
'''simple docstring'''







lowerCAmelCase_      =   1_0_0_0







def   lowerCAmelCase(  a__    :  float      ):







       '''simple docstring'''






       return x * x







def   lowerCAmelCase(  a__    :  Optional[Any]      , a__    :  float      , a__    :  float      , a__    :  int = 4      ):







       '''simple docstring'''






       assert callable(
           a__      ), f"""the function(object) passed should be callable your input : {function}"""
       assert isinstance(a__      , (float, int)      ), f"""a should be float or integer your input : {a}"""
       assert isinstance(function(a__      )      , (float, int)      ), (
           "the function should return integer or float return type of your function, "
           f"""{type(a__      )}"""
       )
       assert isinstance(a__      , (float, int)      ), f"""b should be float or integer your input : {b}"""
       assert (
           isinstance(a__      , a__      ) and precision > 0
       ), f"""precision should be positive integer your input : {precision}"""

       # just applying the formula of simpson for approximate integration written in
       # mentioned article in first comment of this file and above this function

       lowerCamelCase__				   =      (b - a) / N_STEPS
       lowerCamelCase__				   =      function(a__      ) + function(a__      )

       for i in range(1      , a__      ):
              lowerCamelCase__				   =      a + h * i
              result += function(a__      ) * (4 if i % 2 else 2)

       result *= h / 3
       return round(a__      , a__      )


if __name__ == "__main__":
    import doctest

    doctest.testmod()



'''simple docstring'''







from typing import List, Optional, Tuple, Union

from . import logging
from .import_utils import is_torch_available, is_torch_version


if is_torch_available():
    import torch

lowerCAmelCase_      =   logging.get_logger(__name__)  # pylint: disable=invalid-name

try:
    from torch._dynamo import allow_in_graph as maybe_allow_in_graph
except (ImportError, ModuleNotFoundError):







    def   lowerCAmelCase(  cls    :  Dict      ):







           '''simple docstring'''






           return cls







def   lowerCAmelCase(  a__    :  Union[Tuple, List]      , a__    :  Optional[Union[List["torch.Generator"], "torch.Generator"]] = None      , a__    :  Optional["torch.device"] = None      , a__    :  Optional["torch.dtype"] = None      , a__    :  Optional["torch.layout"] = None      , ):







       '''simple docstring'''






       lowerCamelCase__				   =      device
       lowerCamelCase__				   =      shape[0]

       lowerCamelCase__				   =      layout or torch.strided
       lowerCamelCase__				   =      device or torch.device("cpu"      )

       if generator is not None:
              lowerCamelCase__				   =      generator.device.type if not isinstance(a__      , a__      ) else generator[0].device.type
              if gen_device_type != device.type and gen_device_type == "cpu":
                     lowerCamelCase__				   =      "cpu"
                     if device != "mps":
                            logger.info(
                                f"""The passed generator was created on 'cpu' even though a tensor on {device} was expected."""
                                f""" Tensors will be created on 'cpu' and then moved to {device}. Note that one can probably"""
                                f""" slighly speed up this function by passing a generator that was created on the {device} device."""      )
              elif gen_device_type != device.type and gen_device_type == "cuda":
                     raise ValueError(f"""Cannot generate a {device} tensor from a generator of type {gen_device_type}."""      )

       if isinstance(a__      , a__      ):
              lowerCamelCase__				   =      (1,) + shape[1:]
              lowerCamelCase__				   =      [
                  torch.randn(a__      , generator=generator[i]      , device=a__      , dtype=a__      , layout=a__      )
                  for i in range(a__      )
              ]
              lowerCamelCase__				   =      torch.cat(a__      , dim=0      ).to(a__      )
       else:
              lowerCamelCase__				   =      torch.randn(a__      , generator=a__      , device=a__      , dtype=a__      , layout=a__      ).to(a__      )

       return latents







def   lowerCAmelCase(  a__    :  Union[str, Any]      ):







       '''simple docstring'''






       if is_torch_version("<"      , "2.0.0"      ) or not hasattr(a__      , "_dynamo"      ):
              return False
       return isinstance(a__      , torch._dynamo.eval_frame.OptimizedModule      )

