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Copy pathtest_quaternion.py
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1202 lines (937 loc) · 41 KB
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import math
from math import pi
import numpy.testing as nt
import unittest
from unittest.mock import patch
from spatialmath import *
from spatialmath.base import *
from spatialmath.baseposematrix import BasePoseMatrix
import numpy as np
from math import pi, sin, cos
def qcompare(x, y):
if isinstance(x, Quaternion):
x = x.vec
elif isinstance(x, BasePoseMatrix):
x = x.A
if isinstance(y, Quaternion):
y = y.vec
elif isinstance(y, BasePoseMatrix):
y = y.A
nt.assert_array_almost_equal(x, y)
# straight port of the MATLAB unit tests
class TestUnitQuaternion(unittest.TestCase):
def test_constructor_variants(self):
nt.assert_array_almost_equal(UnitQuaternion().vec, np.r_[1, 0, 0, 0])
nt.assert_array_almost_equal(
UnitQuaternion.Rx(90, "deg").vec, np.r_[1, 1, 0, 0] / math.sqrt(2)
)
nt.assert_array_almost_equal(
UnitQuaternion.Rx(-90, "deg").vec, np.r_[1, -1, 0, 0] / math.sqrt(2)
)
nt.assert_array_almost_equal(
UnitQuaternion.Ry(90, "deg").vec, np.r_[1, 0, 1, 0] / math.sqrt(2)
)
nt.assert_array_almost_equal(
UnitQuaternion.Ry(-90, "deg").vec, np.r_[1, 0, -1, 0] / math.sqrt(2)
)
nt.assert_array_almost_equal(
UnitQuaternion.Rz(90, "deg").vec, np.r_[1, 0, 0, 1] / math.sqrt(2)
)
nt.assert_array_almost_equal(
UnitQuaternion.Rz(-90, "deg").vec, np.r_[1, 0, 0, -1] / math.sqrt(2)
)
np.random.seed(73)
q = UnitQuaternion.Rand(theta_range=(0.1, 0.7))
self.assertIsInstance(q, UnitQuaternion)
self.assertLessEqual(q.angvec()[0], 0.7)
self.assertGreaterEqual(q.angvec()[0], 0.1)
q = UnitQuaternion.Rand(theta_range=(0.1, 0.7))
self.assertIsInstance(q, UnitQuaternion)
self.assertLessEqual(q.angvec()[0], 0.7)
self.assertGreaterEqual(q.angvec()[0], 0.1)
def test_constructor(self):
qcompare(UnitQuaternion(), [1, 0, 0, 0])
# from S
qcompare(UnitQuaternion([1, 0, 0, 0]), np.r_[1, 0, 0, 0])
qcompare(UnitQuaternion([0, 1, 0, 0]), np.r_[0, 1, 0, 0])
qcompare(UnitQuaternion([0, 0, 1, 0]), np.r_[0, 0, 1, 0])
qcompare(UnitQuaternion([0, 0, 0, 1]), np.r_[0, 0, 0, 1])
qcompare(UnitQuaternion([2, 0, 0, 0]), np.r_[1, 0, 0, 0])
qcompare(UnitQuaternion([-2, 0, 0, 0]), np.r_[1, 0, 0, 0])
# from [S,V]
qcompare(UnitQuaternion(1, [0, 0, 0]), np.r_[1, 0, 0, 0])
qcompare(UnitQuaternion(0, [1, 0, 0]), np.r_[0, 1, 0, 0])
qcompare(UnitQuaternion(0, [0, 1, 0]), np.r_[0, 0, 1, 0])
qcompare(UnitQuaternion(0, [0, 0, 1]), np.r_[0, 0, 0, 1])
qcompare(UnitQuaternion(2, [0, 0, 0]), np.r_[1, 0, 0, 0])
qcompare(UnitQuaternion(-2, [0, 0, 0]), np.r_[1, 0, 0, 0])
qcompare(UnitQuaternion([1, 2, 3, 4]), UnitQuaternion(v=[1, 2, 3, 4]))
qcompare(UnitQuaternion(s=1, v=[2, 3, 4]), UnitQuaternion(v=[1, 2, 3, 4]))
# from R
qcompare(UnitQuaternion(np.eye(3)), [1, 0, 0, 0])
qcompare(UnitQuaternion(rotx(pi / 2)), np.r_[1, 1, 0, 0] / math.sqrt(2))
qcompare(UnitQuaternion(roty(pi / 2)), np.r_[1, 0, 1, 0] / math.sqrt(2))
qcompare(UnitQuaternion(rotz(pi / 2)), np.r_[1, 0, 0, 1] / math.sqrt(2))
qcompare(UnitQuaternion(rotx(-pi / 2)), np.r_[1, -1, 0, 0] / math.sqrt(2))
qcompare(UnitQuaternion(roty(-pi / 2)), np.r_[1, 0, -1, 0] / math.sqrt(2))
