def test_dotproduct_1():
a = {'x': 1}
assert dotproduct(a, a, normalize=True) == 1.0
a = {'x': 1}
b = {'x': 1}
assert dotproduct(a, b, normalize=True) == 1.0
c = {'x': 1, 'y': 1}
prod = dotproduct(c, c, normalize=True)
assert round(prod, 2) == 1.0
# check a.c => 45 degree angle
a = {'x': 1}
c = {'x': 1, 'y': 1}
angle = 45
rad = math.radians(angle)
cosval = math.cos(rad)
prod = dotproduct(a, c, normalize=True)
assert round(prod, 2) == 0.71
assert round(cosval, 2) == round(prod, 2)
c = {'x': 1, 'y': 1}
d = {'x': 1, 'y': 1}
prod = dotproduct(c, d, normalize=True)
assert round(prod, 2) == 1.0
a = {'x': 1}
e = {'y': 1}
assert dotproduct(a, e, normalize=True) == 0.0
def test_dotproduct_zeroes():
a = {'x': 1}
b = {}
assert dotproduct(a, b) == 0.0
assert dotproduct(b, a) == 0.0