# Copyright 2021 DeepMind Technologies Limited
#
# 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.

"""Modules and utilities for the structure module."""

import functools
from typing import Dict
from alphafold.common import residue_constants
from alphafold.model import all_atom
from alphafold.model import common_modules
from alphafold.model import prng
from alphafold.model import quat_affine
from alphafold.model import r3
from alphafold.model import utils
import haiku as hk
import jax
import jax.numpy as jnp
import ml_collections
import numpy as np


def squared_difference(x, y):
  return jnp.square(x - y)


class InvariantPointAttention(hk.Module):
  """Invariant Point attention module.

  The high-level idea is that this attention module works over a set of points
  and associated orientations in 3D space (e.g. protein residues).

  Each residue outputs a set of queries and keys as points in their local
  reference frame.  The attention is then defined as the euclidean distance
  between the queries and keys in the global frame.

  Jumper et al. (2021) Suppl. Alg. 22 "InvariantPointAttention"
  """

  def __init__(self,
               config,
               global_config,
               dist_epsilon=1e-8,
               name='invariant_point_attention'):
    """Initialize.

    Args:
      config: Structure Module Config
      global_config: Global Config of Model.
      dist_epsilon: Small value to avoid NaN in distance calculation.
      name: Haiku Module name.
    """
    super().__init__(name=name)

    self._dist_epsilon = dist_epsilon
    self._zero_initialize_last = global_config.zero_init

    self.config = config

    self.global_config = global_config

  def __call__(self, inputs_1d, inputs_2d, mask, affine):
    """Compute geometry-aware attention.

    Given a set of query residues (defined by affines and associated scalar
    features), this function computes geometry-aware attention between the
    query residues and target residues.

    The residues produce points in their local reference frame, which
    are converted into the global frame in order to compute attention via
    euclidean distance.

    Equivalently, the target residues produce points in their local frame to be
    used as attention values, which are converted into the query residues'
    local frames.

    Args:
      inputs_1d: (N, C) 1D input embedding that is the basis for the
        scalar queries.
      inputs_2d: (N, M, C') 2D input embedding, used for biases and values.
      mask: (N, 1) mask to indicate which elements of inputs_1d participate
        in the attention.
      affine: QuatAffine object describing the position and orientation of
        every element in inputs_1d.

    Returns:
      Transformation of the input embedding.
    """
    num_residues, _ = inputs_1d.shape

    # Improve readability by removing a large number of 'self's.
    num_head = self.config.num_head
    num_scalar_qk = self.config.num_scalar_qk
    num_point_qk = self.config.num_point_qk
    num_scalar_v = self.config.num_scalar_v
    num_point_v = self.config.num_point_v
    num_output = self.config.num_channel

    assert num_scalar_qk > 0
    assert num_point_qk > 0
    assert num_point_v > 0

    # Construct scalar queries of shape:
    # [num_query_residues, num_head, num_points]
    q_scalar = common_modules.Linear(
        num_head * num_scalar_qk, name='q_scalar')(
            inputs_1d)
    q_scalar = jnp.reshape(
        q_scalar, [num_residues, num_head, num_scalar_qk])

    # Construct scalar keys/values of shape:
    # [num_target_residues, num_head, num_points]
    kv_scalar = common_modules.Linear(
        num_head * (num_scalar_v + num_scalar_qk), name='kv_scalar')(
            inputs_1d)
    kv_scalar = jnp.reshape(kv_scalar,
                            [num_residues, num_head,
                             num_scalar_v + num_scalar_qk])
    k_scalar, v_scalar = jnp.split(kv_scalar, [num_scalar_qk], axis=-1)

    # Construct query points of shape:
    # [num_residues, num_head, num_point_qk]

    # First construct query points in local frame.
    q_point_local = common_modules.Linear(
        num_head * 3 * num_point_qk, name='q_point_local')(
            inputs_1d)
    q_point_local = jnp.split(q_point_local, 3, axis=-1)
    # Project query points into global frame.
    q_point_global = affine.apply_to_point(q_point_local, extra_dims=1)
    # Reshape query point for later use.
    q_point = [
        jnp.reshape(x, [num_residues, num_head, num_point_qk])
        for x in q_point_global]

    # Construct key and value points.
    # Key points have shape [num_residues, num_head, num_point_qk]
    # Value points have shape [num_residues, num_head, num_point_v]

    # Construct key and value points in local frame.
    kv_point_local = common_modules.Linear(
        num_head * 3 * (num_point_qk + num_point_v), name='kv_point_local')(
            inputs_1d)
    kv_point_local = jnp.split(kv_point_local, 3, axis=-1)
    # Project key and value points into global frame.
    kv_point_global = affine.apply_to_point(kv_point_local, extra_dims=1)
    kv_point_global = [
        jnp.reshape(x, [num_residues,
                        num_head, (num_point_qk + num_point_v)])
        for x in kv_point_global]
    # Split key and value points.
    k_point, v_point = list(
        zip(*[
            jnp.split(x, [num_point_qk,], axis=-1)
            for x in kv_point_global
        ]))

