00000001
Restrictions
1) Any kernel files required by this routine must be loaded
before this routine is called.
Literature_ReferencesNone. Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) E.D. Wright (JPL) Version
-CSPICE Version 1.0.2, 03-NOV-2021 (JDR) (NJB)
Updated header to describe use of expanded confinement window.
Edited the header to comply with NAIF standard.
Reduced the search interval to limit the length of the solutions.
Removed "Compile date" printout and unnecessary include files in both
examples.
Updated the description of "cnfine" and "result" arguments.
-CSPICE Version 1.0.1, 28-JUN-2016 (EDW)
Edit to Example code, SpiceInts output as ints using
explicit casting.
-CSPICE Version 1.0.0, 23-OCT-2013 (EDW) (NJB)
Index_EntriesGF user defined boolean function search |
Fri Dec 31 18:41:07 2021