def test_cross():
assert cross(A.x, A.x) == 0
assert cross(A.x, A.y) == A.z
assert cross(A.x, A.z) == -A.y
assert cross(A.y, A.x) == -A.z
assert cross(A.y, A.y) == 0
assert cross(A.y, A.z) == A.x
assert cross(A.z, A.x) == A.y
assert cross(A.z, A.y) == -A.x
assert cross(A.z, A.z) == 0
def test_cross():
assert cross(A.x, A.x) == 0
assert cross(A.x, A.y) == A.z
assert cross(A.x, A.z) == -A.y
assert cross(A.y, A.x) == -A.z
assert cross(A.y, A.y) == 0
assert cross(A.y, A.z) == A.x
assert cross(A.z, A.x) == A.y
assert cross(A.z, A.y) == -A.x
assert cross(A.z, A.z) == 0
def _orient_frames(self):
self.child.frame.orient_axis(self.parent.frame, self.parent_axis, 0)
angle, axis = self._alignment_rotation(self.parent_axis,
self.child_axis)
odd_multiple_pi = False
if angle % pi == 0:
if (angle / pi).is_odd:
odd_multiple_pi = True
with warnings.catch_warnings():
warnings.filterwarnings("ignore", category=UserWarning)
if axis != Vector(0) or odd_multiple_pi:
if odd_multiple_pi:
axis = cross(self.parent_axis, self._generate_vector())
int_frame = ReferenceFrame('int_frame')
int_frame.orient_axis(self.child.frame, self.child_axis, 0)
int_frame.orient_axis(self.parent.frame, axis, angle)
self.child.frame.orient_axis(int_frame, self.parent_axis,
self.coordinates[0])
else:
self.child.frame.orient_axis(self.parent.frame,
self.parent_axis,
self.coordinates[0])
def _generate_vector(self):
parent_frame = self.parent.frame
components = self.parent_axis.to_matrix(parent_frame)
x, y, z = components[0], components[1], components[2]
if x != 0:
if y != 0:
if z != 0:
return cross(self.parent_axis, parent_frame.x)
if z != 0:
return parent_frame.y
return parent_frame.z
if x == 0:
if y != 0:
if z != 0:
return parent_frame.x
return parent_frame.x
return parent_frame.y
def _orient_frames(self):
self.child.frame.orient_axis(self.parent.frame, self.parent_axis, 0)
angle, axis = self._alignment_rotation(self.parent_axis,
self.child_axis)
with warnings.catch_warnings():
warnings.filterwarnings("ignore", category=UserWarning)
if axis != Vector(0) or angle == pi:
if angle == pi:
axis = cross(self.parent_axis, self._generate_vector())
int_frame = ReferenceFrame('int_frame')
int_frame.orient_axis(self.child.frame, self.child_axis, 0)
int_frame.orient_axis(self.parent.frame, axis, angle)
self.child.frame.orient_axis(int_frame, self.parent_axis,
self.coordinates[0])
else:
self.child.frame.orient_axis(self.parent.frame,
self.parent_axis,
self.coordinates[0])
def _alignment_rotation(self, parent, child):
# Returns the axis and angle between two axis(vectors).
angle = parent.angle_between(child)
axis = cross(child, parent).normalize()
return angle, axis
def test_operator_match():
"""Test that the output of dot, cross, outer functions match
operator behavior.
