# Copyright 2018 The TensorFlow Probability Authors.
#
# 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.
# ============================================================================
"""FillTriangular bijector."""

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

# Dependency imports
import numpy as np

import tensorflow.compat.v2 as tf

from tensorflow_probability.python.bijectors import bijector
from tensorflow_probability.python.internal import assert_util
from tensorflow_probability.python.internal import tensorshape_util
from tensorflow_probability.python.math.linalg import fill_triangular
from tensorflow_probability.python.math.linalg import fill_triangular_inverse


__all__ = [
    'FillTriangular',
]


class FillTriangular(bijector.AutoCompositeTensorBijector):
  """Transforms vectors to triangular.

  Triangular matrix elements are filled in a clockwise spiral.

  Given input with shape `batch_shape + [d]`, produces output with
  shape `batch_shape + [n, n]`, where
   `n = (-1 + sqrt(1 + 8 * d))/2`.
  This follows by solving the quadratic equation
   `d = 1 + 2 + ... + n = n * (n + 1)/2`.

  #### Example

  ```python
  b = tfb.FillTriangular(upper=False)
  b.forward([1, 2, 3, 4, 5, 6])
  # ==> [[4, 0, 0],
  #      [6, 5, 0],
  #      [3, 2, 1]]

  b = tfb.FillTriangular(upper=True)
  b.forward([1, 2, 3, 4, 5, 6])
  # ==> [[1, 2, 3],
  #      [0, 5, 6],
  #      [0, 0, 4]]

  ```
  """

  def __init__(self,
               upper=False,
               validate_args=False,
               name='fill_triangular'):
    """Instantiates the `FillTriangular` bijector.

    Args:
      upper: Python `bool` representing whether output matrix should be upper
        triangular (`True`) or lower triangular (`False`, default).
      validate_args: Python `bool` indicating whether arguments should be
        checked for correctness.
      name: Python `str` name given to ops managed by this object.
    """
    parameters = dict(locals())
    with tf.name_scope(name) as name:
      self._upper = upper
      super(FillTriangular, self).__init__(
          forward_min_event_ndims=1,
          inverse_min_event_ndims=2,
          is_constant_jacobian=True,
          validate_args=validate_args,
          parameters=parameters,
          name=name)

  @classmethod
  def _parameter_properties(cls, dtype):
    return dict()

  def _forward(self, x):
    return fill_triangular(x, upper=self._upper)

  def _inverse(self, y):
    return fill_triangular_inverse(y, upper=self._upper)

  def _forward_log_det_jacobian(self, x):
    return tf.zeros([], dtype=x.dtype)

  def _inverse_log_det_jacobian(self, y):
    return tf.zeros([], dtype=y.dtype)

  @property
  def _is_permutation(self):
    return True

  def _forward_event_shape(self, input_shape):
    batch_shape, d = input_shape[:-1], tf.compat.dimension_value(
        input_shape[-1])
    if d is None:
      n = None
    else:
      n = vector_size_to_square_matrix_size(d, self.validate_args)
    return tensorshape_util.concatenate(batch_shape, [n, n])

  def _inverse_event_shape(self, output_shape):
    batch_shape, n1, n2 = (output_shape[:-2],
                           tf.compat.dimension_value(output_shape[-2]),
                           tf.compat.dimension_value(output_shape[-1]))
    if n1 is None or n2 is None:
      m = None
    elif n1 != n2:
      raise ValueError('Matrix must be square. (saw [{}, {}])'.format(n1, n2))
    else:
      m = n1 * (n1 + 1) // 2
    return tensorshape_util.concatenate(batch_shape, [m])

  def _forward_event_shape_tensor(self, input_shape_tensor):
    batch_shape, d = input_shape_tensor[:-1], input_shape_tensor[-1]
    n = vector_size_to_square_matrix_size(d, self.validate_args)
    return tf.concat([batch_shape, [n, n]], axis=0)

  def _inverse_event_shape_tensor(self, output_shape_tensor):
    batch_shape, n = output_shape_tensor[:-2], output_shape_tensor[-1]
    if self.validate_args:
      is_square_matrix = assert_util.assert_equal(
          n, output_shape_tensor[-2], message='Matrix must be square.')
      with tf.control_dependencies([is_square_matrix]):
        n = tf.identity(n)
    d = tf.cast(n * (n + 1) / 2, output_shape_tensor.dtype)
    return tf.concat([batch_shape, [d]], axis=0)


def vector_size_to_square_matrix_size(d, validate_args, name=None):
  """Convert a vector size to a matrix size."""
  if isinstance(d, (float, int, np.generic, np.ndarray)):
    n = (-1 + np.sqrt(1 + 8 * d)) / 2.
    if float(int(n)) != n:
      raise ValueError('Vector length {} is not a triangular number.'.format(d))
    return int(n)
  else:
    with tf.name_scope(name or 'vector_size_to_square_matrix_size') as name:
      n = (-1. + tf.sqrt(1 + 8. * tf.cast(d, dtype=tf.float32))) / 2.
      if validate_args:
        with tf.control_dependencies([
            tf.debugging.Assert(
                tf.math.equal(
                    tf.cast(tf.cast(n, dtype=tf.int32), dtype=tf.float32), n),
                data=['Vector length is not a triangular number: ', d]
            )
        ]):
          n = tf.identity(n)
      return tf.cast(n, d.dtype)
