def test_grad_of_grad():
x2 = ad.Variable(name = "x2")
x3 = ad.Variable(name = "x3")
y = x2 * x2 + x2 * x3
grad_x2, grad_x3 = ad.gradients(y, [x2, x3])
grad_x2_x2, grad_x2_x3 = ad.gradients(grad_x2, [x2, x3])
executor = ad.Executor([y, grad_x2, grad_x3, grad_x2_x2, grad_x2_x3])
x2_val = 2 * np.ones(3)
x3_val = 3 * np.ones(3)
y_val, grad_x2_val, grad_x3_val, grad_x2_x2_val, grad_x2_x3_val = executor.run(feed_dict = {x2: x2_val, x3: x3_val})
expected_yval = x2_val * x2_val + x2_val * x3_val
expected_grad_x2_val = 2 * x2_val + x3_val
expected_grad_x3_val = x2_val
expected_grad_x2_x2_val = 2 * np.ones_like(x2_val)
expected_grad_x2_x3_val = 1 * np.ones_like(x2_val)
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, expected_yval)
assert np.array_equal(grad_x2_val, expected_grad_x2_val)
assert np.array_equal(grad_x3_val, expected_grad_x3_val)
assert np.array_equal(grad_x2_x2_val, expected_grad_x2_x2_val)
assert np.array_equal(grad_x2_x3_val, expected_grad_x2_x3_val)
def test_eq_node():
x2 = ad.Variable(name = "x2")
x3 = ad.Variable(name = "x3")
y = (x2==x3)
executor = ad.Executor([y])
x2_val = 2 * np.ones(3)
x3_val = 2 * np.ones(3)
y_val = executor.run(feed_dict = {x2 : x2_val, x3 : x3_val})
assert np.array_equal(y_val[0], x2_val==x3_val)
def test_mul_two_vars():
x2 = ad.Variable(name = "x2")
x3 = ad.Variable(name = "x3")
y = x2 * x3
grad_x2, grad_x3 = ad.gradients(y, [x2, x3])
executor = ad.Executor([y, grad_x2, grad_x3])
x2_val = 2 * np.ones(3)
x3_val = 3 * np.ones(3)
y_val, grad_x2_val, grad_x3_val = executor.run(feed_dict = {x2: x2_val, x3: x3_val})
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, x2_val * x3_val)
assert np.array_equal(grad_x2_val, x3_val)
assert np.array_equal(grad_x3_val, x2_val)
def test_add_mul_mix_1():
x1 = ad.Variable(name = "x1")
x2 = ad.Variable(name = "x2")
x3 = ad.Variable(name = "x3")
y = x1 + x2 * x3 * x1
grad_x1, grad_x2, grad_x3 = ad.gradients(y, [x1, x2, x3])
executor = ad.Executor([y, grad_x1, grad_x2, grad_x3])
x1_val = 1 * np.ones(3)
x2_val = 2 * np.ones(3)
x3_val = 3 * np.ones(3)
y_val, grad_x1_val, grad_x2_val, grad_x3_val = executor.run(feed_dict = {x1 : x1_val, x2: x2_val, x3 : x3_val})
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, x1_val + x2_val * x3_val)
assert np.array_equal(grad_x1_val, np.ones_like(x1_val) + x2_val * x3_val)
assert np.array_equal(grad_x2_val, x3_val * x1_val)
assert np.array_equal(grad_x3_val, x2_val * x1_val)
def test_ne_const_node():
x2 = ad.Variable(name = "x2")
y = (x2!=2)
executor = ad.Executor([y])
x2_val = 2 * np.ones(3)
y_val = executor.run(feed_dict = {x2 : x2_val})
assert np.array_equal(y_val[0], x2_val!=2)
def test_matmul_two_vars():
x2 = ad.Variable(name = "x2")
x3 = ad.Variable(name = "x3")
y = ad.matmul_op(x2, x3)
grad_x2, grad_x3 = ad.gradients(y, [x2, x3])
executor = ad.Executor([y, grad_x2, grad_x3])
x2_val = np.array([[1, 2], [3, 4], [5, 6]]) # 3x2
x3_val = np.array([[7, 8, 9], [10, 11, 12]]) # 2x3
y_val, grad_x2_val, grad_x3_val = executor.run(feed_dict = {x2: x2_val, x3: x3_val})
expected_yval = np.matmul(x2_val, x3_val)
expected_grad_x2_val = np.matmul(np.ones_like(expected_yval), np.transpose(x3_val))
