def test_sub(self):
x = AD(5)
f = el.power(x, 2) + -5 * x
assert (f.val, f.der) == (0, 5)
f = el.power(x, 2) - 50
assert (f.val, f.der) == (-25, 10)
f = - 50 + el.power(x, 2)
assert (f.val, f.der) == (-25, 10)
f = 50 - el.power(x, 2)
assert (f.val, f.der) == (25, -10)
f = -5 * x + el.power(x, 2)
assert (f.val, f.der) == (0, 5)
f = -x * 5 + el.power(x, 2)
assert (f.val, f.der) == (0, 5)
f = el.power(x, 2) - 5 * x
assert (f.val, f.der) == (0, 5)
f = x * 5 - el.power(x, 2)
assert (f.val, f.der) == (0, -5)
with pytest.raises(AttributeError):
f = el.sin(x) - "5"
def test_exp(self):
# N = 1
f = el.exp(1)
assert (f.val, f.der) == (np.exp(1), 0)
x = AD(1)
f = el.exp(x)
assert (f.val, f.der) == (np.exp(1), np.exp(1))
x = AD(2)
f = el.power(x, 3)
g = el.exp(f)
print(g)
assert (round(g.val, 6), round(g.der[0], 6)) == (round(np.exp(1) ** 8, 6), round(12 * np.exp(1) ** 8, 6))
with pytest.raises(AttributeError):
x = "hello"
f = el.exp(x)
# N > 1
for N in range(2, 10):
x = AD(3, N=N)
f = el.exp(x)
print("N=%d" % N, f)
x = AD(2, N=5)
f = el.exp(x)
assert (f.val, f.der[-1]) == (np.exp(2), np.exp(2))
def test_power(self):
x = AD(5)
f = el.power(x, 2)
assert (f.val, f.der) == (25, 10)
x = 10
f = el.power(x, 3)
assert (f.val, f.der) == (1000, 0)
x = 10.0
f = el.power(x, 3)
assert (f.val, f.der) == (1000, 0)
with pytest.raises(AttributeError):
x = "s"
f = el.power(x, 3)
def test_add(self):
x = AD(5)
f = el.power(x, 2) + 5
assert (f.val, f.der) == (30, 10)
f = 5 + el.power(x, 2)
assert (f.val, f.der) == (30, 10)
f = el.power(x, 2) + 5 * x
assert (f.val, f.der) == (50, 15)
f = x * 5 + el.power(x, 2)
assert (f.val, f.der) == (50, 15)
with pytest.raises(AttributeError):
f = el.power(x, 2) + "5"
f = el.power(x, 2)
g = 5
h = f + g
assert (h.val, h.der) == (30, 10)
f = 5
g = el.power(x, 2)
h = f + g
assert (h.val, h.der) == (30, 10)
def test_pow(self):
x = AD(2)
f = x ** 4
assert (f.val, f.der[-1]) == (16, 32)
x = AD(2)
f = 3 ** x
assert (np.round(f.val, 8), np.round(f.der[-1], 6)) == (9, np.round(9 * np.log(3), 6))
x = AD(2)
f = el.power(x, 2)
assert (f.val, f.der) == (4, 4)
x = AD(2)
f = x ** x
assert (f.val, f.der[-1]) == (4, 4 * np.log(2) + 4)
x = AD(2)
f = (el.power(x, 2)) ** x
assert (f.val, f.der) == (16, 16 * np.log(4) + 32)
f = (el.power(x, 2)) ** 3
assert (f.val, f.der) == (64, 192)
with pytest.raises(AttributeError):
f = (el.power(x, 2)) ** "3"
f = (2 ** x) ** x
assert (f.val, f.der) == (16, 16 * np.log(16))
f = x ** (2 ** x)
assert (f.val, f.der) == (16, 32 + 64 * (np.log(2) ** 2))
x = AD(0)
f = el.sin(x)
g = x
with pytest.raises(ValueError):
h = f ** g
def test_exp(self):
f = el.exp(1)
assert (f.val, f.der) == (np.exp(1), 0)
x = AD(1)
f = el.exp(x)
assert (f.val, f.der) == (np.exp(1), np.exp(1))
x = AD(2)
f = el.power(x, 3)
g = el.exp(f)
assert (np.round(g.val, 6), np.round(g.der, 6)) == (
np.round(np.exp(1) ** 8, 6), np.round(12 * np.exp(1) ** 8, 6))
with pytest.raises(AttributeError):
x = "hello"
f = el.exp(x)
def test_power(self):
x = AD(4, N=3)
f = el.power(x, 4)
assert (f.val, f.der[-1]) == (256, 96)