void gfrr_c ( ConstSpiceChar * target,
ConstSpiceChar * abcorr,
ConstSpiceChar * obsrvr,
ConstSpiceChar * relate,
SpiceDouble refval,
SpiceDouble adjust,
SpiceDouble step,
SpiceInt nintvls,
SpiceCell * cnfine,
SpiceCell * result )
Determine time intervals for which a specified constraint
on the observer-target range rate is met.
GF
NAIF_IDS
SPK
TIME
WINDOWS
EVENT
GEOMETRY
EPHEMERIS
SEARCH
WINDOW
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.
target is the name of a target body. The target body is
an ephemeris object; its trajectory is given by
SPK data.
The string `target' is case-insensitive, and leading
and trailing blanks in `target' are not significant.
Optionally, you may supply a string containing the
integer ID code for the object. 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 which
points from the observer to the target; the time derivative
length of this vector is the "range rate" that serves as
the subject of the search performed by this routine.
abcorr indicates the aberration corrections to be applied to
the observer-target state vector to account for
one-way light time and stellar aberration.
Any aberration correction accepted by the SPICE
routine spkezr_c is accepted here. 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.
"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 blanks are not significant in the string
`abcorr'.
obsrvr is the name of the observing body. The observing body is
an ephemeris object; its trajectory is given by SPK
data. `obsrvr' is case-insensitive, and leading and
trailing blanks in `obsrvr' are not significant.
Optionally, you may supply a string containing the
integer ID code for the object. For example both "MOON"
and "301" are legitimate strings that indicate the Moon
is the observer.
relate is a relational operator used to define a constraint
on observer-target range rate. 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:
">" Distance is greater than the reference
value `refval'.
"=" Distance is equal to the reference
value `refval'.
"<" Distance is less than the reference
value `refval'.
"ABSMAX" Distance is at an absolute maximum.
"ABSMIN" Distance is at an absolute minimum.
"LOCMAX" Distance is at a local maximum.
"LOCMIN" Distance 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
specify 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.
Case is not significant in the string `relate'.
refval is the reference value used together with the argument
`relate' to define an equality or inequality to be
satisfied by the range rate between the specified target
and observer. See the discussion of `relate' above for
further information.
The units of `refval' are km/sec.
adjust is a parameter used to modify searches for absolute
extrema: when `relate' is set to "ABSMAX" or "ABSMIN" and
`adjust' is set to a positive value, gfdist_c will find
times when the observer-target range rate is within
`adjust' km/sec of the specified extreme value.
If `adjust' is non-zero and a search for an absolute
minimum `min' is performed, the result window contains
time intervals when the observer-target range rate has
values between `min' and min+adjust.
If the search is for an absolute maximum `max', the
corresponding range is from max-adjust to `max'.
`adjust' is not used for searches for local extrema,
equality or inequality conditions.
step is the step size to be used in the search. `step' must
be short enough for a search using this step size
to locate the time intervals where the specified
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 a parameter specifying the number of intervals that
can be accommodated by each of the dynamically allocated
windows used internally by this routine. `nintvls' should
be at least as large as the number of intervals within
the search region on which the specified range rate
function is monotone increasing or decreasing. See
the Examples section below for code examples illustrating
the use of this parameter.
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.
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 window of intervals, contained within the
confinement window `cnfine', on which the specified
constraint is satisfied.
If `result' is non-empty on input, its contents will be
discarded before 'gfrr_c' conducts its search.
`result' must be declared with sufficient size to capture
the full set of time intervals within the search region
on which the specified constraint is satisfied.
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
constraint, `result' will be returned with a cardinality
of zero.
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 the relational operator `relate' is not recognized, an
error is signaled by a routine in the call tree of this
routine.
5) If the aberration correction specifier contains an
unrecognized value, an error is signaled by a routine in the
call tree of this routine.
6) If 'adjust' is negative, the error SPICE(VALUEOUTOFRANGE) will
signal from a routine in the call tree of this routine.
A non-zero value for 'adjust' when 'relate' has any value other than
"ABSMIN" or "ABSMAX" causes the error SPICE(INVALIDVALUE) to
signal from a routine in the call tree of this routine.
7) 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.
8) If required ephemerides or other kernel data are not
available, an error is signaled by a routine in the call tree
of this routine.
9) If the workspace interval count is less than 1, the error
SPICE(VALUEOUTOFRANGE) will be signaled.
10) If the required amount of workspace memory cannot be
allocated, the error SPICE(MALLOCFAILURE) will be
signaled.
11) If any input string argument pointer is null, the error
SPICE(NULLPOINTER) will be signaled.
12) If any input string argument is empty, the error
SPICE(EMPTYSTRING) will be signaled.
13) If either input cell has type other than SpiceDouble,
the error SPICE(TYPEMISMATCH) is signaled.
Appropriate kernels must be loaded by the calling program before
this routine is called.
The following data are required:
- SPK data: ephemeris data for target and observer for 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 by the SPK files,
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 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 the 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 specified
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 the set
of points where an equality constraint is met, 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 via 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 range rate is zero can be
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 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 shorter 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 either times when local extrema are
attained or 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 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 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.
