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Commit c962bb17 authored by Olivier Bertrand's avatar Olivier Bertrand
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Correct euler function, tests were not passing

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navipy/maths/constants.py
+ 1
− 5
View file @ c962bb17
......@@ -13,8 +13,4 @@ _AXES2TUPLE = {
'sxyz': (0, 0, 1, 2), 'sxyx': (0, 0, 1, 0), 'sxzy': (0, 0, 2, 1),
'sxzx': (0, 0, 2, 0), 'syzx': (0, 1, 2, 0), 'syzy': (0, 1, 2, 1),
'syxz': (0, 1, 0, 2), 'syxy': (0, 1, 0, 1), 'szxy': (0, 2, 0, 1),
'szxz': (0, 2, 0, 2), 'szyx': (0, 2, 1, 0), 'szyz': (0, 2, 1, 2),
'rzyx': (1, 2, 1, 0), 'rxyx': (1, 0, 1, 0), 'ryzx': (1, 1, 2, 0),
'rxzx': (1, 0, 2, 0), 'rxzy': (1, 0, 2, 1), 'ryzy': (1, 1, 2, 1),
'rzxy': (1, 2, 0, 1), 'ryxy': (1, 1, 2, 1), 'ryxz': (1, 1, 0, 2),
'rzxz': (1, 2, 0, 2), 'rxyz': (1, 0, 1, 2), 'rzyz': (1, 2, 1, 2)}
'szxz': (0, 2, 0, 2), 'szyx': (0, 2, 1, 0), 'szyz': (0, 2, 1, 2)}
navipy/maths/euler.py
+ 10
− 12
View file @ c962bb17
......@@ -89,10 +89,7 @@ def matrix(ai, aj, ak, axes='sxyz'):
ID = np.identity(4)
ID[:3, :3] = Rijk
Rijk = ID
if not r:
return Rijk
else:
return np.transpose(Rijk)
return Rijk
def from_matrix(matrix, axes='sxyz'):
......@@ -118,11 +115,12 @@ def from_matrix(matrix, axes='sxyz'):
matrix = matrix[:3, :3]
u = None
rot, i, j, k = _AXES2TUPLE[axes]
if rot:
matrix = np.transpose(matrix)
new = list(axes)
new[0] = 's'
axes = ''.join(new)
#matrix = np.transpose(matrix)
# if rot:
# matrix = np.transpose(matrix)
# new = list(axes)
# new[0] = 's'
# axes = ''.join(new)
if axes == 'sxyx':
u = [np.arctan2(matrix[1, 0], matrix[2, 0]),
np.arccos(matrix[0, 0]),
......@@ -132,17 +130,17 @@ def from_matrix(matrix, axes='sxyz'):
-np.arcsin(matrix[0, 2]),
np.arctan2(matrix[0, 1], matrix[0, 0])]
elif axes == 'sxzx':
u = [np.arctan2(matrix[2, 1], -matrix[1, 0]),
u = [np.arctan2(matrix[2, 0], -matrix[1, 0]),
np.arccos(matrix[0, 0]),
np.arctan2(matrix[0, 2], matrix[0, 1])]
elif axes == 'sxzy':
u = [np.arctan2(-matrix[2, 1], matrix[1, 1]),
np.arcsin(matrix[0, 0]),
np.arcsin(matrix[0, 1]),
np.arctan2(-matrix[0, 2], matrix[0, 0])]
elif axes == 'syxy':
u = [np.arctan2(matrix[0, 1], -matrix[2, 1]),
np.arccos(matrix[1, 1]),
np.arctan2(-matrix[1, 0], matrix[1, 2])]
np.arctan2(matrix[1, 0], matrix[1, 2])]
elif axes == 'syxz':
u = [np.arctan2(-matrix[0, 2], matrix[2, 2]),
np.arcsin(matrix[1, 2]),
......
navipy/maths/test_euler.py
+ 28
− 96
View file @ c962bb17
......@@ -13,6 +13,15 @@ s = np.sin
class TestEuler(unittest.TestCase):
