# Copyright 2021 AlQuraishi Laboratory
# 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.

from functools import partial
import logging
import ml_collections
import numpy as np
import torch
import torch.nn as nn
from torch.distributions.bernoulli import Bernoulli
from typing import Dict, Optional, Tuple

from openfold.np import residue_constants
from openfold.utils import feats
from openfold.utils.rigid_utils import Rotation, Rigid
from openfold.utils.geometry.vector import Vec3Array, euclidean_distance
from openfold.utils.all_atom_multimer import get_rc_tensor
from openfold.utils.tensor_utils import (
    tree_map,
    tensor_tree_map,
    masked_mean,
    permute_final_dims,
    batched_gather,
)
import random
from openfold.np import residue_constants as rc
import logging 
import procrustes 
from openfold.utils.tensor_utils import tensor_tree_map
import gc
logger = logging.getLogger(__name__)

def softmax_cross_entropy(logits, labels):
    loss = -1 * torch.sum(
        labels * torch.nn.functional.log_softmax(logits, dim=-1),
        dim=-1,
    )
    return loss


def sigmoid_cross_entropy(logits, labels):
    logits_dtype = logits.dtype
    logits = logits.double()
    labels = labels.double()
    log_p = torch.nn.functional.logsigmoid(logits)
    # log_p = torch.log(torch.sigmoid(logits))
    log_not_p = torch.nn.functional.logsigmoid(-1 * logits)
    # log_not_p = torch.log(torch.sigmoid(-logits))
    loss = (-1. * labels) * log_p - (1. - labels) * log_not_p
    loss = loss.to(dtype=logits_dtype)
    return loss


def torsion_angle_loss(
    a,  # [*, N, 7, 2]
    a_gt,  # [*, N, 7, 2]
    a_alt_gt,  # [*, N, 7, 2]
):
    # [*, N, 7]
    norm = torch.norm(a, dim=-1)

    # [*, N, 7, 2]
    a = a / norm.unsqueeze(-1)

    # [*, N, 7]
    diff_norm_gt = torch.norm(a - a_gt, dim=-1)
    diff_norm_alt_gt = torch.norm(a - a_alt_gt, dim=-1)
    min_diff = torch.minimum(diff_norm_gt ** 2, diff_norm_alt_gt ** 2)

    # [*]
    l_torsion = torch.mean(min_diff, dim=(-1, -2))
    l_angle_norm = torch.mean(torch.abs(norm - 1), dim=(-1, -2))

    an_weight = 0.02
    return l_torsion + an_weight * l_angle_norm


def compute_fape(
    pred_frames: Rigid,
    target_frames: Rigid,
    frames_mask: torch.Tensor,
    pred_positions: torch.Tensor,
    target_positions: torch.Tensor,
    positions_mask: torch.Tensor,
    length_scale: float,
    pair_mask: Optional[torch.Tensor] = None,
    l1_clamp_distance: Optional[float] = None,
    eps=1e-8,
) -> torch.Tensor:
    """
        Computes FAPE loss.

        Args:
            pred_frames:
                [*, N_frames] Rigid object of predicted frames
            target_frames:
                [*, N_frames] Rigid object of ground truth frames
            frames_mask:
                [*, N_frames] binary mask for the frames
            pred_positions:
                [*, N_pts, 3] predicted atom positions
            target_positions:
                [*, N_pts, 3] ground truth positions
            positions_mask:
                [*, N_pts] positions mask
            length_scale:
                Length scale by which the loss is divided
            pair_mask:
                [*,  N_frames, N_pts] mask to use for
                separating intra- from inter-chain losses.
            l1_clamp_distance:
                Cutoff above which distance errors are disregarded
            eps:
                Small value used to regularize denominators
        Returns:
            [*] loss tensor
    """
    # [*, N_frames, N_pts, 3]
    local_pred_pos = pred_frames.invert()[..., None].apply(
        pred_positions[..., None, :, :],
    )
    local_target_pos = target_frames.invert()[..., None].apply(
        target_positions[..., None, :, :],
    )

    error_dist = torch.sqrt(
        torch.sum((local_pred_pos - local_target_pos) ** 2, dim=-1) + eps
    )

    if l1_clamp_distance is not None:
        error_dist = torch.clamp(error_dist, min=0, max=l1_clamp_distance)

    normed_error = error_dist / length_scale
    normed_error = normed_error * frames_mask[..., None]
    normed_error = normed_error * positions_mask[..., None, :]

    if pair_mask is not None:
        normed_error = normed_error * pair_mask
        normed_error = torch.sum(normed_error, dim=(-1, -2))

        mask = frames_mask[..., None] * positions_mask[..., None, :] * pair_mask
        norm_factor = torch.sum(mask, dim=(-2, -1))

        normed_error = normed_error / (eps + norm_factor)
    else:
        # FP16-friendly averaging. Roughly equivalent to:
        #
        # norm_factor = (
        #     torch.sum(frames_mask, dim=-1) *
        #     torch.sum(positions_mask, dim=-1)
        # )
        # normed_error = torch.sum(normed_error, dim=(-1, -2)) / (eps + norm_factor)
        #
        # ("roughly" because eps is necessarily duplicated in the latter)
        normed_error = torch.sum(normed_error, dim=-1)
        normed_error = (
            normed_error / (eps + torch.sum(frames_mask, dim=-1))[..., None]
        )
        normed_error = torch.sum(normed_error, dim=-1)
        normed_error = normed_error / (eps + torch.sum(positions_mask, dim=-1))

    return normed_error


def backbone_loss(
    backbone_rigid_tensor: torch.Tensor,
    backbone_rigid_mask: torch.Tensor,
    traj: torch.Tensor,
    pair_mask: Optional[torch.Tensor] = None,
    use_clamped_fape: Optional[torch.Tensor] = None,
    clamp_distance: float = 10.0,
    loss_unit_distance: float = 10.0,
    eps: float = 1e-4,
    **kwargs,
) -> torch.Tensor:
    
    ### need to check if the traj belongs to 4*4 matrix or a tensor_7
    if traj.shape[-1]==7:
        pred_aff = Rigid.from_tensor_7(traj)
    elif traj.shape[-1]==4:
        pred_aff = Rigid.from_tensor_4x4(traj)

    pred_aff = Rigid(
        Rotation(rot_mats=pred_aff.get_rots().get_rot_mats(), quats=None),
        pred_aff.get_trans(),
    )

    # DISCREPANCY: DeepMind somehow gets a hold of a tensor_7 version of
    # backbone tensor, normalizes it, and then turns it back to a rotation
    # matrix. To avoid a potentially numerically unstable rotation matrix
    # to quaternion conversion, we just use the original rotation matrix
    # outright. This one hasn't been composed a bunch of times, though, so
    # it might be fine.
    gt_aff = Rigid.from_tensor_4x4(backbone_rigid_tensor)

    fape_loss = compute_fape(
        pred_aff,
        gt_aff[None],
        backbone_rigid_mask[None],
        pred_aff.get_trans(),
        gt_aff[None].get_trans(),
        backbone_rigid_mask[None],
        pair_mask=pair_mask,
        l1_clamp_distance=clamp_distance,
        length_scale=loss_unit_distance,
        eps=eps,
    )
    if use_clamped_fape is not None:
        unclamped_fape_loss = compute_fape(
            pred_aff,
            gt_aff[None],
            backbone_rigid_mask[None],
            pred_aff.get_trans(),
            gt_aff[None].get_trans(),
            backbone_rigid_mask[None],
            pair_mask=pair_mask,
            l1_clamp_distance=None,
            length_scale=loss_unit_distance,
            eps=eps,
        )

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

    # Average over the batch dimension
    fape_loss = torch.mean(fape_loss)

    return fape_loss


def sidechain_loss(
    sidechain_frames: torch.Tensor,
    sidechain_atom_pos: torch.Tensor,
    rigidgroups_gt_frames: torch.Tensor,
    rigidgroups_alt_gt_frames: torch.Tensor,
    rigidgroups_gt_exists: torch.Tensor,
    renamed_atom14_gt_positions: torch.Tensor,
    renamed_atom14_gt_exists: torch.Tensor,
    alt_naming_is_better: torch.Tensor,
    clamp_distance: float = 10.0,
    length_scale: float = 10.0,
    eps: float = 1e-4,
    **kwargs,
) -> torch.Tensor:
    renamed_gt_frames = (
        1.0 - alt_naming_is_better[..., None, None, None]
    ) * rigidgroups_gt_frames + alt_naming_is_better[
        ..., None, None, None
    ] * rigidgroups_alt_gt_frames

