def __call__(self, x):
"""Implements the chain rule.
INPUTS
=======
x: autodiff.Variable holding a val and grad
RETURNS
========
autodiff.Variable: updated Variable after chain rule was applied
"""
# if autodiff.config.mode == 'forward':
if isinstance(x, Variable):
out_val = self.get_val(x.val)
out_grad = np.dot(self.get_grad(x.val), x.grad)
# out_grad = np.dot(self.get_grad(x.val), x.grad)
return Variable(val=out_val, grad=out_grad)
elif isinstance(x, ReverseVariable):
out_val = self.get_val(x.val)
res = ReverseVariable(out_val)
x.children.append(res)
res.left = x
res.leftgrad = self.get_grad(x.val)
return res
else:
raise ValueError("Not a variable!")
def test_rpow_exception():
x = ReverseVariable([1, 3])
y = ReverseVariable([3, 1])
z = ReverseVariable(2)
a = x + y
with pytest.raises(TypeError):
b = "g"**y
with pytest.raises(ValueError):
b = 2**a
def test_mul_exception():
x = ReverseVariable([1, 2])
y = ReverseVariable([2, 1])
z = ReverseVariable(4)
a = x + y
with pytest.raises(TypeError):
b = a * "g"
with pytest.raises(TypeError):
b = False * y
def test_sub_exception():
x = ReverseVariable([1, 2])
y = ReverseVariable([2, 1])
z = y + x
a = z + [4.4, 3.3]
b = a + z
with pytest.raises(TypeError):
c = b - "g"
with pytest.raises(TypeError):
c = True - b
def test_neg():
x = ReverseVariable([1, 3])
y = ReverseVariable([3, 1])
z = ReverseVariable(4)
a = x + y
b = a / z
c = -b
c.reverse()
assert close(c.val, -np.asarray([[1], [1]]))
assert close(x.grad, np.eye(2) * -0.25)
assert close(y.grad, np.eye(2) * -0.25)
assert close(z.grad, np.asarray([[0.25], [0.25]]))
def test_pow_exception():
x = ReverseVariable([1, 3])
y = ReverseVariable([3, 1])
z = ReverseVariable(2)
a = x + y
with pytest.raises(TypeError):
b = a**"g"
with pytest.raises(ValueError):
b = a**[3, 3]
with pytest.raises(ValueError):
b = a**z
with pytest.raises(ValueError):
b = z**a
def test_create_function_exception():
with pytest.raises(NotImplementedError):
f = F.Function()
x = ReverseVariable([1, 2, 3])
y = f(x)
with pytest.raises(NotImplementedError):
f = F.Function()
x = ReverseVariable([1, 2, 3])
y = f.get_grad(x)
with pytest.raises(NotImplementedError):
f = F.Function()
x = ReverseVariable([1, 2, 3])
y = f.get_val(x)
def test_arccos():
x = ReverseVariable(0.5)
arccos = F.Arccos()
y = arccos(x)
y.reverse()
assert close(y.val, np.pi / 3) and close(x.grad,
-1.0 / np.sqrt(1.0 - 0.5**2))
def test_arcsin():
x = ReverseVariable(0.5)
arcsin = F.Arcsin()
y = arcsin(x)
y.reverse()
assert close(y.val, np.pi / 6) and close(x.grad,
1.0 / np.sqrt(1.0 - 0.5**2))
def test_dot():
x = ReverseVariable([1, 1])
M = np.asarray(([2, 2], [1, 1]))
dotm = F.Dot(M)
y = dotm(x)
y.reverse()
assert close(y.val, np.asarray([[4], [2]])) and close(x.grad, M)
def test_exp():
x = ReverseVariable(2)
exp = F.Exponent()
y = exp(x)
y.reverse()
assert close(y.val, np.exp(2))
assert close(x.grad, np.exp(2))
def test_tanh():
x = ReverseVariable(1)
tanh = F.Tanh()
y = tanh(x)
y.reverse()
assert close(y.val, np.tanh(1)) and close(x.grad,
(np.cosh(1)**2 - np.sinh(1)**2) /
(np.cosh(1)**2))
def test_logistic():
x = ReverseVariable(2)
logi = F.Logistic()
y = logi(x)
y.reverse()
assert close(y.val, 1.0 / (1.0 + np.exp(-(2)))) and close(
x.grad,
(1.0 / (1.0 + np.exp(-(2)))) * (1.0 - (1.0 / (1.0 + np.exp(-(2))))))
def test_add():
x = ReverseVariable([1, 2])
y = ReverseVariable([2, 1])
z = x + y
z.reverse()
assert close(z.val, np.asarray([[3], [3]]))
assert close(x.grad, np.eye(2))
assert close(y.grad, np.eye(2))
a = z + [4.4, 3.3]
b = a + z
b.reverse()
assert close(b.val, np.asarray([[10.4], [9.3]]))
assert close(x.grad, np.eye(2) * 2)
assert close(y.grad, np.eye(2) * 2)
c = [4.4, 3.3] + b
c.reverse()
assert close(c.val, np.asarray([[14.8], [12.6]]))
assert close(x.grad, np.eye(2) * 2)
assert close(y.grad, np.eye(2) * 2)
def test_log():
x = ReverseVariable(2)
log = F.Log()
y = log(x)
y.reverse()
assert close(y.val, np.log(2)) and close(x.grad, 0.5)
log2 = F.Log(2)
y = log2(x)
y.reverse()
assert close(y.val, 1)
assert close(x.grad, 0.5 / np.log(2))