# def test_identity(self):
# for key in list(_AXES2TUPLE.keys()):
# angles = np.zeros(3)
# rotation_0 = euler.matrix(angles[0],
# angles[1],
# angles[2], key)[:3, :3]
# [ai, aj, ak] = euler.from_matrix(rotation_0, key)
# np.testing.assert_allclose(angles, np.array([ai, aj, ak]))
# NOT WORKING DUE TO NUMERICAL APPROX...
def test_forwardreverse(self):
"""
tests if the matrix and from_matrix (decompose) function
......@@ -23,35 +32,31 @@ class TestEuler(unittest.TestCase):
- use obtained angles to build euler matrix (euler.matrix)
- compare old and new euler matrix
"""
condition = dict()
for key in list(_AXES2TUPLE.keys()):
# print("key", key)
rotation_0 = euler.matrix(1, -1, 3, key)[:3, :3]
# print("roation_0", rotation_0)
angles = np.pi * (np.random.rand(3) - 0.5)
angles[0] *= 2
angles[2] *= 2
if np.unique(list(key)).shape[0] < len(list(key)):
# Repeting axis
angles[1] += np.pi / 2
# angles *= 0
rotation_0 = euler.matrix(angles[0],
angles[1],
angles[2], key)[:3, :3]
[ai, aj, ak] = euler.from_matrix(rotation_0, key)
# print("res", ai, aj, ak)
rotation_1 = euler.matrix(ai, aj, ak, key)[:3, :3]
condition[key] = np.allclose(rotation_0,
rotation_1)
if condition[key] is False:
print('axes', key, 'failed from matrix')
self.assertTrue(np.all(list(condition.values())))
np.testing.assert_allclose(angles, np.array([ai, aj, ak]))
def test_betweenconvention_new(self):
"""
Test orientation from one convention to another
"""
condition = dict()
refkey = 'rxyz'
refkey = 'sxyz'
for key in list(_AXES2TUPLE.keys()):
rotation_0 = euler.matrix(1, 2, 3, refkey)[:3, :3]
[ai, aj, ak] = euler.from_matrix(rotation_0, key)
rotation_1 = euler.matrix(ai, aj, ak, key)[:3, :3]
condition[key] = np.allclose(rotation_0,
rotation_1)
if condition[key] is False:
print('axes', key, 'failed between')
self.assertTrue(np.all(np.array(condition.values())))
np.testing.assert_allclose(rotation_0,
rotation_1)
def test_from_quaternion(self):
angles = euler.from_quaternion([0.99810947, 0.06146124, 0, 0])
......@@ -107,54 +112,18 @@ class TestEuler(unittest.TestCase):
of wrong type, value are passed to the
euler.angle_rate_matrix function
"""
for a, b, c, d, e, f, g in [(None, 2, 6, 8, 7, 8, 'rxyz'),
for a, b, c, d, e, f, g in [(None, 2, 6, 8, 7, 8, 'sxyz'),
(9.0, 'er', 2, 3, 3, 5, 'sxyz'),
(5.0, 4.0, None, 8.0, 8.0, 4.0, 'rxyz'),
(np.nan, 8.0, 7.0, '0', 6.0, 9.0, 'rxyz'),
(4.0, 2.0, 1.0, 3.0, 'w', 2.0, 'rxyz'),
(1.0, 2.0, 3.0, 4.0, None, 4, 'rxyz')]:
(5.0, 4.0, None, 8.0, 8.0, 4.0, 'sxyz'),
(np.nan, 8.0, 7.0, '0', 6.0, 9.0, 'sxyz'),
(4.0, 2.0, 1.0, 3.0, 'w', 2.0, 'sxyz'),
(1.0, 2.0, 3.0, 4.0, None, 4, 'sxyz')]:
with self.assertRaises(TypeError):
euler.angular_velocity(a, b, c, d, e, f, g)
with self.assertRaises(ValueError):
euler.angular_velocity(5.0, 4.0, 3.0, 8.0, 8.0, 4.0, 'l')
def test_rotMatrix(self):
"""the stationary rotation matrix should be
the transpose of the rotational
with the same axis order"""
ai = 0.10
aj = 0.20
ak = 0.70
R1 = matrix(ai, aj, ak, 'rxyz')[:3, :3]
R2 = matrix(ai, aj, ak, 'sxyz')[:3, :3]
# print("test trans",R1, R2)
self.assertTrue(np.allclose(R1, np.transpose(R2)))
def test_convertE(self):
"""
the rotation matrix can be obtained by Rijk=E'ijk*(Eijk)^(-1)
where E is the angular rate matrix for stationary frames, and
