code: 
  
  
  
  
  
  
  """simple docstring"""
  
  import inspect
  from typing import Callable, List, Optional, Set, Tuple, Union
  
  import torch
  from packaging import version
  from safetensors.torch import storage_ptr, storage_size
  from torch import nn
  
  from .utils import logging
  
  
  lowercase__      =				[nn.LayerNorm]
  
  lowercase__      =				logging.get_logger(__name__)
  
  lowercase__      =				version.parse(version.parse(torch.__version__).base_version)
  
  lowercase__      =				parsed_torch_version_base >= version.parse("""2.0""")
  lowercase__      =				parsed_torch_version_base >= version.parse("""1.12""")
  lowercase__      =				parsed_torch_version_base >= version.parse("""1.11""")
  lowercase__      =				parsed_torch_version_base < version.parse("""1.11""")
  
  def 	__lowerCamelCase			(						__UpperCamelCase   , __UpperCamelCase   , __UpperCamelCase   , __UpperCamelCase   , self )		->					Dict:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		from torch import _softmax_backward_data
  
  		if is_torch_less_than_1_11:
  				return _softmax_backward_data(__UpperCamelCase   , __UpperCamelCase   , parent.dim   , self )
  		else:
  				return _softmax_backward_data(__UpperCamelCase   , __UpperCamelCase   , parent.dim   , self.dtype )
  
  def 	__lowerCamelCase			(						__UpperCamelCase   , __UpperCamelCase   , __UpperCamelCase = 0 )		->					nn.Linear:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		lowerCAmelCase_     :							str             =    index.to(layer.weight.device )
  		lowerCAmelCase_     :							Optional[Any]             =    layer.weight.index_select(__UpperCamelCase   , __UpperCamelCase ).clone().detach()
  		if layer.bias is not None:
  				if dim == 1:
  						lowerCAmelCase_     :							int             =    layer.bias.clone().detach()
  				else:
  						lowerCAmelCase_     :							Optional[Any]             =    layer.bias[index].clone().detach()
  		lowerCAmelCase_     :							Union[str, Any]             =    list(layer.weight.size() )
  		lowerCAmelCase_     :							str             =    len(__UpperCamelCase )
  		lowerCAmelCase_     :							List[Any]             =    nn.Linear(new_size[1]   , new_size[0]   , bias=layer.bias is not None ).to(layer.weight.device )
  		lowerCAmelCase_     :							List[Any]             =    False
  		new_layer.weight.copy_(W.contiguous() )
  		lowerCAmelCase_     :							int             =    True
  		if layer.bias is not None:
  				lowerCAmelCase_     :							Any             =    False
  				new_layer.bias.copy_(b.contiguous() )
  				lowerCAmelCase_     :							Union[str, Any]             =    True
  		return new_layer
  
  
  class 	__lowerCamelCase       (				nn.Module    ):
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  		def __init__(     self							:			Dict		,    a_							:			List[Any]		,    a_							:			str			):
  				super().__init__()
  				lowerCAmelCase_     :							Optional[int]             =    nf
  				lowerCAmelCase_     :							Optional[int]             =    nn.Parameter(torch.empty(a_		,    a_			)			)
  				lowerCAmelCase_     :							Optional[int]             =    nn.Parameter(torch.zeros(a_			)			)
  				nn.init.normal_(self.weight		,    std=0.02			)
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Dict		,    a_							:			Optional[int]			):
  				lowerCAmelCase_     :							List[Any]             =    x.size()[:-1] + (self.nf,)
  				lowerCAmelCase_     :							Any             =    torch.addmm(self.bias		,    x.view(-1		,    x.size(-1			)			)		,    self.weight			)
  				lowerCAmelCase_     :							str             =    x.view(a_			)
  				return x
  
  
  
  
  