    # We assume that all queries and keys come iid from N(0, 1) distribution
    # and compute the variances of the attention logits.
    # Each scalar pair (q, k) contributes Var q*k = 1
    scalar_variance = max(num_scalar_qk, 1) * 1.
    # Each point pair (q, k) contributes Var [0.5 ||q||^2 - <q, k>] = 9 / 2
    point_variance = max(num_point_qk, 1) * 9. / 2

    # Allocate equal variance to scalar, point and attention 2d parts so that
    # the sum is 1.

    num_logit_terms = 3

    scalar_weights = np.sqrt(1.0 / (num_logit_terms * scalar_variance))
    point_weights = np.sqrt(1.0 / (num_logit_terms * point_variance))
    attention_2d_weights = np.sqrt(1.0 / (num_logit_terms))

    # Trainable per-head weights for points.
    trainable_point_weights = jax.nn.softplus(hk.get_parameter(
        'trainable_point_weights', shape=[num_head],
        # softplus^{-1} (1)
        init=hk.initializers.Constant(np.log(np.exp(1.) - 1.))))
    point_weights *= jnp.expand_dims(trainable_point_weights, axis=1)

    v_point = [jnp.swapaxes(x, -2, -3) for x in v_point]

    q_point = [jnp.swapaxes(x, -2, -3) for x in q_point]
    k_point = [jnp.swapaxes(x, -2, -3) for x in k_point]
    dist2 = [
        squared_difference(qx[:, :, None, :], kx[:, None, :, :])
        for qx, kx in zip(q_point, k_point)
    ]
    dist2 = sum(dist2)
    attn_qk_point = -0.5 * jnp.sum(
        point_weights[:, None, None, :] * dist2, axis=-1)

    v = jnp.swapaxes(v_scalar, -2, -3)
    q = jnp.swapaxes(scalar_weights * q_scalar, -2, -3)
    k = jnp.swapaxes(k_scalar, -2, -3)
    attn_qk_scalar = jnp.matmul(q, jnp.swapaxes(k, -2, -1))
    attn_logits = attn_qk_scalar + attn_qk_point

    attention_2d = common_modules.Linear(
        num_head, name='attention_2d')(
            inputs_2d)

    attention_2d = jnp.transpose(attention_2d, [2, 0, 1])
    attention_2d = attention_2d_weights * attention_2d
    attn_logits += attention_2d

    mask_2d = mask * jnp.swapaxes(mask, -1, -2)
    attn_logits -= 1e5 * (1. - mask_2d)

    # [num_head, num_query_residues, num_target_residues]
    attn = jax.nn.softmax(attn_logits)

    # [num_head, num_query_residues, num_head * num_scalar_v]
    result_scalar = jnp.matmul(attn, v)

    # For point result, implement matmul manually so that it will be a float32
    # on TPU.  This is equivalent to
    # result_point_global = [jnp.einsum('bhqk,bhkc->bhqc', attn, vx)
    #                        for vx in v_point]
    # but on the TPU, doing the multiply and reduce_sum ensures the
    # computation happens in float32 instead of bfloat16.
    result_point_global = [jnp.sum(
        attn[:, :, :, None] * vx[:, None, :, :],
        axis=-2) for vx in v_point]

    # [num_query_residues, num_head, num_head * num_(scalar|point)_v]
    result_scalar = jnp.swapaxes(result_scalar, -2, -3)
    result_point_global = [
        jnp.swapaxes(x, -2, -3)
        for x in result_point_global]

    # Features used in the linear output projection. Should have the size
    # [num_query_residues, ?]
    output_features = []

    result_scalar = jnp.reshape(
        result_scalar, [num_residues, num_head * num_scalar_v])
    output_features.append(result_scalar)

    result_point_global = [
        jnp.reshape(r, [num_residues, num_head * num_point_v])
        for r in result_point_global]
    result_point_local = affine.invert_point(result_point_global, extra_dims=1)
    output_features.extend(result_point_local)

    output_features.append(jnp.sqrt(self._dist_epsilon +
                                    jnp.square(result_point_local[0]) +
                                    jnp.square(result_point_local[1]) +
                                    jnp.square(result_point_local[2])))

    # Dimensions: h = heads, i and j = residues,
    # c = inputs_2d channels
    # Contraction happens over the second residue dimension, similarly to how
    # the usual attention is performed.
    result_attention_over_2d = jnp.einsum('hij, ijc->ihc', attn, inputs_2d)
    num_out = num_head * result_attention_over_2d.shape[-1]
    output_features.append(
        jnp.reshape(result_attention_over_2d,
                    [num_residues, num_out]))

    final_init = 'zeros' if self._zero_initialize_last else 'linear'

    final_act = jnp.concatenate(output_features, axis=-1)

    return common_modules.Linear(
        num_output,
        initializer=final_init,
        name='output_projection')(final_act)


class FoldIteration(hk.Module):
  """A single iteration of the main structure module loop.