    # Steamroll the inputs
    sidechain_frames = sidechain_frames[-1]
    batch_dims = sidechain_frames.shape[:-4]
    sidechain_frames = sidechain_frames.view(*batch_dims, -1, 4, 4)
    sidechain_frames = Rigid.from_tensor_4x4(sidechain_frames)
    renamed_gt_frames = renamed_gt_frames.view(*batch_dims, -1, 4, 4)
    renamed_gt_frames = Rigid.from_tensor_4x4(renamed_gt_frames)
    rigidgroups_gt_exists = rigidgroups_gt_exists.reshape(*batch_dims, -1)
    sidechain_atom_pos = sidechain_atom_pos[-1]
    sidechain_atom_pos = sidechain_atom_pos.view(*batch_dims, -1, 3)
    renamed_atom14_gt_positions = renamed_atom14_gt_positions.view(
        *batch_dims, -1, 3
    )
    renamed_atom14_gt_exists = renamed_atom14_gt_exists.view(*batch_dims, -1)

    fape = compute_fape(
        sidechain_frames,
        renamed_gt_frames,
        rigidgroups_gt_exists,
        sidechain_atom_pos,
        renamed_atom14_gt_positions,
        renamed_atom14_gt_exists,
        pair_mask=None,
        l1_clamp_distance=clamp_distance,
        length_scale=length_scale,
        eps=eps,
    )

    return fape


def fape_loss(
    out: Dict[str, torch.Tensor],
    batch: Dict[str, torch.Tensor],
    config: ml_collections.ConfigDict,
) -> torch.Tensor:

    traj = out["sm"]["frames"]
    asym_id = batch.get("asym_id")
    if asym_id is not None:
        intra_chain_mask = (asym_id[..., None] == asym_id[..., None, :]).to(dtype=traj.dtype)
        intra_chain_bb_loss = backbone_loss(
            traj=traj,
            pair_mask=intra_chain_mask,
            **{**batch, **config.intra_chain_backbone},
        )
        interface_bb_loss = backbone_loss(
            traj=traj,
            pair_mask=1. - intra_chain_mask,
            **{**batch, **config.intra_chain_backbone},
        )
        weighted_bb_loss = (intra_chain_bb_loss * config.intra_chain_backbone.weight
                            + interface_bb_loss * config.intra_chain_backbone.weight)
    else:
        bb_loss = backbone_loss(
            traj=traj,
            **{**batch, **config.backbone},
        )
        weighted_bb_loss = bb_loss * config.backbone.weight

    sc_loss = sidechain_loss(
        out["sm"]["sidechain_frames"],
        out["sm"]["positions"],
        **{**batch, **config.sidechain},
    )

    loss = weighted_bb_loss + config.sidechain.weight * sc_loss
    
    # Average over the batch dimension
    loss = torch.mean(loss)

    return loss


def supervised_chi_loss(
    angles_sin_cos: torch.Tensor,
    unnormalized_angles_sin_cos: torch.Tensor,
    aatype: torch.Tensor,
    seq_mask: torch.Tensor,
    chi_mask: torch.Tensor,
    chi_angles_sin_cos: torch.Tensor,
    chi_weight: float,
    angle_norm_weight: float,
    eps=1e-6,
    **kwargs,
) -> torch.Tensor:
    """
        Implements Algorithm 27 (torsionAngleLoss)

        Args:
            angles_sin_cos:
                [*, N, 7, 2] predicted angles
            unnormalized_angles_sin_cos:
                The same angles, but unnormalized
            aatype:
                [*, N] residue indices
            seq_mask:
                [*, N] sequence mask
            chi_mask:
                [*, N, 7] angle mask
            chi_angles_sin_cos:
                [*, N, 7, 2] ground truth angles
            chi_weight:
                Weight for the angle component of the loss
            angle_norm_weight:
                Weight for the normalization component of the loss
        Returns:
            [*] loss tensor
    """
    pred_angles = angles_sin_cos[..., 3:, :]
    residue_type_one_hot = torch.nn.functional.one_hot(
        aatype,
        residue_constants.restype_num + 1,
    )
    chi_pi_periodic = torch.einsum(
        "...ij,jk->ik",
        residue_type_one_hot.type(angles_sin_cos.dtype),
        angles_sin_cos.new_tensor(residue_constants.chi_pi_periodic),
    )

    true_chi = chi_angles_sin_cos[None]

    shifted_mask = (1 - 2 * chi_pi_periodic).unsqueeze(-1)
    true_chi_shifted = shifted_mask * true_chi
    sq_chi_error = torch.sum((true_chi - pred_angles) ** 2, dim=-1)
    sq_chi_error_shifted = torch.sum(
        (true_chi_shifted - pred_angles) ** 2, dim=-1
    )
    sq_chi_error = torch.minimum(sq_chi_error, sq_chi_error_shifted)
    
    # The ol' switcheroo
    sq_chi_error = sq_chi_error.permute(
        *range(len(sq_chi_error.shape))[1:-2], 0, -2, -1
    )

    sq_chi_loss = masked_mean(
        chi_mask[..., None, :, :], sq_chi_error, dim=(-1, -2, -3)
    )

    loss = chi_weight * sq_chi_loss

    angle_norm = torch.sqrt(
        torch.sum(unnormalized_angles_sin_cos ** 2, dim=-1) + eps
    )
    norm_error = torch.abs(angle_norm - 1.0)
    norm_error = norm_error.permute(
        *range(len(norm_error.shape))[1:-2], 0, -2, -1
    )
    angle_norm_loss = masked_mean(
        seq_mask[..., None, :, None], norm_error, dim=(-1, -2, -3)
    )

    loss = loss + angle_norm_weight * angle_norm_loss

    # Average over the batch dimension
    loss = torch.mean(loss)

    return loss


def compute_plddt(logits: torch.Tensor) -> torch.Tensor:
    num_bins = logits.shape[-1]
    bin_width = 1.0 / num_bins
    bounds = torch.arange(
        start=0.5 * bin_width, end=1.0, step=bin_width, device=logits.device
    )
    probs = torch.nn.functional.softmax(logits, dim=-1)
    pred_lddt_ca = torch.sum(
        probs * bounds.view(*((1,) * len(probs.shape[:-1])), *bounds.shape),
        dim=-1,
    )
    return pred_lddt_ca * 100


def lddt(
    all_atom_pred_pos: torch.Tensor,
    all_atom_positions: torch.Tensor,
    all_atom_mask: torch.Tensor,
    cutoff: float = 15.0,
    eps: float = 1e-10,
    per_residue: bool = True,
) -> torch.Tensor:
    n = all_atom_mask.shape[-2]
    dmat_true = torch.sqrt(
        eps
        + torch.sum(
            (
                all_atom_positions[..., None, :]
                - all_atom_positions[..., None, :, :]
            )
            ** 2,
            dim=-1,
        )
    )

    dmat_pred = torch.sqrt(
        eps
        + torch.sum(
            (
                all_atom_pred_pos[..., None, :]
                - all_atom_pred_pos[..., None, :, :]
            )
            ** 2,
            dim=-1,
        )
    )
    dists_to_score = (
        (dmat_true < cutoff)
        * all_atom_mask
        * permute_final_dims(all_atom_mask, (1, 0))
        * (1.0 - torch.eye(n, device=all_atom_mask.device))
    )

    dist_l1 = torch.abs(dmat_true - dmat_pred)

    score = (
        (dist_l1 < 0.5).type(dist_l1.dtype)
        + (dist_l1 < 1.0).type(dist_l1.dtype)
        + (dist_l1 < 2.0).type(dist_l1.dtype)
        + (dist_l1 < 4.0).type(dist_l1.dtype)
    )
    score = score * 0.25

    dims = (-1,) if per_residue else (-2, -1)
    norm = 1.0 / (eps + torch.sum(dists_to_score, dim=dims))
    score = norm * (eps + torch.sum(dists_to_score * score, dim=dims))

    return score


def lddt_ca(
    all_atom_pred_pos: torch.Tensor,
    all_atom_positions: torch.Tensor,
    all_atom_mask: torch.Tensor,
    cutoff: float = 15.0,
    eps: float = 1e-10,
    per_residue: bool = True,
) -> torch.Tensor:
    ca_pos = residue_constants.atom_order["CA"]
    all_atom_pred_pos = all_atom_pred_pos[..., ca_pos, :]
    all_atom_positions = all_atom_positions[..., ca_pos, :]
    all_atom_mask = all_atom_mask[..., ca_pos : (ca_pos + 1)]  # keep dim

    return lddt(
        all_atom_pred_pos,
        all_atom_positions,
        all_atom_mask,
        cutoff=cutoff,
        eps=eps,
        per_residue=per_residue,
    )


def lddt_loss(
    logits: torch.Tensor,
    all_atom_pred_pos: torch.Tensor,
    all_atom_positions: torch.Tensor,
    all_atom_mask: torch.Tensor,
    resolution: torch.Tensor,
    cutoff: float = 15.0,
    no_bins: int = 50,
    min_resolution: float = 0.1,
    max_resolution: float = 3.0,
    eps: float = 1e-10,
    **kwargs,
) -> torch.Tensor:
    n = all_atom_mask.shape[-2]

    ca_pos = residue_constants.atom_order["CA"]
    all_atom_pred_pos = all_atom_pred_pos[..., ca_pos, :]
    all_atom_positions = all_atom_positions[..., ca_pos, :]
    all_atom_mask = all_atom_mask[..., ca_pos : (ca_pos + 1)]  # keep dim

    score = lddt(
        all_atom_pred_pos, 
        all_atom_positions, 
        all_atom_mask, 
        cutoff=cutoff, 
        eps=eps
    )
    score = torch.nan_to_num(score,nan=torch.nanmean(score))
    score[score<0] = 0
    score = score.detach()
    bin_index = torch.floor(score * no_bins).long()
    bin_index = torch.clamp(bin_index, max=(no_bins - 1))
    lddt_ca_one_hot = torch.nn.functional.one_hot(
        bin_index, num_classes=no_bins
    )

    errors = softmax_cross_entropy(logits, lddt_ca_one_hot)
    all_atom_mask = all_atom_mask.squeeze(-1)
    loss = torch.sum(errors * all_atom_mask, dim=-1) / (
        eps + torch.sum(all_atom_mask, dim=-1)
    )

    loss = loss * (
        (resolution >= min_resolution) & (resolution <= max_resolution)
    )

