Author: bugman
Date: Tue Sep 8 16:40:16 2009
New Revision: 9476
URL: http://svn.gna.org/viewcvs/relax?rev=9476&view=rev
Log:
Created 3 unit tests of the maths_fns.rotation_matrix.quaternion_to_R()
function.
Modified:
1.3/test_suite/unit_tests/_maths_fns/test_rotation_matrix.py
Modified: 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=9476&r1=9475&r2=9476&view=diff
==============================================================================
--- 1.3/test_suite/unit_tests/_maths_fns/test_rotation_matrix.py (original)
+++ 1.3/test_suite/unit_tests/_maths_fns/test_rotation_matrix.py Tue Sep 8
16:40:16 2009
@@ -21,8 +21,9 @@
###############################################################################
# Python module imports.
-from math import pi
-from numpy import float64, zeros
+from math import acos, asin, pi, sqrt
+from numpy import array, eye, float64, zeros
+from numpy.linalg import norm
from random import uniform
from unittest import TestCase
@@ -38,12 +39,56 @@
"""Set up data used by the unit tests."""
- def test_R_euler_zyz_alpha_30(self):
- """Test the rotation matrix from zyz Euler angle conversion using a
beta angle of pi/4."""
-
- # Generate the rotation matrix.
- R = zeros((3, 3), float64)
- R_euler_zyz(R, pi/6, 0.0, 0.0)
+ def test_quaternion_to_R_no_rot(self):
+ """Test the quaternion to rotation matrix conversion for a zero
angle rotation."""
+
+ # Quaternion of zero angle.
+ quat = array([1, 0, 0, 0], float64)
+
+ # The rotation matrix.
+ R = zeros((3, 3), float64)
+ quaternion_to_R(quat, R)
+ print("Rotation matrix:\n%s" % R)
+
+ # The correct result.
+ R_true = eye(3)
+
+ # Checks.
+ for i in range(3):
+ for j in range(3):
+ self.assertEqual(R[i, j], R_true[i, j])
+
+
+ def test_quaternion_to_R_z_30(self):
+ """Test the quaternion to rotation matrix conversion for a 30 degree
rotation about z."""
+
+ # Axis-angle values.
+ axis = array([0, 0, 1], float64)
+ angle = pi / 6
+
+ # First element.
+ w = cos(angle / 2)
+
+ # Vector reduction (quaternion normalisation).
+ factor = sqrt(1 - w**2)
+ axis = axis * factor
+
+ # Quaternion.
+ quat = zeros(4, float64)
+ quat[0] = w
+ quat[1:] = axis
+ print("Quat: %s" % quat)
+ print("Quat norm: %s" % norm(quat))
+
+ # Quaternion check.
+ w_check = cos(asin(sqrt(quat[1]**2 + quat[2]**2 + quat[3]**2)))
+ self.assertEqual(w, w_check)
+ self.assertEqual(norm(quat), 1)
+
+ # Generate the rotation matrix.
+ R = zeros((3, 3), float64)
+ quaternion_to_R(quat, R)
+ print("Rotation matrix:\n%s" % R)
# Axes.
x_axis = array([1, 0, 0], float64)
@@ -71,9 +116,9 @@
# Checks.
for i in range(3):
- self.assertEqual(x_new[i], x_real[i])
- self.assertEqual(y_new[i], y_real[i])
- self.assertEqual(z_new[i], z_real[i])
+ self.assertAlmostEqual(x_new[i], x_real[i])
+ self.assertAlmostEqual(y_new[i], y_real[i])
+ self.assertAlmostEqual(z_new[i], z_real[i])
# Axes (do everything again, this time negative!).
x_axis = array([-1, 0, 0], float64)
@@ -101,17 +146,41 @@
# Checks.
for i in range(3):
- self.assertEqual(x_new[i], x_real[i])
- self.assertEqual(y_new[i], y_real[i])
- self.assertEqual(z_new[i], z_real[i])
-
-
- def test_R_euler_zyz_beta_45(self):
- """Test the rotation matrix from zyz Euler angle conversion using a
beta angle of pi/4."""
-
- # Generate the rotation matrix.
- R = zeros((3, 3), float64)
- R_euler_zyz(R, 0.0, pi/4, 0.0)
+ self.assertAlmostEqual(x_new[i], x_real[i])
+ self.assertAlmostEqual(y_new[i], y_real[i])
+ self.assertAlmostEqual(z_new[i], z_real[i])
+
+
+ def test_quaternion_to_R_180_complex(self):
+ """Test the quaternion to rotation matrix conversion for a 180
degree rotation about [1, 1, 1]."""
