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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 tensorflow.ops.math_ops.matrix_inverse."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import itertools
from absl.testing import parameterized
import numpy as np
from tensorflow.compiler.tests import xla_test
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import linalg_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.platform import test
class QrOpTest(xla_test.XLATestCase, parameterized.TestCase):
def AdjustedNorm(self, x):
"""Computes the norm of matrices in 'x', adjusted for dimension and type."""
norm = np.linalg.norm(x, axis=(-2, -1))
return norm / (max(x.shape[-2:]) * np.finfo(x.dtype).eps)
def CompareOrthogonal(self, x, y, rank):
# We only compare the first 'rank' orthogonal vectors since the
# remainder form an arbitrary orthonormal basis for the
# (row- or column-) null space, whose exact value depends on
# implementation details. Notice that since we check that the
# matrices of singular vectors are unitary elsewhere, we do
# implicitly test that the trailing vectors of x and y span the
# same space.
x = x[..., 0:rank]
y = y[..., 0:rank]
# Q is only unique up to sign (complex phase factor for complex matrices),
# so we normalize the sign first.
sum_of_ratios = np.sum(np.divide(y, x), -2, keepdims=True)
phases = np.divide(sum_of_ratios, np.abs(sum_of_ratios))
x *= phases
self.assertTrue(np.all(self.AdjustedNorm(x - y) < 30.0))
def CheckApproximation(self, a, q, r):
# Tests that a ~= q*r.
precision = self.AdjustedNorm(a - np.matmul(q, r))
self.assertTrue(np.all(precision < 10.0))
def CheckUnitary(self, x):
# Tests that x[...,:,:]^H * x[...,:,:] is close to the identity.
xx = math_ops.matmul(x, x, adjoint_a=True)
identity = array_ops.matrix_band_part(array_ops.ones_like(xx), 0, 0)
precision = self.AdjustedNorm(xx.eval() - identity.eval())
self.assertTrue(np.all(precision < 5.0))
def _test(self, dtype, shape, full_matrices):
np.random.seed(1)
x_np = np.random.uniform(
low=-1.0, high=1.0, size=np.prod(shape)).reshape(shape).astype(dtype)
with self.test_session() as sess:
x_tf = array_ops.placeholder(dtype)
with self.test_scope():
q_tf, r_tf = linalg_ops.qr(x_tf, full_matrices=full_matrices)
q_tf_val, r_tf_val = sess.run([q_tf, r_tf], feed_dict={x_tf: x_np})
q_dims = q_tf_val.shape
np_q = np.ndarray(q_dims, dtype)
np_q_reshape = np.reshape(np_q, (-1, q_dims[-2], q_dims[-1]))
new_first_dim = np_q_reshape.shape[0]
x_reshape = np.reshape(x_np, (-1, x_np.shape[-2], x_np.shape[-1]))
for i in range(new_first_dim):
if full_matrices:
np_q_reshape[i, :, :], _ = np.linalg.qr(
x_reshape[i, :, :], mode="complete")
else:
np_q_reshape[i, :, :], _ = np.linalg.qr(
x_reshape[i, :, :], mode="reduced")
np_q = np.reshape(np_q_reshape, q_dims)
self.CompareOrthogonal(np_q, q_tf_val, min(shape[-2:]))
self.CheckApproximation(x_np, q_tf_val, r_tf_val)
self.CheckUnitary(q_tf_val)
SIZES = [1, 2, 5, 10, 32, 100, 300]
DTYPES = [np.float32]
PARAMS = itertools.product(SIZES, SIZES, DTYPES)
@parameterized.parameters(*PARAMS)
def testQR(self, rows, cols, dtype):
# TODO(b/111317468): implement full_matrices=False, test other types.
for full_matrices in [True]:
# Only tests the (3, 2) case for small numbers of rows/columns.
for batch_dims in [(), (3,)] + [(3, 2)] * (max(rows, cols) < 10):
self._test(dtype, batch_dims + (rows, cols), full_matrices)
def testLarge2000x2000(self):
self._test(np.float32, (2000, 2000), full_matrices=True)
if __name__ == "__main__":
test.main()
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