qcompare(UnitQuaternion(rotz(-pi / 2)), np.r_[1, 0, 0, -1] / math.sqrt(2))
qcompare(UnitQuaternion(rotx(pi)), np.r_[0, 1, 0, 0])
qcompare(UnitQuaternion(roty(pi)), np.r_[0, 0, 1, 0])
qcompare(UnitQuaternion(rotz(pi)), np.r_[0, 0, 0, 1])
# from SO3
qcompare(UnitQuaternion(SO3()), np.r_[1, 0, 0, 0])
qcompare(UnitQuaternion(SO3.Rx(pi / 2)), np.r_[1, 1, 0, 0] / math.sqrt(2))
qcompare(UnitQuaternion(SO3.Ry(pi / 2)), np.r_[1, 0, 1, 0] / math.sqrt(2))
qcompare(UnitQuaternion(SO3.Rz(pi / 2)), np.r_[1, 0, 0, 1] / math.sqrt(2))
qcompare(UnitQuaternion(SO3.Rx(-pi / 2)), np.r_[1, -1, 0, 0] / math.sqrt(2))
qcompare(UnitQuaternion(SO3.Ry(-pi / 2)), np.r_[1, 0, -1, 0] / math.sqrt(2))
qcompare(UnitQuaternion(SO3.Rz(-pi / 2)), np.r_[1, 0, 0, -1] / math.sqrt(2))
qcompare(UnitQuaternion(SO3.Rx(pi)), np.r_[0, 1, 0, 0])
qcompare(UnitQuaternion(SO3.Ry(pi)), np.r_[0, 0, 1, 0])
qcompare(UnitQuaternion(SO3.Rz(pi)), np.r_[0, 0, 0, 1])
# vector of SO3
q = UnitQuaternion([SO3.Rx(pi / 2), SO3.Ry(pi / 2), SO3.Rz(pi / 2)])
self.assertEqual(len(q), 3)
qcompare(q, np.array([[1, 1, 0, 0], [1, 0, 1, 0], [1, 0, 0, 1]]) / math.sqrt(2))
# from SE3
qcompare(UnitQuaternion(SE3()), np.r_[1, 0, 0, 0])
qcompare(UnitQuaternion(SE3.Rx(pi / 2)), np.r_[1, 1, 0, 0] / math.sqrt(2))
qcompare(UnitQuaternion(SE3.Ry(pi / 2)), np.r_[1, 0, 1, 0] / math.sqrt(2))
qcompare(UnitQuaternion(SE3.Rz(pi / 2)), np.r_[1, 0, 0, 1] / math.sqrt(2))
qcompare(UnitQuaternion(SE3.Rx(-pi / 2)), np.r_[1, -1, 0, 0] / math.sqrt(2))
qcompare(UnitQuaternion(SE3.Ry(-pi / 2)), np.r_[1, 0, -1, 0] / math.sqrt(2))
qcompare(UnitQuaternion(SE3.Rz(-pi / 2)), np.r_[1, 0, 0, -1] / math.sqrt(2))
qcompare(UnitQuaternion(SE3.Rx(pi)), np.r_[0, 1, 0, 0])
qcompare(UnitQuaternion(SE3.Ry(pi)), np.r_[0, 0, 1, 0])
qcompare(UnitQuaternion(SE3.Rz(pi)), np.r_[0, 0, 0, 1])
# vector of SE3
q = UnitQuaternion([SE3.Rx(pi / 2), SE3.Ry(pi / 2), SE3.Rz(pi / 2)])
self.assertEqual(len(q), 3)
qcompare(q, np.array([[1, 1, 0, 0], [1, 0, 1, 0], [1, 0, 0, 1]]) / math.sqrt(2))
# from S
M = np.identity(4)
q = UnitQuaternion(M)
self.assertEqual(len(q), 4)
qcompare(q[0], np.r_[1, 0, 0, 0])
qcompare(q[1], np.r_[0, 1, 0, 0])
qcompare(q[2], np.r_[0, 0, 1, 0])
qcompare(q[3], np.r_[0, 0, 0, 1])
# # vectorised forms of R, T
# R = []; T = []
# for theta in [-pi/2, 0, pi/2, pi]:
# R = cat(3, R, rotx(theta), roty(theta), rotz(theta))
# T = cat(3, T, trotx(theta), troty(theta), trotz(theta))
# nt.assert_array_almost_equal(UnitQuaternion(R).R, R)
# nt.assert_array_almost_equal(UnitQuaternion(T).T, T)
# copy constructor
q = UnitQuaternion(rotx(0.3))
qcompare(UnitQuaternion(q), q)
# fail when invalid arrays are provided
# invalid rotation matrix
R = 1.1 * np.eye(3)
with self.assertRaises(ValueError):
UnitQuaternion(R, check=True)
# wrong shape to be anything
R = np.zeros((5, 5))
with self.assertRaises(ValueError):
UnitQuaternion(R, check=True)
with self.assertRaises(ValueError):
UnitQuaternion(R, check=False)
def test_concat(self):
u = UnitQuaternion()
uu = UnitQuaternion([u, u, u, u])
self.assertIsInstance(uu, UnitQuaternion)
self.assertEqual(len(uu), 4)
def test_string(self):
u = UnitQuaternion()
s = str(u)
self.assertIsInstance(s, str)
self.assertTrue(s.endswith(" >>"))
self.assertEqual(s.count("\n"), 0)
q = UnitQuaternion.Rx([0.3, 0.4, 0.5])
