text: from __future__ import division
  
  import math
  import warnings
  
  import torch
  
  # These no_grad_* functions are necessary as wrappers around the parts of these
  # functions that use `with torch.no_grad()`. The JIT doesn't support context
  # managers, so these need to be implemented as builtins. Using these wrappers
  # lets us keep those builtins small and re-usable.
  def _no_grad_uniform_(tensor, a, b):
      with torch.no_grad():
          return tensor.uniform_(a, b)
  
  
  def _no_grad_normal_(tensor, mean, std):
      with torch.no_grad():
          return tensor.normal_(mean, std)
  
  
  def _no_grad_fill_(tensor, val):
      with torch.no_grad():
          return tensor.fill_(val)
  
  
  def _no_grad_zero_(tensor):
      with torch.no_grad():
          return tensor.zero_()
  
  
  def calculate_gain(nonlinearity, param=None):
      r"""Return the recommended gain value for the given nonlinearity function.
      The values are as follows:
  
      ================= ====================================================
      nonlinearity      gain
      ================= ====================================================
      Linear / Identity :math:`1`
      Conv{1,2,3}D      :math:`1`
      Sigmoid           :math:`1`
      Tanh              :math:`\frac{5}{3}`
      ReLU              :math:`\sqrt{2}`
      Leaky Relu        :math:`\sqrt{\frac{2}{1 + \text{negative\_slope}^2}}`
      ================= ====================================================
  
      Args:
          nonlinearity: the non-linear function (`nn.functional` name)
          param: optional parameter for the non-linear function
  
      Examples:
          >>> gain = nn.init.calculate_gain('leaky_relu', 0.2)  # leaky_relu with negative_slope=0.2
      """
      linear_fns = ['linear', 'conv1d', 'conv2d', 'conv3d', 'conv_transpose1d', 'conv_transpose2d', 'conv_transpose3d']
      if nonlinearity in linear_fns or nonlinearity == 'sigmoid':
          return 1
      elif nonlinearity == 'tanh':
          return 5.0 / 3
      elif nonlinearity == 'relu':
          return math.sqrt(2.0)
      elif nonlinearity == 'leaky_relu':
          if param is None:
              negative_slope = 0.01
          elif not isinstance(param, bool) and isinstance(param, int) or isinstance(param, float):
              # True/False are instances of int, hence check above
              negative_slope = param
          else:
              raise ValueError("negative_slope {} not a valid number".format(param))
          return math.sqrt(2.0 / (1 + negative_slope ** 2))
      else:
          raise ValueError("Unsupported nonlinearity {}".format(nonlinearity))
  
  
  def uniform_(tensor, a=0., b=1.):
      # type: (Tensor, float, float) -> Tensor
      r"""Fills the input Tensor with values drawn from the uniform
      distribution :math:`\mathcal{U}(a, b)`.
  
      Args:
          tensor: an n-dimensional `torch.Tensor`
          a: the lower bound of the uniform distribution
          b: the upper bound of the uniform distribution
  
      Examples:
          >>> w = torch.empty(3, 5)
          >>> nn.init.uniform_(w)
      """
      return _no_grad_uniform_(tensor, a, b)
  
  
  def normal_(tensor, mean=0., std=1.):
      # type: (Tensor, float, float) -> Tensor
      r"""Fills the input Tensor with values drawn from the normal
      distribution :math:`\mathcal{N}(\text{mean}, \text{std}^2)`.
  
      Args:
          tensor: an n-dimensional `torch.Tensor`
          mean: the mean of the normal distribution
          std: the standard deviation of the normal distribution
  
      Examples:
          >>> w = torch.empty(3, 5)
          >>> nn.init.normal_(w)
      """
      return _no_grad_normal_(tensor, mean, std)
  
  
  def constant_(tensor, val):
      # type: (Tensor, float) -> Tensor
      r"""Fills the input Tensor with the value :math:`\text{val}`.
  
      Args:
          tensor: an n-dimensional `torch.Tensor`
          val: the value to fill the tensor with
  
      Examples:
          >>> w = torch.empty(3, 5)
          >>> nn.init.constant_(w, 0.3)
      """
      return _no_grad_fill_(tensor, val)
  
  
  def ones_(tensor):
      # type: (Tensor) -> Tensor
      r"""Fills the input Tensor with the scalar value `1`.
  