"""
A = ReferenceFrame('A')
v = A.x + A.y
d = v | v
zerov = Vector(0)
zerod = Dyadic(0)
# dot products
assert d & d == dot(d, d)
assert d & zerod == dot(d, zerod)
assert zerod & d == dot(zerod, d)
assert d & v == dot(d, v)
assert v & d == dot(v, d)
assert d & zerov == dot(d, zerov)
assert zerov & d == dot(zerov, d)
raises(TypeError, lambda: dot(d, S(0)))
raises(TypeError, lambda: dot(S(0), d))
raises(TypeError, lambda: dot(d, 0))
raises(TypeError, lambda: dot(0, d))
assert v & v == dot(v, v)
assert v & zerov == dot(v, zerov)
assert zerov & v == dot(zerov, v)
raises(TypeError, lambda: dot(v, S(0)))
raises(TypeError, lambda: dot(S(0), v))
raises(TypeError, lambda: dot(v, 0))
raises(TypeError, lambda: dot(0, v))
# cross products
raises(TypeError, lambda: cross(d, d))
raises(TypeError, lambda: cross(d, zerod))
raises(TypeError, lambda: cross(zerod, d))
assert d ^ v == cross(d, v)
assert v ^ d == cross(v, d)
assert d ^ zerov == cross(d, zerov)
assert zerov ^ d == cross(zerov, d)
assert zerov ^ d == cross(zerov, d)
raises(TypeError, lambda: cross(d, S(0)))
raises(TypeError, lambda: cross(S(0), d))
raises(TypeError, lambda: cross(d, 0))
raises(TypeError, lambda: cross(0, d))
assert v ^ v == cross(v, v)
assert v ^ zerov == cross(v, zerov)
assert zerov ^ v == cross(zerov, v)
raises(TypeError, lambda: cross(v, S(0)))
raises(TypeError, lambda: cross(S(0), v))
raises(TypeError, lambda: cross(v, 0))
raises(TypeError, lambda: cross(0, v))
# outer products
raises(TypeError, lambda: outer(d, d))
raises(TypeError, lambda: outer(d, zerod))
raises(TypeError, lambda: outer(zerod, d))
raises(TypeError, lambda: outer(d, v))
raises(TypeError, lambda: outer(v, d))
raises(TypeError, lambda: outer(d, zerov))
raises(TypeError, lambda: outer(zerov, d))
raises(TypeError, lambda: outer(zerov, d))
raises(TypeError, lambda: outer(d, S(0)))
raises(TypeError, lambda: outer(S(0), d))
raises(TypeError, lambda: outer(d, 0))
raises(TypeError, lambda: outer(0, d))
assert v | v == outer(v, v)
assert v | zerov == outer(v, zerov)
assert zerov | v == outer(zerov, v)
raises(TypeError, lambda: outer(v, S(0)))
raises(TypeError, lambda: outer(S(0), v))
raises(TypeError, lambda: outer(v, 0))
raises(TypeError, lambda: outer(0, v))
def test_cross_different_frames():
assert cross(N.x, A.x) == sin(q1) * A.z
assert cross(N.x, A.y) == cos(q1) * A.z
assert cross(N.x, A.z) == -sin(q1) * A.x - cos(q1) * A.y
assert cross(N.y, A.x) == -cos(q1) * A.z
assert cross(N.y, A.y) == sin(q1) * A.z
assert cross(N.y, A.z) == cos(q1) * A.x - sin(q1) * A.y
assert cross(N.z, A.x) == A.y
assert cross(N.z, A.y) == -A.x
assert cross(N.z, A.z) == 0
assert cross(N.x, A.x) == sin(q1) * A.z
assert cross(N.x, A.y) == cos(q1) * A.z
assert cross(N.x, A.x + A.y) == sin(q1) * A.z + cos(q1) * A.z
assert cross(A.x + A.y, N.x) == -sin(q1) * A.z - cos(q1) * A.z
assert cross(A.x, C.x) == sin(q3) * C.y
assert cross(A.x, C.y) == -sin(q3) * C.x + cos(q3) * C.z
assert cross(A.x, C.z) == -cos(q3) * C.y
assert cross(C.x, A.x) == -sin(q3) * C.y
assert cross(C.y, A.x) == sin(q3) * C.x - cos(q3) * C.z
assert cross(C.z, A.x) == cos(q3) * C.y
def test_operator_match():
"""Test that the output of dot, cross, outer functions match
operator behavior.
