

'''simple docstring'''




def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   int						):
  if not isinstance(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						):
    UpperCAmelCase													=	f'''Input value of [number={number}] must be an integer'''
    raise TypeError(SCREAMING_SNAKE_CASE						)
  if number < 1:
    raise ValueError('Input must be a positive integer'						)
  return number * (2 * number - 1)


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

_a				: List[Any] 							=						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						):
    return cls


def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   Union[Tuple, List]       ,   SCREAMING_SNAKE_CASE      :   Optional[Union[List["torch.Generator"], "torch.Generator"]] = None       ,   SCREAMING_SNAKE_CASE      :   Optional["torch.device"] = None       ,   SCREAMING_SNAKE_CASE      :   Optional["torch.dtype"] = None       ,   SCREAMING_SNAKE_CASE      :   Optional["torch.layout"] = None       ,   ):
  UpperCAmelCase													=	device
  UpperCAmelCase													=	shape[0]

  UpperCAmelCase													=	layout or torch.strided
  UpperCAmelCase													=	device or torch.device('cpu'						)

  if generator is not None:
    UpperCAmelCase													=	generator.device.type if not isinstance(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						) else generator[0].device.type
    if gen_device_type != device.type and gen_device_type == "cpu":
      UpperCAmelCase													=	'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(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						):
    UpperCAmelCase													=	(1,) + shape[1:]
    UpperCAmelCase													=	[
        torch.randn(SCREAMING_SNAKE_CASE       ,   generator=generator[i]       ,   device=SCREAMING_SNAKE_CASE       ,   dtype=SCREAMING_SNAKE_CASE       ,   layout=SCREAMING_SNAKE_CASE						)
        for i in range(SCREAMING_SNAKE_CASE						)
    ]
    UpperCAmelCase													=	torch.cat(SCREAMING_SNAKE_CASE       ,   dim=0						).to(SCREAMING_SNAKE_CASE						)
  else:
    UpperCAmelCase													=	torch.randn(SCREAMING_SNAKE_CASE       ,   generator=SCREAMING_SNAKE_CASE       ,   device=SCREAMING_SNAKE_CASE       ,   dtype=SCREAMING_SNAKE_CASE       ,   layout=SCREAMING_SNAKE_CASE						).to(SCREAMING_SNAKE_CASE						)

  return latents



def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   Tuple						):
  if is_torch_version('<'       ,   '2.0.0'						) or not hasattr(SCREAMING_SNAKE_CASE       ,   '_dynamo'						):
    return False
  return isinstance(SCREAMING_SNAKE_CASE       ,   torch._dynamo.eval_frame.OptimizedModule						)