  Jumper et al. (2021) Suppl. Alg. 20 "StructureModule" lines 6-21

  First, each residue attends to all residues using InvariantPointAttention.
  Then, we apply transition layers to update the hidden representations.
  Finally, we use the hidden representations to produce an update to the
  affine of each residue.
  """

  def __init__(self, config, global_config,
               name='fold_iteration'):
    super().__init__(name=name)
    self.config = config
    self.global_config = global_config

  def __call__(self,
               activations,
               sequence_mask,
               update_affine,
               is_training,
               initial_act,
               safe_key=None,
               static_feat_2d=None,
               aatype=None):
    c = self.config

    if safe_key is None:
      safe_key = prng.SafeKey(hk.next_rng_key())

    def safe_dropout_fn(tensor, safe_key):
      return prng.safe_dropout(
          tensor=tensor,
          safe_key=safe_key,
          rate=c.dropout,
          is_deterministic=self.global_config.deterministic,
          is_training=is_training)

    affine = quat_affine.QuatAffine.from_tensor(activations['affine'])

    act = activations['act']
    attention_module = InvariantPointAttention(self.config, self.global_config)
    # Attention
    attn = attention_module(
        inputs_1d=act,
        inputs_2d=static_feat_2d,
        mask=sequence_mask,
        affine=affine)
    act += attn
    safe_key, *sub_keys = safe_key.split(3)
    sub_keys = iter(sub_keys)
    act = safe_dropout_fn(act, next(sub_keys))
    act = common_modules.LayerNorm(
        axis=[-1],
        create_scale=True,
        create_offset=True,
        name='attention_layer_norm')(
            act)

    final_init = 'zeros' if self.global_config.zero_init else 'linear'

    # Transition
    input_act = act
    for i in range(c.num_layer_in_transition):
      init = 'relu' if i < c.num_layer_in_transition - 1 else final_init
      act = common_modules.Linear(
          c.num_channel,
          initializer=init,
          name='transition')(
              act)
      if i < c.num_layer_in_transition - 1:
        act = jax.nn.relu(act)
    act += input_act
    act = safe_dropout_fn(act, next(sub_keys))
    act = common_modules.LayerNorm(
        axis=[-1],
        create_scale=True,
        create_offset=True,
        name='transition_layer_norm')(act)

    if update_affine:
      # This block corresponds to
      # Jumper et al. (2021) Alg. 23 "Backbone update"
      affine_update_size = 6

      # Affine update
      affine_update = common_modules.Linear(
          affine_update_size,
          initializer=final_init,
          name='affine_update')(
              act)

      affine = affine.pre_compose(affine_update)

    sc = MultiRigidSidechain(c.sidechain, self.global_config)(
        affine.scale_translation(c.position_scale), [act, initial_act], aatype)

    outputs = {'affine': affine.to_tensor(), 'sc': sc}

    affine = affine.apply_rotation_tensor_fn(jax.lax.stop_gradient)

    new_activations = {
        'act': act,
        'affine': affine.to_tensor()
    }
    return new_activations, outputs


def generate_affines(representations, batch, config, global_config,
                     is_training, safe_key):
  """Generate predicted affines for a single chain.

  Jumper et al. (2021) Suppl. Alg. 20 "StructureModule"

  This is the main part of the structure module - it iteratively applies
  folding to produce a set of predicted residue positions.

  Args:
    representations: Representations dictionary.
    batch: Batch dictionary.
    config: Config for the structure module.
    global_config: Global config.
    is_training: Whether the model is being trained.
    safe_key: A prng.SafeKey object that wraps a PRNG key.

  Returns:
    A dictionary containing residue affines and sidechain positions.
  """
  c = config
  sequence_mask = batch['seq_mask'][:, None]

  act = common_modules.LayerNorm(
      axis=[-1],
      create_scale=True,
      create_offset=True,
      name='single_layer_norm')(
          representations['single'])

  initial_act = act
  act = common_modules.Linear(
      c.num_channel, name='initial_projection')(
          act)

  affine = generate_new_affine(sequence_mask)

  fold_iteration = FoldIteration(
      c, global_config, name='fold_iteration')

  assert len(batch['seq_mask'].shape) == 1

  activations = {'act': act,
                 'affine': affine.to_tensor(),
                 }

  act_2d = common_modules.LayerNorm(
      axis=[-1],
      create_scale=True,
      create_offset=True,
      name='pair_layer_norm')(
          representations['pair'])

  outputs = []
  safe_keys = safe_key.split(c.num_layer)
  for sub_key in safe_keys:
    activations, output = fold_iteration(
        activations,
        initial_act=initial_act,
        static_feat_2d=act_2d,
        safe_key=sub_key,
        sequence_mask=sequence_mask,
        update_affine=True,
        is_training=is_training,
        aatype=batch['aatype'])
    outputs.append(output)

  output = jax.tree_map(lambda *x: jnp.stack(x), *outputs)
  # Include the activations in the output dict for use by the LDDT-Head.
  output['act'] = activations['act']

  return output


class StructureModule(hk.Module):
  """StructureModule as a network head.

