Procedure

     SHARPR ( Sharpen a rotation )

     SUBROUTINE SHARPR ( ROT )

Abstract

     Adjust the columns of a matrix that is "nearly" a rotation
     so that they are numerically unit length and orthogonal,
     going from left to right in the usual printed presentation 
     of a matrix.

Required_Reading

     None.

Keywords

     MATRIX

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION      ROT ( 3, 3 )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     ROT       I-O  The rotation matrix to be sharpened.

Detailed_Input

     ROT      is a 3x3 matrix that is nearly a rotation matrix.

Detailed_Output

     ROT      is the input after sharpening the columns.

Parameters

     None.

Exceptions

     Error free.

     1)  This routine is not meant to be used on singular or near-
         singular matrices (in other words, matrices with determinant
         close to zero).

         If the input matrix is singular, the output matrix may not
         be a rotation matrix. In any case, the results should be
         considered unreliable in this case.

         No error handling is done for invalid input matrices.

Files

     None.

Particulars

     This routine "sharpens" the orthogonality of a potential
     rotation matrix. It is intended for use in those situations
     in which you have a rotation matrix that may be derived
     from single precision inputs or that may have experienced
     round off errors in its construction.

Examples

     Suppose that you have a rotation matrix that needs to be
     converted to a quaternion. The SPICE matrix to quaternion
     conversion routine M2Q performs error checks on the input
     matrix and signals an error if it does not meet the checks
     for a quaternion. By calling this routine you can ensure that
     your rotation matrix (provided it's non-singular) will pass
     the restrictions imposed by M2Q.

         CALL SHARPR ( ROT )
         CALL M2Q    ( ROT, Q )

Restrictions

     1)  See the $Exceptions section above.

Literature_References

     None.

Author_and_Institution

     N.J. Bachman       (JPL)
     J. Diaz del Rio    (ODC Space)
     W.L. Taber         (JPL)

Version

    SPICELIB Version 1.1.1, 26-OCT-2021 (JDR)

        Edited the header to comply with NAIF standard. Removed
        unnecessary $Revisions section.

    SPICELIB Version 1.1.0, 13-OCT-2005 (NJB)

        Updated to remove non-standard use of duplicate arguments
        in VHAT call. Some header updates were made.

    SPICELIB Version 1.0.0, 16-SEP-1999 (WLT)