
import inspect
from typing import Callable, List, Optional, Union

import torch
from transformers import CLIPImageProcessor, CLIPTextModel, CLIPTokenizer

from diffusers import DiffusionPipeline
from diffusers.models import AutoencoderKL, UNetaDConditionModel
from diffusers.pipelines.stable_diffusion import StableDiffusionPipelineOutput
from diffusers.pipelines.stable_diffusion.safety_checker import StableDiffusionSafetyChecker
from diffusers.schedulers import DDIMScheduler, LMSDiscreteScheduler, PNDMScheduler
from diffusers.utils import logging


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







class        lowerCAmelCase__      (   __lowercase	):

						def __init__(			self       ,							a       ,							a       ,							a       ,							a       ,							a       ,							a       ,							a       ,							)					->      Optional[Any]:


								'''simple docstring'''

								super().__init__()
								self.register_modules(
								    vae=a       ,							text_encoder=a       ,							tokenizer=a       ,							unet=a       ,							scheduler=a       ,							safety_checker=a       ,							feature_extractor=a       ,							)

						def  A_				(			self       ,							a = "auto"				)					->      List[str]:


								'''simple docstring'''

								if slice_size == "auto":
										# half the attention head size is usually a good trade-off between
										# speed and memory
										_UpperCamelCase						    =	self.unet.config.attention_head_dim // 2
								self.unet.set_attention_slice(a				)

						def  A_				(			self				)					->      int:


								'''simple docstring'''

								self.enable_attention_slicing(a				)







						@torch.no_grad()
						def __call__(			self       ,							a       ,							a = 5_12       ,							a = 5_12       ,							a = 50       ,							a = 7.5       ,							a = None       ,							a = 1       ,							a = 0.0       ,							a = None       ,							a = None       ,							a = "pil"       ,							a = True       ,							a = None       ,							a = 1       ,							a = None       ,							**a       ,							)					->      int:


								'''simple docstring'''

								if isinstance(a       ,							a				):
										_UpperCamelCase						    =	1
								elif isinstance(a       ,							a				):
										_UpperCamelCase						    =	len(a				)
								else:
										raise ValueError(F'`prompt` has to be of type `str` or `list` but is {type(a				)}'				)

								if height % 8 != 0 or width % 8 != 0:
										raise ValueError(F'`height` and `width` have to be divisible by 8 but are {height} and {width}.'				)

								if (callback_steps is None) or (
								    callback_steps is not None and (not isinstance(a       ,							a				) or callback_steps <= 0)
								):
										raise ValueError(
										    F'`callback_steps` has to be a positive integer but is {callback_steps} of type'
										    F' {type(a				)}.'				)

								# get prompt text embeddings
								_UpperCamelCase						    =	self.tokenizer(
								    a       ,							padding="""max_length"""       ,							max_length=self.tokenizer.model_max_length       ,							return_tensors="""pt"""       ,							)
								_UpperCamelCase						    =	text_inputs.input_ids

								if text_input_ids.shape[-1] > self.tokenizer.model_max_length:
										_UpperCamelCase						    =	self.tokenizer.batch_decode(text_input_ids[:, self.tokenizer.model_max_length :]				)
										logger.warning(
										    """The following part of your input was truncated because CLIP can only handle sequences up to"""
										    F' {self.tokenizer.model_max_length} tokens: {removed_text}'				)
										_UpperCamelCase						    =	text_input_ids[:, : self.tokenizer.model_max_length]

								if text_embeddings is None:
										_UpperCamelCase						    =	self.text_encoder(text_input_ids.to(self.device				)				)[0]

								# duplicate text embeddings for each generation per prompt, using mps friendly method
								_UpperCamelCase    ,	_UpperCamelCase    ,	_UpperCamelCase						    =	text_embeddings.shape
								_UpperCamelCase						    =	text_embeddings.repeat(1       ,							a       ,							1				)
								_UpperCamelCase						    =	text_embeddings.view(bs_embed * num_images_per_prompt       ,							a       ,							-1				)