s = str(q)
self.assertIsInstance(s, str)
self.assertEqual(s.count("\n"), 2)
def test_properties(self):
u = UnitQuaternion()
# s,v
nt.assert_array_almost_equal(UnitQuaternion([1, 0, 0, 0]).s, 1)
nt.assert_array_almost_equal(UnitQuaternion([1, 0, 0, 0]).v, [0, 0, 0])
nt.assert_array_almost_equal(UnitQuaternion([0, 1, 0, 0]).s, 0)
nt.assert_array_almost_equal(UnitQuaternion([0, 1, 0, 0]).v, [1, 0, 0])
nt.assert_array_almost_equal(UnitQuaternion([0, 0, 1, 0]).s, 0)
nt.assert_array_almost_equal(UnitQuaternion([0, 0, 1, 0]).v, [0, 1, 0])
nt.assert_array_almost_equal(UnitQuaternion([0, 0, 0, 1]).s, 0)
nt.assert_array_almost_equal(UnitQuaternion([0, 0, 0, 1]).v, [0, 0, 1])
# R,T
nt.assert_array_almost_equal(u.R, np.eye(3))
nt.assert_array_almost_equal(UnitQuaternion(rotx(pi / 2)).R, rotx(pi / 2))
nt.assert_array_almost_equal(UnitQuaternion(roty(-pi / 2)).R, roty(-pi / 2))
nt.assert_array_almost_equal(UnitQuaternion(rotz(pi)).R, rotz(pi))
qcompare(UnitQuaternion(rotx(pi / 2)).SO3(), SO3.Rx(pi / 2))
qcompare(UnitQuaternion(roty(-pi / 2)).SO3(), SO3.Ry(-pi / 2))
qcompare(UnitQuaternion(rotz(pi)).SO3(), SO3.Rz(pi))
qcompare(UnitQuaternion(rotx(pi / 2)).SE3(), SE3.Rx(pi / 2))
qcompare(UnitQuaternion(roty(-pi / 2)).SE3(), SE3.Ry(-pi / 2))
qcompare(UnitQuaternion(rotz(pi)).SE3(), SE3.Rz(pi))
def test_staticconstructors(self):
# rotation primitives
for theta in [-pi / 2, 0, pi / 2, pi]:
nt.assert_array_almost_equal(UnitQuaternion.Rx(theta).R, rotx(theta))
for theta in [-pi / 2, 0, pi / 2, pi]:
nt.assert_array_almost_equal(UnitQuaternion.Ry(theta).R, roty(theta))
for theta in [-pi / 2, 0, pi / 2, pi]:
nt.assert_array_almost_equal(UnitQuaternion.Rz(theta).R, rotz(theta))
for theta in np.r_[-pi / 2, 0, pi / 2, pi] * 180 / pi:
nt.assert_array_almost_equal(
UnitQuaternion.Rx(theta, "deg").R, rotx(theta, "deg")
)
for theta in [-pi / 2, 0, pi / 2, pi]:
nt.assert_array_almost_equal(
UnitQuaternion.Ry(theta, "deg").R, roty(theta, "deg")
)
for theta in [-pi / 2, 0, pi / 2, pi]:
nt.assert_array_almost_equal(
UnitQuaternion.Rz(theta, "deg").R, rotz(theta, "deg")
)
def test_constructor_RPY(self):
# 3 angle
q = UnitQuaternion.RPY([0.1, 0.2, 0.3])
self.assertIsInstance(q, UnitQuaternion)
self.assertEqual(len(q), 1)
nt.assert_array_almost_equal(q.R, rpy2r(0.1, 0.2, 0.3))
q = UnitQuaternion.RPY(0.1, 0.2, 0.3)
self.assertIsInstance(q, UnitQuaternion)
self.assertEqual(len(q), 1)
nt.assert_array_almost_equal(q.R, rpy2r(0.1, 0.2, 0.3))
q = UnitQuaternion.RPY(np.r_[0.1, 0.2, 0.3])
self.assertIsInstance(q, UnitQuaternion)
self.assertEqual(len(q), 1)
nt.assert_array_almost_equal(q.R, rpy2r(0.1, 0.2, 0.3))
nt.assert_array_almost_equal(
UnitQuaternion.RPY([10, 20, 30], unit="deg").R,
rpy2r(10, 20, 30, unit="deg"),
)
nt.assert_array_almost_equal(
UnitQuaternion.RPY([0.1, 0.2, 0.3], order="xyz").R,
rpy2r(0.1, 0.2, 0.3, order="xyz"),
)
angles = np.array(
[[0.1, 0.2, 0.3], [0.2, 0.3, 0.4], [0.3, 0.4, 0.5], [0.4, 0.5, 0.6]]
)
q = UnitQuaternion.RPY(angles)
self.assertIsInstance(q, UnitQuaternion)
self.assertEqual(len(q), 4)
for i in range(4):
nt.assert_array_almost_equal(q[i].R, rpy2r(angles[i, :]))
q = UnitQuaternion.RPY(angles, order="xyz")
self.assertIsInstance(q, UnitQuaternion)
self.assertEqual(len(q), 4)
for i in range(4):
