SUBROUTINE iau_RM2V ( R, W )
*+
*  - - - - - - - - -
*   i a u _ R M 2 V
*  - - - - - - - - -
*
*  Express an r-matrix as an r-vector.
*
*  This routine is part of the International Astronomical Union's
*  SOFA (Standards of Fundamental Astronomy) software collection.
*
*  Status:  vector/matrix support routine.
*
*  Given:
*     R        d(3,3)    rotation matrix
*
*  Returned:
*     W        d(3)      rotation vector (Note 1)
*
*  Notes:
*
*  1) A rotation matrix describes a rotation through some angle about
*     some arbitrary axis called the Euler axis.  The "rotation vector"
*     returned by this routine has the same direction as the Euler axis,
*     and its magnitude is the angle in radians.  (The magnitude and
*     direction can be separated by means of the routine iau_PN.)
*
*  2) If R is null, so is the result.  If R is not a rotation matrix
*     the result is undefined.  R must be proper (i.e. have a positive
*     determinant) and real orthogonal (inverse = transpose).
*
*  3) The reference frame rotates clockwise as seen looking along
*     the rotation vector from the origin.
*
*  This revision:  2015 January 30
*
*  SOFA release 2023-10-11
*
*  Copyright (C) 2023 IAU SOFA Board.  See notes at end.
*
*-----------------------------------------------------------------------

      IMPLICIT NONE

      DOUBLE PRECISION R(3,3), W(3)

      DOUBLE PRECISION X, Y, Z, S2, C2, PHI, F

* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      X = R(2,3) - R(3,2)
      Y = R(3,1) - R(1,3)
      Z = R(1,2) - R(2,1)
      S2 = SQRT(X*X + Y*Y + Z*Z)
      IF ( S2 .GT. 0D0 ) THEN
         C2 = R(1,1) + R(2,2) + R(3,3) - 1D0
         PHI = ATAN2(S2,C2)
         F = PHI / S2
         W(1) = X * F
         W(2) = Y * F
         W(3) = Z * F
      ELSE
         W(1) = 0D0
         W(2) = 0D0
         W(3) = 0D0
      END IF

*  Finished.

*+----------------------------------------------------------------------
*
*  Copyright (C) 2023
*  Standards of Fundamental Astronomy Board
*  of the International Astronomical Union.
*
*  =====================
*  SOFA Software License
*  =====================
*
*  NOTICE TO USER:
*
*  BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
*  CONDITIONS WHICH APPLY TO ITS USE.
*
*  1. The Software is owned by the IAU SOFA Board ("SOFA").
*
*  2. Permission is granted to anyone to use the SOFA software for any
*     purpose, including commercial applications, free of charge and
*     without payment of royalties, subject to the conditions and
*     restrictions listed below.
*
*  3. You (the user) may copy and distribute SOFA source code to others,
*     and use and adapt its code and algorithms in your own software,
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*     distribution that does not consist of intact and unchanged copies
*     of SOFA source code files is a "derived work" that must comply
*     with the following requirements:
*
*     a) Your work shall be marked or carry a statement that it
*        (i) uses routines and computations derived by you from
*        software provided by SOFA under license to you; and
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*
*     b) The source code of your derived work must contain descriptions
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*        from the original SOFA software.
*
*     c) The names of all routines in your derived work shall not
*        include the prefix "iau" or "sofa" or trivial modifications
*        thereof such as changes of case.
*
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*
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*
*  6. The provision of any version of the SOFA software under the terms
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*
*  In any published work or commercial product which uses the SOFA
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*
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*  follows:
*
*      By email:  sofa@ukho.gov.uk
*      By post:   IAU SOFA Center
*                 HM Nautical Almanac Office
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*
*-----------------------------------------------------------------------

      END