      Args:
          tensor: an n-dimensional `torch.Tensor`
  
      Examples:
          >>> w = torch.empty(3, 5)
          >>> nn.init.ones_(w)
      """
      return _no_grad_fill_(tensor, 1.)
  
  
  def zeros_(tensor):
      # type: (Tensor) -> Tensor
      r"""Fills the input Tensor with the scalar value `0`.
  
      Args:
          tensor: an n-dimensional `torch.Tensor`
  
      Examples:
          >>> w = torch.empty(3, 5)
          >>> nn.init.zeros_(w)
      """
      return _no_grad_zero_(tensor)
  
  
  def eye_(tensor):
      r"""Fills the 2-dimensional input `Tensor` with the identity
      matrix. Preserves the identity of the inputs in `Linear` layers, where as
      many inputs are preserved as possible.
  
      Args:
          tensor: a 2-dimensional `torch.Tensor`
  
      Examples:
          >>> w = torch.empty(3, 5)
          >>> nn.init.eye_(w)
      """
      if tensor.ndimension() != 2:
          raise ValueError("Only tensors with 2 dimensions are supported")
  
      with torch.no_grad():
          torch.eye(*tensor.shape, out=tensor, requires_grad=tensor.requires_grad)
      return tensor
  
  
  def dirac_(tensor, groups=1):
      r"""Fills the {3, 4, 5}-dimensional input `Tensor` with the Dirac
      delta function. Preserves the identity of the inputs in `Convolutional`
      layers, where as many input channels are preserved as possible. In case
      of groups>1, each group of channels preserves identity
  
      Args:
          tensor: a {3, 4, 5}-dimensional `torch.Tensor`
          groups (optional): number of groups in the conv layer (default: 1)
      Examples:
          >>> w = torch.empty(3, 16, 5, 5)
          >>> nn.init.dirac_(w)
          >>> w = torch.empty(3, 24, 5, 5)
          >>> nn.init.dirac_(w, 3)
      """
      dimensions = tensor.ndimension()
      if dimensions not in [3, 4, 5]:
          raise ValueError("Only tensors with 3, 4, or 5 dimensions are supported")
  
      sizes = tensor.size()
  
      if sizes[0] % groups != 0:
          raise ValueError('dim 0 must be divisible by groups')
  
      out_chans_per_grp = sizes[0] // groups
      min_dim = min(out_chans_per_grp, sizes[1])
  
      with torch.no_grad():
          tensor.zero_()
  
          for g in range(groups):
              for d in range(min_dim):
                  if dimensions == 3:  # Temporal convolution
                      tensor[g * out_chans_per_grp + d, d, tensor.size(2) // 2] = 1
                  elif dimensions == 4:  # Spatial convolution
                      tensor[g * out_chans_per_grp + d, d, tensor.size(2) // 2,
                             tensor.size(3) // 2] = 1
                  else:  # Volumetric convolution
                      tensor[g * out_chans_per_grp + d, d, tensor.size(2) // 2,
                             tensor.size(3) // 2, tensor.size(4) // 2] = 1
      return tensor
  
  
  def _calculate_fan_in_and_fan_out(tensor):
      dimensions = tensor.dim()
      if dimensions < 2:
          raise ValueError("Fan in and fan out can not be computed for tensor with fewer than 2 dimensions")
  
      num_input_fmaps = tensor.size(1)
      num_output_fmaps = tensor.size(0)
      receptive_field_size = 1
      if tensor.dim() > 2:
          receptive_field_size = tensor[0][0].numel()
      fan_in = num_input_fmaps * receptive_field_size
      fan_out = num_output_fmaps * receptive_field_size
  
      return fan_in, fan_out
  
  
  def xavier_uniform_(tensor, gain=1.):
      # type: (Tensor, float) -> Tensor
      r"""Fills the input `Tensor` with values according to the method
      described in `Understanding the difficulty of training deep feedforward
      neural networks` - Glorot, X. & Bengio, Y. (2010), using a uniform
      distribution. The resulting tensor will have values sampled from
      :math:`\mathcal{U}(-a, a)` where
  
      .. math::
          a = \text{gain} \times \sqrt{\frac{6}{\text{fan\_in} + \text{fan\_out}}}
  
      Also known as Glorot initialization.
  