  
  
  def 	__lowerCamelCase			(						__UpperCamelCase   , __UpperCamelCase   , __UpperCamelCase = 1 )		->					ConvaD:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		lowerCAmelCase_     :							int             =    index.to(layer.weight.device )
  		lowerCAmelCase_     :							Dict             =    layer.weight.index_select(__UpperCamelCase   , __UpperCamelCase ).clone().detach()
  		if dim == 0:
  				lowerCAmelCase_     :							Optional[Any]             =    layer.bias.clone().detach()
  		else:
  				lowerCAmelCase_     :							int             =    layer.bias[index].clone().detach()
  		lowerCAmelCase_     :							Optional[Any]             =    list(layer.weight.size() )
  		lowerCAmelCase_     :							int             =    len(__UpperCamelCase )
  		lowerCAmelCase_     :							List[Any]             =    ConvaD(new_size[1]   , new_size[0] ).to(layer.weight.device )
  		lowerCAmelCase_     :							List[str]             =    False
  		new_layer.weight.copy_(W.contiguous() )
  		lowerCAmelCase_     :							Dict             =    True
  		lowerCAmelCase_     :							Optional[Any]             =    False
  		new_layer.bias.copy_(b.contiguous() )
  		lowerCAmelCase_     :							Optional[int]             =    True
  		return new_layer
  
  def 	__lowerCamelCase			(						__UpperCamelCase   , __UpperCamelCase   , __UpperCamelCase = None )		->					Union[nn.Linear, ConvaD]:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		if isinstance(__UpperCamelCase   , nn.Linear ):
  				return prune_linear_layer(__UpperCamelCase   , __UpperCamelCase   , dim=0 if dim is None else dim )
  		elif isinstance(__UpperCamelCase   , __UpperCamelCase ):
  				return prune_convad_layer(__UpperCamelCase   , __UpperCamelCase   , dim=1 if dim is None else dim )
  		else:
  				raise ValueError(f'''Can\'t prune layer of class {layer.__class__}''' )
  
  def 	__lowerCamelCase			(						__UpperCamelCase   , __UpperCamelCase   , __UpperCamelCase   , *__UpperCamelCase )		->					torch.Tensor:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		assert len(__UpperCamelCase ) > 0, f'''{input_tensors} has to be a tuple/list of tensors'''
  
  		# inspect.signature exist since python 3.5 and is a python method -> no problem with backward compatibility
  		lowerCAmelCase_     :							Optional[Any]             =    len(inspect.signature(__UpperCamelCase ).parameters )
  		if num_args_in_forward_chunk_fn != len(__UpperCamelCase ):
  				raise ValueError(
  				    f'''forward_chunk_fn expects {num_args_in_forward_chunk_fn} arguments, but only {len(__UpperCamelCase )} input '''
  				    "tensors are given" )
  
  		if chunk_size > 0:
  				lowerCAmelCase_     :							List[Any]             =    input_tensors[0].shape[chunk_dim]
  				for input_tensor in input_tensors:
  						if input_tensor.shape[chunk_dim] != tensor_shape:
  								raise ValueError(
  								    f'''All input tenors have to be of the same shape: {tensor_shape}, '''
  								    f'''found shape {input_tensor.shape[chunk_dim]}''' )
  
  				if input_tensors[0].shape[chunk_dim] % chunk_size != 0:
  						raise ValueError(
  						    f'''The dimension to be chunked {input_tensors[0].shape[chunk_dim]} has to be a multiple of the chunk '''
  						    f'''size {chunk_size}''' )
  
  				lowerCAmelCase_     :							Optional[int]             =    input_tensors[0].shape[chunk_dim] // chunk_size
  
  				# chunk input tensor into tuples
  				lowerCAmelCase_     :							Dict             =    tuple(input_tensor.chunk(__UpperCamelCase   , dim=__UpperCamelCase ) for input_tensor in input_tensors )
  				# apply forward fn to every tuple
  				lowerCAmelCase_     :							Tuple             =    tuple(forward_fn(*__UpperCamelCase ) for input_tensors_chunk in zip(*__UpperCamelCase ) )
  				# concatenate output at same dimension
  				return torch.cat(__UpperCamelCase   , dim=__UpperCamelCase )
  
  		return forward_fn(*__UpperCamelCase )
  
