

from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							np.ndarray		,    SCREAMING_SNAKE_CASE_:							np.ndarray		,    SCREAMING_SNAKE_CASE_:							np.ndarray )     -> np.ndarray:




				'''simple docstring'''





				A__            =     np.stack((horizontal_flow, vertical_flow)		,    2 )

				# Create a grid of all pixel coordinates and subtract the flow to get the
				# target pixels coordinates
				A__            =     np.stack(
				    np.meshgrid(np.arange(0		,    image.shape[1] )		,    np.arange(0		,    image.shape[0] ) )		,    2 )
				A__            =     np.round(grid - flow ).astype(np.intaa )

				# Find the locations outside of the original image
				A__            =     (grid < 0) | (grid >= np.array([image.shape[1], image.shape[0]] ))
				A__            =     0

				A__            =     image[grid[:, :, 1], grid[:, :, 0]]

				# Set pixels at invalid locations to 0
				A__            =     0

				return warped



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							np.ndarray		,    SCREAMING_SNAKE_CASE_:							np.ndarray		,    SCREAMING_SNAKE_CASE_:							SupportsIndex		,    SCREAMING_SNAKE_CASE_:							float | None = None		,    )     -> tuple[np.ndarray, np.ndarray]:




				'''simple docstring'''





				if alpha is None:
								A__            =     0.1

				# Initialize flow
				A__            =     np.zeros_like(SCREAMING_SNAKE_CASE_ )
				A__            =     np.zeros_like(SCREAMING_SNAKE_CASE_ )

				# Prepare kernels for the calculation of the derivatives and the average velocity
				A__            =     np.array([[-1, 1], [-1, 1]] ) * 0.25
				A__            =     np.array([[-1, -1], [1, 1]] ) * 0.25
				A__            =     np.array([[1, 1], [1, 1]] ) * 0.25
				A__            =     np.array(
				    [[1 / 1_2, 1 / 6, 1 / 1_2], [1 / 6, 0, 1 / 6], [1 / 1_2, 1 / 6, 1 / 1_2]] )

				# Iteratively refine the flow
				for _ in range(SCREAMING_SNAKE_CASE_ ):
								A__            =     warp(SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_ )
								A__            =     convolve(SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_ ) + convolve(SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_ )
								A__            =     convolve(SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_ ) + convolve(SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_ )
								A__            =     convolve(SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_ ) + convolve(SCREAMING_SNAKE_CASE_		,    -kernel_t )

								A__            =     convolve(SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_ )
								A__            =     convolve(SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_ )

								# This updates the flow as proposed in the paper (Step 12)
								A__            =     (
								    derivative_x * avg_horizontal_velocity
								    + derivative_y * avg_vertical_velocity
								    + derivative_t
								)
								A__            =     update / (alpha**2 + derivative_x**2 + derivative_y**2)

								A__            =     avg_horizontal_velocity - derivative_x * update
								A__            =     avg_vertical_velocity - derivative_y * update

				return horizontal_flow, vertical_flow


if __name__ == "__main__":
	import doctest

	doctest.testmod()




import torch

from diffusers import DDIMScheduler

from .test_schedulers import SchedulerCommonTest

class    a__  (   snake_case     ):
			"""simple docstring"""







			__lowerCamelCase	    =    (DDIMScheduler,)
			__lowerCamelCase	    =    (('eta', 0.0), ('num_inference_steps', 50))


			def        UpperCamelCase						(      self , **lowercase    )					->  Optional[Any]:
							'''simple docstring'''






							A__            =     {
							    "num_train_timesteps": 1000,
							    "beta_start": 0.0001,
							    "beta_end": 0.02,
							    "beta_schedule": "linear",
							    "clip_sample": True,
							}

							config.update(**lowercase    )
							return config


			def        UpperCamelCase						(      self , **lowercase    )					->  List[Any]:
							'''simple docstring'''






							A__            =     self.scheduler_classes[0]
							A__            =     self.get_scheduler_config(**lowercase    )
							A__            =     scheduler_class(**lowercase    )

							A__      ,			A__            =     10, 0.0

							A__            =     self.dummy_model()
							A__            =     self.dummy_sample_deter

							scheduler.set_timesteps(lowercase    )

							for t in scheduler.timesteps:
											A__            =     model(lowercase , lowercase    )
											A__            =     scheduler.step(lowercase , lowercase , lowercase , lowercase    ).prev_sample

							return sample


			def        UpperCamelCase						(      self    )					->  Optional[Any]:
							'''simple docstring'''






							for timesteps in [100, 500, 1000]:
											self.check_over_configs(num_train_timesteps=lowercase    )


			def        UpperCamelCase						(      self    )					->  Union[str, Any]:
							'''simple docstring'''






							for steps_offset in [0, 1]:
											self.check_over_configs(steps_offset=lowercase    )