    # Average over the batch dimension
    loss = torch.mean(loss)

    return loss


def distogram_loss(
    logits,
    pseudo_beta,
    pseudo_beta_mask,
    min_bin=2.3125,
    max_bin=21.6875,
    no_bins=64,
    eps=1e-6,
    **kwargs,
):
    boundaries = torch.linspace(
        min_bin,
        max_bin,
        no_bins - 1,
        device=logits.device,
    )
    boundaries = boundaries ** 2
    
    dists = torch.sum(
        (pseudo_beta[..., None, :] - pseudo_beta[..., None, :, :]) ** 2,
        dim=-1,
        keepdims=True,
    )

    true_bins = torch.sum(dists > boundaries, dim=-1)

    errors = softmax_cross_entropy(
        logits,
        torch.nn.functional.one_hot(true_bins, no_bins),
    )

    square_mask = pseudo_beta_mask[..., None] * pseudo_beta_mask[..., None, :]

    # FP16-friendly sum. Equivalent to:
    # mean = (torch.sum(errors * square_mask, dim=(-1, -2)) /
    #         (eps + torch.sum(square_mask, dim=(-1, -2))))
    denom = eps + torch.sum(square_mask, dim=(-1, -2))
    mean = errors * square_mask
    mean = torch.sum(mean, dim=-1)
    mean = mean / denom[..., None]
    mean = torch.sum(mean, dim=-1)

    # Average over the batch dimensions
    mean = torch.mean(mean)

    return mean


def _calculate_bin_centers(boundaries: torch.Tensor):
    step = boundaries[1] - boundaries[0]
    bin_centers = boundaries + step / 2
    bin_centers = torch.cat(
        [bin_centers, (bin_centers[-1] + step).unsqueeze(-1)], dim=0
    )
    return bin_centers


def _calculate_expected_aligned_error(
    alignment_confidence_breaks: torch.Tensor,
    aligned_distance_error_probs: torch.Tensor,
) -> Tuple[torch.Tensor, torch.Tensor]:
    bin_centers = _calculate_bin_centers(alignment_confidence_breaks)
    return (
        torch.sum(aligned_distance_error_probs * bin_centers, dim=-1),
        bin_centers[-1],
    )


def compute_predicted_aligned_error(
    logits: torch.Tensor,
    max_bin: int = 31,
    no_bins: int = 64,
    **kwargs,
) -> Dict[str, torch.Tensor]:
    """Computes aligned confidence metrics from logits.

    Args:
      logits: [*, num_res, num_res, num_bins] the logits output from
        PredictedAlignedErrorHead.
      max_bin: Maximum bin value
      no_bins: Number of bins
    Returns:
      aligned_confidence_probs: [*, num_res, num_res, num_bins] the predicted
        aligned error probabilities over bins for each residue pair.
      predicted_aligned_error: [*, num_res, num_res] the expected aligned distance
        error for each pair of residues.
      max_predicted_aligned_error: [*] the maximum predicted error possible.
    """
    boundaries = torch.linspace(
        0, max_bin, steps=(no_bins - 1), device=logits.device
    )

    aligned_confidence_probs = torch.nn.functional.softmax(logits, dim=-1)
    (
        predicted_aligned_error,
        max_predicted_aligned_error,
    ) = _calculate_expected_aligned_error(
        alignment_confidence_breaks=boundaries,
        aligned_distance_error_probs=aligned_confidence_probs,
    )

    return {
        "aligned_confidence_probs": aligned_confidence_probs,
        "predicted_aligned_error": predicted_aligned_error,
        "max_predicted_aligned_error": max_predicted_aligned_error,
    }


def compute_tm(
    logits: torch.Tensor,
    residue_weights: Optional[torch.Tensor] = None,
    asym_id: Optional[torch.Tensor] = None,
    interface: bool = False,
    max_bin: int = 31,
    no_bins: int = 64,
    eps: float = 1e-8,
    **kwargs,
) -> torch.Tensor:
    if residue_weights is None:
        residue_weights = logits.new_ones(logits.shape[-2])

    boundaries = torch.linspace(
        0, max_bin, steps=(no_bins - 1), device=logits.device
    )

    bin_centers = _calculate_bin_centers(boundaries)
    clipped_n = max(torch.sum(residue_weights), 19)

    d0 = 1.24 * (clipped_n - 15) ** (1.0 / 3) - 1.8

    probs = torch.nn.functional.softmax(logits, dim=-1)

    tm_per_bin = 1.0 / (1 + (bin_centers ** 2) / (d0 ** 2))
    predicted_tm_term = torch.sum(probs * tm_per_bin, dim=-1)

    n = residue_weights.shape[-1]
    pair_mask = residue_weights.new_ones((n, n), dtype=torch.int32)
    if interface and (asym_id is not None):
        if len(asym_id.shape)>1:
            assert len(asym_id.shape)<=2
            batch_size = asym_id.shape[0]
            pair_mask = residue_weights.new_ones((batch_size,n, n), dtype=torch.int32)
        pair_mask *= (asym_id[..., None] != asym_id[..., None, :]).to(dtype=pair_mask.dtype)
    
    predicted_tm_term *= pair_mask

    pair_residue_weights = pair_mask * (
        residue_weights[..., None, :] * residue_weights[..., :, None]
    )
    denom = eps + torch.sum(pair_residue_weights, dim=-1, keepdims=True)
    normed_residue_mask = pair_residue_weights / denom
    per_alignment = torch.sum(predicted_tm_term * normed_residue_mask, dim=-1)

    weighted = per_alignment * residue_weights

    argmax = (weighted == torch.max(weighted)).nonzero()[0]
    return per_alignment[tuple(argmax)]

def tm_loss(
    logits,
    final_affine_tensor,
    backbone_rigid_tensor,
    backbone_rigid_mask,
    resolution,
    max_bin=31,
    no_bins=64,
    min_resolution: float = 0.1,
    max_resolution: float = 3.0,
    eps=1e-8,
    **kwargs,
):
    # first check whether this is a tensor_7 or tensor_4*4
    if final_affine_tensor.shape[-1]==7:
        pred_affine = Rigid.from_tensor_7(final_affine_tensor)
    elif final_affine_tensor.shape[-1]==4:
        pred_affine = Rigid.from_tensor_4x4(final_affine_tensor)
    backbone_rigid = Rigid.from_tensor_4x4(backbone_rigid_tensor)

    def _points(affine):
        pts = affine.get_trans()[..., None, :, :]
        return affine.invert()[..., None].apply(pts)

    sq_diff = torch.sum(
        (_points(pred_affine) - _points(backbone_rigid)) ** 2, dim=-1
    )

    sq_diff = sq_diff.detach()

    boundaries = torch.linspace(
        0, max_bin, steps=(no_bins - 1), device=logits.device
    )
    boundaries = boundaries ** 2
    true_bins = torch.sum(sq_diff[..., None] > boundaries, dim=-1)

    errors = softmax_cross_entropy(
        logits, torch.nn.functional.one_hot(true_bins, no_bins)
    )

    square_mask = (
        backbone_rigid_mask[..., None] * backbone_rigid_mask[..., None, :]
    )

    loss = torch.sum(errors * square_mask, dim=-1)
    scale = 0.5  # hack to help FP16 training along
    denom = eps + torch.sum(scale * square_mask, dim=(-1, -2))
    loss = loss / denom[..., None]
    loss = torch.sum(loss, dim=-1)
    loss = loss * scale

    loss = loss * (
        (resolution >= min_resolution) & (resolution <= max_resolution)
    )

    # Average over the batch dimension
    loss = torch.mean(loss)

    return loss


def between_residue_bond_loss(
    pred_atom_positions: torch.Tensor,  # (*, N, 37/14, 3)
    pred_atom_mask: torch.Tensor,  # (*, N, 37/14)
    residue_index: torch.Tensor,  # (*, N)
    aatype: torch.Tensor,  # (*, N)
    tolerance_factor_soft=12.0,
    tolerance_factor_hard=12.0,
    eps=1e-6,
) -> Dict[str, torch.Tensor]:
    """Flat-bottom loss to penalize structural violations between residues.

    This is a loss penalizing any violation of the geometry around the peptide
    bond between consecutive amino acids. This loss corresponds to
    Jumper et al. (2021) Suppl. Sec. 1.9.11, eq 44, 45.

