

from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve
def 		UpperCamelCase_(    snake_case__:						np.ndarray						,					snake_case__:						np.ndarray						,					snake_case__:						np.ndarray     ) ->				np.ndarray:
 UpperCAmelCase__           =       np.stack((horizontal_flow, vertical_flow)						,					2     )

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

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

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

 # Set pixels at invalid locations to 0
 UpperCAmelCase__           =       0

 return warped
def 		UpperCamelCase_(    snake_case__:						np.ndarray						,					snake_case__:						np.ndarray						,					snake_case__:						SupportsIndex						,					snake_case__:						float | None = None						,					) ->				tuple[np.ndarray, np.ndarray]:
 if alpha is None:
  UpperCAmelCase__           =       0.1

 # Initialize flow
 UpperCAmelCase__           =       np.zeros_like(snake_case__     )
 UpperCAmelCase__           =       np.zeros_like(snake_case__     )

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

  UpperCAmelCase__           =       convolve(snake_case__						,					snake_case__     )
  UpperCAmelCase__           =       convolve(snake_case__						,					snake_case__     )

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

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

 return horizontal_flow, vertical_flow


if __name__ == "__main__":
 import doctest

 doctest.testmod()








from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_UpperCamelCase     =    {
    '''configuration_fsmt''': ['''FSMT_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''FSMTConfig'''],
    '''tokenization_fsmt''': ['''FSMTTokenizer'''],
}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _UpperCamelCase     =    ['''FSMTForConditionalGeneration''', '''FSMTModel''', '''PretrainedFSMTModel''']


if TYPE_CHECKING:
 from .configuration_fsmt import FSMT_PRETRAINED_CONFIG_ARCHIVE_MAP, FSMTConfig
 from .tokenization_fsmt import FSMTTokenizer

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_fsmt import FSMTForConditionalGeneration, FSMTModel, PretrainedFSMTModel

else:
 import sys

 _UpperCamelCase     =    _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)



