SUBROUTINE iau_RV2M ( W, R ) *+ * - - - - - - - - - * i a u _ R V 2 M * - - - - - - - - - * * Form the r-matrix corresponding to a given 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: * W d(3) rotation vector (Note 1) * * Returned: * R d(3,3) rotation matrix * * Notes: * * 1) A rotation matrix describes a rotation through some angle about * some arbitrary axis called the Euler axis. The "rotation vector" * supplied to this routine has the same direction as the Euler axis, * and its magnitude is the angle in radians. * * 2) If W is null, the unit matrix is returned. * * 3) The reference frame rotates clockwise as seen looking along the * rotation vector from the origin. * * This revision: 2008 May 10 * * Copyright (C) 2008 IAU SOFA Review Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION W(3), R(3,3) DOUBLE PRECISION X, Y, Z, PHI, S, C, F * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Euler angle (magnitude of rotation vector) and functions. X = W(1) Y = W(2) Z = W(3) PHI = SQRT(X*X + Y*Y + Z*Z) S = SIN(PHI) C = COS(PHI) F = 1D0 - C * Euler axis (direction of rotation vector), perhaps null. IF ( PHI .NE. 0D0 ) THEN X = X / PHI Y = Y / PHI Z = Z / PHI END IF * Form the rotation matrix. R(1,1) = X*X*F + C R(1,2) = X*Y*F + Z*S R(1,3) = X*Z*F - Y*S R(2,1) = Y*X*F - Z*S R(2,2) = Y*Y*F + C R(2,3) = Y*Z*F + X*S R(3,1) = Z*X*F + Y*S R(3,2) = Z*Y*F - X*S R(3,3) = Z*Z*F + C * Finished. *+----------------------------------------------------------------------- * * Copyright (C) 2008 * 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. 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 adapt the SOFA software and its * algorithms for your own purposes and you may copy and distribute * a resulting "derived work" to others on a world-wide, royalty-free * basis, provided that the derived work complies 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 (ii) does not contain * software provided by SOFA or software that has been distributed * by or endorsed by SOFA. * * b) The source code of your derived work must contain descriptions * of how the derived work is based upon and/or differs from the * original SOFA software. * * c) The name(s) of all routine(s) that you distribute shall differ * from the SOFA names, even when the SOFA content has not been * otherwise changed. * * d) The routine-naming prefix "iau" shall not be used. * * e) The origin of the SOFA components of your derived work must not * be misrepresented; you must not claim that you wrote the * original software, nor file a patent application for SOFA * software or algorithms embedded in the SOFA software. * * f) These requirements must be reproduced intact in any source * distribution and shall apply to anyone to whom you have granted * a further right to modify the source code of your derived work. * * 4. In any published work or commercial products which includes * results achieved by using the SOFA software, you shall acknowledge * that the SOFA software was used in obtaining those results. * * 5. You shall not cause the SOFA software to be brought into * disrepute, either by misuse, or use for inappropriate tasks, or by * inappropriate modification. * * 6. The SOFA software is provided "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 SOFA 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. * * 7. The provision of any version of the SOFA 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. * * 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