nt.assert_array_almost_equal(q[i].R, rpy2r(angles[i, :], order="xyz"))
angles *= 10
q = UnitQuaternion.RPY(angles, unit="deg")
self.assertIsInstance(q, UnitQuaternion)
self.assertEqual(len(q), 4)
for i in range(4):
nt.assert_array_almost_equal(q[i].R, rpy2r(angles[i, :], unit="deg"))
def test_constructor_Eul(self):
nt.assert_array_almost_equal(
UnitQuaternion.Eul([0.1, 0.2, 0.3]).R, eul2r(0.1, 0.2, 0.3)
)
nt.assert_array_almost_equal(
UnitQuaternion.Eul([10, 20, 30], unit="deg").R,
eul2r(10, 20, 30, unit="deg"),
)
angles = np.array(
[[0.1, 0.2, 0.3], [0.2, 0.3, 0.4], [0.3, 0.4, 0.5], [0.4, 0.5, 0.6]]
)
q = UnitQuaternion.Eul(angles)
self.assertIsInstance(q, UnitQuaternion)
self.assertEqual(len(q), 4)
for i in range(4):
nt.assert_array_almost_equal(q[i].R, eul2r(angles[i, :]))
angles *= 10
q = UnitQuaternion.Eul(angles, unit="deg")
self.assertIsInstance(q, UnitQuaternion)
self.assertEqual(len(q), 4)
for i in range(4):
nt.assert_array_almost_equal(q[i].R, eul2r(angles[i, :], unit="deg"))
def test_constructor_AngVec(self):
# (theta, v)
th = 0.2
v = unitvec([1, 2, 3])
nt.assert_array_almost_equal(UnitQuaternion.AngVec(th, v).R, angvec2r(th, v))
nt.assert_array_almost_equal(UnitQuaternion.AngVec(-th, v).R, angvec2r(-th, v))
nt.assert_array_almost_equal(
UnitQuaternion.AngVec(-th, -v).R, angvec2r(-th, -v)
)
nt.assert_array_almost_equal(UnitQuaternion.AngVec(th, -v).R, angvec2r(th, -v))
def test_constructor_EulerVec(self):
# (theta, v)
th = 0.2
v = unitvec([1, 2, 3])
nt.assert_array_almost_equal(UnitQuaternion.EulerVec(th * v).R, angvec2r(th, v))
nt.assert_array_almost_equal(
UnitQuaternion.EulerVec(-th * v).R, angvec2r(-th, v)
)
def test_canonic(self):
R = rotx(0)
qcompare(UnitQuaternion(R), [1, 0, 0, 0])
R = rotx(pi / 2)
qcompare(UnitQuaternion(R), np.r_[cos(pi / 4), sin(pi / 4) * np.r_[1, 0, 0]])
R = roty(pi / 2)
qcompare(UnitQuaternion(R), np.r_[cos(pi / 4), sin(pi / 4) * np.r_[0, 1, 0]])
R = rotz(pi / 2)
qcompare(UnitQuaternion(R), np.r_[cos(pi / 4), sin(pi / 4) * np.r_[0, 0, 1]])
R = rotx(-pi / 2)
qcompare(UnitQuaternion(R), np.r_[cos(pi / 4), sin(pi / 4) * np.r_[-1, 0, 0]])
R = roty(-pi / 2)
qcompare(UnitQuaternion(R), np.r_[cos(pi / 4), sin(pi / 4) * np.r_[0, -1, 0]])
R = rotz(-pi / 2)
qcompare(UnitQuaternion(R), np.r_[cos(pi / 4), sin(pi / 4) * np.r_[0, 0, -1]])
R = rotx(pi)
qcompare(UnitQuaternion(R), np.r_[cos(pi / 2), sin(pi / 2) * np.r_[1, 0, 0]])
R = roty(pi)
qcompare(UnitQuaternion(R), np.r_[cos(pi / 2), sin(pi / 2) * np.r_[0, 1, 0]])
R = rotz(pi)
qcompare(UnitQuaternion(R), np.r_[cos(pi / 2), sin(pi / 2) * np.r_[0, 0, 1]])
R = rotx(-pi)
qcompare(UnitQuaternion(R), np.r_[cos(pi / 2), sin(pi / 2) * np.r_[1, 0, 0]])
R = roty(-pi)
qcompare(UnitQuaternion(R), np.r_[cos(pi / 2), sin(pi / 2) * np.r_[0, 1, 0]])
R = rotz(-pi)
qcompare(UnitQuaternion(R), np.r_[cos(pi / 2), sin(pi / 2) * np.r_[0, 0, 1]])
def test_conj(self):
# plain Quaternion: conj negates the vector part only
q = Quaternion([1, 2, 3, 4])
qcompare(q.conj(), [1, -2, -3, -4])
self.assertIsInstance(q.conj(), Quaternion)
# UnitQuaternion, positive scalar part: matches plain conjugate
u = UnitQuaternion(rotx(0.3))
self.assertGreater(u.A[0], 0)
qcompare(u.conj(), qconj(u.A))
self.assertIsInstance(u.conj(), UnitQuaternion)
