| gfrr_c |
|
Table of contents
Procedure
gfrr_c (GF, range rate search )
void gfrr_c ( ConstSpiceChar * target,
ConstSpiceChar * abcorr,
ConstSpiceChar * obsrvr,
ConstSpiceChar * relate,
SpiceDouble refval,
SpiceDouble adjust,
SpiceDouble step,
SpiceInt nintvls,
SpiceCell * cnfine,
SpiceCell * result )
AbstractDetermine time intervals for which a specified constraint on the observer-target range rate is met. Required_ReadingGF NAIF_IDS SPK TIME WINDOWS KeywordsEPHEMERIS EVENT GEOMETRY SEARCH WINDOW Brief_I/O
VARIABLE I/O DESCRIPTION
-------- --- --------------------------------------------------
SPICE_GF_CNVTOL
P Convergence tolerance.
target I Name of the target body.
abcorr I Aberration correction flag.
obsrvr I Name of the observing body.
relate I Relational operator.
refval I Reference value.
adjust I Adjustment value for absolute extrema searches.
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
target is the name of a target body. Optionally, you may supply
the integer ID code for the object as an integer string.
For example both "MOON" and "301" are legitimate strings
that indicate the moon is the target body.
The target and observer define a position vector that
points from the observer to the target. The derivative
with respect to time of the length of this vector is the
"range rate" used by this routine as the geometric
quantity of interest.
Case and leading or trailing blanks are not significant
in the string `target'.
abcorr is the description of the aberration corrections to apply
to the state evaluations to account for one-way light
time and stellar aberration.
This routine accepts the same aberration corrections as
does the SPICE routine spkezr_c. See the header of spkezr_c
for a detailed description of the aberration correction
options. For convenience, the options are listed below:
"NONE" Apply no correction. Returns the "true"
geometric state.
"LT" "Reception" case: correct for
one-way light time using a Newtonian
formulation.
"LT+S" "Reception" case: correct for
one-way light time and stellar
aberration using a Newtonian
formulation.
"CN" "Reception" case: converged
Newtonian light time correction.
"CN+S" "Reception" case: converged
Newtonian light time and stellar
aberration corrections.
"XLT" "Transmission" case: correct for
one-way light time using a Newtonian
formulation.
"XLT+S" "Transmission" case: correct for
one-way light time and stellar
aberration using a Newtonian
formulation.
"XCN" "Transmission" case: converged
Newtonian light time correction.
"XCN+S" "Transmission" case: converged
Newtonian light time and stellar
aberration corrections.
Case and leading or trailing blanks are not significant
in the string `abcorr'.
obsrvr is the name of an observing body. Optionally, you may
supply the ID code of the object as an integer string.
For example, both "EARTH" and "399" are legitimate
strings to indicate that the observer is the Earth.
Case and leading or trailing blanks are not significant
in the string `obsrvr'.
relate is the relational operator that defines the constraint on
the range rate of the observer-target vector. The result
window found by this routine indicates the time intervals
where the constraint is satisfied. Supported values of
`relate' and corresponding meanings are shown below:
">" The range rate value is greater than the
reference value `refval'.
"=" The range rate value is equal to the
reference value `refval'.
"<" The range rate value is less than the
reference value `refval'.
"ABSMAX" The range rate value is at an absolute
maximum.
"ABSMIN" The range rate value is at an absolute
minimum.
"LOCMAX" The range rate value is at a local
maximum.
"LOCMIN" The range rate value is at a local
minimum.
`relate' may be used to specify an "adjusted" absolute
extremum constraint: this requires the range rate to be
within a specified offset relative to an absolute
extremum. The argument `adjust' (described below) is used
to specify this offset.
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.
Case and leading or trailing blanks are not
significant in the string `relate'.
refval is the double precision reference value used together
with the argument `relate' to define an equality or
inequality to satisfy by the range rate of the
observer-target vector. See the discussion of `relate'
above for further information.
The units of `refval' are km/s.
adjust is a double precision value used to modify searches for
absolute extrema: when `relate' is set to "ABSMAX" or
"ABSMIN" and `adjust' is set to a positive value, gfrr_c
finds times when the range rate is within `adjust'
kilometers/second of the specified extreme value.
For `relate' set to "ABSMAX", the `result' window contains
time intervals when the range rate has
values between absmax - adjust and `absmax'.