    Args:
      pred_atom_positions: Atom positions in atom37/14 representation
      pred_atom_mask: Atom mask in atom37/14 representation
      residue_index: Residue index for given amino acid, this is assumed to be
        monotonically increasing.
      aatype: Amino acid type of given residue
      tolerance_factor_soft: soft tolerance factor measured in standard deviations
        of pdb distributions
      tolerance_factor_hard: hard tolerance factor measured in standard deviations
        of pdb distributions

    Returns:
      Dict containing:
        * 'c_n_loss_mean': Loss for peptide bond length violations
        * 'ca_c_n_loss_mean': Loss for violations of bond angle around C spanned
            by CA, C, N
        * 'c_n_ca_loss_mean': Loss for violations of bond angle around N spanned
            by C, N, CA
        * 'per_residue_loss_sum': sum of all losses for each residue
        * 'per_residue_violation_mask': mask denoting all residues with violation
            present.
    """
    # Get the positions of the relevant backbone atoms.
    this_ca_pos = pred_atom_positions[..., :-1, 1, :]
    this_ca_mask = pred_atom_mask[..., :-1, 1]
    this_c_pos = pred_atom_positions[..., :-1, 2, :]
    this_c_mask = pred_atom_mask[..., :-1, 2]
    next_n_pos = pred_atom_positions[..., 1:, 0, :]
    next_n_mask = pred_atom_mask[..., 1:, 0]
    next_ca_pos = pred_atom_positions[..., 1:, 1, :]
    next_ca_mask = pred_atom_mask[..., 1:, 1]
    has_no_gap_mask = (residue_index[..., 1:] - residue_index[..., :-1]) == 1.0

    # Compute loss for the C--N bond.
    c_n_bond_length = torch.sqrt(
        eps + torch.sum((this_c_pos - next_n_pos) ** 2, dim=-1)
    )

    # The C-N bond to proline has slightly different length because of the ring.
    next_is_proline = aatype[..., 1:] == residue_constants.resname_to_idx["PRO"]
    gt_length = (
        ~next_is_proline
    ) * residue_constants.between_res_bond_length_c_n[
        0
    ] + next_is_proline * residue_constants.between_res_bond_length_c_n[
        1
    ]
    gt_stddev = (
        ~next_is_proline
    ) * residue_constants.between_res_bond_length_stddev_c_n[
        0
    ] + next_is_proline * residue_constants.between_res_bond_length_stddev_c_n[
        1
    ]

    c_n_bond_length_error = torch.sqrt(eps + (c_n_bond_length - gt_length) ** 2)
    c_n_loss_per_residue = torch.nn.functional.relu(
        c_n_bond_length_error - tolerance_factor_soft * gt_stddev
    )
    mask = this_c_mask * next_n_mask * has_no_gap_mask
    c_n_loss = torch.sum(mask * c_n_loss_per_residue, dim=-1) / (
        torch.sum(mask, dim=-1) + eps
    )
    c_n_violation_mask = mask * (
        c_n_bond_length_error > (tolerance_factor_hard * gt_stddev)
    )

    # Compute loss for the angles.
    ca_c_bond_length = torch.sqrt(
        eps + torch.sum((this_ca_pos - this_c_pos) ** 2, dim=-1)
    )
    n_ca_bond_length = torch.sqrt(
        eps + torch.sum((next_n_pos - next_ca_pos) ** 2, dim=-1)
    )

    c_ca_unit_vec = (this_ca_pos - this_c_pos) / ca_c_bond_length[..., None]
    c_n_unit_vec = (next_n_pos - this_c_pos) / c_n_bond_length[..., None]
    n_ca_unit_vec = (next_ca_pos - next_n_pos) / n_ca_bond_length[..., None]

    ca_c_n_cos_angle = torch.sum(c_ca_unit_vec * c_n_unit_vec, dim=-1)
    gt_angle = residue_constants.between_res_cos_angles_ca_c_n[0]
    gt_stddev = residue_constants.between_res_bond_length_stddev_c_n[0]
    ca_c_n_cos_angle_error = torch.sqrt(
        eps + (ca_c_n_cos_angle - gt_angle) ** 2
    )
    ca_c_n_loss_per_residue = torch.nn.functional.relu(
        ca_c_n_cos_angle_error - tolerance_factor_soft * gt_stddev
    )
    mask = this_ca_mask * this_c_mask * next_n_mask * has_no_gap_mask
    ca_c_n_loss = torch.sum(mask * ca_c_n_loss_per_residue, dim=-1) / (
        torch.sum(mask, dim=-1) + eps
    )
    ca_c_n_violation_mask = mask * (
        ca_c_n_cos_angle_error > (tolerance_factor_hard * gt_stddev)
    )

    c_n_ca_cos_angle = torch.sum((-c_n_unit_vec) * n_ca_unit_vec, dim=-1)
    gt_angle = residue_constants.between_res_cos_angles_c_n_ca[0]
    gt_stddev = residue_constants.between_res_cos_angles_c_n_ca[1]
    c_n_ca_cos_angle_error = torch.sqrt(
        eps + torch.square(c_n_ca_cos_angle - gt_angle)
    )
    c_n_ca_loss_per_residue = torch.nn.functional.relu(
        c_n_ca_cos_angle_error - tolerance_factor_soft * gt_stddev
    )
    mask = this_c_mask * next_n_mask * next_ca_mask * has_no_gap_mask
    c_n_ca_loss = torch.sum(mask * c_n_ca_loss_per_residue, dim=-1) / (
        torch.sum(mask, dim=-1) + eps
    )
    c_n_ca_violation_mask = mask * (
        c_n_ca_cos_angle_error > (tolerance_factor_hard * gt_stddev)
    )

    # Compute a per residue loss (equally distribute the loss to both
    # neighbouring residues).
    per_residue_loss_sum = (
        c_n_loss_per_residue + ca_c_n_loss_per_residue + c_n_ca_loss_per_residue
    )
    per_residue_loss_sum = 0.5 * (
        torch.nn.functional.pad(per_residue_loss_sum, (0, 1))
        + torch.nn.functional.pad(per_residue_loss_sum, (1, 0))
    )

    # Compute hard violations.
    violation_mask = torch.max(
        torch.stack(
            [c_n_violation_mask, ca_c_n_violation_mask, c_n_ca_violation_mask],
            dim=-2,
        ),
        dim=-2,
    )[0]
    violation_mask = torch.maximum(
        torch.nn.functional.pad(violation_mask, (0, 1)),
        torch.nn.functional.pad(violation_mask, (1, 0)),
    )

    return {
        "c_n_loss_mean": c_n_loss,
        "ca_c_n_loss_mean": ca_c_n_loss,
        "c_n_ca_loss_mean": c_n_ca_loss,
        "per_residue_loss_sum": per_residue_loss_sum,
        "per_residue_violation_mask": violation_mask,
    }


def between_residue_clash_loss(
    atom14_pred_positions: torch.Tensor,
    atom14_atom_exists: torch.Tensor,
    atom14_atom_radius: torch.Tensor,
    residue_index: torch.Tensor,
    asym_id: Optional[torch.Tensor] = None,
    overlap_tolerance_soft=1.5,
    overlap_tolerance_hard=1.5,
    eps=1e-10,
) -> Dict[str, torch.Tensor]:
    """Loss to penalize steric clashes between residues.

    This is a loss penalizing any steric clashes due to non bonded atoms in
    different peptides coming too close. This loss corresponds to the part with
    different residues of
    Jumper et al. (2021) Suppl. Sec. 1.9.11, eq 46.

    Args:
      atom14_pred_positions: Predicted positions of atoms in
        global prediction frame
      atom14_atom_exists: Mask denoting whether atom at positions exists for given
        amino acid type
      atom14_atom_radius: Van der Waals radius for each atom.
      residue_index: Residue index for given amino acid.
      overlap_tolerance_soft: Soft tolerance factor.
      overlap_tolerance_hard: Hard tolerance factor.

    Returns:
      Dict containing:
        * 'mean_loss': average clash loss
        * 'per_atom_loss_sum': sum of all clash losses per atom, shape (N, 14)
        * 'per_atom_clash_mask': mask whether atom clashes with any other atom
            shape (N, 14)
    """
    fp_type = atom14_pred_positions.dtype

    # Create the distance matrix.
    # (N, N, 14, 14)
    dists = torch.sqrt(
        eps
        + torch.sum(
            (
                atom14_pred_positions[..., :, None, :, None, :]
                - atom14_pred_positions[..., None, :, None, :, :]
            )
            ** 2,
            dim=-1,
        )
    )

    # Create the mask for valid distances.
    # shape (N, N, 14, 14)
    dists_mask = (
        atom14_atom_exists[..., :, None, :, None]
        * atom14_atom_exists[..., None, :, None, :]
    ).type(fp_type)

    # Mask out all the duplicate entries in the lower triangular matrix.
    # Also mask out the diagonal (atom-pairs from the same residue) -- these atoms
    # are handled separately.
    dists_mask = dists_mask * (
        residue_index[..., :, None, None, None]
        < residue_index[..., None, :, None, None]
    )

    # Backbone C--N bond between subsequent residues is no clash.
    c_one_hot = torch.nn.functional.one_hot(
        residue_index.new_tensor(2), num_classes=14
    )
    c_one_hot = c_one_hot.reshape(
        *((1,) * len(residue_index.shape[:-1])), *c_one_hot.shape
    )
    c_one_hot = c_one_hot.type(fp_type)
    n_one_hot = torch.nn.functional.one_hot(
        residue_index.new_tensor(0), num_classes=14
    )
    n_one_hot = n_one_hot.reshape(
        *((1,) * len(residue_index.shape[:-1])), *n_one_hot.shape
    )
    n_one_hot = n_one_hot.type(fp_type)

    neighbour_mask = (residue_index[..., :, None] + 1) == residue_index[..., None, :]

    if asym_id is not None:
        neighbour_mask = neighbour_mask & (asym_id[..., :, None] == asym_id[..., None, :])

    neighbour_mask = neighbour_mask[..., None, None]

    c_n_bonds = (
        neighbour_mask
        * c_one_hot[..., None, None, :, None]
        * n_one_hot[..., None, None, None, :]
    )
    dists_mask = dists_mask * (1.0 - c_n_bonds)

    # Disulfide bridge between two cysteines is no clash.
    cys = residue_constants.restype_name_to_atom14_names["CYS"]
    cys_sg_idx = cys.index("SG")
    cys_sg_idx = residue_index.new_tensor(cys_sg_idx)
    cys_sg_idx = cys_sg_idx.reshape(
        *((1,) * len(residue_index.shape[:-1])), 1
    ).squeeze(-1)
    cys_sg_one_hot = torch.nn.functional.one_hot(cys_sg_idx, num_classes=14)
    disulfide_bonds = (
        cys_sg_one_hot[..., None, None, :, None]
        * cys_sg_one_hot[..., None, None, None, :]
    )
    dists_mask = dists_mask * (1.0 - disulfide_bonds)

