def test_multiplication_by_variable():
x = Reverse(1)
y = Reverse(2)
f = x * y
f.gradient_value = 1.0
assert f.value == approx(2)
assert x.get_gradient() == approx(2)
assert y.get_gradient() == approx(1)
def test_vector():
x = Reverse(1)
y = Reverse(2)
functions = [x * 2 * y + y**3, 2 * x**2 * y, 3 * y]
vector = rVector(functions)
# Check for get_values()
assert vector.values == approx([12, 4, 6])
# Check for get_gradients()
assert vector.get_gradients(x) == approx([4.0, 8.0, 0])
assert vector.get_gradients(y) == approx([14.0, 2.0, 3.0])
def test_multiplication():
x = Reverse(1)
f = 4 * x
f.gradient_value = 1.0
assert f.value == approx(4)
assert x.get_gradient() == approx(4)
x = Reverse(1)
f = x * 4
f.gradient_value = 1.0
assert f.value == approx(4)
assert x.get_gradient() == approx(4)
def test_division():
x = Reverse(2)
f = 4 / x
f.gradient_value = 1.0
assert f.value == approx(2)
assert x.get_gradient() == approx(-1)
x = Reverse(5)
f = x / 4
f.gradient_value = 1.0
assert f.value == approx(5 / 4)
assert x.get_gradient() == approx(1 / 4)
def test_subtraction():
x = Reverse(5)
f = 4 * x**2.3 - 3 / x
f.gradient_value = 1.0
assert f.value == approx(4 * 5**2.3 - 3 / 5)
assert x.get_gradient() == approx(4 * 2.3 * 5**1.3 + 3 / (5**2))
x = Reverse(2)
f = 4 - x
f.gradient_value = 1.0
assert f.value == approx(2)
assert x.get_gradient() == approx(-1)
def test_vector_simple():
x = Reverse(-3)
y = Reverse(2)
vector = rVector([x**2, x + y * x])
assert vector.values == approx([9, -3 + 2 * -3])
x_grad = vector.get_gradients(x)
y_grad = vector.get_gradients(y)
assert x_grad == approx([2 * -3, 1 + 2])
assert y_grad == approx([0, -3])
def test_sin():
x = Reverse(5)
f = sin(x) + sin(5)
f.gradient_value = 1.0
assert f.value == approx(np.sin(5) + np.sin(5))
assert x.get_gradient() == approx(np.cos(5))
# Nested case
x = Reverse(5)
f = sin(2 * (-x))
f.gradient_value = 1.0
assert f.value == approx(np.sin(-2 * 5))
assert x.get_gradient() == approx(-2 * np.cos(-2 * 5))
def test_addition():
x = Reverse(3)
y = Reverse(3)
f = 4 * x + y * -6
f.gradient_value = 1.0
assert f.value == approx(4 * 3 + 3 * -6)
assert x.get_gradient() == approx(4)
assert y.get_gradient() == approx(-6)
x = Reverse(3)
f = 4 + x**2
f.gradient_value = 1.0
assert f.value == approx(4 + 3**2)
assert x.get_gradient() == approx(2 * 3)
def test_cos():
x = Reverse(5)
y = Reverse(5)
f = sin(x) * cos(y) + cos(3)
f.gradient_value = 1.0
assert f.value == approx(np.sin(5) * np.cos(5) + np.cos(3))
assert y.get_gradient() == approx((-np.sin(5)) * np.sin(5))
# Nested case
x = Reverse(4)
y = Reverse(3)
f = sin(cos(x * y))
f.gradient_value = 1.0
assert f.value == approx(np.sin(np.cos(3 * 4)))
assert x.get_gradient() == approx(-3 * np.sin(12) * np.cos(np.cos(12)))
def test_pos():
x = Reverse(3)
f = +(x * x)
f.gradient_value = 1
assert f.value == approx(9)
assert x.get_gradient() == approx(2 * 3)
def test_arc_trig_funcs():
x = Reverse(0.5)
f = arcsin(x) + arcsin(0.5)
f.gradient_value = 1.0
assert f.value == approx(np.arcsin(0.5) + np.arcsin(0.5))
assert x.get_gradient() == 1 / np.sqrt(1 - 0.5**2)
x = Reverse(0.5)
f = arccos(x) + arccos(1)
f.gradient_value = 1.0
assert f.value == approx(np.arccos(0.5) + np.arccos(1))
assert x.get_gradient() == -1 / np.sqrt(1 - 0.5**2)
x = Reverse(0.2)
f = arctan(x) + arctan(0.1)
f.gradient_value = 1.0
assert f.value == approx(np.arctan(0.2) + np.arctan(0.1))
assert x.get_gradient() == 1 / (1 + 0.2**2)
