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# Copyright 2016 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 numpy as np
from tensorflow.python.framework import constant_op
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 SvdOpTest(test.TestCase):
def testWrongDimensions(self):
# The input to svd should be a tensor of at least rank 2.
scalar = constant_op.constant(1.)
with self.assertRaisesRegexp(ValueError,
"Shape must be at least rank 2 but is rank 0"):
linalg_ops.svd(scalar)
vector = constant_op.constant([1., 2.])
with self.assertRaisesRegexp(ValueError,
"Shape must be at least rank 2 but is rank 1"):
linalg_ops.svd(vector)
def _GetSvdOpTest(dtype_, shape_, use_static_shape_):
is_complex = dtype_ in (np.complex64, np.complex128)
is_single = dtype_ in (np.float32, np.complex64)
def CompareSingularValues(self, x, y):
if is_single:
tol = 5e-5
else:
tol = 1e-14
self.assertAllClose(x, y, atol=(x[0] + y[0]) * tol)
def CompareSingularVectors(self, x, y, rank):
if is_single:
atol = 5e-4
else:
atol = 5e-14
# We only compare the first 'rank' singular 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]
# Singular vectors are 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.assertAllClose(x, y, atol=atol)
def CheckApproximation(self, a, u, s, v, full_matrices):
if is_single:
tol = 1e-5
else:
tol = 1e-14
# Tests that a ~= u*diag(s)*transpose(v).
batch_shape = a.shape[:-2]
m = a.shape[-2]
n = a.shape[-1]
diag_s = math_ops.cast(array_ops.matrix_diag(s), dtype=dtype_)
if full_matrices:
if m > n:
zeros = array_ops.zeros(batch_shape + (m - n, n), dtype=dtype_)
diag_s = array_ops.concat([diag_s, zeros], a.ndim - 2)
elif n > m:
zeros = array_ops.zeros(batch_shape + (m, n - m), dtype=dtype_)
diag_s = array_ops.concat([diag_s, zeros], a.ndim - 1)
a_recon = math_ops.matmul(u, diag_s)
a_recon = math_ops.matmul(a_recon, v, adjoint_b=True)
self.assertAllClose(a_recon.eval(), a, rtol=tol, atol=tol)
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)
if is_single:
tol = 1e-5
else:
tol = 1e-14
self.assertAllClose(identity.eval(), xx.eval(), atol=tol)
def Test(self):
np.random.seed(1)
x_np = np.random.uniform(
low=-1.0, high=1.0, size=np.prod(shape_)).reshape(shape_).astype(dtype_)
if is_complex:
x_np += 1j * np.random.uniform(
low=-1.0, high=1.0,
size=np.prod(shape_)).reshape(shape_).astype(dtype_)
for compute_uv in False, True:
for full_matrices in False, True:
with self.test_session() as sess:
if use_static_shape_:
x_tf = constant_op.constant(x_np)
else:
x_tf = array_ops.placeholder(dtype_)
if compute_uv:
s_tf, u_tf, v_tf = linalg_ops.svd(x_tf,
compute_uv=compute_uv,
full_matrices=full_matrices)
if use_static_shape_:
s_tf_val, u_tf_val, v_tf_val = sess.run([s_tf, u_tf, v_tf])
else:
s_tf_val, u_tf_val, v_tf_val = sess.run([s_tf, u_tf, v_tf],
feed_dict={x_tf: x_np})
else:
s_tf = linalg_ops.svd(x_tf,
compute_uv=compute_uv,
full_matrices=full_matrices)
if use_static_shape_:
s_tf_val = sess.run(s_tf)
else:
s_tf_val = sess.run(s_tf, feed_dict={x_tf: x_np})
if compute_uv:
u_np, s_np, v_np = np.linalg.svd(x_np,
compute_uv=compute_uv,
full_matrices=full_matrices)
else:
s_np = np.linalg.svd(x_np,
compute_uv=compute_uv,
full_matrices=full_matrices)
# We explicitly avoid the situation where numpy eliminates a first
# dimension that is equal to one
s_np = np.reshape(s_np, s_tf_val.shape)
CompareSingularValues(self, s_np, s_tf_val)
if compute_uv:
CompareSingularVectors(self, u_np, u_tf_val, min(shape_[-2:]))
CompareSingularVectors(self,
np.conj(np.swapaxes(v_np, -2, -1)), v_tf_val,
min(shape_[-2:]))
CheckApproximation(self, x_np, u_tf_val, s_tf_val, v_tf_val,
full_matrices)
CheckUnitary(self, u_tf_val)
CheckUnitary(self, v_tf_val)
return Test
if __name__ == "__main__":
for dtype in np.float32, np.float64, np.complex64, np.complex128:
for rows in 1, 2, 5, 10, 32, 100:
for cols in 1, 2, 5, 10, 32, 100:
for batch_dims in [(), (3,)] + [(3, 2)] * (max(rows, cols) < 10):
shape = batch_dims + (rows, cols)
for use_static_shape in True, False:
name = "%s_%s_%s" % (dtype.__name__, "_".join(map(str, shape)),
use_static_shape)
setattr(SvdOpTest, "testSvd_" + name,
_GetSvdOpTest(dtype, shape, use_static_shape))
test.main()
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