    # Compute the lower bound for the allowed distances.
    # shape (N, N, 14, 14)
    dists_lower_bound = dists_mask * (
        atom14_atom_radius[..., :, None, :, None]
        + atom14_atom_radius[..., None, :, None, :]
    )

    # Compute the error.
    # shape (N, N, 14, 14)
    dists_to_low_error = dists_mask * torch.nn.functional.relu(
        dists_lower_bound - overlap_tolerance_soft - dists
    )

    # Compute the mean loss.
    # shape ()
    mean_loss = torch.sum(dists_to_low_error) / (1e-6 + torch.sum(dists_mask))

    # Compute the per atom loss sum.
    # shape (N, 14)
    per_atom_loss_sum = torch.sum(dists_to_low_error, dim=(-4, -2)) + torch.sum(
        dists_to_low_error, dim=(-3, -1)
    )

    # Compute the hard clash mask.
    # shape (N, N, 14, 14)
    clash_mask = dists_mask * (
            dists < (dists_lower_bound - overlap_tolerance_hard)
    )

    per_atom_num_clash = torch.sum(clash_mask, dim=(-4, -2)) + torch.sum(clash_mask, dim=(-3, -1))

    # Compute the per atom clash.
    # shape (N, 14)
    per_atom_clash_mask = torch.maximum(
        torch.amax(clash_mask, dim=(-4, -2)),
        torch.amax(clash_mask, dim=(-3, -1)),
    )

    return {
        "mean_loss": mean_loss,  # shape ()
        "per_atom_loss_sum": per_atom_loss_sum,  # shape (N, 14)
        "per_atom_clash_mask": per_atom_clash_mask,  # shape (N, 14)
        "per_atom_num_clash": per_atom_num_clash # shape (N, 14)
    }


def within_residue_violations(
    atom14_pred_positions: torch.Tensor,
    atom14_atom_exists: torch.Tensor,
    atom14_dists_lower_bound: torch.Tensor,
    atom14_dists_upper_bound: torch.Tensor,
    tighten_bounds_for_loss=0.0,
    eps=1e-10,
) -> Dict[str, torch.Tensor]:
    """Loss to penalize steric clashes within residues.

    This is a loss penalizing any steric violations or clashes of non-bonded atoms
    in a given peptide. This loss corresponds to the part with
    the same residues of
    Jumper et al. (2021) Suppl. Sec. 1.9.11, eq 46.

    Args:
        atom14_pred_positions ([*, N, 14, 3]):
            Predicted positions of atoms in global prediction frame.
        atom14_atom_exists ([*, N, 14]):
            Mask denoting whether atom at positions exists for given
            amino acid type
        atom14_dists_lower_bound ([*, N, 14]):
            Lower bound on allowed distances.
        atom14_dists_upper_bound ([*, N, 14]):
            Upper bound on allowed distances
        tighten_bounds_for_loss ([*, N]):
            Extra factor to tighten loss

    Returns:
      Dict containing:
        * 'per_atom_loss_sum' ([*, N, 14]):
              sum of all clash losses per atom, shape
        * 'per_atom_clash_mask' ([*, N, 14]):
              mask whether atom clashes with any other atom shape
    """
    # Compute the mask for each residue.
    dists_masks = 1.0 - torch.eye(14, device=atom14_atom_exists.device)[None]
    dists_masks = dists_masks.reshape(
        *((1,) * len(atom14_atom_exists.shape[:-2])), *dists_masks.shape
    )
    dists_masks = (
        atom14_atom_exists[..., :, :, None]
        * atom14_atom_exists[..., :, None, :]
        * dists_masks
    )

    # Distance matrix
    dists = torch.sqrt(
        eps
        + torch.sum(
            (
                atom14_pred_positions[..., :, :, None, :]
                - atom14_pred_positions[..., :, None, :, :]
            )
            ** 2,
            dim=-1,
        )
    )

    # Compute the loss.
    dists_to_low_error = torch.nn.functional.relu(
        atom14_dists_lower_bound + tighten_bounds_for_loss - dists
    )
    dists_to_high_error = torch.nn.functional.relu(
        dists - (atom14_dists_upper_bound - tighten_bounds_for_loss)
    )
    loss = dists_masks * (dists_to_low_error + dists_to_high_error)

    # Compute the per atom loss sum.
    per_atom_loss_sum = torch.sum(loss, dim=-2) + torch.sum(loss, dim=-1)

    # Compute the violations mask.
    violations = dists_masks * (
        (dists < atom14_dists_lower_bound) | (dists > atom14_dists_upper_bound)
    )

    per_atom_num_clash = torch.sum(violations, dim=-2) + torch.sum(violations, dim=-1)

    # Compute the per atom violations.
    per_atom_violations = torch.maximum(
        torch.max(violations, dim=-2)[0], torch.max(violations, axis=-1)[0]
    )

    return {
        "per_atom_loss_sum": per_atom_loss_sum,
        "per_atom_violations": per_atom_violations,
        "per_atom_num_clash": per_atom_num_clash
    }


def find_structural_violations(
    batch: Dict[str, torch.Tensor],
    atom14_pred_positions: torch.Tensor,
    violation_tolerance_factor: float,
    clash_overlap_tolerance: float,
    **kwargs,
) -> Dict[str, torch.Tensor]:
    """Computes several checks for structural violations."""

    # Compute between residue backbone violations of bonds and angles.
    connection_violations = between_residue_bond_loss(
        pred_atom_positions=atom14_pred_positions,
        pred_atom_mask=batch["atom14_atom_exists"],
        residue_index=batch["residue_index"],
        aatype=batch["aatype"],
        tolerance_factor_soft=violation_tolerance_factor,
        tolerance_factor_hard=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 = [
        residue_constants.van_der_waals_radius[name[0]]
        for name in residue_constants.atom_types
    ]

    atomtype_radius = atom14_pred_positions.new_tensor(atomtype_radius)

    #TODO: Consolidate monomer/multimer modes
    asym_id = batch.get("asym_id")
    if asym_id is not None:
        residx_atom14_to_atom37 = get_rc_tensor(
            residue_constants.RESTYPE_ATOM14_TO_ATOM37, batch["aatype"]
        )
        atom14_atom_radius = (
            batch["atom14_atom_exists"]
            * atomtype_radius[residx_atom14_to_atom37.long()]
        )
    else:
        atom14_atom_radius = (
            batch["atom14_atom_exists"]
            * atomtype_radius[batch["residx_atom14_to_atom37"]]
        )

    # Compute the between residue clash loss.
    between_residue_clashes = 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"],
        asym_id=asym_id,
        overlap_tolerance_soft=clash_overlap_tolerance,
        overlap_tolerance_hard=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=clash_overlap_tolerance,
        bond_length_tolerance_factor=violation_tolerance_factor,
    )
    atom14_atom_exists = batch["atom14_atom_exists"]
    atom14_dists_lower_bound = atom14_pred_positions.new_tensor(
        restype_atom14_bounds["lower_bound"]
    )[batch["aatype"]]
    atom14_dists_upper_bound = atom14_pred_positions.new_tensor(
        restype_atom14_bounds["upper_bound"]
    )[batch["aatype"]]
    residue_violations = 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 = torch.max(
        torch.stack(
            [
                connection_violations["per_residue_violation_mask"],
                torch.max(
                    between_residue_clashes["per_atom_clash_mask"], dim=-1
                )[0],
                torch.max(residue_violations["per_atom_violations"], dim=-1)[0],
            ],
            dim=-1,
        ),
        dim=-1,
    )[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)
            "clashes_per_atom_num_clash": between_residue_clashes[
                "per_atom_num_clash"
            ],  # (N, 14)
        },
        "within_residues": {
            "per_atom_loss_sum": residue_violations[
                "per_atom_loss_sum"
            ],  # (N, 14)
            "per_atom_violations": residue_violations[
                "per_atom_violations"
            ],  # (N, 14),
            "per_atom_num_clash": residue_violations[
                "per_atom_num_clash"
            ],  # (N, 14)
        },
        "total_per_residue_violations_mask": per_residue_violations_mask,  # (N)
    }


def find_structural_violations_np(
    batch: Dict[str, np.ndarray],
    atom14_pred_positions: np.ndarray,
    config: ml_collections.ConfigDict,
) -> Dict[str, np.ndarray]:
    to_tensor = lambda x: torch.tensor(x)
    batch = tree_map(to_tensor, batch, np.ndarray)
    atom14_pred_positions = to_tensor(atom14_pred_positions)

    out = find_structural_violations(batch, atom14_pred_positions, **config)

    to_np = lambda x: np.array(x)
    np_out = tensor_tree_map(to_np, out)

    return np_out


def extreme_ca_ca_distance_violations(
    pred_atom_positions: torch.Tensor,  # (N, 37(14), 3)
    pred_atom_mask: torch.Tensor,  # (N, 37(14))
    residue_index: torch.Tensor,  # (N)
    max_angstrom_tolerance=1.5,
    eps=1e-6,
) -> torch.Tensor:
    """Counts residues whose Ca is a large distance from its neighbour.

    Measures the fraction of CA-CA pairs between consecutive amino acids that are
    more than 'max_angstrom_tolerance' apart.

