def test_invertible_from_lu(self):
lower_upper, permutation = tf.linalg.lu([[1., 2, 3], [4, 5, 6],
[0.5, 0., 0.25]])
conv1x1 = tfb.MatvecLU(lower_upper=lower_upper,
permutation=permutation,
validate_args=True)
channels = tf.compat.dimension_value(lower_upper.shape[-1])
x = tf.random.uniform(shape=[2, 28, 28, channels])
fwd = conv1x1.forward(x)
rev_fwd = conv1x1.inverse(fwd)
fldj = conv1x1.forward_log_det_jacobian(x, event_ndims=3)
rev = conv1x1.inverse(x)
fwd_rev = conv1x1.forward(rev)
ildj = conv1x1.inverse_log_det_jacobian(x, event_ndims=3)
[x_, fwd_, rev_, fwd_rev_, rev_fwd_, fldj_,
ildj_] = self.evaluate([x, fwd, rev, fwd_rev, rev_fwd, fldj, ildj])
self.assertAllClose(x_, fwd_rev_, atol=1e-3, rtol=1e-6)
self.assertAllClose(x_, rev_fwd_, atol=1e-3, rtol=1e-6)
self.assertEqual(fldj_, -ildj_)
self.assertTrue(fldj_ > 1.) # Notably, bounded away from zero.
# We now check that the bijector isn't simply the identity function. We do
# this by checking that at least 50% of pixels differ by at least 10%.
self.assertTrue(np.mean(np.abs(x_ - fwd_) > 0.1 * x_) > 0.5)
self.assertTrue(np.mean(np.abs(x_ - rev_) > 0.1 * x_) > 0.5)
def test_invertible_from_trainable_lu_factorization(self):
channels = 3
conv1x1 = tfb.MatvecLU(*trainable_lu_factorization(channels, seed=42),
validate_args=True)
self.evaluate(tf.compat.v1.global_variables_initializer())
x = tf.random.uniform(shape=[2, 28, 28, channels])
fwd = conv1x1.forward(x)
rev_fwd = conv1x1.inverse(fwd)
fldj = conv1x1.forward_log_det_jacobian(x, event_ndims=3)
rev = conv1x1.inverse(x)
fwd_rev = conv1x1.forward(rev)
ildj = conv1x1.inverse_log_det_jacobian(x, event_ndims=3)
[x_, fwd_, rev_, fwd_rev_, rev_fwd_, fldj_,
ildj_] = self.evaluate([x, fwd, rev, fwd_rev, rev_fwd, fldj, ildj])
self.assertAllClose(x_, fwd_rev_, atol=1e-3, rtol=1e-6)
self.assertAllClose(x_, rev_fwd_, atol=1e-3, rtol=1e-6)
self.assertEqual(fldj_, -ildj_)
self.assertNear(0., fldj_, err=1e-3)
# We now check that the bijector isn't simply the identity function. We do
# this by checking that at least 50% of pixels differ by at least 10%.
self.assertTrue(np.mean(np.abs(x_ - fwd_) > 0.1 * x_) > 0.5)
self.assertTrue(np.mean(np.abs(x_ - rev_) > 0.1 * x_) > 0.5)
def testTheoreticalFldj(self):
raw_mat = tf.constant([[1., 2, 3],
[4, 5, 6],
[0.5, 0., 0.25]])
nbatch = 5
batch_mats = raw_mat * tf.range(1., nbatch + 1.)[:, tf.newaxis, tf.newaxis]
lower_upper, permutation = tf.linalg.lu(tf.cast(batch_mats, tf.float64))
bijector = tfb.MatvecLU(
lower_upper=lower_upper, permutation=permutation, validate_args=True)
self.assertEqual(tf.float64, bijector.dtype)
channels = tf.compat.dimension_value(lower_upper.shape[-1])
x = np.random.uniform(size=[2, 7, nbatch, channels]).astype(np.float64)
y = self.evaluate(bijector.forward(x))
bijector_test_util.assert_bijective_and_finite(
bijector,
x,
y,
eval_func=self.evaluate,
event_ndims=1,
inverse_event_ndims=1,
rtol=1e-5)
fldj = bijector.forward_log_det_jacobian(x, event_ndims=1)
# The jacobian is not yet broadcast, since it is constant.
fldj = fldj + tf.zeros(tf.shape(x)[:-1], dtype=x.dtype)
fldj_theoretical = bijector_test_util.get_fldj_theoretical(
bijector, x, event_ndims=1)
self.assertAllClose(
self.evaluate(fldj_theoretical),
self.evaluate(fldj),
atol=1e-5,
rtol=1e-5)
def test_trainable_lu_factorization_init(self):
"""Initial LU factorization parameters do not change per execution."""
channels = 8
lower_upper, permutation = trainable_lu_factorization(channels, seed=42)
conv1x1 = tfb.MatvecLU(lower_upper, permutation, validate_args=True)
self.evaluate([v.initializer for v in conv1x1.variables])
lower_upper_1, permutation_1 = self.evaluate([lower_upper, permutation])
lower_upper_2, permutation_2 = self.evaluate([lower_upper, permutation])
self.assertAllEqual(lower_upper_1, lower_upper_2)
self.assertAllEqual(permutation_1, permutation_2)
def testNonInvertibleLUAssert(self):
lower_upper, permutation = self.evaluate(
tf.linalg.lu([[1., 2, 3], [4, 5, 6], [0.5, 0., 0.25]]))
lower_upper = tf.Variable(lower_upper)
self.evaluate(lower_upper.initializer)
bijector = tfb.MatvecLU(
lower_upper=lower_upper, permutation=permutation, validate_args=True)
self.evaluate(bijector.forward([1., 2, 3]))
with tf.control_dependencies([
lower_upper[1, 1].assign(-lower_upper[1, 1])]):
self.evaluate(bijector.forward([1., 2, 3]))
with self.assertRaisesOpError('`lower_upper` must have nonzero diagonal'):
with tf.control_dependencies([lower_upper[1, 1].assign(0)]):
self.evaluate(bijector.forward([1., 2, 3]))