For `relate' set to "ABSMIN", the `result' window contains
time intervals when the range rate has
values between `absmin' and absmin + adjust.
`adjust' is not used for searches for local extrema,
equality or inequality conditions.
step is the double precision time step size to use in the
search.
`step' must be short enough for a search using this step
size to locate the time intervals where the range rate
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 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.
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 the SPICE window of intervals, contained within the
confinement window `cnfine', on which the specified
constraint is satisfied.
`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 gfrr_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'.
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 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 the SPICE window `result' has insufficient capacity to
contain the number of intervals on which the specified
distance 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 the aberration correction specifier contains an
unrecognized value, an error is signaled by a routine in the
call tree of this routine.
9) If `adjust' is negative, an error is signaled by a routine in
the call tree of this routine.
10) If `adjust' has a non-zero value when `relate' has any value other
than "ABSMIN" or "ABSMAX", an error is signaled by a routine
in the call tree of this routine.
11) If either of the input body names do not map to NAIF ID
codes, an error is signaled by a routine in the call tree of
this routine.
12) If required ephemerides or other kernel data are not
available, an error is signaled by a routine in the call tree
of this routine.
13) If any of the `target', `abcorr', `obsrvr' or `relate' input
string pointers is null, the error SPICE(NULLPOINTER) is
signaled.
14) If any of the `target', `abcorr', `obsrvr' or `relate' input
strings has zero length, the error SPICE(EMPTYSTRING) is
signaled.
15) If any the `cnfine' or `result' cell arguments has a type
other than SpiceDouble, the error SPICE(TYPEMISMATCH) is
signaled.
16) 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 SPK and PCK kernels must be loaded by the calling
program before this routine is called.
The following data are required:
- SPK data: the calling application must load ephemeris data
for the targets, observer, and any intermediate objects in
a chain connecting the targets and observer that cover the
time period specified by the window `cnfine'. 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 using
furnsh_c.
- In some cases the observer's state may be computed at times
outside of `cnfine' by as much as 2 seconds; data required to
compute this state must be provided by loaded kernels. See
-Particulars for details.
Kernel data are normally loaded once per program run, NOT every
time this routine is called.
ParticularsThis routine determines if the caller-specified constraint condition on the geometric event (range rate) is satisfied for any time intervals within the confinement window `cnfine'. If one or more such time intervals exist, those intervals are added to the `result' window. This routine provides a simpler, but less flexible interface than does the routine gfevnt_c for conducting searches for observer-target range rate value events. Applications that require support for progress reporting, interrupt handling, non-default step or refinement functions, or non-default convergence tolerance should call gfevnt_c rather than this routine. 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 range rate 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 range rate 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 range rate 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 range rate 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 range rate 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 target 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" are both times when local extrema are attained and times when the range rate function is equal to a reference value. 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 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 types of searches require the state of the observer, relative to the solar system barycenter, to be computed at times slightly outside the confinement window `cnfine'. The time window that is actually used is the result of "expanding" `cnfine' by a specified amount "T": each time interval of `cnfine' is expanded by shifting the interval's left endpoint to the left and the right endpoint to the right by T seconds. Any overlapping intervals are merged. (The input argument `cnfine' is not modified.) The window expansions listed below are additive: if both conditions apply, the window expansion amount is the sum of the individual amounts. - If a search uses an equality constraint, the time window over which the state of the observer is computed is expanded by 1 second at both ends of all of the time intervals comprising the window over which the search is conducted. - If a search uses stellar aberration corrections, the time window over which the state of the observer is computed is expanded as described above. When light time corrections are used, expansion of the search window also affects the set of times at which the light time- corrected state of the target is computed. In addition to the possible 2 second 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) Determine the time windows from January 1, 2007 UTC to
April 1, 2007 UTC for which the sun-moon range rate satisfies the
relation conditions with respect to a reference value of
0.3365 km/s radians (this range rate known to occur within the
search interval). Also determine the time windows corresponding
to the local maximum and minimum range rate, and the absolute
maximum and minimum range rate during the search interval.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: gfrr_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
--------- --------
de421.bsp Planetary ephemeris
pck00009.tpc Planet orientation and
radii
naif0009.tls Leapseconds
\begindata
KERNELS_TO_LOAD = ( 'de421.bsp',
'pck00009.tpc',
'naif0009.tls' )
\begintext
End of meta-kernel
Example code begins here.
/.
Program gfrr_ex1
./
#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
int main( )
{
/.