    Args:
      pred_atom_positions: Atom positions in atom37/14 representation
      pred_atom_mask: Atom mask in atom37/14 representation
      residue_index: Residue index for given amino acid, this is assumed to be
        monotonically increasing.
      max_angstrom_tolerance: Maximum distance allowed to not count as violation.
    Returns:
      Fraction of consecutive CA-CA pairs with violation.
    """
    this_ca_pos = pred_atom_positions[..., :-1, 1, :]
    this_ca_mask = pred_atom_mask[..., :-1, 1]
    next_ca_pos = pred_atom_positions[..., 1:, 1, :]
    next_ca_mask = pred_atom_mask[..., 1:, 1]
    has_no_gap_mask = (residue_index[..., 1:] - residue_index[..., :-1]) == 1.0
    ca_ca_distance = torch.sqrt(
        eps + torch.sum((this_ca_pos - next_ca_pos) ** 2, dim=-1)
    )
    violations = (
        ca_ca_distance - residue_constants.ca_ca
    ) > max_angstrom_tolerance
    mask = this_ca_mask * next_ca_mask * has_no_gap_mask
    mean = masked_mean(mask, violations, -1)
    return mean


def compute_violation_metrics(
    batch: Dict[str, torch.Tensor],
    atom14_pred_positions: torch.Tensor,  # (N, 14, 3)
    violations: Dict[str, torch.Tensor],
) -> Dict[str, torch.Tensor]:
    """Compute several metrics to assess the structural violations."""
    ret = {}
    extreme_ca_ca_violations = extreme_ca_ca_distance_violations(
        pred_atom_positions=atom14_pred_positions,
        pred_atom_mask=batch["atom14_atom_exists"],
        residue_index=batch["residue_index"],
    )
    ret["violations_extreme_ca_ca_distance"] = extreme_ca_ca_violations
    ret["violations_between_residue_bond"] = masked_mean(
        batch["seq_mask"],
        violations["between_residues"][
            "connections_per_residue_violation_mask"
        ],
        dim=-1,
    )
    ret["violations_between_residue_clash"] = masked_mean(
        mask=batch["seq_mask"],
        value=torch.max(
            violations["between_residues"]["clashes_per_atom_clash_mask"],
            dim=-1,
        )[0],
        dim=-1,
    )
    ret["violations_within_residue"] = masked_mean(
        mask=batch["seq_mask"],
        value=torch.max(
            violations["within_residues"]["per_atom_violations"], dim=-1
        )[0],
        dim=-1,
    )
    ret["violations_per_residue"] = masked_mean(
        mask=batch["seq_mask"],
        value=violations["total_per_residue_violations_mask"],
        dim=-1,
    )
    return ret


def compute_violation_metrics_np(
    batch: Dict[str, np.ndarray],
    atom14_pred_positions: np.ndarray,
    violations: Dict[str, np.ndarray],
) -> Dict[str, np.ndarray]:
    to_tensor = lambda x: torch.tensor(x)
    batch = tree_map(to_tensor, batch, np.ndarray)
    atom14_pred_positions = to_tensor(atom14_pred_positions)
    violations = tree_map(to_tensor, violations, np.ndarray)

    out = compute_violation_metrics(batch, atom14_pred_positions, violations)

    to_np = lambda x: np.array(x)
    return tree_map(to_np, out, torch.Tensor)


def violation_loss(
    violations: Dict[str, torch.Tensor],
    atom14_atom_exists: torch.Tensor,
    average_clashes: bool = False,
    eps=1e-6,
    **kwargs,
) -> torch.Tensor:
    num_atoms = torch.sum(atom14_atom_exists)

    per_atom_clash = (violations["between_residues"]["clashes_per_atom_loss_sum"] +
                      violations["within_residues"]["per_atom_loss_sum"])

    if average_clashes:
        num_clash = (violations["between_residues"]["clashes_per_atom_num_clash"] +
                     violations["within_residues"]["per_atom_num_clash"])
        per_atom_clash = per_atom_clash / (num_clash + eps)

    l_clash = torch.sum(per_atom_clash) / (eps + num_atoms)
    loss = (
        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"]
        + l_clash
    )

    # Average over the batch dimension
    mean = torch.mean(loss)

    return mean


def compute_renamed_ground_truth(
    batch: Dict[str, torch.Tensor],
    atom14_pred_positions: torch.Tensor,
    eps=1e-10,
) -> Dict[str, torch.Tensor]:
    """
    Find optimal renaming of ground truth based on the predicted positions.

    Alg. 26 "renameSymmetricGroundTruthAtoms"

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

    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
    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.
    """

    pred_dists = torch.sqrt(
        eps
        + torch.sum(
            (
                atom14_pred_positions[..., None, :, None, :]
                - atom14_pred_positions[..., None, :, None, :, :]
            )
            ** 2,
            dim=-1,
        )
    )

    atom14_gt_positions = batch["atom14_gt_positions"]
    gt_dists = torch.sqrt(
        eps
        + torch.sum(
            (
                atom14_gt_positions[..., None, :, None, :]
                - atom14_gt_positions[..., None, :, None, :, :]
            )
            ** 2,
            dim=-1,
        )
    )

    atom14_alt_gt_positions = batch["atom14_alt_gt_positions"]
    alt_gt_dists = torch.sqrt(
        eps
        + torch.sum(
            (
                atom14_alt_gt_positions[..., None, :, None, :]
                - atom14_alt_gt_positions[..., None, :, None, :, :]
            )
            ** 2,
            dim=-1,
        )
    )

    lddt = torch.sqrt(eps + (pred_dists - gt_dists) ** 2)
    alt_lddt = torch.sqrt(eps + (pred_dists - alt_gt_dists) ** 2)

    atom14_gt_exists = batch["atom14_gt_exists"]
    atom14_atom_is_ambiguous = batch["atom14_atom_is_ambiguous"]
    mask = (
        atom14_gt_exists[..., None, :, None]
        * atom14_atom_is_ambiguous[..., None, :, None]
        * atom14_gt_exists[..., None, :, None, :]
        * (1.0 - atom14_atom_is_ambiguous[..., None, :, None, :])
    )

    per_res_lddt = torch.sum(mask * lddt, dim=(-1, -2, -3))
    alt_per_res_lddt = torch.sum(mask * alt_lddt, dim=(-1, -2, -3))

    fp_type = atom14_pred_positions.dtype
    alt_naming_is_better = (alt_per_res_lddt < per_res_lddt).type(fp_type)

    renamed_atom14_gt_positions = (
        1.0 - alt_naming_is_better[..., None, None]
    ) * atom14_gt_positions + alt_naming_is_better[
        ..., None, None
    ] * atom14_alt_gt_positions

    renamed_atom14_gt_mask = (
        1.0 - alt_naming_is_better[..., None]
    ) * atom14_gt_exists + alt_naming_is_better[..., None] * batch[
        "atom14_alt_gt_exists"
    ]

    return {
        "alt_naming_is_better": alt_naming_is_better,
        "renamed_atom14_gt_positions": renamed_atom14_gt_positions,
        "renamed_atom14_gt_exists": renamed_atom14_gt_mask,
    }


def experimentally_resolved_loss(
    logits: torch.Tensor,
    atom37_atom_exists: torch.Tensor,
    all_atom_mask: torch.Tensor,
    resolution: torch.Tensor,
    min_resolution: float,
    max_resolution: float,
    eps: float = 1e-8,
    **kwargs,
) -> torch.Tensor:
    errors = sigmoid_cross_entropy(logits, all_atom_mask)
    loss = torch.sum(errors * atom37_atom_exists, dim=-1)
    loss = loss / (eps + torch.sum(atom37_atom_exists, dim=(-1, -2)).unsqueeze(-1))
    loss = torch.sum(loss, dim=-1)
    
    loss = loss * (
        (resolution >= min_resolution) & (resolution <= max_resolution)
    )

    loss = torch.mean(loss)
 
    return loss


def masked_msa_loss(logits, true_msa, bert_mask, num_classes, eps=1e-8, **kwargs):
    """
    Computes BERT-style masked MSA loss. Implements subsection 1.9.9.

    Args:
        logits: [*, N_seq, N_res, 23] predicted residue distribution
        true_msa: [*, N_seq, N_res] true MSA
        bert_mask: [*, N_seq, N_res] MSA mask
    Returns:
        Masked MSA loss
    """
    errors = softmax_cross_entropy(
        logits, torch.nn.functional.one_hot(true_msa, num_classes=num_classes)
    )

    # FP16-friendly averaging. Equivalent to:
    # loss = (
    #     torch.sum(errors * bert_mask, dim=(-1, -2)) /
    #     (eps + torch.sum(bert_mask, dim=(-1, -2)))
    # )
    loss = errors * bert_mask
    loss = torch.sum(loss, dim=-1)
    scale = 0.5
    denom = eps + torch.sum(scale * bert_mask, dim=(-1, -2))
    loss = loss / denom[..., None]
    loss = torch.sum(loss, dim=-1)
    loss = loss * scale

    loss = torch.mean(loss)

    return loss


def chain_center_of_mass_loss(
    all_atom_pred_pos: torch.Tensor,
    all_atom_positions: torch.Tensor,
    all_atom_mask: torch.Tensor,
    asym_id: torch.Tensor,
    clamp_distance: float = -4.0,
    weight: float = 0.05,
    eps: float = 1e-10, **kwargs
) -> torch.Tensor:
    """
    Computes chain centre-of-mass loss. Implements section 2.5, eqn 1 in the Multimer paper.

