def test_add_jacobian_scalar(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x1 = ad.Variable(name="x1", shape=[])
x2 = ad.Variable(name="x2", shape=[])
y = x1 + x2
jacobian_x2, = ad.jacobians(y, [x2])
executor = ad.Executor([y, jacobian_x2])
x1_val = T.tensor(1.)
x2_val = T.tensor(1.)
y_val, jacobian_x2_val = executor.run(feed_dict={
x1: x1_val,
x2: x2_val
})
expected_jacobian_x2_val = T.tensor(1.)
assert isinstance(y, ad.Node)
assert isinstance(jacobian_x2, ad.Node)
assert T.array_equal(y_val, x1_val + x2_val)
assert T.array_equal(jacobian_x2_val, expected_jacobian_x2_val)
def test_mul_jacobian_one_scalar(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x1 = ad.Variable(name="x1", shape=[])
x2 = ad.Variable(name="x2", shape=[2, 2])
# test both cases of left and right multiply a scalar
for y in [x1 * x2, x2 * x1]:
jacobian_x1, jacobian_x2 = ad.jacobians(y, [x1, x2])
executor = ad.Executor([y, jacobian_x1, jacobian_x2])
x1_val = T.tensor(2.)
x2_val = T.tensor([[5., 6.], [7., 8.]])
y_val, jacobian_x1_val, jacobian_x2_val = executor.run(feed_dict={
x1: x1_val,
x2: x2_val
})
I = T.identity(2)
expected_jacobian_x1_val = T.einsum("ai,bj,ij->ab", I, I, x2_val)
expected_jacobian_x2_val = x1_val * T.einsum("ai,bj->abij", I, I)
assert isinstance(y, ad.Node)
assert T.array_equal(y_val, x1_val * x2_val)
assert T.array_equal(jacobian_x1_val, expected_jacobian_x1_val)
assert T.array_equal(jacobian_x2_val, expected_jacobian_x2_val)
def test_jacobian_einsum(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x1 = ad.Variable(name="x1", shape=[3, 3, 3])
x2 = ad.Variable(name="x2", shape=[3, 3, 3])
y = ad.einsum("ikl,jkl->ijk", x1, x2)
jacobian_x1, jacobian_x2 = ad.jacobians(y, [x1, x2])
executor = ad.Executor([y, jacobian_x1, jacobian_x2])
x1_val = T.random((3, 3, 3))
x2_val = T.random((3, 3, 3))
y_val, jacobian_x1_val, jacobian_x2_val = executor.run(feed_dict={
x1: x1_val,
x2: x2_val,
})
I = T.identity(3)
expected_jacobian_x1_val = T.einsum("im,kn,jno->ijkmno", I, I, x2_val)
expected_jacobian_x2_val = T.einsum("jm,kn,ino->ijkmno", I, I, x1_val)
assert isinstance(y, ad.Node)
assert T.array_equal(y_val, T.einsum("ikl,jkl->ijk", x1_val, x2_val))
assert T.array_equal(jacobian_x1_val, expected_jacobian_x1_val)
assert T.array_equal(jacobian_x2_val, expected_jacobian_x2_val)
def test_three_mul_jacobian_scalars(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x1 = ad.Variable(name="x1", shape=[])
x2 = ad.Variable(name="x2", shape=[])
x3 = ad.Variable(name="x3", shape=[])
y = x1 * x2 * x3
jacobian_x1, = ad.jacobians(y, [x1])
executor = ad.Executor([y, jacobian_x1])
x1_val = T.tensor(1.)
x2_val = T.tensor(2.)
x3_val = T.tensor(3.)
y_val, jacobian_x1_val = executor.run(feed_dict={
x1: x1_val,
x2: x2_val,
x3: x3_val
})
expected_jacobian_x1_val = x2_val * x3_val
assert isinstance(y, ad.Node)
assert T.array_equal(y_val, x1_val * x2_val * x3_val)
assert T.array_equal(jacobian_x1_val, expected_jacobian_x1_val)
def test_three_mul_jacobian(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x1 = ad.Variable(name="x1", shape=[2, 2])
x2 = ad.Variable(name="x2", shape=[2, 2])
x3 = ad.Variable(name="x3", shape=[2, 2])
y = x1 * x2 * x3
jacobian_x1, = ad.jacobians(y, [x1])
executor = ad.Executor([y, jacobian_x1])
x1_val = T.tensor([[1., 2.], [3., 4.]])
x2_val = T.tensor([[5., 6.], [7., 8.]])
x3_val = T.tensor([[9., 10.], [11., 12.]])
