Author: bugman
Date: Tue Sep 1 16:02:48 2009
New Revision: 9422
URL: http://svn.gna.org/viewcvs/relax?rev=9422&view=rev
Log:
Created the new maths_fns.rotation_matrix.R_to_euler_zyz() function and
associated unit test.
Added:
1.3/test_suite/unit_tests/_maths_fns/test_rotation_matrix.py
Modified:
1.3/maths_fns/rotation_matrix.py
Modified: 1.3/maths_fns/rotation_matrix.py
URL:
http://svn.gna.org/viewcvs/relax/1.3/maths_fns/rotation_matrix.py?rev=9422&r1=9421&r2=9422&view=diff
==============================================================================
--- 1.3/maths_fns/rotation_matrix.py (original)
+++ 1.3/maths_fns/rotation_matrix.py Tue Sep 1 16:02:48 2009
@@ -21,7 +21,7 @@
###############################################################################
# Python module imports.
-from math import acos, atan2, cos, pi, sin
+from math import acos, asin, atan2, cos, pi, sin
from numpy import array, cross, dot, float64, hypot, zeros
from numpy.linalg import norm
from random import gauss, uniform
@@ -296,6 +296,57 @@
matrix[2,2] = cos_b
+def R_to_euler_zyz(matrix):
+ """Calculate the z-y-z Euler angles from the given rotation matrix.
+
+ Unit vectors
+ ============
+
+ The unit mux vector is::
+
+ | -sin(alpha) * sin(gamma) + cos(alpha) * cos(beta) *
cos(gamma) |
+ mux = | -sin(alpha) * cos(gamma) - cos(alpha) * cos(beta) *
sin(gamma) |.
+ | cos(alpha) * sin(beta)
|
+
+ The unit muy vector is::
+
+ | cos(alpha) * sin(gamma) + sin(alpha) * cos(beta) *
cos(gamma) |
+ muy = | cos(alpha) * cos(gamma) - sin(alpha) * cos(beta) *
sin(gamma) |.
+ | sin(alpha) * sin(beta)
|
+
+ The unit muz vector is::
+
+ | -sin(beta) * cos(gamma) |
+ muz = | sin(beta) * sin(gamma) |.
+ | cos(beta) |
+
+ Rotation matrix
+ ===============
+
+ The rotation matrix is defined as the vector of unit vectors::
+
+ R = [mux, muy, muz].
+
+
+ @param matrix: The 3x3 rotation matrix to update.
+ @type matrix: 3x3 numpy array
+ @return: The alpha, beta, and gamma Euler angles in the z-y-z
convention.
+ @rtype: float, float, float
+ """
+
+ # The beta Euler angle.
+ beta = acos(matrix[2,2])
+
+ # The alpha Euler angle.
+ alpha = atan2(matrix[2,1], matrix[2,0])
+
+ # The gamma Euler angle.
+ gamma = atan2(matrix[1,2], -matrix[0,2])
+
+ # Return the angles.
+ return alpha, beta, gamma
+
+
def R_random_axis(matrix, angle=0.0):
"""Generate a random rotation matrix of fixed angle via the axis-angle
notation.
Added: 1.3/test_suite/unit_tests/_maths_fns/test_rotation_matrix.py
URL:
http://svn.gna.org/viewcvs/relax/1.3/test_suite/unit_tests/_maths_fns/test_rotation_matrix.py?rev=9422&view=auto
==============================================================================
--- 1.3/test_suite/unit_tests/_maths_fns/test_rotation_matrix.py (added)
+++ 1.3/test_suite/unit_tests/_maths_fns/test_rotation_matrix.py Tue Sep 1
16:02:48 2009
@@ -1,0 +1,76 @@
+###############################################################################
+#
#
+# Copyright (C) 2009 Edward d'Auvergne
#
+#
#
+# This file is part of the program relax.
#
+#
#
+# relax 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.
#
+#
#
+# relax 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 relax; if not, write to the Free Software
#
+# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
#
+#
#
+###############################################################################
+
+# Python module imports.
+from math import pi
+from numpy import float64, zeros
+from random import uniform
+from unittest import TestCase
+
+# relax module imports.
+from generic_fns.angles import wrap_angles
+from maths_fns.rotation_matrix import *
+
+
+class Test_rotation_matrix(TestCase):
+ """Unit tests for the maths_fns.rotation_matrix relax module."""
+
+ def setUp(self):
+ """Set up data used by the unit tests."""
+
+
+ def test_R_to_euler_zyz(self):
+ """Test the rotation matrix to zyz Euler angle conversion."""
+
+ # Starting angles.
+ alpha = uniform(0, 2*pi)
+ beta = uniform(0, pi)
+ gamma = uniform(0, 2*pi)
+
+ # Print out.
+ print("Original angles:")
+ print("alpha: %s" % alpha)
+ print("beta: %s" % beta)
+ print("gamma: %s\n" % gamma)
+
+ # Generate the rotation matrix.
+ R = zeros((3,3), float64)
+ R_euler_zyz(R, alpha, beta, gamma)
+
+ # Get back the angles.
+ alpha_new, beta_new, gamma_new = R_to_euler_zyz(R)
+
+ # Wrap the angles.
+ alpha_new = wrap_angles(alpha_new, 0, 2*pi)
+ beta_new = wrap_angles(beta_new, 0, 2*pi)
+ gamma_new = wrap_angles(gamma_new, 0, 2*pi)
+
+ # Print out.
+ print("New angles:")
+ print("alpha: %s" % alpha_new)
+ print("beta: %s" % beta_new)
+ print("gamma: %s\n" % gamma_new)
+
+ # Checks.
+ self.assertAlmostEqual(alpha, alpha_new)
+ self.assertAlmostEqual(beta, beta_new)
+ self.assertAlmostEqual(gamma, gamma_new)
r9422 - in /1.3: maths_fns/rotation_matrix.py test_suite/unit_tests/_maths_fns/test_rotation_matrix.py