


"""simple docstring"""




from typing import List, Optional, Tuple, Union

import torch

from ...utils import logging, randn_tensor
from ..pipeline_utils import AudioPipelineOutput, DiffusionPipeline


__UpperCamelCase						=      logging.get_logger(__name__)  # pylint: disable=invalid-name
class 					lowerCAmelCase	(					lowerCamelCase_    ):




		'''simple docstring'''







		def __init__(	self						,       lowerCAmelCase__						,       lowerCAmelCase__				)     ->							Optional[int]:
								super().__init__()
								self.register_modules(unet=lowerCAmelCase__						,       scheduler=lowerCAmelCase__				)







		@torch.no_grad()
		def __call__(	self						,       lowerCAmelCase__ = 1						,       lowerCAmelCase__ = 100						,       lowerCAmelCase__ = None						,       lowerCAmelCase__ = None						,       lowerCAmelCase__ = True						,       )     ->							Union[AudioPipelineOutput, Tuple]:

								if audio_length_in_s is None:
														SCREAMING_SNAKE_CASE													=					self.unet.config.sample_size / self.unet.config.sample_rate

								SCREAMING_SNAKE_CASE													=					audio_length_in_s * self.unet.config.sample_rate

								SCREAMING_SNAKE_CASE													=					2 ** len(self.unet.up_blocks				)
								if sample_size < 3 * down_scale_factor:
														raise ValueError(
														    F'{audio_length_in_s} is too small. Make sure it\'s bigger or equal to'
														    F' {3 * down_scale_factor / self.unet.config.sample_rate}.'				)

								SCREAMING_SNAKE_CASE													=					int(lowerCAmelCase__				)
								if sample_size % down_scale_factor != 0:
														SCREAMING_SNAKE_CASE													=					(
														    (audio_length_in_s * self.unet.config.sample_rate) // down_scale_factor + 1
														) * down_scale_factor
														logger.info(
														    F'{audio_length_in_s} is increased to {sample_size / self.unet.config.sample_rate} so that it can be handled'
														    F' by the model. It will be cut to {original_sample_size / self.unet.config.sample_rate} after the denoising'
														    ' process.'				)
								SCREAMING_SNAKE_CASE													=					int(lowerCAmelCase__				)

								SCREAMING_SNAKE_CASE													=					next(iter(self.unet.parameters()				)				).dtype
								SCREAMING_SNAKE_CASE													=					(batch_size, self.unet.config.in_channels, sample_size)
								if isinstance(lowerCAmelCase__						,       lowerCAmelCase__				) and len(lowerCAmelCase__				) != batch_size:
														raise ValueError(
														    F'You have passed a list of generators of length {len(lowerCAmelCase__				)}, but requested an effective batch'
														    F' size of {batch_size}. Make sure the batch size matches the length of the generators.'				)

								SCREAMING_SNAKE_CASE													=					randn_tensor(lowerCAmelCase__						,       generator=lowerCAmelCase__						,       device=self.device						,       dtype=lowerCAmelCase__				)

								# set step values
								self.scheduler.set_timesteps(lowerCAmelCase__						,       device=audio.device				)
								SCREAMING_SNAKE_CASE													=					self.scheduler.timesteps.to(lowerCAmelCase__				)

								for t in self.progress_bar(self.scheduler.timesteps				):
														# 1. predict noise model_output
														SCREAMING_SNAKE_CASE													=					self.unet(lowerCAmelCase__						,       lowerCAmelCase__				).sample

														# 2. compute previous image: x_t -> t_t-1
														SCREAMING_SNAKE_CASE													=					self.scheduler.step(lowerCAmelCase__						,       lowerCAmelCase__						,       lowerCAmelCase__				).prev_sample

								SCREAMING_SNAKE_CASE													=					audio.clamp(-1						,       1				).float().cpu().numpy()

								SCREAMING_SNAKE_CASE													=					audio[:, :, :original_sample_size]

								if not return_dict:
														return (audio,)

								return AudioPipelineOutput(audios=lowerCAmelCase__				)






"""simple docstring"""




from math import isclose, sqrt


def     lowercase			(SCREAMING_SNAKE_CASE_		:				float ,			SCREAMING_SNAKE_CASE_		:				float ,			SCREAMING_SNAKE_CASE_		:				float  )   ->						tuple[float, float, float]:
						SCREAMING_SNAKE_CASE													=					point_y / 4 / point_x
						SCREAMING_SNAKE_CASE													=					2 * normal_gradient / (1 + normal_gradient * normal_gradient)
						SCREAMING_SNAKE_CASE													=					(1 - normal_gradient * normal_gradient) / (
						    1 + normal_gradient * normal_gradient
						)
						SCREAMING_SNAKE_CASE													=					(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
						SCREAMING_SNAKE_CASE													=					outgoing_gradient**2 + 4
						SCREAMING_SNAKE_CASE													=					2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
						SCREAMING_SNAKE_CASE													=					(point_y - outgoing_gradient * point_x) ** 2 - 1_00

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

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

						return next_x, next_y, outgoing_gradient


def     lowercase			(SCREAMING_SNAKE_CASE_		:				float = 1.4 ,			SCREAMING_SNAKE_CASE_		:				float = -9.6  )   ->						int:
						SCREAMING_SNAKE_CASE													=					0
						SCREAMING_SNAKE_CASE													=					first_x_coord
						SCREAMING_SNAKE_CASE													=					first_y_coord
						SCREAMING_SNAKE_CASE													=					(10.1 - point_y) / (0.0 - point_x)

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

						return num_reflections


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