							A__            =     self.scheduler_classes[0]
							A__            =     self.get_scheduler_config(steps_offset=1    )
							A__            =     scheduler_class(**lowercase    )
							scheduler.set_timesteps(5    )
							assert torch.equal(scheduler.timesteps , torch.LongTensor([801, 601, 401, 201, 1]    )    )


			def        UpperCamelCase						(      self    )					->  Dict:
							'''simple docstring'''






							for beta_start, beta_end in zip([0.0001, 0.001, 0.01, 0.1] , [0.002, 0.02, 0.2, 2]    ):
											self.check_over_configs(beta_start=lowercase , beta_end=lowercase    )


			def        UpperCamelCase						(      self    )					->  Optional[int]:
							'''simple docstring'''






							for schedule in ["linear", "squaredcos_cap_v2"]:
											self.check_over_configs(beta_schedule=lowercase    )


			def        UpperCamelCase						(      self    )					->  Dict:
							'''simple docstring'''






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


			def        UpperCamelCase						(      self    )					->  Dict:
							'''simple docstring'''






							for clip_sample in [True, False]:
											self.check_over_configs(clip_sample=lowercase    )


			def        UpperCamelCase						(      self    )					->  int:
							'''simple docstring'''






							for timestep_spacing in ["trailing", "leading"]:
											self.check_over_configs(timestep_spacing=lowercase    )


			def        UpperCamelCase						(      self    )					->  int:
							'''simple docstring'''






							for rescale_betas_zero_snr in [True, False]:
											self.check_over_configs(rescale_betas_zero_snr=lowercase    )


			def        UpperCamelCase						(      self    )					->  Union[str, Any]:
							'''simple docstring'''






							self.check_over_configs(thresholding=lowercase    )
							for threshold in [0.5, 1.0, 2.0]:
											for prediction_type in ["epsilon", "v_prediction"]:
															self.check_over_configs(
															    thresholding=lowercase , prediction_type=lowercase , sample_max_value=lowercase , )


			def        UpperCamelCase						(      self    )					->  Dict:
							'''simple docstring'''






							for t in [1, 10, 49]:
											self.check_over_forward(time_step=lowercase    )


			def        UpperCamelCase						(      self    )					->  int:
							'''simple docstring'''






							for t, num_inference_steps in zip([1, 10, 50] , [10, 50, 500]    ):
											self.check_over_forward(time_step=lowercase , num_inference_steps=lowercase    )


			def        UpperCamelCase						(      self    )					->  List[str]:
							'''simple docstring'''






							for t, eta in zip([1, 10, 49] , [0.0, 0.5, 1.0]    ):
											self.check_over_forward(time_step=lowercase , eta=lowercase    )


			def        UpperCamelCase						(      self    )					->  int:
							'''simple docstring'''






							A__            =     self.scheduler_classes[0]
							A__            =     self.get_scheduler_config()
							A__            =     scheduler_class(**lowercase    )

							assert torch.sum(torch.abs(scheduler._get_variance(0 , 0    ) - 0.0    )    ) < 1e-5
							assert torch.sum(torch.abs(scheduler._get_variance(420 , 400    ) - 0.1_4771    )    ) < 1e-5
							assert torch.sum(torch.abs(scheduler._get_variance(980 , 960    ) - 0.3_2460    )    ) < 1e-5
							assert torch.sum(torch.abs(scheduler._get_variance(0 , 0    ) - 0.0    )    ) < 1e-5
							assert torch.sum(torch.abs(scheduler._get_variance(487 , 486    ) - 0.0_0979    )    ) < 1e-5
							assert torch.sum(torch.abs(scheduler._get_variance(999 , 998    ) - 0.02    )    ) < 1e-5


			def        UpperCamelCase						(      self    )					->  str:
							'''simple docstring'''






							A__            =     self.full_loop()

							A__            =     torch.sum(torch.abs(lowercase    )    )
							A__            =     torch.mean(torch.abs(lowercase    )    )

							assert abs(result_sum.item() - 172.0067    ) < 1e-2
							assert abs(result_mean.item() - 0.22_3967    ) < 1e-3


			def        UpperCamelCase						(      self    )					->  Dict:
							'''simple docstring'''






							A__            =     self.full_loop(prediction_type="v_prediction"    )

							A__            =     torch.sum(torch.abs(lowercase    )    )
							A__            =     torch.mean(torch.abs(lowercase    )    )

							assert abs(result_sum.item() - 52.5302    ) < 1e-2
							assert abs(result_mean.item() - 0.0684    ) < 1e-3


			def        UpperCamelCase						(      self    )					->  List[Any]:
							'''simple docstring'''






							A__            =     self.full_loop(set_alpha_to_one=lowercase , beta_start=0.01    )
							A__            =     torch.sum(torch.abs(lowercase    )    )
							A__            =     torch.mean(torch.abs(lowercase    )    )

							assert abs(result_sum.item() - 149.8295    ) < 1e-2
							assert abs(result_mean.item() - 0.1951    ) < 1e-3


			def        UpperCamelCase						(      self    )					->  Tuple:
							'''simple docstring'''






							A__            =     self.full_loop(set_alpha_to_one=lowercase , beta_start=0.01    )
							A__            =     torch.sum(torch.abs(lowercase    )    )
							A__            =     torch.mean(torch.abs(lowercase    )    )

							assert abs(result_sum.item() - 149.0784    ) < 1e-2
							assert abs(result_mean.item() - 0.1941    ) < 1e-3