  Jumper et al. (2021) Suppl. Alg. 20 "StructureModule"
  """

  def __init__(self, config, global_config, compute_loss=True,
               name='structure_module'):
    super().__init__(name=name)
    self.config = config
    self.global_config = global_config
    self.compute_loss = compute_loss

  def __call__(self, representations, batch, is_training,
               safe_key=None):
    c = self.config
    ret = {}

    if safe_key is None:
      safe_key = prng.SafeKey(hk.next_rng_key())

    output = generate_affines(
        representations=representations,
        batch=batch,
        config=self.config,
        global_config=self.global_config,
        is_training=is_training,
        safe_key=safe_key)

    ret['representations'] = {'structure_module': output['act']}

    ret['traj'] = output['affine'] * jnp.array([1.] * 4 +
                                               [c.position_scale] * 3)

    ret['sidechains'] = output['sc']

    atom14_pred_positions = r3.vecs_to_tensor(output['sc']['atom_pos'])[-1]
    ret['final_atom14_positions'] = atom14_pred_positions  # (N, 14, 3)
    ret['final_atom14_mask'] = batch['atom14_atom_exists']  # (N, 14)

    atom37_pred_positions = all_atom.atom14_to_atom37(atom14_pred_positions,
                                                      batch)
    atom37_pred_positions *= batch['atom37_atom_exists'][:, :, None]
    ret['final_atom_positions'] = atom37_pred_positions  # (N, 37, 3)

    ret['final_atom_mask'] = batch['atom37_atom_exists']  # (N, 37)
    ret['final_affines'] = ret['traj'][-1]

    if self.compute_loss:
      return ret
    else:
      no_loss_features = ['final_atom_positions', 'final_atom_mask',
                          'representations']
      no_loss_ret = {k: ret[k] for k in no_loss_features}
      return no_loss_ret

  def loss(self, value, batch):
    ret = {'loss': 0.}

    ret['metrics'] = {}
    # If requested, compute in-graph metrics.
    if self.config.compute_in_graph_metrics:
      atom14_pred_positions = value['final_atom14_positions']
      # Compute renaming and violations.
      value.update(compute_renamed_ground_truth(batch, atom14_pred_positions))
      value['violations'] = find_structural_violations(
          batch, atom14_pred_positions, self.config)

      # Several violation metrics:
      violation_metrics = compute_violation_metrics(
          batch=batch,
          atom14_pred_positions=atom14_pred_positions,
          violations=value['violations'])
      ret['metrics'].update(violation_metrics)

    backbone_loss(ret, batch, value, self.config)

    if 'renamed_atom14_gt_positions' not in value:
      value.update(compute_renamed_ground_truth(
          batch, value['final_atom14_positions']))
    sc_loss = sidechain_loss(batch, value, self.config)

    ret['loss'] = ((1 - self.config.sidechain.weight_frac) * ret['loss'] +
                   self.config.sidechain.weight_frac * sc_loss['loss'])
    ret['sidechain_fape'] = sc_loss['fape']

    supervised_chi_loss(ret, batch, value, self.config)

    if self.config.structural_violation_loss_weight:
      if 'violations' not in value:
        value['violations'] = find_structural_violations(
            batch, value['final_atom14_positions'], self.config)
      structural_violation_loss(ret, batch, value, self.config)

    return ret


def compute_renamed_ground_truth(
    batch: Dict[str, jnp.ndarray],
    atom14_pred_positions: jnp.ndarray,
    ) -> Dict[str, jnp.ndarray]:
  """Find optimal renaming of ground truth based on the predicted positions.

  Jumper et al. (2021) Suppl. Alg. 26 "renameSymmetricGroundTruthAtoms"

  This renamed ground truth is then used for all losses,
  such that each loss moves the atoms in the same direction.
  Shape (N).