+
+ # Axis-angle values.
+ axis = array([1, 1, 1], float64) / sqrt(3)
+ angle = 2 * pi / 3
+
+ # First element.
+ w = cos(angle / 2)
+
+ # Vector reduction (quaternion normalisation).
+ factor = sqrt(1 - w**2)
+ axis = axis * factor
+
+ # Quaternion.
+ quat = zeros(4, float64)
+ quat[0] = w
+ quat[1:] = axis
+ print("Quat: %s" % quat)
+ print("Quat norm: %s" % norm(quat))
+
+ # Quaternion check.
+ w_check = cos(asin(sqrt(quat[1]**2 + quat[2]**2 + quat[3]**2)))
+ self.assertAlmostEqual(w, w_check)
+ self.assertEqual(norm(quat), 1)
+
+ # Generate the rotation matrix.
+ R = zeros((3, 3), float64)
+ quaternion_to_R(quat, R)
+ print("Rotation matrix:\n%s" % R)
# Axes.
x_axis = array([1, 0, 0], float64)
@@ -119,29 +188,29 @@
z_axis = array([0, 0, 1], float64)
# Rotated axis (real values).
- x_real = array([cos(pi/4), 0, -sin(pi/4)], float64)
- y_real = array([0, 1, 0], float64)
- z_real = array([sin(pi/4), 0, cos(pi/4)], float64)
-
- # Rotation.
- x_new = dot(R, x_axis)
- y_new = dot(R, y_axis)
- z_new = dot(R, z_axis)
-
- # Print out.
- print("Rotated and true axes (beta = pi/4):")
- print(("x rot: %s" % x_new))
- print(("x real: %s\n" % x_real))
- print(("y rot: %s" % y_new))
- print(("y real: %s\n" % y_real))
- print(("z rot: %s" % z_new))
- print(("z real: %s\n" % z_real))
-
- # Checks.
- for i in range(3):
- self.assertEqual(x_new[i], x_real[i])
- self.assertEqual(y_new[i], y_real[i])
- self.assertEqual(z_new[i], z_real[i])
+ x_real = array([0, 1, 0], float64)
+ y_real = array([0, 0, 1], float64)
+ z_real = array([1, 0, 0], float64)
+
+ # Rotation.
+ x_new = dot(R, x_axis)
+ y_new = dot(R, y_axis)
+ z_new = dot(R, z_axis)
+
+ # Print out.
+ print("Rotated and true axes (beta = pi/4):")
+ print(("x rot: %s" % x_new))
+ print(("x real: %s\n" % x_real))
+ print(("y rot: %s" % y_new))
+ print(("y real: %s\n" % y_real))
+ print(("z rot: %s" % z_new))
+ print(("z real: %s\n" % z_real))
+
+ # Checks.
+ for i in range(3):
+ self.assertAlmostEqual(x_new[i], x_real[i])
+ self.assertAlmostEqual(y_new[i], y_real[i])
+ self.assertAlmostEqual(z_new[i], z_real[i])
# Axes (do everything again, this time negative!).
x_axis = array([-1, 0, 0], float64)
@@ -149,37 +218,37 @@
z_axis = array([0, 0, -1], float64)
# Rotated axis (real values).
- x_real = array([-cos(pi/4), 0, sin(pi/4)], float64)
- y_real = array([0, -1, 0], float64)
- z_real = array([-sin(pi/4), 0, -cos(pi/4)], float64)
-
- # Rotation.
- x_new = dot(R, x_axis)
- y_new = dot(R, y_axis)
- z_new = dot(R, z_axis)
-
- # Print out.
- print("Rotated and true axes (beta = pi/4):")
- print(("x rot: %s" % x_new))
- print(("x real: %s\n" % x_real))
- print(("y rot: %s" % y_new))
- print(("y real: %s\n" % y_real))
- print(("z rot: %s" % z_new))
- print(("z real: %s\n" % z_real))
-
- # Checks.
- for i in range(3):
- self.assertEqual(x_new[i], x_real[i])
- self.assertEqual(y_new[i], y_real[i])
- self.assertEqual(z_new[i], z_real[i])
-
-
- def test_R_euler_zyz_gamma_15(self):
+ x_real = array([0, -1, 0], float64)
+ y_real = array([0, 0, -1], float64)
+ z_real = array([-1, 0, 0], float64)
+
+ # Rotation.
+ x_new = dot(R, x_axis)
+ y_new = dot(R, y_axis)
+ z_new = dot(R, z_axis)
+
+ # Print out.