expected_grad_x3_val = np.matmul(np.transpose(x2_val), np.ones_like(expected_yval))
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, expected_yval)
assert np.array_equal(grad_x2_val, expected_grad_x2_val)
assert np.array_equal(grad_x3_val, expected_grad_x3_val)
def test_add_mul_mix_3():
x2 = ad.Variable(name = "x2")
x3 = ad.Variable(name = "x3")
z = x2 * x2 + x2 + x3 + 3
y = z * z + x3
grad_x2, grad_x3 = ad.gradients(y, [x2, x3])
executor = ad.Executor([y, grad_x2, grad_x3])
x2_val = 2 * np.ones(3)
x3_val = 3 * np.ones(3)
y_val, grad_x2_val, grad_x3_val = executor.run(feed_dict = {x2: x2_val, x3: x3_val})
z_val = x2_val * x2_val + x2_val + x3_val + 3
expected_yval = z_val * z_val + x3_val
expected_grad_x2_val = 2 * (x2_val * x2_val + x2_val + x3_val + 3) * (2 * x2_val + 1)
expected_grad_x3_val = 2 * (x2_val * x2_val + x2_val + x3_val + 3) + 1
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, expected_yval)
assert np.array_equal(grad_x2_val, expected_grad_x2_val)
assert np.array_equal(grad_x3_val, expected_grad_x3_val)
def test_mul_by_const():
x2 = ad.Variable(name = "x2")
y = 5 * x2
grad_x2, = ad.gradients(y, [x2])
executor = ad.Executor([y, grad_x2])
x2_val = 2 * np.ones(3)
y_val, grad_x2_val= executor.run(feed_dict = {x2 : x2_val})
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, x2_val * 5)
assert np.array_equal(grad_x2_val, np.ones_like(x2_val) * 5)
def test_log():
x2 = ad.Variable(name = "x2")
y = ad.log_op(x2, 5)
grad_x2, = ad.gradients(y, [x2])
executor = ad.Executor([y, grad_x2])
x2_val = 0.5 * np.ones(3)
y_val, grad_x2_val= executor.run(feed_dict = {x2 : x2_val})
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, np.log(x2_val)/np.log(5))
assert (abs(grad_x2_val - 1./(x2_val*np.log(5)))<1e-7 ).all()
def test_tanh():
# this can test tan, cos, sin and power at the same time
x2 = ad.Variable(name = "x2")
y = ad.tanh_op(x2)
grad_x2, = ad.gradients(y, [x2])
executor = ad.Executor([y, grad_x2])
x2_val = 2 * np.ones(3)
y_val, grad_x2_val= executor.run(feed_dict = {x2 : x2_val})
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, np.tanh(x2_val))
assert np.array_equal(grad_x2_val, (np.cosh(x2_val)**2 - np.sinh(x2_val)**2)/np.cosh(x2_val)**2)
def test_logistic():
x2 = ad.Variable(name = "x2")
y = ad.logistic_op(x2)
grad_x2, = ad.gradients(y, [x2])
executor = ad.Executor([y, grad_x2])
x2_val = 0.5 * np.ones(3)
y_val, grad_x2_val= executor.run(feed_dict = {x2 : x2_val})
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, 1./(1+np.exp(-x2_val)))
print(grad_x2_val - 2*(1./(1+np.exp(-x2_val)))*(1-1./(1+np.exp(-x2_val))))
assert (abs(grad_x2_val - (1./(1+np.exp(-x2_val)))*(1-1./(1+np.exp(-x2_val))))<1e-7 ).all()
def test_arccos():
# this can test tan, cos, sin and power at the same time
x2 = ad.Variable(name = "x2")
y = ad.arccos_op(x2)
grad_x2, = ad.gradients(y, [x2])
executor = ad.Executor([y, grad_x2])
x2_val = 0.5 * np.ones(3)
y_val, grad_x2_val= executor.run(feed_dict = {x2 : x2_val})
assert isinstance(y, ad.Node)
assert np.array_equal(y_val, np.arccos(x2_val))
assert (abs(grad_x2_val + 1./(1-x2_val**2)**0.5)<1e-7 ).all()
