





from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve


def        A__						(							SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_		) ->  Tuple:
		lowerCamelCase :			int    		=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 :			str    		=np.stack(
		    np.meshgrid(np.arange(0				,							image.shape[1]		)				,							np.arange(0				,							image.shape[0]		)		)				,							2		)
		lowerCamelCase :			Optional[int]    		=np.round(grid - flow		).astype(np.intaa		)

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

		lowerCamelCase :			List[str]    		=image[grid[:, :, 1], grid[:, :, 0]]

		# Set pixels at invalid locations to 0
		lowerCamelCase :			Union[str, Any]    		=0

		return warped


def        A__						(							SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_ = None				,							) ->  Dict:





		if alpha is None:
				lowerCamelCase :			Any    		=0.1

		# Initialize flow
		lowerCamelCase :			Tuple    		=np.zeros_like(lowerCamelCase_		)
		lowerCamelCase :			Union[str, Any]    		=np.zeros_like(lowerCamelCase_		)

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

				lowerCamelCase :			Optional[Any]    		=convolve(lowerCamelCase_				,							lowerCamelCase_		)
				lowerCamelCase :			List[str]    		=convolve(lowerCamelCase_				,							lowerCamelCase_		)

				# This updates the flow as proposed in the paper (Step 12)
				lowerCamelCase :			List[Any]    		=(
				    derivative_x * avg_horizontal_velocity
				    + derivative_y * avg_vertical_velocity
				    + derivative_t
				)
				lowerCamelCase :			Optional[int]    		=update / (alpha**2 + derivative_x**2 + derivative_y**2)

				lowerCamelCase :			str    		=avg_horizontal_velocity - derivative_x * update
				lowerCamelCase :			Optional[int]    		=avg_vertical_velocity - derivative_y * update

		return horizontal_flow, vertical_flow


if __name__ == "__main__":
				import doctest

				doctest.testmod()


'''simple docstring'''


import sys
from dataclasses import dataclass
from typing import TYPE_CHECKING, Dict, List, Optional, Tuple, Union

import pandas as pd
import pyarrow as pa

import datasets
import datasets.config
from datasets.features.features import require_storage_cast
from datasets.table import table_cast


if TYPE_CHECKING:
 import sqlitea

 import sqlalchemy


snake_case__	:     int      =    datasets.utils.logging.get_logger(__name__)






@dataclass
class 	__SCREAMING_SNAKE_CASE		(			datasets.BuilderConfig			):







  '''simple docstring'''






  lowerCamelCase_						:Union[str, "sqlalchemy.sql.Selectable"]		       =						None
  lowerCamelCase_						:Union[str, "sqlalchemy.engine.Connection", "sqlalchemy.engine.Engine", "sqlite3.Connection"]		       =						None
  lowerCamelCase_						:Optional[Union[str, List[str]]]		       =						None
  lowerCamelCase_						:bool		       =						True
  lowerCamelCase_						:Optional[Union[List, Tuple, Dict]]		       =						None
  lowerCamelCase_						:Optional[Union[List, Dict]]		       =						None
  lowerCamelCase_						:Optional[List[str]]		       =						None
  lowerCamelCase_						:Optional[int]		       =						1_0000
  lowerCamelCase_						:Optional[datasets.Features]		       =						None


  def _UpperCamelCase	(					self		):




       '''simple docstring'''

       if self.sql is None:
            raise ValueError('sql must be specified'		)
       if self.con is None:
            raise ValueError('con must be specified'		)


  def _UpperCamelCase	(					self ,						snake_case_ ,						snake_case_ = None ,						):




       '''simple docstring'''

       UpperCAmelCase_				:  List[Any]  = config_kwargs.copy()
       # We need to stringify the Selectable object to make its hash deterministic

       # The process of stringifying is explained here: http://docs.sqlalchemy.org/en/latest/faq/sqlexpressions.html
       UpperCAmelCase_				:  str  = config_kwargs['sql']
       if not isinstance(snake_case_ ,						snake_case_		):
            if datasets.config.SQLALCHEMY_AVAILABLE and "sqlalchemy" in sys.modules:
                 import sqlalchemy

                 if isinstance(snake_case_ ,						sqlalchemy.sql.Selectable		):
                      UpperCAmelCase_				:  Any  = sqlalchemy.create_engine(config_kwargs['con'].split('://'		)[0] + '://'		)
                      UpperCAmelCase_				:  int  = str(sql.compile(dialect=engine.dialect		)		)
                      UpperCAmelCase_				:  str  = sql_str
                 else:
                      raise TypeError(
                          F'''Supported types for \'sql\' are string and sqlalchemy.sql.Selectable but got {type(snake_case_		)}: {sql}'''		)
            else:
                 raise TypeError(
                     F'''Supported types for \'sql\' are string and sqlalchemy.sql.Selectable but got {type(snake_case_		)}: {sql}'''		)
       UpperCAmelCase_				:  Union[str, Any]  = config_kwargs['con']
       if not isinstance(snake_case_ ,						snake_case_		):
            UpperCAmelCase_				:  Optional[Any]  = id(snake_case_		)
            logger.info(
                F'''SQL connection \'con\' of type {type(snake_case_		)} couldn\'t be hashed properly. To enable hashing, specify \'con\' as URI string instead.'''		)

       return super().create_config_id(snake_case_ ,						custom_features=snake_case_		)






  @property
  def _UpperCamelCase	(					self		):




       '''simple docstring'''

       UpperCAmelCase_				:  List[Any]  = {
           'index_col': self.index_col,
           'columns': self.columns,
           'params': self.params,
           'coerce_float': self.coerce_float,
           'parse_dates': self.parse_dates,
       }
       return pd_read_sql_kwargs







class 	__SCREAMING_SNAKE_CASE		(			datasets.ArrowBasedBuilder			):







  '''simple docstring'''






  lowerCamelCase_						:Any		       =						SqlConfig


  def _UpperCamelCase	(					self		):




       '''simple docstring'''

       return datasets.DatasetInfo(features=self.config.features		)


  def _UpperCamelCase	(					self ,						snake_case_		):




       '''simple docstring'''

       return [datasets.SplitGenerator(name=datasets.Split.TRAIN ,						gen_kwargs={}		)]


  def _UpperCamelCase	(					self ,						snake_case_		):




       '''simple docstring'''

       if self.config.features is not None:
            UpperCAmelCase_				:  Tuple  = self.config.features.arrow_schema
            if all(not require_storage_cast(snake_case_		) for feature in self.config.features.values()		):
                 # cheaper cast
                 UpperCAmelCase_				:  Tuple  = pa.Table.from_arrays([pa_table[field.name] for field in schema] ,						schema=snake_case_		)
            else:
                 # more expensive cast; allows str <-> int/float or str to Audio for example
                 UpperCAmelCase_				:  Union[str, Any]  = table_cast(snake_case_ ,						snake_case_		)
       return pa_table






  def _UpperCamelCase	(					self		):




       '''simple docstring'''

       UpperCAmelCase_				:  Optional[Any]  = self.config.chunksize
       UpperCAmelCase_				:  Optional[Any]  = pd.read_sql(
           self.config.sql ,						self.config.con ,						chunksize=snake_case_ ,						**self.config.pd_read_sql_kwargs		)
       UpperCAmelCase_				:  int  = [sql_reader] if chunksize is None else sql_reader
       for chunk_idx, df in enumerate(snake_case_		):
            UpperCAmelCase_				:  Optional[Any]  = pa.Table.from_pandas(snake_case_		)
            yield chunk_idx, self._cast_table(snake_case_		)






