def testNoBatchStatic(self):
x = np.array([[1., 0], [2, 1]]) # np.linalg.cholesky(y)
y = np.array([[1., 2], [2, 5]]) # np.matmul(x, x.T)
with self.test_session() as sess:
y_actual = bijectors.CholeskyOuterProduct().forward(x=x)
x_actual = bijectors.CholeskyOuterProduct().inverse(y=y)
[y_actual_, x_actual_] = sess.run([y_actual, x_actual])
self.assertAllEqual([2, 2], y_actual.get_shape())
self.assertAllEqual([2, 2], x_actual.get_shape())
self.assertAllClose(y, y_actual_)
self.assertAllClose(x, x_actual_)
def testNoBatchDeferred(self):
x = np.array([[1., 0], [2, 1]]) # np.linalg.cholesky(y)
y = np.array([[1., 2], [2, 5]]) # np.matmul(x, x.T)
with self.test_session() as sess:
x_pl = array_ops.placeholder(dtypes.float32)
y_pl = array_ops.placeholder(dtypes.float32)
y_actual = bijectors.CholeskyOuterProduct().forward(x=x_pl)
x_actual = bijectors.CholeskyOuterProduct().inverse(y=y_pl)
[y_actual_, x_actual_] = sess.run([y_actual, x_actual],
feed_dict={x_pl: x, y_pl: y})
self.assertEqual(None, y_actual.get_shape())
self.assertEqual(None, x_actual.get_shape())
self.assertAllClose(y, y_actual_)
self.assertAllClose(x, x_actual_)
def testBijectorMatrix(self):
with self.test_session():
bijector = bijectors.CholeskyOuterProduct(validate_args=True)
self.assertEqual("cholesky_outer_product", bijector.name)
x = [[[1., 0], [2, 1]], [[np.sqrt(2.), 0], [np.sqrt(8.), 1]]]
y = np.matmul(x, np.transpose(x, axes=(0, 2, 1)))
# Fairly easy to compute differentials since we have 2x2.
dx_dy = [[[2. * 1, 0, 0], [2, 1, 0], [0, 2 * 2, 2 * 1]],
[[2 * np.sqrt(2.), 0, 0], [np.sqrt(8.),
np.sqrt(2.), 0],
[0, 2 * np.sqrt(8.), 2 * 1]]]
ildj = -np.sum(np.log(
np.asarray(dx_dy).diagonal(offset=0, axis1=1, axis2=2)),
axis=1)
self.assertAllEqual((2, 2, 2), bijector.forward(x).get_shape())
self.assertAllEqual((2, 2, 2), bijector.inverse(y).get_shape())
self.assertAllClose(y, bijector.forward(x).eval())
self.assertAllClose(x, bijector.inverse(y).eval())
self.assertAllClose(ildj,
bijector.inverse_log_det_jacobian(y).eval(),
atol=0.,
rtol=1e-7)
self.assertAllClose(-bijector.inverse_log_det_jacobian(y).eval(),
bijector.forward_log_det_jacobian(x).eval(),
atol=0.,
rtol=1e-7)
def testNoBatchStaticJacobian(self):
x = np.eye(2)
bijector = bijectors.CholeskyOuterProduct()
# The Jacobian matrix is 2 * tf.eye(2), which has jacobian determinant 4.
self.assertAllClose(
np.log(4),
self.evaluate(bijector.forward_log_det_jacobian(x, event_ndims=2)))
def testScalarCongruency(self):
with self.test_session():
bijector = bijectors.CholeskyOuterProduct(event_ndims=0,
validate_args=True)
assert_scalar_congruency(bijector,
lower_x=1e-3,
upper_x=1.5,
rtol=0.05)
def testNoBatchDynamicJacobian(self):
x = np.eye(2)
bijector = bijectors.CholeskyOuterProduct()
x_pl = array_ops.placeholder(dtypes.float32)
with self.test_session():
log_det_jacobian = bijector.forward_log_det_jacobian(x_pl,
event_ndims=2)
# The Jacobian matrix is 2 * tf.eye(2), which has jacobian determinant 4.
self.assertAllClose(np.log(4), log_det_jacobian.eval({x_pl: x}))
def testBijectorScalar(self):
with self.test_session():
bijector = bijectors.CholeskyOuterProduct(event_ndims=0,
validate_args=True)
self.assertEqual("cholesky_outer_product", bijector.name)
x = [[[1., 5], [2, 1]], [[np.sqrt(2.), 3], [np.sqrt(8.), 1]]]
y = np.square(x)
ildj = -np.log(2.) - np.log(x)
self.assertAllClose(y, bijector.forward(x).eval())
self.assertAllClose(x, bijector.inverse(y).eval())
self.assertAllClose(ildj,
bijector.inverse_log_det_jacobian(y).eval(),
atol=0.,
rtol=1e-7)
self.assertAllClose(-bijector.inverse_log_det_jacobian(y).eval(),
bijector.forward_log_det_jacobian(x).eval(),
atol=0.,
rtol=1e-7)