To use a different tolerance value, a lower-level GF routine such
as gfevnt_c must be called. Making 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 affect 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.
Consider the following example: suppose one wishes to find the
times when the range rate between Io and the Earth attains a global
minimum over some (lengthy) time interval. There is one local
minimum every few days. The required step size for this search
must be smaller than the shortest interval on which the range rate
is monotone increasing or decreasing; this step size will be less
than half the average time between local minima. However, we know
that a global minimum can't occur when the Jupiter-Sun-Earth
angle is greater than 90 degrees. We can use a step size of a
half year to find the time period, within our original time
interval, during which this angle is less than 90 degrees; this
time period becomes the confinement window for our Earth-Io
range rate search. This way we've used a quick (due to the large
step size) search to cut out about half of the search period over
which we must perform a slower search using a small step size.
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.
The examples shown below require a "standard" set of SPICE
kernels. We list these kernels in a meta kernel named
'standard.tm'.
#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( int argc, char **argv )
{
/.
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( "standard.tm" );
/.
Store the time bounds of our search interval in
the cnfine confinement window.
./
str2et_c( "2007 JAN 01", &begtim );
str2et_c( "2007 APR 01", &endtim );
wninsd_c ( begtim, endtim, &cnfine );
/.
Search using a step size of 1 day (in units of seconds).
The reference value is .3365 km/s. We're not using the
adjustment feature, so we set 'adjust' to zero.
./
step = spd_c();
adjust = 0.;
refval = .3365;
for ( j = 0; j < NLOOPS; j++ )
{
printf ( "Relation condition: %s \n", relate[j] );
/.
Perform the search. The SPICE window 'result' contains
the set of times when the condition is met.
./
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");
}
/.
It's always good form to unload kernels after use,
particularly in IDL due to data persistence.
./
kclear_c();
return( 0 );
}
The program outputs:
Relation condition: =
Start time, drdt = 2007-JAN-02 00:35:19.574
Stop time, drdt = 2007-JAN-02 00:35:19.574
Start time, drdt = 2007-JAN-19 22:04:54.899
Stop time, drdt = 2007-JAN-19 22:04:54.899
Start time, drdt = 2007-FEB-01 23:30:13.428
Stop time, drdt = 2007-FEB-01 23:30:13.428
Start time, drdt = 2007-FEB-17 11:10:46.540
Stop time, drdt = 2007-FEB-17 11:10:46.540
Start time, drdt = 2007-MAR-04 15:50:19.929
Stop time, drdt = 2007-MAR-04 15:50:19.929
Start time, drdt = 2007-MAR-18 09:59:05.959
Stop time, drdt = 2007-MAR-18 09:59:05.959
Relation condition: <
Start time, drdt = 2007-JAN-02 00:35:19.574
Stop time, drdt = 2007-JAN-19 22:04:54.899
Start time, drdt = 2007-FEB-01 23:30:13.428
Stop time, drdt = 2007-FEB-17 11:10:46.540
Start time, drdt = 2007-MAR-04 15:50:19.929
Stop time, drdt = 2007-MAR-18 09:59:05.959
Relation condition: >
Start time, drdt = 2007-JAN-01 00:00:00.000
Stop time, drdt = 2007-JAN-02 00:35:19.574
Start time, drdt = 2007-JAN-19 22:04:54.899
Stop time, drdt = 2007-FEB-01 23:30:13.428
Start time, drdt = 2007-FEB-17 11:10:46.540
Stop time, drdt = 2007-MAR-04 15:50:19.929
Start time, drdt = 2007-MAR-18 09:59:05.959
Stop time, drdt = 2007-APR-01 00:00:00.000
Relation condition: LOCMIN
Start time, drdt = 2007-JAN-11 07:03:58.988
Stop time, drdt = 2007-JAN-11 07:03:58.988
Start time, drdt = 2007-FEB-10 06:26:15.439
Stop time, drdt = 2007-FEB-10 06:26:15.439
Start time, drdt = 2007-MAR-12 03:28:36.404
Stop time, drdt = 2007-MAR-12 03:28:36.404
Relation condition: ABSMIN
Start time, drdt = 2007-JAN-11 07:03:58.988
Stop time, drdt = 2007-JAN-11 07:03:58.988
Relation condition: LOCMAX
Start time, drdt = 2007-JAN-26 02:27:33.766
Stop time, drdt = 2007-JAN-26 02:27:33.766
Start time, drdt = 2007-FEB-24 09:35:07.816
Stop time, drdt = 2007-FEB-24 09:35:07.816
Start time, drdt = 2007-MAR-25 17:26:56.150
Stop time, drdt = 2007-MAR-25 17:26:56.150
Relation condition: ABSMAX
Start time, drdt = 2007-MAR-25 17:26:56.150
Stop time, drdt = 2007-MAR-25 17:26:56.150
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.
None.
N.J. Bachman (JPL)
E.D. Wright (JPL)
-CSPICE Version 1.0.0, 26-AUG-2009 (EDW)
GF range rate search
Link to routine gfrr_c source file gfrr_c.c
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