  Args:
    batch: Dictionary containing:
      * atom14_gt_positions: Ground truth positions.
      * atom14_alt_gt_positions: Ground truth positions with renaming swaps.
      * atom14_atom_is_ambiguous: 1.0 for atoms that are affected by
          renaming swaps.
      * atom14_gt_exists: Mask for which atoms exist in ground truth.
      * atom14_alt_gt_exists: Mask for which atoms exist in ground truth
          after renaming.
      * atom14_atom_exists: Mask for whether each atom is part of the given
          amino acid type.
    atom14_pred_positions: Array of atom positions in global frame with shape
      (N, 14, 3).
  Returns:
    Dictionary containing:
      alt_naming_is_better: Array with 1.0 where alternative swap is better.
      renamed_atom14_gt_positions: Array of optimal ground truth positions
        after renaming swaps are performed.
      renamed_atom14_gt_exists: Mask after renaming swap is performed.
  """
  alt_naming_is_better = all_atom.find_optimal_renaming(
      atom14_gt_positions=batch['atom14_gt_positions'],
      atom14_alt_gt_positions=batch['atom14_alt_gt_positions'],
      atom14_atom_is_ambiguous=batch['atom14_atom_is_ambiguous'],
      atom14_gt_exists=batch['atom14_gt_exists'],
      atom14_pred_positions=atom14_pred_positions,
      atom14_atom_exists=batch['atom14_atom_exists'])

  renamed_atom14_gt_positions = (
      (1. - alt_naming_is_better[:, None, None])
      * batch['atom14_gt_positions']
      + alt_naming_is_better[:, None, None]
      * batch['atom14_alt_gt_positions'])

  renamed_atom14_gt_mask = (
      (1. - alt_naming_is_better[:, None]) * batch['atom14_gt_exists']
      + alt_naming_is_better[:, None] * batch['atom14_alt_gt_exists'])

  return {
      'alt_naming_is_better': alt_naming_is_better,  # (N)
      'renamed_atom14_gt_positions': renamed_atom14_gt_positions,  # (N, 14, 3)
      'renamed_atom14_gt_exists': renamed_atom14_gt_mask,  # (N, 14)
  }


def backbone_loss(ret, batch, value, config):
  """Backbone FAPE Loss.

  Jumper et al. (2021) Suppl. Alg. 20 "StructureModule" line 17

  Args:
    ret: Dictionary to write outputs into, needs to contain 'loss'.
    batch: Batch, needs to contain 'backbone_affine_tensor',
      'backbone_affine_mask'.
    value: Dictionary containing structure module output, needs to contain
      'traj', a trajectory of rigids.
    config: Configuration of loss, should contain 'fape.clamp_distance' and
      'fape.loss_unit_distance'.
  """
  affine_trajectory = quat_affine.QuatAffine.from_tensor(value['traj'])
  rigid_trajectory = r3.rigids_from_quataffine(affine_trajectory)

  gt_affine = quat_affine.QuatAffine.from_tensor(
      batch['backbone_affine_tensor'])
  gt_rigid = r3.rigids_from_quataffine(gt_affine)
  backbone_mask = batch['backbone_affine_mask']

  fape_loss_fn = functools.partial(
      all_atom.frame_aligned_point_error,
      l1_clamp_distance=config.fape.clamp_distance,
      length_scale=config.fape.loss_unit_distance)

  fape_loss_fn = jax.vmap(fape_loss_fn, (0, None, None, 0, None, None))
  fape_loss = fape_loss_fn(rigid_trajectory, gt_rigid, backbone_mask,
                           rigid_trajectory.trans, gt_rigid.trans,
                           backbone_mask)

  if 'use_clamped_fape' in batch:
    # Jumper et al. (2021) Suppl. Sec. 1.11.5 "Loss clamping details"
    use_clamped_fape = jnp.asarray(batch['use_clamped_fape'], jnp.float32)
    unclamped_fape_loss_fn = functools.partial(
        all_atom.frame_aligned_point_error,
        l1_clamp_distance=None,
        length_scale=config.fape.loss_unit_distance)
    unclamped_fape_loss_fn = jax.vmap(unclamped_fape_loss_fn,
                                      (0, None, None, 0, None, None))
    fape_loss_unclamped = unclamped_fape_loss_fn(rigid_trajectory, gt_rigid,
                                                 backbone_mask,
                                                 rigid_trajectory.trans,
                                                 gt_rigid.trans,
                                                 backbone_mask)

    fape_loss = (fape_loss * use_clamped_fape +
                 fape_loss_unclamped * (1 - use_clamped_fape))

  ret['fape'] = fape_loss[-1]
  ret['loss'] += jnp.mean(fape_loss)


def sidechain_loss(batch, value, config):
  """All Atom FAPE Loss using renamed rigids."""
  # Rename Frames
  # Jumper et al. (2021) Suppl. Alg. 26 "renameSymmetricGroundTruthAtoms" line 7
  alt_naming_is_better = value['alt_naming_is_better']
  renamed_gt_frames = (
      (1. - alt_naming_is_better[:, None, None])
      * batch['rigidgroups_gt_frames']
      + alt_naming_is_better[:, None, None]
      * batch['rigidgroups_alt_gt_frames'])

  flat_gt_frames = r3.rigids_from_tensor_flat12(
      jnp.reshape(renamed_gt_frames, [-1, 12]))
  flat_frames_mask = jnp.reshape(batch['rigidgroups_gt_exists'], [-1])

  flat_gt_positions = r3.vecs_from_tensor(
      jnp.reshape(value['renamed_atom14_gt_positions'], [-1, 3]))
  flat_positions_mask = jnp.reshape(value['renamed_atom14_gt_exists'], [-1])

