from math import factorial

def 			lowercase_				(			_lowerCamelCase							:       Union[str, Any]		,	_lowerCamelCase							:       Dict		,	_lowerCamelCase							:       int):
    if successes > trials:
        raise ValueError("successes must be lower or equal to trials")
    if trials < 0 or successes < 0:
        raise ValueError("the function is defined for non-negative integers")
    if not isinstance(__A		,	__A) or not isinstance(__A		,	__A):
        raise ValueError("the function is defined for non-negative integers")
    if not 0 < prob < 1:
        raise ValueError("prob has to be in range of 1 - 0")
    lowercase__ :   List[str]    					=				(prob**successes) * ((1 - prob) ** (trials - successes))
    # Calculate the binomial coefficient: n! / k!(n-k)!
    lowercase__ :   str    					=				float(factorial(__A))
    coefficient /= factorial(__A) * factorial(trials - successes)
    return probability * coefficient


if __name__ == "__main__":
      from doctest import testmod

      testmod()
      print('''Probability of 2 successes out of 4 trails''')
      print('''with probability of 0.75 is:''', end=''' ''')
      print(binomial_distribution(2, 4, 0.75))





'''simple docstring'''







import argparse

import intel_extension_for_pytorch as ipex
import torch

from diffusers import DPMSolverMultistepScheduler, StableDiffusionPipeline


lowercase    :							Optional[Any]      =					argparse.ArgumentParser("Stable Diffusion script with intel optimization", add_help=False)
parser.add_argument("--dpm", action="store_true", help="Enable DPMSolver or not")
parser.add_argument("--steps", default=None, type=int, help="Num inference steps")
lowercase    :							Tuple      =					parser.parse_args()


lowercase    :							Optional[int]      =					"cpu"
lowercase    :							Optional[Any]      =					"a lovely <dicoo> in red dress and hat, in the snowly and brightly night, with many brighly buildings"

lowercase    :							Optional[int]      =					"path-to-your-trained-model"
lowercase    :							List[str]      =					StableDiffusionPipeline.from_pretrained(model_id)
if args.dpm:
					lowercase    :							str      =					DPMSolverMultistepScheduler.from_config(pipe.scheduler.config)
lowercase    :							Dict      =					pipe.to(device)

# to channels last
lowercase    :							Optional[Any]      =					pipe.unet.to(memory_format=torch.channels_last)
lowercase    :							int      =					pipe.vae.to(memory_format=torch.channels_last)
lowercase    :							Optional[Any]      =					pipe.text_encoder.to(memory_format=torch.channels_last)
if pipe.requires_safety_checker:
					lowercase    :							Optional[int]      =					pipe.safety_checker.to(memory_format=torch.channels_last)

# optimize with ipex
lowercase    :							Any      =					torch.randn(2, 4, 64, 64)
lowercase    :							Optional[int]      =					torch.rand(1) * 999
lowercase    :							Optional[Any]      =					torch.randn(2, 77, 768)
lowercase    :							Optional[Any]      =					(sample, timestep, encoder_hidden_status)
try:
					lowercase    :							List[Any]      =					ipex.optimize(pipe.unet.eval(), dtype=torch.bfloataa, inplace=True, sample_input=input_example)
except Exception:
					lowercase    :							List[str]      =					ipex.optimize(pipe.unet.eval(), dtype=torch.bfloataa, inplace=True)
lowercase    :							Tuple      =					ipex.optimize(pipe.vae.eval(), dtype=torch.bfloataa, inplace=True)
lowercase    :							Optional[Any]      =					ipex.optimize(pipe.text_encoder.eval(), dtype=torch.bfloataa, inplace=True)
if pipe.requires_safety_checker:
					lowercase    :							Tuple      =					ipex.optimize(pipe.safety_checker.eval(), dtype=torch.bfloataa, inplace=True)

# compute
lowercase    :							List[str]      =					666
lowercase    :							Tuple      =					torch.Generator(device).manual_seed(seed)
lowercase    :							Union[str, Any]      =					{"generator": generator}
if args.steps is not None:
					lowercase    :							Dict      =					args.steps

with torch.cpu.amp.autocast(enabled=True, dtype=torch.bfloataa):
					lowercase    :							List[str]      =					pipe(prompt, **generate_kwargs).images[0]

# save image
image.save("generated.png")

