def test_root_is_found2(Solver, a, b, root):
epsilon = 1e-3
solver = Solver(epsilon=epsilon)
f = lambda x: x**3 - x**2 - 3 * x + 2 # three roots: -1.618, 0.618, 2
result = solver(f, a, b)
assert result.converged
assert nearly_equal(result.x0, root, epsilon)
assert nearly_equal(result.fx0, 0, epsilon)
assert result.msg == Solver.messages["convergence"]
def test_root_is_found2(Solver, a, b, root):
epsilon = 1e-3
solver = Solver(epsilon=epsilon)
f = lambda x: x**3 - x**2 - 3 * x + 2 # three roots: -1.618, 0.618, 2
result = solver(f, a, b)
assert result.converged
assert nearly_equal(result.x0, root, epsilon)
assert nearly_equal(result.fx0, 0, epsilon)
assert result.msg == Solver.messages["convergence"]
def test_root_is_found(Solver):
f = lambda x: x**2 - 3 * x + 2
a, b = (0.5, 1.5)
epsilon = 1e-5
solver = Solver(epsilon=epsilon)
result = solver(f, a, b)
assert result.converged
assert nearly_equal(result.x0, 1, epsilon)
assert nearly_equal(result.fx0, 0, epsilon)
assert result.msg == Solver.messages["convergence"]
def test_root_is_found(Solver):
f = lambda x: x**2 - 3 * x + 2
a, b = (0.5, 1.5)
epsilon=1e-5
solver = Solver(epsilon=epsilon)
result = solver(f, a, b)
assert result.converged
assert nearly_equal(result.x0, 1, epsilon)
assert nearly_equal(result.fx0, 0, epsilon)
assert result.msg == Solver.messages["convergence"]
def test_root_is_found3(Solver):
# http://en.wikipedia.org/wiki/Bisection_method#Example:_Finding_the_root_of_a_polynomial
f = lambda x: x**3 - x - 2
a, b = (1, 2)
epsilon = 1e-3
solver = Solver(epsilon=epsilon)
result = solver(f, a, b)
assert result.converged
assert nearly_equal(result.x0, 1.521, epsilon)
assert nearly_equal(result.fx0, 0, epsilon)
assert result.msg == Solver.messages["convergence"]
def test_root_is_found3(Solver):
# http://en.wikipedia.org/wiki/Bisection_method#Example:_Finding_the_root_of_a_polynomial
f = lambda x: x**3 - x - 2
a, b = (1, 2)
epsilon = 1e-3
solver = Solver(epsilon=epsilon)
result = solver(f, a, b)
assert result.converged
assert nearly_equal(result.x0, 1.521, epsilon)
assert nearly_equal(result.fx0, 0, epsilon)
assert result.msg == Solver.messages["convergence"]
def test_infinities(epsilon):
""" Test comparisons with infinity. """
pinf = float("inf")
ninf = -pinf
max_float = sys.float_info.max
min_float = -max_float
# infinite is equal to itself no matter the epsilon value used.
assert nearly_equal(pinf, pinf, epsilon)
assert nearly_equal(ninf, ninf, epsilon)
# but the two infs compare as unequal
assert not nearly_equal(pinf, ninf, epsilon)
# infinite is not equal to the extreme allowed float values.
assert not nearly_equal(ninf, min_float, epsilon)
assert not nearly_equal(pinf, max_float, epsilon)
def test_opposite_sign2():
""" Test numbers with opposite sign. """
# mpf is a very small positive value. Something in the order of 1e-300
# The following compraisons are valid for epsilons > sys.float_info.epsilon
mpf = sys.float_info.min
epsilon = 1e-5
assert not nearly_equal(-1.0, 1.0, epsilon=epsilon)
assert not nearly_equal(1.0, -1.0, epsilon=epsilon)
assert not nearly_equal(1.000000001, -1.0, epsilon=epsilon)
assert not nearly_equal(-1.0, 1.000000001, epsilon=epsilon)
assert not nearly_equal(-1.000000001, 1.0, epsilon=epsilon)
assert not nearly_equal(1.0, -1.000000001, epsilon=epsilon)
assert not nearly_equal(1e-3, -1e-3, epsilon=epsilon)
assert nearly_equal(1e-7, -1e-7, epsilon=epsilon)
assert nearly_equal(10 * mpf, 10 * -mpf, epsilon=epsilon)
assert nearly_equal(1e6 * mpf, 1e7 * -mpf, epsilon=epsilon)
def test_opposite_sign(num, epsilon):
""" Test numbers with opposite sign. """