  # Compute frame_aligned_point_error score for the final layer.
  pred_frames = value['sidechains']['frames']
  pred_positions = value['sidechains']['atom_pos']

  def _slice_last_layer_and_flatten(x):
    return jnp.reshape(x[-1], [-1])
  flat_pred_frames = jax.tree_map(
      _slice_last_layer_and_flatten, pred_frames)
  flat_pred_positions = jax.tree_map(
      _slice_last_layer_and_flatten, pred_positions)
  # FAPE Loss on sidechains
  fape = all_atom.frame_aligned_point_error(
      pred_frames=flat_pred_frames,
      target_frames=flat_gt_frames,
      frames_mask=flat_frames_mask,
      pred_positions=flat_pred_positions,
      target_positions=flat_gt_positions,
      positions_mask=flat_positions_mask,
      l1_clamp_distance=config.sidechain.atom_clamp_distance,
      length_scale=config.sidechain.length_scale)

  return {
      'fape': fape,
      'loss': fape}


def structural_violation_loss(ret, batch, value, config):
  """Computes loss for structural violations."""
  assert config.sidechain.weight_frac

  # Put all violation losses together to one large loss.
  violations = value['violations']
  num_atoms = jnp.sum(batch['atom14_atom_exists']).astype(jnp.float32)
  ret['loss'] += (config.structural_violation_loss_weight * (
      violations['between_residues']['bonds_c_n_loss_mean'] +
      violations['between_residues']['angles_ca_c_n_loss_mean'] +
      violations['between_residues']['angles_c_n_ca_loss_mean'] +
      jnp.sum(
          violations['between_residues']['clashes_per_atom_loss_sum'] +
          violations['within_residues']['per_atom_loss_sum']) /
      (1e-6 + num_atoms)))


def find_structural_violations(
    batch: Dict[str, jnp.ndarray],
    atom14_pred_positions: jnp.ndarray,  # (N, 14, 3)
    config: ml_collections.ConfigDict
    ):
  """Computes several checks for structural violations."""

  # Compute between residue backbone violations of bonds and angles.
  connection_violations = all_atom.between_residue_bond_loss(
      pred_atom_positions=atom14_pred_positions,
      pred_atom_mask=batch['atom14_atom_exists'].astype(jnp.float32),
      residue_index=batch['residue_index'].astype(jnp.float32),
      aatype=batch['aatype'],
      tolerance_factor_soft=config.violation_tolerance_factor,
      tolerance_factor_hard=config.violation_tolerance_factor)

  # Compute the Van der Waals radius for every atom
  # (the first letter of the atom name is the element type).
  # Shape: (N, 14).
  atomtype_radius = jnp.array([
      residue_constants.van_der_waals_radius[name[0]]
      for name in residue_constants.atom_types
  ])
  atom14_atom_radius = batch['atom14_atom_exists'] * utils.batched_gather(
      atomtype_radius, batch['residx_atom14_to_atom37'])

  # Compute the between residue clash loss.
  between_residue_clashes = all_atom.between_residue_clash_loss(
      atom14_pred_positions=atom14_pred_positions,
      atom14_atom_exists=batch['atom14_atom_exists'],
      atom14_atom_radius=atom14_atom_radius,
      residue_index=batch['residue_index'],
      overlap_tolerance_soft=config.clash_overlap_tolerance,
      overlap_tolerance_hard=config.clash_overlap_tolerance)

  # Compute all within-residue violations (clashes,
  # bond length and angle violations).
  restype_atom14_bounds = residue_constants.make_atom14_dists_bounds(
      overlap_tolerance=config.clash_overlap_tolerance,
      bond_length_tolerance_factor=config.violation_tolerance_factor)
  atom14_dists_lower_bound = utils.batched_gather(
      restype_atom14_bounds['lower_bound'], batch['aatype'])
  atom14_dists_upper_bound = utils.batched_gather(
      restype_atom14_bounds['upper_bound'], batch['aatype'])
  within_residue_violations = all_atom.within_residue_violations(
      atom14_pred_positions=atom14_pred_positions,
      atom14_atom_exists=batch['atom14_atom_exists'],
      atom14_dists_lower_bound=atom14_dists_lower_bound,
      atom14_dists_upper_bound=atom14_dists_upper_bound,
      tighten_bounds_for_loss=0.0)