"""
A = ReferenceFrame('A')
v = A.x + A.y
d = v | v
zerov = Vector(0)
zerod = Dyadic(0)
# dot products
assert d & d == dot(d, d)
assert d & zerod == dot(d, zerod)
assert zerod & d == dot(zerod, d)
assert d & v == dot(d, v)
assert v & d == dot(v, d)
assert d & zerov == dot(d, zerov)
assert zerov & d == dot(zerov, d)
raises(TypeError, lambda: dot(d, S(0)))
raises(TypeError, lambda: dot(S(0), d))
raises(TypeError, lambda: dot(d, 0))
raises(TypeError, lambda: dot(0, d))
assert v & v == dot(v, v)
assert v & zerov == dot(v, zerov)
assert zerov & v == dot(zerov, v)
raises(TypeError, lambda: dot(v, S(0)))
raises(TypeError, lambda: dot(S(0), v))
raises(TypeError, lambda: dot(v, 0))
raises(TypeError, lambda: dot(0, v))
# cross products
raises(TypeError, lambda: cross(d, d))
raises(TypeError, lambda: cross(d, zerod))
raises(TypeError, lambda: cross(zerod, d))
assert d ^ v == cross(d, v)
assert v ^ d == cross(v, d)
assert d ^ zerov == cross(d, zerov)
assert zerov ^ d == cross(zerov, d)
assert zerov ^ d == cross(zerov, d)
raises(TypeError, lambda: cross(d, S(0)))
raises(TypeError, lambda: cross(S(0), d))
raises(TypeError, lambda: cross(d, 0))
raises(TypeError, lambda: cross(0, d))
assert v ^ v == cross(v, v)
assert v ^ zerov == cross(v, zerov)
assert zerov ^ v == cross(zerov, v)
raises(TypeError, lambda: cross(v, S(0)))
raises(TypeError, lambda: cross(S(0), v))
raises(TypeError, lambda: cross(v, 0))
raises(TypeError, lambda: cross(0, v))
# outer products
raises(TypeError, lambda: outer(d, d))
raises(TypeError, lambda: outer(d, zerod))
raises(TypeError, lambda: outer(zerod, d))
raises(TypeError, lambda: outer(d, v))
raises(TypeError, lambda: outer(v, d))
raises(TypeError, lambda: outer(d, zerov))
raises(TypeError, lambda: outer(zerov, d))
raises(TypeError, lambda: outer(zerov, d))
raises(TypeError, lambda: outer(d, S(0)))
raises(TypeError, lambda: outer(S(0), d))
raises(TypeError, lambda: outer(d, 0))
raises(TypeError, lambda: outer(0, d))
assert v | v == outer(v, v)
assert v | zerov == outer(v, zerov)
assert zerov | v == outer(zerov, v)
raises(TypeError, lambda: outer(v, S(0)))
raises(TypeError, lambda: outer(S(0), v))
raises(TypeError, lambda: outer(v, 0))
raises(TypeError, lambda: outer(0, v))
def test_cross_different_frames():
assert cross(N.x, A.x) == sin(q1)*A.z
assert cross(N.x, A.y) == cos(q1)*A.z
assert cross(N.x, A.z) == -sin(q1)*A.x - cos(q1)*A.y
assert cross(N.y, A.x) == -cos(q1)*A.z
assert cross(N.y, A.y) == sin(q1)*A.z
assert cross(N.y, A.z) == cos(q1)*A.x - sin(q1)*A.y
assert cross(N.z, A.x) == A.y
assert cross(N.z, A.y) == -A.x
assert cross(N.z, A.z) == 0
assert cross(N.x, A.x) == sin(q1)*A.z
assert cross(N.x, A.y) == cos(q1)*A.z
assert cross(N.x, A.x + A.y) == sin(q1)*A.z + cos(q1)*A.z
assert cross(A.x + A.y, N.x) == -sin(q1)*A.z - cos(q1)*A.z
assert cross(A.x, C.x) == sin(q3)*C.y
assert cross(A.x, C.y) == -sin(q3)*C.x + cos(q3)*C.z
assert cross(A.x, C.z) == -cos(q3)*C.y
assert cross(C.x, A.x) == -sin(q3)*C.y
assert cross(C.y, A.x) == sin(q3)*C.x - cos(q3)*C.z
assert cross(C.z, A.x) == cos(q3)*C.y