def test_mul_c2_addx():
x = AD(1, 1, 'x')
y = AD(2, 2, 'y')
z = x * y * 4 + x
assert z.val == [9]
np.testing.assert_array_equal(z.der, np.array([9, 8]).reshape(1, -1))
assert z.name == ['x', 'y']
def test_le_values():
x = AD(2, 1, 'x')
y = AD(3, 1, 'y')
z = AD(3, 1, 'z')
assert (x <= y) == True
assert (y <= x) == False
assert (z <= y) == True
def test_add_list():
x = AD(1, 1, 'x')
y = AD(2, 2, 'y')
w = AD([x + y, y - x])
z = [1, 2]
with pytest.raises(ValueError):
w + z
def test_pow_2():
x = AD(1, 4, 'x')
y = AD(2, 7, 'y')
z = x**y
assert z.name == ['x', 'y']
assert z.val == [1]
np.testing.assert_array_equal(z.der, np.array([8, 0]).reshape(1, -1))
def test_div():
x = AD(1, 4, 'x')
y = AD(2, 7, 'y')
z = x / y
assert z.name == ['x', 'y']
assert z.val == [0.5]
np.testing.assert_array_equal(z.der, np.array([2, -7 / 4]).reshape(1, -1))
def test_ne_different_dim():
x = AD(1, 1, 'x')
y = AD(3, 1, 'y')
z = AD(4, 1, 'z')
w = x + y
with pytest.raises(AttributeError):
w != z
def test_ge_values():
x = AD(2, 1, 'x')
y = AD(3, 1, 'y')
z = AD(3, 1, 'z')
assert (y >= x) == True
assert (x >= y) == False
assert (z >= y) == True
def test_ne_values():
x = AD(2, 1, 'x')
y = AD(3, 1, 'y')
z = AD(3, 1, 'z')
assert (y != x) == True
assert (x != y) == True
assert (z != y) == False
def test_add_2_vec_diff_dim():
x = AD(1, 1, 'x')
y = AD(2, 2, 'y')
w = AD([x + y, y - x])
z = np.array([1.0, 2.0, 3.0])
with pytest.raises(ValueError):
w + z
def test_mul_c1(): # todo: same
x = AD(1, 1, 'x')
y = AD(2, 2, 'y')
z = x * y + 4
assert z.val == [6]
np.testing.assert_array_equal(z.der, np.array([2, 2]).reshape(1, -1))
assert z.name == ['x', 'y']
def test_add_vec_str():
x = AD(1, 1, 'x')
y = AD(2, 2, 'y')
w = AD([x + y, y - x])
z = np.array(['x', 2.0]).reshape(2, 1)
with pytest.raises(TypeError):
w + z
def test_add_c():
x = AD(1, 1, 'x')
y = AD(2, 2, 'y')
z = x + y + 4
assert z.val == [7]
np.testing.assert_array_equal(z.der, np.array([1, 2]).reshape(1, -1))
assert z.name == ['x', 'y']
def test_add_2_vec():
x = AD(1, 1, 'x')
y = AD(2, 2, 'y')
w = AD([x + y, y - x])
z = np.array([1.0, 2.0]).reshape(2, 1)
q = w + z
np.testing.assert_array_equal(q.val, np.array([[4.0], [3.0]]))
def test_eq_values():
x = AD(2, 1, 'x')
y = AD(3, 1, 'y')
z = AD(3, 1, 'z')
assert (y == x) == False
assert (x == y) == False
assert (z == y) == True
def test_add_2_vec_str():
x = AD(1, 1, 'x')
y = AD(2, 2, 'y')
w = AD([x + y, y - x])
z = np.array(['a', 'b'])
with pytest.raises(ValueError):
q = w + z
def test_rtrue_div():
x = AD(1, 4, 'x')
y = AD(2, 7, 'y')
z = 2 / (x + y)
assert z.name == ['x', 'y']