Create the needed windows. Note, one window
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 ];
SpiceChar * target = "MOON";
SpiceChar * abcorr = "NONE";
SpiceChar * obsrvr = "SUN";
SpiceInt count;
SpiceInt i;
SpiceInt j;
ConstSpiceChar * relate [NLOOPS] = { "=",
"<",
">",
"LOCMIN",
"ABSMIN",
"LOCMAX",
"ABSMAX",
};
/.
Load kernels.
./
furnsh_c( "gfrr_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.
./
gfrr_c ( target,
abcorr,
obsrvr,
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");
}
return( 0 );
}
When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:
Relation condition: =
Start time, drdt = 2007-JAN-02 00:35:19.571
Stop time, drdt = 2007-JAN-02 00:35:19.571
Start time, drdt = 2007-JAN-19 22:04:54.897
Stop time, drdt = 2007-JAN-19 22:04:54.897
Start time, drdt = 2007-FEB-01 23:30:13.427
Stop time, drdt = 2007-FEB-01 23:30:13.427
Start time, drdt = 2007-FEB-17 11:10:46.538
Stop time, drdt = 2007-FEB-17 11:10:46.538
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 09:59:05.957
Stop time, drdt = 2007-MAR-18 09:59:05.957
Relation condition: <
Start time, drdt = 2007-JAN-02 00:35:19.571
Stop time, drdt = 2007-JAN-19 22:04:54.897
Start time, drdt = 2007-FEB-01 23:30:13.427
Stop time, drdt = 2007-FEB-17 11:10:46.538
Start time, drdt = 2007-MAR-04 15:50:19.929
Stop time, drdt = 2007-MAR-18 09:59:05.957
Relation condition: >
Start time, drdt = 2007-JAN-01 00:00:00.000
Stop time, drdt = 2007-JAN-02 00:35:19.571
Start time, drdt = 2007-JAN-19 22:04:54.897
Stop time, drdt = 2007-FEB-01 23:30:13.427
Start time, drdt = 2007-FEB-17 11:10:46.538
Stop time, drdt = 2007-MAR-04 15:50:19.929
Start time, drdt = 2007-MAR-18 09:59:05.957
Stop time, drdt = 2007-APR-01 00:00:00.000
Relation condition: LOCMIN
Start time, drdt = 2007-JAN-11 07:03:58.991
Stop time, drdt = 2007-JAN-11 07:03:58.991
Start time, drdt = 2007-FEB-10 06:26:15.441
Stop time, drdt = 2007-FEB-10 06:26:15.441
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 07:03:58.991
Stop time, drdt = 2007-JAN-11 07:03:58.991
Relation condition: LOCMAX
Start time, drdt = 2007-JAN-26 02:27:33.762
Stop time, drdt = 2007-JAN-26 02:27:33.762
Start time, drdt = 2007-FEB-24 09:35:07.812
Stop time, drdt = 2007-FEB-24 09:35:07.812
Start time, drdt = 2007-MAR-25 17:26:56.148
Stop time, drdt = 2007-MAR-25 17:26:56.148
Relation condition: ABSMAX
Start time, drdt = 2007-MAR-25 17:26:56.148
Stop time, drdt = 2007-MAR-25 17:26:56.148
Restrictions
1) The kernel files to be used by this routine must be loaded
(normally using the CSPICE routine furnsh_c) before this
routine is called.
2) This routine has the side effect of re-initializing the
range rate quantity utility package. Callers may themselves
need to re-initialize the range rate quantity utility
package after calling this routine.
Literature_ReferencesNone. Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) E.D. Wright (JPL) Version
-CSPICE Version 1.1.0, 01-NOV-2021 (JDR) (EDW)
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 and #5 and replaced former entry #6 by
new entries #9 and #10 in -Exceptions section.
-CSPICE Version 1.0.2, 31-JUL-2014 (EDW)
Edit to header, replaced ' character with character " to indicate
C strings.
Edit to header, correct Required Reading entry eliminating ".REQ"
suffix.
-CSPICE Version 1.0.1, 28-FEB-2013 (NJB) (EDW)
Header was updated to discuss use of gfstol_c.
Edit to comments to correct search description.
Edits to Example section, proper description of "standard.tm"
meta kernel.
-CSPICE Version 1.0.0, 26-AUG-2009 (EDW) (NJB)
Index_EntriesGF range rate search |
Fri Dec 31 18:41:07 2021