y_val, jacobian_x1_val = executor.run(feed_dict={
x1: x1_val,
x2: x2_val,
x3: x3_val
})
I = T.identity(2)
expected_jacobian_x1_val = T.einsum("ai,bj,ij,ij->abij", I, I, x2_val,
x3_val)
assert isinstance(y, ad.Node)
assert T.array_equal(y_val, x1_val * x2_val * x3_val)
assert T.array_equal(jacobian_x1_val, expected_jacobian_x1_val)
def test_sub_jacobian_w_chain(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x1 = ad.Variable(name="x1", shape=[2, 2])
x2 = ad.Variable(name="x2", shape=[2, 2])
x3 = ad.Variable(name="x3", shape=[2, 2])
y = x1 - x2
z = x3 - y
jacobian_x2, = ad.jacobians(z, [x2])
executor = ad.Executor([z, jacobian_x2])
x1_val = T.tensor([[1, 1], [1, 1]])
x2_val = T.tensor([[1, 1], [1, 1]])
x3_val = T.tensor([[1, 1], [1, 1]])
z_val, jacobian_x2_val = executor.run(feed_dict={
x1: x1_val,
x2: x2_val,
x3: x3_val
})
I = T.identity(2)
expected_jacobian_x2_val = T.einsum("ac,bd->abcd", I, I)
assert isinstance(z, ad.Node)
assert isinstance(jacobian_x2, ad.Node)
assert T.array_equal(z_val, x3_val - x1_val + x2_val)
assert T.array_equal(jacobian_x2_val, expected_jacobian_x2_val)
def test_add_jacobian(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x1 = ad.Variable(name="x1", shape=[2, 2])
x2 = ad.Variable(name="x2", shape=[2, 2])
y = x1 + x2
jacobian_x2, = ad.jacobians(y, [x2])
executor = ad.Executor([y, jacobian_x2])
x1_val = T.tensor([[1, 1], [1, 1]])
x2_val = T.tensor([[1, 1], [1, 1]])
y_val, jacobian_x2_val = executor.run(feed_dict={
x1: x1_val,
x2: x2_val
})
I = T.identity(2)
expected_jacobian_x2_val = T.einsum("ac,bd->abcd", I, I)
assert isinstance(y, ad.Node)
assert isinstance(jacobian_x2, ad.Node)
assert T.array_equal(y_val, x1_val + x2_val)
assert T.array_equal(jacobian_x2_val, expected_jacobian_x2_val)
def test_mul_const_jacobian(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x1 = ad.Variable(name="x2", shape=[2, 2])
jacobian_x1, = ad.jacobians(2 * x1, [x1])
executor = ad.Executor([jacobian_x1])
x1_val = T.tensor([[5., 6.], [7., 8.]])
jacobian_x1_val, = executor.run(feed_dict={x1: x1_val})
I = T.identity(2)
expected_jacobian_x1_val = 2 * T.einsum("ai,bj->abij", I, I)
assert T.array_equal(jacobian_x1_val, expected_jacobian_x1_val)
def test_jacobian_trace_einsum(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x = ad.Variable(name="x", shape=[2, 2])
trace = ad.einsum('ii->', x)
grad_x, = ad.jacobians(trace, [x])
executor = ad.Executor([trace, grad_x])
x_val = T.tensor([[1., 2.], [3., 4.]])
trace_val, grad_x_val = executor.run(feed_dict={x: x_val})
expected_trace_val = T.einsum('ii->', x_val)
expected_grad_x_val = T.identity(2)
assert T.array_equal(trace_val, expected_trace_val)
assert T.array_equal(grad_x_val, expected_grad_x_val)
def test_jacobian_summation_einsum(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x = ad.Variable(name="x", shape=[2, 2])
x_sum = ad.einsum('ij->', x)
grad_x, = ad.jacobians(x_sum, [x])
executor = ad.Executor([x_sum, grad_x])
x_val = T.tensor([[1., 2.], [3., 4.]])
x_sum_val, grad_x_val = executor.run(feed_dict={x: x_val})
expected_x_sum_val = T.sum(x_val)
expected_grad_x_val = T.ones_like(x_val)
assert T.array_equal(x_sum_val, expected_x_sum_val)
assert T.array_equal(grad_x_val, expected_grad_x_val)
def test_jacobian_summation_einsum_2(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x = ad.Variable(name="x", shape=[2, 2])
y = ad.Variable(name="y", shape=[2, 2])
out = ad.einsum('ij,ab->ab', x, y)
grad_x, = ad.jacobians(out, [x])
executor = ad.Executor([out, grad_x])
x_val = T.tensor([[1., 2.], [3., 4.]])
y_val = T.tensor([[5., 6.], [7., 8.]])
out_val, grad_x_val = executor.run(feed_dict={x: x_val, y: y_val})
expected_out_val = T.einsum('ij,ab->ab', x_val, y_val)
expected_grad_x_val = T.einsum('ij,ab->abij', T.ones(x_val.shape),
y_val)
assert T.array_equal(out_val, expected_out_val)
assert T.array_equal(grad_x_val, expected_grad_x_val)
def test_add_jacobian_w_chain(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x1 = ad.Variable(name="x1", shape=[2, 2])
x2 = ad.Variable(name="x2", shape=[2, 2])
x3 = ad.Variable(name="x3", shape=[2, 2])
y = x1 + x2
z = y + x3
jacobian_x2, = ad.jacobians(z, [x2])
executor = ad.Executor([z, jacobian_x2])
x1_val = T.tensor([[1, 1], [1, 1]])
x2_val = T.tensor([[1, 1], [1, 1]])
x3_val = T.tensor([[1, 1], [1, 1]])
z_val, jacobian_x2_val = executor.run(feed_dict={
x1: x1_val,
x2: x2_val,
x3: x3_val
})
I = T.identity(2)
# jacobian_z_y = T.einsum("ae,bf->abef", I, I)
# jacobian_y_x2 = T.einsum("ec,fd->efcd", I, I)
# jacobian_z_x2 = T.einsum("abef,efcd->abcd", jacobian_z_y, jacobian_y_x2)
# = T.einsum("ae,bf,ec,fd->abcd", I, I, I, I)
# = T.einsum("ac,bd->abcd", I, I)
expected_jacobian_x2_val = T.einsum("ac,bd->abcd", I, I)
assert isinstance(z, ad.Node)
assert isinstance(jacobian_x2, ad.Node)
assert T.array_equal(z_val, x1_val + x2_val + x3_val)
assert T.array_equal(jacobian_x2_val, expected_jacobian_x2_val)
