gfpa_c |

Table of contents## Proceduregfpa_c ( GF, phase angle search ) void gfpa_c ( ConstSpiceChar * target, ConstSpiceChar * illmn, 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 phase angle between an illumination source, a target, and observer body centers is met. ## Required_ReadingGF NAIF_IDS SPK TIME WINDOWS ## KeywordsEPHEMERIS EVENT GEOMETRY SEARCH WINDOW ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- SPICE_GF_CNVTOL P Default convergence tolerance. target I Name of the target body. illmn I Name of the illuminating 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_Inputtarget is the name of a target body. 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. Case and leading or trailing blanks are not significant in the string `target'. illmn is the name of the illuminating body. This will normally be "SUN" but the algorithm can use any ephemeris object. Case and leading or trailing blanks are not significant in the string `illmn'. 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 only reception mode aberration corrections. See the header of spkezr_c for a detailed description of the aberration correction options. For convenience, the allowed aberration 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. 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 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. Case and leading or trailing blanks are not significant in the string `obsrvr'. relate is a relational operator used to define a constraint on a specified phase angle. 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 phase angle value is greater than the reference value `refval'. "=" The phase angle value is equal to the reference value `refval'. "<" The phase angle value is less than the reference value `refval'. "ABSMAX" The phase angle value is at an absolute maximum. "ABSMIN" The phase angle value is at an absolute minimum. "LOCMAX" The phase angle value is at a local maximum. "LOCMIN" The phase angle value is at a local minimum. `relate' may be used to specify an "adjusted" absolute extremum constraint: this requires the phase angle 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 be satisfied by the phase angle. See the discussion of `relate' above for further information. The units of `refval' are radians. 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, ## Detailed_Outputcnfine 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 phase angle 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 ## ParametersSPICE_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. ## Exceptions1) 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 result window, `result', is not at least 2 and an even value, the error SPICE(INVALIDDIMENSION) is signaled by a routine in the call tree of this routine is signaled. 5) If `result' has insufficient capacity to contain the number of intervals on which the specified angle 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 `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. 10) If any of the input body names, `target', `illmn', `obsrvr', do not map to NAIF ID codes, an error is signaled by a routine in the call tree of this routine. 11) If the input body names, `target', `illmn', `obsrvr', are not distinct, 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 the aberration correction specifier contains an unrecognized value, an error is signaled by a routine in the call tree of this routine. 14) If a transmit mode aberration correction is requested, an error is signaled by a routine in the call tree of this routine. 15) If any of the `target', `illmn', `abcorr', `obsrvr' or `relate' input string pointers is null, the error SPICE(NULLPOINTER) is signaled. 16) If any of the `target', `illmn', `abcorr', `obsrvr' or `relate' input strings has zero length, the error SPICE(EMPTYSTRING) is signaled. 17) If any the `cnfine' or `result' cell arguments has a type other than SpiceDouble, the error SPICE(TYPEMISMATCH) is signaled. 18) 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. ## FilesAppropriate 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. ## Particularsillmn OBS illmn as seen * / from TARG at | / et - lt. | / >|..../< phase angle | / . | / . | / . * TARG as seen from OBS SEP . TARG at `et' . / / * This routine determines if the caller-specified constraint condition on the geometric event (phase angle) 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 illuminator-target-observer phase angle value events. Applications that require support for progress reporting, interrupt handling, non-default step or refinement functions 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 phase angle 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 phase angle 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 phase angle 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 phase angle 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 phase angle 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, illumination source, 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 geometric quantity 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. ## ExamplesThe 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 December 1, 2006 UTC to January 31, 2007 UTC for which the sun-moon-earth configuration phase angle satisfies the relation conditions with respect to a reference value of .57598845 radians (the phase angle at January 1, 2007 00:00:00.000 UTC, 33.001707 degrees). Also determine the time windows corresponding to the local maximum and minimum phase angles, and the absolute maximum and minimum phase angles during the search interval. The configuration defines the sun as the illuminator, the moon as the target, and the earth as the observer. Use the meta-kernel shown below to load the required SPICE kernels. KPL/MK File name: gfpa_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 gfpa_ex1 ./ #include <stdio.h> #include "SpiceUsr.h" #define TIMFMT "YYYY MON DD HR:MN:SC.###" #define NINTVL 5000 #define TIMLEN 41 #define NLOOPS 7 int main() { /. Local variables ./ SpiceChar begstr [ TIMLEN ]; SpiceChar endstr [ TIMLEN ]; SPICEDOUBLE_CELL ( cnfine, 2 ); SPICEDOUBLE_CELL ( result, NINTVL*2 ); SpiceDouble adjust; SpiceDouble et0; SpiceDouble et1; SpiceDouble phaseq; SpiceDouble refval; SpiceDouble start; SpiceDouble step; SpiceDouble stop; SpiceInt i; SpiceInt j; /. Define the values for target, observer, illuminator, and aberration correction. ./ ConstSpiceChar * target = "moon"; ConstSpiceChar * illmn = "sun"; ConstSpiceChar * abcorr = "lt+s"; ConstSpiceChar * obsrvr = "earth"; ConstSpiceChar * relate [NLOOPS] = { "=", "<", ">", "LOCMIN", "ABSMIN", "LOCMAX", "ABSMAX", }; /. Load kernels. ./ furnsh_c ( "gfpa_ex1.tm" ); /. Store the time bounds of our search interval in the confinement window. ./ str2et_c ( "2006 DEC 01", &et0 ); str2et_c ( "2007 JAN 31", &et1 ); wninsd_c ( et0, et1, &cnfine ); /. Search using a step size of 1 day (in units of seconds). The reference value is 0.57598845 radians. We're not using the adjustment feature, so we set ADJUST to zero. ./ step = spd_c(); refval = 0.57598845; adjust = 0.0; 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. ./ ## Restrictions1) The kernel files to be used by this routine must be loaded (normally using the CSPICE routine furnsh_c) 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, 01-NOV-2021 (JDR) (EDW) Updated short error message for consistency within CSPICE wrapper interface: MALLOCFAILURE -> MALLOCFAILED. 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. Replaced entry #8 by new entries #8 and #9, and added entry #11 in -Exceptions section. -CSPICE Version 1.0.0, 15-JUL-2014 (EDW) (NJB) ## Index_EntriesGF phase angle search |

Fri Dec 31 18:41:07 2021