def test_truediv(self):
x = AD(4)
f = el.log(x, 2) / 3 ** x
assert (np.round(f.val, 6), np.round(f.der[-1], 6)) == (
np.round(2 / 81, 6), np.round((81 / (4 * np.log(2)) - 162 * np.log(3)) / 3 ** 8, 6))
f = el.sin(x) / 4
assert (f.val, f.der) == ((np.sin(4)) / 4, (np.cos(4)) / 4)
with pytest.raises(ZeroDivisionError):
f = el.cos(x) / el.sin(0)
with pytest.raises(ZeroDivisionError):
f = el.cos(x) / 0
f = 3 ** x / el.log(x, 2)
assert (np.round(f.val, 6), np.round(f.der, 6)) == (np.round(81 / 2, 6),
np.round((162 * np.log(3) - 81 / (4 * np.log(2))) / (
np.log(4) / np.log(2)) ** 2, 6))
with pytest.raises(AttributeError):
f = el.cos(x) / "el.sin(0)"
x = AD(0)
f = el.sin(x) / el.cos(x)
assert (f.val, f.der) == (0, 1)
with pytest.raises(ZeroDivisionError):
f = el.cos(x) / el.sin(x)
def test_sub(self):
# N > 1
x = AD(5, N=3)
f = el.sin(x)
g = 10
h = f - g
assert (h.val, np.round(h.der[-1]), 6) == (np.sin(5) - 10, np.round(-np.cos(5)), 6)
f = el.sin(x)
g = x ** 2
h = f - g
assert (h.val, np.round(h.der[-1]), 6) == (np.sin(5) - 25, np.round(-np.cos(5)), 6)
def test_sin(self):
# N = 1
x = AD(0)
f = el.sin(x)
assert (f.val, f.der) == (0.0, 1.0)
x = 13
f = el.sin(x)
assert (f.val, f.der) == (np.sin(13), 0)
x = 13.0
f = el.sin(x)
assert (f.val, f.der) == (np.sin(13), 0)
# N > 1
x = AD(2, N=4)
f = el.sin(x)
# print(f)
assert (f.val, np.round(f.der[-1], 6)) == (np.sin(2), np.round(np.sin(2), 6))
x = AD(2, N=3)
f = el.sin(x)
# print(f)
assert (f.val, np.round(f.der[-1], 6)) == (np.sin(2), np.round(-np.cos(2), 6))
f = el.sin(x) + 3
assert (f.val, np.round(f.der[-1], 6)) == (np.sin(2) + 3, np.round(-np.cos(2), 6))
f = el.sin(x) - 2
assert (f.val, np.round(f.der[-1], 6)) == (np.sin(2) - 2, np.round(-np.cos(2), 6))
f = el.sin(x) * 4
assert (f.val, np.round(f.der[-1], 6)) == (4 * np.sin(2), np.round(-4 * np.cos(2), 6))
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_sin(self):
x = AD(0)
f = el.sin(x)
assert (f.val, f.der) == (0.0, 1.0)
x = 13
f = el.sin(x)
assert (f.val, f.der) == (np.sin(13), 0)
x = 13.0
f = el.sin(x)
assert (f.val, f.der) == (np.sin(13), 0)
with pytest.raises(AttributeError):
x = "!"
f = el.sin(x)
def test_add(self):
# N > 1
x = AD(5, N=3)
f = el.sin(x)
g = 10
h = f + g
assert (h.val, np.round(h.der[-1]), 6) == (np.sin(5) + 10, np.round(-np.cos(5)), 6)
f = 10
g = el.sin(x)
h = f + g
assert (h.val, np.round(h.der[-1]), 6) == (np.sin(5) + 10, np.round(-np.cos(5)), 6)
f = el.sin(x)
g = x ** 2
h = f + g
assert (h.val, np.round(h.der[-1]), 6) == (np.sin(5) + 25, np.round(-np.cos(5)), 6)
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