





import torch

from diffusers import EulerDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest



class  __lowerCAmelCase	(      _a					):
			lowerCamelCase_					:					Optional[int]             =				(EulerDiscreteScheduler,)
			lowerCamelCase_					:					Tuple             =				10






			def       lowerCamelCase  (self ,							**__magic_name__   )					->       Any:


							'''simple docstring'''



							snake_case_						:   str           =  {
							    "num_train_timesteps": 1100,
							    "beta_start": 0.0_001,
							    "beta_end": 0.02,
							    "beta_schedule": "linear",
							}

							config.update(**lowerCAmelCase__   )
							return config






			def       lowerCamelCase  (self   )					->       Union[str, Any]:


							'''simple docstring'''



							for timesteps in [10, 50, 100, 1000]:
											self.check_over_configs(num_train_timesteps=lowerCAmelCase__   )






			def       lowerCamelCase  (self   )					->       List[str]:


							'''simple docstring'''



							for beta_start, beta_end in zip([0.00_001, 0.0_001, 0.001] ,							[0.0_002, 0.002, 0.02]   ):
											self.check_over_configs(beta_start=lowerCAmelCase__ ,							beta_end=lowerCAmelCase__   )






			def       lowerCamelCase  (self   )					->       List[str]:


							'''simple docstring'''



							for schedule in ["linear", "scaled_linear"]:
											self.check_over_configs(beta_schedule=lowerCAmelCase__   )






			def       lowerCamelCase  (self   )					->       Optional[Any]:


							'''simple docstring'''



							for prediction_type in ["epsilon", "v_prediction"]:
											self.check_over_configs(prediction_type=lowerCAmelCase__   )






			def       lowerCamelCase  (self   )					->       List[Any]:


							'''simple docstring'''



							snake_case_						:   List[str]           =  self.scheduler_classes[0]
							snake_case_						:   int           =  self.get_scheduler_config()
							snake_case_						:   Optional[int]           =  scheduler_class(**lowerCAmelCase__   )

							scheduler.set_timesteps(self.num_inference_steps   )

							snake_case_						:   int           =  torch.manual_seed(0   )

							snake_case_						:   Any           =  self.dummy_model()
							snake_case_						:   List[str]           =  self.dummy_sample_deter * scheduler.init_noise_sigma
							snake_case_						:   List[Any]           =  sample.to(lowerCAmelCase__   )

							for i, t in enumerate(scheduler.timesteps   ):
											snake_case_						:   List[str]           =  scheduler.scale_model_input(lowerCAmelCase__ ,							lowerCAmelCase__   )

											snake_case_						:   int           =  model(lowerCAmelCase__ ,							lowerCAmelCase__   )

											snake_case_						:   int           =  scheduler.step(lowerCAmelCase__ ,							lowerCAmelCase__ ,							lowerCAmelCase__ ,							generator=lowerCAmelCase__   )
											snake_case_						:   Optional[int]           =  output.prev_sample

							snake_case_						:   Optional[Any]           =  torch.sum(torch.abs(lowerCAmelCase__   )   )
							snake_case_						:   Tuple           =  torch.mean(torch.abs(lowerCAmelCase__   )   )

							assert abs(result_sum.item() - 10.0_807   ) < 1e-2
							assert abs(result_mean.item() - 0.0_131   ) < 1e-3






			def       lowerCamelCase  (self   )					->       List[Any]:


							'''simple docstring'''



							snake_case_						:   Any           =  self.scheduler_classes[0]
							snake_case_						:   List[Any]           =  self.get_scheduler_config(prediction_type='''v_prediction'''   )
							snake_case_						:   Any           =  scheduler_class(**lowerCAmelCase__   )

							scheduler.set_timesteps(self.num_inference_steps   )

							snake_case_						:   str           =  torch.manual_seed(0   )

							snake_case_						:   Optional[Any]           =  self.dummy_model()
							snake_case_						:   Union[str, Any]           =  self.dummy_sample_deter * scheduler.init_noise_sigma
							snake_case_						:   Tuple           =  sample.to(lowerCAmelCase__   )

							for i, t in enumerate(scheduler.timesteps   ):
											snake_case_						:   Union[str, Any]           =  scheduler.scale_model_input(lowerCAmelCase__ ,							lowerCAmelCase__   )

											snake_case_						:   int           =  model(lowerCAmelCase__ ,							lowerCAmelCase__   )

											snake_case_						:   Union[str, Any]           =  scheduler.step(lowerCAmelCase__ ,							lowerCAmelCase__ ,							lowerCAmelCase__ ,							generator=lowerCAmelCase__   )
											snake_case_						:   Union[str, Any]           =  output.prev_sample

							snake_case_						:   Tuple           =  torch.sum(torch.abs(lowerCAmelCase__   )   )
							snake_case_						:   Any           =  torch.mean(torch.abs(lowerCAmelCase__   )   )

							assert abs(result_sum.item() - 0.0_002   ) < 1e-2
							assert abs(result_mean.item() - 2.2676e-06   ) < 1e-3






			def       lowerCamelCase  (self   )					->       str:


							'''simple docstring'''



							snake_case_						:   Optional[int]           =  self.scheduler_classes[0]
							snake_case_						:   List[Any]           =  self.get_scheduler_config()
							snake_case_						:   int           =  scheduler_class(**lowerCAmelCase__   )

							scheduler.set_timesteps(self.num_inference_steps ,							device=lowerCAmelCase__   )

							snake_case_						:   Optional[int]           =  torch.manual_seed(0   )

							snake_case_						:   str           =  self.dummy_model()
							snake_case_						:   Any           =  self.dummy_sample_deter * scheduler.init_noise_sigma.cpu()
							snake_case_						:   str           =  sample.to(lowerCAmelCase__   )

							for t in scheduler.timesteps:
											snake_case_						:   List[str]           =  scheduler.scale_model_input(lowerCAmelCase__ ,							lowerCAmelCase__   )

											snake_case_						:   Any           =  model(lowerCAmelCase__ ,							lowerCAmelCase__   )

											snake_case_						:   Tuple           =  scheduler.step(lowerCAmelCase__ ,							lowerCAmelCase__ ,							lowerCAmelCase__ ,							generator=lowerCAmelCase__   )
											snake_case_						:   int           =  output.prev_sample

							snake_case_						:   List[Any]           =  torch.sum(torch.abs(lowerCAmelCase__   )   )
							snake_case_						:   str           =  torch.mean(torch.abs(lowerCAmelCase__   )   )

							assert abs(result_sum.item() - 10.0_807   ) < 1e-2
							assert abs(result_mean.item() - 0.0_131   ) < 1e-3






			def       lowerCamelCase  (self   )					->       int:


							'''simple docstring'''



							snake_case_						:   List[Any]           =  self.scheduler_classes[0]
							snake_case_						:   int           =  self.get_scheduler_config()
							snake_case_						:   Union[str, Any]           =  scheduler_class(**lowerCAmelCase__ ,							use_karras_sigmas=lowerCAmelCase__   )

							scheduler.set_timesteps(self.num_inference_steps ,							device=lowerCAmelCase__   )

							snake_case_						:   Optional[int]           =  torch.manual_seed(0   )

							snake_case_						:   List[str]           =  self.dummy_model()
							snake_case_						:   str           =  self.dummy_sample_deter * scheduler.init_noise_sigma.cpu()
							snake_case_						:   Optional[int]           =  sample.to(lowerCAmelCase__   )

							for t in scheduler.timesteps:
											snake_case_						:   List[Any]           =  scheduler.scale_model_input(lowerCAmelCase__ ,							lowerCAmelCase__   )

											snake_case_						:   str           =  model(lowerCAmelCase__ ,							lowerCAmelCase__   )

											snake_case_						:   Optional[Any]           =  scheduler.step(lowerCAmelCase__ ,							lowerCAmelCase__ ,							lowerCAmelCase__ ,							generator=lowerCAmelCase__   )
											snake_case_						:   List[Any]           =  output.prev_sample

							snake_case_						:   List[Any]           =  torch.sum(torch.abs(lowerCAmelCase__   )   )
							snake_case_						:   Optional[Any]           =  torch.mean(torch.abs(lowerCAmelCase__   )   )

							assert abs(result_sum.item() - 124.52_299_499_511_719   ) < 1e-2
							assert abs(result_mean.item() - 0.16_213_932_633_399_963   ) < 1e-3







from math import isclose, sqrt






def 					lowerCamelCase_						(    _UpperCamelCase			,    _UpperCamelCase			,    _UpperCamelCase			)		->						tuple[float, float, float]:






				"""simple docstring"""


				snake_case_						:   Dict           =  point_y / 4 / point_x
				snake_case_						:   List[str]           =  2 * normal_gradient / (1 + normal_gradient * normal_gradient)
				snake_case_						:   Union[str, Any]           =  (1 - normal_gradient * normal_gradient) / (
				    1 + normal_gradient * normal_gradient
				)
				snake_case_						:   Tuple           =  (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
				snake_case_						:   Union[str, Any]           =  outgoing_gradient**2 + 4
				snake_case_						:   Tuple           =  2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
				snake_case_						:   Optional[Any]           =  (point_y - outgoing_gradient * point_x) ** 2 - 100

				snake_case_						:   Dict           =  (
				    -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term			)
				) / (2 * quadratic_term)
				snake_case_						:   Optional[int]           =  (
				    -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term			)
				) / (2 * quadratic_term)

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

				return next_x, next_y, outgoing_gradient






def 					lowerCamelCase_						(    _UpperCamelCase = 1.4			,    _UpperCamelCase = -9.6			)		->						int:






				"""simple docstring"""


				snake_case_						:   int           =  0
				snake_case_						:   float           =  first_x_coord
				snake_case_						:   float           =  first_y_coord
				snake_case_						:   float           =  (10.1 - point_y) / (0.0 - point_x)

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

				return num_reflections


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