# UnitQuaternion, negative scalar part (reachable via norm=False,
# e.g. a >180 deg rotation before its own construction-time
# canonicalization -- constructed directly here to isolate conj()):
# conj() must NOT re-canonicalize the result's sign to be
# positive, unlike normal UnitQuaternion construction. If it did,
# this would silently return -conj(u) instead of the true
# conjugate, breaking the identity u * conj(u) == 1 that
# downstream algebra (e.g. DualQuaternion) depends on.
u = UnitQuaternion(np.array([[-0.5, 0.5, 0.5, 0.5]]), norm=False)
self.assertLess(u.A[0], 0)
qcompare(u.conj(), [-0.5, -0.5, -0.5, -0.5])
self.assertIsInstance(u.conj(), UnitQuaternion)
# the algebraic identity that must hold regardless of sign
qcompare(u * u.conj(), [1, 0, 0, 0])
# multi-valued UnitQuaternion, mixed signs
us = UnitQuaternion(
np.array([[-0.5, 0.5, 0.5, 0.5], [0.5, -0.5, -0.5, -0.5]]), norm=False
)
conjs = us.conj()
qcompare(conjs.data[0], [-0.5, -0.5, -0.5, -0.5])
qcompare(conjs.data[1], [0.5, 0.5, 0.5, 0.5])
def test_convert(self):
# test conversion from rotn matrix to u.quaternion and back
R = rotx(0)
qcompare(UnitQuaternion(R).R, R)
R = rotx(pi / 2)
qcompare(UnitQuaternion(R).R, R)
R = roty(pi / 2)
qcompare(UnitQuaternion(R).R, R)
R = rotz(pi / 2)
qcompare(UnitQuaternion(R).R, R)
R = rotx(-pi / 2)
qcompare(UnitQuaternion(R).R, R)
R = roty(-pi / 2)
qcompare(UnitQuaternion(R).R, R)
R = rotz(-pi / 2)
qcompare(UnitQuaternion(R).R, R)
R = rotx(pi)
qcompare(UnitQuaternion(R).R, R)
R = roty(pi)
qcompare(UnitQuaternion(R).R, R)
R = rotz(pi)
qcompare(UnitQuaternion(R).R, R)
R = rotx(-pi)
qcompare(UnitQuaternion(R).R, R)
R = roty(-pi)
qcompare(UnitQuaternion(R).R, R)
R = rotz(-pi)
qcompare(UnitQuaternion(R).R, R)
def test_resulttype(self):
q = Quaternion([2, 0, 0, 0])
u = UnitQuaternion()
self.assertIsInstance(q * q, Quaternion)
self.assertIsInstance(q * u, Quaternion)
self.assertIsInstance(u * q, Quaternion)
self.assertIsInstance(u * u, UnitQuaternion)
# self.assertIsInstance(u.*u, UnitQuaternion)
# other combos all fail, test this?
self.assertIsInstance(u / u, UnitQuaternion)
self.assertIsInstance(u.conj(), UnitQuaternion)
self.assertIsInstance(u.inv(), UnitQuaternion)
self.assertIsInstance(u.unit(), UnitQuaternion)
self.assertIsInstance(q.unit(), UnitQuaternion)
self.assertIsInstance(q.conj(), Quaternion)
self.assertIsInstance(q + q, Quaternion)
self.assertIsInstance(q - q, Quaternion)
self.assertIsInstance(u + u, Quaternion)
self.assertIsInstance(u - u, Quaternion)
# self.assertIsInstance(q+u, Quaternion)
# self.assertIsInstance(u+q, Quaternion)
# self.assertIsInstance(q-u, Quaternion)
# self.assertIsInstance(u-q, Quaternion)
# TODO test for ValueError in these cases
self.assertIsInstance(u.SO3(), SO3)
self.assertIsInstance(u.SE3(), SE3)
def test_multiply(self):
vx = np.r_[1, 0, 0]
vy = np.r_[0, 1, 0]
vz = np.r_[0, 0, 1]
rx = UnitQuaternion.Rx(pi / 2)
ry = UnitQuaternion.Ry(pi / 2)
rz = UnitQuaternion.Rz(pi / 2)
u = UnitQuaternion()
# quat-quat product
# scalar x scalar
qcompare(rx * u, rx)
qcompare(u * rx, rx)
# vector x vector
qcompare(
UnitQuaternion([ry, rz, rx]) * UnitQuaternion([rx, ry, rz]),
UnitQuaternion([ry * rx, rz * ry, rx * rz]),
)
# scalar x vector
qcompare(
ry * UnitQuaternion([rx, ry, rz]),
UnitQuaternion([ry * rx, ry * ry, ry * rz]),
)
# vector x scalar
qcompare(
UnitQuaternion([rx, ry, rz]) * ry,
UnitQuaternion([rx * ry, ry * ry, rz * ry]),
)
# quatvector product
# scalar x scalar
qcompare(rx * vy, vz)
# scalar x vector
nt.assert_array_almost_equal(ry * np.c_[vx, vy, vz], np.c_[-vz, vy, vx])
# vector x scalar
nt.assert_array_almost_equal(
UnitQuaternion([ry, rz, rx]) * vy, np.c_[vy, -vx, vz]
)
def test_matmul(self):
rx = UnitQuaternion.Rx(pi / 2)
ry = UnitQuaternion.Ry(pi / 2)
rz = UnitQuaternion.Rz(pi / 2)
qcompare(rx @ ry, rx * ry)
qcompare(
UnitQuaternion([ry, rz, rx]) @ UnitQuaternion([rx, ry, rz]),
UnitQuaternion([ry * rx, rz * ry, rx * rz]),
)
# @= is @ as an augmented assignment, not *=
q = rx
