text: # Copyright 2021 Alibaba Group Holding Limited. All Rights Reserved.
  
  # _no_grad_trunc_normal_ & trunc_normal_ & variance_scaling_ & lecun_normal_
  # Modified from https://github.com/rwightman/pytorch-image-models/blob/master/timm/models/layers/weight_init.py.
  
  # Copyright 2019 Ross Wightman
  # 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.
  
  # _init_transformer_weights & c2_msra_fill & _init_convnet_weights
  # Modified from https://github.com/facebookresearch/SlowFast/blob/main/slowfast/utils/weight_init_helper.py.
  
  # Copyright 2019, Facebook, Inc
  #
  # 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.
  
  
  import math
  import warnings
  
  import torch
  import torch.nn as nn
  from torch.nn.init import _calculate_fan_in_and_fan_out
  
  
  def _no_grad_trunc_normal_(tensor, mean, std, a, b):
      # Cut & paste from PyTorch official master until it's in a few official releases - RW
      # Method based on https://people.sc.fsu.edu/~jburkardt/presentations/truncated_normal.pdf
      def norm_cdf(x):
          # Computes standard normal cumulative distribution function
          return (1. + math.erf(x / math.sqrt(2.))) / 2.
  
      if (mean < a - 2 * std) or (mean > b + 2 * std):
          warnings.warn("mean is more than 2 std from [a, b] in nn.init.trunc_normal_. "
                        "The distribution of values may be incorrect.",
                        stacklevel=2)
  
      with torch.no_grad():
          # Values are generated by using a truncated uniform distribution and
          # then using the inverse CDF for the normal distribution.
          # Get upper and lower cdf values
          l = norm_cdf((a - mean) / std)
          u = norm_cdf((b - mean) / std)
  
          # Uniformly fill tensor with values from [l, u], then translate to
          # [2l-1, 2u-1].
          tensor.uniform_(2 * l - 1, 2 * u - 1)
  
          # Use inverse cdf transform for normal distribution to get truncated
          # standard normal
          tensor.erfinv_()
  
          # Transform to proper mean, std
          tensor.mul_(std * math.sqrt(2.))
          tensor.add_(mean)
  
          # Clamp to ensure it's in the proper range
          tensor.clamp_(min=a, max=b)
          return tensor
  
  
  def trunc_normal_(tensor, mean=0., std=1., a=-2., b=2.):
      # type: (Tensor, float, float, float, float) -> Tensor
      r"""Fills the input Tensor with values drawn from a truncated
      normal distribution. The values are effectively drawn from the
      normal distribution :math:`\mathcal{N}(\text{mean}, \text{std}^2)`
      with values outside :math:`[a, b]` redrawn until they are within
      the bounds. The method used for generating the random values works
      best when :math:`a \leq \text{mean} \leq b`.
      Args:
          tensor: an n-dimensional `torch.Tensor`
          mean: the mean of the normal distribution
          std: the standard deviation of the normal distribution
          a: the minimum cutoff value
          b: the maximum cutoff value
      Examples:
          >>> w = torch.empty(3, 5)
          >>> nn.init.trunc_normal_(w)
      """
      return _no_grad_trunc_normal_(tensor, mean, std, a, b)
  
  
  def variance_scaling_(tensor, scale=1.0, mode='fan_in', distribution='normal'):
      fan_in, fan_out = _calculate_fan_in_and_fan_out(tensor)
      if mode == 'fan_in':
          denom = fan_in
      elif mode == 'fan_out':
          denom = fan_out
      elif mode == 'fan_avg':
          denom = (fan_in + fan_out) / 2
  
      variance = scale / denom
  
      if distribution == "truncated_normal":
          # constant is stddev of standard normal truncated to (-2, 2)
          trunc_normal_(tensor, std=math.sqrt(variance) / .87962566103423978)
      elif distribution == "normal":
          tensor.normal_(std=math.sqrt(variance))
      elif distribution == "uniform":
          bound = math.sqrt(3 * variance)
          tensor.uniform_(-bound, bound)
      else:
          raise ValueError(f"invalid distribution {distribution}")
  
  
  def lecun_normal_(tensor):
      variance_scaling_(tensor, mode='fan_in', distribution='truncated_normal')
  
  
  def _init_transformer_weights(m):
      if isinstance(m, nn.Linear):
          trunc_normal_(m.weight, std=.02)
          if m.bias is not None:
              nn.init.zeros_(m.bias)
      elif isinstance(m, nn.LayerNorm):
          nn.init.zeros_(m.bias)
          nn.init.ones_(m.weight)
  
  
  def c2_msra_fill(module: nn.Module) -> None:
      """
      Initialize `module.weight` using the "MSRAFill" implemented in Caffe2.
      Also initializes `module.bias` to 0.
      Args:
          module (torch.nn.Module): module to initialize.
      """
      # pyre-ignore
      nn.init.kaiming_normal_(module.weight, mode="fan_out", nonlinearity="relu")
      if module.bias is not None:  # pyre-ignore
          nn.init.constant_(module.bias, 0)
  
  
  def _init_convnet_weights(model, fc_init_std=0.01, zero_init_final_bn=True):
      """
      Performs ResNet style weight initialization.
      Args:
          fc_init_std (float): the expected standard deviation for fc layer.
          zero_init_final_bn (bool): if True, zero initialize the final bn for
              every bottleneck.
      """
      for m in model.modules():
          if hasattr(m, "skip_init"):
              continue
          if isinstance(m, nn.Conv3d) and not hasattr(m, "linear"):
              """
              Follow the initialization method proposed in:
              {He, Kaiming, et al.
              "Delving deep into rectifiers: Surpassing human-level
              performance on imagenet classification."
              arXiv preprint arXiv:1502.01852 (2015)}
              """
              c2_msra_fill(m)
          elif isinstance(m, nn.BatchNorm3d):
              if (
                      hasattr(m, "transform_final_bn")
                      and m.transform_final_bn
                      and zero_init_final_bn
              ):
                  batchnorm_weight = 0.0
              else:
                  batchnorm_weight = 1.0
              if m.weight is not None:
                  m.weight.data.fill_(batchnorm_weight)
              if m.bias is not None:
                  m.bias.data.zero_()
          if isinstance(m, nn.Linear) or hasattr(m, "linear"):
              m.weight.data.normal_(mean=0.0, std=fc_init_std)
              if m.bias is not None:
                  m.bias.data.zero_()
  