								# here `guidance_scale` is defined analog to the guidance weight `w` of equation (2)
								# of the Imagen paper: https://arxiv.org/pdf/2205.11487.pdf . `guidance_scale = 1`
								# corresponds to doing no classifier free guidance.
								_UpperCamelCase						    =	guidance_scale > 1.0
								# get unconditional embeddings for classifier free guidance
								if do_classifier_free_guidance:
										_UpperCamelCase						    =	42
										if negative_prompt is None:
												_UpperCamelCase						    =	[""""""]
										elif type(a				) is not type(a				):
												raise TypeError(
												    F'`negative_prompt` should be the same type to `prompt`, but got {type(a				)} !='
												    F' {type(a				)}.'				)
										elif isinstance(a       ,							a				):
												_UpperCamelCase						    =	[negative_prompt]
										elif batch_size != len(a				):
												raise ValueError(
												    F'`negative_prompt`: {negative_prompt} has batch size {len(a				)}, but `prompt`:'
												    F' {prompt} has batch size {batch_size}. Please make sure that passed `negative_prompt` matches'
												    """ the batch size of `prompt`."""				)
										else:
												_UpperCamelCase						    =	negative_prompt

										_UpperCamelCase						    =	text_input_ids.shape[-1]
										_UpperCamelCase						    =	self.tokenizer(
										    a       ,							padding="""max_length"""       ,							max_length=a       ,							truncation=a       ,							return_tensors="""pt"""       ,							)
										_UpperCamelCase						    =	self.text_encoder(uncond_input.input_ids.to(self.device				)				)[0]

										# duplicate unconditional embeddings for each generation per prompt, using mps friendly method
										_UpperCamelCase						    =	uncond_embeddings.shape[1]
										_UpperCamelCase						    =	uncond_embeddings.repeat(a       ,							a       ,							1				)
										_UpperCamelCase						    =	uncond_embeddings.view(batch_size * num_images_per_prompt       ,							a       ,							-1				)

										# For classifier free guidance, we need to do two forward passes.
										# Here we concatenate the unconditional and text embeddings into a single batch
										# to avoid doing two forward passes
										_UpperCamelCase						    =	torch.cat([uncond_embeddings, text_embeddings]				)

								# get the initial random noise unless the user supplied it

								# Unlike in other pipelines, latents need to be generated in the target device
								# for 1-to-1 results reproducibility with the CompVis implementation.
								# However this currently doesn't work in `mps`.
								_UpperCamelCase						    =	(batch_size * num_images_per_prompt, self.unet.config.in_channels, height // 8, width // 8)
								_UpperCamelCase						    =	(batch_size * num_images_per_prompt, self.unet.config.in_channels, 64, 64)
								_UpperCamelCase						    =	text_embeddings.dtype
								if latents is None:
										if self.device.type == "mps":
												# randn does not exist on mps
												_UpperCamelCase						    =	torch.randn(
												    a       ,							generator=a       ,							device="""cpu"""       ,							dtype=a				).to(self.device				)
												_UpperCamelCase						    =	torch.randn(a       ,							generator=a       ,							device="""cpu"""       ,							dtype=a				).to(
												    self.device				)
										else:
												_UpperCamelCase						    =	torch.randn(
												    a       ,							generator=a       ,							device=self.device       ,							dtype=a				)
												_UpperCamelCase						    =	torch.randn(a       ,							generator=a       ,							device=self.device       ,							dtype=a				)
								else:
										if latents_reference.shape != latents_shape:
												raise ValueError(F'Unexpected latents shape, got {latents.shape}, expected {latents_shape}'				)
										_UpperCamelCase						    =	latents_reference.to(self.device				)
										_UpperCamelCase						    =	latents.to(self.device				)

								# This is the key part of the pipeline where we
								# try to ensure that the generated images w/ the same seed
								# but different sizes actually result in similar images
								_UpperCamelCase						    =	(latents_shape[3] - latents_shape_reference[3]) // 2
								_UpperCamelCase						    =	(latents_shape[2] - latents_shape_reference[2]) // 2
								_UpperCamelCase						    =	latents_shape_reference[3] if dx >= 0 else latents_shape_reference[3] + 2 * dx
								_UpperCamelCase						    =	latents_shape_reference[2] if dy >= 0 else latents_shape_reference[2] + 2 * dy
								_UpperCamelCase						    =	0 if dx < 0 else dx
								_UpperCamelCase						    =	0 if dy < 0 else dy
								_UpperCamelCase						    =	max(-dx       ,							0				)
								_UpperCamelCase						    =	max(-dy       ,							0				)
								# import pdb
								# pdb.set_trace()
								_UpperCamelCase						    =	latents_reference[:, :, dy : dy + h, dx : dx + w]

								# set timesteps
								self.scheduler.set_timesteps(a				)

								# Some schedulers like PNDM have timesteps as arrays
								# It's more optimized to move all timesteps to correct device beforehand
								_UpperCamelCase						    =	self.scheduler.timesteps.to(self.device				)

