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# Copyright 2018 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Tests for MatrixInverseTriL bijector."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
from tensorflow.contrib.distributions.python.ops import bijectors
from tensorflow.python.framework import errors
from tensorflow.python.framework import test_util
from tensorflow.python.platform import test
class MatrixInverseTriLBijectorTest(test.TestCase):
"""Tests the correctness of the Y = inv(tril) transformation."""
#The inverse of 0 is undefined, as the numbers above the main
#diagonal must be zero, we zero out these numbers after running inverse.
#See: https://github.com/numpy/numpy/issues/11445
def _inv(self, x):
y = np.linalg.inv(x)
#triu_indices only works on 2d arrays
#need to iterate over all the 2d arrays in a x-dimensional array.
for idx in np.ndindex(y.shape[0:-2]):
y[idx][np.triu_indices(y[idx].shape[-1], 1)] = 0
return y
@test_util.run_in_graph_and_eager_modes
def testComputesCorrectValues(self):
inv = bijectors.MatrixInverseTriL(validate_args=True)
self.assertEqual("matrix_inverse_tril", inv.name)
x_ = np.array([[0.7, 0., 0.],
[0.1, -1., 0.],
[0.3, 0.25, 0.5]], dtype=np.float32)
x_inv_ = np.linalg.inv(x_)
expected_fldj_ = -6. * np.sum(np.log(np.abs(np.diag(x_))))
y = inv.forward(x_)
x_back = inv.inverse(x_inv_)
fldj = inv.forward_log_det_jacobian(x_, event_ndims=2)
ildj = inv.inverse_log_det_jacobian(x_inv_, event_ndims=2)
y_, x_back_, fldj_, ildj_ = self.evaluate([y, x_back, fldj, ildj])
self.assertAllClose(x_inv_, y_, atol=0., rtol=1e-5)
self.assertAllClose(x_, x_back_, atol=0., rtol=1e-5)
self.assertNear(expected_fldj_, fldj_, err=1e-3)
self.assertNear(-expected_fldj_, ildj_, err=1e-3)
@test_util.run_in_graph_and_eager_modes
def testOneByOneMatrix(self):
inv = bijectors.MatrixInverseTriL(validate_args=True)
x_ = np.array([[5.]], dtype=np.float32)
x_inv_ = np.array([[0.2]], dtype=np.float32)
expected_fldj_ = np.log(0.04)
y = inv.forward(x_)
x_back = inv.inverse(x_inv_)
fldj = inv.forward_log_det_jacobian(x_, event_ndims=2)
ildj = inv.inverse_log_det_jacobian(x_inv_, event_ndims=2)
y_, x_back_, fldj_, ildj_ = self.evaluate([y, x_back, fldj, ildj])
self.assertAllClose(x_inv_, y_, atol=0., rtol=1e-5)
self.assertAllClose(x_, x_back_, atol=0., rtol=1e-5)
self.assertNear(expected_fldj_, fldj_, err=1e-3)
self.assertNear(-expected_fldj_, ildj_, err=1e-3)
@test_util.run_in_graph_and_eager_modes
def testZeroByZeroMatrix(self):
inv = bijectors.MatrixInverseTriL(validate_args=True)
x_ = np.eye(0, dtype=np.float32)
x_inv_ = np.eye(0, dtype=np.float32)
expected_fldj_ = 0.
y = inv.forward(x_)
x_back = inv.inverse(x_inv_)
fldj = inv.forward_log_det_jacobian(x_, event_ndims=2)
ildj = inv.inverse_log_det_jacobian(x_inv_, event_ndims=2)
y_, x_back_, fldj_, ildj_ = self.evaluate([y, x_back, fldj, ildj])
self.assertAllClose(x_inv_, y_, atol=0., rtol=1e-5)
self.assertAllClose(x_, x_back_, atol=0., rtol=1e-5)
self.assertNear(expected_fldj_, fldj_, err=1e-3)
self.assertNear(-expected_fldj_, ildj_, err=1e-3)
@test_util.run_in_graph_and_eager_modes
def testBatch(self):