  # Combine them to a single per-residue violation mask (used later for LDDT).
  per_residue_violations_mask = jnp.max(jnp.stack([
      connection_violations['per_residue_violation_mask'],
      jnp.max(between_residue_clashes['per_atom_clash_mask'], axis=-1),
      jnp.max(within_residue_violations['per_atom_violations'],
              axis=-1)]), axis=0)

  return {
      'between_residues': {
          'bonds_c_n_loss_mean':
              connection_violations['c_n_loss_mean'],  # ()
          'angles_ca_c_n_loss_mean':
              connection_violations['ca_c_n_loss_mean'],  # ()
          'angles_c_n_ca_loss_mean':
              connection_violations['c_n_ca_loss_mean'],  # ()
          'connections_per_residue_loss_sum':
              connection_violations['per_residue_loss_sum'],  # (N)
          'connections_per_residue_violation_mask':
              connection_violations['per_residue_violation_mask'],  # (N)
          'clashes_mean_loss':
              between_residue_clashes['mean_loss'],  # ()
          'clashes_per_atom_loss_sum':
              between_residue_clashes['per_atom_loss_sum'],  # (N, 14)
          'clashes_per_atom_clash_mask':
              between_residue_clashes['per_atom_clash_mask'],  # (N, 14)
      },
      'within_residues': {
          'per_atom_loss_sum':
              within_residue_violations['per_atom_loss_sum'],  # (N, 14)
          'per_atom_violations':
              within_residue_violations['per_atom_violations'],  # (N, 14),
      },
      'total_per_residue_violations_mask':
          per_residue_violations_mask,  # (N)
  }


def compute_violation_metrics(
    batch: Dict[str, jnp.ndarray],
    atom14_pred_positions: jnp.ndarray,  # (N, 14, 3)
    violations: Dict[str, jnp.ndarray],
    ) -> Dict[str, jnp.ndarray]:
  """Compute several metrics to assess the structural violations."""

  ret = {}
  extreme_ca_ca_violations = all_atom.extreme_ca_ca_distance_violations(
      pred_atom_positions=atom14_pred_positions,
      pred_atom_mask=batch['atom14_atom_exists'].astype(jnp.float32),
      residue_index=batch['residue_index'].astype(jnp.float32))
  ret['violations_extreme_ca_ca_distance'] = extreme_ca_ca_violations
  ret['violations_between_residue_bond'] = utils.mask_mean(
      mask=batch['seq_mask'],
      value=violations['between_residues'][
          'connections_per_residue_violation_mask'])
  ret['violations_between_residue_clash'] = utils.mask_mean(
      mask=batch['seq_mask'],
      value=jnp.max(
          violations['between_residues']['clashes_per_atom_clash_mask'],
          axis=-1))
  ret['violations_within_residue'] = utils.mask_mean(
      mask=batch['seq_mask'],
      value=jnp.max(
          violations['within_residues']['per_atom_violations'], axis=-1))
  ret['violations_per_residue'] = utils.mask_mean(
      mask=batch['seq_mask'],
      value=violations['total_per_residue_violations_mask'])
  return ret


def supervised_chi_loss(ret, batch, value, config):
  """Computes loss for direct chi angle supervision.

  Jumper et al. (2021) Suppl. Alg. 27 "torsionAngleLoss"

  Args:
    ret: Dictionary to write outputs into, needs to contain 'loss'.
    batch: Batch, needs to contain 'seq_mask', 'chi_mask', 'chi_angles'.
    value: Dictionary containing structure module output, needs to contain
      value['sidechains']['angles_sin_cos'] for angles and
      value['sidechains']['unnormalized_angles_sin_cos'] for unnormalized
      angles.
    config: Configuration of loss, should contain 'chi_weight' and
      'angle_norm_weight', 'angle_norm_weight' scales angle norm term,
      'chi_weight' scales torsion term.
  """
  eps = 1e-6

  sequence_mask = batch['seq_mask']
  num_res = sequence_mask.shape[0]
  chi_mask = batch['chi_mask'].astype(jnp.float32)
  pred_angles = jnp.reshape(
      value['sidechains']['angles_sin_cos'], [-1, num_res, 7, 2])
  pred_angles = pred_angles[:, :, 3:]

  residue_type_one_hot = jax.nn.one_hot(
      batch['aatype'], residue_constants.restype_num + 1,
      dtype=jnp.float32)[None]
  chi_pi_periodic = jnp.einsum('ijk, kl->ijl', residue_type_one_hot,
                               jnp.asarray(residue_constants.chi_pi_periodic))

  true_chi = batch['chi_angles'][None]
  sin_true_chi = jnp.sin(true_chi)
  cos_true_chi = jnp.cos(true_chi)
  sin_cos_true_chi = jnp.stack([sin_true_chi, cos_true_chi], axis=-1)

