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# Copyright 2024 ByteDance and/or its affiliates.
#
# 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 typing import Optional
import torch
def rmsd(
pred_pose: torch.Tensor,
true_pose: torch.Tensor,
mask: torch.Tensor = None,
eps: float = 0.0,
reduce: bool = True,
):
"""
compute rmsd between two poses, with the same shape
Arguments:
pred_pose/true_pose: [...,N,3], two poses with the same shape
mask: [..., N], mask to indicate which atoms/pseudo_betas/etc to compute
eps: add a tolerance to avoid floating number issue
reduce: decide the return shape of rmsd;
Return:
rmsd: if reduce = true, return the mean of rmsd over batches;
else return a tensor containing each rmsd separately
"""
# mask [..., N]
assert pred_pose.shape == true_pose.shape # [..., N, 3]
if mask is None:
mask = torch.ones(true_pose.shape[:-1], device=true_pose.device)
# [...]
err2 = (torch.square(pred_pose - true_pose).sum(dim=-1) * mask).sum(
dim=-1
) / mask.sum(dim=-1)
rmsd = err2.add(eps).sqrt()
if reduce:
rmsd = rmsd.mean()
return rmsd
def align_pred_to_true(
pred_pose: torch.Tensor,
true_pose: torch.Tensor,
atom_mask: Optional[torch.Tensor] = None,
weight: Optional[torch.Tensor] = None,
allowing_reflection: bool = False,
):
"""Find optimal transformation, rotation (and reflection) of two poses.
Arguments:
pred_pose: [...,N,3] the pose to perform transformation on
true_pose: [...,N,3] the target pose to align pred_pose to
atom_mask: [..., N] a mask for atoms
weight: [..., N] a weight vector to be applied.
allow_reflection: whether to allow reflection when finding optimal alignment
return:
aligned_pose: [...,N,3] the transformed pose
rot: optimal rotation
translate: optimal translation
"""
if atom_mask is not None:
pred_pose = pred_pose * atom_mask.unsqueeze(-1)
true_pose = true_pose * atom_mask.unsqueeze(-1)
else:
atom_mask = torch.ones(*pred_pose.shape[:-1]).to(pred_pose.device)
if weight is None:
weight = atom_mask
else:
weight = weight * atom_mask
weighted_n_atoms = torch.sum(weight, dim=-1, keepdim=True).unsqueeze(-1)
pred_pose_centroid = (
torch.sum(pred_pose * weight.unsqueeze(-1), dim=-2, keepdim=True)
/ weighted_n_atoms
)
pred_pose_centered = pred_pose - pred_pose_centroid
true_pose_centroid = (
torch.sum(true_pose * weight.unsqueeze(-1), dim=-2, keepdim=True)
/ weighted_n_atoms
)
true_pose_centered = true_pose - true_pose_centroid
H_mat = torch.matmul(
(pred_pose_centered * weight.unsqueeze(-1)).transpose(-2, -1),
true_pose_centered * atom_mask.unsqueeze(-1),
)
u, s, v = torch.svd(H_mat)
u = u.transpose(-1, -2)
if not allowing_reflection:
det = torch.linalg.det(torch.matmul(v, u))
diagonal = torch.stack(
[torch.ones_like(det), torch.ones_like(det), det], dim=-1
)
rot = torch.matmul(
torch.diag_embed(diagonal).to(u.device),
u,
)
rot = torch.matmul(v, rot)
else:
rot = torch.matmul(v, u)
translate = true_pose_centroid - torch.matmul(
pred_pose_centroid, rot.transpose(-1, -2)
)
pred_pose_translated = (
torch.matmul(pred_pose_centered, rot.transpose(-1, -2)) + true_pose_centroid
)
return pred_pose_translated, rot, translate
def partially_aligned_rmsd(
pred_pose: torch.Tensor,
true_pose: torch.Tensor,
align_mask: torch.Tensor,
atom_mask: torch.Tensor,
weight: Optional[torch.Tensor] = None,
eps: float = 0.0,
reduce: bool = True,
allowing_reflection: bool = False,
):
"""RMSD when aligning parts of the complex coordinate, does NOT take permutation symmetricity into consideration
Arguments:
pred_pose: native predicted pose, [..., N,3]
true_pose: ground truth pose, [..., N, 3]
align_mask: a mask representing which coordinates to align [..., N]
atom_mask: a mask representing which coordinates to compute loss [..., N]
