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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.
# ==============================================================================
"""Utility functions for solvers."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import collections
from tensorflow.python.framework import constant_op
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import nn_ops
def create_operator(matrix):
"""Creates a linear operator from a rank-2 tensor."""
linear_operator = collections.namedtuple(
"LinearOperator", ["shape", "dtype", "apply", "apply_adjoint"])
# TODO(rmlarsen): Handle SparseTensor.
shape = matrix.get_shape()
if shape.is_fully_defined():
shape = shape.as_list()
else:
shape = array_ops.shape(matrix)
return linear_operator(
shape=shape,
dtype=matrix.dtype,
apply=lambda v: math_ops.matmul(matrix, v, adjoint_a=False),
apply_adjoint=lambda v: math_ops.matmul(matrix, v, adjoint_a=True))
def identity_operator(matrix):
"""Creates a linear operator from a rank-2 identity tensor."""
linear_operator = collections.namedtuple(
"LinearOperator", ["shape", "dtype", "apply", "apply_adjoint"])
shape = matrix.get_shape()
if shape.is_fully_defined():
shape = shape.as_list()
else:
shape = array_ops.shape(matrix)
return linear_operator(
shape=shape,
dtype=matrix.dtype,
apply=lambda v: v,
apply_adjoint=lambda v: v)
# TODO(rmlarsen): Measure if we should just call matmul.
def dot(x, y):
return math_ops.reduce_sum(math_ops.conj(x) * y)
# TODO(rmlarsen): Implement matrix/vector norm op in C++ in core.
# We need 1-norm, inf-norm, and Frobenius norm.
def l2norm_squared(v):
return constant_op.constant(2, dtype=v.dtype.base_dtype) * nn_ops.l2_loss(v)
def l2norm(v):
return math_ops.sqrt(l2norm_squared(v))
def l2normalize(v):
norm = l2norm(v)
return v / norm, norm
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