+ print("Rotated and true axes (beta = pi/4):")
+ print(("x rot: %s" % x_new))
+ print(("x real: %s\n" % x_real))
+ print(("y rot: %s" % y_new))
+ print(("y real: %s\n" % y_real))
+ print(("z rot: %s" % z_new))
+ print(("z real: %s\n" % z_real))
+
+ # Checks.
+ for i in range(3):
+ self.assertAlmostEqual(x_new[i], x_real[i])
+ self.assertAlmostEqual(y_new[i], y_real[i])
+ self.assertAlmostEqual(z_new[i], z_real[i])
+
+
+ def test_R_euler_zyz_alpha_30(self):
"""Test the rotation matrix from zyz Euler angle conversion using a
beta angle of pi/4."""
# Generate the rotation matrix.
R = zeros((3, 3), float64)
- R_euler_zyz(R, 0.0, 0.0, pi/12)
+ R_euler_zyz(R, pi/6, 0.0, 0.0)
# Axes.
x_axis = array([1, 0, 0], float64)
@@ -187,8 +256,8 @@
z_axis = array([0, 0, 1], float64)
# Rotated axis (real values).
- x_real = array([cos(pi/12), sin(pi/12), 0], float64)
- y_real = array([-sin(pi/12), cos(pi/12), 0], float64)
+ x_real = array([cos(pi/6), sin(pi/6), 0], float64)
+ y_real = array([-sin(pi/6), cos(pi/6), 0], float64)
z_real = array([0, 0, 1], float64)
# Rotation.
@@ -217,8 +286,8 @@
z_axis = array([0, 0, -1], float64)
# Rotated axis (real values).
- x_real = array([-cos(pi/12), -sin(pi/12), 0], float64)
- y_real = array([sin(pi/12), -cos(pi/12), 0], float64)
+ x_real = array([-cos(pi/6), -sin(pi/6), 0], float64)
+ y_real = array([sin(pi/6), -cos(pi/6), 0], float64)
z_real = array([0, 0, -1], float64)
# Rotation.
@@ -239,14 +308,15 @@
for i in range(3):
self.assertEqual(x_new[i], x_real[i])
self.assertEqual(y_new[i], y_real[i])
-
-
- def test_R_euler_zyz_alpha_15_gamma_15(self):
+ self.assertEqual(z_new[i], z_real[i])
+
+
+ def test_R_euler_zyz_beta_45(self):
"""Test the rotation matrix from zyz Euler angle conversion using a
beta angle of pi/4."""
# Generate the rotation matrix.
R = zeros((3, 3), float64)
- R_euler_zyz(R, pi/12, 0.0, pi/12)
+ R_euler_zyz(R, 0.0, pi/4, 0.0)
# Axes.
x_axis = array([1, 0, 0], float64)
@@ -254,9 +324,9 @@
z_axis = array([0, 0, 1], float64)
# Rotated axis (real values).
- x_real = array([cos(pi/6), sin(pi/6), 0], float64)
- y_real = array([-sin(pi/6), cos(pi/6), 0], float64)
- z_real = array([0, 0, 1], float64)
+ x_real = array([cos(pi/4), 0, -sin(pi/4)], float64)
+ y_real = array([0, 1, 0], float64)
+ z_real = array([sin(pi/4), 0, cos(pi/4)], float64)
# Rotation.
x_new = dot(R, x_axis)
@@ -284,6 +354,141 @@
z_axis = array([0, 0, -1], float64)
# Rotated axis (real values).
+ x_real = array([-cos(pi/4), 0, sin(pi/4)], float64)
+ y_real = array([0, -1, 0], float64)
+ z_real = array([-sin(pi/4), 0, -cos(pi/4)], float64)
+
+ # Rotation.
+ x_new = dot(R, x_axis)
+ y_new = dot(R, y_axis)
+ z_new = dot(R, z_axis)
+
+ # Print out.
+ print("Rotated and true axes (beta = pi/4):")
+ print(("x rot: %s" % x_new))
+ print(("x real: %s\n" % x_real))
+ print(("y rot: %s" % y_new))
+ print(("y real: %s\n" % y_real))
+ print(("z rot: %s" % z_new))
+ print(("z real: %s\n" % z_real))
+
+ # Checks.
+ for i in range(3):
+ self.assertEqual(x_new[i], x_real[i])
+ self.assertEqual(y_new[i], y_real[i])
+ self.assertEqual(z_new[i], z_real[i])
+
+
+ def test_R_euler_zyz_gamma_15(self):
+ """Test the rotation matrix from zyz Euler angle conversion using a
beta angle of pi/4."""
