def test_sin():
x = random.random()
assert_delta((np.sin(x * np.pi)), (np.sin((x * np.pi) + (2 * np.pi))))
return "sin({})={}\nsin(2pi+{})={}\n{}".format(
x * np.pi, round(np.sin(x * np.pi), 6), x * np.pi,
round(np.sin((x * np.pi) + 2 * np.pi), 6),
"They are equal so the test passes")
def test_cos():
x = random.random()
assert_delta((np.cos(x * np.pi)), (np.cos(x * np.pi + (2 * np.pi))))
return "cos({})={}\ncos(2pi+{})={}\n{}".format(
x * np.pi, round(np.cos(x * np.pi), 6), x * np.pi,
round(np.cos((x * np.pi) + 2 * np.pi), 6),
"They are equal so the test passes")
def test_determinant_2():
A = gen_matrix(25, 25, square=True)
B = np.copy(A)
scale_factor = random()
B[randrange(0, B.shape[0]
), :] *= scale_factor # scale a random row by scale_factor
assert_delta(scale_factor * np.linalg.det(A), np.linalg.det(B))
def test_norm_4():
a = random() * 2 - 1
dim = randrange(1, 5)
diag = np.identity(dim) * a
norm = np.linalg.norm(diag)
assert_delta(norm, np.abs(a) * np.sqrt(dim))
return """A =\n{}\n|a|*sqrt(dimension) = |{}|*sqrt({}) = {}\nNorm = {}
They are equal so the test passes""".format(diag, a, dim,
np.abs(a) * np.sqrt(dim), norm)
def test_determinant_1():
# determinant can become quite large for large matrices
# throwing off assert_delta, so the dimension must be restricted to 50
A = gen_matrix(25, 25, square=True)
B = np.copy(A)
# swap two random rows in B
row1, row2 = randrange(0, B.shape[0]), randrange(0, B.shape[0])
B[[row1, row2]] = B[[row2, row1]]
assert_delta(abs(np.linalg.det(A)), abs(np.linalg.det(B)))
def test_norm_2():
A = gen_matrix(100, 100)
scalar = random() * 2 - 1 # random number on interval [-1, 1]
assert_delta(np.linalg.norm(scalar * A), abs(scalar) * np.linalg.norm(A))
def test_norm_1():
A = gen_matrix(100, 100)
assert_delta(np.linalg.norm(A), np.linalg.norm(A.T))
def test_determinant_3():
A = gen_matrix(25, 25, square=True, non_singular=True)
B = np.linalg.inv(A)
assert_delta(np.linalg.det(A), 1 / np.linalg.det(B))
def test_assert_delta_1(x):
a = random()
b = a + 0.00019 * (random() - 0.5)
assert_delta(a, b, delta=0.0001)
return "{} = {} within a delta of .0001".format(a, b)
def test_assert_delta_2(x):
a = random()
b = a + randrange(1, 100)
with pytest.raises(AssertionError):
assert_delta(a, a + b)
return "{} != {} within a delta of .0001".format(a, b)
def test_square_root_2():
x = random.uniform(1, 100.0)
assert_delta(x, (np.sqrt(x)**2))
def test_arctan():
x = random.random()
assert_delta((np.tan(np.arctan(x))), x)
def test_arccos():
x = random.random()
assert_delta((np.cos(np.arccos(x))), x)
def test_metaTan():
x = random.random()
assert_delta((np.tan(x * np.pi)), -(np.tan((2 * np.pi) - (x * np.pi))))
def test_metaCos():
x = random.random()
assert_delta((np.cos(x * np.pi)), (np.cos((2 * np.pi) - (x * np.pi))))
