Procedure

     WNRELD ( Compare two DP windows )

     LOGICAL FUNCTION  WNRELD ( A, OP, B )

Abstract

     Compare two double precision windows.

Required_Reading

     WINDOWS

Keywords

     WINDOWS

Declarations

     IMPLICIT NONE

     INTEGER               LBCELL
     PARAMETER           ( LBCELL = -5 )

     DOUBLE PRECISION      A        ( LBCELL:* )
     CHARACTER*(*)         OP
     DOUBLE PRECISION      B        ( LBCELL:* )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     A          I   First window.
     OP         I   Comparison operator.
     B          I   Second window.

     The function returns the result of comparison: A (OP) B.

Detailed_Input

     A,
     B        are SPICE windows, each of which contains zero or more
              intervals.

     OP       is a comparison operator, indicating the way in which the
              input sets are to be compared. OP may be any of the
              following:

                 Operator             Meaning
                 --------  -------------------------------------------
                   '='     A = B is .TRUE. if A and B are equal
                           (contain the same intervals).

                   '<>'    A <> B is .TRUE. if A and B are not equal.

                   '<='    A <= B is .TRUE. if A is a subset of B.

                   '<'     A < B is .TRUE. if A is a proper subset
                           of B.

                   '>='    A >= B is .TRUE. if B is a subset of A.

                   '>'     A > B is .TRUE. if B is a proper subset
                           of A.

Detailed_Output

     The function returns the result of the comparison.

Parameters

     None.

Exceptions

     1)  If the relational operator is not recognized, the error
         SPICE(INVALIDOPERATION) is signaled.

     2)  The cardinality of the input windows must be even. Left
         endpoints of stored intervals must be strictly greater than
         preceding right endpoints. Right endpoints must be greater
         than or equal to corresponding left endpoints. Invalid window
         data are not diagnosed by this routine and may lead to
         unpredictable results.

Files

     None.

Particulars

     This function returns .TRUE. whenever the specified relationship
     between the input windows, A and B, is satisfied. For example,
     the expression

        WNRELD ( NEEDED, '<=', AVAIL )

     is .TRUE. whenever the window NEEDED is a subset of the window
     AVAIL. One window is a subset of another window if each of
     the intervals in the first window is included in one of the
     intervals in the second window. In addition, the first window
     is a proper subset of the second if the second window contains
     at least one point not contained in the first window. (Thus,
     '<' implies '<=', and '>' implies '>='.)

     The following pairs of expressions are equivalent.

        WNRELD ( A, '>', B )
        WNRELD ( B, '<', A )

        WNRELD ( A, '>=', B )
        WNRELD ( B, '<=', A )

Examples

     Let A contain the intervals

           [ 1, 3 ]  [ 7, 11 ]  [ 23, 27 ]

     Let B and C contain the intervals

           [ 1, 2 ]  [ 9, 9 ]  [ 24, 27 ]

     Let D contain the intervals

           [ 5, 10 ]  [ 15, 25 ]

     Finally, let E and F be empty windows (containing no intervals).

     Because B and C contain the same intervals,

           WNRELD ( B, '=',  C )
           WNRELD ( B, '<=', C )
           WNRELD ( B, '>=', C )

     are all true, while

           WNRELD ( B, '<>', C )

     is .FALSE. Because neither B nor C contains any points not also
     contained by the other, neither is a proper subset of the other.
     Thus,

           WNRELD ( B, '<', C )
           WNRELD ( B, '>', C )

     are both false.

     Every point contained in B and C is also contained in A. Thus,

           WNRELD ( B, '<=', A )
           WNRELD ( A, '>=', C )

     are both true. In addition, A contains points not contained in
     B and C. (That is, the differences A-B and A-C are not empty.)
     Thus, B and C are proper subsets of A as well, and

           WNRELD ( B, '<', A )
           WNRELD ( A, '>', B )

     are both true.

     Although A and D have points in common, neither contains the
     other. Thus

           WNRELD ( A, '=',  D )
           WNRELD ( A, '<=', D )
           WNRELD ( A, '>=', D )

     are all false.

     In addition, any window is equal to itself, a subset of itself,
     and a superset of itself. Thus,

           WNRELD ( A, '=',  A )
           WNRELD ( A, '<=', A )
           WNRELD ( A, '>=', A )

     are always true. However, no window is a proper subset or a
     proper superset of itself. Thus,

           WNRELD ( A, '<', A )
           WNRELD ( A, '>', A )

     are always false.

     Finally, an empty window is a a proper subset of any window
     except another empty window. Thus,

           WNRELD ( E, '<', A )

     is .TRUE., but

           WNRELD ( E, '<', F )

     is .FALSE.

Restrictions

     None.

Literature_References

     None.

Author_and_Institution

     N.J. Bachman       (JPL)
     J. Diaz del Rio    (ODC Space)
     H.A. Neilan        (JPL)
     W.L. Taber         (JPL)
     I.M. Underwood     (JPL)

Version

    SPICELIB Version 1.2.0, 24-AUG-2021 (JDR) (NJB)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard. Added entry #2
        in $Exceptions section.

    SPICELIB Version 1.1.0, 17-MAY-1994 (HAN)

        Set the default function value to either 0, 0.0D0, .FALSE.,
        or blank depending on the type of the function.

    SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)

        Comment section for permuted index source lines was added
        following the header.

    SPICELIB Version 1.0.0, 31-JAN-1990 (WLT) (IMU) (HAN)