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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.
# ==============================================================================
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
from tensorflow.contrib.solvers.python.ops import linear_equations
from tensorflow.contrib.solvers.python.ops import util
from tensorflow.python.framework import constant_op
from tensorflow.python.ops import array_ops
from tensorflow.python.platform import test as test_lib
def _add_test(test, test_name, fn):
test_name = "_".join(["test", test_name])
if hasattr(test, test_name):
raise RuntimeError("Test %s defined more than once" % test_name)
setattr(test, test_name, fn)
class LinearEquationsTest(test_lib.TestCase):
pass # Filled in below.
def _get_linear_equations_tests(dtype_, use_static_shape_, shape_):
def test_conjugate_gradient(self):
np.random.seed(1)
a_np = np.random.uniform(
low=-1.0, high=1.0, size=np.prod(shape_)).reshape(shape_).astype(dtype_)
# Make a selfadjoint, positive definite.
a_np = np.dot(a_np.T, a_np)
# jacobi preconditioner
jacobi_np = np.zeros_like(a_np)
jacobi_np[range(a_np.shape[0]), range(a_np.shape[1])] = (
1.0 / a_np.diagonal())
rhs_np = np.random.uniform(
low=-1.0, high=1.0, size=shape_[0]).astype(dtype_)
x_np = np.zeros_like(rhs_np)
tol = 1e-6 if dtype_ == np.float64 else 1e-3
max_iter = 20
with self.test_session() as sess:
if use_static_shape_:
a = constant_op.constant(a_np)
rhs = constant_op.constant(rhs_np)
x = constant_op.constant(x_np)
jacobi = constant_op.constant(jacobi_np)
else:
a = array_ops.placeholder(dtype_)
rhs = array_ops.placeholder(dtype_)
x = array_ops.placeholder(dtype_)
jacobi = array_ops.placeholder(dtype_)
operator = util.create_operator(a)
preconditioners = [
None, util.identity_operator(a),
util.create_operator(jacobi)
]
cg_results = []
for preconditioner in preconditioners:
cg_graph = linear_equations.conjugate_gradient(
operator,
rhs,
preconditioner=preconditioner,
x=x,
tol=tol,
max_iter=max_iter)
if use_static_shape_:
cg_val = sess.run(cg_graph)
else:
cg_val = sess.run(
cg_graph,
feed_dict={
a: a_np,
rhs: rhs_np,
x: x_np,
jacobi: jacobi_np
})
norm_r0 = np.linalg.norm(rhs_np)
norm_r = np.linalg.norm(cg_val.r)
self.assertLessEqual(norm_r, tol * norm_r0)
# Validate that we get an equally small residual norm with numpy
# using the computed solution.
r_np = rhs_np - np.dot(a_np, cg_val.x)
norm_r_np = np.linalg.norm(r_np)
self.assertLessEqual(norm_r_np, tol * norm_r0)
cg_results.append(cg_val)
# Validate that we get same results using identity_preconditioner
# and None
self.assertEqual(cg_results[0].i, cg_results[1].i)
self.assertAlmostEqual(cg_results[0].gamma, cg_results[1].gamma)
self.assertAllClose(cg_results[0].r, cg_results[1].r, rtol=tol)
self.assertAllClose(cg_results[0].x, cg_results[1].x, rtol=tol)
self.assertAllClose(cg_results[0].p, cg_results[1].p, rtol=tol)
return [test_conjugate_gradient]
if __name__ == "__main__":
for dtype in np.float32, np.float64:
for size in 1, 4, 10:
for use_static_shape in True, False:
shape = [size, size]
arg_string = "%s_%s_staticshape_%s" % (dtype.__name__, size,
use_static_shape)
for test_fn in _get_linear_equations_tests(dtype, use_static_shape,
shape):
name = "_".join(["LinearEquations", test_fn.__name__, arg_string])
_add_test(LinearEquationsTest, name, test_fn)
test_lib.main()
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