+
+ # Generate the rotation matrix.
+ R = zeros((3, 3), float64)
+ R_euler_zyz(R, 0.0, 0.0, pi/12)
+
+ # Axes.
+ x_axis = array([1, 0, 0], float64)
+ y_axis = array([0, 1, 0], float64)
+ z_axis = array([0, 0, 1], float64)
+
+ # Rotated axis (real values).
+ x_real = array([cos(pi/12), sin(pi/12), 0], float64)
+ y_real = array([-sin(pi/12), cos(pi/12), 0], float64)
+ z_real = array([0, 0, 1], float64)
+
+ # Rotation.
+ x_new = dot(R, x_axis)
+ y_new = dot(R, y_axis)
+ z_new = dot(R, z_axis)
+
+ # Print out.
+ print("Rotated and true axes (beta = pi/4):")
+ print(("x rot: %s" % x_new))
+ print(("x real: %s\n" % x_real))
+ print(("y rot: %s" % y_new))
+ print(("y real: %s\n" % y_real))
+ print(("z rot: %s" % z_new))
+ print(("z real: %s\n" % z_real))
+
+ # Checks.
+ for i in range(3):
+ self.assertEqual(x_new[i], x_real[i])
+ self.assertEqual(y_new[i], y_real[i])
+ self.assertEqual(z_new[i], z_real[i])
+
+ # Axes (do everything again, this time negative!).
+ x_axis = array([-1, 0, 0], float64)
+ y_axis = array([0, -1, 0], float64)
+ z_axis = array([0, 0, -1], float64)
+
+ # Rotated axis (real values).
+ x_real = array([-cos(pi/12), -sin(pi/12), 0], float64)
+ y_real = array([sin(pi/12), -cos(pi/12), 0], float64)
+ z_real = array([0, 0, -1], float64)
+
+ # Rotation.
+ x_new = dot(R, x_axis)
+ y_new = dot(R, y_axis)
+ z_new = dot(R, z_axis)
+
+ # Print out.
+ print("Rotated and true axes (beta = pi/4):")
+ print(("x rot: %s" % x_new))
+ print(("x real: %s\n" % x_real))
+ print(("y rot: %s" % y_new))
+ print(("y real: %s\n" % y_real))
+ print(("z rot: %s" % z_new))
+ print(("z real: %s\n" % z_real))
+
+ # Checks.
+ for i in range(3):
+ self.assertEqual(x_new[i], x_real[i])
+ self.assertEqual(y_new[i], y_real[i])
+
+
+ def test_R_euler_zyz_alpha_15_gamma_15(self):
+ """Test the rotation matrix from zyz Euler angle conversion using a
beta angle of pi/4."""
+
+ # Generate the rotation matrix.
+ R = zeros((3, 3), float64)
+ R_euler_zyz(R, pi/12, 0.0, pi/12)
+
+ # Axes.
+ x_axis = array([1, 0, 0], float64)
+ y_axis = array([0, 1, 0], float64)
+ z_axis = array([0, 0, 1], float64)
+
+ # Rotated axis (real values).
+ x_real = array([cos(pi/6), sin(pi/6), 0], float64)
+ y_real = array([-sin(pi/6), cos(pi/6), 0], float64)
+ z_real = array([0, 0, 1], float64)
+
+ # Rotation.
+ x_new = dot(R, x_axis)
+ y_new = dot(R, y_axis)
+ z_new = dot(R, z_axis)
+
+ # Print out.
+ print("Rotated and true axes (beta = pi/4):")
+ print(("x rot: %s" % x_new))
+ print(("x real: %s\n" % x_real))
+ print(("y rot: %s" % y_new))
+ print(("y real: %s\n" % y_real))
+ print(("z rot: %s" % z_new))
+ print(("z real: %s\n" % z_real))
+
+ # Checks.
+ for i in range(3):
+ self.assertEqual(x_new[i], x_real[i])
+ self.assertEqual(y_new[i], y_real[i])
+ self.assertEqual(z_new[i], z_real[i])
+
+ # Axes (do everything again, this time negative!).
+ x_axis = array([-1, 0, 0], float64)
+ y_axis = array([0, -1, 0], float64)
+ z_axis = array([0, 0, -1], float64)
+
+ # Rotated axis (real values).
x_real = array([-cos(pi/6), -sin(pi/6), 0], float64)
y_real = array([sin(pi/6), -cos(pi/6), 0], float64)
z_real = array([0, 0, -1], float64)
r9476 - /1.3/test_suite/unit_tests/_maths_fns/test_rotation_matrix.py