q @= ry
qcompare(q, rx @ ry)
# def multiply_test_normalized(self):
# vx = [1, 0, 0]; vy = [0, 1, 0]; vz = [0, 0, 1]
# rx = UnitQuaternion.Rx(pi/2)
# ry = UnitQuaternion.Ry(pi/2)
# rz = UnitQuaternion.Rz(pi/2)
# u = UnitQuaternion()
# # quat-quat product
# # scalar x scalar
# nt.assert_array_almost_equal(double(rx.*u), double(rx))
# nt.assert_array_almost_equal(double(u.*rx), double(rx))
# # shouldn't make that much difference here
# nt.assert_array_almost_equal(double(rx.*ry), double(rx*ry))
# nt.assert_array_almost_equal(double(rx.*rz), double(rx*rz))
# #vector x vector
# #nt.assert_array_almost_equal([ry, rz, rx] .* [rx, ry, rz], [ry.*rx, rz.*ry, rx.*rz])
# # scalar x vector
# #nt.assert_array_almost_equal(ry .* [rx, ry, rz], [ry.*rx, ry.*ry, ry.*rz])
# #vector x scalar
# #nt.assert_array_almost_equal([rx, ry, rz] .* ry, [rx.*ry, ry.*ry, rz.*ry])
def test_divide(self):
rx = UnitQuaternion.Rx(pi / 2)
ry = UnitQuaternion.Ry(pi / 2)
rz = UnitQuaternion.Rz(pi / 2)
u = UnitQuaternion()
# scalar / scalar
# implicity tests inv
qcompare(rx / u, rx)
qcompare(ry / ry, u)
# vector /vector
qcompare(
UnitQuaternion([ry, rz, rx]) / UnitQuaternion([rx, ry, rz]),
UnitQuaternion([ry / rx, rz / ry, rx / rz]),
)
# vector / scalar
qcompare(
UnitQuaternion([rx, ry, rz]) / ry,
UnitQuaternion([rx / ry, ry / ry, rz / ry]),
)
# scalar /vector
qcompare(
ry / UnitQuaternion([rx, ry, rz]),
UnitQuaternion([ry / rx, ry / ry, ry / rz]),
)
def test_angle(self):
# angle between quaternions
uq1 = UnitQuaternion.Rx(0.1)
uq2 = UnitQuaternion.Ry(0.1)
for metric in range(5):
self.assertEqual(uq1.angdist(other=uq1, metric=metric), 0.0)
self.assertEqual(uq2.angdist(other=uq2, metric=metric), 0.0)
self.assertEqual(
uq1.angdist(other=uq2, metric=metric),
uq2.angdist(other=uq1, metric=metric),
)
self.assertTrue(uq1.angdist(other=uq2, metric=metric) > 0)
def test_conversions(self):
# , 3 angle
qcompare(UnitQuaternion.RPY([0.1, 0.2, 0.3]).rpy(), [0.1, 0.2, 0.3])
qcompare(UnitQuaternion.RPY(0.1, 0.2, 0.3).rpy(), [0.1, 0.2, 0.3])
qcompare(UnitQuaternion.Eul([0.1, 0.2, 0.3]).eul(), [0.1, 0.2, 0.3])
qcompare(UnitQuaternion.Eul(0.1, 0.2, 0.3).eul(), [0.1, 0.2, 0.3])
qcompare(
UnitQuaternion.RPY([10, 20, 30], unit="deg").R,
rpy2r(10, 20, 30, unit="deg"),
)
qcompare(
UnitQuaternion.Eul([10, 20, 30], unit="deg").R,
eul2r(10, 20, 30, unit="deg"),
)
# (theta, v)
th = 0.2
v = unitvec([1, 2, 3])
[a, b] = UnitQuaternion.AngVec(th, v).angvec()
self.assertAlmostEqual(a, th)
nt.assert_array_almost_equal(b, v)
[a, b] = UnitQuaternion.AngVec(-th, v).angvec()
self.assertAlmostEqual(a, th)
nt.assert_array_almost_equal(b, -v)
# null rotation case
th = 0
v = unitvec([1, 2, 3])
[a, b] = UnitQuaternion.AngVec(th, v).angvec()
self.assertAlmostEqual(a, th)
# SO3 convert to SO3 class
# SE3 convert to SE3 class
def test_miscellany(self):
# AbsTol not used since Quaternion supports eq() operator
rx = UnitQuaternion.Rx(pi / 2)
ry = UnitQuaternion.Ry(pi / 2)
rz = UnitQuaternion.Rz(pi / 2)
u = UnitQuaternion()
# norm
qcompare(rx.norm(), 1)
qcompare(UnitQuaternion([rx, ry, rz]).norm(), [1, 1, 1])
# unit
qcompare(rx.unit(), rx)
qcompare(UnitQuaternion([rx, ry, rz]).unit(), UnitQuaternion([rx, ry, rz]))
# inner
nt.assert_array_almost_equal(u.inner(u), 1)
nt.assert_array_almost_equal(rx.inner(ry), 0.5)
nt.assert_array_almost_equal(rz.inner(rz), 1)
q = rx * ry * rz
qcompare(q**0, u)
qcompare(q ** (-1), q.inv())
qcompare(q**2, q * q)
# angle
# self.assertEqual(angle(u, u), 0)
# self.assertEqual(angle(u, rx), pi/4)
# self.assertEqual(angle(u, [rx, u]), pi/4*np.r_[1, 0])
# self.assertEqual(angle([rx, u], u), pi/4*np.r_[1, 0])
# self.assertEqual(angle([rx, u], [u, rx]), pi/4*np.r_[1, 1])
# TODO angle
# increment
# w = [0.02, 0.03, 0.04]
# nt.assert_array_almost_equal(rx.increment(w), rx*UnitQuaternion.omega(w))
def test_interp(self):
rx = UnitQuaternion.Rx(pi / 2)
ry = UnitQuaternion.Ry(pi / 2)
rz = UnitQuaternion.Rz(pi / 2)
u = UnitQuaternion()