# Test batch computation with input shape (2, 1, 2, 2), i.e. batch shape
# (2, 1).
inv = bijectors.MatrixInverseTriL(validate_args=True)
x_ = np.array([[[[1., 0.],
[2., 3.]]],
[[[4., 0.],
[5., -6.]]]], dtype=np.float32)
x_inv_ = self._inv(x_)
expected_fldj_ = -4. * np.sum(
np.log(np.abs(np.diagonal(x_, axis1=-2, axis2=-1))), axis=-1)
y = inv.forward(x_)
x_back = inv.inverse(x_inv_)
fldj = inv.forward_log_det_jacobian(x_, event_ndims=2)
ildj = inv.inverse_log_det_jacobian(x_inv_, event_ndims=2)
y_, x_back_, fldj_, ildj_ = self.evaluate([y, x_back, fldj, ildj])
self.assertAllClose(x_inv_, y_, atol=0., rtol=1e-5)
self.assertAllClose(x_, x_back_, atol=0., rtol=1e-5)
self.assertAllClose(expected_fldj_, fldj_, atol=0., rtol=1e-3)
self.assertAllClose(-expected_fldj_, ildj_, atol=0., rtol=1e-3)
@test_util.run_in_graph_and_eager_modes
def testErrorOnInputRankTooLow(self):
inv = bijectors.MatrixInverseTriL(validate_args=True)
x_ = np.array([0.1], dtype=np.float32)
rank_error_msg = "must have rank at least 2"
with self.test_session():
with self.assertRaisesWithPredicateMatch(ValueError, rank_error_msg):
inv.forward(x_).eval()
with self.assertRaisesWithPredicateMatch(ValueError, rank_error_msg):
inv.inverse(x_).eval()
with self.assertRaisesWithPredicateMatch(ValueError, rank_error_msg):
inv.forward_log_det_jacobian(x_, event_ndims=2).eval()
with self.assertRaisesWithPredicateMatch(ValueError, rank_error_msg):
inv.inverse_log_det_jacobian(x_, event_ndims=2).eval()
# TODO(b/80481923): Figure out why these assertions fail, and fix them.
## def testErrorOnInputNonSquare(self):
## inv = bijectors.MatrixInverseTriL(validate_args=True)
## x_ = np.array([[1., 2., 3.],
## [4., 5., 6.]], dtype=np.float32)
## square_error_msg = "must be a square matrix"
## with self.test_session():
## with self.assertRaisesWithPredicateMatch(errors.InvalidArgumentError,
## square_error_msg):
## inv.forward(x_).eval()
## with self.assertRaisesWithPredicateMatch(errors.InvalidArgumentError,
## square_error_msg):
## inv.inverse(x_).eval()
## with self.assertRaisesWithPredicateMatch(errors.InvalidArgumentError,
## square_error_msg):
## inv.forward_log_det_jacobian(x_, event_ndims=2).eval()
## with self.assertRaisesWithPredicateMatch(errors.InvalidArgumentError,
## square_error_msg):
## inv.inverse_log_det_jacobian(x_, event_ndims=2).eval()
@test_util.run_in_graph_and_eager_modes
def testErrorOnInputNotLowerTriangular(self):
inv = bijectors.MatrixInverseTriL(validate_args=True)
x_ = np.array([[1., 2.],
[3., 4.]], dtype=np.float32)
triangular_error_msg = "must be lower triangular"
with self.test_session():
with self.assertRaisesWithPredicateMatch(errors.InvalidArgumentError,
triangular_error_msg):
inv.forward(x_).eval()
with self.assertRaisesWithPredicateMatch(errors.InvalidArgumentError,
triangular_error_msg):
inv.inverse(x_).eval()
with self.assertRaisesWithPredicateMatch(errors.InvalidArgumentError,
triangular_error_msg):
inv.forward_log_det_jacobian(x_, event_ndims=2).eval()
with self.assertRaisesWithPredicateMatch(errors.InvalidArgumentError,
triangular_error_msg):
inv.inverse_log_det_jacobian(x_, event_ndims=2).eval()
@test_util.run_in_graph_and_eager_modes
def testErrorOnInputSingular(self):
inv = bijectors.MatrixInverseTriL(validate_args=True)
x_ = np.array([[1., 0.],
[0., 0.]], dtype=np.float32)
nonsingular_error_msg = "must have all diagonal entries nonzero"
with self.test_session():
with self.assertRaisesOpError(nonsingular_error_msg):
inv.forward(x_).eval()
with self.assertRaisesOpError(nonsingular_error_msg):
inv.inverse(x_).eval()
with self.assertRaisesOpError(nonsingular_error_msg):
inv.forward_log_det_jacobian(x_, event_ndims=2).eval()
with self.assertRaisesOpError(nonsingular_error_msg):
inv.inverse_log_det_jacobian(x_, event_ndims=2).eval()
if __name__ == "__main__":
test.main()
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