gfpa |

Table of contents## ProcedureGFPA ( GF, phase angle search ) SUBROUTINE GFPA ( TARGET, ILLMN, ABCORR, OBSRVR, . RELATE, REFVAL, ADJUST, STEP, . CNFINE, MW, NW, WORK, . 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 ## DeclarationsIMPLICIT NONE INCLUDE 'gf.inc' INCLUDE 'zzholdd.inc' INTEGER LBCELL PARAMETER ( LBCELL = -5 ) CHARACTER*(*) TARGET CHARACTER*(*) ILLMN CHARACTER*(*) ABCORR CHARACTER*(*) OBSRVR CHARACTER*(*) RELATE DOUBLE PRECISION REFVAL DOUBLE PRECISION ADJUST DOUBLE PRECISION STEP DOUBLE PRECISION CNFINE ( LBCELL : * ) INTEGER MW INTEGER NW DOUBLE PRECISION WORK ( LBCELL : MW, NW ) DOUBLE PRECISION RESULT ( LBCELL : * ) ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- LBCELL P SPICE Cell lower bound. 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. CNFINE I SPICE window to which the search is confined. MW I Workspace window size. NW I The number of workspace windows needed for the search. WORK O Array of workspace windows. RESULT I-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 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_OutputWORK is an array used to store workspace windows. This array should be declared by the caller as shown: INCLUDE 'gf.inc' ... DOUBLE PRECISION WORK ( LBCELL : MW, NWPA ) where MW is a constant declared by the caller and NWPA is a constant defined in the SPICELIB INCLUDE file gf.inc. See the discussion of MW above. WORK need not be initialized by the caller. WORK is modified by this routine. The caller should re-initialize this array before attempting to use it for any other purpose. RESULT is the SPICE window of intervals, contained within the confinement window CNFINE, on which the specified phase angle constraint is satisfied. 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. ## ParametersLBCELL is the integer value defining the lower bound for SPICE Cell arrays (a SPICE window is a kind of cell). CNVTOL is the default convergence tolerance used for finding endpoints of the intervals comprising the result window. CNVTOL is also used for finding intermediate results; in particular, CNVTOL is used for finding the windows on which the phase angle is increasing or decreasing. CNVTOL is used to determine when binary searches for roots should terminate: when a root is bracketed within an interval of length 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. See INCLUDE file gf.inc for declarations and descriptions of parameters used throughout the GF system. ## 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. 3) If workspace window size, MW, is not at least 2 and an even value, the error SPICE(INVALIDDIMENSION) is signaled is signaled. 4) If workspace window count, NW, is not at least NWPA, the error SPICE(INVALIDDIMENSION) is signaled is signaled. 5) If result window, RESULT, is not at least 2 and an even value, the error SPICE(INVALIDDIMENSION) is signaled is signaled. 6) 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. 7) If an error (typically cell overflow) occurs during window arithmetic, the error is signaled by a routine in the call tree of this routine. 8) If the relational operator RELATE is not recognized, 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 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. 12) 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. 13) If required ephemerides or other kernel data are not available, an error is signaled by a routine in the call tree of this routine. 14) If the aberration correction specifier contains an unrecognized value, an error is signaled by a routine in the call tree of this routine. 15) If a transmit mode aberration correction is requested, an error is signaled by a routine in the call tree of this routine. ## 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. - 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 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 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 CNVTOL (defined in gf.inc). The value of 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 CNVTOL value by calling the routine GFSTOL, e.g. CALL GFSTOL( tolerance value ) Call GFSTOL prior to calling this routine. All subsequent searches will use the updated tolerance value. Setting the tolerance tighter than 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 IMPLICIT NONE C C Include GF parameter declarations: C INCLUDE 'gf.inc' C C SPICELIB functions C DOUBLE PRECISION SPD DOUBLE PRECISION PHASEQ INTEGER WNCARD C C Local parameters C INTEGER LBCELL PARAMETER ( LBCELL = -5 ) C C Use the parameter MAXWIN for both the result window size C and the workspace size. C INTEGER MAXWIN PARAMETER ( MAXWIN = 1000 ) C C Length of strings: C INTEGER TIMLEN PARAMETER ( TIMLEN = 26 ) INTEGER NLOOPS PARAMETER ( NLOOPS = 7 ) C C Local variables C CHARACTER*(TIMLEN) RELATE (NLOOPS) CHARACTER*(6) ABCORR CHARACTER*(6) ILLMN CHARACTER*(6) OBSRVR CHARACTER*(6) TARGET CHARACTER*(TIMLEN) TIMSTR DOUBLE PRECISION CNFINE ( LBCELL : 2 ) DOUBLE PRECISION RESULT ( LBCELL : MAXWIN ) DOUBLE PRECISION WORK ( LBCELL : MAXWIN, NWPA ) DOUBLE PRECISION ADJUST DOUBLE PRECISION ET0 DOUBLE PRECISION ET1 DOUBLE PRECISION FINISH DOUBLE PRECISION PHASE DOUBLE PRECISION REFVAL DOUBLE PRECISION START DOUBLE PRECISION STEP INTEGER I INTEGER J C C Saved variables C C The confinement, workspace and result windows CNFINE, C WORK and RESULT are saved because this practice helps to C prevent stack overflow. C SAVE CNFINE SAVE RESULT SAVE WORK C C The relation values for the search. C DATA RELATE / '=', . '<', . '>', . 'LOCMIN', . 'ABSMIN', . 'LOCMAX', . 'ABSMAX' / C C Load kernels. C CALL FURNSH ( 'gfpa_ex1.tm' ) C C Initialize windows. C CALL SSIZED ( MAXWIN, RESULT ) CALL SSIZED ( 2, CNFINE ) C C Store the time bounds of our search interval in C the confinement window. C CALL STR2ET ( '2006 DEC 01', ET0 ) CALL STR2ET ( '2007 JAN 31', ET1 ) CALL WNINSD ( ET0, ET1, CNFINE ) C C Search using a step size of 1 day (in units of seconds). C The reference value is 0.57598845 radians. We're not C using the adjustment feature, so we set ADJUST to zero. C STEP = SPD() REFVAL = 0.57598845D0 ADJUST = 0.D0 C C Define the values for target, observer, illuminator, and C aberration correction. C TARGET = 'MOON' ILLMN = 'SUN' ABCORR = 'LT+S' OBSRVR = 'EARTH' DO J=1, NLOOPS WRITE(*,*) 'Relation condition: ', RELATE(J) C C Perform the search. The SPICE window RESULT contains C the set of times when the condition is met. C CALL ## Restrictions1) The kernel files to be used by this routine must be loaded (normally using the SPICELIB routine FURNSH) before this routine is called. ## Literature_ReferencesNone. ## Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) E.D. Wright (JPL) ## VersionSPICELIB Version 1.0.1, 27-OCT-2021 (JDR) (NJB) Edited the header to comply with NAIF standard. Updated description of RELATE, REFVAL, WORK and RESULT arguments in $Brief_I/O, $Detailed_Input and $Detailed_Output. Added SAVE statements for CNFINE, WORK and RESULT variables in code example. Replaced entry #9 by new entries #9 and #10, and added entry #14 in $Exceptions. Updated header to describe use of expanded confinement window. SPICELIB Version 1.0.0, 15-JUL-2014 (EDW) (NJB) |

Fri Dec 31 18:36:24 2021