code: # Copyright (c) Facebook, Inc. and its affiliates.
  import torch
  import torch.distributed as dist
  from fvcore.nn.distributed import differentiable_all_reduce
  from torch import nn
  from torch.nn import functional as F
  
  from ..utils import comm, env
  
  from .wrappers import BatchNorm2d
  
  
  class FrozenBatchNorm2d(nn.Module):
      """
      BatchNorm2d where the batch statistics and the affine parameters are fixed.
  
      It contains non-trainable buffers called
      "weight" and "bias", "running_mean", "running_var",
      initialized to perform identity transformation.
  
      The pre-trained backbone models from Caffe2 only contain "weight" and "bias",
      which are computed from the original four parameters of BN.
      The affine transform `x * weight + bias` will perform the equivalent
      computation of `(x - running_mean) / sqrt(running_var) * weight + bias`.
      When loading a backbone model from Caffe2, "running_mean" and "running_var"
      will be left unchanged as identity transformation.
  
      Other pre-trained backbone models may contain all 4 parameters.
  
      The forward is implemented by `F.batch_norm(..., training=False)`.
      """
  
      _version = 3
  
      def __init__(self, num_features, eps=1e-5):
          super().__init__()
          self.num_features = num_features
          self.eps = eps
          self.register_buffer("weight", torch.ones(num_features))
          self.register_buffer("bias", torch.zeros(num_features))
          self.register_buffer("running_mean", torch.zeros(num_features))
          self.register_buffer("running_var", torch.ones(num_features) - eps)
  
      def forward(self, x):
          if x.requires_grad:
              # When gradients are needed, F.batch_norm will use extra memory
              # because its backward op computes gradients for weight/bias as well.
              scale = self.weight * (self.running_var + self.eps).rsqrt()
              bias = self.bias - self.running_mean * scale
              scale = scale.reshape(1, -1, 1, 1)
              bias = bias.reshape(1, -1, 1, 1)
              out_dtype = x.dtype  # may be half
              return x * scale.to(out_dtype) + bias.to(out_dtype)
          else:
              # When gradients are not needed, F.batch_norm is a single fused op
              # and provide more optimization opportunities.
              return F.batch_norm(
                  x,
                  self.running_mean,
                  self.running_var,
                  self.weight,
                  self.bias,
                  training=False,
                  eps=self.eps,
              )
  
      def _load_from_state_dict(
          self, state_dict, prefix, local_metadata, strict, missing_keys, unexpected_keys, error_msgs
      ):
          version = local_metadata.get("version", None)
  
          if version is None or version < 2:
              # No running_mean/var in early versions
              # This will silent the warnings
              if prefix + "running_mean" not in state_dict:
                  state_dict[prefix + "running_mean"] = torch.zeros_like(self.running_mean)
              if prefix + "running_var" not in state_dict:
                  state_dict[prefix + "running_var"] = torch.ones_like(self.running_var)
  
          super()._load_from_state_dict(
              state_dict, prefix, local_metadata, strict, missing_keys, unexpected_keys, error_msgs
          )
  
      def __repr__(self):
          return "FrozenBatchNorm2d(num_features={}, eps={})".format(self.num_features, self.eps)
  
      @classmethod
      def convert_frozen_batchnorm(cls, module):
          """
          Convert all BatchNorm/SyncBatchNorm in module into FrozenBatchNorm.
  
          Args:
              module (torch.nn.Module):
  
          Returns:
              If module is BatchNorm/SyncBatchNorm, returns a new module.
              Otherwise, in-place convert module and return it.
  
          Similar to convert_sync_batchnorm in
          https://github.com/pytorch/pytorch/blob/master/torch/nn/modules/batchnorm.py
          """
          bn_module = nn.modules.batchnorm
          bn_module = (bn_module.BatchNorm2d, bn_module.SyncBatchNorm)
          res = module
          if isinstance(module, bn_module):
              res = cls(module.num_features)
              if module.affine:
                  res.weight.data = module.weight.data.clone().detach()
                  res.bias.data = module.bias.data.clone().detach()
              res.running_mean.data = module.running_mean.data
              res.running_var.data = module.running_var.data
              res.eps = module.eps
          else:
              for name, child in module.named_children():
                  new_child = cls.convert_frozen_batchnorm(child)
                  if new_child is not child:
                      res.add_module(name, new_child)
          return res
  
  
  def get_norm(norm, out_channels):
      """
      Args:
          norm (str or callable): either one of BN, SyncBN, FrozenBN, GN;
              or a callable that takes a channel number and returns
              the normalization layer as a nn.Module.
  
