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: 2015 January 30 * * SOFA release 2019-07-22 * * Copyright (C) 2019 IAU SOFA 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 .GT. 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) 2019 * 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, * on a world-wide, royalty-free basis. That portion of your * 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 * (ii) does not itself constitute software provided by and/or * endorsed by SOFA. * * b) The source code of your derived work must contain descriptions * of how the derived work is based upon, contains and/or differs * 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. * * d) 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. * * e) 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. * * Note that, as originally distributed, the SOFA software is * intended to be a definitive implementation of the IAU standards, * and consequently third-party modifications are discouraged. 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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. * * In any published work or commercial product which uses the SOFA * software directly, acknowledgement (see www.iausofa.org) is * appreciated. * * Correspondence concerning SOFA software should be addressed as * follows: * * By email: sofa@ukho.gov.uk * By post: IAU SOFA Center * HM Nautical Almanac Office * UK Hydrographic Office * Admiralty Way, Taunton * Somerset, TA1 2DN * United Kingdom * *----------------------------------------------------------------------- END