code: 
  
  import random
  from typing import List, Optional, Union
  
  import numpy as np
  import torch
  
  from ..state import AcceleratorState
  from .constants import CUDA_DISTRIBUTED_TYPES
  from .dataclasses import DistributedType, RNGType
  from .imports import is_npu_available, is_tpu_available, is_xpu_available
  
  
  if is_tpu_available(check_device=False):
         import torch_xla.core.xla_model as xm
  
  
  def       __a       (   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE = False      )      ->     Union[str, Any]:
  
  
  
  
  
  
      '''simple docstring'''
      if device_specific:
          seed += AcceleratorState().process_index
      random.seed(SCREAMING_SNAKE_CASE      )
      np.random.seed(SCREAMING_SNAKE_CASE      )
      torch.manual_seed(SCREAMING_SNAKE_CASE      )
      if is_xpu_available():
          torch.xpu.manual_seed_all(SCREAMING_SNAKE_CASE      )
      elif is_npu_available():
          torch.npu.manual_seed_all(SCREAMING_SNAKE_CASE      )
      else:
          torch.cuda.manual_seed_all(SCREAMING_SNAKE_CASE      )
      # ^^ safe to call this function even if cuda is not available
      if is_tpu_available():
          xm.set_rng_state(SCREAMING_SNAKE_CASE      )
  
  
  def       __a       (   SCREAMING_SNAKE_CASE = None       ,   SCREAMING_SNAKE_CASE = None      )      ->     Tuple:
  
  
  
  
  
  
      '''simple docstring'''
      # Get the proper rng state
      if rng_type == RNGType.TORCH:
          __UpperCAmelCase									=			torch.get_rng_state()
      elif rng_type == RNGType.CUDA:
          __UpperCAmelCase									=			torch.cuda.get_rng_state()
      elif rng_type == RNGType.XLA:
          assert is_tpu_available(), "Can't synchronize XLA seeds on an environment without TPUs."
          __UpperCAmelCase									=			torch.tensor(xm.get_rng_state()      )
      elif rng_type == RNGType.NPU:
          assert is_npu_available(), "Can't synchronize NPU seeds on an environment without NPUs."
          __UpperCAmelCase									=			torch.npu.get_rng_state()
      elif rng_type == RNGType.XPU:
          assert is_xpu_available(), "Can't synchronize XPU seeds on an environment without XPUs."
          __UpperCAmelCase									=			torch.xpu.get_rng_state()
      elif rng_type == RNGType.GENERATOR:
          assert generator is not None, "Need a generator to synchronize its seed."
          __UpperCAmelCase									=			generator.get_state()
  
      # Broadcast the rng state from device 0 to other devices
      __UpperCAmelCase									=			AcceleratorState()
      if state.distributed_type == DistributedType.TPU:
          __UpperCAmelCase									=			rng_state.to(xm.xla_device()      )
          xm.collective_broadcast([rng_state]      )
          xm.mark_step()
          __UpperCAmelCase									=			rng_state.cpu()
      elif (
          state.distributed_type in CUDA_DISTRIBUTED_TYPES
          or state.distributed_type == DistributedType.MULTI_NPU
          or state.distributed_type == DistributedType.MULTI_XPU
      ):
          __UpperCAmelCase									=			rng_state.to(state.device      )
          torch.distributed.broadcast(SCREAMING_SNAKE_CASE       ,   0      )
          __UpperCAmelCase									=			rng_state.cpu()
      elif state.distributed_type == DistributedType.MULTI_CPU:
          torch.distributed.broadcast(SCREAMING_SNAKE_CASE       ,   0      )
  
      # Set the broadcast rng state
      if rng_type == RNGType.TORCH:
          torch.set_rng_state(SCREAMING_SNAKE_CASE      )
      elif rng_type == RNGType.CUDA:
          torch.cuda.set_rng_state(SCREAMING_SNAKE_CASE      )
      elif rng_type == RNGType.NPU:
          torch.npu.set_rng_state(SCREAMING_SNAKE_CASE      )
      elif rng_type == RNGType.XPU:
          torch.xpu.set_rng_state(SCREAMING_SNAKE_CASE      )
      elif rng_type == RNGType.XLA:
          xm.set_rng_state(rng_state.item()      )
      elif rng_type == RNGType.GENERATOR:
          generator.set_state(SCREAMING_SNAKE_CASE      )
  
  
  def       __a       (   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE = None      )      ->     Any:
  
  
  
  
  
  
      '''simple docstring'''
      for rng_type in rng_types:
          synchronize_rng_state(RNGType(SCREAMING_SNAKE_CASE      )       ,   generator=SCREAMING_SNAKE_CASE      )
  
  
  
  
  
style_context: 
  
  import numpy as np
  
  
  def       __a       (   SCREAMING_SNAKE_CASE      )      ->     Tuple:
  
  
  
  
  
  
      '''simple docstring'''
      __UpperCAmelCase					,     __UpperCAmelCase									=			a.shape
      __UpperCAmelCase									=			min(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE      )
      __UpperCAmelCase									=			np.eye(SCREAMING_SNAKE_CASE      )
      __UpperCAmelCase									=			a.copy()
  
      for k in range(t - 1      ):
          # select a column of modified matrix A':
          __UpperCAmelCase									=			r[k:, [k]]
          # construct first basis vector
          __UpperCAmelCase									=			np.zeros_like(SCREAMING_SNAKE_CASE      )
          __UpperCAmelCase									=			1.0
          # determine scaling factor
          __UpperCAmelCase									=			np.linalg.norm(SCREAMING_SNAKE_CASE      )
          # construct vector v for Householder reflection
          __UpperCAmelCase									=			x + np.sign(x[0]      ) * alpha * ea
          v /= np.linalg.norm(SCREAMING_SNAKE_CASE      )
  
          # construct the Householder matrix
          __UpperCAmelCase									=			np.eye(m - k      ) - 2.0 * v @ v.T
          # pad with ones and zeros as necessary
          __UpperCAmelCase									=			np.block([[np.eye(SCREAMING_SNAKE_CASE      ), np.zeros((k, m - k)      )], [np.zeros((m - k, k)      ), q_k]]      )
  
          __UpperCAmelCase									=			q @ q_k.T
          __UpperCAmelCase									=			q_k @ r
  
      return q, r
  
  
  if __name__ == "__main__":
         import doctest
  
         doctest.testmod()
  
  
  
  
  