# 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.
# ============================================================================
"""Utilities for TensorFlow Probability ODE solvers."""

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

import tensorflow.compat.v2 as tf

from tensorflow_probability.python.internal import dtype_util
from tensorflow_probability.python.internal import prefer_static as ps
from tensorflow_probability.python.math import gradient as tfp_gradient

from tensorflow.python.util import nest  # pylint: disable=g-direct-tensorflow-import


class Bunch(dict):
  """Dict-subclass which exposes keys as attributes."""

  def __getattr__(self, name):
    return self[name]

  def __setattr__(self, name, value):
    self[name] = value

  def __delattr__(self, name):
    del self[name]


def assert_increasing(tensor, identifier):
  """Assert if a `Tensor` is strictly increasing."""
  return tf.Assert(
      tf.reduce_all(tensor[1:] > tensor[:-1]),
      ['`{}` must be strictly increasing.'.format(identifier)])


def assert_nonnegative(tensor, identifier):
  """Assert if a `Tensor` is nonnegative."""
  return tf.Assert(
      tf.reduce_all(tensor >= tf.zeros([], dtype=tensor.dtype)),
      ['`{}` must be nonnegative'.format(identifier)])


def assert_positive(tensor, identifier):
  """Assert if a `Tensor` is positive."""
  return tf.Assert(
      tf.reduce_all(tensor > tf.zeros([], dtype=tensor.dtype)),
      ['`{}` must be positive.'.format(identifier)])


def error_if_not_real_or_complex(tensor, identifier):
  """Raise a `TypeError` if the `Tensor` is neither real nor complex."""
  if not (dtype_util.is_floating(tensor.dtype) or
          dtype_util.is_complex(tensor.dtype)):
    raise TypeError(
        '`{}` must have a floating point or complex floating point dtype.'
        .format(identifier))


def error_if_not_vector(tensor, identifier):
  """Raise a `ValueError` if the `Tensor` is not 1-D."""
  if len(list(tensor.shape)) != 1:
    raise ValueError('`{}` must be a 1-D tensor.'.format(identifier))


def _flatten_nested_jacobian(jacobian, state_shape):
  """Flattens a nested Jacobian into a matrix.

  The flattening and concatenation follows the interpretation of the structure
  as being a leading 'axis', meaning that if the input has 'shape':
  [input_structure, A, B], and the output has 'shape':
  [output_structure, C, D], the input Jacobian should have the 'shape':
  [input_structure, output_structure, A, B, C, D]. As with the regular axes, the
  encoding is input major.

  Args:
    jacobian: A nested Jacobian.
    state_shape: A nested collection of state shapes.

  Returns:
    jacobian_mat: The Jacobian matrix.

  #### Examples

  Non-structured state:

  ```python
  input = tf.zeros([1, 2])
  output = tf.zeros([3])
  jacobian = tf.zeros([1, 2, 3])
  ```

  Structured state:

  ```python
  input = {'x': tf.zeros([1, 2])}
  output = {'y': tf.zeros([3])}
  jacobian = {'x': {'y': tf.zeros([1, 2, 3])}}
  ```

  A more complicated structure:

  ```python
  input = [tf.zeros([1, 2]), tf.zeros([])]
  output = {'y': tf.zeros([3])}
  jacobian = [{'y': tf.zeros([1, 2, 3])}, {'y': tf.zeros([3]}]
  ```

  """

  def _flatten_row(jacobian_row, state_shape_part):
    state_size = ps.reduce_prod(state_shape_part)
    jacobian_row_mats = tf.nest.map_structure(
        lambda j: tf.reshape(j, ps.stack([state_size, -1], axis=0)),
        jacobian_row)
    return tf.concat(tf.nest.flatten(jacobian_row_mats), axis=-1)

  flat_rows = nest.map_structure_up_to(state_shape, _flatten_row, jacobian,
                                       state_shape)
  return tf.concat(tf.nest.flatten(flat_rows), axis=0)


def get_jacobian_fn_mat(jacobian_fn, ode_fn_vec, state_shape, dtype):
  """Returns a wrapper around the user-specified `jacobian_fn` argument.

  `jacobian_fn` is an optional argument that can either be a constant `Tensor`
  or a function of the form `jacobian_fn(time, state)`. This function returns a
  wrapper `jacobian_fn_mat(time, state_vec)` whose second argument and output
  are 1 and 2-D `Tensor`s, respectively, corresponding reshaped versions of
  `state` and `jacobian_fn(time, state)`.

  Args:
    jacobian_fn: User-specified `jacobian_fn` passed to `solve`.
    ode_fn_vec: Result of `get_ode_fn_vec`.
    state_shape: The shape of the second argument and output of `ode_fn`.
    dtype: If `jacobian_fn` is constant, what dtype to convert it to.

