def test_expm1():
def grad_grad_op(x):
return nd.exp(x)
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_second_order_unary(array, nd.expm1, grad_grad_op)
def test_log1p():
def grad_grad_op(x):
return -1 / ((1 + x)**2)
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_second_order_unary(array, nd.log1p, grad_grad_op)
def test_square():
def grad_grad_op(x):
return nd.ones_like(x) * 2
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_second_order_unary(array, nd.square, grad_grad_op)
def test_arctanh():
def arctanh(x):
return nd.arctanh(x)
def grad_grad_op(x):
return (2 * x) / ((1 - x**2)**2)
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_second_order_unary(array, arctanh, grad_grad_op)
def test_cos():
def cos(x):
return nd.cos(x)
def grad_grad_op(x):
return -nd.cos(x)
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_second_order_unary(array, cos, grad_grad_op)
def test_sinh():
def sinh(x):
return nd.sinh(x)
def grad_grad_op(x):
return sinh(x)
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_second_order_unary(array, sinh, grad_grad_op)
def test_reciprocal():
def reciprocal(x):
return nd.reciprocal(x)
def grad_grad_op(x):
return 2 / x**3
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_second_order_unary(array, reciprocal, grad_grad_op)
def test_log10():
def log10(x):
return nd.log10(x)
def grad_grad_op(x):
return -1 / ((x**2) * math.log(10))
arrays = random_arrays((2, 2), (2, 3), (4, 5, 2), (3, 1, 4, 5))
for array in arrays:
check_second_order_unary(array, log10, grad_grad_op)
def test_dropout():
def dropout(x):
return nd.Dropout(x)
def grad_grad_op(x):
return nd.zeros_like(x)
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_second_order_unary(array, dropout, grad_grad_op)
def test_abs():
def abs(x):
return nd.abs(x)
def grad_grad_op(x):
return nd.zeros_like(x)
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_second_order_unary(array, abs, grad_grad_op)
def test_log10():
def log10(x):
return nd.log10(x)
def grad_grad_op(x):
return -1 / ((x**2) * math.log(10))
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_second_order_unary(array, log10, grad_grad_op)
def test_arcsinh():
def arcsinh(x):
return nd.arcsinh(x)
def grad_grad_op(x):
return x / nd.sqrt((nd.square(x) + 1)**3)
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_second_order_unary(array, arcsinh, grad_grad_op)
def test_clip():
def clip(x):
a_min, a_max = sorted([random.random(), random.random()])
return nd.clip(x, a_min, a_max)
def grad_grad_op(x):
return nd.zeros_like(x)
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_second_order_unary(array, clip, grad_grad_op)
def test_arctan():
def arctan(x):
return nd.arctan(x)
def grad_grad_op(x):
return (-2 * x) / ((1 + x**2)**2)
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
# Domain of arctan is all real numbers.
# Scale std_dev
array *= random.randint(500, 10000)
check_second_order_unary(array, arctan, grad_grad_op)
def test_tan():
def tan(x):
return nd.tan(x)
def grad_op(x):
return 1 / nd.cos(x)**2
def grad_grad_op(x):
return 2 * tan(x) * grad_op(x)
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_second_order_unary(array, tan, grad_grad_op)
def test_sigmoid():
def sigmoid(x):
return nd.sigmoid(x)
def grad_op(x):
return sigmoid(x) * (1 - sigmoid(x))
def grad_grad_op(x):
return grad_op(x) * (1 - 2 * sigmoid(x))
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_second_order_unary(array, sigmoid, grad_grad_op)
def test_tanh():
def tanh(x):
return nd.tanh(x)
def grad_op(x):
return 1 - tanh(x)**2
def grad_grad_op(x):
return -2 * tanh(x) * grad_op(x)
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_nth_order_unary(array, tanh, grad_op, 1, rtol=1e-6, atol=1e-6)
check_second_order_unary(
array, tanh, grad_grad_op, rtol=1e-6, atol=1e-5)
def test_arccos():
def arccos(x):
return nd.arccos(x)
def grad_grad_op(x):
return -x / nd.sqrt((1 - x**2)**3)
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
# Hack: Decrease std_dev to make
# sure all elements
# are in range -1 to 1
# i.e. Domain of arccos
array *= 0.2
check_second_order_unary(array, arccos, grad_grad_op)
def test_log():
def log(x):
return nd.log(x)
def grad_op(x):
return 1 / x
def grad_grad_op(x):
return -1 / (x**2)
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_second_order_unary(array, log, grad_grad_op)
# TODO(kshitij12345): Remove
check_nth_order_unary(array, log, [grad_op, grad_grad_op], [1, 2])
def test_cos():
def cos(x):
return nd.cos(x)
def grad_grad_op(x):
return -nd.cos(x)
def grad_grad_grad_op(x):
return nd.sin(x)
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_second_order_unary(array, cos, grad_grad_op)
# TODO(kshitij12345): Remove
check_nth_order_unary(array, cos, [grad_grad_op, grad_grad_grad_op],
[2, 3])
def test_rcbrt():
def rcbrt(x):
return nd.rcbrt(x)
def grad_grad_op(x):
return 4 / (9 * nd.cbrt(x**7))
sigma = random.randint(25, 100)
mu = random.randint(500, 1000)
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
array = sigma * array + mu
# Only positive numbers
assert ((array > 0).all())
check_second_order_unary(array, rcbrt, grad_grad_op)
def test_sigmoid():
def sigmoid(x):
return nd.sigmoid(x)
def grad_op(x):
return sigmoid(x) * (1 - sigmoid(x))
def grad_grad_op(x):
return grad_op(x) * (1 - 2 * sigmoid(x))
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
check_second_order_unary(array, sigmoid, grad_grad_op)
# TODO(kshitij12345): Remove
check_nth_order_unary(array, sigmoid, [grad_op, grad_grad_op], [1, 2])
check_nth_order_unary(array, sigmoid, grad_grad_op, 2)
def test_arccosh():
def arccosh(x):
return nd.arccosh(x)
def grad_grad_op(x):
return x / (nd.sqrt(x - 1) * nd.sqrt(x + 1) * (x + 1) * (x - 1))
sigma = random.randint(25, 100)
mu = random.randint(500, 1000)
for dim in range(1, 5):
shape = rand_shape_nd(dim)
array = random_arrays(shape)
array = array * sigma + mu
# Domain of arccosh 1 to infinity.
assert ((array > 1).all())
check_second_order_unary(array, arccosh, grad_grad_op)