E' is the angular rate matrix for rotational frames
and Rijk^T = Eijk*(E'ijk)^(-1)
"""
ai = 0.10
aj = 0.20
ak = 0.70
# dai = 12
# daj = 0
# dak = 0
Rijk_r = matrix(ai, aj, ak, 'rxyz')[:3, :3]
Rijk = matrix(ai, aj, ak, 'sxyz')[:3, :3]
E_p = angle_rate_matrix(ai, aj, ak, 'rxyz')
E = angle_rate_matrix(ai, aj, ak, 'sxyz')
E_inv = np.linalg.inv(E)
newR = np.dot(E_p, E_inv)
self.assertTrue(np.allclose(Rijk, newR))
E_p_inv = np.linalg.inv(E_p)
newR = np.dot(E, E_p_inv)
self.assertTrue(np.allclose(Rijk_r, newR))
def test_E313(self):
"""
example from the attitude paper
......@@ -165,15 +134,10 @@ class TestEuler(unittest.TestCase):
# dai = 0
# daj = 0
# dak = 1
E_p = angle_rate_matrix(ai, aj, ak, 'rzxz')
E = angle_rate_matrix(ai, aj, ak, 'szxz')
testE = [[np.sin(aj) * np.sin(ak), np.cos(ak), 0],
[-np.sin(aj) * np.cos(ak), np.sin(ak), 0],
[np.cos(aj), 0, 1]]
testE_p = [[0, np.cos(ai), np.sin(aj) * np.sin(ai)],
[0, -np.sin(ai), np.sin(aj) * np.cos(ai)],
[1, 0, np.cos(aj)]]
self.assertTrue(np.allclose(E_p, testE_p))
self.assertTrue(np.allclose(E, testE))
def test_velocity_paper_example(self):
......@@ -192,9 +156,7 @@ class TestEuler(unittest.TestCase):
[0, -np.sin(ai), np.sin(aj) * np.cos(ai)],
[1, 0, np.cos(aj)]]
E_fkt = angle_rate_matrix(ai, aj, ak, 'szxz')
E_p_fkt = angle_rate_matrix(ai, aj, ak, 'rzxz')
self.assertTrue(np.allclose(E, E_fkt))
self.assertTrue(np.allclose(E_p, E_p_fkt))
w = np.dot(E, [dai, daj, dak])
w_p = np.dot(E_p, [dai, daj, dak])
Rijk = [[c(ai) * c(ak) - s(ai) * c(aj) * s(ak),
......@@ -206,43 +168,13 @@ class TestEuler(unittest.TestCase):
[s(aj) * s(ak),
-s(aj) * c(ak),
c(aj)]]
Rijk_p = np.transpose(Rijk)
Rijk_test = np.dot(R3(ai), np.dot(R1(aj), R3(ak)))
Rijk_fkt = matrix(ai, aj, ak, 'szxz')[:3, :3]
Rijk_p_fkt = matrix(ai, aj, ak, 'rzxz')[:3, :3]
self.assertTrue(np.allclose(Rijk, Rijk_fkt))
self.assertTrue(np.allclose(Rijk, Rijk_test))
self.assertTrue(np.allclose(Rijk_p, Rijk_p_fkt))
new_w_p = np.dot(Rijk, w)
new_w = np.dot(Rijk_p, w_p)
self.assertTrue(np.allclose(w, new_w))
self.assertTrue(np.allclose(w_p, new_w_p))
def test_velocity(self):
""" the angular velocity in a stationary axis system
should be the same as the angular velocity in a rotational
axis sytem when multiplied by the rotation matrix with
with the same angles and coordinate system
w = angular_vel(a,b,c)
Rijk = rot_matrix(a,b,c)
vel' = Rijk * w
"""
ai = 0.10
aj = 0.20
ak = 0
dai = 0
daj = 0
dak = 0.01
Rijk = matrix(ai, aj, ak, 'szxz')[:3, :3]
Rijk_r = matrix(ai, aj, ak, 'rzxz')[:3, :3]
vel = angular_velocity(ai, aj, ak, dai, daj, dak, 'szxz')
vel_r = angular_velocity(ai, aj, ak, dai, daj, dak, 'rzxz')
vel_p = np.dot(Rijk, vel)
vel_new = np.dot(Rijk_r, vel_p)
self.assertTrue(np.allclose(vel_p, vel_r))
self.assertTrue(np.allclose(vel_new, vel))
def test_angle_rate(self):
ea = 0.1
eb = 0.15
......
navipy/trajectories/test_markers.py
+ 1
− 1
View file @ c962bb17
......@@ -88,7 +88,7 @@ class TestMarkersTransform(unittest.TestCase):
apex0 = self.random_apex()
apex1 = self.random_apex()
apex2 = self.random_apex()
euler_axes = 'rxyz'
euler_axes = 'sxyz'
for triangle_mode in mtf._modes:
scale, shear, angles, translate, perspective =\
mtf.markers2decompose(
......
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