def test_pow():
# Scalar
a = rAd_Var(2)
b = 3
f = a**b
ders = f.get_ders()
assert (f.get_val() == 8)
assert (ders == [12])
# Type test.
try:
_ = a**"NaN"
except:
print("test_pow type checking successful!")
# Rpow.
c = rAd_Var(4)
d = 3
g = d**c
ders_g = g.get_ders()
assert (g.get_val() == 81)
assert (ders_g == [81 * np.log(3)])
# Rpow bad input test.
try:
_ = 'NaN'**c
except:
print("Rpow non-numeric base test passed!")
# Gradient
x = rAd_Var(2)
y = rAd_Var(2)
z = rAd_Var(2)
x1 = x**y**z
ders = x1.get_ders()
assert (x1.get_val() == 16)
assert (ders == [32, 64 * np.log(2), 64 * (np.log(2)**2)]).all()
def test_multi_parent():
x = rAd_Var(1)
y = rAd_Var(2)
x1 = x * y
x2 = x1.exp()
x3 = x1 + x2
ders = x3.get_ders()
np.testing.assert_almost_equal(x3.get_val(), 2 + (np.e**2))
np.testing.assert_array_almost_equal(ders,
[2 + (2 * np.e**2), 1 + (np.e**2)])
def test_log():
# Scalar
a = rAd_Var(5)
b = a.log()
ders = b.get_ders()
assert (b.get_val() == np.log(5))
assert (ders == .2)
c = rAd_Var(np.e)
d = c.log()
ders = d.get_ders()
assert (d.get_val() == 1)
assert (ders == 1 / np.e)
def test_inverse_trig():
# Improper input test
try:
_ = rAd_Var(-2).arcsin()
except ValueError:
print("Arcsin domain test passed!")
try:
_ = rAd_Var(-2).arccos()
except ValueError:
print("Arcos domain test passed!")
# Scalar
a1, a2, a3 = rAd_Var(0.1), rAd_Var(0.1), rAd_Var(0.1)
b = rAd_Var.arcsin(a1)
c = rAd_Var.arccos(a2)
d = rAd_Var.arctan(a3)
ders_b = b.get_ders()
ders_c = c.get_ders()
ders_d = d.get_ders()
assert b.get_val() == np.arcsin(0.1)
assert ders_b == 1 / np.sqrt(1 - 0.1**2)
assert c.get_val() == np.arccos(0.1)
assert ders_c == -1 / np.sqrt(1 - 0.1**2)
assert d.get_val() == np.arctan(0.1)
assert ders_d == 1 / (1 + 0.1**2)
# Gradient
x1 = rAd_Var(0.1)
x2 = rAd_Var(0.2)
x3 = rAd_Var(0.3)
f = rAd_Var.arcsin(x1) + rAd_Var.arccos(x2) + rAd_Var.arctan(x3)
ders = f.get_ders()
assert f.get_val() == 1.7610626216439926
assert (ders == [
1.005037815259212, -1.0206207261596576, 0.9174311926605504
]).all()
def test_exp():
# Scalar
a = rAd_Var(2)
f = a.exp()
ders = f.get_ders()
assert (f.get_val() == np.exp(2))
assert (ders == [np.exp(2)])
# Gradient
x = rAd_Var(3)
y = rAd_Var(-4)
x1 = rAd_Var.exp(x + y)
ders = x1.get_ders()
assert (x1.get_val() == np.exp(-1))
assert (ders == [np.exp(-1), np.exp(-1)]).all()
def test_trig():
# Scalar
b = rAd_Var.sin(rAd_Var(np.pi / 4))
c = rAd_Var.cos(rAd_Var(np.pi / 4))
d = rAd_Var(np.pi)
e = rAd_Var.tan(d)
ders_b = b.get_ders()
ders_c = c.get_ders()
ders_e = e.get_ders()
assert (b.get_val() == np.sin(np.pi / 4))
np.testing.assert_almost_equal(ders_b, np.cos(np.pi / 4))
assert (c.get_val() == np.cos(np.pi / 4))
np.testing.assert_almost_equal(ders_c, -np.sin(np.pi / 4))
assert (e.get_val() == np.tan(np.pi))
np.testing.assert_almost_equal(ders_e, 1 / np.cos(np.pi)**2)
a1 = rAd_Var(np.pi)
a2 = a1.sin()
a2.get_ders()
# Gradient
x = rAd_Var(np.pi / 4).sin()
y = rAd_Var(np.pi / 4).cos()
z = rAd_Var(np.pi / 4).tan()
x1 = x + y + z
ders = x1.get_ders()
assert (x1.get_val() == 2**0.5 + 1)
np.testing.assert_array_almost_equal(
ders,
[np.cos(np.pi / 4), -np.sin(np.pi / 4), 1 / np.cos(np.pi / 4)**2])
def test_input():
try:
print(rAd_Var('NaN'))
except TypeError:
print("Input test 1 passed.")
try:
print(rAd_Var(None))
except TypeError:
print("Input test 2 passed.")
try:
_ = rAd_Var(5) + Ad_Var(5)
except TypeError:
print("rAd_Var and Ad_Var incompatibility check passed.")
