



import os
from typing import Any, Callable, Dict, List, Optional, Tuple, Union

import torch
from torch import nn

from ...models.controlnet import ControlNetModel, ControlNetOutput
from ...models.modeling_utils import ModelMixin
from ...utils import logging


A__	      =       logging.get_logger(__name__)





class 					__lowerCAmelCase (     lowerCamelCase__       ):




				def __init__(							self						,				_snake_case		):



									"""simple docstring"""





									super().__init__()
									_lowerCAmelCase						=    nn.ModuleList(_snake_case		)




				def 							snake_case   (							self						,				_snake_case						,				_snake_case						,				_snake_case						,				_snake_case						,				_snake_case						,				_snake_case = None						,				_snake_case = None						,				_snake_case = None						,				_snake_case = None						,				_snake_case = False						,				_snake_case = True						,				):



									"""simple docstring"""





									for i, (image, scale, controlnet) in enumerate(zip(_snake_case						,				_snake_case						,				self.nets		)		):
														_lowerCAmelCase	,	_lowerCAmelCase						=    controlnet(
														    _snake_case						,				_snake_case						,				_snake_case						,				_snake_case						,				_snake_case						,				_snake_case						,				_snake_case						,				_snake_case						,				_snake_case						,				_snake_case						,				_snake_case						,				)

														# merge samples
														if i == 0:
																			_lowerCAmelCase	,	_lowerCAmelCase						=    down_samples, mid_sample
														else:
																			_lowerCAmelCase						=    [
																			    samples_prev + samples_curr
																			    for samples_prev, samples_curr in zip(_snake_case						,				_snake_case		)
																			]
																			mid_block_res_sample += mid_sample

									return down_block_res_samples, mid_block_res_sample




				def 							snake_case   (							self						,				_snake_case						,				_snake_case = True						,				_snake_case = None						,				_snake_case = False						,				_snake_case = None						,				):



									"""simple docstring"""





									_lowerCAmelCase						=    0
									_lowerCAmelCase						=    save_directory
									for controlnet in self.nets:
														controlnet.save_pretrained(
														    _snake_case						,				is_main_process=_snake_case						,				save_function=_snake_case						,				safe_serialization=_snake_case						,				variant=_snake_case						,				)

														idx += 1
														_lowerCAmelCase						=    model_path_to_save + F'_{idx}'




				@classmethod
				def 							snake_case   (							cls						,				_snake_case						,				**_snake_case		):



									"""simple docstring"""





									_lowerCAmelCase						=    0
									_lowerCAmelCase						=    []

									# load controlnet and append to list until no controlnet directory exists anymore
									# first controlnet has to be saved under `./mydirectory/controlnet` to be compliant with `DiffusionPipeline.from_prertained`
									# second, third, ... controlnets have to be saved under `./mydirectory/controlnet_1`, `./mydirectory/controlnet_2`, ...
									_lowerCAmelCase						=    pretrained_model_path
									while os.path.isdir(_snake_case		):
														_lowerCAmelCase						=    ControlNetModel.from_pretrained(_snake_case						,				**_snake_case		)
														controlnets.append(_snake_case		)

														idx += 1
														_lowerCAmelCase						=    pretrained_model_path + F'_{idx}'

									logger.info(F'{len(_snake_case		)} controlnets loaded from {pretrained_model_path}.'		)

									if len(_snake_case		) == 0:
														raise ValueError(
														    F'No ControlNets found under {os.path.dirname(_snake_case		)}. Expected at least {pretrained_model_path + "_0"}.'		)

									return cls(_snake_case		)







"""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() = }''')