q = UnitQuaternion.RPY([0.2, 0.3, 0.4])
# from null
qcompare(q.interp1(0), u)
qcompare(q.interp1(1), q)
# self.assertEqual(length(q.interp(linspace(0,1, 10))), 10)
# self.assertTrue(all( q.interp([0, 1]) == [u, q]))
# TODO vectorizing
q0_5 = q.interp1(0.5)
qcompare(q0_5 * q0_5, q)
qq = rx.interp1(11)
self.assertEqual(len(qq), 11)
# between two quaternions
qcompare(q.interp(rx, 0), q)
qcompare(q.interp(rx, 1), rx)
# test vectorised results
qq = q.interp(rx, [0, 1])
self.assertEqual(len(qq), 2)
qcompare(qq[0], q)
qcompare(qq[1], rx)
qq = rx.interp(q, 11)
self.assertEqual(len(qq), 11)
# self.assertTrue(all( q.interp([0, 1], dest=rx, ) == [q, rx]))
# test shortest option
# q1 = UnitQuaternion.Rx(0.9*pi)
# q2 = UnitQuaternion.Rx(-0.9*pi)
# qq = q1.interp(q2, 11)
# qcompare( qq(6), UnitQuaternion.Rx(0) )
# qq = q1.interp(q2, 11, 'shortest')
# qcompare( qq(6), UnitQuaternion.Rx(pi) )
# TODO interp
def test_interp_same_rotation(self):
# endpoints that are the same rotation make the slerp weights singular
q = UnitQuaternion.Rx(0.3)
for s in (0, 0.4, 1):
for shortest in (False, True):
qcompare(q.interp(q, s, shortest=shortest), q)
qcompare(
q.interp(UnitQuaternion.Rx(0.3 + 1e-9), s, shortest=shortest), q
)
qq = q.interp(q, 5)
self.assertEqual(len(qq), 5)
qcompare(qq[3], q)
u = UnitQuaternion()
for s in (0, 0.4, 1):
qcompare(u.interp1(s), u)
qcompare(UnitQuaternion.Rx(1e-9).interp1(s), u)
self.assertEqual(len(u.interp1(5)), 5)
# Rx(pi) and Rx(-pi) are the same rotation, with a dot product of -1
p = UnitQuaternion.Rx(pi)
m = UnitQuaternion.Rx(-pi)
self.assertAlmostEqual(np.dot(p.vec, m.vec), -1)
for shortest in (False, True):
for s in (0, 0.4, 1):
qi = p.interp(m, s, shortest=shortest)
self.assertAlmostEqual(np.linalg.norm(qi.vec), 1)
nt.assert_array_almost_equal(qi.R, p.R)
for qi in p.interp(m, 5):
nt.assert_array_almost_equal(qi.R, p.R)
def test_interp_prepares_slerp_once(self):
q0 = UnitQuaternion.RPY([0.2, 0.3, 0.4])
q1 = UnitQuaternion.RPY([-0.3, 0.1, 0.2])
for interpolate in (lambda: q0.interp1(5), lambda: q0.interp(q1, 5)):
with patch("spatialmath.base.quaternions.np.dot", wraps=np.dot) as dot:
self.assertEqual(len(interpolate()), 5)
self.assertEqual(dot.call_count, 1)
def test_increment(self):
q = UnitQuaternion()
q.increment([0, 0, 0])
qcompare(q, UnitQuaternion())
q.increment([0, 0, 0], normalize=True)
qcompare(q, UnitQuaternion())
for i in range(10):
q.increment([0.1, 0, 0])
qcompare(q, UnitQuaternion.Rx(1))
q = UnitQuaternion()
for i in range(10):
q.increment([0.1, 0, 0], normalize=True)
qcompare(q, UnitQuaternion.Rx(1))
def test_eq(self):
q1 = UnitQuaternion([0, 1, 0, 0])
q2 = UnitQuaternion([0, -1, 0, 0])
q3 = UnitQuaternion.Rz(pi / 2)
self.assertTrue(q1 == q1)
self.assertTrue(q2 == q2)
self.assertTrue(q3 == q3)
self.assertTrue(q1 == q2) # because of double wrapping
self.assertFalse(q1 == q3)
nt.assert_array_almost_equal(
UnitQuaternion([q1, q1, q1]) == UnitQuaternion([q1, q1, q1]),
[True, True, True],
)
nt.assert_array_almost_equal(
UnitQuaternion([q1, q2, q3]) == UnitQuaternion([q1, q2, q3]),
[True, True, True],
)
nt.assert_array_almost_equal(
UnitQuaternion([q1, q1, q3]) == q1, [True, True, False]
)
nt.assert_array_almost_equal(
q3 == UnitQuaternion([q1, q1, q3]), [False, False, True]
)
def test_logical(self):
rx = UnitQuaternion.Rx(pi / 2)
ry = UnitQuaternion.Ry(pi / 2)
# equality tests
self.assertTrue(rx == rx)
self.assertFalse(rx != rx)
self.assertFalse(rx == ry)
def test_dot(self):
q = UnitQuaternion()
omega = np.r_[1, 2, 3]
nt.assert_array_almost_equal(q.dot(omega), np.r_[0, omega / 2])
nt.assert_array_almost_equal(q.dotb(omega), np.r_[0, omega / 2])
q = UnitQuaternion.Rx(pi / 2)
qcompare(q.dot(omega), 0.5 * Quaternion.Pure(omega) * q)
qcompare(q.dotb(omega), 0.5 * q * Quaternion.Pure(omega))
def test_matrix(self):
q1 = UnitQuaternion.RPY([0.1, 0.2, 0.3])
q2 = UnitQuaternion.RPY([0.2, 0.3, 0.4])
qcompare(q1 * q2, q1.matrix @ q2.vec)
def test_vec3(self):
q1 = UnitQuaternion.RPY([0.1, 0.2, 0.3])