a = rAd_Var(np.array([42]))
a.set_val(5)
assert (a.get_val() == 5)
print("Testing for __str__ method:\n", a)
repr(a)
def test_add():
# Scalar
a, b = rAd_Var(99), rAd_Var(99)
f = a + 1
g = 1 + b
ders_f = f.get_ders()
ders_g = g.get_ders()
assert (ders_f == ders_g and f.get_val() == g.get_val())
assert (f.get_val() == 100)
assert (ders_f == [1])
# Gradient
x = rAd_Var(4)
y = rAd_Var(8)
z = rAd_Var(-2)
x1 = x + y + z
ders = x1.get_ders()
assert (x1.get_val() == 10)
assert (ders == [1, 1, 1]).all()
def test_logistic():
def sigmoid(x):
return 1.0 / (1 + np.exp(-x))
def sigmoid_derivative(x):
der = (1 - sigmoid(x)) * sigmoid(x)
return der
a = rAd_Var(1)
b = rAd_Var.logistic(a)
ders = b.get_ders()
assert b.get_val() == sigmoid(1)
np.testing.assert_almost_equal(ders, sigmoid_derivative(1))
x1 = rAd_Var(0.1)
x2 = rAd_Var(0.2)
f = rAd_Var.logistic(x1) - rAd_Var.logistic(x2)
ders = f.get_ders()
assert f.get_val() == sigmoid(0.1) - sigmoid(0.2)
np.testing.assert_array_almost_equal(
ders, [sigmoid_derivative(0.1), -sigmoid_derivative(0.2)])
def test_div():
# Scalar
a = rAd_Var(20)
b = 2
f = a / b
c = rAd_Var(20)
g = b / c
ders_f = f.get_ders()
ders_g = g.get_ders()
assert (f.get_val() == 10)
assert (g.get_val() == 0.1)
assert (ders_f == 1 / 2)
assert (ders_g == -1 / 200)
# Gradient
x = rAd_Var(10)
y = rAd_Var(5)
x1 = x / y
ders = x1.get_ders()
assert (x1.get_val() == 2)
assert (ders == [1 / 5, -2 / 5]).all()
def test_mul():
# Scalar
a = rAd_Var(12)
b = 3
f = a * b
c = rAd_Var(12)
g = b * c
ders_f = f.get_ders()
ders_g = g.get_ders()
assert (f.get_val() == g.get_val() == 36)
assert (ders_f == ders_g)
assert (ders_f == [3]).all()
# Gradient
x = rAd_Var(3)
y = rAd_Var(-2)
z = rAd_Var(3)
x1 = x * y * z
ders = x1.get_ders()
assert (x1.get_val() == -18)
assert (ders == [-6, 9, -6]).all()
def test_sub():
# Scalar
a = rAd_Var(101)
b = 1
f = a - b
ders = f.get_ders()
assert (f.get_val() == 100)
assert (ders == [1])
# Rsub
c = rAd_Var(50)
d = 100
g = d - c
ders = g.get_ders()
assert (g.get_val() == 50)
assert (ders == -1)
# Gradient
x = rAd_Var(500)
y = rAd_Var(100)
z = rAd_Var(-100)
x1 = x - y - z
ders = x1.get_ders()
assert (x1.get_val() == 500)
assert (ders == [1, -1, -1]).all()
def test_input():
try:
f = Ad_Var('s', 2)
except TypeError:
print("TypeError sucessfully catched - value1")
try:
f = Ad_Var([2, 3, 4], 2)
except TypeError:
print("TypeError sucessfully catched - value2")
try:
f = Ad_Var(2, 's')
except TypeError:
print("TypeError sucessfully catched - der1")
try:
f = Ad_Var(2, np.array([1, 2, 'dog']))
except TypeError:
print("TypeError sucessfully catched - der2")
try:
a = Ad_Var(20)
b = rAd_Var(5)
f = a + b
except TypeError:
print("TypeError successfully catched - _typecheck_other")
def test_hyperbolic():
# Scalar
a1, a2, a3 = rAd_Var(0.1), rAd_Var(0.1), rAd_Var(0.1)
b = rAd_Var.sinh(a1)
c = rAd_Var.cosh(a2)
d = rAd_Var.tanh(a3)
ders_b = b.get_ders()
ders_c = c.get_ders()
ders_d = d.get_ders()
assert b.get_val() == np.sinh(0.1)
assert ders_b == np.cosh(0.1)
assert c.get_val() == np.cosh(0.1)
assert ders_c == np.sinh(0.1)
assert d.get_val() == np.tanh(0.1)
assert ders_d == (1 - np.tanh(0.1)**2)
# Gradient
x1 = rAd_Var(0.1)
x2 = rAd_Var(0.2)
x3 = rAd_Var(0.3)
f = rAd_Var.sinh(x1) + rAd_Var.cosh(x2) - rAd_Var.tanh(x3)
ders = f.get_ders()
assert f.get_val() == np.sinh(0.1) + np.cosh(0.2) - np.tanh(0.3)
np.testing.assert_array_almost_equal(
ders, [np.cosh(0.1), np.sinh(0.2), -1 + np.tanh(0.3)**2])
def test_eq():
a = rAd_Var(1)
b = rAd_Var(1)
c = rAd_Var(2)
assert (a == b and a != c)
def test_neg():
a = rAd_Var(5)
f = -a
ders = f.get_ders()
assert (f.get_val() == -5)
assert (ders == -1)
def test_sqrt():
a = rAd_Var(16)
f = a.sqrt()
ders = f.get_ders()
assert (f.get_val() == 4)
assert (ders == 1 / 8)