
'''simple docstring'''
import inspect
from typing import List, Optional, Tuple, Union

import numpy as np
import PIL
import torch
import torch.utils.checkpoint

from ...models import UNetaDModel, VQModel
from ...schedulers import (
    DDIMScheduler,
    DPMSolverMultistepScheduler,
    EulerAncestralDiscreteScheduler,
    EulerDiscreteScheduler,
    LMSDiscreteScheduler,
    PNDMScheduler,
)
from ...utils import PIL_INTERPOLATION, randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput






def      UpperCamelCase_				(      A__						):
	a_				,  a_      				=						image.size
	a_				,  a_      				=						(x - x % 32 for x in (w, h))  # resize to integer multiple of 32
	a_      				=						image.resize((w, h)  ,      resample=PIL_INTERPOLATION["""lanczos"""]						)
	a_      				=						np.array(A__						).astype(np.floataa						) / 255.0
	a_      				=						image[None].transpose(0  ,      3  ,      1  ,      2						)
	a_      				=						torch.from_numpy(A__						)
	return 2.0 * image - 1.0







class   a_ (      UpperCamelCase__					):




			def __init__(       self					,   UpperCAmelCase					,   UpperCAmelCase					,   UpperCAmelCase					,   ):
				super().__init__()
				self.register_modules(vqvae=UpperCAmelCase					,   unet=UpperCAmelCase					,   scheduler=UpperCAmelCase	)






			@torch.no_grad()
			def __call__(       self					,   UpperCAmelCase = None					,   UpperCAmelCase = 1					,   UpperCAmelCase = 1_00					,   UpperCAmelCase = 0.0					,   UpperCAmelCase = None					,   UpperCAmelCase = "pil"					,   UpperCAmelCase = True					,   ):
				if isinstance(UpperCAmelCase					,   PIL.Image.Image	):
					a_      				=						1
				elif isinstance(UpperCAmelCase					,   torch.Tensor	):
					a_      				=						image.shape[0]
				else:
					raise ValueError(f'''`image` has to be of type `PIL.Image.Image` or `torch.Tensor` but is {type(UpperCAmelCase	)}'''	)

				if isinstance(UpperCAmelCase					,   PIL.Image.Image	):
					a_      				=						preprocess(UpperCAmelCase	)

				a_				,  a_      				=						image.shape[-2:]

				# in_channels should be 6: 3 for latents, 3 for low resolution image
				a_      				=						(batch_size, self.unet.config.in_channels // 2, height, width)
				a_      				=						next(self.unet.parameters()	).dtype

				a_      				=						randn_tensor(UpperCAmelCase					,   generator=UpperCAmelCase					,   device=self.device					,   dtype=UpperCAmelCase	)

				a_      				=						image.to(device=self.device					,   dtype=UpperCAmelCase	)

				# set timesteps and move to the correct device
				self.scheduler.set_timesteps(UpperCAmelCase					,   device=self.device	)
				a_      				=						self.scheduler.timesteps

				# scale the initial noise by the standard deviation required by the scheduler
				a_      				=						latents * self.scheduler.init_noise_sigma

				# prepare extra kwargs for the scheduler step, since not all schedulers have the same signature.
				# eta (η) is only used with the DDIMScheduler, it will be ignored for other schedulers.
				# eta corresponds to η in DDIM paper: https://arxiv.org/abs/2010.02502
				# and should be between [0, 1]
				a_      				=						"""eta""" in set(inspect.signature(self.scheduler.step	).parameters.keys()	)
				a_      				=						{}
				if accepts_eta:
					a_      				=						eta

				for t in self.progress_bar(UpperCAmelCase	):
					# concat latents and low resolution image in the channel dimension.
					a_      				=						torch.cat([latents, image]					,   dim=1	)
					a_      				=						self.scheduler.scale_model_input(UpperCAmelCase					,   UpperCAmelCase	)
					# predict the noise residual
					a_      				=						self.unet(UpperCAmelCase					,   UpperCAmelCase	).sample
					# compute the previous noisy sample x_t -> x_t-1
					a_      				=						self.scheduler.step(UpperCAmelCase					,   UpperCAmelCase					,   UpperCAmelCase					,   **UpperCAmelCase	).prev_sample

				# decode the image latents with the VQVAE
				a_      				=						self.vqvae.decode(UpperCAmelCase	).sample
				a_      				=						torch.clamp(UpperCAmelCase					,   -1.0					,   1.0	)
				a_      				=						image / 2 + 0.5
				a_      				=						image.cpu().permute(0					,   2					,   3					,   1	).numpy()

				if output_type == "pil":
					a_      				=						self.numpy_to_pil(UpperCAmelCase	)

				if not return_dict:
					return (image,)

				return ImagePipelineOutput(images=UpperCAmelCase	)


'''simple docstring'''
import math






def      UpperCamelCase_				(      A__ = 1_00						):
	a_      				=						sum(i * i for i in range(1  ,      n + 1						)						)
	a_      				=						int(math.pow(sum(range(1  ,      n + 1						)						)  ,      2						)						)
	return square_of_sum - sum_of_squares


if __name__ == "__main__":
		print(F"""{solution() = }""")
