# Copyright 2019 DeepMind Technologies Limited. 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.
# ==============================================================================
"""Gradient clipping transformations.

Note that complex numbers are also supported, see
https://gist.github.com/wdphy16/118aef6fb5f82c49790d7678cf87da29
"""

import chex
import jax
from jax import tree_util as jtu
import jax.numpy as jnp

from optax import tree_utils as otu
from optax._src import base
from optax._src import linear_algebra
from optax._src import numerics


def clip(max_delta: chex.Numeric) -> base.GradientTransformation:
  """Clips updates element-wise, to be in ``[-max_delta, +max_delta]``.

  Args:
    max_delta: The maximum absolute value for each element in the update.

  Returns:
    A `GradientTransformation` object.
  """

  def update_fn(updates, state, params=None):
    del params
    return otu.tree_clip(updates, -max_delta, max_delta), state

  return base.GradientTransformation(base.init_empty_state, update_fn)


def clip_by_block_rms(threshold: float) -> base.GradientTransformation:
  """Clips updates to a max rms for the gradient of each param vector or matrix.

  A `block` is here a weight vector (e.g. in a Linear layer) or a weight matrix
  (e.g. in a convolutional layer) appearing as a leaf in the grads/param pytree.

  Args:
    threshold: The maximum rms for the gradient of each param vector or matrix.

  Returns:
    A `GradientTransformation` object.
  """

  def update_fn(updates, state, params=None):
    del params

    def _clip_fn(u):
      clip_denom = jnp.maximum(
          1.0,
          jnp.sqrt(jnp.mean(numerics.abs_sq(u))) / threshold)
      return u / clip_denom

    updates = jtu.tree_map(_clip_fn, updates)
    return updates, state

  return base.GradientTransformation(base.init_empty_state, update_fn)


def clip_by_global_norm(max_norm: float) -> base.GradientTransformation:
  """Clips updates using their global norm.

  References:
    [Pascanu et al, 2012](https://arxiv.org/abs/1211.5063)

  Args:
    max_norm: The maximum global norm for an update.

  Returns:
    A `GradientTransformation` object.
  """

  def update_fn(updates, state, params=None):
    del params
    g_norm = linear_algebra.global_norm(updates)
    # TODO(b/163995078): revert back to the following (faster) implementation
    # once analysed how it affects backprop through update (e.g. meta-gradients)
    # g_norm = jnp.maximum(max_norm, g_norm)
    # updates = jtu.tree_map(lambda t: (t / g_norm) * max_norm, updates)
    trigger = jnp.squeeze(g_norm < max_norm)
    chex.assert_shape(trigger, ())  # A scalar.

    def clip_fn(t):
      return jax.lax.select(trigger, t, (t / g_norm.astype(t.dtype)) * max_norm)

    updates = jtu.tree_map(clip_fn, updates)
    return updates, state

  return base.GradientTransformation(base.init_empty_state, update_fn)


def per_example_global_norm_clip(
    grads: list[chex.Array], l2_norm_clip: float
) -> tuple[list[chex.Array], jax.Array]:
  """Applies gradient clipping per-example using their global norm.

  References:
    [Abadi et al, 2016](https://arxiv.org/abs/1607.00133)

  Args:
    grads: flattened update; the function expects these to have a batch
      dimension on the 0th axis.
    l2_norm_clip: maximum L2 norm of the per-example gradients.

  Returns:
    A tuple containing sum of the clipped per-example grads, and the number of
    per-example grads that were clipped.
  """
  bsize = grads[0].shape[0]

  if any(g.ndim == 0 or bsize != g.shape[0] for g in grads):
    raise ValueError(
        'Unlike other transforms, `per_example_global_norm_clip` expects'
        ' `grads` to have a batch dimension in the 0th axis.')

  global_grad_norms = jax.vmap(linear_algebra.global_norm)(grads)
  divisors = jnp.maximum(global_grad_norms / l2_norm_clip, 1.0)
  num_clipped = jnp.greater(divisors, 1.0).sum()
  clipped_sum = [(jnp.moveaxis(g, 0, -1) / divisors).sum(-1) for g in grads]
  return clipped_sum, num_clipped


def per_example_layer_norm_clip(
    grads: list[chex.Array],
    global_l2_norm_clip: float,
    uniform: bool = True,
    eps: float = 1e-8,
) -> tuple[list[chex.Array], list[chex.Array]]:
  """Applies gradient clipping per-example using per-layer norms.

  References:
    [McMahan et al, 2012](https://arxiv.org/abs/1710.06963)]

  Args:
    grads: flattened update; i.e. a list of gradients in which each item is
      the gradient for one layer; the function expects these to have a batch
      dimension on the 0th axis.
    global_l2_norm_clip: overall L2 clip norm to use.
    uniform: If `True`, per-layer clip norm is global_l2_norm_clip/sqrt(L),
      where L is the number of layers. Otherwise, per-layer clip norm is
      global_l2_norm_clip * sqrt(f), where f is the fraction of total model
      parameters that are in this layer.
    eps: Small positive value to add to norms to avoid possible division by
      zero.

