| gfuds_c |
|
Table of contents
Procedure
gfuds_c ( GF, user defined scalar )
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 )
AbstractPerform a GF search on a user defined scalar 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'.
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 confined.
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 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 prototype
of `udqdec' is:
void ( * udqdec ) ( void ( * udfuns )
( SpiceDouble et,
SpiceDouble * value ),
SpiceDouble et,
SpiceBoolean * 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 SPICETRUE 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 SPICE_GF_CNVTOL for
details.
`step' has units of TDB seconds.
nintvls is an integer parameter specifying the number of intervals
that can be accommodated by each of the dynamically allocated
workspace windows used internally by this routine.
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 `nintvls' must be set according to the actual
workspace requirement. A rule of thumb for the number of
intervals 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.
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
condition on the scalar quantity is met.
`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 gfuds_c conducts its search.
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.
`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'.
ParametersNone. 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 the number of intervals `nintvls' is less than 1, the error
SPICE(VALUEOUTOFRANGE) is signaled.
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 an error (typically cell overflow) occurs during
window arithmetic, the error is signaled by a routine
in the call tree of this routine.
7) If the relational operator `relate' is not recognized, an
error is signaled by a routine in the call tree of this
routine.
8) If `adjust' is negative, an error is signaled by a routine in
the call tree of this routine.
9) If 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.
10) If required ephemerides or other kernel data are not
available, an error is signaled by a routine in the call tree
of this routine.
11) If the `relate' input string pointer is null, the error
SPICE(NULLPOINTER) is signaled.
12) If the `relate' input string has zero length, the error
SPICE(EMPTYSTRING) is signaled.
13) If any the `cnfine' or `result' cell arguments has a type
other than SpiceDouble, the error SPICE(TYPEMISMATCH) is
signaled.
14) If memory cannot be allocated to create the temporary variable
required for the execution of the underlying Fortran routine,
the error SPICE(MALLOCFAILED) is signaled.
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_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 `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.
ParticularsThis 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_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. 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, et, dt, isdecr ); return; } 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 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. 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_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 `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
./
#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( )
{
/.
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( "gfuds_ex1.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, < );
/.
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'.
./
uddc_c( udfuns, et, dt, isdecr );
return;
}
When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:
Compile date Mar 20 2018, 17:48:10
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_ReferencesNone. Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) E.D. Wright (JPL) Version
-CSPICE Version 1.1.0, 03-NOV-2021 (JDR) (EDW) (NJB)
Added use of ALLOC_CHECK_INTRA to check net null effect on
alloc count.
Updated header to describe use of expanded confinement window.
Edited the header to comply with NAIF standard.
Updated the description of "nintvls", "cnfine" and "result"
arguments.
Added entries #4, #5 and #14 in -Exceptions sections, and
replaced old entry #5 by new entries #8 and #9.
-CSPICE Version 1.0.1, 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_EntriesGF user defined scalar function search |
Fri Dec 31 18:41:07 2021