  def 	__lowerCamelCase			(						__UpperCamelCase   , __UpperCamelCase   , __UpperCamelCase   , __UpperCamelCase )		->					Tuple[Set[int], torch.LongTensor]:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		lowerCAmelCase_     :							Dict             =    torch.ones(__UpperCamelCase   , __UpperCamelCase )
  		lowerCAmelCase_     :							Tuple             =    set(__UpperCamelCase ) - already_pruned_heads  # Convert to set and remove already pruned heads
  		for head in heads:
  				# Compute how many pruned heads are before the head and move the index accordingly
  				lowerCAmelCase_     :							List[str]             =    head - sum(1 if h < head else 0 for h in already_pruned_heads )
  				lowerCAmelCase_     :							Optional[Any]             =    0
  		lowerCAmelCase_     :							Union[str, Any]             =    mask.view(-1 ).contiguous().eq(1 )
  		lowerCAmelCase_     :							torch.LongTensor             =    torch.arange(len(__UpperCamelCase ) )[mask].long()
  		return heads, index
  
  def 	__lowerCamelCase			(						*__UpperCamelCase   , __UpperCamelCase = None )		->					Tuple[torch.Tensor, ...]:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		return torch.meshgrid(*__UpperCamelCase   , indexing=__UpperCamelCase )
  
  
  
  def 	__lowerCamelCase			(						__UpperCamelCase )		->					Tuple[torch.device, int, int]:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		return tensor.device, storage_ptr(__UpperCamelCase ), storage_size(__UpperCamelCase )
  
style_context: 
  
  
  
  
  
  
  """simple docstring"""
  
  from __future__ import annotations
  
  import random
  
  # Adjacency list representation of this graph:
  # https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
  lowercase__      =				{
      """1""": ["""2""", """3""", """4""", """5"""],
      """2""": ["""1""", """3""", """4""", """5"""],
      """3""": ["""1""", """2""", """4""", """5""", """10"""],
      """4""": ["""1""", """2""", """3""", """5""", """6"""],
      """5""": ["""1""", """2""", """3""", """4""", """7"""],
      """6""": ["""7""", """8""", """9""", """10""", """4"""],
      """7""": ["""6""", """8""", """9""", """10""", """5"""],
      """8""": ["""6""", """7""", """9""", """10"""],
      """9""": ["""6""", """7""", """8""", """10"""],
      """10""": ["""6""", """7""", """8""", """9""", """3"""],
  }
  
  def 	__lowerCamelCase			(						__UpperCamelCase )		->					set[tuple[str, str]]:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		lowerCAmelCase_     :							Union[str, Any]             =    {node: {node} for node in graph}
  
  		lowerCAmelCase_     :							List[str]             =    {node: graph[node][:] for node in graph}
  
  		while len(__UpperCamelCase ) > 2:
  				# Choose a random edge.
  				lowerCAmelCase_     :							int             =    random.choice(list(graph_copy.keys() ) )
  				lowerCAmelCase_     :							Any             =    random.choice(graph_copy[u] )
  
  				# Contract edge (u, v) to new node uv
  				lowerCAmelCase_     :							Union[str, Any]             =    u + v
  				lowerCAmelCase_     :							List[Any]             =    list(set(graph_copy[u] + graph_copy[v] ) )
  				uv_neighbors.remove(__UpperCamelCase )
  				uv_neighbors.remove(__UpperCamelCase )
  				lowerCAmelCase_     :							str             =    uv_neighbors
  				for neighbor in uv_neighbors:
  						graph_copy[neighbor].append(__UpperCamelCase )
  
  				lowerCAmelCase_     :							Optional[int]             =    set(contracted_nodes[u].union(contracted_nodes[v] ) )
  
  				# Remove nodes u and v.
  				del graph_copy[u]
  				del graph_copy[v]
  				for neighbor in uv_neighbors:
  						if u in graph_copy[neighbor]:
  								graph_copy[neighbor].remove(__UpperCamelCase )
  						if v in graph_copy[neighbor]:
  								graph_copy[neighbor].remove(__UpperCamelCase )
  
      # Find cutset.
  		lowerCAmelCase_     :							Union[str, Any]             =    [contracted_nodes[node] for node in graph_copy]
  		return {
  		    (node, neighbor)
  		    for node in groups[0]
  		    for neighbor in graph[node]
  		    if neighbor in groups[1]
  		}
  
  
  if __name__ == "__main__":
  					print(partition_graph(TEST_GRAPH))
  