



from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve






def        a( A			:       np.ndarray					,	A			:       np.ndarray					,	A			:       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        a( A			:       np.ndarray					,	A			:       np.ndarray					,	A			:       SupportsIndex					,	A			:       float | None = None					,	)						->			tuple[np.ndarray, np.ndarray]:
					"""simple docstring"""





					if alpha is None:
										a   	=  0.1

					# Initialize flow
					a   	=  np.zeros_like(A			)
					a   	=  np.zeros_like(A			)

					# 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 / 12, 1 / 6, 1 / 12], [1 / 6, 0, 1 / 6], [1 / 12, 1 / 6, 1 / 12]]			)

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

										a   	=  convolve(A					,	A			)
										a   	=  convolve(A					,	A			)

										# 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()





from .pipeline_kandinskya_a import KandinskyVaaPipeline
from .pipeline_kandinsky2_2_controlnet import KandinskyVaaControlnetPipeline
from .pipeline_kandinsky2_2_controlnet_img2img import KandinskyVaaControlnetImgaImgPipeline
from .pipeline_kandinsky2_2_img2img import KandinskyVaaImgaImgPipeline
from .pipeline_kandinsky2_2_inpainting import KandinskyVaaInpaintPipeline
from .pipeline_kandinsky2_2_prior import KandinskyVaaPriorPipeline
from .pipeline_kandinsky2_2_prior_emb2emb import KandinskyVaaPriorEmbaEmbPipeline