# mpf is a very small positive value. Something in the order of 1e-300
# The following compraisons are valid for epsilons > sys.float_info.epsilon
mpf = sys.float_info.min
# Comparing very small numbers should evaluate to True even if the numbers
# have opposite signs.
assert nearly_equal(mpf, mpf, epsilon=epsilon)
assert nearly_equal(mpf, -mpf, epsilon=epsilon)
assert nearly_equal(-mpf, -mpf, epsilon=epsilon)
# comparing very big numbers with opposite sings should evaluate to False
num = 1e40
assert not nearly_equal(num, -num, epsilon=epsilon)
assert not nearly_equal(-num, num, epsilon=epsilon)
def test_ulp(epsilon):
# mpf is a very small positive value. Something in the order of 1e-300
# The following compraisons are valid for epsilons > sys.float_info.epsilon
mpf = sys.float_info.min
assert nearly_equal(mpf, -mpf, epsilon)
assert nearly_equal(mpf, 0, epsilon)
assert nearly_equal(0, mpf, epsilon)
assert nearly_equal(-mpf, 0, epsilon)
assert nearly_equal(0, -mpf, epsilon)
assert nearly_equal(1e-40, -mpf, epsilon)
assert nearly_equal(1e-40, mpf, epsilon)
assert nearly_equal(mpf, 1e-40, epsilon)
assert nearly_equal(-mpf, 1e-40, epsilon)
def test_same_sign(num, epsilon):
""" Test numbers with the same sign. """
# Define two "big" numbers
n1 = num
n2 = num + 9 * epsilon # if we change "9" to "10" tests will fail!!!
# epsilon >= diff(n1, n2)
assert nearly_equal(n1, n2, epsilon=epsilon * 1e+1)
assert nearly_equal(n2, n1, epsilon=epsilon * 1e+1)
assert nearly_equal(n1, n2, epsilon=epsilon * 1e+3)
assert nearly_equal(n2, n1, epsilon=epsilon * 1e+3)
assert nearly_equal(n1, n2, epsilon=epsilon * 1e+6)
assert nearly_equal(n2, n1, epsilon=epsilon * 1e+6)
# epsilon < diff(n1, n2)
assert not nearly_equal(n1, n2, epsilon=epsilon * 1e-1)
assert not nearly_equal(n2, n1, epsilon=epsilon * 1e-1)
assert not nearly_equal(n1, n2, epsilon=epsilon * 1e-3)
assert not nearly_equal(n2, n1, epsilon=epsilon * 1e-3)
assert not nearly_equal(n1, n2, epsilon=epsilon * 1e-6)
assert not nearly_equal(n2, n1, epsilon=epsilon * 1e-6)
def test_nan(epsilon):
""" Test comparisons with NaN. """
pos = float("inf")
neg = -float("inf")
nan = float("nan")
max_float = sys.float_info.max
min_float = -max_float
assert not nearly_equal(nan, nan, epsilon=epsilon)
assert not nearly_equal(nan, 0.0, epsilon=epsilon)
assert not nearly_equal(-0.0, nan, epsilon=epsilon)
assert not nearly_equal(nan, -0.0, epsilon=epsilon)
assert not nearly_equal(0.0, nan, epsilon=epsilon)
assert not nearly_equal(nan, pos, epsilon=epsilon)
assert not nearly_equal(pos, nan, epsilon=epsilon)
assert not nearly_equal(nan, neg, epsilon=epsilon)
assert not nearly_equal(neg, nan, epsilon=epsilon)
assert not nearly_equal(nan, max_float, epsilon=epsilon)
assert not nearly_equal(max_float, nan, epsilon=epsilon)
assert not nearly_equal(nan, min_float, epsilon=epsilon)
assert not nearly_equal(min_float, nan, epsilon=epsilon)
assert not nearly_equal(nan, min_float, epsilon=epsilon)
assert not nearly_equal(min_float, nan, epsilon=epsilon)
assert not nearly_equal(nan, -min_float, epsilon=epsilon)
assert not nearly_equal(-min_float, nan, epsilon=epsilon)
def test_zero(epsilon):
""" Test comparisons involving zero. """
# zero equals itself... (duh)
assert nearly_equal(0.0, 0.0, epsilon=epsilon)
assert nearly_equal(0.0, -0.0, epsilon=epsilon)
assert nearly_equal(-0.0, -0.0, epsilon=epsilon)