def test_composite1():
x1 = Var(-3)
x2 = Var(5)
x3 = Var(10)
y = abs(x1) / x2 * x3
x1.forward()
assert y.grad(x1) == -2.
def test_composite_trig():
x = Var(5)
x2 = ops.sin(x) / ops.cos(x)
x3 = ops.tan(x)
x.forward()
assert np.all(x2.val == pytest.approx(x3.val))
assert np.all(x2.grad(x) == pytest.approx(x3.grad(x)))
def test_composite2():
x1 = Var(-3)
x2 = Var(5)
x3 = Var(1)
y = x2**x1 / x3
x3.forward()
assert y.grad(x3) == -.008
def test_composite2():
x1 = Var(-3)
x2 = Var([5, 10])
x3 = Var([1, 1])
y = x2**x1 / x3
x3.forward()
assert np.all(y.grad(x3) == [-.008, -.001])
def test_composite1():
x1 = Var(-3)
x2 = Var([5, 10])
x3 = Var([10, 100])
y = abs(x1) / x2 * x3
x1.forward()
assert np.all(y.grad(x1) == [-2, -10])
def test_sub_vars():
x1 = Var([1, 1, 1])
x2 = Var([1, 2, 3])
y = x1 - x2
x1.forward()
x2.forward()
assert np.all(y == Var([0, -1, -2]))
assert np.all(y.grad(x1) == np.array([1, 1, 1]))
assert np.all(y.grad(x2) == np.array([-1, -1, -1]))
def test_add_vars():
x1 = Var([1, 2, 3])
x2 = Var([1, 2, 3])
y = x1 + x2
x1.forward()
x2.forward()
assert np.all(y == Var([2, 4, 6]))
assert np.all(y.grad(x1) == np.array([1, 1, 1]))
assert np.all(y.grad(x2) == np.array([1, 1, 1]))
def test_mul_vars():
x1 = Var(8)
x2 = Var([2, 2, 2])
y = x1 * x2
x1.forward()
x2.forward()
assert np.all(y == Var([16, 16, 16]))
assert np.all(y.grad(x1) == np.array([2, 2, 2]))
assert np.all(y.grad(x2) == np.array([8, 8, 8]))
def test_pow_vars_forward():
x = Var(np.e)
x2 = Var(2)
y = x**x2
x.forward()
x2.forward()
assert y.val == np.e**2
assert np.all(y.grad(x) == np.array([2 * np.e]))
assert np.all(y.grad(x2) == np.array([np.e**2]))
def test_div_vars():
x = Var([8, 1])
x2 = Var([2, 1])
y = x / x2
x.forward()
x2.forward()
assert np.all(y == Var([4, 1]))
assert np.all(y.grad(x) == np.array([0.5, 1]))
assert np.all(y.grad(x2) == np.array([-2., -1]))
def test_sub_vars_forward():
x1 = Var(1)
x2 = Var(2)
y = x1 - x2
x1.forward()
x2.forward()
assert y.val == -1
assert np.all(y.grad(x1) == np.array([1]))
assert np.all(y.grad(x2) == np.array([-1]))
def test_mul_vars_forward():
x1 = Var(8)
x2 = Var(2)
y = x1 * x2
x1.forward()
x2.forward()
assert y.val == 16
assert np.all(y.grad(x1) == np.array([2]))
assert np.all(y.grad(x2) == np.array([8]))
def test_add_vars_forward():
x1 = Var(1)
x2 = Var(2)
y = x1 + x2
x1.forward()
x2.forward()
assert y.val == 3
assert np.all(y.grad(x1) == np.array([1]))
assert np.all(y.grad(x2) == np.array([1]))
def test_pow_vars():
x = Var(np.e)
x2 = Var([1, 2, 3])
y = x**x2
x.forward()
x2.forward()
assert np.all(y == Var([np.e**1, np.e**2, np.e**3]))
assert np.all(y.grad(x) == np.array([1, 2 * np.e, 3 * np.e**2]))
assert np.all(y.grad(x2) == np.array([np.e, np.e**2, np.e**3]))
def test_div_vars_forward():
x = Var(8)
x2 = Var(2)
y = x / x2
x.forward()
x2.forward()
assert y.val == 4
assert np.all(y.grad(x) == np.array([0.5]))
assert np.all(y.grad(x2) == np.array([-2]))
def test_radd_var_forward():
x = Var(3)
y = 6 + x
x.forward()
assert y.val == 9
assert np.all(y.grad(x) == np.array([1]))
def test_add_var_number_forward():
x = Var(3)
y = x + 5
x.forward()
assert y.val == 8
assert np.all(y.grad(x) == np.array([1]))
def test_abs_forward():
x = Var(-2)
y = abs(x)
x.forward()
assert y.val == 2
assert y.grad(x) == np.array([-1])
def test_rmul_vars_forward():
x = Var(3)
y = 6 * x
x.forward()
assert y.val == 18
assert np.all(y.grad(x) == np.array([6]))
def test_rpow_vars_forward():
x = Var(3)
y = np.e**x
x.forward()
assert y.val == np.e**3
assert np.all(y.grad(x) == np.array([np.e**3]))
def test_pow_var_number_forward():
x = Var(3)
y = x**5
x.forward()
assert y.val == 243
assert np.all(y.grad(x) == np.array([405]))
def test_neg_forward():
x = Var(2)
y = -x
assert y.val == -2
x.forward()
assert y.grad(x) == np.array([-1])
def test_rdiv_vars_forward():
x = Var(3)
y = 6 / x
x.forward()
assert y.val == 2
assert np.all(y.grad(x) == np.array([-2 / 3]))
def test_div_var_number_forward():
x = Var(10)
y = x / 5
x.forward()
assert y.val == 2.
assert np.all(y.grad(x) == np.array([0.2]))
def test_sub_var_number_forward():
x = Var(3)
y = x - 5
x.forward()
assert y.val == -2
assert np.all(y.grad(x) == np.array([1]))
def test_sub_var_number():
x = Var([1, 2, 3])
y = x - 5
x.forward()
assert np.all(y == Var([-4, -3, -2]))
assert np.all(y.grad(x) == np.array([1, 1, 1]))
def test_rsub_var_forward():
x = Var(3)
y = 6 - x
x.forward()
assert y.val == 3
assert np.all(y.grad(x) == np.array([-1]))
def test_radd_var():
x = Var([1, 2, 3])
y = 6 + x
x.forward()
assert np.all(y == Var([7, 8, 9]))
assert np.all(y.grad(x) == np.array([1, 1, 1]))
def test_mul_var_number_forward():
x = Var(3)
y = x * 5
x.forward()
assert y.val == 15
assert np.all(y.grad(x) == np.array([5]))
def test_rsub_var():
x = Var([1, 2, 3])
y = 6 - x
x.forward()
assert np.all(y == Var([5, 4, 3]))
assert np.all(y.grad(x) == np.array([-1, -1, -1]))