      Returns:
          nn.Module or None: the normalization layer
      """
      if norm is None:
          return None
      if isinstance(norm, str):
          if len(norm) == 0:
              return None
          norm = {
              "BN": BatchNorm2d,
              # Fixed in https://github.com/pytorch/pytorch/pull/36382
              "SyncBN": NaiveSyncBatchNorm if env.TORCH_VERSION <= (1, 5) else nn.SyncBatchNorm,
              "FrozenBN": FrozenBatchNorm2d,
              "GN": lambda channels: nn.GroupNorm(32, channels),
              # for debugging:
              "nnSyncBN": nn.SyncBatchNorm,
              "naiveSyncBN": NaiveSyncBatchNorm,
          }[norm]
      return norm(out_channels)
  
  
  class NaiveSyncBatchNorm(BatchNorm2d):
      """
      In PyTorch<=1.5, ``nn.SyncBatchNorm`` has incorrect gradient
      when the batch size on each worker is different.
      (e.g., when scale augmentation is used, or when it is applied to mask head).
  
      This is a slower but correct alternative to `nn.SyncBatchNorm`.
  
      Note:
          There isn't a single definition of Sync BatchNorm.
  
          When ``stats_mode==""``, this module computes overall statistics by using
          statistics of each worker with equal weight.  The result is true statistics
          of all samples (as if they are all on one worker) only when all workers
          have the same (N, H, W). This mode does not support inputs with zero batch size.
  
          When ``stats_mode=="N"``, this module computes overall statistics by weighting
          the statistics of each worker by their ``N``. The result is true statistics
          of all samples (as if they are all on one worker) only when all workers
          have the same (H, W). It is slower than ``stats_mode==""``.
  
          Even though the result of this module may not be the true statistics of all samples,
          it may still be reasonable because it might be preferrable to assign equal weights
          to all workers, regardless of their (H, W) dimension, instead of putting larger weight
          on larger images. From preliminary experiments, little difference is found between such
          a simplified implementation and an accurate computation of overall mean & variance.
      """
  
      def __init__(self, *args, stats_mode="", **kwargs):
          super().__init__(*args, **kwargs)
          assert stats_mode in ["", "N"]
          self._stats_mode = stats_mode
  
      def forward(self, input):
          if comm.get_world_size() == 1 or not self.training:
              return super().forward(input)
  
          B, C = input.shape[0], input.shape[1]
  
          half_input = input.dtype == torch.float16
          if half_input:
              # fp16 does not have good enough numerics for the reduction here
              input = input.float()
          mean = torch.mean(input, dim=[0, 2, 3])
          meansqr = torch.mean(input * input, dim=[0, 2, 3])
  
          if self._stats_mode == "":
              assert B > 0, 'SyncBatchNorm(stats_mode="") does not support zero batch size.'
              vec = torch.cat([mean, meansqr], dim=0)
              vec = differentiable_all_reduce(vec) * (1.0 / dist.get_world_size())
              mean, meansqr = torch.split(vec, C)
              momentum = self.momentum
          else:
              if B == 0:
                  vec = torch.zeros([2 * C + 1], device=mean.device, dtype=mean.dtype)
                  vec = vec + input.sum()  # make sure there is gradient w.r.t input
              else:
                  vec = torch.cat(
                      [mean, meansqr, torch.ones([1], device=mean.device, dtype=mean.dtype)], dim=0
                  )
              vec = differentiable_all_reduce(vec * B)
  
              total_batch = vec[-1].detach()
              momentum = total_batch.clamp(max=1) * self.momentum  # no update if total_batch is 0
              mean, meansqr, _ = torch.split(vec / total_batch.clamp(min=1), C)  # avoid div-by-zero
  
          var = meansqr - mean * mean
          invstd = torch.rsqrt(var + self.eps)
          scale = self.weight * invstd
          bias = self.bias - mean * scale
          scale = scale.reshape(1, -1, 1, 1)
          bias = bias.reshape(1, -1, 1, 1)
  
          self.running_mean += momentum * (mean.detach() - self.running_mean)
          self.running_var += momentum * (var.detach() - self.running_var)
          ret = input * scale + bias
          if half_input:
              ret = ret.half()
          return ret
  
apis: torch.ones_like torch.ones torch.nn.GroupNorm torch.distributed.get_world_size torch.split torch.zeros_like torch.nn.functional.batch_norm torch.rsqrt torch.zeros torch.cat torch.mean