def test_power():
# Variable root
x = Reverse(3)
f = x**5
f.gradient_value = 1.0
assert f.value == approx(3**5)
assert x.get_gradient() == approx(5 * 3**4)
x = Reverse(2)
f = x**2.5
f.gradient_value = 1.0
assert f.value == approx(2**2.5)
assert x.get_gradient() == approx(2.5 * 2**1.5)
# Numeric root
x = Reverse(3)
f = 5**x
f.gradient_value = 1.0
assert f.value == approx(5**3)
assert x.get_gradient() == approx(5**3 * np.log(5))
def test_eq_ne():
x = Reverse(5)
f = sin(x) + 2
g = sin(x) + 2
h = cos(x) + 2
f.gradient_value = 1.0
g.gradient_value = 1.0
h.gradient_value = 1.0
assert x == 5
assert x != 7
assert f == g
assert f != h
def test_log():
x = Reverse(4)
f = log(x) + log(5) + ln(5)
f.gradient_value = 1.0
assert f.value == approx(np.log(4) + 2 * np.log(5))
assert x.get_gradient() == approx(1 / 4)
# Harder case
x = Reverse(3)
y = Reverse(7)
f = log(x**y)
f.gradient_value = 1.0
assert f.value == approx(np.log(3**7))
assert x.get_gradient() == approx((7 * (3**6)) * 1 / (3**7))
# log2 and log10
x = Reverse(3)
f = log2(x) + log10(x)
f.gradient_value = 1.0
assert f.value == approx(np.log2(3) + np.log10(3))
assert x.get_gradient() == approx(1 / (3 * np.log(10)) + 1 /
(3 * np.log(2)))
def test_other_trig_funcs():
x = Reverse(2)
f = sinh(x) + sinh(2)
f.gradient_value = 1.0
assert f.value == approx(2 * np.sinh(2))
assert x.get_gradient() == approx(np.cosh(2))
x = Reverse(2)
f = cosh(x) + cosh(2)
f.gradient_value = 1.0
assert f.value == approx(2 * np.cosh(2))
assert x.get_gradient() == approx(np.sinh(2))
x = Reverse(2)
f = tanh(x) + tanh(2)
f.gradient_value = 1.0
assert f.value == approx(2 * np.tanh(2))
assert x.get_gradient() == approx(
(np.cosh(2)**2 - np.sinh(2)**2) / np.cosh(2)**2)
x = Reverse(2)
f = sech(x) + sech(2)
f.gradient_value = 1.0
assert f.value == approx(2 * 1 / np.cosh(2))
assert x.get_gradient() == approx(
(-1 / np.cosh(2)) * (np.sinh(2) / np.cosh(2)))
x = Reverse(2)
f = csch(x) + csch(2)
f.gradient_value = 1.0
assert f.value == approx(2 * 1 / np.sinh(2))
assert x.get_gradient() == approx(
(-1 / np.sinh(2)) * (np.cosh(2) / np.sinh(2)))
x = Reverse(2)
f = coth(x) + coth(2)
f.gradient_value = 1.0
assert f.value == approx(2 * (np.cosh(2) / np.sinh(2)))
assert x.get_gradient() == approx(-1 / (np.sinh(2)**2))
def test_sqrt():
x = Reverse(2)
f = sqrt(x)
f.gradient_value = 1.0
assert f.value == approx(2**0.5)
assert x.get_gradient() == approx(0.5 * (2**(-0.5)))
def test_weirdness():
x = Reverse(2)
f = x**x
f.gradient_value = 1.0
assert f.value == approx(4)
assert x.get_gradient() == approx(4 + np.log(16))
def test_cot():
x = Reverse(5)
f = cot(x)
f.gradient_value = 1.0
assert f.value == approx(1 / np.tan(5))
assert x.get_gradient() == approx(-1 / np.sin(5)**2)
def test_single_var():
x = Reverse(1) + 2
f = x
f.gradient_value = 1.0
assert f.value == approx(3)
assert x.get_gradient() == approx(1)
def test_str():
x = Reverse(5)
f = x**2 + 3
f.gradient_value = 1
assert str(f) == '[28, 1]'
def test_sec():
x = Reverse(2)
f = sec(x)
f.gradient_value = 1.0
assert f.value == approx(1 / np.cos(2))
assert x.get_gradient() == approx(np.tan(2) / np.cos(2))
def test_cosec():
x = Reverse(-1)
f = csc(x)
f.gradient_value = 1.0
assert f.value == approx(1 / np.sin(-1))
assert x.get_gradient() == approx(-1 / np.tan(-1) / np.sin(-1))
def test_exp():
x = Reverse(0)
f = exp(x) + exp(0)
f.gradient_value = 1.0
assert f.value == approx(2)
assert x.get_gradient() == approx(1)
