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 )
Perform a GF search on a user defined boolean quantity.
GF
WINDOWS
EVENT
GEOMETRY
SEARCH
WINDOW
VARIABLE I/O DESCRIPTION
-------- --- --------------------------------------------------
udfuns I Name of the routine that computes a scalar quantity of
interest corresponding to an `et'.
udfunb I Name of the routine returning the boolean value
corresponding to an `et'.
step I Step size used for locating extrema and roots.
cnfine I-O SPICE window to which the search is restricted.
result O SPICE window containing results.
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 a double precision value representing
ephemeris time, expressed as seconds past
J2000 TDB at which to evaluate "udfuns."
value is the value of the geometric quantity
at `et'.
udfunb the user defined routine returning a boolean value
for an epoch ET. The calling sequence for "udfunb" is:
udfunb ( udfuns, et, 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 the double precision time step size to use 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 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.
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.
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.
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 required ephemerides or other kernel data are not
available, an error is signaled by a routine in the call tree
of this routine.
5) If the output SPICE window `result' has insufficient capacity to
contain the number of intervals on which the specified geometric
condition is met, the error will be diagnosed by a routine in
the call tree of this routine. If the result window has size
less than 2, the error SPICE(INVALIDDIMENSION) will signal.
6) If either input cell has type other than SpiceDouble,
the error SPICE(TYPEMISMATCH) will signaled from a routine
in the call tree of this routine.
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.
This 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 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 )
Call gfstol_c prior to calling this routine. All subsequent
searches will use the updated reference 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.
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.
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 = ( 'de418.bsp',
'pck00008.tpc',
'naif0009.tls' )
\begintext
Example(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.
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "SpiceUsr.h"
#include "SpiceZfc.h"
#include "SpiceZad.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( 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 left;
SpiceDouble right;
SpiceDouble step;
SpiceDouble ltime;
SpiceDouble state [6];
SpiceChar begstr [ TIMLEN ];
SpiceChar endstr [ TIMLEN ];
SpiceInt count;
SpiceInt i;
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 ( "Jan 1 2011", &begtim );
str2et_c ( "Jan 1 2012", &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, <ime);
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, <ime);
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;
}
The program outputs:
Interval 0
Interval start: 2011-JAN-09 15:24:23.415
Z= -3.67969050785e-08
Vz= 0.396984084929
Interval end : 2011-JAN-16 16:08:28.563
Z= 156247.488202
Vz= 3.76859567858e-13
Interval 1
Interval start: 2011-FEB-05 23:17:57.359
Z= -3.98442807636e-08
Vz= 0.396781283223
Interval end : 2011-FEB-13 01:38:28.425
Z= 157016.055162
Vz= 3.2238816651e-13
Interval 2
Interval start: 2011-MAR-05 06:08:17.667
Z= -1.16190221888e-08
Vz= 0.393990253999
Interval end : 2011-MAR-12 10:27:45.188
Z= 157503.773934
Vz= -3.41879302646e-13
...
Interval 11
Interval start: 2011-NOV-05 18:43:39.742
Z= -1.80199890565e-08
Vz= 0.373937629543
Interval end : 2011-NOV-13 03:50:17.153
Z= 153172.086618
Vz= -3.62962481251e-13
Interval 12
Interval start: 2011-DEC-03 01:16:40.817
Z= 1.30391470066e-07
Vz= 0.374257845032
Interval end : 2011-DEC-10 09:51:07.718
Z= 152511.720377
Vz= 2.11386680729e-13
Interval 13
Interval start: 2011-DEC-30 09:48:57.409
Z= 9.79434844339e-09
Vz= 0.377333201453
Interval end : 2012-JAN-01 00:00:00.000
Z= 50793.0833127
Vz= 0.354549969268
Example(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).
Code:
#include <stdio.h>
#include <stdlib.h>
#include <string.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( 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 left;
SpiceDouble right;
SpiceDouble step;
SpiceDouble ltime;
SpiceDouble state [6];
SpiceChar begstr [ TIMLEN ];
SpiceChar endstr [ TIMLEN ];
SpiceInt count;
SpiceInt i;
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 ( "Jan 1 2011", &begtim );
str2et_c ( "Jan 1 2012", &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, <ime);
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, <ime);
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;
}
The program outputs:
Interval 0
Interval start: 2011-JAN-09 14:42:24.484
Z= -999.999999903
Interval end : 2011-JAN-09 16:06:22.502
Z= 1000.00000009
Interval 1
Interval start: 2011-JAN-23 04:07:44.455
Z= 1000.00000012
Interval end : 2011-JAN-23 05:23:06.243
Z= -1000.00000011
Interval 2
Interval start: 2011-FEB-05 22:35:57.156
Z= -999.999999975
Interval end : 2011-FEB-05 23:59:57.748
Z= 999.999999891
...
Interval 24
Interval start: 2011-DEC-03 00:32:08.820
Z= -999.99999988
Interval end : 2011-DEC-03 02:01:12.769
Z= 999.999999876
Interval 25
Interval start: 2011-DEC-17 10:17:24.039
Z= 1000.00000008
Interval end : 2011-DEC-17 11:40:37.223
Z= -999.999999975
Interval 26
Interval start: 2011-DEC-30 09:04:47.275
Z= -1000.00000005
Interval end : 2011-DEC-30 10:33:07.670
Z= 999.999999868
Recall the default convergence tolerance for the GF system has
value 10^-6 seconds.
1) Any kernel files required by this routine must be loaded
before this routine is called.
None.
N.J. Bachman (JPL)
E.D. Wright (JPL)
-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)
GF user defined boolean function search
Link to routine gfudb_c source file gfudb_c.c
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