  Returns:
    The wrapper described above.
  """
  if jacobian_fn is None:
    return _AutomaticJacobian(ode_fn_vec)

  if not callable(jacobian_fn):
    jacobian_fn = tf.nest.map_structure(
        lambda x: tf.convert_to_tensor(x, dtype=dtype), jacobian_fn)
    constant_jacobian_mat = _flatten_nested_jacobian(jacobian_fn, state_shape)

    def constant_jacobian_fn_mat(*_):
      return constant_jacobian_mat

    return constant_jacobian_fn_mat

  def jacobian_fn_mat(time, state_vec):
    return _flatten_nested_jacobian(
        jacobian_fn(time, get_state_from_vec(state_vec, state_shape)),
        state_shape)

  return jacobian_fn_mat


def get_state_vec(state):
  """Converts a possibly nested state into a vector."""
  return tf.concat(
      tf.nest.flatten(
          tf.nest.map_structure(lambda s: tf.reshape(s, [-1]), state)),
      axis=-1)


def get_state_from_vec(state_vec, state_shape):
  """Inverse of `get_state_vec`."""
  state_sizes = tf.nest.map_structure(ps.reduce_prod, state_shape)
  state_vec_parts = tf.nest.pack_sequence_as(
      state_shape, tf.split(state_vec, tf.nest.flatten(state_sizes), axis=-1))
  batch_shape = ps.shape(state_vec)[:-1]

  return tf.nest.map_structure(
      lambda sv, s: tf.reshape(sv, ps.concat([batch_shape, s], axis=0)),
      state_vec_parts, state_shape)


def get_ode_fn_vec(ode_fn, state_shape):
  """Returns a wrapper around the user-specified `ode_fn` argument.

  The second argument and output of `ode_fn(time, state)` are N-D `Tensor`s.
  This function returns a wrapper `ode_fn_vec(time, state_vec)` whose
  second argument and output are 1-D `Tensor`s corresponding to reshaped
  versions of `state` and `ode_fn(time, state)`.

  Args:
    ode_fn: User-specified `ode_fn` passed to `solve`.
    state_shape: The shape of the second argument and output of `ode_fn`.

  Returns:
    The wrapper described above.
  """

  def ode_fn_vec(time, state_vec):
    return get_state_vec(
        ode_fn(time, get_state_from_vec(state_vec, state_shape)))

  return ode_fn_vec


def next_step_size(step_size, order, error_ratio, safety_factor,
                   min_step_size_factor, max_step_size_factor):
  """Computes the next step size to use.

  Computes the next step size by applying a multiplicative factor to the current
  step size. This factor is
  ```none
  factor_unclamped = error_ratio**(-1. / (order + 1)) * safety_factor
  factor = clamp(factor_unclamped, min_step_size_factor, max_step_size_factor)
  ```

  Args:
    step_size: Scalar float `Tensor` specifying the current step size.
    order: Scalar integer `Tensor` specifying the order of the method.
    error_ratio: Scalar float `Tensor` specifying the ratio of the error in the
      computed state and the tolerance.
    safety_factor: Scalar float `Tensor`.
    min_step_size_factor: Scalar float `Tensor` specifying a lower bound on the
      multiplicative factor.
    max_step_size_factor: Scalar float `Tensor` specifying an upper bound on the
      multiplicative factor.

  Returns:
    Scalar float `Tensor` specifying the next step size.
  """
  order_cast = tf.cast(order, error_ratio.dtype)
  factor = error_ratio**(-1. / (order_cast + 1.))
  return step_size * tf.clip_by_value(
      safety_factor * factor, min_step_size_factor, max_step_size_factor)


def stop_gradient_of_real_or_complex_entries(nested):
  """Calls `tf.stop_gradient` on real or complex elements of a nested structure.

  Args:
    nested: The nested structure. May contain `Tensor`s with different `dtype`s.

  Returns:
    The resulting nested structure.
  """
  def _one_part(tensor):
    tensor = tf.convert_to_tensor(tensor)
    if dtype_util.is_floating(tensor.dtype) or dtype_util.is_complex(
        tensor.dtype):
      return tf.stop_gradient(tensor)
    else:
      return tensor

  return tf.nest.map_structure(_one_part, nested)


def right_mult_by_jacobian_mat(jacobian_fn_mat, ode_fn_vec, time, state_vec,
                               vec):
  """Right multiplies a vector by the Jacobian.

  The Jacobian is constructed by calling `jacobian_fn_mat(time, state_vec)` if
  doing so does not require automatic differentiation. Otherwise, chain rule
  automatic differentiation is applied to `ode_fn_vec` to obtain the Jacobian.

  Args:
    jacobian_fn_mat: Result of `get_jacobian_fn_mat`.
    ode_fn_vec: Result of `get_ode_fn_vec`.
    time: Scalar float `Tensor` time at which to evalute the Jacobian.
    state_vec: `Tensor` state at which to evaluate the Jacobian.
    vec: `Tensor` with shape is compatible with the Jacobian.

  Returns:
    `Tensor` representing the dot product.
  """
  if isinstance(jacobian_fn_mat, _AutomaticJacobian):
    # Compute the dot product by using chain rule automatic differentiation.
    _, dot_product = tfp_gradient.value_and_gradient(
        lambda x: ode_fn_vec(time, x), state_vec, output_gradients=vec)
  else:
    # Compute the dot product by explicitly constructing the Jacobian matrix.
    jacobian_mat = jacobian_fn_mat(time, state_vec)
    dot_product = tf.reshape(tf.matmul(vec[tf.newaxis, :], jacobian_mat), [-1])
  return dot_product


class _AutomaticJacobian(object):
  """Callable that returns a Jacobian computed by automatic differentiation."""

  def __init__(self, ode_fn_vec):
    self._ode_fn_vec = ode_fn_vec

  def __call__(self, time, state_vec):
    jacobian_mat = tfp_gradient.batch_jacobian(
        lambda state_vec: self._ode_fn_vec(time, state_vec[0])[tf.newaxis],
        state_vec[tf.newaxis])

    if jacobian_mat is None:
      return tf.zeros([tf.size(state_vec)] * 2, dtype=state_vec.dtype)
    return jacobian_mat[0]