assert z.val == [2 / 3]
np.testing.assert_array_equal(z.der,
np.array([-8 / 9, -14 / 9]).reshape(1, -1))
def test_div_3_var():
x = AD(1, 4, 'x')
y = AD(2, 7, 'y')
z = AD(3, 2, 'z')
w = x * y * z
assert w.name == ['x', 'y', 'z']
assert w.val == [6]
np.testing.assert_array_equal(w.der, np.array([24, 21, 4]).reshape(1, -1))
def test_mul_last():
x = AD(1, 4, 'x')
y = AD(2, 7, 'y')
w = x * y
z = x + y
v = z * w
assert v.name == ['x', 'y']
assert v.val == [6]
def test_fn_power_array2():
x = AD(0, 1, 'x')
y = AD(0, 1, 'x')
z = AD([x, y])
n = AD(0, 1, 'n')
with pytest.raises(TypeError):
w = z**n
def _function(init_vals):
for k, v in init_vals.items():
globals()[k] = AD(v, 1, k)
f = x1**2 - x2
g = x1 - 2 * x2
v = AD([f, g])
v.sort(['x1', 'x2'])
return v
def test_arccos():
x = AD(0.5, 3, 'x')
z = x.arccos()
print('x=', x)
print(z)
assert z.val == [np.arccos(0.5)]
# np.testing.assert_array_equal(z.der, np.array([-3/np.sqrt(1 - 0.5**2)]))
assert z.der == [-3 * (1 - 0.5**2)**(-0.5)]
def test_beug():
x = AD(1, 1, 'x')
y = AD(2, 1, 'y')
f1 = AD([10 * x, 10 * y])
f2 = AD([3 * x, 3 * y])
z = f1 + f2
np.testing.assert_array_equal(z.val, np.array([13, 26]).reshape(2, 1))
np.testing.assert_array_equal(
z.sort(order=['x', 'y']).der, np.array([[13, 0], [0, 13]]))
def test_pow_1():
x = AD(3, 4, 'x')
y = AD(2, 7, 'y')
z = x**(y + x)
assert z.name == ['x', 'y']
assert z.val == [3**5]
np.testing.assert_array_equal(
z.der,
np.array([(4 * np.log(3) + 20 / 3) * 3**5,
7 * np.log(3) * 3**5]).reshape(1, -1))
def test_div_hard(): # we should cover the lines in rtruediv here
x = AD(1, 4, 'x')
y = AD(2, 7, 'y')
z = x * y
w = x + y
u = z / w
assert u.name == ['x', 'y']
assert u.val == 2 / 3
np.testing.assert_array_equal(u.der,
np.array([16 / 9, 7 / 9]).reshape(1, -1))
def test_multi_dim_2():
x = AD(1, 4, 'x')
y = AD(2, 3, 'y')
z = AD(1, 7, 'z')
print('1 x value is', x)
print(x * y)
print(y + z)
print(z + x)
print('y value is', y)
print('2 x value is', x)
print(x + y)
v = AD([x * y, y + z, z + x, 4, x + y, x + y])
print(v)
def test_sub():
x = AD(1, 1, 'x')
y = AD(2, 2, 'y')
z = y - x
assert z.val == [1]
np.testing.assert_array_equal(z.der, np.array([2, -1]).reshape(1, -1))
def test_sqrt2():
x = AD(10, 3, 'x')
y = x.sqrt()
assert y.val == np.sqrt(10)
assert y.der == 0.5 * 3 * 10**(-0.5)
def test_sqrt1():
x = AD(-1, 1, 'x')
with pytest.raises(ValueError):
y = x.sqrt()
def test_rpow_4():
x = AD(-1, 1, 'x')
with pytest.raises(ZeroDivisionError):
y = (0)**x
def test_order():
x = AD(1, 1, 'x')
y = AD(2, 2, 'y')
z = y + x
z.sort(['x', 'y'])
print(z)