    Args:
        all_atom_pred_pos:
            [*, N_pts, 37, 3] All-atom predicted atom positions
        all_atom_positions:
            [*, N_pts, 37, 3] Ground truth all-atom positions
        all_atom_mask:
            [*, N_pts, 37] All-atom positions mask
        asym_id:
            [*, N_pts] Chain asym IDs
        clamp_distance:
            Cutoff above which distance errors are disregarded
        weight:
            Weight for loss
        eps:
            Small value used to regularize denominators
    Returns:
        [*] loss tensor
    """
    ca_pos = residue_constants.atom_order["CA"]
    all_atom_pred_pos = all_atom_pred_pos[..., ca_pos, :]
    all_atom_positions = all_atom_positions[..., ca_pos, :]
    all_atom_mask = all_atom_mask[..., ca_pos: (ca_pos + 1)]  # keep dim
    chains, _ = asym_id.unique(return_counts=True)
    one_hot = torch.nn.functional.one_hot(asym_id.to(torch.int64)-1, # have to reduce asym_id by one because class values must be smaller than num_classes  
                                          num_classes=chains.shape[0]).to(dtype=all_atom_mask.dtype) # make sure asym_id dtype is int
    one_hot = one_hot * all_atom_mask
    chain_pos_mask = one_hot.transpose(-2, -1)
    chain_exists = torch.any(chain_pos_mask, dim=-1).float()

    def get_chain_center_of_mass(pos):
        center_sum = (chain_pos_mask[..., None] * pos[..., None, :, :]).sum(dim=-2)
        centers = center_sum / (torch.sum(chain_pos_mask, dim=-1, keepdim=True) + eps)
        return Vec3Array.from_array(centers)

    pred_centers = get_chain_center_of_mass(all_atom_pred_pos)  # [B, NC, 3]
    true_centers = get_chain_center_of_mass(all_atom_positions)  # [B, NC, 3]

    pred_dists = euclidean_distance(pred_centers[..., None, :], pred_centers[..., :, None], epsilon=eps)
    true_dists = euclidean_distance(true_centers[..., None, :], true_centers[..., :, None], epsilon=eps)
    losses = torch.clamp((weight * (pred_dists - true_dists - clamp_distance)), max=0) ** 2
    loss_mask = chain_exists[..., :, None] * chain_exists[..., None, :]

    loss = masked_mean(loss_mask, losses, dim=(-1, -2))
    return loss

# #
# below are the functions required for permutations
# #
def kabsch_rotation(P, Q):
    """
    Use procrustes package to calculate best rotation that minimises
    the RMSD betwee P and Q

    The optimal rotation matrix was calculated using 
    the rotational() function from procrustes package. Details can be found here:
    https://procrustes.qcdevs.org/api/rotational.html#rotational

    Args:
    P: [N * 3] Nres is the number of atoms and each row corresponds to the atom's x,y,z coordinates
    Q: [N * 3] the same dimension as P

    return:
    A 3*3 rotation matrix 
    """

    assert P.shape == torch.Size([Q.shape[0],Q.shape[1]])
    rotation = procrustes.rotational(P.detach().cpu().numpy(),
                                  Q.detach().cpu().numpy(),translate=False,scale=False)
    rotation = torch.tensor(rotation.t,dtype=torch.float) # rotation.t doesn't mean transpose, t only means get the matrix out of the procruste object
    assert rotation.shape == torch.Size([3,3])
    return rotation.to('cuda')

def get_optimal_transform(
    src_atoms: torch.Tensor,
    tgt_atoms: torch.Tensor,
    mask: torch.Tensor = None,
):
    """
    src_atoms: predicted CA positions, shape:[num_res,3]
    tgt_atoms: ground-truth CA positions, shape:[num_res,3] 
    mask: a vector of boolean values, shape:[num_res]
    """
    assert src_atoms.shape == tgt_atoms.shape, (src_atoms.shape, tgt_atoms.shape)
    assert src_atoms.shape[-1] == 3
    assert len(mask.shape) ==1,"mask should have the shape of [num_res]"
    if torch.isnan(src_atoms).any() or torch.isinf(src_atoms).any():
        #
        # sometimes using fake test inputs generates NaN in the predicted atom positions
        # #
        logging.warning(f"src_atom has nan or inf")
        src_atoms = torch.nan_to_num(src_atoms,nan=0.0,posinf=1.0,neginf=1.0)

    if mask is not None:
        assert mask.dtype == torch.bool
        assert mask.shape[-1] == src_atoms.shape[-2]
        if mask.sum() == 0:
            src_atoms = torch.zeros((1, 3), device=src_atoms.device).float()
            tgt_atoms = src_atoms
        else:
            src_atoms = src_atoms[mask, :]
            tgt_atoms = tgt_atoms[mask, :]
    src_center = src_atoms.mean(-2, keepdim=True)
    tgt_center = tgt_atoms.mean(-2, keepdim=True)
    r = kabsch_rotation(src_atoms,tgt_atoms)
    del src_atoms,tgt_atoms,
    gc.collect()

    tgt_center,src_center = tgt_center.to('cuda:0'),src_center.to('cuda:0')
    x = tgt_center.to('cpu') - src_center.to('cpu') @ r.to('cpu')

    del tgt_center,src_center,mask
    gc.collect()

    return r, x.to('cuda')


def compute_rmsd(
    true_atom_pos: torch.Tensor,
    pred_atom_pos: torch.Tensor,
    atom_mask: torch.Tensor = None,
    eps: float = 1e-6,
) -> torch.Tensor:
    # shape check
    true_atom_pos = true_atom_pos.to('cuda:0')
    pred_atom_pos = pred_atom_pos.to('cuda:0')
    sq_diff = torch.square(true_atom_pos - pred_atom_pos).sum(dim=-1, keepdim=False)
    del true_atom_pos
    del pred_atom_pos
    gc.collect()
    if atom_mask is not None:
        sq_diff = sq_diff.to('cpu')[atom_mask.to('cpu')] # somehow it causes overflow on cuda so moved to cpu
    msd = torch.mean(sq_diff)
    msd = torch.nan_to_num(msd, nan=1e8)
    return torch.sqrt(msd + eps)


def get_least_asym_entity_or_longest_length(batch):
    """
    First check how many subunit(s) one sequence has, if there is no tie, e.g. AABBB then select 
    one of the A as anchor

    If there is a tie, e.g. AABB, first check which sequence is the longer/longest,
    then choose one of the corresponding subunits as anchor 
    """
    unique_entity_ids = torch.unique(batch["entity_id"])
    entity_asym_count = {}
    entity_length = {}

    for entity_id in unique_entity_ids:
        asym_ids = torch.unique(batch["asym_id"][batch["entity_id"] == entity_id])
        entity_asym_count[int(entity_id)] = len(asym_ids)
        
        # Calculate entity length
        entity_mask = (batch["entity_id"] == entity_id)
        entity_length[int(entity_id)] = entity_mask.sum().item()

    min_asym_count = min(entity_asym_count.values())
    least_asym_entities = [entity for entity, count in entity_asym_count.items() if count == min_asym_count]

    # If multiple entities have the least asym_id count, return those with the shortest length
    if len(least_asym_entities) > 1:
        max_length = max([entity_length[entity] for entity in least_asym_entities])
        least_asym_entities = [entity for entity in least_asym_entities if entity_length[entity] == max_length]

    # If still multiple entities, return a random one
    if len(least_asym_entities) > 1:
        least_asym_entities = random.choice(least_asym_entities)
    assert len(least_asym_entities)==1
    best_pred_asym = torch.unique(batch["asym_id"][batch["entity_id"] == least_asym_entities[0]])
    
    # If there is more than one chain in the predicted output that has the same sequence
    # as the chosen ground truth anchor, then randomly picke one
    if len(best_pred_asym) > 1:
        best_pred_asym = random.choice(best_pred_asym)
    return least_asym_entities[0], best_pred_asym


def greedy_align(
    batch,
    per_asym_residue_index,
    unique_asym_ids,
    entity_2_asym_list,
    pred_ca_pos,
    pred_ca_mask,
    true_ca_poses,
    true_ca_masks,
):
    used = [False for _ in range(len(true_ca_poses))]
    align = []
    for cur_asym_id in unique_asym_ids:
        # skip padding
        if cur_asym_id == 0:
            continue
        i = int(cur_asym_id - 1)
        asym_mask = batch["asym_id"] == cur_asym_id
        entity_id = batch["entity_id"][asym_mask][0]
        # don't need to align
        if (entity_id) == 1:
            align.append((i, i))
            assert used[i] == False
            used[i] = True
            continue
        cur_entity_ids = batch["entity_id"][asym_mask][0]
        best_rmsd = torch.inf    
        best_idx = None
        cur_asym_list = entity_2_asym_list[int(cur_entity_ids)]
        cur_residue_index = per_asym_residue_index[int(cur_asym_id)]
        cur_pred_pos = pred_ca_pos[asym_mask]
        cur_pred_mask = pred_ca_mask[asym_mask]
        for next_asym_id in cur_asym_list:
            if next_asym_id == 0:
                continue
            j = int(next_asym_id - 1)
            if not used[j]:  # possible candidate
                while best_idx is None:
                    cropped_pos = true_ca_poses[j]
                    mask = true_ca_masks[j][cur_residue_index]
                    rmsd = compute_rmsd(
                        cropped_pos, cur_pred_pos, (cur_pred_mask.to('cuda:0') * mask.to('cuda:0')).bool()
                    )
                    
                    if (rmsd is not None) and (rmsd < best_rmsd):   
                        best_rmsd = rmsd
                        best_idx = j
        assert best_idx is not None
        used[best_idx] = True
        align.append((i, best_idx))
    return align


