



'''simple docstring'''


from dataclasses import dataclass, field
from typing import Tuple

from ..utils import cached_property, is_torch_available, is_torch_tpu_available, logging, requires_backends
from .benchmark_args_utils import BenchmarkArguments


if is_torch_available():
  import torch

if is_torch_tpu_available(check_device=False):
  import torch_xla.core.xla_model as xm


lowercase							       =			logging.get_logger(__name__)







@dataclass
class 	UpperCAmelCase	(		__a):


 '''simple docstring'''




 __magic_name__					: List[Any]  =      [
     "no_inference",
     "no_cuda",
     "no_tpu",
     "no_speed",
     "no_memory",
     "no_env_print",
     "no_multi_process",
 ]




 def __init__(   self							,  **lowerCAmelCase_) ->      List[Any]:



      """simple docstring"""







      for deprecated_arg in self.deprecated_args:
           if deprecated_arg in kwargs:
                a_       		=deprecated_arg[3:]
                setattr(self							,  lowerCAmelCase_							,  not kwargs.pop(lowerCAmelCase_))
                logger.warning(
                    f"""{deprecated_arg} is depreciated. Please use --no_{positive_arg} or"""
                    f""" {positive_arg}={kwargs[positive_arg]}""")

      a_       		=kwargs.pop("torchscript"							,  self.torchscript)
      a_       		=kwargs.pop("torch_xla_tpu_print_metrics"							,  self.torch_xla_tpu_print_metrics)
      a_       		=kwargs.pop("fp16_opt_level"							,  self.fpaa_opt_level)
      super().__init__(**lowerCAmelCase_)

 __magic_name__					: bool  =      field(default=__a					,	metadata={"help": "Trace the models using torchscript"})
 __magic_name__					: bool  =      field(default=__a					,	metadata={"help": "Print Xla/PyTorch tpu metrics"})
 __magic_name__					: str  =      field(
     default="O1"					,	metadata={
         "help": (
             "For fp16: Apex AMP optimization level selected in ['O0', 'O1', 'O2', and 'O3']. "
             "See details at https://nvidia.github.io/apex/amp.html"
         )
     }					,	)




 @cached_property
 def       lowercase_  (   self) ->      Tuple["torch.device", int]:



      """simple docstring"""







      requires_backends(self							,  ["torch"])
      logger.info("PyTorch: setting up devices")
      if not self.cuda:
           a_       		=torch.device("cpu")
           a_       		=0
      elif is_torch_tpu_available():
           a_       		=xm.xla_device()
           a_       		=0
      else:
           a_       		=torch.device("cuda" if torch.cuda.is_available() else "cpu")
           a_       		=torch.cuda.device_count()
      return device, n_gpu




 @property
 def       lowercase_  (   self) ->      List[str]:



      """simple docstring"""







      return is_torch_tpu_available() and self.tpu




 @property
 def       lowercase_  (   self) ->      int:



      """simple docstring"""







      requires_backends(self							,  ["torch"])
      # TODO(PVP): currently only single GPU is supported
      return torch.cuda.current_device()




 @property
 def       lowercase_  (   self) ->      "torch.device":



      """simple docstring"""







      requires_backends(self							,  ["torch"])
      return self._setup_devices[0]




 @property
 def       lowercase_  (   self) ->      str:



      """simple docstring"""







      requires_backends(self							,  ["torch"])
      return self._setup_devices[1]




 @property
 def       lowercase_  (   self) ->      Tuple:



      """simple docstring"""







      return self.n_gpu > 0







'''simple docstring'''


from typing import Any

import numpy as np






def  UpperCAmelCase_       (		lowercase__       ):


     '''simple docstring'''







     return np.array_equal(lowercase__       ,	matrix.conjugate().T       )






def  UpperCAmelCase_       (		lowercase__       ,	lowercase__       ):


     '''simple docstring'''







     a_       		=v.conjugate().T
     a_       		=v_star.dot(lowercase__       )
     assert isinstance(lowercase__       ,	np.ndarray       )
     return (v_star_dot.dot(lowercase__       )) / (v_star.dot(lowercase__       ))






def  UpperCAmelCase_       (		):


     '''simple docstring'''







     a_       		=np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]       )
     a_       		=np.array([[1], [2], [3]]       )
     assert is_hermitian(lowercase__       ), F"""{a} is not hermitian."""
     print(rayleigh_quotient(lowercase__       ,	lowercase__       )       )

     a_       		=np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]       )
     assert is_hermitian(lowercase__       ), F"""{a} is not hermitian."""
     assert rayleigh_quotient(lowercase__       ,	lowercase__       ) == float(3       )


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  tests()