      Args:
          tensor: an n-dimensional `torch.Tensor`
          gain: an optional scaling factor
  
      Examples:
          >>> w = torch.empty(3, 5)
          >>> nn.init.xavier_uniform_(w, gain=nn.init.calculate_gain('relu'))
      """
      fan_in, fan_out = _calculate_fan_in_and_fan_out(tensor)
      std = gain * math.sqrt(2.0 / float(fan_in + fan_out))
      a = math.sqrt(3.0) * std  # Calculate uniform bounds from standard deviation
  
      return _no_grad_uniform_(tensor, -a, a)
  
  
  def xavier_normal_(tensor, gain=1.):
      # type: (Tensor, float) -> Tensor
      r"""Fills the input `Tensor` with values according to the method
      described in `Understanding the difficulty of training deep feedforward
      neural networks` - Glorot, X. & Bengio, Y. (2010), using a normal
      distribution. The resulting tensor will have values sampled from
      :math:`\mathcal{N}(0, \text{std}^2)` where
  
      .. math::
          \text{std} = \text{gain} \times \sqrt{\frac{2}{\text{fan\_in} + \text{fan\_out}}}
  
      Also known as Glorot initialization.
  
      Args:
          tensor: an n-dimensional `torch.Tensor`
          gain: an optional scaling factor
  
      Examples:
          >>> w = torch.empty(3, 5)
          >>> nn.init.xavier_normal_(w)
      """
      fan_in, fan_out = _calculate_fan_in_and_fan_out(tensor)
      std = gain * math.sqrt(2.0 / float(fan_in + fan_out))
  
      return _no_grad_normal_(tensor, 0., std)
  
  
  def _calculate_correct_fan(tensor, mode):
      mode = mode.lower()
      valid_modes = ['fan_in', 'fan_out']
      if mode not in valid_modes:
          raise ValueError("Mode {} not supported, please use one of {}".format(mode, valid_modes))
  
      fan_in, fan_out = _calculate_fan_in_and_fan_out(tensor)
      return fan_in if mode == 'fan_in' else fan_out
  
  
  def kaiming_uniform_(tensor, a=0, mode='fan_in', nonlinearity='leaky_relu'):
      r"""Fills the input `Tensor` with values according to the method
      described in `Delving deep into rectifiers: Surpassing human-level
      performance on ImageNet classification` - He, K. et al. (2015), using a
      uniform distribution. The resulting tensor will have values sampled from
      :math:`\mathcal{U}(-\text{bound}, \text{bound})` where
  
      .. math::
          \text{bound} = \text{gain} \times \sqrt{\frac{3}{\text{fan\_mode}}}
  
      Also known as He initialization.
  
      Args:
          tensor: an n-dimensional `torch.Tensor`
          a: the negative slope of the rectifier used after this layer (only 
          used with ``'leaky_relu'``)
          mode: either ``'fan_in'`` (default) or ``'fan_out'``. Choosing ``'fan_in'``
              preserves the magnitude of the variance of the weights in the
              forward pass. Choosing ``'fan_out'`` preserves the magnitudes in the
              backwards pass.
          nonlinearity: the non-linear function (`nn.functional` name),
              recommended to use only with ``'relu'`` or ``'leaky_relu'`` (default).
  
      Examples:
          >>> w = torch.empty(3, 5)
          >>> nn.init.kaiming_uniform_(w, mode='fan_in', nonlinearity='relu')
      """
      fan = _calculate_correct_fan(tensor, mode)
      gain = calculate_gain(nonlinearity, a)
      std = gain / math.sqrt(fan)
      bound = math.sqrt(3.0) * std  # Calculate uniform bounds from standard deviation
      with torch.no_grad():
          return tensor.uniform_(-bound, bound)
  
  
  def kaiming_normal_(tensor, a=0, mode='fan_in', nonlinearity='leaky_relu'):
      r"""Fills the input `Tensor` with values according to the method
      described in `Delving deep into rectifiers: Surpassing human-level
      performance on ImageNet classification` - He, K. et al. (2015), using a
      normal distribution. The resulting tensor will have values sampled from
      :math:`\mathcal{N}(0, \text{std}^2)` where
  
      .. math::
          \text{std} = \frac{\text{gain}}{\sqrt{\text{fan\_mode}}}
  
      Also known as He initialization.
  
      Args:
          tensor: an n-dimensional `torch.Tensor`
          a: the negative slope of the rectifier used after this layer (only 
          used with ``'leaky_relu'``)
          mode: either ``'fan_in'`` (default) or ``'fan_out'``. Choosing ``'fan_in'``
              preserves the magnitude of the variance of the weights in the
              forward pass. Choosing ``'fan_out'`` preserves the magnitudes in the
              backwards pass.
          nonlinearity: the non-linear function (`nn.functional` name),
              recommended to use only with ``'relu'`` or ``'leaky_relu'`` (default).
  