def merge_labels(per_asym_residue_index, labels, align):
    """
    per_asym_residue_index: A dictionary that record which asym_id corresponds to which regions of residues in the multimer complex.
    labels: list of original ground truth feats
    align: list of tuples, each entry specify the corresponding label of the asym.
    """
    outs = {}
    for k, v in labels[0].items():
        cur_out = {}
        for i, j in align:
            label = labels[j][k]
            cur_num_res = labels[j]['aatype'].shape[-1]
            # to 1-based
            cur_residue_index = per_asym_residue_index[i + 1]
            if len(v.shape)==0 or "template" in k:
                continue
            else:    
                dimension_to_merge = label.shape.index(cur_num_res) if cur_num_res in label.shape else 0
                cur_out[i] = label.index_select(dimension_to_merge,cur_residue_index)
        cur_out = [x[1] for x in sorted(cur_out.items())]
        if len(cur_out)>0:
            new_v = torch.concat(cur_out, dim=dimension_to_merge)
            outs[k] = new_v
    return outs


class AlphaFoldLoss(nn.Module):
    """Aggregation of the various losses described in the supplement"""
    def __init__(self, config):
        super(AlphaFoldLoss, self).__init__()
        self.config = config

    def loss(self, out, batch, _return_breakdown=False):
        """
        Rename previous forward() as loss()
        so that can be reused in the subclass 
        """
        if "violation" not in out.keys():
            out["violation"] = find_structural_violations(
                batch,
                out["sm"]["positions"][-1],
                **self.config.violation,
            )

        if "renamed_atom14_gt_positions" not in out.keys():
            batch.update(
                compute_renamed_ground_truth(
                    batch,
                    out["sm"]["positions"][-1],
                )
            )

        loss_fns = {
            "distogram": lambda: distogram_loss(
                logits=out["distogram_logits"],
                **{**batch, **self.config.distogram},
            ),
            "experimentally_resolved": lambda: experimentally_resolved_loss(
                logits=out["experimentally_resolved_logits"],
                **{**batch, **self.config.experimentally_resolved},
            ),
            "fape": lambda: fape_loss(
                out,
                batch,
                self.config.fape,
            ),
            "plddt_loss": lambda: lddt_loss(
                logits=out["lddt_logits"],
                all_atom_pred_pos=out["final_atom_positions"],
                **{**batch, **self.config.plddt_loss},
            ),
            "masked_msa": lambda: masked_msa_loss(
                logits=out["masked_msa_logits"],
                **{**batch, **self.config.masked_msa},
            ),
            "supervised_chi": lambda: supervised_chi_loss(
                out["sm"]["angles"],
                out["sm"]["unnormalized_angles"],
                **{**batch, **self.config.supervised_chi},
            ),
            "violation": lambda: violation_loss(
                out["violation"],
                **{**batch, **self.config.violation},
            ),
        }

        if(self.config.tm.enabled):
            loss_fns["tm"] = lambda: tm_loss(
                logits=out["tm_logits"],
                **{**batch, **out, **self.config.tm},
            )

        if (self.config.chain_center_of_mass.enabled):
            loss_fns["chain_center_of_mass"] = lambda: chain_center_of_mass_loss(
                all_atom_pred_pos=out["final_atom_positions"],
                **{**batch, **self.config.chain_center_of_mass},
            )

        cum_loss = 0.
        losses = {}
        for loss_name, loss_fn in loss_fns.items():
            weight = self.config[loss_name].weight
            loss = loss_fn()
            if(torch.isnan(loss) or torch.isinf(loss)):
                #for k,v in batch.items():
                #    if(torch.any(torch.isnan(v)) or torch.any(torch.isinf(v))):
                #        logging.warning(f"{k}: is nan")
                #logging.warning(f"{loss_name}: {loss}")
                logging.warning(f"{loss_name} loss is NaN. Skipping...")
                loss = loss.new_tensor(0., requires_grad=True)
            cum_loss = cum_loss + weight * loss
            losses[loss_name] = loss.detach().clone()
        losses["unscaled_loss"] = cum_loss.detach().clone()

        # Scale the loss by the square root of the minimum of the crop size and
        # the (average) sequence length. See subsection 1.9.
        seq_len = torch.mean(batch["seq_length"].float())
        crop_len = batch["aatype"].shape[-1]
        cum_loss = cum_loss * torch.sqrt(min(seq_len, crop_len))

        losses["loss"] = cum_loss.detach().clone()

        if(not _return_breakdown):
            return cum_loss
        
        return cum_loss, losses
    
    def forward(self, out, batch, _return_breakdown=False):
            if(not _return_breakdown):
                cum_loss = self.loss(out,batch,_return_breakdown)
                return cum_loss
            else:
                cum_loss,losses = self.loss(out,batch,_return_breakdown)
                return cum_loss, losses

class AlphaFoldMultimerLoss(AlphaFoldLoss):
    """
    Add multi-chain permutation on top of 
    AlphaFoldLoss
    """
    def __init__(self, config):
        super(AlphaFoldMultimerLoss, self).__init__(config)
        self.config = config

    def multi_chain_perm_align(self,out, batch, labels, shuffle_times=2):
        """
        A class method that first permutate chains in ground truth first
        before calculating the loss.

        Details are described in Section 7.3 in the Supplementary of AlphaFold-Multimer paper:
        https://www.biorxiv.org/content/10.1101/2021.10.04.463034v2
        """
        assert isinstance(labels, list)
        ca_idx = rc.atom_order["CA"]
        pred_ca_pos = out["final_atom_positions"][..., ca_idx, :].float()  # [bsz, nres, 3]
        pred_ca_mask = out["final_atom_mask"][..., ca_idx].float()  # [bsz, nres]
        true_ca_poses = [
            l["all_atom_positions"][..., ca_idx, :].float() for l in labels
        ]  # list([nres, 3])
        true_ca_masks = [
            l["all_atom_mask"][..., ca_idx].float() for l in labels
        ]  # list([nres,])
        unique_asym_ids = torch.unique(batch["asym_id"])

        per_asym_residue_index = {}
        for cur_asym_id in unique_asym_ids:
            asym_mask = (batch["asym_id"] == cur_asym_id).bool()
            per_asym_residue_index[int(cur_asym_id)] = torch.masked_select(batch["residue_index"],asym_mask)

        anchor_gt_asym, anchor_pred_asym = get_least_asym_entity_or_longest_length(batch)
        anchor_gt_idx = int(anchor_gt_asym) - 1

        unique_entity_ids = torch.unique(batch["entity_id"])
        entity_2_asym_list = {}
        for cur_ent_id in unique_entity_ids:
            ent_mask = batch["entity_id"] == cur_ent_id
            cur_asym_id = torch.unique(batch["asym_id"][ent_mask])
            entity_2_asym_list[int(cur_ent_id)] = cur_asym_id
        asym_mask = (batch["asym_id"] == anchor_pred_asym).bool()
        anchor_residue_idx = per_asym_residue_index[int(anchor_pred_asym)]
        anchor_true_pos = torch.index_select(true_ca_poses[anchor_gt_idx],1,anchor_residue_idx)
        anchor_pred_pos = pred_ca_pos[asym_mask]
        
        # anchor_pred_pos = anchor_pred_pos.to('cuda')
        anchor_true_mask = torch.index_select(true_ca_masks[anchor_gt_idx],1,anchor_residue_idx)
        anchor_pred_mask =pred_ca_mask[asym_mask]
        # anchor_pred_mask = anchor_pred_mask.to('cuda')
        input_mask = (anchor_true_mask * anchor_pred_mask).bool()
        r, x = get_optimal_transform(
            anchor_pred_pos,anchor_true_pos[0],
            mask=input_mask[0]
        )
        del input_mask # just to save memory
        del anchor_pred_mask
        del anchor_true_mask
        gc.collect()

        aligned_true_ca_poses = [ca @ r + x for ca in true_ca_poses]  # apply transforms
        align = greedy_align(
                batch,
                per_asym_residue_index,
                unique_asym_ids ,
                entity_2_asym_list,
                pred_ca_pos,
                pred_ca_mask,
                aligned_true_ca_poses,
                true_ca_masks,
            )
        
        del aligned_true_ca_poses
        del r,x
        gc.collect()
        print(f"finished multi-chain permutation and final align is {align}")
        merged_labels = merge_labels(
            per_asym_residue_index,
            labels,
            align,
        )
                
        return merged_labels

    def forward(self,out,batch,_return_breakdown=False):
        """
        Overwrite AlphaFoldLoss forward function so that
        it first compute multi-chain permutation 

        args:
        out: the output of model.forward()
        batch: a pair of input features and its corresponding ground truth structure
        """
        features,labels = batch
        # first remove the recycling dimention of input features
        features = tensor_tree_map(lambda t: t[..., -1], features)
        features['resolution'] = labels[0]['resolution']
        # then permutate ground truth chains before calculating the loss
        permutated_labels = self.multi_chain_perm_align(out,features,labels)
        permutated_labels.pop('aatype')
        features.update(permutated_labels)
        move_to_cpu = lambda t: (t.to('cpu'))
        # features = tensor_tree_map(move_to_cpu,features)
        if (not _return_breakdown):
            cum_loss = self.loss(out,features,_return_breakdown)
            print(f"cum_loss: {cum_loss}")
            return cum_loss
        else:
            cum_loss,losses = self.loss(out,features,_return_breakdown)
            print(f"cum_loss: {cum_loss} losses: {losses}")
            return cum_loss, losses