# 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.

# ==============================================================================

"""`LinearOperator` coming from a [[nested] block] circulant matrix."""

from __future__ import absolute_import

from __future__ import division

from __future__ import print_function

import numpy as np

from tensorflow.python.framework import dtypes

from tensorflow.python.framework import ops

from tensorflow.python.framework import tensor_shape

from tensorflow.python.ops import array_ops

from tensorflow.python.ops import check_ops

from tensorflow.python.ops import math_ops

from tensorflow.python.ops.distributions import util as distribution_util

from tensorflow.python.ops.linalg import linalg_impl as linalg

from tensorflow.python.ops.linalg import linear_operator

from tensorflow.python.ops.linalg import linear_operator_util

from tensorflow.python.ops.signal import fft_ops

from tensorflow.python.util.tf_export import tf_export

__all__ = [

]

# Different FFT Ops will be used for different block depths.

_FFT_OP = {1: fft_ops.fft, 2: fft_ops.fft2d, 3: fft_ops.fft3d}

_IFFT_OP = {1: fft_ops.ifft, 2: fft_ops.ifft2d, 3: fft_ops.ifft3d}

# TODO(langmore) Add transformations that create common spectrums, e.g.

# starting with the convolution kernel

# start with half a spectrum, and create a Hermitian one.

# common filters.

# TODO(langmore) Support rectangular Toeplitz matrices.

class _BaseLinearOperatorCirculant(linear_operator.LinearOperator):

return math_ops.cast(math_ops.complex(re_d_value, im_d_value), self.dtype)

@tf_export("linalg.LinearOperatorCirculant")

class LinearOperatorCirculant(_BaseLinearOperatorCirculant):

name=name)

@tf_export("linalg.LinearOperatorCirculant2D")

class LinearOperatorCirculant2D(_BaseLinearOperatorCirculant):

name=name)

@tf_export("linalg.LinearOperatorCirculant3D")

class LinearOperatorCirculant3D(_BaseLinearOperatorCirculant):