  # This is -1 if chi is pi-periodic and +1 if it's 2pi-periodic
  shifted_mask = (1 - 2 * chi_pi_periodic)[..., None]
  sin_cos_true_chi_shifted = shifted_mask * sin_cos_true_chi

  sq_chi_error = jnp.sum(
      squared_difference(sin_cos_true_chi, pred_angles), -1)
  sq_chi_error_shifted = jnp.sum(
      squared_difference(sin_cos_true_chi_shifted, pred_angles), -1)
  sq_chi_error = jnp.minimum(sq_chi_error, sq_chi_error_shifted)

  sq_chi_loss = utils.mask_mean(mask=chi_mask[None], value=sq_chi_error)
  ret['chi_loss'] = sq_chi_loss
  ret['loss'] += config.chi_weight * sq_chi_loss
  unnormed_angles = jnp.reshape(
      value['sidechains']['unnormalized_angles_sin_cos'], [-1, num_res, 7, 2])
  angle_norm = jnp.sqrt(jnp.sum(jnp.square(unnormed_angles), axis=-1) + eps)
  norm_error = jnp.abs(angle_norm - 1.)
  angle_norm_loss = utils.mask_mean(mask=sequence_mask[None, :, None],
                                    value=norm_error)

  ret['angle_norm_loss'] = angle_norm_loss
  ret['loss'] += config.angle_norm_weight * angle_norm_loss


def generate_new_affine(sequence_mask):
  num_residues, _ = sequence_mask.shape
  quaternion = jnp.tile(
      jnp.reshape(jnp.asarray([1., 0., 0., 0.]), [1, 4]),
      [num_residues, 1])

  translation = jnp.zeros([num_residues, 3])
  return quat_affine.QuatAffine(quaternion, translation, unstack_inputs=True)


def l2_normalize(x, axis=-1, epsilon=1e-12):
  return x / jnp.sqrt(
      jnp.maximum(jnp.sum(x**2, axis=axis, keepdims=True), epsilon))


class MultiRigidSidechain(hk.Module):
  """Class to make side chain atoms."""

  def __init__(self, config, global_config, name='rigid_sidechain'):
    super().__init__(name=name)
    self.config = config
    self.global_config = global_config

  def __call__(self, affine, representations_list, aatype):
    """Predict side chains using multi-rigid representations.

    Args:
      affine: The affines for each residue (translations in angstroms).
      representations_list: A list of activations to predict side chains from.
      aatype: Amino acid types.

    Returns:
      Dict containing atom positions and frames (in angstroms).
    """
    act = [
        common_modules.Linear(  # pylint: disable=g-complex-comprehension
            self.config.num_channel,
            name='input_projection')(jax.nn.relu(x))
        for x in representations_list
    ]
    # Sum the activation list (equivalent to concat then Linear).
    act = sum(act)

    final_init = 'zeros' if self.global_config.zero_init else 'linear'

    # Mapping with some residual blocks.
    for _ in range(self.config.num_residual_block):
      old_act = act
      act = common_modules.Linear(
          self.config.num_channel,
          initializer='relu',
          name='resblock1')(
              jax.nn.relu(act))
      act = common_modules.Linear(
          self.config.num_channel,
          initializer=final_init,
          name='resblock2')(
              jax.nn.relu(act))
      act += old_act

    # Map activations to torsion angles. Shape: (num_res, 14).
    num_res = act.shape[0]
    unnormalized_angles = common_modules.Linear(
        14, name='unnormalized_angles')(
            jax.nn.relu(act))
    unnormalized_angles = jnp.reshape(
        unnormalized_angles, [num_res, 7, 2])
    angles = l2_normalize(unnormalized_angles, axis=-1)

    outputs = {
        'angles_sin_cos': angles,  # jnp.ndarray (N, 7, 2)
        'unnormalized_angles_sin_cos':
            unnormalized_angles,  # jnp.ndarray (N, 7, 2)
    }

    # Map torsion angles to frames.
    backb_to_global = r3.rigids_from_quataffine(affine)

    # Jumper et al. (2021) Suppl. Alg. 24 "computeAllAtomCoordinates"

    # r3.Rigids with shape (N, 8).
    all_frames_to_global = all_atom.torsion_angles_to_frames(
        aatype,
        backb_to_global,
        angles)

    # Use frames and literature positions to create the final atom coordinates.
    # r3.Vecs with shape (N, 14).
    pred_positions = all_atom.frames_and_literature_positions_to_atom14_pos(
        aatype, all_frames_to_global)

    outputs.update({
        'atom_pos': pred_positions,  # r3.Vecs (N, 14)
        'frames': all_frames_to_global,  # r3.Rigids (N, 8)
    })
    return outputs
