from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve

def 	__lowerCamelCase							(				__a    : np.ndarray      ,							__a    : np.ndarray      ,							__a    : np.ndarray		)      ->       np.ndarray:
	_lowercase   =np.stack((horizontal_flow, vertical_flow)      ,							2		)

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

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

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

	# Set pixels at invalid locations to 0
	_lowercase   =0

	return warped

def 	__lowerCamelCase							(				__a    : np.ndarray      ,							__a    : np.ndarray      ,							__a    : SupportsIndex      ,							__a    : float | None = None      ,							)      ->       tuple[np.ndarray, np.ndarray]:
	if alpha is None:
		_lowercase   =0.1

	# Initialize flow
	_lowercase   =np.zeros_like(__a		)
	_lowercase   =np.zeros_like(__a		)

	# Prepare kernels for the calculation of the derivatives and the average velocity
	_lowercase   =np.array([[-1, 1], [-1, 1]]		) * 0.25
	_lowercase   =np.array([[-1, -1], [1, 1]]		) * 0.25
	_lowercase   =np.array([[1, 1], [1, 1]]		) * 0.25
	_lowercase   =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		):
		_lowercase   =warp(__a      ,							__a      ,							__a		)
		_lowercase   =convolve(__a      ,							__a		) + convolve(__a      ,							__a		)
		_lowercase   =convolve(__a      ,							__a		) + convolve(__a      ,							__a		)
		_lowercase   =convolve(__a      ,							__a		) + convolve(__a      ,							-kernel_t		)

		_lowercase   =convolve(__a      ,							__a		)
		_lowercase   =convolve(__a      ,							__a		)

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

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

	return horizontal_flow, vertical_flow


if __name__ == "__main__":
						import doctest

						doctest.testmod()





import numpy as np
class 	_a  :



	"""simple docstring"""



	def __init__(   self       ,  lowerCAmelCase_=5       ,  lowerCAmelCase_=5       ):
		_lowercase   =depth
		_lowercase   =0
		_lowercase   =None
		_lowercase   =None
		_lowercase   =min_leaf_size
		_lowercase   =None


	def __lowerCAmelCase      (   self       ,  lowerCAmelCase_       ,  lowerCAmelCase_       ):
		if labels.ndim != 1:
			print("Error: Input labels must be one dimensional"       )

		return np.mean((labels - prediction) ** 2       )


	def __lowerCAmelCase      (   self       ,  lowerCAmelCase_       ,  lowerCAmelCase_       ):
		if x.ndim != 1:
			print("Error: Input data set must be one dimensional"       )
			return
		if len(lowerCAmelCase_       ) != len(lowerCAmelCase_       ):
			print("Error: X and y have different lengths"       )
			return
		if y.ndim != 1:
			print("Error: Data set labels must be one dimensional"       )
			return

		if len(lowerCAmelCase_       ) < 2 * self.min_leaf_size:
			_lowercase   =np.mean(lowerCAmelCase_       )
			return

		if self.depth == 1:
			_lowercase   =np.mean(lowerCAmelCase_       )
			return

		_lowercase   =0
		_lowercase   =self.mean_squared_error(lowerCAmelCase_       ,  np.mean(lowerCAmelCase_       )       ) * 2
		for i in range(len(lowerCAmelCase_       )       ):
			if len(x[:i]       ) < self.min_leaf_size:
				continue
			elif len(x[i:]       ) < self.min_leaf_size:
				continue
			else:
				_lowercase   =self.mean_squared_error(x[:i]       ,  np.mean(y[:i]       )       )
				_lowercase   =self.mean_squared_error(x[i:]       ,  np.mean(y[i:]       )       )
				_lowercase   =error_left + error_right
				if error < min_error:
					_lowercase   =i
					_lowercase   =error

		if best_split != 0:
			_lowercase   =x[:best_split]
			_lowercase   =y[:best_split]
			_lowercase   =x[best_split:]
			_lowercase   =y[best_split:]

			_lowercase   =x[best_split]
			_lowercase   =DecisionTree(
			    depth=self.depth - 1       ,  min_leaf_size=self.min_leaf_size       )
			_lowercase   =DecisionTree(
			    depth=self.depth - 1       ,  min_leaf_size=self.min_leaf_size       )
			self.left.train(lowerCAmelCase_       ,  lowerCAmelCase_       )
			self.right.train(lowerCAmelCase_       ,  lowerCAmelCase_       )
		else:
			_lowercase   =np.mean(lowerCAmelCase_       )

		return


	def __lowerCAmelCase      (   self       ,  lowerCAmelCase_       ):
		if self.prediction is not None:
			return self.prediction
		elif self.left or self.right is not None:
			if x >= self.decision_boundary:
				return self.right.predict(lowerCAmelCase_       )
			else:
				return self.left.predict(lowerCAmelCase_       )
		else:
			print("Error: Decision tree not yet trained"       )
			return None

class 	_a  :



	"""simple docstring"""



	@staticmethod
	def __lowerCAmelCase      (   lowerCAmelCase_       ,  lowerCAmelCase_       ):
		_lowercase   =float(0       )
		for label in labels:
			squared_error_sum += (label - prediction) ** 2

		return float(squared_error_sum / labels.size       )

def 	__lowerCamelCase							(				)      ->       Union[str, Any]:
	_lowercase   =np.arange(-1.0      ,							1.0      ,							0.005		)
	_lowercase   =np.sin(__a		)

	_lowercase   =DecisionTree(depth=10      ,							min_leaf_size=10		)
	tree.train(__a      ,							__a		)

	_lowercase   =(np.random.rand(10		) * 2) - 1
	_lowercase   =np.array([tree.predict(__a		) for x in test_cases]		)
	_lowercase   =np.mean((predictions - test_cases) ** 2		)

	print("Test values: " + str(__a		)		)
	print("Predictions: " + str(__a		)		)
	print("Average error: " + str(__a		)		)


if __name__ == "__main__":
						main()
						import doctest

						doctest.testmod(name="mean_squarred_error", verbose=True)




