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 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.Zero))
raises(TypeError, lambda: dot(S.Zero, 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.Zero))
raises(TypeError, lambda: dot(S.Zero, 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.Zero))
raises(TypeError, lambda: cross(S.Zero, 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.Zero))
raises(TypeError, lambda: cross(S.Zero, 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.Zero))
raises(TypeError, lambda: outer(S.Zero, 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.Zero))
raises(TypeError, lambda: outer(S.Zero, 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