weight: a weight tensor assining weights in alignment for each atom [..., N]
eps: add a tolerance to avoid floating number issue in sqrt
reduce: decide the return shape of rmsd;
allowing_reflection: whether to allow reflection when finding optimal alignment
return:
aligned_part_rmsd: the rmsd of part being align_masked
unaligned_part_rmsd: the rmsd of unaligned part
transformed_pred_pose:
rot: optimal rotation
trans: optimal translation
"""
_, rot, translate = align_pred_to_true(
pred_pose,
true_pose,
atom_mask=atom_mask * align_mask,
weight=weight,
allowing_reflection=allowing_reflection,
)
transformed_pose = torch.matmul(pred_pose, rot.transpose(-1, -2)) + translate
err_atom = torch.square(transformed_pose - true_pose).sum(dim=-1) * atom_mask
aligned_mask, unaligned_mask = atom_mask * align_mask.float(), atom_mask * (
1 - align_mask.float()
)
aligned_part_err_square = (err_atom * aligned_mask).sum(dim=-1) / aligned_mask.sum(
dim=-1
)
unaligned_part_err_square = (err_atom * unaligned_mask).sum(
dim=-1
) / unaligned_mask.sum(dim=-1)
aligned_part_rmsd = aligned_part_err_square.add(eps).sqrt()
unaligned_part_rmsd = unaligned_part_err_square.add(eps).sqrt()
if reduce:
aligned_part_rmsd = aligned_part_rmsd.mean()
unaligned_part_rmsd = unaligned_part_rmsd.mean()
return aligned_part_rmsd, unaligned_part_rmsd, transformed_pose, rot, translate
def self_aligned_rmsd(
pred_pose: torch.Tensor,
true_pose: torch.Tensor,
atom_mask: torch.Tensor,
eps: float = 0.0,
reduce: bool = True,
allowing_reflection: bool = False,
):
"""RMSD when aligning one molecule with ground truth and compute rmsd.
Arguments:
pred_pose: native predicted pose, [..., N,3]
true_pose: ground truth pose, [..., N, 3]
atom_mask: a mask representing which coordinates to compute loss [..., N]
eps: add a tolerance to avoid floating number issue in sqrt
reduce: decide the return shape of rmsd;
allowing_reflection: whether to allow reflection when finding optimal alignment
return:
aligned_rmsd: the rmsd of part being align_masked
transformed_pred_pose: the aligned pose
rot: optimal rotation matrix
trans: optimal translation
"""
aligned_rmsd, _, transformed_pred_pose, rot, trans = partially_aligned_rmsd(
pred_pose=pred_pose,
true_pose=true_pose,
align_mask=atom_mask,
atom_mask=atom_mask,
eps=eps,
reduce=reduce,
allowing_reflection=allowing_reflection,
)
return aligned_rmsd, transformed_pred_pose, rot, trans
def weighted_rigid_align(
x: torch.Tensor,
x_target: torch.Tensor,
atom_weight: torch.Tensor,
stop_gradient: bool = True,
) -> tuple[torch.Tensor]:
"""Implements Algorithm 28 in AF3. Wrap `align_pred_to_true`.
Args:
x (torch.Tensor): input coordinates, it will be moved to match x_target.
[..., N_atom, 3]
x_target (torch.Tensor): target coordinates for the input to match.
[..., N_atom, 3]
atom_weight (torch.Tensor): weights for each atom.
[..., N_atom] or [N_atom]
stop_gradient (bool): whether to detach the output. If true, will run it with no_grad() ctx.
Returns:
x_aligned (torch.Tensor): rotated, translated x which should be closer to x_target.
[..., N_atom, 3]
"""
if len(atom_weight.shape) == len(x.shape) - 1:
assert atom_weight.shape[:-1] == x.shape[:-2]
else:
assert len(atom_weight.shape) == 1 and atom_weight.shape[-1] == x.shape[-2]
if stop_gradient:
with torch.no_grad():
x_aligned, rot, trans = align_pred_to_true(
pred_pose=x,
true_pose=x_target,
atom_mask=None,
weight=atom_weight,
allowing_reflection=False,
)
return x_aligned.detach()
else:
x_aligned, rot, trans = align_pred_to_true(
pred_pose=x,
true_pose=x_target,
atom_mask=None,
weight=atom_weight,
allowing_reflection=False,
)
return x_aligned
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