  Let C = `global_l2_norm_clip value`. Then per-layer clipping is done as
  follows:
  (1) If `uniform` is `True`, each of the K layers has an individual clip
      norm of C / sqrt(K).
  (2) If `uniform` is `False`, each of the K layers has an individual clip
      norm of C * sqrt(D_i / D) where D_i is the number of parameters in
      layer i, and D is the total number of parameters in the model.

  Returns:
    A tuple containing sum of the clipped per-example grads and the number of
    per-example grads that were clipped for each layer.
  """
  bsize = grads[0].shape[0]

  if any(g.ndim == 0 or bsize != g.shape[0] for g in grads):
    raise ValueError(
        'Unlike other transforms, `per_example_layer_norm_clip` expects'
        ' `grads` to have a batch dimension in the 0th axis; got shapes:'
        f' {(g.shape for g in grads)}.'
    )

  num_layers = len(grads)

  # Compute per-layer clip norms, based on whether we are using uniform
  # variant or not.
  if uniform:
    # Create list of length `num_layers` of per-layer clip norm.
    layer_clip_norms = (
        global_l2_norm_clip * (1.0 / num_layers) ** 0.5,
    ) * num_layers
  else:
    total_params = sum(g[0].size for g in grads)
    layer_clip_norms = tuple(
        global_l2_norm_clip * (g[0].size / float(total_params)) ** 0.5
        for g in grads
    )

  # Compute per-layer grad norms.
  def map_layer_norm(grads_list):
    return [jnp.linalg.norm(g, ord=None, axis=None) for g in grads_list]

  layer_grad_norms_per_example = jax.vmap(map_layer_norm)(grads)

  # Perform clipping.
  divisors = (
      tuple(
          jnp.maximum(
              layer_grad_norm / (layer_clip_norm + eps), 1.0
          )
          for layer_grad_norm, layer_clip_norm in zip(
              layer_grad_norms_per_example, layer_clip_norms
          )
      )
  )
  num_clipped = [jnp.greater(divisor, 1.0).sum() for divisor in divisors]
  clipped_sum = [
      (g / jnp.expand_dims(d, axis=[i for i in range(1, g.ndim)])).sum(0)
      for g, d in zip(grads, divisors)
  ]
  return clipped_sum, num_clipped


def unitwise_norm(x: chex.Array) -> chex.Array:
  """Computes norms of each output unit separately."""
  if jnp.squeeze(x).ndim <= 1:  # Scalars and vectors
    squared_norm = jnp.sum(numerics.abs_sq(x), keepdims=True)
  # Note that this assumes parameters with a shape of length 3 are multihead
  # linear parameters--if you wish to apply AGC to 1D convs, you may need
  # to modify this line.
  elif x.ndim in (2, 3):  # Linear layers of shape IO or multihead linear
    squared_norm = jnp.sum(numerics.abs_sq(x), axis=0, keepdims=True)
  elif x.ndim == 4:  # Conv kernels of shape HWIO
    squared_norm = jnp.sum(numerics.abs_sq(x), axis=(0, 1, 2), keepdims=True)
  else:
    raise ValueError(
        f'Expected parameter with shape in {1, 2, 3, 4}, got {x.shape}.')
  chex.assert_is_broadcastable(squared_norm.shape, x.shape)
  return jnp.broadcast_to(jnp.sqrt(squared_norm), x.shape)


def unitwise_clip(g_norm: chex.Array,
                  max_norm: chex.Array,
                  grad: chex.Array,
                  div_eps: float = 1e-6) -> chex.Array:
  """Applies gradient clipping unit-wise."""
  # This little max(., div_eps) is distinct from the normal eps and just
  # prevents division by zero. It technically should be impossible to engage.
  clipped_grad = grad * (max_norm / jnp.maximum(g_norm, div_eps))
  chex.assert_equal_shape((g_norm, max_norm, grad, clipped_grad))
  return jnp.where(g_norm < max_norm, grad, clipped_grad)


def adaptive_grad_clip(clipping: float,
                       eps: float = 1e-3) -> base.GradientTransformation:
  """Clips updates to be at most ``clipping * parameter_norm``, unit-wise.

  References:
    [Brock, Smith, De, Simonyan 2021] High-Performance Large-Scale Image
    Recognition Without Normalization. (https://arxiv.org/abs/2102.06171)

  Args:
    clipping: The maximum allowed ratio of update norm to parameter norm.
    eps: An epsilon term to prevent clipping of zero-initialized params.

  Returns:
    A `GradientTransformation` object.
  """

  def update_fn(updates, state, params):
    if params is None:
      raise ValueError(base.NO_PARAMS_MSG)
    g_norm, p_norm = jtu.tree_map(unitwise_norm, (updates, params))
    # Maximum allowable norm.
    max_norm = jtu.tree_map(
        lambda x: clipping * jnp.maximum(x, eps), p_norm)
    # If grad norm > clipping * param_norm, rescale.
    updates = jtu.tree_map(unitwise_clip, g_norm, max_norm, updates)
    return updates, state

  return base.GradientTransformation(base.init_empty_state, update_fn)