from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve






def       __lowerCamelCase		(						lowerCAmelCase__	,  lowerCAmelCase__	,  lowerCAmelCase__	):
       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       __lowerCamelCase		(						lowerCAmelCase__	,  lowerCAmelCase__	,  lowerCAmelCase__	,  lowerCAmelCase__ = None	,  ):
       if alpha is None:
              lowerCAmelCase__     	=					0.1

       # Initialize flow
       lowerCAmelCase__     	=					np.zeros_like(lowerCAmelCase__	)
       lowerCAmelCase__     	=					np.zeros_like(lowerCAmelCase__	)

       # 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 / 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(lowerCAmelCase__	):
              lowerCAmelCase__     	=					warp(lowerCAmelCase__	,  lowerCAmelCase__	,  lowerCAmelCase__	)
              lowerCAmelCase__     	=					convolve(lowerCAmelCase__	,  lowerCAmelCase__	) + convolve(lowerCAmelCase__	,  lowerCAmelCase__	)
              lowerCAmelCase__     	=					convolve(lowerCAmelCase__	,  lowerCAmelCase__	) + convolve(lowerCAmelCase__	,  lowerCAmelCase__	)
              lowerCAmelCase__     	=					convolve(lowerCAmelCase__	,  lowerCAmelCase__	) + convolve(lowerCAmelCase__	,  -kernel_t	)

              lowerCAmelCase__     	=					convolve(lowerCAmelCase__	,  lowerCAmelCase__	)
              lowerCAmelCase__     	=					convolve(lowerCAmelCase__	,  lowerCAmelCase__	)

              # 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()






from typing import Optional, Union

from ...file_utils import TensorType
from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding, PaddingStrategy, TruncationStrategy



class 			a     (   _A			):

     '''simple docstring'''





     lowerCAmelCase				:       Any   		=  'MarkupLMFeatureExtractor'
     lowerCAmelCase				:       Optional[Any]   		=  ('MarkupLMTokenizer', 'MarkupLMTokenizerFast')
     lowerCAmelCase				:       List[Any]   		=  True
     def __call__(	self   :			Dict					,    __snake_case   :			Tuple=None					,    __snake_case   :			List[Any]=None					,    __snake_case   :			Tuple=None					,    __snake_case   :			Tuple=None					,    __snake_case   :			Any=None					,    __snake_case   :			bool = True					,    __snake_case   :			Union[bool, str, PaddingStrategy] = False					,    __snake_case   :			Union[bool, str, TruncationStrategy] = None					,    __snake_case   :			Optional[int] = None					,    __snake_case   :			int = 0					,    __snake_case   :			Optional[int] = None					,    __snake_case   :			Optional[bool] = None					,    __snake_case   :			Optional[bool] = None					,    __snake_case   :			bool = False					,    __snake_case   :			bool = False					,    __snake_case   :			bool = False					,    __snake_case   :			bool = False					,    __snake_case   :			bool = True					,    __snake_case   :			Optional[Union[str, TensorType]] = None					,    **__snake_case   :			Any					,    ):
         # first, create nodes and xpaths
         if self.parse_html:
             if html_strings is None:
                 raise ValueError('''Make sure to pass HTML strings in case `parse_html` is set to `True`'''				)

             if nodes is not None or xpaths is not None or node_labels is not None:
                 raise ValueError(
                     '''Please don\'t pass nodes, xpaths nor node labels in case `parse_html` is set to `True`'''				)

             UpperCAmelCase_							 =     self.feature_extractor(__snake_case				)
             UpperCAmelCase_							 =     features['''nodes''']
             UpperCAmelCase_							 =     features['''xpaths''']
         else:
             if html_strings is not None:
                 raise ValueError('''You have passed HTML strings but `parse_html` is set to `False`.'''				)
             if nodes is None or xpaths is None:
                 raise ValueError('''Make sure to pass nodes and xpaths in case `parse_html` is set to `False`'''				)

        # # second, apply the tokenizer
         if questions is not None and self.parse_html:
             if isinstance(__snake_case					,    __snake_case				):
                 UpperCAmelCase_							 =     [questions]  # add batch dimension (as the feature extractor always adds a batch dimension)

         UpperCAmelCase_							 =     self.tokenizer(
             text=questions if questions is not None else nodes					,    text_pair=nodes if questions is not None else None					,    xpaths=__snake_case					,    node_labels=__snake_case					,    add_special_tokens=__snake_case					,    padding=__snake_case					,    truncation=__snake_case					,    max_length=__snake_case					,    stride=__snake_case					,    pad_to_multiple_of=__snake_case					,    return_token_type_ids=__snake_case					,    return_attention_mask=__snake_case					,    return_overflowing_tokens=__snake_case					,    return_special_tokens_mask=__snake_case					,    return_offsets_mapping=__snake_case					,    return_length=__snake_case					,    verbose=__snake_case					,    return_tensors=__snake_case					,    **__snake_case					,    )

         return encoded_inputs
     def   lowerCamelCase_   (	self   :			List[Any]					,    *__snake_case   :			Dict					,    **__snake_case   :			Optional[int]				):
         return self.tokenizer.batch_decode(*__snake_case					,    **__snake_case				)
     def   lowerCamelCase_   (	self   :			Optional[Any]					,    *__snake_case   :			Any					,    **__snake_case   :			Dict				):
         return self.tokenizer.decode(*__snake_case					,    **__snake_case				)




     @property
     def   lowerCamelCase_   (	self   :			Dict				):
         UpperCAmelCase_							 =     self.tokenizer.model_input_names
         return tokenizer_input_names