q2 = UnitQuaternion.RPY([0.2, 0.3, 0.4])
q12 = q1 * q2
q1v = q1.vec3
q2v = q2.vec3
q12v = UnitQuaternion.qvmul(q1v, q2v)
q12_ = UnitQuaternion.Vec3(q12v)
qcompare(q12, q12_)
# def test_display(self):
# ry = UnitQuaternion.Ry(pi/2)
# ry.plot()
# h = ry.plot()
# ry.animate()
# ry.animate('rgb')
# ry.animate( UnitQuaternion.Rx(pi/2), 'rgb' )
class TestQuaternion(unittest.TestCase):
def test_constructor(self):
q = Quaternion()
self.assertEqual(len(q), 1)
self.assertIsInstance(q, Quaternion)
nt.assert_array_almost_equal(Quaternion().vec, [0, 0, 0, 0])
# from S
nt.assert_array_almost_equal(Quaternion([1, 0, 0, 0]).vec, [1, 0, 0, 0])
nt.assert_array_almost_equal(Quaternion([0, 1, 0, 0]).vec, [0, 1, 0, 0])
nt.assert_array_almost_equal(Quaternion([0, 0, 1, 0]).vec, [0, 0, 1, 0])
nt.assert_array_almost_equal(Quaternion([0, 0, 0, 1]).vec, [0, 0, 0, 1])
nt.assert_array_almost_equal(Quaternion([2, 0, 0, 0]).vec, [2, 0, 0, 0])
nt.assert_array_almost_equal(Quaternion([-2, 0, 0, 0]).vec, [-2, 0, 0, 0])
# from [S,V]
nt.assert_array_almost_equal(Quaternion(1, [0, 0, 0]).vec, [1, 0, 0, 0])
nt.assert_array_almost_equal(Quaternion(0, [1, 0, 0]).vec, [0, 1, 0, 0])
nt.assert_array_almost_equal(Quaternion(0, [0, 1, 0]).vec, [0, 0, 1, 0])
nt.assert_array_almost_equal(Quaternion(0, [0, 0, 1]).vec, [0, 0, 0, 1])
nt.assert_array_almost_equal(Quaternion(2, [0, 0, 0]).vec, [2, 0, 0, 0])
nt.assert_array_almost_equal(Quaternion(-2, [0, 0, 0]).vec, [-2, 0, 0, 0])
qcompare(Quaternion([1, 2, 3, 4]), Quaternion(v=[1, 2, 3, 4]))
qcompare(Quaternion(s=1, v=[2, 3, 4]), Quaternion(v=[1, 2, 3, 4]))
# pure
v = [5, 6, 7]
nt.assert_array_almost_equal(
Quaternion.Pure(v).vec,
[
0,
]
+ v,
)
# tc.verifyError( @() Quaternion.pure([1, 2]), 'SMTB:Quaternion:badarg')
# copy constructor
q = Quaternion([1, 2, 3, 4])
nt.assert_array_almost_equal(Quaternion(q).vec, q.vec)
# errors
# tc.verifyError( @() Quaternion(2), 'SMTB:Quaternion:badarg')
# tc.verifyError( @() Quaternion([1, 2, 3]), 'SMTB:Quaternion:badarg')
def test_string(self):
u = Quaternion()
s = str(u)
self.assertIsInstance(s, str)
self.assertTrue(s.endswith(" >"))
self.assertEqual(s.count("\n"), 0)
self.assertEqual(len(s), 37)
q = Quaternion([u, u, u])
s = str(q)
self.assertIsInstance(s, str)
self.assertEqual(s.count("\n"), 2)
def test_properties(self):
q = Quaternion([1, 2, 3, 4])
self.assertEqual(q.s, 1)
nt.assert_array_almost_equal(q.v, np.r_[2, 3, 4])
nt.assert_array_almost_equal(q.vec, np.r_[1, 2, 3, 4])
def log_test_exp(self):
q1 = Quaternion([4, 3, 2, 1])
q2 = Quaternion([-1, 2, -3, 4])
nt.assert_array_almost_equal(exp(log(q1)), q1)
nt.assert_array_almost_equal(exp(log(q2)), q2)
def test_log(self):
q1 = Quaternion([4, 3, 2, 1])
q2 = Quaternion([-1, 2, -3, 4])
self.assertTrue(isscalar(q1.log().s))
self.assertTrue(isvector(q1.log().v, 3))
nt.assert_array_almost_equal(q1.log().exp(), q1)
nt.assert_array_almost_equal(q2.log().exp(), q2)
q = Quaternion([q1, q2, q1, q2])
qlog = q.log()
nt.assert_array_almost_equal(qlog[0].exp(), q1)
nt.assert_array_almost_equal(qlog[1].exp(), q2)
nt.assert_array_almost_equal(qlog[2].exp(), q1)
nt.assert_array_almost_equal(qlog[3].exp(), q2)
q = UnitQuaternion() # identity
qlog = q.log()
nt.assert_array_almost_equal(qlog.vec, np.zeros(4))
qq = qlog.exp()
self.assertIsInstance(qq, UnitQuaternion)
nt.assert_array_almost_equal(qq.vec, np.r_[1, 0, 0, 0])
def test_concat(self):
u = Quaternion()
uu = Quaternion([u, u, u, u])
self.assertIsInstance(uu, Quaternion)
self.assertEqual(len(uu), 4)
def primitive_test_convert(self):
# s,v
nt.assert_array_almost_equal(Quaternion([1, 0, 0, 0]).s, 1)
nt.assert_array_almost_equal(Quaternion([1, 0, 0, 0]).v, [0, 0, 0])
nt.assert_array_almost_equal(Quaternion([0, 1, 0, 0]).s, 0)
nt.assert_array_almost_equal(Quaternion([0, 1, 0, 0]).v, [1, 0, 0])
nt.assert_array_almost_equal(Quaternion([0, 0, 1, 0]).s, 0)
nt.assert_array_almost_equal(Quaternion([0, 0, 1, 0]).v, [0, 1, 0])
nt.assert_array_almost_equal(Quaternion([0, 0, 0, 1]).s, 0)