




'''simple docstring'''




from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve





def   a_							(   __snake_case							:    np.ndarray     , __snake_case							:    np.ndarray     , __snake_case							:    np.ndarray     )							->		np.ndarray:



       """simple docstring"""
       lowerCamelCase_							=np.stack((horizontal_flow, vertical_flow)     , 2     )

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

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

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

       # Set pixels at invalid locations to 0
       lowerCamelCase_							=0

       return warped





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



       """simple docstring"""
       if alpha is None:
              lowerCamelCase_							=0.1

       # Initialize flow
       lowerCamelCase_							=np.zeros_like(__snake_case     )
       lowerCamelCase_							=np.zeros_like(__snake_case     )

       # Prepare kernels for the calculation of the derivatives and the average velocity
       lowerCamelCase_							=np.array([[-1, 1], [-1, 1]]     ) * 0.2_5
       lowerCamelCase_							=np.array([[-1, -1], [1, 1]]     ) * 0.2_5
       lowerCamelCase_							=np.array([[1, 1], [1, 1]]     ) * 0.2_5
       lowerCamelCase_							=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(__snake_case     ):
              lowerCamelCase_							=warp(__snake_case     , __snake_case     , __snake_case     )
              lowerCamelCase_							=convolve(__snake_case     , __snake_case     ) + convolve(__snake_case     , __snake_case     )
              lowerCamelCase_							=convolve(__snake_case     , __snake_case     ) + convolve(__snake_case     , __snake_case     )
              lowerCamelCase_							=convolve(__snake_case     , __snake_case     ) + convolve(__snake_case     , -kernel_t     )

              lowerCamelCase_							=convolve(__snake_case     , __snake_case     )
              lowerCamelCase_							=convolve(__snake_case     , __snake_case     )

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

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

       return horizontal_flow, vertical_flow


if __name__ == "__main__":
     import doctest

     doctest.testmod()










'''simple docstring'''




import warnings

from .generation import FlaxGenerationMixin


class 						__UpperCamelCase (				lowerCamelCase__       ):
       # warning at import time
       warnings.warn(
           'Importing `FlaxGenerationMixin` from `src/transformers/generation_flax_utils.py` is deprecated and will '
           'be removed in Transformers v5. Import as `from transformers import FlaxGenerationMixin` instead.'    ,      lowerCamelCase__    ,      )




