# Copyright 2019 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.
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# ==============================================================================
"""`LinearOperator` acting like a Householder transformation."""

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

from tensorflow.python.framework import errors
from tensorflow.python.framework import ops
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import control_flow_ops
from tensorflow.python.ops import math_ops
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.util.tf_export import tf_export

__all__ = ["LinearOperatorHouseholder",]


@tf_export("linalg.LinearOperatorHouseholder")
class LinearOperatorHouseholder(linear_operator.LinearOperator):
  """`LinearOperator` acting like a [batch] of Householder transformations.

  This operator acts like a [batch] of householder reflections with shape
  `[B1,...,Bb, N, N]` for some `b >= 0`.  The first `b` indices index a
  batch member.  For every batch index `(i1,...,ib)`, `A[i1,...,ib, : :]` is
  an `N x N` matrix.  This matrix `A` is not materialized, but for
  purposes of broadcasting this shape will be relevant.

  `LinearOperatorHouseholder` is initialized with a (batch) vector.

  A Householder reflection, defined via a vector `v`, which reflects points
  in `R^n` about the hyperplane orthogonal to `v` and through the origin.

  ```python
  # Create a 2 x 2 householder transform.
  vec = [1 / np.sqrt(2), 1. / np.sqrt(2)]
  operator = LinearOperatorHouseholder(vec)

  operator.to_dense()
  ==> [[0.,  -1.]
       [-1., -0.]]

  operator.shape
  ==> [2, 2]

  operator.log_abs_determinant()
  ==> scalar Tensor

  x = ... Shape [2, 4] Tensor
  operator.matmul(x)
  ==> Shape [2, 4] Tensor
  ```

  #### Shape compatibility

  This operator acts on [batch] matrix with compatible shape.
  `x` is a batch matrix with compatible shape for `matmul` and `solve` if

  ```
  operator.shape = [B1,...,Bb] + [N, N],  with b >= 0
  x.shape =   [C1,...,Cc] + [N, R],
  and [C1,...,Cc] broadcasts with [B1,...,Bb] to [D1,...,Dd]
  ```

  #### Matrix property hints

  This `LinearOperator` is initialized with boolean flags of the form `is_X`,
  for `X = non_singular, self_adjoint, positive_definite, square`.
  These have the following meaning:

  * If `is_X == True`, callers should expect the operator to have the
    property `X`.  This is a promise that should be fulfilled, but is *not* a
    runtime assert.  For example, finite floating point precision may result
    in these promises being violated.
  * If `is_X == False`, callers should expect the operator to not have `X`.
  * If `is_X == None` (the default), callers should have no expectation either
    way.
  """

  def __init__(self,
               reflection_axis,
               is_non_singular=None,
               is_self_adjoint=None,
               is_positive_definite=None,
               is_square=None,
               name="LinearOperatorHouseholder"):
    r"""Initialize a `LinearOperatorHouseholder`.

    Args:
      reflection_axis:  Shape `[B1,...,Bb, N]` `Tensor` with `b >= 0` `N >= 0`.
        The vector defining the hyperplane to reflect about.
        Allowed dtypes: `float16`, `float32`, `float64`, `complex64`,
        `complex128`.
      is_non_singular:  Expect that this operator is non-singular.
      is_self_adjoint:  Expect that this operator is equal to its hermitian
        transpose.  This is autoset to true
      is_positive_definite:  Expect that this operator is positive definite,
        meaning the quadratic form `x^H A x` has positive real part for all
        nonzero `x`.  Note that we do not require the operator to be
        self-adjoint to be positive-definite.  See:
        https://en.wikipedia.org/wiki/Positive-definite_matrix#Extension_for_non-symmetric_matrices
        This is autoset to false.
      is_square:  Expect that this operator acts like square [batch] matrices.
        This is autoset to true.
      name: A name for this `LinearOperator`.

    Raises:
      ValueError:  `is_self_adjoint` is not `True`, `is_positive_definite` is
        not `False` or `is_square` is not `True`.
    """

    with ops.name_scope(name, values=[reflection_axis]):
      self._reflection_axis = linear_operator_util.convert_nonref_to_tensor(
          reflection_axis, name="reflection_axis")
      self._check_reflection_axis(self._reflection_axis)

      # Check and auto-set hints.
      if is_self_adjoint is False:  # pylint:disable=g-bool-id-comparison
        raise ValueError("A Householder operator is always self adjoint.")
      else:
        is_self_adjoint = True

      if is_positive_definite is True:  # pylint:disable=g-bool-id-comparison
        raise ValueError(
            "A Householder operator is always non-positive definite.")
      else:
        is_positive_definite = False