def test_pow():
x = ReverseVariable([1, 3])
y = ReverseVariable([3, 1])
z = ReverseVariable(2)
a = x + y
b = z**2
b.reverse()
assert close(b.val, 4)
assert close(z.grad, 4)
b = a**2
b.reverse()
assert close(b.val, np.asarray([[16], [16]]))
assert close(x.grad, np.eye(2) * 8)
assert close(y.grad, np.eye(2) * 8)
c = z
d = z**c
d.reverse()
assert close(d.val, 4)
print(z.grad)
assert close(z.grad, 4 * (np.log(2) + 1))
def test_sub():
x = ReverseVariable([1, 2])
y = ReverseVariable([2, 1])
z = y + x
a = z + [4.4, 3.3]
b = a + z
c = b - x
c.reverse()
assert close(c.val, np.asarray([[9.4], [7.3]]))
assert close(x.grad, np.eye(2))
assert close(y.grad, np.eye(2) * 2)
d = 3 - c
d.reverse()
assert close(d.val, np.asarray([[-6.4], [-4.3]]))
assert close(x.grad, np.eye(2) * -1)
assert close(y.grad, np.eye(2) * -2)
e = c - 2.1
e.reverse()
assert close(e.val, np.asarray([[7.3], [5.2]]))
assert close(x.grad, np.eye(2))
assert close(y.grad, np.eye(2) * 2)
def test_div_exception():
x = ReverseVariable([1, 3])
y = ReverseVariable([3, 1])
z = ReverseVariable(0)
a = x + y
with pytest.raises(ValueError):
b = a / x
with pytest.raises(ValueError):
b = a / z
with pytest.raises(ValueError):
b = 4.0 / z
with pytest.raises(ValueError):
b = a / 0.0
with pytest.raises(ValueError):
b = a / np.asarray([1, 1])
with pytest.raises(ValueError):
b = 4.0 / x
with pytest.raises(TypeError):
b = a / "g"
with pytest.raises(TypeError):
a = True / y
def test_div():
x = ReverseVariable([1, 3])
y = ReverseVariable([3, 1])
z = ReverseVariable(4)
a = x + y
b = a / z
b.reverse()
assert close(b.val, np.asarray([[1], [1]]))
assert close(x.grad, np.eye(2) * 0.25)
assert close(y.grad, np.eye(2) * 0.25)
assert close(z.grad, np.asarray([[-0.25], [-0.25]]))
c = b / 0.25
c.reverse()
assert close(c.val, np.asarray([[4], [4]]))
assert close(x.grad, np.eye(2))
assert close(y.grad, np.eye(2))
assert close(z.grad, np.asarray([[-1], [-1]]))
d = 4 / z
d.reverse()
assert close(d.val, 1)
assert close(z.grad, -0.25)
def test_mul():
x = ReverseVariable([1, 2])
y = ReverseVariable([2, 1])
z = ReverseVariable(4)
a = x + y
b = a * z
b.reverse()
assert close(b.val, np.asarray([[12], [12]]))
assert close(x.grad, np.eye(2) * 4)
assert close(y.grad, np.eye(2) * 4)
assert close(z.grad, np.asarray([[3], [3]]))
c = b * 4
c.reverse()
assert close(c.val, np.asarray([[48], [48]]))
assert close(x.grad, np.eye(2) * 16)
assert close(y.grad, np.eye(2) * 16)
assert close(z.grad, np.asarray([[12], [12]]))
d = 2 * b
d.reverse()
assert close(d.val, np.asarray([[24], [24]]))
assert close(x.grad, np.eye(2) * 8)
assert close(y.grad, np.eye(2) * 8)
assert close(z.grad, np.asarray([[6], [6]]))
def test_arctan():
x = ReverseVariable(1)
arctan = F.Arctan()
y = arctan(x)
y.reverse()
assert close(y.val, np.pi / 4) and close(x.grad, 0.5)
def test_add_exception():
x = ReverseVariable([1, 2, 3])
with pytest.raises(TypeError):
y = x + "g"
with pytest.raises(TypeError):
y = True + x
def test_exp_exception():
x = ReverseVariable([1, 2, 3])
exp = F.Exponent()
with pytest.raises(ValueError):
y = exp(x)
def test_sin():
x = ReverseVariable(np.pi / 6)
sin = F.Sinus()
y = sin(x)
y.reverse()
assert abs(y.val - 0.5) < 1e-4 and abs(x.grad - np.sqrt(3) / 2) < 1e-4
def test_rpow():
z = ReverseVariable(2)
b = 2**z
b.reverse()
assert close(b.val, 4)
assert close(z.grad, np.log(2) * 4)
def test_cos():
x = ReverseVariable(np.pi / 3)
cos = F.Cosinus()
y = cos(x)
y.reverse()
assert abs(y.val - 0.5) < 1e-4 and abs(x.grad + np.sqrt(3) / 2) < 1e-4
def test_tan():
x = ReverseVariable(np.pi / 4)
tan = F.Tangent()
y = tan(x)
y.reverse()
assert abs(y.val - 1) < 1e-4 and abs(x.grad - 2) < 1e-4
def test_tan_exception():
x = ReverseVariable(np.pi / 2)
tan = F.Tangent()
with pytest.raises(ValueError):
y = tan(x)
def test_create_variable():
X = ReverseVariable([1, 2, 3])
assert close(X.val, np.asarray([[1], [2], [3]]))
y = ReverseVariable(1)
assert close(y.val, 1)
def test_sinh():
x = ReverseVariable(1)
sinh = F.Sinh()
y = sinh(x)
y.reverse()
assert close(y.val, np.sinh(1)) and close(x.grad, np.cosh(1))