								# scale the initial noise by the standard deviation required by the scheduler
								_UpperCamelCase						    =	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]
								_UpperCamelCase						    =	"""eta""" in set(inspect.signature(self.scheduler.step				).parameters.keys()				)
								_UpperCamelCase						    =	{}
								if accepts_eta:
										_UpperCamelCase						    =	eta

								for i, t in enumerate(self.progress_bar(a				)				):
										# expand the latents if we are doing classifier free guidance
										_UpperCamelCase						    =	torch.cat([latents] * 2				) if do_classifier_free_guidance else latents
										_UpperCamelCase						    =	self.scheduler.scale_model_input(a       ,							a				)

										# predict the noise residual
										_UpperCamelCase						    =	self.unet(a       ,							a       ,							encoder_hidden_states=a				).sample

										# perform guidance
										if do_classifier_free_guidance:
												_UpperCamelCase    ,	_UpperCamelCase						    =	noise_pred.chunk(2				)
												_UpperCamelCase						    =	noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)

										# compute the previous noisy sample x_t -> x_t-1
										_UpperCamelCase						    =	self.scheduler.step(a       ,							a       ,							a       ,							**a				).prev_sample

										# call the callback, if provided
										if callback is not None and i % callback_steps == 0:
												callback(a       ,							a       ,							a				)

								_UpperCamelCase						    =	1 / 0.1_8215 * latents
								_UpperCamelCase						    =	self.vae.decode(a				).sample

								_UpperCamelCase						    =	(image / 2 + 0.5).clamp(0       ,							1				)

								# we always cast to float32 as this does not cause significant overhead and is compatible with bfloat16
								_UpperCamelCase						    =	image.cpu().permute(0       ,							2       ,							3       ,							1				).float().numpy()

								if self.safety_checker is not None:
										_UpperCamelCase						    =	self.feature_extractor(self.numpy_to_pil(a				)       ,							return_tensors="""pt"""				).to(
										    self.device				)
										_UpperCamelCase    ,	_UpperCamelCase						    =	self.safety_checker(
										    images=a       ,							clip_input=safety_checker_input.pixel_values.to(text_embeddings.dtype				)				)
								else:
										_UpperCamelCase						    =	None

								if output_type == "pil":
										_UpperCamelCase						    =	self.numpy_to_pil(a				)

								if not return_dict:
										return (image, has_nsfw_concept)

								return StableDiffusionPipelineOutput(images=a       ,							nsfw_content_detected=a				)





from math import isclose, sqrt


def 							__A(lowerCAmelCase						,  lowerCAmelCase						,  lowerCAmelCase )		->				tuple[float, float, float]:

		"""simple docstring"""






		_UpperCamelCase						    =	point_y / 4 / point_x
		_UpperCamelCase						    =	2 * normal_gradient / (1 + normal_gradient * normal_gradient)
		_UpperCamelCase						    =	(1 - normal_gradient * normal_gradient) / (
		    1 + normal_gradient * normal_gradient
		)
		_UpperCamelCase						    =	(sa - ca * incoming_gradient) / (ca + sa * incoming_gradient)

		# to find the next point, solve the simultaeneous equations:
		# y^2 + 4x^2 = 100
		# y - b = m * (x - a)
		# ==> A x^2 + B x + C = 0
		_UpperCamelCase						    =	outgoing_gradient**2 + 4
		_UpperCamelCase						    =	2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
		_UpperCamelCase						    =	(point_y - outgoing_gradient * point_x) ** 2 - 1_0_0

		_UpperCamelCase						    =	(
		    -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term )
		) / (2 * quadratic_term)
		_UpperCamelCase						    =	(
		    -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term )
		) / (2 * quadratic_term)

		# two solutions, one of which is our input point
		_UpperCamelCase						    =	x_minus if isclose(lowerCAmelCase						,  lowerCAmelCase ) else x_plus
		_UpperCamelCase						    =	point_y + outgoing_gradient * (next_x - point_x)

		return next_x, next_y, outgoing_gradient


def 							__A(lowerCAmelCase = 1.4						,  lowerCAmelCase = -9.6 )		->				int:

		"""simple docstring"""






		_UpperCamelCase						    =	0
		_UpperCamelCase						    =	first_x_coord
		_UpperCamelCase						    =	first_y_coord
		_UpperCamelCase						    =	(10.1 - point_y) / (0.0 - point_x)

		while not (-0.01 <= point_x <= 0.01 and point_y > 0):
				_UpperCamelCase    ,	_UpperCamelCase    ,	_UpperCamelCase						    =	next_point(lowerCAmelCase						,  lowerCAmelCase						,  lowerCAmelCase )
				num_reflections += 1

		return num_reflections


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



