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: 2006 April 13 * * Copyright (C) 2007 IAU SOFA Review 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 .NE. 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) 2007 * Standards Of Fundamental Astronomy Review Board * of the International Astronomical Union. * * ===================== * SOFA Software License * ===================== * * NOTICE TO USER: * * BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING TERMS AND CONDITIONS * WHICH APPLY TO ITS USE. * * 1. The Software is owned by the IAU SOFA Review Board ("the Board"). * * 2. The Software is made available free of charge for use by: * * a) private individuals for non-profit research; and * * b) non-profit educational, academic and research institutions. * * 3. Commercial use of the Software is specifically excluded from the * terms and conditions of this license. Commercial use of the * Software is subject to the prior written agreement of the Board on * terms to be agreed. * * 4. The provision of any version of the Software under the terms and * conditions specified herein does not imply that future versions * will also be made available under the same terms and conditions. * * 5. The user may modify the Software for his/her own purposes. The * user may distribute the modified software provided that the Board * is informed and that a copy of the modified software is made * available to the Board on request. All modifications made by the * user shall be clearly identified to show how the modified software * differs from the original Software, and the name(s) of the * affected routine(s) shall be changed. The original SOFA Software * License text must be present. * * 6. In any published work produced by the user and which includes * results achieved by using the Software, the user shall acknowledge * that the Software was used in producing the information contained * in such publication. * * 7. The user may incorporate or embed the Software into other software * products which he/she may then give away free of charge but not * sell provided the user makes due acknowledgement of the use which * he/she has made of the Software in creating such software * products. Any redistribution of the Software in this way shall be * made under the same terms and conditions under which the user * received it from the SOFA Center. * * 8. The user shall not cause the Software to be brought into * disrepute, either by misuse, or use for inappropriate tasks, or by * inappropriate modification. * * 9. The Software is provided to the user "as is" and the Board makes * no warranty as to its use or performance. The Board does not and * cannot warrant the performance or results which the user may * obtain by using the Software. The Board makes no warranties, * express or implied, as to non-infringement of third party rights, * merchantability, or fitness for any particular purpose. In no * event will the Board be liable to the user for any consequential, * incidental, or special damages, including any lost profits or lost * savings, even if a Board representative has been advised of such * damages, or for any claim by any third party. * * Correspondence concerning SOFA software should be addressed as * follows: * * Internet email: sofa@rl.ac.uk * Postal address: IAU SOFA Center * Rutherford Appleton Laboratory * Chilton, Didcot, Oxon OX11 0QX * United Kingdom * * *----------------------------------------------------------------------- END