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Diffstat (limited to 'math/slalib/deuler.f')
| -rw-r--r-- | math/slalib/deuler.f | 181 |
1 files changed, 181 insertions, 0 deletions
diff --git a/math/slalib/deuler.f b/math/slalib/deuler.f new file mode 100644 index 00000000..1ae50acf --- /dev/null +++ b/math/slalib/deuler.f @@ -0,0 +1,181 @@ + SUBROUTINE slDEUL (ORDER, PHI, THETA, PSI, RMAT) +*+ +* - - - - - - - +* D E U L +* - - - - - - - +* +* Form a rotation matrix from the Euler angles - three successive +* rotations about specified Cartesian axes (double precision) +* +* Given: +* ORDER c*(*) specifies about which axes the rotations occur +* PHI d 1st rotation (radians) +* THETA d 2nd rotation ( " ) +* PSI d 3rd rotation ( " ) +* +* Returned: +* RMAT d(3,3) rotation matrix +* +* A rotation is positive when the reference frame rotates +* anticlockwise as seen looking towards the origin from the +* positive region of the specified axis. +* +* The characters of ORDER define which axes the three successive +* rotations are about. A typical value is 'ZXZ', indicating that +* RMAT is to become the direction cosine matrix corresponding to +* rotations of the reference frame through PHI radians about the +* old Z-axis, followed by THETA radians about the resulting X-axis, +* then PSI radians about the resulting Z-axis. +* +* The axis names can be any of the following, in any order or +* combination: X, Y, Z, uppercase or lowercase, 1, 2, 3. Normal +* axis labelling/numbering conventions apply; the xyz (=123) +* triad is right-handed. Thus, the 'ZXZ' example given above +* could be written 'zxz' or '313' (or even 'ZxZ' or '3xZ'). ORDER +* is terminated by length or by the first unrecognized character. +* +* Fewer than three rotations are acceptable, in which case the later +* angle arguments are ignored. If all rotations are zero, the +* identity matrix is produced. +* +* P.T.Wallace Starlink 23 May 1997 +* +* Copyright (C) 1997 Rutherford Appleton Laboratory +* +* License: +* This program is free software; you can redistribute it and/or modify +* it under the terms of the GNU General Public License as published by +* the Free Software Foundation; either version 2 of the License, or +* (at your option) any later version. +* +* This program is distributed in the hope that it will be useful, +* but WITHOUT ANY WARRANTY; without even the implied warranty of +* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +* GNU General Public License for more details. +* +* You should have received a copy of the GNU General Public License +* along with this program (see SLA_CONDITIONS); if not, write to the +* Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, +* Boston, MA 02110-1301 USA +* +* Copyright (C) 1995 Association of Universities for Research in Astronomy Inc. +*- + + IMPLICIT NONE + + CHARACTER*(*) ORDER + DOUBLE PRECISION PHI,THETA,PSI,RMAT(3,3) + + INTEGER J,I,L,N,K + DOUBLE PRECISION RESULT(3,3),ROTN(3,3),ANGLE,S,C,W,WM(3,3) + CHARACTER AXIS + + + +* Initialize result matrix + DO J=1,3 + DO I=1,3 + IF (I.NE.J) THEN + RESULT(I,J) = 0D0 + ELSE + RESULT(I,J) = 1D0 + END IF + END DO + END DO + +* Establish length of axis string + L = LEN(ORDER) + +* Look at each character of axis string until finished + DO N=1,3 + IF (N.LE.L) THEN + +* Initialize rotation matrix for the current rotation + DO J=1,3 + DO I=1,3 + IF (I.NE.J) THEN + ROTN(I,J) = 0D0 + ELSE + ROTN(I,J) = 1D0 + END IF + END DO + END DO + +* Pick up the appropriate Euler angle and take sine & cosine + IF (N.EQ.1) THEN + ANGLE = PHI + ELSE IF (N.EQ.2) THEN + ANGLE = THETA + ELSE + ANGLE = PSI + END IF + S = SIN(ANGLE) + C = COS(ANGLE) + +* Identify the axis + AXIS = ORDER(N:N) + IF (AXIS.EQ.'X'.OR. + : AXIS.EQ.'x'.OR. + : AXIS.EQ.'1') THEN + +* Matrix for x-rotation + ROTN(2,2) = C + ROTN(2,3) = S + ROTN(3,2) = -S + ROTN(3,3) = C + + ELSE IF (AXIS.EQ.'Y'.OR. + : AXIS.EQ.'y'.OR. + : AXIS.EQ.'2') THEN + +* Matrix for y-rotation + ROTN(1,1) = C + ROTN(1,3) = -S + ROTN(3,1) = S + ROTN(3,3) = C + + ELSE IF (AXIS.EQ.'Z'.OR. + : AXIS.EQ.'z'.OR. + : AXIS.EQ.'3') THEN + +* Matrix for z-rotation + ROTN(1,1) = C + ROTN(1,2) = S + ROTN(2,1) = -S + ROTN(2,2) = C + + ELSE + +* Unrecognized character - fake end of string + L = 0 + + END IF + +* Apply the current rotation (matrix ROTN x matrix RESULT) + DO I=1,3 + DO J=1,3 + W = 0D0 + DO K=1,3 + W = W+ROTN(I,K)*RESULT(K,J) + END DO + WM(I,J) = W + END DO + END DO + DO J=1,3 + DO I=1,3 + RESULT(I,J) = WM(I,J) + END DO + END DO + + END IF + + END DO + +* Copy the result + DO J=1,3 + DO I=1,3 + RMAT(I,J) = RESULT(I,J) + END DO + END DO + + END |