      Examples:
          >>> w = torch.empty(3, 5)
          >>> nn.init.kaiming_normal_(w, mode='fan_out', nonlinearity='relu')
      """
      fan = _calculate_correct_fan(tensor, mode)
      gain = calculate_gain(nonlinearity, a)
      std = gain / math.sqrt(fan)
      with torch.no_grad():
          return tensor.normal_(0, std)
  
  
  def orthogonal_(tensor, gain=1):
      r"""Fills the input `Tensor` with a (semi) orthogonal matrix, as
      described in `Exact solutions to the nonlinear dynamics of learning in deep
      linear neural networks` - Saxe, A. et al. (2013). The input tensor must have
      at least 2 dimensions, and for tensors with more than 2 dimensions the
      trailing dimensions are flattened.
  
      Args:
          tensor: an n-dimensional `torch.Tensor`, where :math:`n \geq 2`
          gain: optional scaling factor
  
      Examples:
          >>> w = torch.empty(3, 5)
          >>> nn.init.orthogonal_(w)
      """
      if tensor.ndimension() < 2:
          raise ValueError("Only tensors with 2 or more dimensions are supported")
  
      rows = tensor.size(0)
      cols = tensor.numel() // rows
      flattened = tensor.new(rows, cols).normal_(0, 1)
  
      if rows < cols:
          flattened.t_()
  
      # Compute the qr factorization
      q, r = torch.qr(flattened)
      # Make Q uniform according to https://arxiv.org/pdf/math-ph/0609050.pdf
      d = torch.diag(r, 0)
      ph = d.sign()
      q *= ph
  
      if rows < cols:
          q.t_()
  
      with torch.no_grad():
          tensor.view_as(q).copy_(q)
          tensor.mul_(gain)
      return tensor
  
  
  def sparse_(tensor, sparsity, std=0.01):
      r"""Fills the 2D input `Tensor` as a sparse matrix, where the
      non-zero elements will be drawn from the normal distribution
      :math:`\mathcal{N}(0, 0.01)`, as described in `Deep learning via
      Hessian-free optimization` - Martens, J. (2010).
  
      Args:
          tensor: an n-dimensional `torch.Tensor`
          sparsity: The fraction of elements in each column to be set to zero
          std: the standard deviation of the normal distribution used to generate
              the non-zero values
  
      Examples:
          >>> w = torch.empty(3, 5)
          >>> nn.init.sparse_(w, sparsity=0.1)
      """
      if tensor.ndimension() != 2:
          raise ValueError("Only tensors with 2 dimensions are supported")
  
      rows, cols = tensor.shape
      num_zeros = int(math.ceil(sparsity * rows))
  
      with torch.no_grad():
          tensor.normal_(0, std)
          for col_idx in range(cols):
              row_indices = torch.randperm(rows)
              zero_indices = row_indices[:num_zeros]
              tensor[zero_indices, col_idx] = 0
      return tensor
  
  
  # for backward compatibility
  def _make_deprecate(meth):
      new_name = meth.__name__
      old_name = new_name[:-1]
  
      def deprecated_init(*args, **kwargs):
          warnings.warn("nn.init.{} is now deprecated in favor of nn.init.{}."
                        .format(old_name, new_name), stacklevel=2)
          return meth(*args, **kwargs)
  
      deprecated_init.__doc__ = r"""
      {old_name}(...)
  
      .. warning::
          This method is now deprecated in favor of :func:`torch.nn.init.{new_name}`.
  
      See :func:`~torch.nn.init.{new_name}` for details.""".format(
          old_name=old_name, new_name=new_name)
      deprecated_init.__name__ = old_name
      return deprecated_init
  
  
  uniform = _make_deprecate(uniform_)
  normal = _make_deprecate(normal_)
  constant = _make_deprecate(constant_)
  eye = _make_deprecate(eye_)
  dirac = _make_deprecate(dirac_)
  xavier_uniform = _make_deprecate(xavier_uniform_)
  xavier_normal = _make_deprecate(xavier_normal_)
  kaiming_uniform = _make_deprecate(kaiming_uniform_)
  kaiming_normal = _make_deprecate(kaiming_normal_)
  orthogonal = _make_deprecate(orthogonal_)
  sparse = _make_deprecate(sparse_)
  